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Whitehead attempts to understand human experience as a process belonging to nature, as a physical existence. Such a daring plan led Whitehead, on the one hand, to reject the philosophical tradition that defined subjective experience in terms of consciousness, thinking and sensory perception, and on the other hand, to interpret the entire physical existence in terms of joy, feeling, need, appetite and longing. that is, forced him to cross the sword with what he called “scientific materialism,” which was born in the 17th century. Like Bergson, Whitehead noted the main weaknesses of the theoretical framework developed by seventeenth-century natural science:

“The seventeenth century finally produced a framework of scientific thought formulated by mathematicians for mathematicians. The remarkable feature of the mathematical mind will be its ability to operate with abstractions and extract them from clear demonstrative chains of reasoning, quite satisfactory as long as the abstractions are exactly those that you want to think about. The colossal success of scientific abstractions (giving, on the one hand, matter with its simple position in time and space, and on the other, mind, perceiving, suffering, reasoning, but not interfering) imposed on philosophy the task of accepting abstractions as the most concrete interpretation of a fact.

Let us note that thereby modern philosophy was reduced to ruins. It is worth noting that she began to make complex fluctuations between three extreme points of view: dualists, who accept matter and mind on equal terms, and two varieties of monists, one of which places mind inside matter, and the other - matter inside mind. But juggling with abstractions, of course, is powerless to overcome the internal chaos caused by the attribution of erroneously addressed concreteness to the scientific scheme of the 17th century.”

At the same time, Whitehead believed that the situation in philosophy was exclusively temporary. Science, in his opinion, is not doomed to remain a prisoner of chaos and confusion.

We have already touched upon the question of whether it is possible to formulate a natural philosophy that would not be directed against natural science. It is important to note that one of the most ambitious attempts in this direction is Whitehead's cosmology. Whitehead did not see a fundamental contradiction between natural science and philosophy. He saw his goal as defining a conceptual field that would make it possible to consistently analyze the problem of human experience and physical processes and determine the conditions for its solvability. It is worth saying that for this purpose it was extremely important to formulate principles that would make it possible to characterize all forms of existence - from stones to humans. According to Whitehead, it is this universality that gives his approach the characteristics of “philosophy.” While every scientific theory selects and abstracts from the complexities of the world some specific set of relations, philosophy cannot privilege any one area of human experience over another. Through conceptual experimentation, philosophy should strive to construct a consistent framework that includes all dimensions of experience, whether they belong to physics, physiology, psychology, biology, data science, etc.

Whitehead recognized (perhaps more keenly than anyone else) that the creative evolution of nature could not be known if its constituent elements were immutable individual entities, preserving the same identity through all changes and interactions. But Whitehead was just as clearly aware that to declare all immutability illusory, to reject what has become in the name of what is becoming, to reject individual essences in favor of a continuously and ever-changing flux, would be to again find oneself in the trap that always awaits philosophy - “to perform brilliant feats of justification.”

Whitehead saw the task of philosophy as combining permanence and change, to think of things as processes, to show how the becoming, the emerging forms individual entities, how individual identities are born and die. A detailed exposition of Whitehead's system is beyond the scope of this book. We would like to emphasize exclusively that Whitehead convincingly demonstrated the connection between the philosophy of relation (no element of nature will be the permanent basis of changing relations, each element acquires identity from its relations with other elements) and the philosophy of innovative becoming. In the process of its genesis, everything that exists unifies the diversity of the world, since it adds to this diversity a certain additional set of relationships. With the creation of each new entity, “the many things become unified and grow as one.”

At the end of our book we will once again encounter the problem of permanence and change posed by Whitehead, this time in physics. We will talk about the structures that arise during irreversible interaction with the outside world. Modern physics has discovered that differences between structural units and relationships are as important as interdependencies. It is worth saying that in order for the interaction to be real, the “nature” of things connected to each other by certain relations must, as modern physics believes, stem from these relations, and the relations themselves must necessarily follow from the “nature” of things (see Chap. 10) Based on all of the above, we come to the conclusion that Whitehead can rightfully be considered the forerunner of “self-consistent” descriptions such as the “bootstrap” philosophy in particle physics, which asserts the universal interconnectedness of all particles. But at the time when Whitehead created his work “Process and Reality,” the situation in physics was completely different and Whitehead’s philosophy found a response exclusively in biology.

Whitehead's case, like Bergson's, demonstrates that only an unfolding, expanding science can put an end to the schism between natural science and philosophy. This expansion of science is only possible if we reconsider our concept of time. To deny time, that is, to allow it to manifest one or another reversible law, means to refuse the opportunity to formulate a concept of nature consistent with the hypothesis that nature gave birth to living beings, and in particular humans. The denial of time condemns us to a fruitless choice between anti-scientific philosophy and alienated natural science.

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Alfred North Whitehead was born in Ramsgate (Kent) in 1861. He devoted himself to mathematics (but did not neglect the study of classical languages and history), and in 1898 a Treatise on General Algebra was published. Together with Russell, Whitehead created the three-volume work “Principia mathematical (1910-1913). Until 1924, he taught mathematics in Cambridge and London, then, until 1937, philosophy at Harvard University. He died in 1947. Among his many philosophical Let's name the following works: “Science and the Modern World” (1925), “Religion in Creation” (1926), “Process and Reality” (1929), “Adventures of Ideas” (1933), “Ways of Thought” (1938).

“The three books: Science and the Modern World, Process and Reality, and Adventures of Ideas,” wrote Whitehead, “form an attempt to express a way of understanding the nature of things, showing how this way is confirmed by changes that have occurred in human experience.” “Speculative philosophy,” we read in Process and Reality, “is the effort to create a coherent system of logically necessary general ideas by which every element of our experience can be explained.” Particular sciences illuminate specific aspects of reality, the internal connection of which is supported by this effort. Philosophy and science are inseparable. "One helps the other. The task of philosophy is to work on the harmonization of ideas that are united following the concrete facts of the real world... Science and philosophy mutually criticize each other, supplying each other with material for the imagination. A philosophical system must be able to interpret the concrete facts from which science abstracts And the sciences then find their own principles in the concrete facts presented by the philosophical system. The history of thought is therefore the history of the failures and successes of this joint enterprise."

In other words, science supplies “stubborn and irreducible” facts, which are met by philosophical generalizations; on the other hand, we see how “philosophical intuitions” are transformed into the “scientific method”. The task of philosophy is to “challenge the half-truths that form scientific first principles” in order to arrive at an organic vision of principles in interconnection. Consequently, there is nothing scandalous in the fact of the plurality of philosophical systems replacing each other over time. Moreover, “the contrast of theories is not a problem, but an opportunity for practical use.”

It is clear that Whitehead was one of the first to recognize the importance of the theory of relativity for metaphysics, which does not want to engage in empty word debates. In 1919, Eddington's expedition to North Africa (where photographs of a total solar eclipse were taken on March 29) confirmed Einstein's theory (as a counterweight to Newton's). Whitehead, who attended a meeting of the Royal Society where photographs of light reflections when a light source passed near the sun were shown, says: “The atmosphere of intense interest was reminiscent of Greek drama: we were a chorus commenting on the verdicts of fate at moments of extraordinary events. And even the scenography enhanced the dramatic moments: traditional ceremony against the backdrop of Newton's portrait as a reminder that even the greatest scientific generalization, two centuries later, did not escape modification. It was a personal interest in the great adventure of a thought thrown ashore at the end of the journey. But it is appropriate to recall that the dramatic essence of the tragedy was not, in fact, a misfortune. Its root lies in the fatal process of uncontrollable change of events..."

Not only the life of mankind, according to Whitehead, but the entire history of the Universe is a process. It turns out that it is not so much that we experience qualities and essences, but rather the non-stop event process that tests us to understand the relationships. If the object of mechanistic philosophy was “static elementary particles, now science is interested in the totality of connections arising from their intentionality relations with the entire Universe” (M. Dal Prga). It is not the substance, but the concept of the event that helps to understand the world. Substance, “inert matter,” absolute space and time are concepts of Newtonian physics. Modern physics, having abandoned them, is forced to talk about events in the space-time continuum. The universe as a process is not a machine, but rather a growing organism. Moreover, the starting point of this process is not the subject at all, as the idealists believed. Self-awareness is the final point, not always achievable, the starting point is a set of events of a corporate nature, the human body.

The Universe is an organism whose past is not forgotten; moreover, it creates ever new syntheses, what Plato called “eternal essences”, “forms”. The latter are potential opportunities, some of them are selected and implemented. Thus, the process consists of preservation and maturation, and Whitehead calls the totality of eternal objects God. Or rather: as “original nature” God contains eternal objects, and as “final nature” God is the principle of concrete reality. He lives and grows along with the Universe. “God is not the creator of the world, He is its savior,” writes Whitehead. “Actual integrity” realizes eternal values, thanks to them, and therefore to God, the world is filled with events that are not devoid of meaning. God as the original nature is in the harmony of all values realized in the process. In this sense, “God is present in us with the joy of realized value and the sorrow of desecrated or unsaved value, the possibility of loss of good. But He is above us, He is present in the transcendental possibility to which we strive, feels it in both good and evil as the original value peace" (E. Paci).

We have already noted that the element common to Kant, Hegel and Bergson is the search for an approach to reality that is different from the approach of classical science. Whitehead’s philosophy, which is obviously pre-Kantian in its principles, sees its main goal in this. In his most important work, Process and Reality, Whitehead takes us back to the great philosophies of the classical period and their commitment to rigorous conceptual experimentation.

Whitehead attempts to understand human experience as a process belonging to nature, as a physical existence. Such a daring plan led Whitehead, on the one hand, to a rejection of the philosophical tradition that defined subjective experience in terms of consciousness, thinking and sensory perception, and on the other hand, to the interpretation of everything physical existence in terms of joy, feeling, need, appetite and longing, that is, forced him to cross the sword with what he called “scientific materialism”, which was born in the 17th century. Like Bergson, Whitehead noted the main weaknesses of the theoretical framework developed by seventeenth-century natural science:

“The seventeenth century finally produced a framework of scientific thought formulated by mathematicians for mathematicians. A remarkable feature of the mathematical mind is its ability to operate with abstract

ations and extract them from clear evidentiary chains of reasoning, quite satisfactory as long as they are exactly the abstractions you want to think about. The colossal success of scientific abstractions (giving, on the one hand, matter with its simple position in time and space, and on the other, mind, perceiving, suffering, reasoning, but not interfering) imposed on philosophy the task of accepting abstractions as the most concrete interpretation of a fact.

Thus modern philosophy was reduced to ruins. She began to oscillate complexly between three extreme points of view: dualists, who accept matter and mind on equal terms, and two varieties of monists, one of which places mind inside matter, and the other puts matter inside mind. But juggling with abstractions, of course, is powerless to overcome the internal chaos caused by the attribution of erroneously addressed concreteness to the scientific scheme of the 17th century.” 20

However, Whitehead believed that the situation in philosophy was only temporary. Science, in his opinion, is not doomed to remain a prisoner of chaos and confusion.

We have already touched upon the question of whether it is possible to formulate a natural philosophy that would not be directed against natural science. One of the most ambitious attempts in this direction is Whitehead's cosmology. Whitehead did not see a fundamental contradiction between natural science and philosophy. He saw his goal as defining a conceptual field that would make it possible to consistently analyze the problem of human experience and physical processes and determine the conditions for its solvability. To do this, it was necessary to formulate principles that would make it possible to characterize all forms of existence - from stones to humans. According to Whitehead, it is this universality that gives his approach the characteristics of “philosophy.” While every scientific theory selects and abstracts from the complexities of the world some specific set of relations, philosophy cannot privilege any one area of human experience over another. Through a conceptual experiment

tization, philosophy should strive to build a consistent scheme that includes all types of measurement of experience, regardless of whether they belong to physics, physiology, psychology, biology, ethics, etc.

Whitehead recognized (perhaps more keenly than anyone else) that the creative evolution of nature could not be known if its constituent elements were immutable individual entities, maintaining their identity through all changes and interactions. But Whitehead was just as clearly aware that to declare all immutability illusory, to reject what has become in the name of what is becoming, to reject individual essences in favor of a continuously and ever-changing flux would mean again to find oneself in the trap that always awaits philosophy - “to perform brilliant feats of justification” 21.

Whitehead saw the task of philosophy as combining permanence and change, to think of things as processes, to show how what becomes and emerges forms individual entities, how individual identities are born and die. A detailed exposition of Whitehead's system is beyond the scope of this book. We would only like to emphasize that Whitehead convincingly demonstrated the connection between philosophy relationship(no element of nature is a permanent basis of changing relationships, each element acquires identity from its relationships with other elements) and philosophy innovative becoming. In the process of its genesis, everything that exists unifies the diversity of the world, since it adds to this diversity some additional set of relations. With the creation of each new entity, “the many things acquire unity and grow as one” 22 .

At the end of our book we will once again encounter Whitehead's problem of permanence and change, this time in physics. We will talk about the structures that arise during irreversible interaction with the outside world. Modern physics has discovered that differences between structural units and relationships are as important as interdependencies. In order for the interaction to be real, "nature"

things interconnected by certain relations must, as modern physics believes, stem from these relations, and the relations themselves must necessarily follow from the “nature” of things (see Chapter 10). Thus, Whitehead can rightfully be considered the forerunner of “self-consistent” descriptions such as the “bootstrap” philosophy in particle physics, which asserts the universal interconnectedness of all particles. But at the time when Whitehead created his work “Process and Reality,” the situation in physics was completely different and Whitehead’s philosophy found a response only in biology 23 .

Whitehead's case, like Bergson's, demonstrates that only an unfolding, expanding science can put an end to the schism between natural science and philosophy. This expansion of science is only possible if we reconsider our concept of time. To deny time, that is, to reduce it to the manifestation of one or another reversible law, means to refuse the opportunity to formulate a concept of nature consistent with the hypothesis that nature gave birth to living beings, and in particular man. The denial of time condemns us to a fruitless choice between anti-scientific philosophy and alienated natural science.

However, Whitehead believed that the situation in philosophy was only temporary. Science, in his opinion, is not doomed to remain a prisoner of chaos and confusion.

Whitehead recognized (perhaps more keenly than anyone else) that the creative evolution of nature could not be known if its constituent elements were immutable individual entities, maintaining their identity through all changes and interactions. But Whitehead was just as clearly aware that to declare all immutability illusory, to reject what has become in the name of what is becoming, to reject individual essences in favor of a continuously and ever-changing flux would mean again to find oneself in the trap that always awaits philosophy - “to perform brilliant feats of justification” 21.

Whitehead's case, like Bergson's, demonstrates that only an unfolding, expanding science can put an end to the schism between natural science and philosophy. This expansion of science is only possible if we reconsider our concept of time. To deny time, that is, to reduce it to the manifestation of one or another reversible law, means to refuse the opportunity to formulate a concept of nature consistent with the hypothesis that nature gave birth to living beings, and in particular man. The denial of time condemns us to a fruitless choice between anti-scientific philosophy and alienated natural science.

Chapter 1. Speculative philosophy

1 This course of lectures is an essay on speculative philosophy. His first task is to define "speculative philosophy" as a method that produces meaningful knowledge.

Speculative philosophy is the attempt to create a coherent, logical and necessary system of general ideas in terms of which every element of our experience can be interpreted. By "interpretation" I mean that situation in which whatever we are aware of as being enjoyed, perceived, desired, or thought will have the character of a particular instance of a given general scheme. Thus, a philosophical scheme must be coherent, logical and, in relation to its interpretation, applicable and adequate. In this case, the word "applicable" means that some elements of experience are interpreted that way, and the word "adequate" means that there are no elements that cannot be interpreted that way.

“Coherence” in our understanding means that the fundamental ideas on the basis of which the scheme develops are so presupposed by each other that in isolation they become meaningless. This requirement does not mean that the ideas are definable in terms of each other; it only means that what is indefinable in one such concept cannot be abstracted from its relation

to other concepts. This is precisely the ideal of regulatory philosophy, that its fundamental concepts cannot be abstracted from each other. In other words, it is assumed that no entity can be considered in complete abstraction from the entire system of the universe, and that the task of speculative philosophy is to demonstrate this truth. This feature of it is connectivity.

The term “logical” has its usual meaning, including “logical” consistency, or absence of contradiction, definition of constructs in logical terms, exemplification of general logical concepts in particular examples, principles of inference. It will be discovered that logical concepts themselves must find their places in the scheme of philosophical concepts.

It will also be noticeable that this ideal of speculative philosophy has both a rational and an empirical side. The rational side is expressed by the terms “coherent” and “logical”. The empirical side is expressed by the terms “applicable” and “adequate”. But both sides fit together if we remove the uncertainty that remains in the previous explanation of the term “adequate”. The adequacy of the scheme in relation to each of its elements does not mean adequacy to those elements that have already been considered. This means that the texture of the observed experience that illustrates the philosophical scheme is such that all corresponding experience must exhibit a similar structure. Thus, a philosophical scheme must be "necessary" in the sense of having its own guarantee of (preservation of) universality through all experience, while we limit ourselves to contact with the immediate content. But that which does not come into such contact is the unknowable, and the unknowable is the unknown, and therefore the universality defined by “communication” will suffice.

This doctrine of the necessity of universality means that there is an entity in the universe that does not allow any relationships outside itself, which (otherwise) would be a violation of its rationality. Speculative philosophy is precisely looking for such an essence.

2. Philosophers dare not hope ever definitively

formulate these metaphysical principles. Obstacles such as weakness of intuition and shortcomings of language inevitably appear in their path. Words and phrases must “stretch” to such a universality that is alien to everyday use; and no matter how the special (meaning) of such elements of language is stabilized, they remain metaphors, silently demanding from us a flight of imagination.

There is no first principle that in itself would be unknowable, not grasped by a flash of insight. But leaving aside linguistic difficulties, the lack of imaginative insight allows progress (of knowledge) only in the form of an asymptomatic approach to a scheme of principles described exclusively in terms of the ideal to which they are supposed to satisfy.

This difficulty lies in the empirical side of philosophy. We are given an actual world, including ourselves, which in the form of our direct experience extends to observation. The clarification of direct experience is the only definition for thought, and the starting point of thinking is the analytical observation of the components of such experience. But we are by no means given a final analysis of immediate experience down to the various details that embrace its definiteness. Out of habit, we observe using the method of discrimination. In this sense, for example, sometimes we see an elephant and sometimes we don’t. Eventually we begin to notice when it is present. The very power of observation depends on the fact that the object being observed is important when it is present and sometimes when it is not.

The first metaphysical principles cannot but be confirmed by concrete examples. After all, we would never have comprehended the real world without their influence. The method of bringing thought to a strict systematization on the basis of detailed distinctions of previous observations is not suitable for creating metaphysics. This weakness of the method of strict empiricism is manifested not only in metaphysics. It always occurs when we strive for broad generalizations. In natural science, such a rigorous method is Bacon's method of induction, which, if consistently applied, would leave science where we found it. After all, Bacon missed the game

free imagination, controlled by the requirements of coherence and logic. The true method of discovery is like the flight of an airplane. It takes off from the surface of concrete observation; he flies through the transparent air of imaginary generalizations; and he lands again to obtain new observations, which by rational interpretation are made more insightful. The reason for the success of this method of imaginative rationality is that when the method of discrimination fails, the ever-present factors can nevertheless be observed through imaginative thinking. Such thinking provides us with differences that are not given to direct observation. It can even deal with inconsistency, and can also illuminate the consistent and constant elements of experience, comparing them in the imagination with what is incompatible with them. Negative judgment is the pinnacle of mentality. But at the same time, it is necessary to strictly follow the conditions necessary for the success of the imaginative construction. First, this construction must stem from a generalization of specific factors identified in certain areas of human interest, in physics, for example, or in physiology, psychology, (the field of) ethical beliefs, in sociology, or in languages, considered as the storehouses of human experience. In this way the first requirement is guaranteed, namely that in any case there must be an important application. The success of an imaginative experiment must always be tested by the applicability of its results beyond the limited area in which it arose. In the absence of such extended application, a generalization in physics, for example, remains only an alternative expression of concepts applicable within it. A partially successful philosophical generalization, even if it stems from physics, can find application in areas of experience outside of physics. It will clear up surveillance in distant areas, so general principles can be revealed, as in the process of illustration, since in the absence of imaginative generalization they are obscured by constant specification (exemplification).

So the first requirement is to follow a generalization method to achieve some application; and the success of this is manifested in the very

application beyond its immediate source. In other words, some synoptic vision is gained.

In our description of the philosophical method, the term "philosophical generalization" meant "the use of certain concepts, applied to a limited group of facts, to divinate generic concepts applicable to all facts."

In using this method, natural science demonstrated a curious combination of rationalism and irrationalism. The prevailing tone of thinking in natural science was staunchly rationalistic within its own boundaries and dogmatically irrational outside these boundaries. In fact, such an approach becomes a dogmatic denial that there are any factors in the world that are completely inexpressible in terms of its primary, not yet generalized concepts. Such denial is self-denial of thinking.

The second condition for the success of an imaginative construction is the relentless search for two rationalistic ideals—coherence and logical perfection.

Logical perfection does not require any detailed explanation here. An example of its importance is the very role that mathematics plays within the sciences. The history of mathematics demonstrates the process of generalization of special concepts comprehended in specific cases. In any area of mathematics, its concepts presuppose each other. And this is a wonderful feature of the history of thought: areas of mathematics developed under the influence of pure imagination eventually find important applications. But this takes time. Conic sections had to wait one thousand eight hundred years (for their use). More recently, examples include probability theory, tensor theory, and matrix theory.

The requirement of coherence does much to preserve rationalist sanity. However, criticism of this requirement is not always allowed. If we consider philosophical disputes, we will see that their participants demand coherence from their opponents, freeing themselves from such a requirement. It has been noted that a philosophical system is never refuted: it is only abandoned. The reason for this is that logical

contradictions, with the exception of simple errors of mind (of which there are plenty, but which are only transitory), are the most gratuitous of errors, and they are usually trivial. So, after criticism, systems no longer demonstrate simple illogicality. They suffer from inadequacy and incoherence. The failure to incorporate certain obvious elements of experience within the system is compensated for by outright denial of the facts. And also, when a philosophical system retains any attraction of novelty, it receives full indulgence for its incoherence. But after a system becomes orthodox and is taught as an authority, it comes under severe criticism. Its negative aspects and inconsistencies are recognized as intolerable, and a backlash begins.

Incoherence is an arbitrary separation of first principles. In modern philosophy, incoherence is illustrated by Descartes' two types of substance—bodily and spiritual. In his philosophy there is no explanation as to why there cannot be a world of one substance—either a corporeal world or only a spiritual world. According to Descartes, substantial individuality “requires nothing but itself for its existence.” Thus this system elevates its incoherence into a virtue. But, on the other hand, the facts themselves seem consistent, but Descartes’ system does not. For example, when he considers a psychophysical problem. Clearly the Cartesian system says something true. But its concepts are too abstract to penetrate into the nature of things.

The attractiveness of Spinoza's philosophy lies in his modification of the Cartesian position towards greater coherence. He begins with one substance, cause sui, and considers its most important attributes and individual modes, i.e. affectiones substantiae. The gap in this system is the arbitrary introduction of “modes”. And, nevertheless, the diversity of modes is a necessary requirement if only this scheme retains any direct relation to many events of the perceived world.

The philosophy of the organism as a whole is consistent with Spinoza’s scheme of thinking. But it is distinguished by its rejection of subject-predicate forms of thinking

insofar as it concerns the assumption that such forms are the immediate embodiment of the very original characteristics of the facts. As a result, it becomes possible to avoid the concept of “substance-quality”; this morphological description is replaced by a description of the dynamic process. Spinoza's modes then become pure actualities, so that although their analysis increases our understanding, it still does not lead to the discovery of any higher level of reality. The coherence that the system seeks to preserve is the discovery that the process, or concrescence, of any actual entity entails another of the existing actual entities. In this way the obvious unity of the world receives its explanation.

In all philosophical theories there is something primordial that is relevant due to its accidents. Only in its accidental incarnations can it be characterized, and outside of them it is devoid of relevance. In the “philosophy of the organism” this original is called creativity, and the deity appears as the original, timeless accident. In the monistic philosophies of Spinoza or in absolute idealism, this primordial is the deity, which is equally designated as the “Absolute”. In such monistic schemes, a final, “higher” reality is illegally attributed to the primordial, going “beyond the limits of what is attributed to any of its accidents. In its general position, the “philosophy of the organism” seems closer to certain varieties of Indian or Chinese thought than to the thought of Western Asian or European. One side makes the process primary, the other makes the fact primary.

3. Any philosophy in turn experiences dethronement. But the totality of philosophical systems expresses a variety of universal truths about the universe, requiring mutual coordination and recognition of their various spheres of validity. Such progress in coordination is presupposed by the very development of philosophy; in this sense, philosophy has developed from Plato to the present day. In accordance with this understanding of the achievements of rationalism, the main mistake in philosophy turns out to be exaggeration. The desire for generalization is justified, but assessing the success of this process

exaggerated. There are two main forms of such exaggeration.

First of all, this is what I elsewhere called the error of substitution of the concrete.” This error consists in ignoring the degree of abstraction that occurs when considering an actual entity that exhibits certain categories of thought. There are aspects of actualities that are simply ignored as long as we limit our thinking to these categories. So the success of philosophy should be measured by its comparative ability to avoid the mistake of limiting thinking only to its own categories.

Another form of exaggeration consists in a false assessment of the role of a logical procedure in relation to its evidence and its premises. Philosophy, unfortunately, has been haunted by the idea that its method must point dogmatically to premises which are accordingly clear, distinct and obvious, and then build upon these premises a deductive system of thought.

But the exact expression of the final generalities is the goal of the discussion, and not its source. Philosophy has been misled by the example of mathematics; but even in mathematics, the affirmation of the original logical principles is associated with difficulties that have not yet been overcome. The confirmation of the rationalistic scheme is to be seen in its general successful result, and not in the special evidence, or initial clarity, of its first principles. In this connection it is worth noting the abuse of the ex absurdo argument; many philosophical arguments were distorted by him. The only logical conclusion that can be drawn when a contradiction appears in the process of reasoning is that at least one of the premises of the conclusion is false. Without asking additional questions, they recklessly assume that an erroneous premise can be immediately discovered. In mathematics, such an assumption is often justified, which misleads philosophers. But in the absence of a well-defined categorical scheme of entities embodied in a satisfactory metaphysical system, every premise of philosophical argumentation is suspect.

Philosophy will not regain its corresponding status until the consistent development of categorical schemes, clearly established for each stage of development, is recognized as its corresponding goal. They can

there are competing schemes opposed to each other, each with its own advantages and disadvantages. And then the goal of the study becomes the reconciliation of contradictions. Metaphysical categories are not dogmatic statements of the obvious; they are tentative formulations of underlying generalities.

If we consider any scheme of philosophical categories as a complex single statement, applying to it the logical alternative of true or false, then the answer we get is that this scheme is false. A similar answer must be given to a similar question concerning the existing formulations of the principles of any science.

Our scheme is true together with unformulated clarifications, exceptions, limitations and new interpretations in terms of general concepts. We don't yet know how to transform our circuit into a logical truth. But a schema as such is a matrix from which true propositions applicable to particular circumstances can be derived. At present we can only trust the ability of our trained instincts to distinguish between the circumstances in respect of which our scheme operates.

The use of a matrix like this is to serve as a basis for strong argumentation using rigorous logic. To make such an argument possible, the scheme must be established with the greatest precision and certainty. The conclusion of an argument must be weighed against the circumstances to which it applies.

The main benefit we get from this is that we no longer question experience through the paralyzing suppression of common sense. The penetration of reasonable expectation generated by the conclusion of our proof increases in observation. The result of this procedure takes one of three forms: 1) the conclusion may be consistent with the observed facts; 2) the conclusion may demonstrate general agreement at the same time as disagreement in details; 3) the conclusion may be in complete disagreement with the facts.

In the first case, the facts are known with greater adequacy,

and the applicability of our system to the world is also clarified. In the second case, criticism of the observation of facts and the observation of the details of the scheme are equally required. The history of thought shows that false interpretations of facts intrude into reports of their observation. Thus, both theory and accepted notions of facts are called into question. In the third case, a fundamental reorganization of the theory is required, either by limiting it to some special area or by completely abandoning its main categories of thought.

Once the initial basis of intelligent life with a civilized language had been established, all productive thinking developed either through the poetic insight of artists or through the imaginative development of patterns of thought capable of being used as logical premises. In one way or another, progress always means going beyond the obvious.

Rationalism will never escape its status as an experimental adventure. The combined influence of mathematics and religion, which played a huge role in the emergence of philosophy, unfortunately, however, imposed on it an inert dogmatism. Rationalism is therefore an evolving and never-ending adventure in the clarification of thinking. But this is an adventure for which any, even partial, success is important.

4. The field of a particular science is always limited to one kind of facts in the sense that no statements about facts lie outside the limits of this kind. The fact that science arose naturally in connection with certain facts guarantees that there are relations between the facts of a given type that are obvious to all mankind. The general obviousness of things arises when their clear comprehension turns out to be directly important for the purposes of survival or pleasure, i.e. for the purposes of "existence" and "prosperity". Those elements of human experience which are distinguished in this way correspond to the richness of language and, within certain limits, its precision. Thus, the concrete sciences deal with questions that are open to direct observation and ready for verbal expression.

The study of philosophy is a journey to ever greater communities. That is why, during the infancy of science, when the main emphasis was on the discovery of the most general ideas usefully applied to the issue under consideration, philosophy was not yet clearly separated from science. To date, the new science, the concepts of which have substantial novelty, is in some sense viewed as purely philosophical. In the later stages of their development, most sciences, despite some exceptions, without any doubt, accept the general concepts in which their development is clothed. The main emphasis is on agreement and direct verification of more specific statements. During such periods, scientists reject philosophy: Newton, rightly satisfied with his own physical principles, rejected metaphysics.

The fate of Newtonian physics reminds us that fundamental scientific principles evolve and that their original forms can only be preserved through interpretations of the meaning and limitations of their field of application—interpretations and limitations that went unnoticed during the first period of successful application of scientific principles. One of the chapters of cultural history has to do with the growth of communities. It shows how old communities, like old hills, fall apart and become smaller, so that they are surpassed by younger “rivals”.

Thus, the goal of philosophy is to challenge those semi-truths from which the first scientific principles are formed. The systematization of knowledge cannot take place in waterproof compartments. All general truths condition one another, and the limits of their applicability cannot be adequately determined apart from their correlation with the help of even broader generalities. The critique of principles must primarily take the form of determining the appropriate meanings to be given to the fundamental concepts of the various sciences when these concepts are considered in relation to the status they have in relation to each other. Determining this status requires a generality that goes beyond any special subject of consideration.

If the Pythagorean tradition can be trusted, then

The formation of European philosophy was largely stimulated by the development of mathematics as a science of abstract universality. But in the course of the subsequent development of philosophy, its method began to deteriorate from this. The original method of mathematics is deduction, and the original method of philosophy is descriptive generalization. Under the influence of mathematics, deduction was imposed on philosophy as its standard method, instead of taking its original place as an essential auxiliary method of verification in the field of application of generalities. This misunderstanding of the philosophical method disguised significant philosophical progress, expressed in the creation of generic concepts that give clarity to our comprehension of experimental facts. The "overthrows" of Plato, Aristotle, Thomas Aquinas, Descartes, Spinoza, Leibniz, Locke, Berkeley, Hume, Kant and Hegel simply mean that the ideas introduced by these people into the philosophical tradition must be constructed with such limitations, adaptations and inversions as they either they were unknown or they absolutely rejected them. New idea always introduces a new alternative, and we are no less indebted to one thinker or another when we accept the alternative he rejected. Philosophy never returns to its old position after the shock caused by a certain great philosopher.

5. Every science must invent its own instruments. The tool that philosophy requires is language. Philosophy reconstructs language just as physical science reconstructs the means at its disposal. It is at this point that appeal to facts is a very difficult operation. And this concerns not only the expression of facts in everyday language statements. The main issue for consideration is the adequacy of such proposals. It is true that the general agreement of mankind regarding the facts of experience is best expressed in language. But literary language fails precisely when it attempts to solve the problem of expressing in explicit form large generalities—the very generalities that metaphysics tries to express.

The point is that each sentence points to a universe that has a universal and systemic metaphysical character. Outside such a foundation, separate entities

forming the proposal, and the proposal itself as a whole do not yet have a definite character. Nothing is predetermined, for every determinate entity requires a systematized universe in order to maintain its necessary status. Thus, every sentence expressing a fact must, when fully analyzed, express that universal character of the universe which the given fact requires. There are no independent facts floating in anything. This doctrine, according to which it is impossible to tear a sentence out of its systematic context in the real world, is a direct consequence of the 4th and 12th fundamental categorical explanations, which we will further develop and illustrate. A sentence is capable of embodying a partial truth because it requires only a certain type of systematic environment, which is already presupposed in its very meaning. It does not designate the universe in all its details.

One of the practical goals of metaphysics is the precise analysis of sentences—not just metaphysical sentences, but quite ordinary sentences like “Today there is meat for lunch” and “Socrates is mortal.” One particular class of facts, which form the field of some special science, requires a general metaphysical premise concerning the universe. It would be frivolous to accept verbal phrases as adequate expressions of sentences. The distinction between verbal phrases and complete sentences is one of the reasons why the logician's rigid alternative of "true or false" is so inconsistent with the desire for knowledge.

Excessive reliance on linguistic phrases is a well-known reason that had such a negative influence on the philosophy and physics of the ancient Greeks, as well as those medieval thinkers who continued the Greek traditions. For example, John Stuart Mill writes: “The Greek philosophers found it exceedingly difficult to distinguish the things which their language confused, or to combine in the mind those which their language distinguished; they could hardly unite natural objects into any classes other than those established for these objects by local popular expressions, or at least unwittingly considered these classes to be natural, and all others arbitrary and artificial. As a result, speculative

Greek schools and their successors in the Middle Ages, scientific research was little more than the simple isolation and analysis of concepts associated with ordinary language. These philosophers thought that by determining the meaning of words, they could become familiar with the facts." Mill then quotes a paragraph from Whewell illustrating the same weakness in Greek thinking.

But neither Mill nor Whewell traces this linguistic difficulty back to its origins. They both assume that the language produces correctly defined sentences. This is quite untrue. Language is essentially undefined, and this is due to the fact that every event presupposes some systematic type of environment.

For example, the word "Socrates" referring to a philosopher in one sentence may stand for an entity that implies a more precisely defined basis than the word "Socrates" with the same meaning (reference) but in another sentence. The word "mortal" provides a similar possibility. Strict language must await the emergence of complete metaphysical knowledge. The technical language of philosophy embodies the attempts of various schools of thought to find clear expression of the general ideas implied by the facts of experience. It follows that any novelty in metaphysical doctrines demonstrates a certain degree of disagreement with statements of fact found in the current philosophical literature. The degree of disagreement captures the degree of metaphysical disagreement. Therefore, it will not be true to criticize any metaphysical school if we point out that its doctrines do not follow from the verbal expressions of facts accepted by another school. The main point is that both of these doctrines are approximations to fully expressed propositions.

Truth in itself is nothing more than the way in which the complex natures of the organic actualities of the world receive an adequate reflection in the divine nature. Such reflections constitute the “secondary nature” of God, who changes in his relation to the changing world without weakening the eternal completeness of his original conceptual nature. And in this way the “ontological principle” is supported, since there cannot be a certain truth,

which would impartially harmonize the partial experiences of different actual entities independently of the actual single entity that it may indicate. The reaction of the temporal world to the divine nature is further discussed in Part 5: it is there that it is called the “secondary nature of God.”

What is discovered in “practice” must lie within the limits of metaphysical description. Then, when the description fails to include “practice,” the metaphysics is inadequate and requires revision. As long as we remain satisfied with our metaphysical doctrines, there is no need to supplement metaphysics with practice. Metaphysics is nothing more than a description of generalities that apply to all details of practice.

No metaphysical system can hope to fully satisfy these pragmatic criteria. At best, such a system will remain only an approximation to the desired general truths. In particular, there are no precisely established axiomatic evidences with which to begin. There is not even a language in which they could be formalized. The only possible procedure would be to begin directly with verbal expressions, which, taken in themselves and with modern meaning their constituent words are poorly defined and ambiguous. These are not premises from which one can immediately reason independently of their clarification in further discussion; these are attempts to assert general principles that will be specified in the subsequent description of experimental facts. This further work should clarify the meanings assigned to the words and phrases we use. Such meanings cannot be precisely grasped in abstraction from the corresponding precise grasp of the metaphysical basis which the universe provides for them.

But language cannot be anything other than elliptical, involving a leap of imagination in order to understand its meaning in relation to direct experience. The position of metaphysics in the development of culture cannot be understood unless we remember that no verbal statement is an adequate expression of a sentence.

A long-formed metaphysical system creates

around herself a false atmosphere of some adequate precision only due to the fact that her words and phrases have passed into current literature. Thus, propositions expressed in its language correlate more easily with our changing intuitions about metaphysical truth. When we trust these verbal statements and reason as if they adequately analyze the meaning, we are faced with difficulties that take the form of denials of what is supposed in practice. But then, when they are offered as first principles, they undeservedly acquire the quality of sober evidence. Their disadvantage is that the true propositions they express lose their fundamental character when adequately expressed. For example, consider the type of sentences like “The grass is green” and “The whale is big.” This subject-predicate form of statement seems so simple, leading directly to the original metaphysical principle; and yet in these examples it hides such complex, even different meanings.

6. It has been objected to that speculative philosophy is extremely ambitious. It was assumed that rationalism is a method through which development is achieved within specific sciences. However, it is felt that this limited success should discourage attempts to formulate ambitious schemes expressing the general nature of things.

One of the supposed confirmations of this criticism is the failure itself: European thought is presented as polluted by metaphysical systems, abandoned and irreconcilable.

Such a statement implicitly imposes on philosophy the old dogmatic form of verification. The same criterion can attribute failure to science itself. After all, we have no more preserved the physics of the 17th century than the Cartesian philosophy of that time. However, within their boundaries, both systems express important truths. We also begin to understand broad categories that define their own limits of proper application. Of course, dogmatic views dominated that century; therefore the very applicability of both physical and Cartesian concepts was misunderstood. Humanity never fully knows what it needs. When we look at history

thoughts and in a similar way consider the history of practice, we find that one idea after another has been tested, its limits determined and the true core revealed. In relation to the instinct for intellectual adventure required in certain eras, much is true in Augustine’s rhetorical phrase “The heedless judge the whole world.” At least people are doing what they can in the matter of systematization, and in this case they are achieving something. The adequate test is not completion, but progress itself.

But the main objection, dating back to the 16th century. and which received complete expression from Francis Bacon, lies in (stating) the uselessness of philosophical speculation. Related to this is the position that we must carefully describe facts and identify laws to a degree of generality that is strictly limited to the systematization of the facts described. It is believed that general interpretation does not affect this procedure and therefore any system of general interpretation, regardless of whether it is true or false, remains essentially sterile. However, unfortunately for this position there are no brute, self-sufficient facts that can be understood independently of their interpretation as elements of some system. When we try to express the fact of immediate experience, we find that the understanding of the fact takes us beyond it, to its contemporaries, to its past and future, and also to those universals in terms of which its determination is represented. But such universals, by virtue of their very universal character, embody the potentiality of other facts with different types of certainty. So understanding immediate, brute facts requires their metaphysical interpretation as elements of the world that stand in some systematic relation to it. When (speculative) thinking enters the picture, it reveals interpretations in the practice itself. Philosophy does not introduce any new interpretations. Her search for a rational scheme is a search for more adequate criticism and more adequate justification for those interpretations that we accept willy-nilly. Our habitual experience is a unity of successes and failures in the matter of interpretation. If we wish to record uninterpreted experience, we will have to record the autobiography of the stone. Any

the scientific memoir, as evidence of “facts,” is thoroughly permeated with interpretation. The methodology of rational interpretation is a product of the intermittent vagueness (vagueness) of consciousness. Those elements that shine with their immediate clarity in some events retreat into twilight and even absolute darkness in other events. And yet, all events proclaim themselves to be actualities that require unity of interpretation within the limits of change in a stable world.

Philosophy is the very correction of consciousness from the original excess of subjectivity. Each actual event adds to the circumstances of its origin additional formative elements that deepen its specific individuality. Consciousness is only the last and greatest of such elements, by which the selective character of the individual obscures the external totality from which he comes and which he embodies. Actual individuality of such a high level relates to the totality of things precisely because of its pure actuality; but it achieves the individual depth of being by means of selective highlighting suited to its purposes. The task of philosophy is to restore the totality distorted by such selection. It replaces in rational experience that which was plunged into sensory experience of a higher order and then went even deeper thanks to the original operations of consciousness itself. The selectivity of individual experience has a moral nature insofar as it corresponds to the balance of comparative importance found in rational evaluation. Conversely, the transformation of intellectual insight into emotional power corrects sensory experience in its relation to morality. Such correction is proportional to the rationality of our insight.

The morality of a view is inseparably connected with its universality. It is possible to exclude the opposition of the general good and individual interest if the individual's interest becomes the general good, which will mark the loss of smaller intensities with the aim of their new acquisition in a better ratio and with a broader interest.

Philosophy frees itself from the taint of inefficiency by establishing closer relationships

with religion and science (natural and social). It acquires greater importance by mixing both, namely religion and science, into one rational scheme of thought. Religion must combine the rational universality of philosophy with those emotions and goals that arise in a certain society, in a certain era and are conditioned by certain preconditions. Religion is the translation of general ideas into specific thoughts, emotions and goals; it aims to expand individual interest beyond its self-limiting particularity. Philosophy finds religion and modifies it. And, conversely, religion is found among those data of experience that philosophy must weave into its scheme. Religion is the original desire to infuse into the obvious particularity of emotion that timeless universality that originally belongs only to conceptual thinking. In higher organisms the differences in rhythm between pure emotion and conceptual experience give rise to life's boredom until this perfect fusion occurs. Both sides of the organism require a reconciliation in which emotional experience illustrates conceptual reasoning, and conceptual experience finds emotional illustration.

This need for an intellectual justification of brute experience was also a motivating force in the development of European science. In this sense, scientific interest is only another form of religious interest. Any examination of the scientific commitment to "truth" as an ideal will only confirm this statement. At the same time, there is a serious discrepancy between science and religion regarding the stages of individual experience with which they deal. Religion is focused on the harmony of rational thinking with the reaction to the perceived, which gives rise to experience. Science is interested in the harmony of rational thinking with the perceived itself. When science deals with emotions, then these emotions are what is perceived, and not immediate passions, i.e. emotions of other people, but not your own; or, at least, your emotions in memory, but not directly experienced. Religion deals with the formation of the experiencing subject, while science deals with objects that represent the data for the formation of the initial phase of experience. The subject arises from (and among) already existing

conditions - science reconciles thinking with this initial fact, and religion reconciles thinking included in this process with the corresponding sensitive reaction. The process is nothing other than the subject himself receiving the experience. This explanation assumes that such a subject turns out to be a manifestation of a sensitive reaction to the actual world. Science finds religious experience among the perceptible, and religion finds scientific concepts among those kinds of conceptual experience which merge with concrete sensory reactions.

The conclusion of this discussion is, first, the affirmation of the old doctrine regarding the breadth of thought, reacting with the intensity of sensitivity, and this appears as the original requirement of existence; and secondly, in the assertion that, on the empirical plane, the development of self-justifying thinking was achieved by a complex process of generalization of particular points, imaginative schematization of generalizations, and, finally, a new comparison of the imaginary scheme with the direct experience to which it was to be applied.

There is no justification for a testing generalization at any particular stage. Each phase of generalization demonstrates its own specific elements(simplicities) that appear only at a certain stage and not at any other. There are elements associated with the movement of a piece of steel which become distorted if we refuse to abstract them from the (movement of) individual molecules. And there are certain elements associated with human behavior that are distorted if we refuse to abstract them from the individual characteristics of specific cases (specimens). In like manner there are certain general truths about actual things in the world of our activity which become distorted when attention is limited to some particular and detailed way of considering them. These general truths, included in the meaning of any specific concept of the actions of things, are the object of consideration of speculative philosophy.

Philosophy ceases to be useful when it indulges in the art of self-justification. In this case, it invades the territory of concrete sciences with erroneous baggage. It mainly appeals to the general consciousness of what we perceive in practice.

The connecting thread of premises which characterizes social expression throughout the various epochs of a rational society must find its place in philosophical theory. Speculative audacity must be balanced by complete submission to logic and fact. We are then dealing with a disease of philosophy in which it is neither defiant nor submissive, but is simply a reflection of the mental predispositions of outstanding personalities. Likewise, we do not trust any reworking of a scientific theory based only on a single and unrepeatable manifestation of a deviant experiment. The final test is always widespread and repeated experience, and the more general the rational scheme, the more important is this final appeal. A useful function of philosophy is to promote the most general systematization of civilized thinking. There is a constant interaction between specialization and common sense. The task of the special sciences is to modify common sense. Philosophy is a certain fusion of imagination and common sense. both limiting specialists and enhancing their flight of imagination. By presenting generic concepts, philosophy makes it easier to comprehend the infinite variety of specific instances that previously lay unrealized in the womb of nature.

Notes

". This doctrine represents a paradox. Falling into false modesty, “cautious” philosophers still dare to define the paradox. ^ Cf.: “Science and the Modern World,” Chapter 3. "Cf.: Principia Mathematica by Bertrand Russell and A. N. Whitehead, vol. 1. Preface and Preface to the second edition. These introductory arguments are practically Russell's. * The general categorical scheme is outlined by Whitehead in the next chapter, which was not included in the Russian translation.—Approx. ed. "See: Logic, book V, chapter Ill (Russian, trans. 1878, p. 300).—Editor’s note * See Whewell’s “History of the Inductive Sciences.”

PART 2. Process.

Chapter 10 Process

1- That “all things change (flow)” represents the first vague generalization that was made by unsystematic and still far from analytical human intuition. This is the theme of the best examples of Hebrew poetry in the Psalms; as a phrase of Heraclitus, it is one of the first generalizations of ancient Greek philosophy; amidst the later barbarism of Anglo-Saxon thought, it appears again in the story of “the sparrow that fluttered through the banquet hall of the Northumbrian king”; and in general, at all stages of civilization, the memory of this is capable of inspiring poetry. Without a doubt, if we return to the original and holistic experience, not distorted by any theoretical subtleties, i.e. to that experience, the clarification of which is the final goal of philosophy, then the “becoming (flux) of things” will turn out to be the original generalization around which we must build our philosophical system.

In this case, we have transformed the phrase “all things change” into the alternative phrase “things becoming.” In doing this, we considered the concept of “becoming” as requiring analysis first of all. But the sentence “all things change” contains three words, and we started by highlighting the last word. Then we go back to the next word, “things,” and ask: What kind of things change? Finally we reach the first word

"all" and ask: what is the meaning of the "many" things involved in this general change, and in what sense, if any, can the word "all" refer to a particular set of these many things?

Clarifying the meaning of the phrase “all things change” is the main task of metaphysics.

But there is also a competing concept, antithetical to the one mentioned. At the moment I cannot remember one immortal phrase that expresses this concept with the same completeness as Heraclitus’s phrase about the concept of “becoming.” This concept is based on the constancy of things - solid earth, mountains, stones, Egyptian pyramids, the human spirit. God. The best reproduction of a holistic experience, expressing it general shape in its purest form, is most often found in religiously inspired utterances. One of the reasons for the weakness of modern metaphysics is its inattention to such rich expression of primordial experience. Accordingly, in the first two lines of the famous hymn we find the full expression of the unity of both concepts in total experience:

Be with me;

Evening is coming quickly.

Here the first line, by mentioning I and Being, thereby expresses certain constancies; and the second line establishes these constancies in the midst of inevitable becoming. Here we will find a detailed formulation of the entire problem of metaphysics. The philosophers who begin with the first line have given us the metaphysics of “substance”; and those who begin on the second line have developed a metaphysics of “becoming.”

But in truth, both of these lines cannot be torn from each other in this way; and we discover that the fluctuating relationship between them is a characteristic feature of the teachings of a large number of philosophers. Plato found his constancies in the motionless spiritual heavens, and he discovered formation in the misadventures of forms amid the imperfections of the physical world. I would like to draw your attention to the word “imperfection”. I make statements about Plato with reservations; but I am sure that behind the doctrine that mutable things are imperfect in the sense of their "limitation" and in the sense that they definitely exclude everything that they could be and what they are not, stands the authority of Plato. The quoted lines of the hymn serve as an almost perfect expression of the immediate intuition from which the main point of view of Platonic philosophy follows. Aristotle corrected his Platonism by establishing a slightly different relationship. He found himself committed to the concepts of "substance" and "attribute", as well as the classifying logic that these concepts implied. But on the other hand, he skillfully carried out an analysis of the concept of “generation”. Aristotle personally expressed a fair protest against Plato’s tendency to separate the motionless spiritual world from the developing world of external experience. The later Platonic schools intensified this tendency; In a similar way, medieval Aristotelianism made it possible, on the basis of the static concepts of Aristotelian logic, to formulate some of the main metaphysical problems in terms that have existed down to the present day.

In general, the history of philosophy confirms the accusation made by Bergson regarding the human intellect, which considers the entire “universe as space,” i.e. that the intellect tends to ignore becoming and analyze the world in terms of static categories. Moreover, Bergson even considered this tendency as internally necessary for the intellect. Although I do not believe in the truth of this last charge, I do believe that "spatialization" is a shortcut to a very limited philosophy, expressed in a fairly familiar language. And Descartes presented an almost perfect example of such a system of thinking. The problems of the Cartesian doctrine of three clearly defined substances, which is based on the concepts of “duration” and “measurable time,” clearly show the result of underestimating becoming. This can all be found in the above hymn, and in Plato’s vision of heavenly perfection, and in Aristotle’s logical concepts, and in Descartes’ mathematical thinking. Newton—that Napoleon of (scientific) thought—resolutely returned the becoming to a world organized by “absolute mathematical time, flowing uniformly and without regard to anything external.” He also gave rise to a generalized mathematical form of the theory of fluxions.

During this period, a group of philosophers of the 17th and 18th centuries practically made a discovery that, although it

and is clearly revealed in their works, they themselves were only partially able to realize. This discovery is; that there are two types of becoming. One of them is “concrescence,” which in Locke’s language is “the real internal construction of a separately existing thing.” The second type of becoming is the transition from one separately existing to another. Again, in Lockean language, this transition is represented as “permanently ceasing,” and this is one aspect of the concept of time. In another aspect, the transition appears to be the emergence of the present in accordance with the “power” of the past.

The phrase “the real internal construction of something separately existing,” the description of human understanding as a process of reflection on data, the phrase “perpetually ceasing,” and the explanation of the word “power” can all be found in Locke’s Essay Concerning Human Understanding. , although due to the limitations of his research, Locke was never able to bring together and generalize his disparate ideas. This implicit understanding of two types of becoming was also unconsciously inherent in Hume. Kash almost made it explicit, but at the same time, I think, described it inaccurately. Finally, this understanding was lost in the evolutionary monism of Hegel and the Hegelian schools. For all his inconsistency, Locke is the philosopher to whom it is most useful to return when we seek to explicate this discovery of the two kinds of becoming required to describe a changing world. The first type of becoming is inherent in the process of constructing a separately existing thing. I called this type “fusion.” The second type is formation, due to which the cessation of the process in the case of the formation of a separately existing one constitutes this existing one as the initial element of the construction of other separately existing ones, which are revealed when the process is repeated. I called this type “transition”. "Fusion" is directed towards its final cause, which represents its subjective goal; “transition” is a mechanism of an efficient cause, which is the immortal past.

Discussion about how individual current events become the starting elements for a new creation,

called objectification theory. Individual objectified events together constitute the basis for creative “fusion.” But, acquiring a certain degree of coherence, their internal relationships are eliminated, while some elements of the structure create others. Thus, objectification is a mutually agreed upon operation of abstraction, or elimination, due to which many events of the real world form one complex value. This fact of elimination by synthesis is sometimes viewed as a real-world perspective from the perspective of “fusion.” Each actual event determines its own world in which it occurs. No two events can have identical worlds.

2. “Concrescence” is the name of the process in which the universe of things acquires individual unity as a result of the subordination of “many” of them to the construction of “one” new thing.

The most general term “thing”, or, accordingly, “essence”, is significant for cases of “fusion”. Each such case in itself is nothing more than the ability to be one of those “many” things that find a niche for a new separate thing. There is no “fusion” and “new thing”: when we analyze new thing, then we find nothing but the “fusion” itself. “Actuality” means this original inherence of the concrete, from which only nothing is possible in abstraction. In other words, any abstraction from the concept of “inherence in the concrete” is self-contradictory, since it requires us to perceive a thing not as a thing.

Some individual case of “fusion” is called an “actual entity”, or, accordingly, an “actual event”. There is no one complete set of things that are actual events. For creativity is an obligatory fundamental fact, thanks to which there cannot be “many things” that are not subordinated into a specific unity. Thus, the totality of all actual events is, by its very nature, a standpoint for another “fusion” that extracts a specific unity from this set of actual events. Hence we cannot study the real world except from the point of view of immediate “fusion”, which denies the previous completion of the process. That creativity, due to which anyone

The relatively completed actual world is, by its very nature, the basis for a new “fusion”, called “transition”. Likewise, thanks to the transition, the “actual world” is always a relative term, indicating the basis of the supposed actual events that serve as the starting point for a new “fusion.”

The current event is analyzed. In this case, analysis reveals those operations that transform individually alien entities into components of a whole, which is a concrete unity. The term “feeling” will be used to describe such operations generally. Therefore we say that the actual event is a “fusion” caused by the process of feeling.

Feeling can be considered in relation to: 1) experienced actual events, 2) experienced eternal objects, 3) experienced feelings and 4) one's own subjective forms of intensity. In the process of “fusion”, various feelings pass into broader universalities of integral feeling.

Such universality is the feeling of an integral complex of feelings, including the specific elements of identity and difference inherent in them. And this process of integration of feeling continues until a specific unity of feeling is achieved. From such a concrete unity any uncertainty regarding the realization of possibilities is already excluded. Many entities in the universe, including those that arose in the “fusion” itself, receive corresponding roles in this final unity. Such final unity is called “satisfaction.” “Satisfaction” is the culmination of the “fusion” of Entities into a completely definite reality. But at each of the previous stages, the “fusion” demonstrates complete uncertainty regarding the (nature of) connection (nexus) between its components.

3. The actual event is nothing other than the unity that must be inherent in each individual “fusion.” Such “fusion” is therefore “real internal construction”. Analysis of the formal construction of the actual essence allows us to distinguish three stages of the process of “feeling”: 1) response phase,

2) an additional stage and 3) “satisfaction”.

“Satisfaction” is simply the culminating moment of the disappearance of all uncertainty; so that in relation to all kinds of feelings and entities in the universe, the actual entity that has achieved “satisfaction” embodies a decisive “yes” or “no.” So, “satisfaction” turns out to be the achievement of an individual (private) ideal, which is the final cause of “fusion.” But this process itself is contained in two preceding phases. In the first phase, there is a pure reception of the actual world, appearing under the guise of what is objectively given for aesthetic synthesis. At this phase, there is a perception of the world as a multitude of individual centers of feeling, mutually presupposing each other. These feelings are experienced as belonging to external centers and therefore are by no means dissolved in individual spontaneity. The second stage is determined by the individual ideal, which gradually takes shape in this process itself. Thanks to this, many feelings, initially experienced as alien, are transformed into an aesthetic unity, directly experienced as individual. This means the emergence of "aspiration", which in its highest manifestations we call "vision". In the language of physical science, here the “scalar” form prevails over the original “vector” form: the initial premises turn out to be subordinate to individual experience. In this case, the vector form does not disappear, but simply disappears from view, being the basis of the scalar superstructure.

In this second stage, feelings acquire an emotional character due to the influx of conceptual feelings. But in individual emotion the initial premises do not disappear simply because there are no purely individual elements in the universe at all. If we could carry out a complete analysis of meaning, then in it the concept of pure subjectivity (privacy) would seem itself contradictory. Emotional feeling, in spite of everything, is subject to the third metaphysical principle: “To be something means to be able to achieve real unity with other entities.” Hence, “to be a real component of an actual entity” in some way means “to realize a given possibility.” This "emotion" is an "emotional feeling"

and “what is felt” is the intended vector of the situation. In physical science, this principle takes a formulation that will not be lost in any deep speculation, namely: that scalar quantities are constructs derived from vector quantities. In more familiar language this can be expressed by saying that the concept of "passing on" is more fundamental than the concept of an individual fact. In the abstract language adopted here, in which we make metaphysical statements, “flow” becomes “creativity” (in the dictionary sense of the verb “creare” - “to cause, generate, produce”). Thus, in accordance with the third (metaphysical) principle, no entity can be separated from the concept of creativity. An essence is some individual form capable of incorporating its individuality into the (process of) creativity. The actual essence, or at least the phase of the actual essence, is more than this; and already, at least, she has this.

Locke's “particular ideas” act as direct predecessors of actual entities, manifesting the function of including their individuality in the “flow,” which is the primary phase of “the real internal constitution of a given actual entity.” In accordance with the prevailing misunderstanding, Locke called this entity "spirit" and began to discuss its structure, when he should have discussed "mental operations" in their role as the final phases of the constitution of actual entities. Locke himself expresses only in passing this fundamental vectorial function of his “ideas.” In a paragraph, part of which has already been quoted, he writes: “I admit that power involves some kind of attitude—to action or change. Indeed, which of our ideas of any kind does not contain it, if we carefully consider them? (II, 21.3).

4. The second, additional phase is itself, in turn, divided into two phases. They are both quite obvious: at the same time, they are not completely separable from each other, because they interact through tension and inhibition. If they are such, then the entire second phase is simply a decisive negation of individual emergence; this process here passively passes into the stage of “satisfaction”.

In such a case, the actual essence acts only as a mechanism for transmitting the acquired properties of feeling, and its individual immediacy becomes invisible. Of the named subphases, the first - if they are given in order - is the phase of aesthetic addition, the last is the phase of intellectual addition.

With aesthetic addition, there is an emotional perception of contrasts and rhythms that are inherent in the process of unification of objective content in the “fusion” of some current event. In this phase, perception is enhanced by the assimilation of pain and pleasure, beauty and disgust. This is the phase of inhibition and tension. In this phase, “blue”, for example, becomes more intense due to the existing contrasts, and the form becomes dominant due to its beauty. What was originally considered alien is recreated as individual. This is the receptive phase, which includes emotional reactions on susceptibility. In it, individual spontaneity melted existing data into a new fact of blind sensitivity. A purely aesthetic addition solved its problem. This phase requires an influx of conceptual feelings and their integration with purely physical feelings.

But the blindness of the process still leaves some uncertainty. Therefore, there must be either a decisive denial of intellectual “seeing” or its assumption. In the first case, eternal objects that have the abstract status of pure potentialities are rejected as unacceptable. “What could be” contrasts appropriately with “what is.” If pure potentialities that are in an abstract state are rejected, then the second subphase becomes obvious. In such a case, the process constitutes a “blind” actual event—“blind” in the sense that intellectual operations do not take place in it, although conceptual operations always take place. Therefore, there is always a mentality in the form of “vision” and not always a mentality in the form of conscious “intellectuality”.

But in case some eternal objects, which are in an abstract state, are considered as belonging to an actual fact, the actual

event with intelligent operations. The complex of such intellectual operations is sometimes called the “spirit” of the actual event, and the actual event is also called “conscious”. It is true that the term "spirit" alludes to some independent substance. But this is not what is meant here: the best, therefore, will be the term “consciousness”, which belongs to the actual event.

The eternal object, realized in relation to its pure potentiality as corresponding to a certain logical subject, is called “propositional feeling” in the mentality of a specific actual event. Consciousness belonging to some actual event appears under a phase when this subphase is not completely obvious. This subphase is the inclusion in feeling of the entire contrast between purely propositional potentiality and realized fact.

5. To summarize: there are two types of process: macroscopic and microscopic. The macroscopic process is the transition from actuality achieved to actuality in achievement; the microscopic process is the transformation of simply real conditions into a certain actuality. The first process affects the transition from the “actual” to the simply “real”; the latter process influences the ascent (growth) from the real to the actual. The first process is active, the last is teleological. The future is simply real without being actual. At the same time, the past is a connection of actualities. Actualities are constituted in their real genetic phases. The present is the immediacy of the teleological process through which reality becomes actual. The first process provides the conditions that guide achievement, while the latter process provides actual achievable goals. The concept of “organism” is combined in two ways with the concept of “process”. The community of actual things is an organism, but this organism is by no means static. In the process of creating something new, it is always incomplete. Hence the expansion of the universe of actual things turns out to be the first meaning of “process”; the universe itself, at any stage of its expansion, is the first meaning of “organism.” In this sense, any organism is a nexus.

First of all, every actual entity in itself can only be described as an organic process. It repeats in microcosm what the universe is in macrocosm. It is a process that occurs from phase to phase; Moreover, each phase serves as a real basis for its successor to complete a specific thing. Any actual entity carries in its structure “reasons” for why its state is exactly as it is. These “reasons” are other actual entities objectified for her.

The “object” is the transcendental element that characterizes the certainty with which our “experience” must be consistent. In this sense, the future has an objective reality in the present, but not formal actuality. For already in the structure of immediate, present actuality is the fact that it will be overcome by the future. Likewise, the states with which this future must be consistent (including real relations with the present) are truly objective in immediate actuality.

Thus, any actual entity, even despite its completeness in the sense of a microscopic process, is nevertheless incomplete due to its objective inclusion in a macroscopic process. She does perceive a future that must be actual, although the completed actualities of such a future are uncertain. In this sense, every actual event perceives its own objective immortality.

Note. The function that is here attributed to the “object” is generally consistent with the paragraph (2nd edition) of the “Commentary” to Kant’s “Critique” by Prof. Kemp Smith, where he examines Kant's "Objective Deduction" from the first edition of the Critique. “When we examine the objective, we find that the main characteristic that distinguishes it from the subjective is that it imposes a certain binding force on our minds, forcing us to think about it in a certain way. By object is meant something that does not allow us to think randomly.” Of course, among other things, there is a serious difference, for where Kemp Smith, interpreting Kant, refers to “thinking,” the philosophy of organism substitutes “experiencing” in this place.

Essays on Science and Philosophy

PART 2. Philosophy

Chapter 1. Immortality

In this lecture, the main emphasis will be on the concept of immortality, and humanity will be discussed in the broadest context. We will assume that all entities or factors in the universe are largely dependent on each other's existence. The full explanation for this lies outside our conscious experience. In the future, the doctrine of essential relevance will be applied to the interpretation of those fundamental beliefs that relate to the concept of immortality.

1-There is finitude—if this is not so, then infinity will not matter. The contrast between finitude and infinity stems from the fundamental metaphysical proposition that every entity presupposes an infinite set of perspectives, each of which expresses the finite characteristics of that or that entity. But no finite perspective allows the essence to free itself from its close relationship with the universal. The infinite background will always remain the unanalyzed reason why the finite perspective of some entity is what it is. Any analysis of this limited perspective always assumes some additional factors related to the foundation. In this case, the essence is comprehended in a broader final perspective, which inevitably presupposes a basis, which is the universe itself in its relation to this essence.

Consider, for example, this lecture hall. In relation to him we all have an immediate final

experience. To understand this experience, we expand the analysis of the apparent relationships of this room. The hall is part of the building; the building is located in Cambridge (Massachusetts) - Cambridge is on the surface of the Earth; The Earth is a “planet of the solar system; the solar system belongs to a certain nebula; this nebula belongs to a system of nebulae related to each other in space; these nebulae represent a system with a finite existence in time; they arose due to previous and inaccessible to our understanding of circumstances in the future transform into other forms of existence that are beyond the limits of our imagination. We have no reason to believe that our present knowledge of these nebulae represents facts directly related to their own forms of activity. In fact, everything speaks of the doubtfulness of such an assumption. For human history. thoughts in the past are a regrettable story of self-satisfaction with the supposed adequacy of our knowledge regarding the factors of human existence. We now realize that such self-satisfaction in the past was a deception. Accordingly, when we evaluate ourselves and our colleagues, we have every reason to subject. questioning the adequacy of our knowledge about any particular thing. Knowledge is a process of exploration. It has something to do with truth. And self-satisfaction has a certain justification. To a certain extent, this room has solid walls resting on a fixed foundation. Our ancestors believed that this was the whole truth. We know that this embodies a truth that is important only to lawyers and to the university corporation responsible for the property. But outside such finite limitations this will no longer be true.

Today we are discussing the immortality of human beings using this hall. And for the purposes of such a discussion, the limited perspectives of legal systems and university corporations are irrelevant.

2. “Immortality of man”—what can this phrase mean? Let us consider the term “immortality” and try to understand it by pointing to its antithesis “mortality”. Both words refer to those two aspects of the universe that are presupposed in every experience we have. I will call these aspects “two worlds.” They assume each other

each other and jointly constitute a concrete universe. Considered in itself, each of the worlds is an abstraction. For this reason, any adequate description of one of the worlds includes characteristics of the other in order to represent the particular universe in its relation to each of the two aspects. These worlds are prime examples of the universe's perspectives. The word "evaluation" denotes the clarification of one of the abstractions by pointing to another.

3. That World which increases the variety of mortal things is the World of Activity. This is the World of Generation (Emergence), the World of Creativity. He creates the present, modifying the past and anticipating the future. When we emphasize active creativity itself, the emphasis is placed precisely on the present, namely on “creation now,” where there is no indication of any transition.

And yet, activity loses its meaning when it is reduced to mere “creation now”: the absence of value destroys any reasonable possibility. “Creation now” is a factual state that is one aspect of the universe, namely the fact of immediate generation. In this case, the concepts of past and future are only shadows in the fact of the present.

4. The World that increases the duration of existence is the World of Value. Value by its very nature is timeless and immortal. Its essence is not rooted in any transitory circumstances. The immediacy of any circumstance subject to mortality is of value only if it participates in immortality. The inherent value of the universe is completely independent of any moment of time and, moreover, can lose its significance regardless of its necessary participation in the world of transitory facts. Value points to Fact, and Fact points to Value. (This statement is in direct contradiction to Plato and the theological tradition based on this thinker.)

But neither the heroism of any act nor the heinous character of an unworthy act depends on the particular second of time during which they occur, unless a change in time places them in a different sequence of values. Value judgment

points beyond the immediacy of historical fact.

The description of each of these two worlds involves its own stages, which include characteristics borrowed from the other world. The fact is that these worlds are abstractions of the universe, and each abstraction implies an indication of the universality of existence. There is no such thing as a self-sufficient abstraction.

That is why value cannot be considered separately from activity, which is the main characteristic of another world. “Value” is a general name for a whole infinity of values, partly consistent and partly inconsistent with each other. The essence of these values is their ability to be realized in the World of Activity. Such a realization entails the exclusion of incompatible values. Thus, the World of Value should be seen as active, as a world of consistent possibilities for realization. This activity of internal coordination is expressed in our moral and aesthetic judgments. Such judgments presuppose basic concepts of “best” and “worst.” For the purposes of this discussion, the noted internal activity of the World of Value will be called evaluation. This characteristic of assessment is one of the meanings of the term “judgment.” Judgment is a process of unification, which necessarily presupposes the relationship of values.

Value also relates to the process of implementation in the World of Activity. Thus, there is a further inclusion of judgment, which is here called "evaluation." This term will be used to denote the analysis of specific facts in the World of Activity in order to determine which values are realized and which are excluded. The universal character of the universe cannot be avoided, and exclusion is an activity comparable to inclusion. Any fact in the World of Activity has a positive relationship to the entire sphere of the World of Value. Evaluation indicates both assumptions and non-assumptions.

Evaluation entails a process of modification: the World of Activity is modified by the World of Value. Evaluations cause pleasure or disgust in the World of Activity. Approval or refusal becomes characteristic of him, he receives his perspective of the past and his goal for

future. This interaction of two worlds is an evaluation, a modifying activity.

But evaluation always involves abstraction from the pure immediacy of the fact: it points to evaluation.

If you enjoy food and recognize the deliciousness of apple pie, then its taste is what gives you pleasure. Of course, the pie had to appear at exactly the right time. But it is not the moment recorded on the clock that gives it significance, but the sequence of types of value, for example, the predestined nature of food and your initial hunger. In this way, you can express what food means to you in terms of a sequence of timeless evaluations.

In this way, the process of evaluation demonstrates the immortal world of coordinated value. Therefore, the two sides of the universe are the World of Generation and the World of Value. The value itself is timeless, and at the same time, as a result of its transformation into evaluation, it receives the function of modifying events in time. Any of the worlds can be explained only by pointing to another world; but this indication does not depend on words or other explicit forms of description. This statement is a summary of the attempt made in this chapter to avoid the weak Platonic doctrine of "imitation" and the even more shallow modern pragmatist denial of "immortality."

5. Let us summarize what has been said: generation is creation, while value is realized in the modification of creative action. Creation is directed toward value, while value is saved from the futility of abstraction by its influence on the process of creation. But in this combination, value retains its immortality. In what sense does a creative action derive its immortality from value? This is the subject of our lecture.

The concept of efficiency cannot be separated from the understanding of the World of Value. Understanding the purely abstract self-realization of values without any indication of the effectiveness of action was the fundamental error of Greek philosophy. It was inherited by the Christian hermits of the first centuries, and it is not so unknown in the modern educated world.

The activity of conceptual evaluation is, in essence, the driving force behind the development of the universe. She

becomes evil when it strives for an impossible abstraction from the universal activity of action. Both worlds—Values and Activities—are united with each other in the life of the universe, so that the immortal factor of value is included in the active creation of the temporal fact.

Evaluation actively functions as a factor of motivation and aversion. It is a drive that includes the "drive towards" and the "deterrence from" variety of possibilities.

Thus. The World of Activity is based on the multiplicity of finite acts, and the World of Value is based on the unity of active coordination of various possibilities of value. The essential combination of the two worlds imparts a unity of coordinated values to the multiplicity of final acts. The meaning of acts is found in actualized values, and the meaning of evaluation is found in facts, which are the realization of their share of value.

Thus, each of the worlds in itself is useless, except for the function of embodying another world.

6. The noted merging of worlds suggests that each of them can be described only with the help of factors common to both of them. Such factors have a dual aspect, and each of the worlds emphasizes one of the aspects. These factors are the famous Ideas, the discovery of which glorified Greek thought; However, the tragedy of this thought was a misunderstanding of the status of Ideas in the universe.

The concept of “independent existence” is precisely the misunderstanding that has plagued philosophical literature for centuries. In reality there is no such kind of existence, for each entity can only be understood by pointing out its intertwining with the rest of the universe. Unfortunately, this fundamental philosophical doctrine was not applied either to the concept of God or (in the Greek tradition) to the concept of Ideas. An idea is an entity that answers questions like “how?”. Questions like these ask about the “sort of” things that are happening. For example: “How come the car stopped?” The answer turns out to be the phenomenon of “red at the traffic light” among the corresponding environment. Thus, the penetration of the idea of “red color” into the World of Fact explains the special behavior of a fact, which is the stopping of a car.

The “red color” functions differently when we admire a beautiful sunset. In this example, the realized value is clear. The third case represents the artist's intention to paint a sunset. This intention is directed towards implementation, which is characteristic of the World of Value. But intention itself is realization within the universe.

Thus, any Idea has two sides. namely: the shape of the value and the shape of the fact. When we experience “realized value,” we experience the self as an essential combination of two worlds. But when we place emphasis on a simple fact or a simple possibility, then we are carrying out mental abstraction. When we feel a fact as the realization of a certain value, or we feel a possibility as an impulse for realization, then we thereby emphasize the original character of the universe. This character has two sides: one is the mortal world of becoming facts, acquiring the immortality of realized value, and the other side is the timeless world of pure possibility of obtaining temporary realization. The bridge between both is the two-way Idea.

7. So, the topic “Immortality of Man” turns out to be the other side of a broader topic - “Immortality of realized value”, namely the temporary nature of the very fact of acquiring immortality of value.

Our first question will be: “Can we discover any general feature of the World of Fact which would express its fitness for the embodiment of value?” The answer to this question is the tendency of changeable factual events to unite in sequences of personal identity. Any such personality sequence presupposes the ability of its members to maintain identity of value. In this way, value experience creates in the emerging World of Fact an imitation of its own immortality. This assumption is nothing new. It is as old as Plato himself. The systematic thought of ancient authors has now become almost worthless, but their individual insights are still priceless. This statement can be considered to indicate characteristic features of Platonic thinking.

The preservation of personal identity in the midst of the immediacy of actual events turns out to be the most remarkable feature of the World of Fact. In a manner

this is a denial of its transitional nature. Stability appears under the influence of value. Another aspect of this stability can be found in the scientific laws of nature. It is now fashionable to deny any evidence for the stability of the laws of nature and at the same time implicitly imply such stability. Personal identity is an outstanding example of stability.

Let us look more closely at the nature of personal identity. The whole sequence of actual events (each with its own immediacy of the present) is such that any event combines in its being the previous members of this sequence with the obvious perception of the personal identity of the past in the immediacy of the present. This is the realization of personal identity. It varies over time. For short periods it is so dominant that we hardly notice it. For example, take any syllable word like the word “predominant” used in the previous sentence. Of course, the person who uttered “pre” is identical with the person who uttered “shchy.” But there was a second's interval between both events. And at the same time, the speaker felt his own identity while pronouncing the word, and the listeners never doubted the self-identity of the speaker. Also, during a given period of utterance, everyone, including the speaker himself, believed that he would complete the sentence in the near future and that the sentence itself began in the more distant past.

8. This problem of “personal identity” in the changing world of events turns out to be a key example for understanding the essential fusion of the World of Activity with the World of Value. Value immortality has penetrated into variability, which is an essential feature of activity. “Personal identity” occurs when a change in factual details demonstrates an original identity among subsequent changes in value. This identity plays a dual role: formalizing a fact and realizing a specific value.

This preservation of a type of value in a sequence of change is a type of highlighting of what is important. The unity of style in the flow of elements gives them significance, which illustrates the intrinsic Value of the style itself, which

builds such an emphasis from individual details. The mixing of the diverse is transformed into a dominant coherent unity. The many become one and through this miracle achieve the triumph of efficiency once or for all. This achievement is the essence of art and moral purpose. In separation from the types of unity obtained by preserving the dominant properties of value, the World of Fact would disintegrate into an insignificant disorder.

9. Personality is the most striking example of the ongoing implementation of a value type. The coordination of a social system is a more vague form. In a brief lecture, discussion of social systems should be omitted, since the topic extends from the physical laws of nature to tribes and nations of human beings. But one point must still be made, namely, that the most effective social systems involve a great mixture of different types of individuals as subordinate elements, such as animal bodies, or communities of animals, such as human beings.

“Personal identity” is a complex concept. It dominates human experience, and the concepts of civil law are based on it. The very person who committed the theft is sent to prison; the same materials are preserved for centuries and millions of years. We cannot throw away personal identity without throwing away all human thought expressed in any given language.

10. All the literature of European peoples on this subject is based on concepts that have been completely rejected over the last hundred years. The concept of the immutability of species and genera, as well as the concept of the unconditional certainty of their difference from each other, dominates the literary traditions of Philosophy, Religion and Science. Today, the prerequisites for the concepts of immutability and certainty have clearly disappeared, and yet these concepts continue to dominate the scientific literature. Learning preserves both the mistakes of the past and its wisdom. It is for this reason that dictionaries pose a public danger, although they are necessary.

Any particular case of personal identity is a special way of giving the ideal world limited effectiveness. Preserving character is the way to

in which the limitation of the World of actuality embraces the infinity of possibility. In each individual the vast infinity of possibility is recessive and ineffective, but some prospect of an ideal existence becomes actual. This formation occurs to a greater or lesser extent: there are degrees of dominance and recessivity. The pattern of such degrees and the ideal introductions which they presuppose constitutes the character of the permanent fact of personal identity in the World of Activity. The essential coordination of values dominates the essential differentiation of facts.

We are by no means capable of analyzing personal existence completely adequately; to an even lesser extent there is precision in the division into species and genera. For practical purposes of the immediate environment, such divisions act as necessary ways of developing thinking. But we cannot give suitable definitions of what we mean by “practical purposes” or “immediate environment.” As a result, we are faced with a vague proliferation of human, animal and plant life, living cells, as well as material objects possessing a personal identity, devoid of life in the ordinary sense of the word.

II. The concept of character as the essential factor of personal identity illustrates the truth that the concept of Ideas presupposes gradations of community. For example, the character of an animal belongs to a higher level of ideas than the particular taste of food experienced at a certain moment in its existence. Also in relation to art, a certain shade of blue in a painting belongs to a lower level of ideas in comparison with the special aesthetic beauty of the painting as a whole. Any painting is beautiful in its own way, and this beauty can only be reproduced by another painting with the same concept and in the same colors. There are also degrees of aesthetic beauty that constitute the ideals of various schools and periods of art.

Thus the variation of degrees of Ideas is infinite, and must be treated as a distinct line of increasing generality. This diversity can be seen as growth, implying an infinity of dimensions. We can only comprehend the final fragment

this growth of degrees. But when we choose one line of progress towards generality, we are obviously confronted with a higher type of value. For example, we may admire a color, but admiring a painting if it good picture, implies a higher degree of value.

One aspect of evil occurs when a higher degree of adequate intensity is upset by the introduction of a lower degree.

That is why the purely Material World does not inspire us with any concepts of good and evil, for we cannot detect in it any system of degrees of value.

12. The world of Value contains both evil and good. In this respect, the philosophical tradition coming from classical Greek thought is surprisingly artificial. It reveals the emotional position of successful individuals living in the World of Beauty. Hebrew literature emphasizes morality. Palestine turned out to be a miserable battleground for opposing civilizations. As a result, its gifted population became characterized by both a deep moral sense and barbaric concepts. In Christian theology, Jewish and Hellenistic thought merged, but their most powerful insights were largely lost. But together Hellenistic and Hebrew literature demonstrate the genius of aesthetic and moral revelation on which any attempt to understand the functioning of the World of Value must be based.

Values require each other. The essential characteristic of the World of Value is coordination. Its activity consists in approaching multiplicity by combining different potentialities into finite unities—each unity with an intertwining group of dominant value ideas, and by reducing the infinity of values to a graduated perspective, gradually weakening until its complete exclusion.

Thus, the reality inherent in the World of Value presupposes the primary experience of the ultimate perspective for realization in the essential diversity of the World of Activity. But the World of Value emphasizes the essential unity of the many, while the World of Fact emphasizes

essential multiplicity in the realization of this unity. Thus, the universe, which embraces both worlds, demonstrates the one as many and the many as one.

13. The main thesis of this lecture is that we naturally simplify the complex nature of the universe by considering it in the form of two Abstractions, namely: the World of Multiple Activities and the World of Coordinated Value. The primary characteristic of one world is change, the other - immortality. But understanding the universe requires that each world exhibit the imprint of another world in it.

It is for this reason that the World of Change creates a stable personal identity as an effective aspect of value realization. Outside of any type of personality, only the trivialization of value occurs.

But implementation turns out to be an essential factor in the World of Value, saving it from useless abstract hypotheses. Thus, the effective realization of value in the World of Change must find its counterpart in the World of Value; this means that a temporary personality in one world presupposes an immortal personality in another.

Another way of putting this conclusion is that every factor in the universe has two aspects of our mental abstractions. A certain factor can be considered from the temporal side in the World of Change and from the immortality side in the World of Value. We have already applied this doctrine to Plato's Ideas—they are temporary characteristics and immortal types of value. (We use, with some distortion, Plato's doctrine of "imitation".)

14. The World of Value reveals a significant unification of the universe. So, while revealing the aspect of immortality of many personalities, it also suggests the unification of personality. This is the concept of God. (But this is neither the God of the learned tradition of Christian theology, nor the diffuse God of the Hindu-Buddhist tradition. Our concept of God lies somewhere in the middle. God is an elusive fact underlying finite existence.

Firstly, the World of Value is not the World of Active Creativity. It represents the necessary coordination of the essential diversity of the creative

actions. Thus, God, whose existence is based on value, is necessary for the coordination of Ideas.

He also turns out to be an amalgamation of the many personalities of the World of Activity. Thus, we consider the World of Value from the point of view of the coordination of many personal individualities as factors of the divine nature.

But according to the doctrine here advanced this is only half the truth. For God in the World of Value is equally a factor in each of the many personal existences of the World of Change. The emphasis on the divine factor in human nature is essential to religious thinking.

15. Discussion of this conclusion leads to an exploration of the concepts of Life, Consciousness, Memory and Anticipation.

The nature of consciousness may vary. In its essence it requires an emphasis on finitude, namely on the recognition of “this” and “that”. It may also involve a varying amount of memory or may be limited to the immediacy of the present, devoid of memory or anticipation. Memory varies greatly, and, with the exception of a small part of experience, most of our experiences are felt and passed. The same is true for anticipation.

Our sensory experience is external and cannot reflect the enormous self-satisfaction that arises from bodily internal functions. Indeed, human experience can be described as a stream of self-gratification, differentiated by a stream of conscious memory and conscious anticipation. The development of literary skills drew attention to the external character of such sensory experiences as visual and auditory; the deeper concepts of “compassion” and “loving hearts” stem from human experience as it functioned three thousand years ago. Today these are just outdated literary devices (gestures). And now, for example, an attentive doctor, while he observes the nature of the bodily manifestations of his patient, will definitely sit down and begin to talk with him.

When memory and anticipation are completely absent, then there is complete agreement with the ordinary influence of the immediate past. There is no

conscious confrontation of memory with possibility. This situation gives rise to the activity of pure matter. When there is memory, however weak and short-lived it may be, the normal influence of the immediate past or future ceases to be dominant. Then a reaction arises against the exclusive dominance of matter. Thus the universe is material in proportion to the limitation of memory and anticipation.

In relation to this assessment of the World of Activity, there is no need to postulate two essentially different types of active entities, namely, purely material entities and entities animated by different types of experience. The latter type will be sufficient for assessing the characteristics of this world if we allow a variety of recessiveness and dominance among the basic facts of experience, namely, consciousness, memory and anticipation. This conclusion has the merit that it points to the possibility of the emergence of life from lifeless material, namely the gradual emergence of memory and anticipation.

6. Now we have to consider the structure of the World of Value, which arises as a result of its embodiment in the World of Fact.

The main elements of the World of Fact are finite activities; The main feature of the World of Values is the timeless coordination of the infinity of possibilities for their implementation. In the universe, the World of Fact has the status of an abstraction that requires values and goals to complete its concrete reality. The World of Value has the status of an abstraction in the universe, requiring the actuality of finite activity to complete its concrete reality. And now we come to this second question.

The original basis of the World of Value is the coordination of all possibilities of entry into the active World of Fact. Such coordination involves harmony and its violation, beauty and ugliness, attraction and repulsion. There is also a measure of combination in relation to each pair of antitheses, for example, a certain possibility of realization will require both a certain degree of harmony and a certain degree of disharmony, and so on for any other antithetical pair.

Long tradition of European philosophy and theology

has hitherto been burdened with two misconceptions. One of them is the concept of independent existence. This error has a double origin - civilized and barbaric. The civilized source of the concept of independent existence is the tendency of impressionable men, when they perceive any value factor in its noblest form, to believe that they perceive some original essence in the universe and therefore its existence must involve absolute independence from all lower types. It is precisely this final conclusion about the absolute nature of independence that I object to. This error haunted Plato in his attitude to the Ideas, and especially in relation to the mathematical Ideas, which he so admired.

The second type of error arises from the early types of fully or partially civilized social systems. They emphasized apparatus for maintaining unity. These structures implied despotic rule, sometimes better, sometimes worse. With the advent of civilization, the social system required similar methods of coordination.

We have evidence that the ancient Hebrews felt the ineffectiveness of casual leadership and, to the disdain of their priests, or at least the later priests who wrote about it, demanded a king for themselves.

So the subconscious attitude spread that a successful social system requires despotism. This understanding was based on the brute fact of barbarian life, as if cruelty was the original way of maintaining large-scale social existence. And this belief has not disappeared to this day. We can detect the emergence of civilized concepts in the Greek and Jewish social systems, and also in the attention paid by the Roman Empire to the development of an almost independent legal system. The Roman legions were stationed mainly on the borders of the empire.

But in later times in Europe, monasteries provide an excellent example of the emergence of civilized concepts early Middle Ages. Institutions like the monastery of Cluny during its heyday espoused the ideal of a social system that was free of cruelty and at the same time retained high efficiency. Unfortunately, all human

buildings require repair and reconstruction, but our enormous debt to medieval monasteries cannot be obscured by the fact that at the end of their era they were in need of reform. The insightful people of the 18th century put into words the ideals that had been realized centuries earlier. In the modern world, Cluny's activity has been more closely replicated in the monasteries of areas such as Brittany and New England than in places where religion is associated with wealth.

At the moment, sociological analysis concentrates precisely on those factors that are easiest to identify. A similar factor turned out to be, for example, an economic motive. It would be unfair to attribute this limited view entirely to Adam Smith, although such a view did indeed dominate among his later supporters. Idealism was pushed back; his final effort was to abolish slavery. The first example of European civilization after the fall of the Western Roman Empire is represented by the early Christian monasteries.

17. The conclusion from this discussion is twofold. On the one hand, attributing pure happiness and arbitrary power to the nature of God is a profanation. This nature, considered as a unification originating from the World of Value, is based on the ideals of moral and aesthetic perfection. In its unity it accepts the disordered effectiveness of religious activity, transformed by the superiority of its own ideals. The result is Tragedy, Sympathy and Happiness, caused by effective heroism.

Of course, we are not able to comprehend the experience of the Supreme Unity of Existence. However, there are human concepts with which we can look at the pursuit of limited ideals of perfection that haunts the universe. This immortality of the World of Action, arising from its transformation in the divine nature, is beyond the power of our imagination. Various attempts to describe it often turn out to be shocking profanity. What really excites our imagination is that the immediate facts of present action acquire permanent significance for the universe. Important concepts such as Right and Wrong

Achievement and Failure depend on this foundation. Otherwise, any activity will be something extremely insignificant.

18. The final topic of the discussion opens a big question. So far the lecture has moved forward in the form of dogmatic statements. But what is the evidence to which she appeals?

The only answer will be the reaction of our own nature to the universal aspect of life in the universe.

This answer is completely at odds with the widespread tradition of philosophical thought. This erroneous tradition presupposes independent existences and entails the possibility of an adequate description of the final act. As a result, the assumption arises that separate adequate premises are possible, from which the argument begins.

Philosophical thinking is often based on a false adequacy of the assessment of various types of human experience. From here we seem to reach some simple conclusion regarding the essential characteristics of human knowledge and its essential limitations. Namely: we know what we cannot know.

Please understand that I am not denying the importance of reflecting on experience. Against. The progress of human thought results from the progressive enlightenment brought about through this analysis. The only thing I disagree with is the absurd reliance on the adequacy of our knowledge. The complacency of scientists represents the tragicomedy of civilization.

There is no sentence that adequately asserts its own meaning. There is always a precondition that cannot be analyzed due to its infinity.

Let's take the simplest case, such as the sentence "One plus one equals two."

Obviously, this proposal omits some necessary limitation. For one thing in itself constitutes one thing. Therefore we must say: “One thing and another thing make two things.” This must mean that the combination of one thing with another creates a group of two things.

At this stage various difficulties arise. In the corresponding kind of connection there must be a corresponding kind of things. The combination of spark and gunpowder gives rise to

an explosion that is quite different from these two things. So we should say: "The appropriate kind of connection of one thing with another produces that kind of group which we call two things." Common sense tells you right away what is meant. But, unfortunately, there is no adequate analysis of common sense itself, because it precisely presupposes our attitude towards the infinity of the universe.

There is another difficulty. When something is placed in a different situation, it changes. Every housewife takes this truth into account if she invites guests to a party; the same is assumed by the cook preparing dinner. Of course, the statement “one plus one equals two” assumes that changes in conditions are unimportant. But it is impossible for us to analyze this concept of “unimportant change.” We must use common sense.

In fact, there are no sentences or words with meanings that are independent of the circumstances of utterance. The essence of scientific thought comes down to ignoring this truth. It is also the essence of common sense to ignore these differences of foundation when they do not affect the achievement of the immediate goal. My point is that we cannot rely on adequate explicit analysis.

19. The conclusion is that logic, considered as an adequate analysis of the development of knowledge, turns out to be only a fake. This is a wonderful tool, but it requires common sense as a basis.

Let's take another example. Let us consider the “accurate” statements of various schools of Christian theology. If the leaders of any religious organization now existing had been transported back to the sixteenth century and expressed all their historical and doctrinal convictions in Geneva or in Spain at that time, Calvin or the inquisitors would have been deeply shocked and would have acted accordingly. how they are used to acting in such cases. Perhaps, as a result of some explanation, both Calvin and the inquisitors would have realized the need for a change in emphasis in their beliefs. But this is another question that does not concern us.

I believe that the final view of the philosophical

thinking cannot be based on precise statements that form the basis of the special sciences.

Accuracy is fake.

Chapter 2 Mathematics and goodness

1-About 2300 years ago, a famous lecture was given. The audience was outstanding: among others, it included Aristotle and Xenophon. The topic of the lecture was. the concept of good as such. The lecturer turned out to be competent—after all, it was Plato.

But the lecture, however, was a failure in terms of explaining the stated topic, since the lecturer mainly focused on mathematics. After Plato and the circle of his immediate students, the concept of good was separated from mathematics. Also in the modern era, outstanding followers of Plato, with rare exceptions, successfully hide their interest in mathematics. But throughout his life Plato maintained a sense of the importance of mathematical thought for the search for an ideal. In one of his early texts he calls ignorance about this "swinish." This is how he would have characterized most Platonists of the last century. This epithet belongs to him, not to me.

Yet there is no doubt that his lecture was unsuccessful, for he failed to make evident to future generations his intuition regarding the ability of mathematics to clarify the concept of the good. Many mathematicians were good people themselves, such as Pascal and Newton. Also, many philosophers were mathematicians. The peculiar combination of mathematics and goodness has, however, remained an undeveloped topic since it was first introduced by Plato. There were, however, studies of this topic, considered only as an interesting characteristic of Platonic consciousness. But this doctrine itself, interpreted as the original philosophical truth, faded away after the first, actually Platonic, era. During different periods of European civilization, moral philosophy and mathematics were assigned different departments in university life.

The purpose of this essay is to explore this topic in the light of modern knowledge. The progress of thought and the expansion of the powers of language now make it comparatively accessible to the popular explanation of those ideas which Plato was able to express only by means of confused sentences and misleading myths. You understand, of course, that I am not writing about Plato as such. My topic is the connection between modern mathematics and the concept of good. This does not, in fact, require reference to any specific mathematical theorems. We will consider the general nature of science, which is currently in the process of development. This is a philosophical study. Many mathematicians are masters of concrete details, but ignorant of any philosophical characteristic of their science.

2. During the period of 60 or 70 years preceding the present time, the progressive civilization of the European nations underwent one of the most profound changes in human history. The whole world was affected, but the beginning of this revolution is connected precisely with the peoples Western Europe and North America. It was a change in perspective itself. Scientific thought developed in a uniform manner during four centuries, namely the 16th, 17th, 18th and 19th centuries. In the 17th century Galileo, Descartes, Newton and Leibniz developed a system of mathematical and physical concepts within which all this movement was found. Its culmination can be attributed to the 10th anniversary of 1870-1880. At this time, Helmholtz, Pasteur, Darwin and Maxwell made their discoveries. It was a triumph that summed up the entire period under review. The change has affected every area of thinking. In this chapter I highlight mainly the shift in the field of mathematical knowledge. Many of the discoveries that contributed to this revolution were made 100 years before the 10th anniversary that is cited here as a culmination. But widespread awareness of their cumulative impact occurred 50 years after 1880. Let me, in addition to the main theme of "Mathematics and the Good," emphasize that this chapter is also intended to illustrate how thinking develops

from one era to another, slowly realizing their semi-discoveries. Without such knowledge you will not be able to understand Plato or any other philosopher.

3. In order to understand the change, let us imagine the development of intellectual life, which began in 1870, as having an age of 9 or 10 years. The whole story then reads like a modern version of a Platonic dialogue, such as Theaetetus or Parmenides. By the beginning of this intellectual life, the child should have known the multiplication table up to 12x12. Addition, subtraction, multiplication and division were mastered. Prime fractions have become familiar concepts. In the next two to three years, decimal notation for fractions was added. In this way the entire basis of arithmetic was soon mastered by the young student.

During the same period, acquaintance with geometry and algebra occurs. In geometry, the concepts of point, line, plane and other surfaces are fundamental. The procedure is to introduce some complex pattern of these entities, defined by particular relations between its parts, and then to explore what other relationships of that pattern are implicit in the given assumptions. For example, a right triangle is entered. Then, based on Euclidean geometry, it is proved that the square of the hypotenuse is equal to the sum of the squares of its other sides.

This example is of interest, because a child may well see the figure of a right triangle drawn by the teacher on the blackboard without the concept of a square of sides appearing in his mind. In other words, the pattern being described—such as a right triangle—does not directly reveal all its subtleties to consciousness.

This remarkable limitation of conscious understanding is a fundamental fact of epistemology. The child knew what his teacher was talking about, namely, a right triangle, clearly represented on the board by clear chalk lines. And yet the child was unaware of the infinity of the implicitly assumed properties of the triangle.

The primary factors that arose in him when he looked at the board, the concept of a right triangle were points, lines, straightness of lines, angles, rectangularity. None of these concepts have meaning without reference to the all-encompassing space. The point occupies

a certain position in space, however, as explained below, does not have any extension. Lines, including straight lines, take their position and are also in spatial relationships to each other. Thus, none of the concepts associated with a right triangle have meaning without reference to the corresponding spatial system.

4. At that time, with the exception of only a few mathematicians, it was assumed that only one consistent analysis of the concept of space was possible. In other words, it was believed that any two people talking about space must mean the same system of relations if a full analysis of the entire variety of meanings analyzed by these people was carried out. The purpose of mathematics, according to such beliefs, as well as those of Plato and Euclid, was to adequately express this unique, coherent concept of spatiality. We now know that this concept, which has been successful for almost 2400 years as a necessary foundation for any physical science, has been proven wrong. This was a glorious mistake, for without this simplification of the foundations of thinking in our modern physical science there would not have been a consistent simplification of those of its premises with the help of which it could express itself.

Thus, the error gave impetus to the development of knowledge until the end of the 19th century. At the very end of this period, it began to interfere with the adequate expression of scientific ideas. Fortunately, mathematicians, at least some of them, were far ahead of many sober scientists and invented all sorts of fantastic deviations from classical (orthodox) geometry. At the turn of the century, that is, between 1890 and 1910, it was discovered that these other types of geometry are extremely important for the expression of our modern scientific knowledge.

From the very origin of geometry in Egypt and Mesopotamia to modern times there is a period of almost 4000 years. And throughout this period, the erroneous belief in a unique geometry prevailed. Our current concepts have only a 100- or 150-year history. We get the pleasant satisfaction of “now we know.”

We will never understand the history of exact science until we examine the relation of the feeling of “now we know” to the types of learning prevailing in each era. In one form or another, it is constantly present among the dominant group that preserves and supports civilized learning. To support any enterprise, it is necessary to “abuse” this feeling of success. Is it possible to characterize such “abuse”? We can complete the phrase “now we know” with an adverb. We can mean “now we know partially” or “now we know completely.” The difference between the two phrases seems to capture the difference between Plato and Aristotle, so far as their influence on future generations is concerned. The concept of complete self-sufficiency, of some kind of finite knowledge, is a fundamental fallacy of dogmatism. Any such variety acquires its truth, and indeed its very meaning, from an unanalyzed relationship to the basis, which is the unlimited Universe. Even the simplest concept of arithmetic cannot escape this “inevitable” condition of existence. Every bit of our knowledge derives its significance from the fact that we are all factors in the universe and every element of our experience depends on it. A consistent skeptic is a dogmatist. He enjoys the illusion of complete emptiness. Where there is a sense of self-sufficient completeness, there is contained the germ of vicious dogmatism. There is no entity that feels the isolated self-sufficiency of existence. In other words, the limb is not independent.

The final conclusion of the discussion is that geometry, as it has been studied for centuries, is a “chapter” of the doctrine of a model, which, being known to the cognitive finite faculties, is partly revealed in its relation to the basis - the Universe. The term "geometry" also indicates a genus of specimens that includes many species.

5. We now turn to the discussion about number, considered as a fundamental mathematical concept. This section may be shortened since many of the relevant considerations have already been stated in our discussion of geometry.

The doctrine of number from the Greek period onwards

always involved strange little contradictions that sensible people simply ignored. In the last quarter of the 19th century, a more in-depth study of this entire subject, begun by Georg G. Cantor and G. Frege in Germany, G. Peano and M. Pieri in Italy, and in England by representatives of mathematical logic, revealed a number of complex issues. Finally, Bertrand Russell discovered a particularly striking self-contradiction in modern reasoning. I remember well that he explained it to Frege in a personal letter. Frege's answer began with the exclamation: “Alas, arithmetic is unsteady!”

Frege was right: arithmetic was shaky and is still shaky. But Bertrand Russell rose to the occasion. At that time, he and I were in the midst of working on a book called Principia Mathematica. Russell introduced the concept of "type" of entities. According to his doctrine, the concept of number should apply exclusively to a group of entities of the same type. Thus, the number 3 applied to entities of one type has a different meaning compared to the number 3 applied to entities of another type. For example, if we consider two different types, then there are two different meanings for the number 3.

Russell was absolutely right. All difficulties can be avoided by limiting numerical reasoning to one type. He discovered the safety rule. But unfortunately, this rule cannot be expressed independently of the premise that the concept of number is applicable outside the rule. For the number 3 in each type itself belongs to different types. Also, each type itself is different in type from other types. Thus, in accordance with this rule, the concept of two different types turns out to be nonsense, as well as the concept of two different meanings of the number 3. It follows from this that the only possible way for us to understand the rule turns out to be meaningless. And from this, in turn, it follows that the rule must be limited to the concept of “safety rule” and that a complete explanation of “number” still awaits an understanding of the relationship of the types of varieties to the infinity of things. Even in arithmetic you cannot escape the subconscious reference to the unlimited universe. You abstract particulars from the generality and impose limits on your abstraction. Remember that refusal to think about any entities does not mean for thinking that they do not exist. Our conscious thought is an abstraction of entities from the ground of existence. Thinking is one of the forms of emphasizing what is important (emphasis).

6. At the end of this study of mathematical concepts we come to algebra. Who invented algebra? You will all, of course, want to tell me that it was invented in Arabia or India. In one sense this is true, namely, that useful symbolic notation for algebraic ideas arose in one country or the other, and perhaps in both at the same time. But there is one more question that I am sure would have interested Plato if he had known algebra. Who invented the fundamental ideas that were thus symbolized?

What fundamental concept underlies algebra? It is the concept of "any instance of a given kind in abstraction from some particular exemplification of that instance or of that kind."

7. The first animal on Earth, which at least for a moment possessed this concept, turned out to be the first rational being. Of course, one can observe how animals choose between this thing and that thing. But animal intelligence requires specific examples. The human intellect is able to imagine the type of things in abstraction from such examples. The most obvious manifestation of this human trait is mathematical concepts and ideals of goodness, i.e. ideals that are beyond the possibility of their immediate implementation.

Humanity is not given the ability to practically perceive the accuracy of implementation, while mathematics and the ideals of perfection are interested in precisely such accuracy. This is the difference between practice and theory. Any theory, one way or another, requires precise concepts, no matter how much it hides it. In practice, precision disappears, and the only problem remains: “Does it work?” But the purpose of practice can only be determined by using theory, so the question "does it work?" there is simply a reference to theory. Vague practice is stimulated by the clarity of ideal experience.

No one has yet observed the exact mathematical concept in practice. Notice the child learning geometry. He never observed the point

such or a strict line, strict straightness or a strict circle. In the child's mind, such things were unrealized ideals. Almost any sane person will agree with all this. But when we get to arithmetic, he starts to prevaricate. You can hear him say (probably you say it yourself): “I see 1 chair, 2,3,4,5 chairs, and I am able to observe that 2 and 3 chairs, when connected together, form a group in 5 chairs." In this way, our sensible friend could supposedly observe exact examples of arithmetic concepts and the arithmetic theorem.

So our question is: “Did he observe accurately, that is, did he have the exact concepts established in his conceptual experience?” In what sense did he observe exactly one chair? He observed a vague differentiation in the overall context of his visual experience. But imagine if we caught it at one billionth of an inch. Where does the chair end and other things begin? Which atom belongs to the chair and which to the surrounding space? Stool is constantly gaining and losing atoms. It is not strictly differentiated from its environment, nor is it self-identical over time. Again, consider the chair over long periods. It is constantly changing—even all its hard wooden parts are changing. For example, over a million years of being in a cave, it becomes fragile and disintegrates on contact. Slow, unperceived change occurs constantly.

Recall that human concepts of one inch of length or one second of time, being small basic quantities, are entirely consistent with human life. Moreover, modern discoveries of physicists and astronomers have shown us the importance of both the most insignificant and enormous events. Our precise conceptual experience is a kind of highlighting of what is important. He brings to life the ideals that give power to real events. It adds the perception of value and beauty to the mere flow of sensory experience. It is because of the conceptual stimulus that the sunset reveals the full splendor of the sky. By this, of course, we do not mean that the mere flow of our conscious thoughts creates such a miracle. This is the transformation of real experience into its ideal limit. Our existence

strengthened by conceptual ideals that modify vague perceptions.

We do not comprehend the flow that constitutes our sensory experience until we realize that it rises above the emptiness of infinity by means of successive varieties of highlighting of the important, generating the active energy of finite associations. Prejudicial fear of infinity turned out to be pure poison for philosophy. The infinite has no properties. Any value is a gift from finitude, which is a necessary condition activities. Activity means the emergence of structures (patterns) of associations; these structures are studied by mathematics. Here we find the main clue to the relationship of mathematics to the study of the concepts of good and evil.

8. You will notice how we emphasized earlier in this essay that there are no self-existent finite entities. The finite necessarily points to the unlimited basis. Now we come to the opposite doctrine, namely, that infinity in itself is meaningless and devoid of value. It receives meaning and value as a result of being embodied in finite entities. Outside the finite, the infinite is meaningless and indistinguishable from anything. The concept of the essential relationship of all things is the initial step towards understanding how finite entities require an unlimited universe and how the universe receives meaning and value by embodying the activity of the finite in it.

Among philosophers, it was Spinoza who emphasized this fundamental infinity and introduced subordinate differentiation with the help of finite modes. Leibniz, on the contrary, emphasized the necessity of finite monads and laid down the substratum of divine (deistic) infinity as their foundation. But none of these philosophers has been able to adequately emphasize the fact that infinity is only emptiness without finite values embodied in it, and that finite values have no meaning apart from their external relationships. The concept of “understanding” requires comprehension of how the finitude of a certain entity requires infinity, as well as some concept of how infinity requires finitude. This search for such understanding is the definition of philosophy. For this reason

topics dealing with finite structures deal with the concepts of good and bad.

The great religions illustrate this doctrine. Buddhism emphasizes the pure infinity of the divine Divine principle, and thereby the practical influence of this principle is deprived of energetic activity. The followers of this religion lack impulse. The doctrinal skirmishes of Christians concerned the evaluation of the infinite in terms of the finite. It was impossible to think of energy in any other terms. The very concept of good was considered in terms of active opposition to the forces of evil and, in connection with this, in terms of the limitation of deity. Such a restriction was explicitly rejected, but was implicitly accepted.

9. The history of the science of algebra is the history of improving the technique of notation of finite structures. Algebra is just one “chapter” in the larger technique that is language. True, in general, language indicates its meanings with the help of random associations that arise in human history. It is true that language tends to embody some aspects of these meanings in its very structure. After all, a deeply thought-out word can embody the seriousness of sadness. In fact, the task of the art of literature, oral or written, is to adapt language so that it embodies what it points to.

But most of what language is physically has nothing to do with the meaning it indicates. A sentence is a sequence of words. But in general this sequence is irrelevant to the meaning. For example, “Humpty Dumpty sat on the wall” is a sequence that is meaningless. The Wall doesn't follow Shorty in any sense. Also, the sitting position could have arisen simultaneously with the appearance of the sitter and the wall. Thus, the order of words has the most insignificant relation to the idea conveyed. It is true, of course, that through the sense of anticipation, as well as through delay, the order of words influences the emotions of the perceiver. But the nature of the emotion evoked in this way depends on the character of the perceiver. Algebra completely changes the relative importance of factors in ordinary language. In essence, it is a written language, and it seeks to demonstrate in its

written structures are those models whose transmission is its purpose. These efforts do not always lead to complete success. But it does indeed overturn the usual habits of language. In the application of algebra, the pattern of signs on paper is a specific variety of the pattern to be conveyed by thought.

Also (in algebra) there is an expansion of the concept “any”. In arithmetic we write: 2+3=3+ 2. We consider two combination processes. The type of combination itself is indicated by a word or a “+” sign, and its meaning is limited to indicating a number. It is understood that both procedures should result in groups with the same number of members. In this case it will be the number 5, although it is not mentioned.

So, in algebra one avoids limiting thinking to specific numbers only. We write x+y=y+x, where x and y are any two numbers. This reinforces our emphasis on the model itself, as distinct from the specific entities involved in it. Thus, the introduction of algebra brought about remarkable progress in the study of the model. Relationships between different patterns, such as those represented in the binomial theorem, have permeated human thinking. Of course, algebra developed slowly. For centuries it was considered only as a way to find solutions to equations. Somewhere in the Middle Ages, an unfortunate emperor or some other important person, along with his court, had to listen to a learned Italian explain the solution to the cubic equation. Poor fellows! A wonderful Italian afternoon was wasted. They would even begin to yawn if their interest were not supported by a sense of magic.

10.B early XIX For centuries, algebra has studied patterns associated with different types of combinations of numbers, with each such combination yielding one specific number as its result. The relation of equality between the two combinations meant that they both pointed to the same number. But interest was drawn to the patterns of combination themselves with the same way of indicating. In this way, certain general characteristics of the numerical patterns realized in the evolving universe were identified with the characteristics of the patterns of signs on two-dimensional surfaces - usually on pieces of paper. Similar identities of models of meaning with a sample of written signs or their sound variant

are a minor characteristic of the everyday, although they are important for oral speech. But this identity turns out to be the main characteristic of the algebraic language.

Today, as we survey the first half of the 20th century, we find a tremendous expansion in algebra. It has gone beyond the realm of numbers and is now applied to a large group of specimens in which number is only a secondary factor. Very often, in the case of explicit use of a number, its main task is to name, just as is done when naming houses. Thus, mathematics has now become an intellectual analysis of types of models.

The concept of importance of a model is as old as civilization itself. Any art is based on the study of a model. Also, the cohesion of social systems depends on the maintenance of behavioral structures, and the development of civilization depends on the successful modification of such structures. Therefore, the inclusion of structure in natural events, as well as the stability of structures and the possibility of their modification, turn out to be a necessary condition for the realization of the good.

Mathematics is the most powerful technique for understanding patterns as well as analyzing their relationships. And here we reach the fundamental justification for the theme of Plato’s lecture. If we take into account the vastness of the subject of mathematics, then even modern mathematics seems to be a science in early childhood. If civilization continues to advance, the dominant innovation in human thought for the next two thousand years will be that of mathematical understanding.

The essence of such generalized mathematics is the study of the most accessible examples of relevant structures. And applied mathematics will transfer this study to other examples of the implementation of structures.

II. The model is only one of the factors in our realization of experience either as immediate value or as a stimulus to activity for future value. For example, in a painting, the geometric model may be good, but the color relationship is terrible. Also, each color individually can be very poor, vague, and inexpressive. This example highlights

the truth that no entity can be characterized simply by its individual character or by its relationships. Each entity initially has an individual character and, moreover, is the limit of relationships, potential or actual. Some of the factors of individual character are included in relationships, and, conversely, relationships are included in character itself. In other words, no entity can be considered in abstraction from the entire universe, and no entity can be deprived of its own individuality. Traditional logic has placed too much emphasis on the concept of individual character. The concept “any” does not free us from such a concept, but there is no such entity that would be simply “any”. So when algebra is applied, factors outside of algebraic thinking are relevant to the whole situation. Returning to the example with the painting, it must be said that pure geometry is not everything. Colors are important too.

In a painting, color (including black and white) may be kept to a minimum, as in an ink sketch. But still some color differentiation is necessary for the physical embodiment of a geometric design. On the other hand, color can dominate great works of art. Further, the drawing may turn out to be good, but the color effect is unsuccessful. This is where the very theme of good and evil arises. And you cannot discuss good and evil without pointing out the intertwining of different patterns of experience. The antecedent situation may require depth of implementation, and a weak model may interfere with conceptual expectations. Then there is such an evil as triviality, which is like a sketch that replaces the whole picture. Again, two patterns that reveal significant experience may interfere with each other. There is also a great evil of active deprivation. This type of evil comes in three forms: a concept can contradict reality, two realities can contradict each other, two concepts can be mutually contradictory.

There may be other types of evil. But we are looking at the inconsistency of the structures of experience. A holistic structure limits the independence of its parts. But what is said is meaningless without indicating the basis of the experience

that is, emotional and analytical experience within which a holistic structure emerges. Each abstraction becomes significant as a result of indication based on experience, which tends towards the unity of individuation in its immediate present. In itself, this model is neither good nor bad. But each model can exist only due to its purpose for implementation, actual or conceptual. And this purpose trusts the model to play its part in the influx of feeling that is the awakening of the infinite in relation to finite activity. This is the nature of existence: it is the acquisition of structure in feeling, emphasizing the role of a finite group of selected individuals, which are structured entities (for example, the spatial arrangement of colors, as well as the coordination of sounds). But these individualities are not necessarily purely qualitative. A human being is more than a collection of colors and sounds. The concept of a model emphasizes the relativity of existence, namely the relativity of how things are related. But things connected in this way are themselves entities. Each essence of any model, entering into other models, retains its own individuality in this diversity of existence. The riddle of philosophy is how to maintain a balance between the individuality of existence and its relativity. Also, each individual entity of a model may be capable of analysis in order to demonstrate itself as a unit of an accomplished model. I emphasize precisely the function of the model in generating good or evil in the final unit of feeling, which includes the sensation of this model. Also, an essential characteristic of mathematics is the study of a model in abstraction from the individuals that fall under it.

12. When Plato in his lecture connected mathematics with the concept of the good, he was defending, consciously or unconsciously, the traditional ways of thinking common among all peoples. The novelty lay in the method of abstraction, which the Greek genius gradually strengthened. Mathematics, as studied in Plato's Academy, was an abstraction of geometric and numerical characteristics from the concrete facts of Athenian life. Aristotle dissected animals

and at the same time analyzed political systems. He thought about genera and species. In this way he abstracted logical characteristics from full-blooded experience. A new era of scientific abstractions was beginning.

One of the dangers of using this technique is that it uses logic in such a simple-minded way that an erroneous proposal is immediately rejected. But all propositions are fallacious unless they point to a basis which we perceive without any conscious analysis. Any scientific proposal that was put forward by the great scientists of the mid-19th century turned out to be erroneous precisely in the sense in which it was then formulated. Their doctrine of space was erroneous, and so were their doctrines of matter and evidence. The constant interest in Plato's dialogues is not due to the fact that they proclaim abstract doctrines. The dialogues are filled with implicit references to concrete units of experience through which each abstract topic becomes interesting.

13. Abstraction presupposes emphasis, and emphasis enlivens experience—for better or worse. All characteristics corresponding to actualities are varieties of emphasis with the help of which the finite animates the infinite. Creativity involves the generation of value experience through the influx of the infinite into the finite, receiving its special character from individual details and the entire finite model. This is the abstraction that participates in the creation of actuality, with its own unity of finitude and infinity. But consciousness moves to the second order of abstraction, when its finite components are abstracted from the actual thing. This procedure is necessary for finite thinking, although it weakens the sense of reality. This is the basis of science. The task of philosophy is to reverse this process and thus merge analysis with reality. It follows from this that philosophy is not a science.

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