Chapter 80 Chapter 31 Logical Analytical Philosophy

In philosophy, since the time of Pythagoras, there has been an opposition between those whose ideas are chiefly inspired by mathematics, and those who are more influenced by empirical science.Plato, Thomas Aquinas, Spinoza, and Kant belong to what may be called the school of mathematics, and to the opposite school the modern empiricists from Democritus, Aristotle, and Locke onwards.In modern times a school of philosophy has arisen which has set out to eliminate the Pythagoreanism of the principles of mathematics and has begun to combine empiricism with attention to the deductive part of human knowledge.The aims of this school are less grand than those of most philosophers of the past, but some of its achievements are as solid as those of the scientists.

The philosophy of this school of thought has its roots in the achievements of mathematicians who set out to rid their subjects of fallacies and crude reasoning.The great mathematicians of the seventeenth century were optimistic and eager for quick results; therefore, they allowed analytic geometry and the infinitesimal algorithm to rest on shaky ground.Leibniz believed in the existence of actual infinitesimals, but this belief, although appropriate to his metaphysics, was mathematically unfounded.Shortly after the middle of the nineteenth century Weierstrass finally made calculus logically sound by showing how to build calculus without resorting to infinitesimals.Then there was Georg Cantor, who developed the theory of continuity and infinite numbers. "Continuity" has always been a vague word before he defined it, which is very convenient for philosophers like Hegel who want to introduce the muddy ideas of metaphysics into mathematics.Cantor gave the word a precise meaning and showed that the kind of continuity he defined was exactly what mathematicians and physicists needed.By this means a large number of mysteries, such as those of Bergson, are made obsolete.

Cantor also overcame those long-standing logical puzzles about infinite numbers. Take the series of integers starting from 1, how many of these numbers are there?Obviously, this number is not finite.Up to a thousand, there are a thousand numbers; up to a million, there are a million numbers.No matter what finite number you come up with, there are obviously more numbers than this, because there are exactly that many numbers from 1 to this number, and then there are other larger numbers.Therefore, the number of finite integers must be an infinite number.But now there is a wonderful fact: the number of even numbers must be as many as the number of all integers.Try the following two rows:

1, 2, 3, 4, 5, 6, ... 2, 4, 6, 8, 10, 12, ... For every item in the upper row, there is a corresponding item in the lower row; therefore, there must be an equal number of items in both rows, although the lower row consists of only half of the items in the upper row. Leibniz noticed this and thought it was a contradiction, so he concluded that although there are infinite groups, there are no infinite numbers.On the contrary, Georg Cantor boldly denies that this is a contradiction.He was right; it was just an oddity. Georg Cantor defined an "infinite" group as a group that has a partial group that contains as many terms as the whole group.On this basis he was able to build a very interesting mathematical theory of infinite numbers, thereby bringing within the bounds of strict logic a whole field previously resigned to mysteries and confusion.

The next important figure was Frege, who published his first work in 1879 and his definition of "number" in 1884; but, despite the epoch-making character of his various discoveries, it was not until 1903 He had been completely unrecognized until I called attention to him in 2010.It is worth noting that before Frege, all definitions of numbers proposed by everyone contained basic logical errors.By convention, "number" and "multiple" are always regarded as the same thing.However, the specific instance of "number" is a specific number, such as 3, and the specific instance of 3 is a specific triple.A triple is a multiplicity, but the class of all triples—which Frege thought was the number 3 itself—is a multiplicity of pluralities, and the general number of which 3 is an instance , is a multivariate composed of some pluralities composed of some pluralities.By confusing this multiplicity with the simple multiplicity of a known triad, and committing this fundamental grammatical error, Frege's previous philosophy of all numbers turned out to be a litany of nonsense, "nonsense in the strictest sense. ".

It can be inferred from Frege's work that arithmetic, and pure mathematics in general, is nothing but a prolongation of deductive logic.This proves that Kant's theory that arithmetic propositions are "synthetic" and include time relations is wrong.Whitehead and I co-authored "Princi-pia Mathematica" (Princi-pia Mathematica), which described in detail how to develop pure mathematics from logic. It has gradually become clear that a large part of philosophy can be reduced to something that may be called "syntax," although the word syntax has to be used in a somewhat wider sense than hitherto customary.Some, notably Carnap, have advanced the theory that all philosophical problems are really problems of syntax, and that a philosophical problem is either solved or proves insoluble if syntactic errors are avoided.I think this is exaggerated, and Carnap now agrees with me, but there is no doubt that philosophical syntax is very useful in relation to traditional problems.

I would like to briefly explain the so-called description theory to illustrate the utility of philosophical syntax.By "describing" I mean a phrase like "the current president of the United States," which designates a person or a thing not by name, but by some supposed or known quality peculiar to him or it.Phrases like this have caused a lot of trouble.Suppose I say "the golden mountain does not exist", and then suppose you ask "what does not exist?" If I say "it is the golden mountain", then it seems that I attribute some kind of existence to the golden mountain.Obviously, my saying this is not the same statement as saying "round squares don't exist".This seems to imply that the gold mountain is one thing, and the round square is another, although neither exists.Description theory is intended to cope with this and other difficulties.

According to this theory, a statement containing a phrase of the form "the so-and-so" (the so-and-so), if properly analyzed, the phrase "the so-and-so" is absent.For example, take the statement "Scotus is the author of Waverley."Description theory interprets this statement as saying: "There was one man, and only one man, who wrote Waverley, and that man was Scotus." Or, to put it more fully: "There is an entity c such that the statement 'x wrote Waverley' is true if x is c, and false otherwise; and c is Scotus." The first part of this sentence, that is, the part before the word "and", is defined to mean "the author of "Waverly" exists (or has existed, or will exist)." Therefore, the meaning of "Jinshan does not exist" meaning is:

"There is no entity c such that 'x is golden and a mountain' is true when x is c, and otherwise it is not true." With this definition, the conundrum about what it means to say "the golden mountain doesn't exist" disappears. According to this theory, "existence" can only be used to assert description.We can say 'the author of Waverley exists', but it is ungrammatical, or rather, ungrammatical, to say 'Scotus exists'.This clarifies the confusion about "existence" for two thousand years, starting from Plato's Theaetetus.

One result of the work described above was to deprive mathematics of the exalted position it had occupied since Pythagoras and Plato, and to shatter the presumed grounds derived from mathematics against empiricism.It is true that mathematical knowledge is not acquired by induction from experience; and our reason for believing that 2 plus 2 is 4 is not that we find by observation very often that two things combined with two other things make four things.In this sense, mathematical knowledge is still not empirical knowledge.But neither is prior knowledge about the world.In fact, this kind of knowledge is only the knowledge of words. "3" means "2+1", and "4" means "3+1".It can be seen (although it is very long to prove) that "4" and "2+2" refer to the same meaning.Thus mathematical knowledge is no longer mysterious.It is of exactly the same nature as the "natural truth" that there are three feet in a yard.

Not only pure mathematics, but physics also provides material for logical analysis philosophy; In particular, materials are fed by relativity and quantum mechanics. The important thing for the philosopher in the theory of relativity is to replace space and time with space-time.According to common sense, the physical world is considered to be composed of some "things" that last for a certain period of time and move in space.Philosophy and physics develop the concept of "thing" into the concept of "material entity", and regard the material entity as composed of some particles, each particle is very small, and they all exist forever.Einstein replaced particles with elements; there is a relationship called "interval" between each element and other elements, which can be decomposed into a time factor and a space factor in different ways.The choice of these different approaches is arbitrary, and no one is theoretically preferable to any other.Suppose two facts A and B are given in different regions, then it may be the case that according to one convention, both are simultaneous, according to another convention, A is earlier than B, and according to another convention, A is earlier than B, and according to another An agreement that B is earlier than A.There is no physical fact comparable to these different conventions. From all this it seems to follow that events should be the "stuff" of physics, and particles should not.Particles, which have always been considered, must be considered as a series of events.This series of events in place of particles has certain important physical properties, and therefore demands our attention; but it is no more substantial than any other series of events which we may choose at will.Thus "matter" is not part of the basic stuff of the world, but just a convenient way of grouping things into bundles. Quantum theory also supports this conclusion, but the philosophical significance of quantum theory lies in the fact that physical phenomena may be considered discontinuous.Quantum theory states that within an atom (as explained above) a certain state of affairs lasts for a while and then suddenly changes to a finitely different state of affairs.The continuity of motion that has been assumed in the past seems to be nothing more than a prejudice.However, the philosophy peculiar to quantum theory has not yet been fully developed.I think quantum theory may require a more fundamental departure from the traditional theory of space and time than the theory of relativity. Physics has been making matter less material, and psychology has been making mind less spiritual.In a previous chapter we had occasion to compare associations of ideas with conditioning.The latter is obviously much more physiological, and it has replaced the former. (This is just an illustration; I don't want to exaggerate the extent of conditioning.) So physics and psychology have been moving towards each other from opposite ends, making the "neutral monism" implied in William James' critique of "consciousness" The theory is more likely to hold.The distinction between mind and matter was carried over from religion to philosophy, although for a long time there seemed to be valid reasons for the distinction.I thought both mind and matter were just convenient ways of grouping things.I should admit that there are individual events which belong to the physical group only, but others which belong to both groups, and are therefore both mental and physical.This doctrine leads to a significant simplification of our picture of the structure of the world. Modern physics and physiology have introduced new facts that help to illuminate the age-old problem of perception.If there is to be anything that may be called "perception," it must in some measure be the effect of the object perceived, and if it is to be a source of knowledge about the object, it must be more or less like the object. .The first necessary condition can only be satisfied if there is a causal chain that is somewhat independent of the rest of the world.According to physics, this chain exists.The light wave goes from the sun to the earth, and this matter obeys the law of the light wave itself.This is only roughly true.Einstein proved that light is affected by gravity.When light rays reach our atmosphere, they are refracted, and some rays are scattered more than others.When the light reaches the human eye, all sorts of things happen that don't happen anywhere else, and the end result is what we call "seeing the sun."However, the sun in our visual experience is quite different from the astronomer's sun, but it is still a source of knowledge about the latter, because the difference between "seeing the sun" and "seeing the moon" is the same as the astronomer's sun and astronomy. There is a causal connection between the difference of the home moon.But all that we can thus know about physical objects are certain abstract structural properties.We can know that the sun is round in some sense, though not quite in the sense in which we see it; but we have no reason to suppose that the sun is bright or warm, since it is not assumed to be so. , physics can also explain why it seems to be so.So, our knowledge about the physical world is only abstract mathematical knowledge. What I have said above is the outline of modern analytic empiricism; this empiricism differs from that of Locke, Berkeley, and Hume in that it incorporates mathematics and develops a powerful logical technique.Definite answers can thus be drawn to certain questions which are more scientific than philosophical.Compared with the various schools of philosophy of the system builders, modern analytical empiricism has the advantage of being able to deal with problems one at a time, without having to create a whole set of theories about the whole universe in one fell swoop.In this respect its method is similar to that of science.I have no doubt that philosophical knowledge, so far as it is possible, must be sought by such methods; nor do I doubt that many ancient problems can be quite solved by this method. Still, there is a broad area traditionally included in philosophy where the scientific method is insufficient.This area includes fundamental questions about value; for example, science alone cannot prove that taking pleasure in being cruel to people is a bad thing.Everything that can be known can be known through science; but those things that are supposed to be matters of emotion are outside the scope of science. Philosophy throughout its history has consisted of two incongruously mixed parts: a theory of the nature of the world on the one hand, and an ethical or political doctrine of the best way of life on the other.The failure to separate these two parts sufficiently clearly has been a source of a great deal of confusion.Philosophers, from Plato to William James, have allowed their ideas about the constitution of the universe to be influenced by a desire to moralize: they imagine they know which beliefs make a man moral, and they invent, often very sophistically Sexual reasons to prove that these beliefs are true.As for me, I condemn such prejudices on both moral and intellectual grounds.Morally, a philosopher who uses his professional abilities for anything other than an impartial search for truth is guilty of a treachery.If he presupposes, before undertaking his investigations, that certain beliefs, whether true or false, are those which promote good conduct, he limits the scope of philosophical speculation, and thereby makes philosophy a trifle; · Avoid preconceptions.If any limits, consciously or unconsciously, are placed on the pursuit of truth, philosophy is paralyzed by fear, paving the way for government censorship to punish those who utter "dangerous thoughts"—indeed, philosophers have already criticized their own Research work is coupled with such censorship. Intellectually, the influence of false moral considerations on philosophy has always been a great hindrance to progress.I personally don't believe philosophy can prove that religious dogma is or isn't true, but most philosophers since Plato have seen it as part of their task to come up with "proofs" of immortality and the existence of God.They condemned the proofs of their predecessors—St. Thomas's against St. Anselm's, Kant's against Descartes'—but they all presented new proofs of their own.To make their proofs seem plausible, they have had to twist logic, mystify mathematics, and pretend that some deep-rooted prejudices are god-given intuitions. All this is denied by philosophers who make logical analysis the main task of philosophy.They frankly admit that human reason cannot find the final answers to many questions of great importance to mankind, but they refuse to believe that there is some "higher" method of understanding that enables us to discover what science and reason cannot see. truth.They have been rewarded for denying this by discovering that many questions which were formerly shrouded in the fog of metaphysics can be answered precisely, and by objective methods which have nothing to do with the philosopher's personal temperament except his intellectual curiosity.Take such questions as: What is a number?What are space and time?What is spirit and what is matter?I do not say that we can here and now give definite answers to all these ancient questions, but I do say that a method has been discovered which leads to a gradual approach to the truth as in science, in which each new stage is formed by improving produced by the previous stage, not by negating the previous stage. Among the chaos of opposing fanaticisms, one of the few unifying forces is scientific factuality; and by scientific factuality I mean basing our beliefs on what is humanly possible. Habits of personal observation and inference free from regional and temperamental biases.The school of philosophy to which I belong has always insisted on introducing this virtue into philosophy, and has initiated a powerful method of making philosophy fruitful, and these are its chief merits.The habit of careful realism, formed in the practice of this philosophical method, extends to the whole sphere of human activity, and results in a weakening of fanaticism wherever it exists, and with it the faculties of sympathy and mutual understanding. enhanced.Philosophy abandons some of its arbitrary pomp and luxury, but continues to suggest a way of life.