Chapter 6 Chapter 5: Into Pluralism

Towards the end of 1898 Moore and I betrayed Kant and Hegel.Moore led the way, and I followed closely.I think the first published account of this new philosophy is Moore's article in Mind, on "The Nature of Judgment."Although he and I do not now firmly believe all the teachings in the article, I (and I think he) still agree with the negative part of the article, that is, with the doctrine that, in general, facts is independent of experience.Although we agree, I think we differ as to what interests us most in our new philosophy.I think Moore is most concerned with the denial of idealism, and I am most interested in the denial of monism, but the two are closely linked.Its close connection is due to the doctrine of relationships.This theory was extracted by Bradley from Hegel's philosophy. I call it "the theory of internal relations", and I call my view "the theory of external relations".

The internal relationship theory holds that each relationship between two items basically expresses the internal properties of these two items, and in the final analysis, expresses the properties of the whole composed of these two items.For some relationships, this perception makes sense.Take love and hate as an example.If A loves B, this relationship is reflected in (or it can be said to be formed from) certain moods of A.Even an atheist cannot deny that one can love God.So loving God is a state in which one feels this love, not really a relational fact.But the relationship I'm interested in is a more abstract kind.

Suppose A and B are two things, and A precedes B.I do not think that this means that there is something in A which gives A (which does not involve B at all) a property, and it would be incorrect for us to refer to B to denote this property.Leibniz gave an extreme example.He said that if a man who lives in Europe has a wife in India and his wife dies, he has no idea.At the moment of her death, he had a fundamental change.It was this doctrine which I objected to at the time.In my opinion, the theory of internal relations is especially inappropriate for "asymmetric" relations, that is, if there is a relationship between A and B, but there is no relationship between B and A.Let's look at the "before" relationship again.If A is prior to B, B is not prior to A.If you want to use the adjectives of A and B to express the relationship of A to B, you cannot resort to the word for date.You could say that A's date is an attribute of A, and B's date is an attribute of B.But that is of no use to you, because you have to go on to say that A's date precedes B's date.So you find that you still can't escape the relationship.You are even worse off if you adopt a plan in which relation is a property of the whole of A and B.Since A and B have no order in that whole, you cannot distinguish between "A precedes B" and "B precedes A".In most of mathematics, asymmetric relations are dominant.So this doctrine is very important.

I think that the importance of this question is perhaps best illustrated by quoting part of an article I read at the Aristotle Society in 1907.This article is about the book "The Nature of Truth" by Khaled Zurchin. The doctrines we consider may all be deduced from a central logical doctrine which may be expressed thus: "Every relation is based on properties of the terms involved."We might call this the "inherent relation axiom".The immediate conclusion from this axiom must be that reality or the whole of truth must be a meaningful whole in Mr. Jochin's sense.For every part will have a quality which expresses its relation to every other part or whole; therefore, if the nature of any part is fully understood, the nature of the whole and of each part is also fully understood; and vice versa. , if the nature of the whole is fully understood, it involves knowledge of its relation to each part, and therefore knowledge of the relation of each part to each part, and therefore knowledge of the nature of each part.And it is clear that if reality or truth is a meaningful whole in the sense of Mr. Chochin, the axiom of internal relations must be true.Therefore, this axiom is equivalent to the monist doctrine of truth.

Nay, if we do not distinguish between a thing and its properties, it must follow from this axiom that it is vain to consider anything except in relation to the whole.For, if we consider "A is related to B," this A and this B are also related to anything else.To say what A and B are is to imply a relation to anything else in the universe.If we consider only that part of the property by which A relates to B, we may say to consider A in relation to B; but this is an abstract way of considering A, and only a partly true way.For the nature of A (which is the same thing as A) contains the ground of A's relation to B, and also of A's relation to everything else.Therefore, A can never be said to be true without explaining the whole universe; then, the explanation of A is the same as the explanation of everything else, because the nature of various things is also the same as that of Leibniz. The properties of the monads are the same, and they must all represent the same relational system.

Let us now consider more closely the meaning of the intrinsic relation axiom, and the arguments for and against it.First, according to the claim that each relation is a property of a self-term or a property of a whole composed of self-terms, or that each relation has a basis in these properties, the axiom of internal relations has two possibilities meaning.I do not see spiritualists making a distinction between these two meanings.Indeed, in general, they tend to equate a proposition with its consequences, thus absorbing an obvious claim of pragmatism.But the difference between the two senses is not so important, since, as we shall see, both lead to the view that "relationship" is nonexistent at all.

As Mr. Bradley urges, (cf. Appearance and Reality, 2nd ed., p. 519: "Reality is one, it must be one, for if the many are taken to be true, the many It is self-contradictory. Much implies relation, and, because of its relation, it must always affirm a higher unity.") The axiom of immanent relation, in either form, involves the conclusion that there is no "Relationship", there are not many things, but only one thing. (Spiritualists will add: last. But that just means that it is often convenient to forget about conclusions.) This conclusion is reached because many relationships are considered. For if there are really two things, A and B, (this is many,) it is impossible to completely reduce this multiplication to the adjectives of A and B, it must be that A and B should have different adjectives, and the " "Many" cannot be explained by the fact that they have different adjectives, otherwise there will be infinite regress. Because, when A has the adjective "different from B" and B has the adjective "different from A", if we say that A different from B, we must assume that these two adjectives are different. Then, "different from A" must have the adjective "different from 'different from B'", which must be different from "different from 'different from A'" , etc., to infinity. We cannot take "different from B" as an adjective that does not require further reduction, because we have to ask what the "different" in this phrase really means. It actually starts from a relationship An adjective derived from an adjective is not a relationship derived from an adjective. In this way, if there are many, there must be one that cannot be reduced to "different adjectives", that is to say, the reason is not in the "different terms" properties". Therefore, if the intrinsic relation axiom is true, it must follow that there are not many, but only one thing.

In this way, the axiom of internal relations is tantamount to the assumption of ontological monism, which is tantamount to denying the existence of any relations.Whenever we feel that there is a "relationship", this is actually an adjective about the whole, which is formed by the terms of the assumed relationship. In this way, the axiom of internal relations amounts to the assumption that every proposition has a subject and a predicate. For a proposition affirming a relation must always be reduced to a subject-predicate proposition about the whole of which the terms of the relation consist.In this way, moving towards a larger and larger whole, we gradually correct some of our initial rough and abstract judgments, and get closer and closer to the truth about the whole.That final complete truth must be derived from a proposition with a subject (that is, the whole) and a predicate.But since this involves a distinction between subject and predicate, as if they could be many, and even this is not entirely true, the most we can say is that "intellectually" it is "uncorrectable," that is, it is True as much as any truth is true; but even absolute truths are never quite true. "See Appearance and Reality, first edition, p. 544: "So even absolute truths seem to turn out to be false in the end. It must be admitted that, in the end, none of the possible truths is quite true; What is being translated as a whole is fragmented and incomplete.

This inner contradiction is in any case the inherent nature of truth.Nevertheless, the distinction between absolute truth and relative truth is maintained because, in short, the former is intellectually uncorrectable. ") If we ask ourselves what are the grounds for the axiom of internal relations, those who believe in this axiom make us suspicious. For example, Mr. Chochin always affirms this axiom and presents no arguments for it. So far as we can find grounds There seem to be two of them, although they are really indistinguishable. The first is the law of sufficient reason. This law says that everything cannot be simply a fact, but must have some reason for it to be so. , not like that.

(See Appearance and Reality, 2nd edition, p. 575: "If terms and terms do not constitute a relation in their own intrinsic nature, there is absolutely no reason for them to appear to be related, and , with respect to which the relation is imposed." And see p. 577.) Second, there is the fact that, if two terms have a relation, they must have it; if they There is no such relation, they are different; and this seems to show that there is something in the terms themselves which makes them thus related to each other. (1) The law of sufficient reason is not easy to say with certainty.It cannot simply mean that every true proposition is logically deduced from some other true proposition, since this is an obvious truth which does not produce the result required by the law.For example, 2+2=4 can be deduced from 4+4=8.But it is absurd to see 4+4=8 as a reason for 2+2=4.The reason of a proposition should always be one or more simpler propositions.So the principle of sufficient reason should mean that every proposition can be deduced from simpler propositions.This seems plainly wrong, and in any case it cannot be proper to consider idealism.Idealism maintains that the simpler the proposition, the less true it is.Therefore, it is absurd to insist on starting from simple propositions.My conclusion, therefore, is that, if any form of the principle of sufficient reason is proper, it must be discovered by examining the second ground supporting the axiom of relation, namely, that the terms that are related cannot but be related to each other as they actually are.

(2) I think that the strength of the argument rests mainly on a misstatement. Perhaps it could be said: "If A and B are related in some way, you must admit that if they were not related, they would not be the same as they are now. Therefore, there must be something in them, which is very important to the relationship. It is of the utmost importance that they are now related to each other." However, if two terms are related in some way, the consequence is that if they are not related in this way, every conceivable result will follow.For, if they are so related, then the assumption that they are not so related is false.From a false assumption, anything can be drawn.Therefore, the above statement must be changed.We can say: "If A and B are related in some way, anything that is not so related is not A and B, therefore, etc."However, this only proves that things that are not related like A and B must be numerically different from A or B, and cannot prove that the adjectives are different, unless we assume that the axiom of internal relationship is true.Therefore, this argument has only rhetorical strength and cannot prove its conclusion without falling into a vicious circle. It is time to ask, is there any basis for objecting to the axiom of internal relations?The first argument that comes naturally to the opponent of this axiom is that it is difficult to implement it in practice.Regarding "different", we have already had such an example.In many other instances, the difficulty is even more pronounced.For example, assuming that one book is larger than the other, we can turn the "bigger than" of the two books into an adjective for the two books, saying that the size of one is so-and-so, and the size of the other is It is like that.But the size of one must be larger than the size of the other.If we want to reduce this new relation to adjectives of two sizes, those adjectives must still have a relation equivalent to "larger than", etc.Hence, without being caught in an infinite regress, we have to admit that sooner or later we come to a relation which can no longer be reduced to an adjective of related terms.This argument applies in particular to all asymmetric relations, that is to say, relations that A has with B and B has not with A. (Arguments of the kind indicated above are fully discussed in my Principia Mathematica, BB 212-16.) A stronger argument against the axiom of intrinsic relations comes from considering what the "nature" of the term is Meaning, is the nature of the item the same as the item itself, or is it different?If it is different, it must be related to the item.The relation of a term to its properties cannot be reduced to something that is not a relation without falling into infinite regress. So, if we stick to this axiom, we must assume that a term and its properties are not two different things.If so, every true proposition which adds a predicate to a subject is entirely analytic, since that subject is its own whole property, and that predicate is a part of that property.But if so, what is the connective which connects predicates to predicates of the same subject? If a subject is nothing but a system of its own predicates, any accidental collection of predicates is said to constitute a subject.If the "property" of a term consists of some of its predicates and is at the same time the same thing as the term itself, it is impossible to understand what we mean when we ask "whether S has the predicate P".For this cannot mean: "Is P one of the predicates enumerated in explaining the meaning of S?" On this view it seems difficult to see that this could mean anything else.We cannot attempt to introduce a coherent relation between predicates by which these predicates may be called the predicates of a subject; for this would base the "additional predicate" on the basis of the relation rather than relativizing it. To add a predicate.So whether affirming or denying a subject is not its "nature," we are in the same difficulty. (On this subject see my The Philosophy of Leibniz, §§21, 24, 25.) Also, the axiom of internal relations is incompatible with all "complexity" because, as has been said, This axiom leads to a strict monism, there is only one thing, only one proposition, and this proposition (and this proposition is not only the only true proposition, but the only proposition) attaches a predicate to this one subject.But this proposition is not entirely true, since it involves distinguishing the predicate from the subject.But there is a difficulty: if the addition of the predicate involves the difference between the predicate and the subject, and if the predicate does not differ from the subject, we shall think that there cannot even be a predicate which adds the predicate to the subject. A false proposition from the subject.We would therefore have to assume that adding a predicate does not imply a difference between the predicate and the subject, and that this one predicate and this one subject are identical.But what is most important about the philosophy we are discussing is the denial of absolute equality and the preservation of "equivalence in difference."Otherwise, the superficial abundance in the real world cannot be explained.The difficulty is that if we firmly believe in strict monism, "equivalence in difference" is impossible, because "equivalence in difference" contains many partial truths.These many partial truths become a whole truth due to mutual concession and combination. But these partial truths are not only not true in strict monism, but they do not exist at all. If there is such a proposition, whether it is true or false, "many" will be produced.In short, the whole idea of ​​"equivalence in difference" is inconsistent with the axiom of internal relations; but without this idea, monism cannot explain the world. It collapses like a collapsible hat in opera.My conclusion is that this axiom is bogus. Therefore, those parts on which spiritualism is based are groundless. Thus, there seems to be some reason to object to the axiom that relations are based on the "properties" of the terms in a relation, or of the whole of which these terms are composed.There seems to be no reason to support this axiom. If this axiom is denied, it is meaningless to talk about the "nature" of the term of the relationship: correlation is not enough to prove "complexity".A relationship can exist between many pairs of items, and an item can have many different relationships to different items. The "identity in difference" disappears: there is the same and there is the difference, and the complex may have some elements that are the same and some that are different; "In a sense" is both the same and different, and this kind of "meaning" is something that needs no definition.Thus we get a world of many things.Their relation cannot be derived from a so-called "quality" or scholastic essence of the things concerned. In this world, all complex things are simple things with their own relations.Analysis no longer encounters an endless regression at every step.Now that such a world is assumed, it is finally necessary to ask what we can say about the nature of truth. I first became aware of the importance of relational problems when I was studying Leibniz.I found that his metaphysics was clearly based on the doctrine that every proposition is a predicate added to a subject, and that (almost the same thing for him) every fact is (This discovery of mine was not made clear by Leibniz.) I found that Spinoza, Hegel, and Bradley also took this same doctrine as Base.In fact they developed the theory with a more rigorous logic than Leibniz's. But it wasn't just these dry, logical doctrines that got me hooked on this new philosophy.In fact, I feel that this is a kind of great liberation, as if I escaped from a hot house to a windswept highland, thinking that space and time only exist in my heart. Very disgusting.I think the starry sky is cuter than the moral law.I cannot bear the idea that Kant thought that the one I liked was but a figment of my mind.In the ecstasy of my first emancipation, I became a naive realist, delighted to think that the grass was really green, even though all philosophers since Locke held the contrary opinion.I could not always retain the original force of this pleasant belief, but I could no longer shut myself up in a subjective prison. Hegelians have had various arguments to prove that this or that is not "true".Number, space, time, matter are said to have been judged to be contradictory.They assure us that nothing but the "absolute" is true. The Absolute can only think itself, because there is nothing else it can think, and it thinks eternally what the idealist philosophers think in their books. All the arguments that Hegelians use to condemn what mathematics and physics say rely on the axiom of internal relations. So, when I denied this axiom, I came to believe everything that the Hegelians did not believe. That gives me a very fleshed out universe.In my imagination, all the numbers are lined up and sitting in Plato's heaven. (See my "Nightmare of Celebrities", "Nightmare of a Mathematician".) I thought that the points of space and the instants of time are real entities, and matter is probably made of real elements, such as physics Those elements that homes make for convenience.I believe that there is a world of universals that is mostly made up of the meanings of verbs and prepositions.Most importantly, I no longer have to think that mathematics is not all truth.It is not entirely true that the Hegelians have always maintained that two plus two equals four.But they do not mean that two plus two equals 4.00001 or some such number.Although they didn't say it, they really meant it: "Definitely find something better to capture its heart than doing addition", but they didn't like to say such a thing in such simple language. As time goes by, my universe becomes less rich.When I first betrayed Hegel, I believed that if Hegel's proof that a thing cannot exist is false, that thing must exist.Slowly, Occam's razor gave me a cleaner-shaven picture of reality.I don't mean that it disproves that the entities it shows to be unnecessary are not true, I only mean that it eliminates the arguments for them to be true.I still think it is impossible to disprove the existence of whole numbers, points, instants, or Olympian gods. As far as I know, this may all be true, but there is not the slightest reason to think that it is. Early in the development of this new philosophy I was occupied with mainly linguistic issues.My concern is what makes a composite thing a unity, especially the unity of a sentence.The difference between a sentence and a word eludes me.I have found that the unity of a sentence depends on the fact that it contains a verb, but it seems to me that this verb has exactly the same meaning as the corresponding gerund, although this gerund no longer divides the complex The ability to connect its parts together. The difference between is and being bothers me.My mother-in-law, a well-known, pungent religious leader, assured me that philosophy is only difficult because of the length of its words.I dealt with her with the following sentence (from a note I made that day): "'Existence' signifies existence, and is therefore different from 'existence', since 'existence' 'existence' is Confused words." Can't say that the reason why this sentence is difficult to understand is because the words in the sentence are long.As time went by, I stopped being haunted by questions like this. These questions arise from the belief that if a word means something, there must be something it means. The "Description Theory" I created in 1905 showed this kind of error, and wiped out many problems that could not be solved before. Although I have changed my mind about many things since those early days, some points of great importance then and now have not.I still hold on to the doctrine of external relations and the pluralism that accompanies it.I still maintain that an isolated truth can be the whole truth.I still maintain that analysis is not misinterpretation.I still maintain that if a proposition that is not a synonym is true, it is true because it has a relation to a fact, and, in general, the fact is independent of experience.I don't see how it's impossible for a universe to have no experience at all.Instead, I see experience as a very limited, insignificant aspect of a very small part of the universe.My views on these matters have not changed since I abandoned the teachings of Kant and Hegel.