Commonplace Book

1919-1953

Moore, George Edward

• Publisher: Routledge
• Year: 2013
• ISBN:
  9781317828341
• Edition: 1
• Topic: Filosofía
• Subtopic: Historia y teoría filosóficas

First published in 2002. The Library of Philosophy was designed as a contribution to the History of Modern Philosophy under the heads: first of different Schools of Thought-Sensationalist, Realist, Idealist, Intuitivist; secondly of different Subjects-Psychology, Ethics, Aesthetics, Political Philosophy, Theology. This is volume XVI of twenty-two in a series of 20th Century Philosophy focuses on the commonplace book of George Moore. The papers include nine notebooks, written at various times between 1919 and 1953.

Notebook VI

(Begun Feb. 1, 1944)

1 Analysis and “Analytic”

Nagel (Mind, Jan. 44, p. 64)¹ says the connexion between A. “x is a cube” & B. “x has 12 edges”, in virtue of which the second follows from the first, is entirely an analytic one.

He asserts that B does follow from A; but follows in virtue of “an analytic connexion” between the 2. This must mean that there is some analytic connexion, such that from the fact that it holds between A & B it follows that B follows from A. Nagel implies that the assertion that B follows from A is not identical with the assertion of a particular analytic connexion between them.

What does he mean by an “analytic connexion”? He apparently holds that to say there is an “analytic connexion” between A & B means that B is “analytically contained” in A, or “logically contained”.

But what is meant by “contained” (= “included”)?

There is one obvious meaning of “q is contained in p”, viz. that p is a conjunction of which q is one of the conjuncts; and another in which every prop. of form (∃ x). φx · χx contains the corresponding prop. of forms (∃ x). φx & (∃ x). χx.

In Kant’s use of “analytic”: “Every body is extended” is analytic: = ~ (∃x) · x is a body · ~ (x is extended), which is like ~ (∃ x) · x is a brother. ~ (x is male) = ~ (∃ x). x is male & a sibling. ~ (x is male). And here though (∃ x). x is male · x is a sibling does contain (∃ x). x is male, it is not a conjunction of (∃ x). x is male & (∃ x). x is a sibling.

But I think Nagel would wish to say that

(a) D. “~ (~ (cats mew). ~ (dogs bark))” is “logically contained” in C. “cats mew.” Certainly D “logically follows” from C. But is D, & all the other props. of the form ~ (~(cats mew). ~ (q)) which follow from “cats mew”, contained in “cats mew”? If so, in what sense? certainly not in any natural sense; not in conjunctive senses.

(b) “Socrates was mortal” is contained in “~(∃x).x is a man. ~ (x is mortal). Socrates was man”. If so, in what sense? Not in conjunctive senses.

(c) “This tie is red” & “This tie is not green” are contained in “This tie is scarlet”. In what sense? Not that of conjunction.

If q is “contained” in p, you can also say that “q is part of what you assert in asserting p”.

This holds in the conjunctive cases, but does not hold for (a), (b) & (c).

Analysis

In G. E. M.² I give 5 conditions, each of which I take to be a necessary condition if a man is to be said to have given an analysis of a given concept.

I think it is true that not only I, but everybody else, when speaking correctly, only says that a person has given an analysis of a concept when these 5 conditions are fulfilled.

But I do not say that I intend to use it in that way: I say, I think I both used & intended so to use it.

P. 666.1 say you can’t be properly said to be “giving an analysis” of a concept unless (1) you use 2 different expressions each of which expresses the same (in some sense) concept, (2) the one expression explicitly mentions concepts not explicitly mentioned by the other and also mentions 〈?〉 the way in which these are combined.

The 3 conditions on p. 663 are (as regards (a) & (b)) conditions for distinguishing the sense in which the concept mentioned must be the same—i.e. the sense in which the two expressions must be synonymous.

I do not say these conditions are sufficient: e.g. ““cats mew” is the same prop. as “~ (~ (cats mew))”” seems to fulfil them, but, in saying this, no-one would say you are giving an analysis of “cats mew”; and “ “cats mew” is the same prop. as “it’s true that cats mew”” also gives no analysis of “cats mew”. On the other hand “Most cats on this earth mew” does give an analysis of one prop. that is meant by “cats mew”; and this in its turn is further analysed by saying it is the same prop. as “There are many cats on this earth, and there are more cats on this earth which mew than there are which don’t”.

Another example of analysis is Langford’s ““That is a small elephant” is the same prop. as “That is an elephant & that is smaller than most elephants””. And this is enlightening because it shews that to say it’s identical with “That is an elephant, & that is small” does not give a correct analysis.

Similarly to say “(∃ x). φx. χx” is the same prop. as “(∃ x) · φx. (∃ x). χx” is to give an incorrect analysis; and this is an example in which no complete analysis is possible. You are giving a correct partial analysis if you say it asserts (∃ x). φx & also asserts (∃ x). χx; but though it says more than these 2 things, it is not a conjunction of these 2 props. with any third.

To say the prop. “cats mew” contains as a part ~ (~(cats mew). ~ (dogs bark)), i.e. (cats mew ∨ dogs bark), is to give a false partial analysis of “cats mew”; since this, though it logically follows from “cats mew”, is not “a part of”, “contained in”, “included in” the prop. “cats mew”.

Similarly to say, as Hempel does, that (∃ x) · φx is the same proposition as (∃x) · φx · ~ (φx · ~ φx) is incorrect, because the latter does contain (∃ x) · ~ (φx · ~ φx) whereas the former does not. If the former is the same as the latter it is also the same as (∃ x). φx · ~ (χx · ~ χx) or (∃ x) · φx · ~ (ψx · ~ ψx): and hence also (∃ x). ~ (∃ x · ~ (φx. ~ φx) must be the same as (∃ x). ~ (χx. ~ χx) etc. That is to say, he is committed to the view that every tautology is the same as every other tautology (a contradiction);—every contradiction the same as every other contradiction. (He thinks that ~ (∃ x) · ~ (φx · ~ φx) is a contradiction, & therefore (∃ x). ~ (φx · ~ φx) a tautology; but both seem doubtful).

Even if ~ (∃ x) · ~ {φx · ~ φx) is the same as ~ (∃ x) · ~ (χx. ~ χx), it seems clear that (∃ x). φx · χx · ~ χx though a contradiction, is not the same as (∃ x). ψx · χx · ~ χx which is also a contradiction.

2 Syntax and Entailment

Hempel says (p. 38):³ “With respect to language systems with a precisely determined logical structure, deductive logic has succeeded in establishing purely formal, or syntactical, CRITERIA of consequence”, & refers especially to Carnap’s Logical Syntax, § 72 & Introd. to Semantics, p. 250.⁴

Acc. he speaks (p. 38) of the sentences “Swan(a)” and “White(a)” being able to be inferred or deduced from the sentence “~ (∃ x). Swan(x). ~ white(x)”.

To talk of deducing one sentence from another sentence is not English. What these people must mean is deducing what is expressed by one sentence from what is expressed by another.

With this sense of “S₂ can be deduced from (is a consequence of) S₁” whether this relation holds between S₁ & S₂ depends on whether what is expressed by S₂ can be deduced (in ordinary sense) from what is expressed by E.g. [the truth of the proposition] “the sentence “Swans exist” can be deduced from the sentence “White swans exist” in English” depends on whether it is true that the proposition that swans exist can be deduced from the proposition that white swans exist, since the sentence “swans exist” in English expresses the prop. that swans exist, and the sentence “white swans exist” in English expresses the prop. that white swans exist. If it were not true both that the prop. that swans exist can be deduced from the prop. that white swans exist, & also true that the sentences “swans exist” & “white swans exist” do in English express these 2 props., it would not necessarily be true that the first sentence can in English be deduced from the second. The sentences might have been used in English in such a sense that the first did not “follow” from the second.

Now there might be rules of English syntax (?) such that from the construction of the two sentences, if you knew they were correctly formed English sentences, you might be able to tell that the first “followed” from the second, without knowing what they meant. But this could only be the case if the rules were such that 2 sentences related in that way were never used except with such meanings that the first meaning followed from the second: and you would have to know this in order to know that the first sentence “followed” from the second. And I suppose that by “a language system with a precisely determined logical structure” is meant simply a language which is such that any pair of sentences which express a pair of props. of which the first follows from the second are structurally related in a way in which no other pairs of sentences are. If this be the meaning, then Hempel’s statement becomes a tautology, in so far as it states that in any such language there will be syntactical criteria for “following” between sentences. Certain relations of structure between sentences will be such that in the case of every pair which exhibits them the prop. conveyed by the first will entail that conveyed by the second; and also whenever the prop. conveyed by one sentence entails that conveyed by another the 2 sentences will exhibit these relations of structure. They will be “criteria” in the sense in which if men were the only featherless bipeds & there are no feathered men, being a featherless biped would be a “criterion” of being a man. But it wouldn’t be true that why sentences with that relation “entailed” one another, was because they were of that structure; any more than it would be true that why a person was a man was because he was a featherless biped.

What Carnap, Hempel, etc. imagine, I am afraid, is that there might be a language having rules (rules of transformation?) such that from the structure of 2 sentences, & S₂, it would follow that the prop. expressed by S₂ followed from that expressed by S₂, & that there were syntactical c...