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Meaning and Verification

Subject: 'Either it snowed on New Year's Day or it did not snow on New Year's Day.' Must that proposition be true or false?

Background: How is language with meaning distinguished from language without meaning in the discussion of philosophy? That is the subject of "logic of language".

Outline of this page ...

"The Meaning is the Method of Verification"

Note: this continues the discussion Statements-of-fact and Logical Positivism and Nonsense.

[Does] reality accord with the picture or not? And this picture seems to determine what we have to do, what to look for, and how -- but it doesn't do so, just because we do not know how it is to be applied.

Asking whether and how a proposition can be verified is only a particular way of asking "How do you mean?" The answer is a contribution to the proposition's "grammar" or "logic". (PI §§ 352, 353)

I used at one time to say that, in order to get clear about how a certain sentence is used, it was a good idea to ask oneself the question: "How would one try to verify such an assertion?" But that's just one way among others of getting clear about the use of a word or sentence. For example, another question which is very useful to ask oneself is: "How is this word learned?" "How would one set about teaching a child to use this word?" But some people have turned this suggestion about asking for the verification into a dogma -- as if I'd been advancing a theory about meaning. (D.A.T. G[asking] and A.C. J[ackson], "Ludwig Wittgenstein" in The Australasian Journal of Philosophy 29, no. 2 (1951); the authors say that Wittgenstein made this statement at the Moral Sciences Club at Cambridge; however, they do not indicate in which year that was.)

A "theory of meaning" would be a statement about "what the meaning of language really is", which I say in my Introduction is not what Wittgenstein's logic of language is. Malcolm recalled Wittgenstein telling him a story (which I shall retell this way): Suppose a policeman were recording the personal information of suspects; he would of course want to know what their occupation was -- but if a suspect was unemployed he would record that fact too. (Memoir 2nd ed., p. 55) That is, if you know that a proposition is unverifiable, then you know something important about its grammar, but not that it is necessarily nonsense. For example 'I have a toothache' is unverifiable, but it is not nonsense. Similarly, if you know -- i.e. if it is a true account of the grammar of our word 'taste', and I don't know whether it is, to say -- that "There is no disputing taste" (Seneca), you know something important about the grammar of the word 'taste', not that it is meaningless; for, of course, that word has many uses in our language.

The decisive step consists in passing from the question 'Are the two events simultaneous?' to the question 'What exactly does it mean to say that they are simultaneous?' [cf. "My new way of philosophizing"]. The answer to this is that initially it does not mean anything; for the word 'simultaneous' has only a clear meaning when it is applied to events at more or less the same place. If it is used to refer to events in quite different places [e.g. on Earth and many light years away on the star Sirius], we require a statement of what it is to mean in this new context.

This step was taken by Einstein. He neither discovered hitherto unknown facts, nor did he suggest a hypothesis which explains better the known facts ... He simply drew attention to the fact that the word 'simultaneous' must be redefined if it is to be used to apply to events in quite different portions of space.

The realization that it is here a matter of our having to determine the use of a word at once made the difficulties of classical physics disappear. For these were precisely due to the fact that one regarded what is only a matter of convention as if it were a problem of physics, that one tried to ascertain whether certain events were simultaneous instead of defining the word 'simultaneous'. (Friedrich Waismann, The Principles of Linguistic Philosophy, ed. R. Harré (1965), p. 12-13).

[There] is no way of understanding any meaning without ultimate reference to ostensive definitions, and this means ... 'possibility of verification'.

The most famous case of an explicit formulation of our criterion is Einstein's answer to the question, What do we mean when we speak of two events at distant places happening simultaneously? This answer consisted in a description of an experimental method by which the simultaneity of such events was actually ascertained. Einstein's philosophical opponents maintained ... that they knew the meaning of the above question independently of any method of verification. (Moritz Schlick, "Meaning and Verification" in The Philosophical Review, July 1936, p. 342-343)

"... no way of understanding any meaning without ultimate reference to ostensive definitions" -- That won't do you know. Pure mathematics is not defined ostensively (although 'counting by means of addition and subtraction' e.g. is). The language of a tautology need not be defined ostensively if it is judged by its form alone. A case where Waismann's proposition may be true is in the case of "the power or force of gravity": here maybe we can say that the meaning is the method of measurement, for the word 'power' or 'force' goes undefined otherwise, a mere ghost of meaning (i.e. meaningless).

"Either it snowed or it did not snow"

Above all that is a picture that seems inescapable, and indeed, to the old way, i.e. the way before Wittgenstein's later work, of thinking about sense and nonsense in language, that picture is inescapable.

Bertrand Russell imagined an unverifiable proposition that seems to assert that either something is the case or it isn't the case -- and "there is no third possibility" ["law of the excluded middle"] (PI § 352). [The only "third possibility" here would be that the proposition is nonsensical.] For example: 'It snowed on Manhattan Island on the 1st January in the year 1 A.D.' Russell said: "There is no conceivable method by which we can discover whether this proposition is true or false, but it seems preposterous to maintain that it is neither." (My Philosophical Development (London: 1959), Chapter x, p. 111) Russell presents "a picture which looks as if it must already contain both the problem and its solution" (PI § 352). But what is the word 'solution' to mean here?

Try to imagine circumstances that a sentence like Russell's might enter into. E.g. suppose some meteorologists were trying to compile a natural -- or a climatic -- history of the island of Manhattan. What would they do? Suppose they consulted the written historical record. They might find that there are daily records beginning with the year 1875. Then to the question "Was it snowing on January 1st 1874?", what reply should we expect? "Our records only go back to 1875. We don't know [i.e. here 'to know' = 'to have written records', because in this case reliable written records count as sufficient evidence [which is the criterion for applying the word 'knowledge'] to affirm or deny the truth of a proposition (Is that the meaning of the word 'know' here? That question asks for a definition of 'meaning'. What we can say is the what counts as sufficient evidence will vary from type of case to type of case)] the weather for days before the first of that year." And that would be where the question was dropped. That is, the rejection of the question is the question's only solution. ["(And that is of course not an answer but a rejection of the question.)" (ibid. § 47)]

Except that: Russell was a philosopher and what he really meant was: 'There are propositions that are true or false regardless of whether or not it is possible to verify or falsify them.' Now that sentence would clearly belong to logic or grammar. (It would be "preposterous" to maintain that it was an empirical proposition about propositions. 'The proposition 'It is snowing' has three words' might be called an empirical proposition about a proposition.) And now ask yourself: what are the words 'true' and 'false' to mean in this case if they are divorced from the concepts 'verified' and 'falsified'? Look at the words 'true' and 'false' as tools that we use (ibid. § 360).

We might want to say that Russell -- although of course he does not see it this way -- is proposing a rule of grammar. But merely calling a proposition a "rule of grammar" does not explain what we are to do with it.

Russell's intent was to make an ontological statement. But what would this statement be: 'On any given day in history, either it snows or it doesn't snow'? But that is of course a tautology, like 'Either it is raining or it is not raining' (Tractatus Logico-Philosophicus 4.461). Or it is "metaphysical nonsense" -- i.e. an attempt to say by the use of language what ought to be embodied in [i.e. can only belong to] the grammar of the language (cf. (PP iii, p. 312). But we have to be taught how to use a rule of grammar, and Russell does not teach us that: he assumes that we already know.

Like Russell's own 'The present king of France is bald', the proposition 'It snowed on Manhattan Island on 1st January in the year 1 A.D.' does not logically admit of a Yes or No answer. And that belongs to the "grammar" or "logic" of that proposition as an essential part of its meaning. Russell's sentence has the form but not the meaning of an empirical proposition; it is only a construction made by analogy to actual empirical propositions ("A proposition therefore is any expression that can be significantly negated" (Wittgenstein's Lectures, Cambridge, 1930-1932, ed. Desmond Lee [1980], p. 22); but it is equally impossible -- logically-grammatically impossible -- to either affirm or negate Russell's expression).

When Russell analysed the proposition 'The present King of France is not bald' he was giving a grammatical rule. (ibid. p. 112)

Russell did not think that 'true' should be identified with 'verifiable', and that is correct: in this context 'true' should be identified with 'verified' plus the means [grounds] by which this verification is done. To know what it means to say that a proposition is 'true' is to know how the proposition is verified. So that if Russell maintains that there is "no conceivable method" of verification here [cf. "... for we ourselves made it unverifiable" (Z § 259)] -- then the question becomes: what is the word 'true' to mean now? [Russell thinks he can rely on grammatical analogies or "abstraction".]

Suppose we asked the meteorologists whether it snowed on January 1st 1 A.D. (which is identical with asking whether it is true that it snowed on January 1st 1 A.D.), what could the meteorologists answer except: we don't know (where the meaning of 'know' depends upon the grounds for knowing, which are the written record; so that, 'we don't know' means: 'there is no written record for the year 1 A.D.') [This not simply an answer but also a rejection of the question; it makes reference to the rules of the game. Russell is as it were trying to move a piece off the chessboard, something which the rules of the game do not allow -- i.e. do not define as a possible move.]

Russell's intent was to say something like: 'The sun rises and sets regardless of whether there is anyone there to see it happen.' But that is no more than an assertion of an acceptance of the principle of the uniformity of nature.

It is clear that by 'conceivable' Russell meant 'empirically possible' in Schlick's sense: "anything that does not contradict the laws of nature" [Elsewhere I used the expression 'real possibility', with a more restrictive sense, to contrast with 'logical possibility']. 'Empirical possibility' means 'compatibility with natural law', not necessarily 'compatibility with the actual state of the universe' (i.e. a proposition can be empirically possible and false: e.g. it is not raining at present, but it might be). ("Meaning and Verification", p. 347)

[Schlick adds: "since we cannot boast of a complete and sure knowledge of nature's laws, it is evident that we can never assert with certainty the empirical possibility of any fact ..." (ibid. p. 348) But this addition is a rule of grammar or nonsense: because the 'can never' is logical possibility. But that rule does not belong to the actual practice of scientists: it is counter to Newton's fourth rule for Reasoning in Philosophy which was intended to exclude idle "hypotheses". Nonetheless Schlick does express the care philosophers, following Socrates, take to distinguish what is known from what is only thought to be known.]

Schlick calls a "fact ... 'logically possible' if it can be described, i.e., if the sentence which is supposed to describe it obeys the rules of grammar we have stipulated for our language" (ibid. p. 349). There are problems with that way of speaking because it does not distinguish between 'statement of fact' and 'artifact'; all artifacts are logically possible, but not all expressions that have the form statement-of-fact are. Rather than "described" we could in many cases say "put into word pictures", but in any case the meaning of the word 'described' has to be explained -- by means of examples of descriptions and how the meanings of descriptions are explained. Russell, however, did not mean by his word 'conceivable' Schlick's 'logically possible' because we might imagine e.g. "if the ancient stones could talk" or "traveling in a time machine", etc.

It is as if Russell said, "Surely you know what it means to say that it snowed on 1st January 1 A.D.", we could only answer: these words may lead us to imagine many things, e.g. falling snow and a calendar with the day's date on it, but this picture goes no further (cf. PI § 351). It's as though Russell wanted -- and of course did not want -- to say that: God saw (or sees) what we did (do) not (cf. ibid. § 352).

'It snowed ...' -- If you know that a proposition is unverifiable you know something important about its grammar (meaning), not that it is necessarily nonsense (meaningless). Consider the proposition 'There is life on other planets'. If the universe really is as vast as astronomers claim, then it seems that this proposition is not falsifiable if its falsification requires the surveying [exploration] of the whole universe. Does this very general fact of nature -- i.e. the vastness of the universe --, if fact it is, belong to the grammar of that proposition? No, but the criteria for a proposition's verification or falsification do (e.g. astronomers might accept a statistical sample rather than demanding the whole as their criterion for falsification, although on the other hand there are the black swans of Australia).

Was Russell talking nonsense? If trying to state a fact with a grammatical proposition ('It must have snowed or not snowed') is to talk 'nonsense' (The quotes mean: this is a definition of that word), then yes.

That human beings are inclined to draw/invent word-pictures the sense of which requires the inclusion of a deity (god) as an observer -- shows something very characteristic of our "form of life" (or even "life form"). Human beings are myth-makers ("metaphysicians") by nature -- i.e. instinct, it appears. I don't know whether we can say that language is responsible for this, either alone or even partly.

'Either it snowed or it did not snow' is a tautology, like 'Either it is raining or it is not raining' (TLP 4.461). It tells us nothing about the actual weather -- i.e. the world of facts; its meaning does not extend beyond its form: P OR NOT-P. Russell might simply have said: "Surely one or the other must be the case: p or not-p." -- But what kind of "must" is this? It is grammatical-logical [It belongs to "grammar" in Wittgenstein's jargon], nothing more.

Grammatical Abstractions

Metaphysics tries to treat all questions as if they were questions of fact ("It must be true or false that it snowed"), whereas philosophical questions show themselves to be about language ("But what are 'true' and 'false' to mean in this case?") [(RPP i § 949: "A metaphysical question is always in appearance a factual one, although the problem is a conceptual one"]. Russell of course did not accept that. But in this case that makes him like someone who says: "Surely if I know how to use the words 'at the same time' here, then I must know (and it would be preposterous to deny that I know) how to use them everywhere: surely I must have learned their meaning: I must have extracted the essence of 'at the same time'. -- Otherwise how could I use those words at all; how could I know what I was talking about at all?" As if to say: "True is always true and false is always false, regardless of the particular propositions to which the words 'true' and 'false' are applied." [The picture of the meaning of a word as a halo the word carries around with it.]

[As if the meaning of language were] a kind of entity ... hidden in it like a nut in its shell, so that the philosopher would have to crack the shell ... in order to reveal the nut or meaning. (Schlick, "Meaning and Verification", p. 348)

And of course once the shell is cracked open it remains forever open. Wittgenstein said of the rationalists that "they let the words speak to them". (Wittgenstein's Lectures, Cambridge, 1930-1932 [1980], p. 79) And whatever the words said that "seemed correct" (PI § 258) to them they accepted as the words' true or real meaning.

"Otherwise how could I use those words at all?" If this question is asked in the context of "theories of learning", I do not know. Such theories do not belong to logic: logic only describes what we do, not e.g. "how it is psychologically possible" for us to do it. Logic does know how we master "family likeness", how we are able use words by that technique rather than the technique of "general [essential, common nature] definitions" (which in any case still must be applied in the particular case).

[Philosophy does even answer the most fundamental question of why the world exists, so you mustn't expect too much of it. The world does exist -- "It is there -- like our life" (OC § 559) -- but there is no answer to why the world is there rather than nothing.]

"A proposition can be significantly negated" [i.e. the proposition produced by its negation is not nonsense]

A proposition therefore is any expression that can be significantly negated. (Wittgenstein's Lectures, Cambridge, 1930-1932 [1980], p. 22)

Imagine a primitive tribe, living in caves overlooking a threshing ground. Could a child be taught 'The wolf is not here' before learning to use the proposition 'The wolf is here'? If the child does not know what the word 'wolf' refers to, what can it do but ask the adult again and again: 'Is the wolf here?' And what can the adult respond except 'No, the wolf is not here' again and again? This is why Wittgenstein said 'that can be significantly negated' rather than 'significantly affirmed'. (Pascal used the expression "subject to contradiction".)

If p, then '~p' is nonsense

A tautology is an example of a proposition that "cannot be significantly negated" -- i.e. its negation is an undefined combination of words: If p, then 'not-p' is nonsense. (The possibility here is logical possibility.)

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