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Truth-function, general form, and sense-perception [message #5198] Tue, 20 July 2010 00:48
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I have been been making headway in the Philosophical Grammar rather slowly. I want to put it down and finish Zettel, but that is the sort of book that can be picked up and put away; the PG is so long that I can not tell at this point whether I can do something like that. I know the TLP and PR and PI probably shouldn't, but talk about a big typescript! Wink

For the first hundred or so pages I've seen many latter notions brought up, e.g. language-games. I thought that many of the TLP notions were left behind or only alluded to at best (like when he speaks of 'a fact is a complex' as nonsense but doesn't say much on it as a descriptive claim). Needless to say, I was shocked when I ran into this long chain of description relating to some of the most pertinent and elusive notions from the TLP, e.g. the relation between propositions and truth-functions, between truth-functions and the general form of propositions, and the general form's relation to nonsense. I think these passages, mildly cropped, throw much light on earlier notions and would probably be helpful to anyone interested in the TLP or Wittgenstein.


end of 76:

Socrates pulls up the pupil who when asked what knowledge is enumerates cases of knowledge. And Socrates doesn't regard that as even a preliminary step in answering the question.

But our answers consist in giving such an enumeration and a few analogies. (In a certain sense we are always making things easier and easier for ourselves in philosophy.)


The philosophy of logic speaks of sentences and words in exactly the same sense in which we speak of them in ordinary life when we say "Here is a Chinese sentence", or "No, that only looks like writing; it is actually just an ornament" and so on.

We are talking about the spatial and temporal phenomenon of language, not about some non-spatial, non-temporal phantasm. But we talk about it as we do about the pieces in chess when we are stating the rules of the game, not describing their physical properties.

The question "what is a word?" is analogous to "What is a piece in chess (say the king)?"


Again, we cannot achieve a greater generality in philosophy than in what we say in life and in science. Here too (as in mathematics) we leave everything as it is.


If we ask about the general form of proposition- bear in mind that in normal language sentences have a particular rhythm and sound but we don;t call everything 'that sounds like a sentence' a sentence. -Hence we speak also of significant and non-significant "sentences".

On the other hand, sounding like a sentence in this way isn't essential to what we call a proposition in logic. The expression "sugar good" doesn't sound like an English sentence, but it may very well replace the proposition "Sugar tastes good". And not e.g. in such a way that we should have to add in thought something that is missing. (Rather, all that matters is the system of expressions to which the expression "sugar good" belongs.)

So the question arises whether if we disregard this misleading business of sounding like a sentence we still have a general concept of proposition.


The definition "A proposition is whatever can be true or false" fixes tge concept of proposition in a particular language system as what in that system can be an argument of a truth-function.

And if we speak of what makes a proposition a proposition, we are inclined to mean the truth-functions.

"A proposition is whatever can be true or false" means the same as "a proposition is whatever can be denied".

"p" is true = p
"p" is false = ~p
What he says is true = Things are as he says


One can't of course say that a proposition is whatever one can predicate 'true' or 'false' of, as if one could put symbols together with the words 'true' or 'false' by way of experiment to see whether the results make sense. For something could only be decided by this experiment if 'true' and 'false' already have definite meanings, and they can only have that if the contexts in which they can occur are already settled. -(Think also of identifying parts of speech by questions. "Who or what...?")


In the schema "This is how things stand" the "how things stand" is really a handle for the truth-functions.

"Things stand", then, is an expression from a notation of truth-functions. An expression which shows us what part of grammar comes into play here.

If I let "that is how things stand" count as the general form of a proposition, then I must count "2 + 2 = 4" as a proposition. Further rules are needed if we are to exclude the propositions of arithmetic.

Can one give the general form of proposition? - Why not? In the same way as one might give the general form of number, for example by the sign "|o, E, E +1|". [supposed to be a sigma, iirc] I am free to restrict the name "number" to that, and in the same way I can give analogous formula for the construction of propositions or laws and use the word "proposition" or "law" as equivalent to tat formula. -If someone objects and says that this will only demarcate certain laws from others, I reply: of course you can't draw a boundary if you've decided in advance not to recognize one. But of course the question remains: how do you use the word "proposition"? In contrast to what?


A general propositional form determines a proposition as part of a calculus.


Are the rules that say such and such a combination of words yields no sense comparable to the stipulations in chess that the game does not allow two pieces to stand on the same square, for instance, or a piece to stand on a line between two squares? Those proposition in their turn are like certain actions; like e.g. cutting a chess board out of a larger sheet of squared paper. They draw no boundary.

So what does it mean to say "this combination of words has no sense"? One can say of a name (of a succession of sounds): "I haven;t given anyone this name"; and name-giving is a definite action (attaching a label). Think of the representation of an explorer's route by a line drawn in each of the two hemispheres projected on the page: we may say that a bit of line going outside the circles on the page makes no sense in this projection. We might also express it thus: no stipulation has been made about it.

"How do I manage always to use a word significantly? Do I always look up the grammar? No, the fact that I mean something, -what I mean prevents me from talking nonsense." -But what do I mean? -I would like to say: I speak of bits of an apple, but not bits of the color red, because in connection with the words "bits of an apple", unlike the expression "bits of the color red", I can imagine something, picture something, want something. It would be more correct to say I do imagine, picture, or want something in connection with the words "bits of an apple" but not in connection with the expression "bits of the color red".


"How do I know that the color red can;t be cut into bits?" Tat isn't a question either.

I would like to say: "I must begin with the distinction between sense and nonsense. Nothing is possible prior to that. I can't give it a foundation."

He had a wonderful life.

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