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Notes Dictated to G.E. Moore in Norway: Difference between revisions

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Every ''real'' proposition ''shews'' something, besides what it says, about the Universe: ''for,'' if it has no sense, it can't be used; and if it has a sense, it mirrors some logical property of the Universe.
Every ''real'' proposition ''shews'' something, besides what it says, about the Universe: ''for,'' if it has no sense, it can't be used; and if it has a sense, it mirrors some logical property of the Universe.


E.g., take ''φ''a, ''φ''a ⊃ ''ψ''a, ''ψ''a. By merely looking at these three, I can see that 3 follows from 1 and 2; i.e. I can see what is called the truth of a logical proposition, namely, of [the] proposition ''φ''a . ''φ''a ⊃ ''ψ''a : ⊃ : ''ψ''a. But this is ''not'' a proposition; but by seeing that it is a tautology I can see what I already saw by looking at the three propositions: the difference is that I ''now'' see THAT it is a tautology. [''Cf''. 6.1221.]
E.g., take ''φ''a, ''φ''a ⊃ ''ψ''a, ''ψ''a. By merely looking at these three, I can see that 3 follows from 1 and 2; i.e. I can see what is called the truth of a logical proposition, namely, of [the] proposition ''φ''a . ''φ''a ⊃ ''ψ''a : ⊃ : ''ψ''a. But this is ''not'' a proposition; but by seeing that it is a tautology I can see what I already saw by looking at the three propositions: the difference is that I ''now'' see {{smallcaps|that}} it is a tautology. [''Cf''. 6.1221.]


We want to say, in order to understand [the] above, what properties a symbol must have, in order to be a tautology.
We want to say, in order to understand [the] above, what properties a symbol must have, in order to be a tautology.
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This same distinction between what can be ''shewn'' by the language but not ''said,'' explains the difficulty that is felt about types-e.g., as to [the] difference between things, facts, properties, relations. That M is a ''thing'' can't be ''said''; it is nonsense: but ''something'' is ''shewn'' by the symbol "M". In [the] same way, that a ''proposition'' is a subject-predicate proposition can't be said: but it is ''shown'' by the symbol.
This same distinction between what can be ''shewn'' by the language but not ''said,'' explains the difficulty that is felt about types-e.g., as to [the] difference between things, facts, properties, relations. That M is a ''thing'' can't be ''said''; it is nonsense: but ''something'' is ''shewn'' by the symbol "M". In [the] same way, that a ''proposition'' is a subject-predicate proposition can't be said: but it is ''shown'' by the symbol.


Therefore a THEORY ''of types'' is impossible. It tries to say something about the types, when you can only talk about the symbols. But ''what'' you say about the symbols is not that this symbol has that type, which would be nonsense for [the] same reason: but you say simply: ''This'' is the symbol, to prevent a misunderstanding. E.g., in "aRb", "R" is ''not'' a symbol, but ''that'' "R" is between one name and another symbolizes. Here we have ''not'' said: this symbol is not of this type but of that, but only: ''This'' symbolizes and not that. This seems again to make the same mistake, because "symbolizes" is "typically ambiguous". The true analysis is: "R" is no proper name, and, that "R" stands between "a" and "b" expresses a ''relation.'' Here are two propositions ''of different type'' connected by "and".
Therefore a {{smallcaps|theory}} ''of types'' is impossible. It tries to say something about the types, when you can only talk about the symbols. But ''what'' you say about the symbols is not that this symbol has that type, which would be nonsense for [the] same reason: but you say simply: ''This'' is the symbol, to prevent a misunderstanding. E.g., in "aRb", "R" is ''not'' a symbol, but ''that'' "R" is between one name and another symbolizes. Here we have ''not'' said: this symbol is not of this type but of that, but only: ''This'' symbolizes and not that. This seems again to make the same mistake, because "symbolizes" is "typically ambiguous". The true analysis is: "R" is no proper name, and, that "R" stands between "a" and "b" expresses a ''relation.'' Here are two propositions ''of different type'' connected by "and".


It is ''obvious'' that, e.g., with a subject-predicate proposition, ''if'' it has any sense at all, you ''see'' the form, so soon as you ''understand'' the proposition, in spite of not knowing whether it is true or false. Even if there ''were'' propositions of [the] form "Mis a thing" they would be superfluous (tautologous) because what this tries to say is something which is already ''seen'' when you see "M".
It is ''obvious'' that, e.g., with a subject-predicate proposition, ''if'' it has any sense at all, you ''see'' the form, so soon as you ''understand'' the proposition, in spite of not knowing whether it is true or false. Even if there ''were'' propositions of [the] form "Mis a thing" they would be superfluous (tautologous) because what this tries to say is something which is already ''seen'' when you see "M".
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In analysing ''Bedeutung,'' you come upon ''Sinn'' as follows: We want to explain the relation of propositions to reality.
In analysing ''Bedeutung,'' you come upon ''Sinn'' as follows: We want to explain the relation of propositions to reality.


The relation is as follows: Its ''simples'' have meaning = are names of simples; and its relations have a quite different relation to relations; and these two facts already establish a sort of correspondence between proposition which contains these and only these, and reality: i.e. if all the simples of a proposition are known, we already know that we CAN describe reality by saying that it ''behaves''<ref>Presumably "verhält sich zu", i.e. "is related." [''Edd''.]</ref> in a certain way to the whole proposition. (This amounts to saying that we can ''compare'' reality with the proposition. In the case of two lines we can ''compare'' them in respect of their length without any convention: the comarison is automatic. But in our case the possibility of comparison depends upon the conventions by which we have given meanings to our simples (names and relations).)
The relation is as follows: Its ''simples'' have meaning = are names of simples; and its relations have a quite different relation to relations; and these two facts already establish a sort of correspondence between proposition which contains these and only these, and reality: i.e. if all the simples of a proposition are known, we already know that we {{smallcaps|can}} describe reality by saying that it ''behaves''<ref>Presumably "verhält sich zu", i.e. "is related." [''Edd''.]</ref> in a certain way to the whole proposition. (This amounts to saying that we can ''compare'' reality with the proposition. In the case of two lines we can ''compare'' them in respect of their length without any convention: the comarison is automatic. But in our case the possibility of comparison depends upon the conventions by which we have given meanings to our simples (names and relations).)


It only remains to fix the method of comparison by saying ''what'' about our simples is to ''say'' what about reality. E.g., suppose we take two lines of unequal length: and say that the fact that the shorter is of the length it is is to mean that the longer is of the length ''it'' is. We should then have established a convention as to the meaning of the shorter, of the sort we are now to give.
It only remains to fix the method of comparison by saying ''what'' about our simples is to ''say'' what about reality. E.g., suppose we take two lines of unequal length: and say that the fact that the shorter is of the length it is is to mean that the longer is of the length ''it'' is. We should then have established a convention as to the meaning of the shorter, of the sort we are now to give.
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Take p.q and q. When you write p.q in the ab notation, it is impossible to see from the symbol alone that q follows from it, for if you were to interpret the true-pole as the false, the same symbol would stand for p ∨ q, from which q doesn't follow. But the moment you say ''which'' symbols are tautologies, it at once becomes possible to see from the fact that they are and the original symbol that q does follow.
Take p.q and q. When you write p.q in the ab notation, it is impossible to see from the symbol alone that q follows from it, for if you were to interpret the true-pole as the false, the same symbol would stand for p ∨ q, from which q doesn't follow. But the moment you say ''which'' symbols are tautologies, it at once becomes possible to see from the fact that they are and the original symbol that q does follow.


''Logical propositions'', OF COURSE, all shew something different: all of them shew, ''in the same way'', viz. by the fact that they are tautologies, but they are different tautologies and therefore shew each something different.
''Logical propositions'', {{smallcaps|of course}}, all shew something different: all of them shew, ''in the same way'', viz. by the fact that they are tautologies, but they are different tautologies and therefore shew each something different.


What is unarbitrary about our symbols is not them, nor the rules we give; but the fact that, having given certain rules, others are fixed = follow logically. [''Cf.'' 3.342.]
What is unarbitrary about our symbols is not them, nor the rules we give; but the fact that, having given certain rules, others are fixed = follow logically. [''Cf.'' 3.342.]
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they must ''symbolize'', but not ''what'' they symbolize.
they must ''symbolize'', but not ''what'' they symbolize.


It's obvious that the dots and brackets are symbols, and obvious that they haven't any ''independent'' meaning. You must, therefore, in order to introduce so-called "logical constants" properly, introduce the general notion of ''all possible'' combinations of them = the general
It's obvious that the dots and brackets are symbols, and obvious that they haven't any ''independent'' meaning. You must, therefore, in order to introduce so-called "logical constants" properly, introduce the general notion of ''all possible'' combinations of them = the general form of a proposition. You thus introduce both ab-functions, identity,
 
form of a proposition. You thus introduce both ab-functions, identity,


and universality (the three fundamental constants) simultaneously.
and universality (the three fundamental constants) simultaneously.
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The relation of "I believe p" to "p" can be compared to the relation of' "p" says (besagt) p' to p: it is just as impossible that ''I'' should be a simple as that "p" should be. [''Cf''. 5.542.]
The relation of "I believe p" to "p" can be compared to the relation of' "p" says (besagt) p' to p: it is just as impossible that ''I'' should be a simple as that "p" should be. [''Cf''. 5.542.]
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