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

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 Every ''real'' proposition ''shows'' 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 φa, φa ⊃ ψa, ψa. 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 φa . φa ⊃ ψa :  ⊃ : ψa. But this is ''not'' a proposition; but by seeing that it is a tautology I can
+E.g., take φa, φa ⊃ ψa, ψa. 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 φa . φa ⊃ ψa :  ⊃ : ψa. 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.]
+We want to say, in order to understand [the] above, what properties a symbol must have, in order to be a tautology.
+Many ways of saying this are possible:
+One way is to give ''certain symbols;'' then to give a set of rules for combining them; and then to say: any symbol formed from those symbols, by combining them according to one of the given rules, is a tautology. This obviously says something about the kind of symbol you can get in this way.
+This is the actual procedure of [the] ''old'' Logic: it gives so-called primitive propositions; so-called rules of deduction; and then says that what you get by applying the rules to the propositions is a ''logical'' proposition that you have ''proved.'' The truth is, it tells you something ''about'' the kind of propositions you have got, viz. that it can be derived from the first symbols by these rules of combination (= is a tautology).
+Therefore, if we say one ''logical'' proposition ''follows'' logically from another, this means something quite different from saying that a ''real'' proposition follows logically from ''another.'' For so-called ''proof'' of a logical proposition does  not prove its ''truth '' (logical propositions are neither true nor false) but proves ''that'' it is a logical proposition (= is a tautology). [''Cf''. 6.1263.]
+Logical propositions ''are forms of proof:'' they shew that one or more propositions ''follow'' from one (or more). [''Cf''. 6.1264.]
+Logical propositions ''shew'' something, ''because'' the language in which they are expressed can ''say'' everything that can be ''said.''
+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".
+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".
+In the above expression "aRb", we were talking only of this particular "R", whereas what we want to do is to talk of all similar symbols. We have to say: in ''any'' symbol of this form what corresponds to "R" is not a proper name, and the fact that ["R" stands between "a" and "b"] expresses a relation. This is what is sought  to  be expressed by the nonsensical assertion: Symbols like this are of a certain type. This you can't say, because in order to say it you must  first know what the symbol is: and in knowing this you ''see'' [the] type and therefore also [the] type of [what is] symbolized. I.e. in knowing ''what'' symbolizes, you know all that is to be known; you can't ''say'' anything ''about'' the symbol.
+For instance: Consider the two propositions (1) "What symbolizes here  is a  thing",  (2) "What  symbolizes  here is  a  relational  fact (= relation)". These are nonsensical for  two reasons:  (''a'')  because they mention "thing" and "relation"; (''b'') because they mention  them  in propositions of the same form. The two propositions must be expressed in entirely different forms, if properly analysed; and neither the word "thing" nor "relation" must occur.
+''Now'' we shall see how properly to analyse propositions in which "thing", "relation", etc., occur.
+(1) Take φx. We want to explain the meaning of 'In "φx" a ''thing'' symbolizes'. The analysis is:—
+(∃y) . y symbolizes . y = "x" . "φx"
+["x" is the name of y: "φx" = '"φ" is at [the] left of "x"' and ''says'' φx.]
+N.B. "x" can't be the name of this actual  scratch y, because  this isn't a thing: but it can be the name of ''a thing;'' and we must understand that what we are doing is to explain what would be meant  by saying  of an ideal symbol, which did actually consist in one ''thing's'' being to the left of another, that in it a ''thing'' symbolized.