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Notes Dictated to G.E. Moore in Norway: Difference between revisions
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In settling that it is to be interpreted as a tautology and not as a contradiction, I am not assigning a ''meaning'' to a and b; i.e. saying that they symbolize different things but in the same way. What I am doing is to say that the way in which the a-pole is connected with the whole symbol symbolizes in a ''different way'' from that in which it would symbolize if the symbol were interpreted as a contradiction. And I add the scratches a and b merely in order to shew in which ways the connexion is symbolizing, so that it may be evident that wherever the same scratch occurs in the corresponding place in another symbol, there also the connexion is symbolizing in the same way. | In settling that it is to be interpreted as a tautology and not as a contradiction, I am not assigning a ''meaning'' to a and b; i.e. saying that they symbolize different things but in the same way. What I am doing is to say that the way in which the a-pole is connected with the whole symbol symbolizes in a ''different way'' from that in which it would symbolize if the symbol were interpreted as a contradiction. And I add the scratches a and b merely in order to shew in which ways the connexion is symbolizing, so that it may be evident that wherever the same scratch occurs in the corresponding place in another symbol, there also the connexion is symbolizing in the same way. | ||
We could, of course, symbolize any ab-function without using two ''outside'' poles at all, merely, e.g., omitting the b-pole; and here what would symbolize would be that the three pairs of inside poles of the propositions were connected in a certain way with the a-pole, while the other pair was ''not'' connected with it. And thus the difference between the scratches a and b, where we do use them, merely shews that it is a different state of things that is symbolizing in the one case and the other: in the one case that certain inside poles ''are '' connected in a certain way with an outside pole, in the other ''that'' they are ''not.''<references /> | We could, of course, symbolize any ab-function without using two ''outside'' poles at all, merely, e.g., omitting the b-pole; and here what would symbolize would be that the three pairs of inside poles of the propositions were connected in a certain way with the a-pole, while the other pair was ''not'' connected with it. And thus the difference between the scratches a and b, where we do use them, merely shews that it is a different state of things that is symbolizing in the one case and the other: in the one case that certain inside poles ''are '' connected in a certain way with an outside pole, in the other ''that'' they are ''not.'' | ||
The symbol for a tautology, in whatever form we put it, e.g., whether by omitting the a-pole or by omitting the b, would always be capable of being used as the symbol for a contradiction; only not in the same language. | |||
The reason why ~x is meaningless, is simply that we have given no meaning to the symbol ~ξ. I.e. whereas φx and φp look as if they were of the same type, they are not so because in order to give a meaning to ~x you would have to have some ''property'' ~ξ. What symbolizes in φξ is ''that'' φ stands to the left of ''a'' proper name and obviously this is not so in ~p. What is common to all propositions in which the name of a property (to speak loosely) occurs is that this name stands to the left of a ''name-form.'' | |||
The reason why, e.g., it seems as if "Plato Socrates" might have a meaning, while "Abracadabra Socrates" will never be suspected to have one, is because we know that "Plato" has one, and do not observe that in order that the whole phrase should have one, what is necessary is ''not'' that "Plato" should have one, but that the fact ''that'' "Plato" ''is to the left of a name'' should. | |||
The reason why "The property of not being green is not green" is ''nonsense,'' is because we have only given meaning to the fact that "green" stands to the right of a name; and "the property of not being green" is obviously not ''that.'' | |||
φ cannot possibly stand to the left of (or in any other relation to) the symbol of a property. For the symbol of a property, e.g., ψx is ''that'' ψ stands to the left of a name form, and another symbol φ cannot possibly stand to the left of such a ''fact'': if it could, we should have an illogical language, which is impossible.<blockquote>p is false = ~(p is true) Def.</blockquote>It is very important that the apparent logical relations ∨, ⊃, etc. need brackets, dots, etc., i.e. have "ranges"; which by itself shews they are not relations. This fact has been overlooked, because it is so universal —the very thing which makes it so important. [''Cf''. 5.461.] | |||
There are ''internal'' relations between one proposition and another; but a proposition cannot have to another ''the'' internal relation which a ''name'' has to the proposition of which it is a constituent, and which ought to be meant by saying it "occurs" in it. In this sense one proposition can't "occur" in another. | |||
''Internal'' relations are relations between types, which can't be expressed in propositions, but are all shewn in the symbols themselves, and can be exhibited systematically in tautologies. Why we come to<references /> | |||