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Notes Dictated to G.E. Moore in Norway: Difference between revisions
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Logical so-called propositions ''shew'' [the] logical properties of language and therefore of [the] Universe, but ''say'' nothing. <!--[''Cf''. 6.12.]--> | Logical so-called propositions ''shew'' [the] logical properties of language and therefore of [the] Universe, but ''say'' nothing.<!--[''Cf''. 6.12.]--> | ||
This means that by merely looking at them you can ''see'' these proper ties; whereas, in a proposition proper, you cannot see what is true by looking at it. <!--[''Cf''. 6.113.]--> | This means that by merely looking at them you can ''see'' these proper ties; whereas, in a proposition proper, you cannot see what is true by looking at it.<!--[''Cf''. 6.113.]--> | ||
It is impossible to ''say'' what these properties are, because in order to do so, you would need a language, which hadn't got the properties in question, and it is impossible that this should be a ''proper'' language. Impossible to construct [an] illogical language. | It is impossible to ''say'' what these properties are, because in order to do so, you would need a language, which hadn't got the properties in question, and it is impossible that this should be a ''proper'' language. Impossible to construct [an] illogical language. | ||
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How, usually, logical propositions do shew these properties is this: We give a certain description of a kind of symbol; we find that other symbols, combined in certain ways, yield a symbol of this description; and ''that'' they do shews something about these symbols. | How, usually, logical propositions do shew these properties is this: We give a certain description of a kind of symbol; we find that other symbols, combined in certain ways, yield a symbol of this description; and ''that'' they do shews something about these symbols. | ||
As a rule the description [given] in ordinary Logic is the description of a tautology; but ''others'' might shew equally well, e.g., a contradiction. <!--[''Cf''. 6.1202.]--> | As a rule the description [given] in ordinary Logic is the description of a tautology; but ''others'' might shew equally well, e.g., a contradiction.<!--[''Cf''. 6.1202.]--> | ||
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 {{small caps|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 {{small caps|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 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). | 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.]--> | 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 ''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''. | Logical propositions ''shew'' something, ''because'' the language in which they are expressed can ''say'' everything that can be ''said''. | ||
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''Logical propositions'', {{small caps|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'', {{small caps|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.]--> | ||
Thus, though it would be possible to interpret the form which we take as the form of a tautology as that of a contradiction and vice versa, they ''are'' different in logical form because though the apparent form of the symbols is the same, what ''symbolizes'' in them is different, and hence what follows about the symbols from the one interpretation will be different from what follows from the other. But the difference between a and b is ''not'' one of logical form, so that nothing will follow from this difference alone as to the interpretation of other symbols. Thus, e.g., p.q, p ∨ q seem symbols of exactly the ''same'' logical form in the ab notation. Yet they say something entirely different; and, if you ask why, the answer seems to be: In the one case the scratch at the top has the shape b, in the other the shape a. Whereas the interpretation of a tautology as a tautology is an interpretation of a ''logical form'', not the giving of a meaning to a scratch of a particular shape. The important thing is that the interpretation of the form of the symbolism must be fixed by giving an interpretation to its ''logical properties'', ''not'' by giving interpretations to particular scratches. | Thus, though it would be possible to interpret the form which we take as the form of a tautology as that of a contradiction and vice versa, they ''are'' different in logical form because though the apparent form of the symbols is the same, what ''symbolizes'' in them is different, and hence what follows about the symbols from the one interpretation will be different from what follows from the other. But the difference between a and b is ''not'' one of logical form, so that nothing will follow from this difference alone as to the interpretation of other symbols. Thus, e.g., p.q, p ∨ q seem symbols of exactly the ''same'' logical form in the ab notation. Yet they say something entirely different; and, if you ask why, the answer seems to be: In the one case the scratch at the top has the shape b, in the other the shape a. Whereas the interpretation of a tautology as a tautology is an interpretation of a ''logical form'', not the giving of a meaning to a scratch of a particular shape. The important thing is that the interpretation of the form of the symbolism must be fixed by giving an interpretation to its ''logical properties'', ''not'' by giving interpretations to particular scratches. | ||
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[[File:Notes Dictated to G.E. Moore in Norway schema corrected.png|300px|center|link=]] | [[File:Notes Dictated to G.E. Moore in Norway schema corrected.png|300px|center|link=]] | ||
This symbol might be interpreted either as a tautology or a contradiction.<ref>''Note of the editor of the [[Main Page|Ludwig Wittgenstein Project]]’s digital edition:'' The diagram originally drawn by Moore looked like this: | This symbol might be interpreted either as a tautology or a contradiction.<ref class="noebook">''Note of the editor of the [[Main Page|Ludwig Wittgenstein Project]]’s digital edition:'' The diagram originally drawn by Moore looked like this: | ||
[[File:Notes Dictated to G.E. Moore in Norway schema.png|300px|center|link=]] | [[File:Notes Dictated to G.E. Moore in Norway schema.png|300px|center|link=]] | ||
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{{p indent|p is false <nowiki>=</nowiki> ~(p is true) Def.}} | {{p indent|p is false <nowiki>=</nowiki> ~(p is true) Def.}} | ||
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 | 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. | 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. | ||
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The proposition (∃x) . ''ϕ''x . x = a : ≡ : ''ϕ''a can be seen to be a tautology, if one expresses the ''conditions'' of the truth of (∃x) . ''ϕ''x . x = a, successively, e.g., by saying: This is true ''if'' so and so; and this again is true ''if'' so and so, etc., for (∃x) . ''ϕ''x . x = a; and then also for ''ϕ''a. To express the matter in this way is itself a cumbrous notation, of which the ab-notation is a neater translation. | The proposition (∃x) . ''ϕ''x . x = a : ≡ : ''ϕ''a can be seen to be a tautology, if one expresses the ''conditions'' of the truth of (∃x) . ''ϕ''x . x = a, successively, e.g., by saying: This is true ''if'' so and so; and this again is true ''if'' so and so, etc., for (∃x) . ''ϕ''x . x = a; and then also for ''ϕ''a. To express the matter in this way is itself a cumbrous notation, of which the ab-notation is a neater translation. | ||
What symbolizes in a symbol, is that which is common to all the symbols which could in accordance with the rules of logic = syntactical rules for manipulation of symbols, be substituted for it. <!--[''Cf.'' 3.344.]--> | What symbolizes in a symbol, is that which is common to all the symbols which could in accordance with the rules of logic = syntactical rules for manipulation of symbols, be substituted for it.<!--[''Cf.'' 3.344.]--> | ||
The question whether a proposition has sense (''Sinn'') can never depend on the ''truth'' of another proposition about a constituent of the first. E.g., the question whether (x) x = x has meaning (''Sinn'') can't depend on the question whether (∃x) x = x is ''true''. It doesn't describe reality at all, and deals therefore solely with symbols; and it says that they must ''symbolize'', but not ''what'' they symbolize. | The question whether a proposition has sense (''Sinn'') can never depend on the ''truth'' of another proposition about a constituent of the first. E.g., the question whether (x) x = x has meaning (''Sinn'') can't depend on the question whether (∃x) x = x is ''true''. It doesn't describe reality at all, and deals therefore solely with symbols; and it says that they must ''symbolize'', but not ''what'' they symbolize. | ||
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The question arises how can one proposition (or function) occur in another proposition? The proposition or function itself can't possibly stand in relation to the other symbols. For this reason we must introduce functions as well as names at once in our general form of a proposition; explaining what is meant, by assigning meaning to the fact that the names stand between the |,<!--<ref>Possibly "between the Sheffer-strokes". [''Edd''.]</ref>--> and that the function stands on the left of the names. | The question arises how can one proposition (or function) occur in another proposition? The proposition or function itself can't possibly stand in relation to the other symbols. For this reason we must introduce functions as well as names at once in our general form of a proposition; explaining what is meant, by assigning meaning to the fact that the names stand between the |,<!--<ref>Possibly "between the Sheffer-strokes". [''Edd''.]</ref>--> and that the function stands on the left of the names. | ||
It is true, in a sense, that logical propositions are "postulates"—something which we "demand"; for we ''demand'' a satisfactory notation. <!--[''Cf.'' 6.12.2.3.]--> | It is true, in a sense, that logical propositions are "postulates"—something which we "demand"; for we ''demand'' a satisfactory notation.<!--[''Cf.'' 6.12.2.3.]--> | ||
A tautology (''not'' a logical proposition) is not nonsense in the same sense in which, e.g., a proposition in which words which have no meaning occur is nonsense. What happens in it is that all its simple parts have meaning, but it is such that the connexions between these paralyse or destroy one another, so that they are all connected only in some irrelevant manner. | A tautology (''not'' a logical proposition) is not nonsense in the same sense in which, e.g., a proposition in which words which have no meaning occur is nonsense. What happens in it is that all its simple parts have meaning, but it is such that the connexions between these paralyse or destroy one another, so that they are all connected only in some irrelevant manner. | ||
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Different logical types can have nothing whatever in common. But the mere fact that we can talk of the possibility of a relation of n places, or of an analogy between one with two places and one with four, shews that relations with different numbers of places have something in common, that therefore the difference is not one of type, but like the difference between different names—something which depends on experience. This answers the question how we can know that we have really got the most general form of a proposition. We have only to introduce what is ''common'' to all relations of whatever number of places. | Different logical types can have nothing whatever in common. But the mere fact that we can talk of the possibility of a relation of n places, or of an analogy between one with two places and one with four, shews that relations with different numbers of places have something in common, that therefore the difference is not one of type, but like the difference between different names—something which depends on experience. This answers the question how we can know that we have really got the most general form of a proposition. We have only to introduce what is ''common'' to all relations of whatever number of places. | ||
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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[[Category:Original texts]] | [[Category:Original texts]] | ||