Notes Dictated to G.E. Moore in Norway: Difference between revisions
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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 | 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.]--> | ||
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Many ways of saying this are possible: | Many ways of saying this are possible: | ||
One way is to give ''certain symbols | 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 | 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 | 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 | 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''. | ||
This same distinction between what can be ''shewn'' by the language but not ''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 {{small caps|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 | Therefore a {{small caps|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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["x" is the name of y: "''φ''x" = '"''φ''" is at [the] left of "x"' and ''says'' ''φ''x.] | ["x" is the name of y: "''φ''x" = '"''φ''" is at [the] left of "x"' and ''says'' ''φ''x.] | ||
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 | 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. | ||
(N.B. In [the] expression (∃y). ''φ''y, one ''is'' apt to say this means "There is a ''thing'' such that...". But in fact we should say "There is a y, such that..."; the fact that the y symbolizes expressing what we mean.) | (N.B. In [the] expression (∃y). ''φ''y, one ''is'' apt to say this means "There is a ''thing'' such that...". But in fact we should say "There is a y, such that..."; the fact that the y symbolizes expressing what we mean.) | ||
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N.B. In any ordinary proposition, e.g., "Moore good", this ''shews'' and does not say that "''Moore''" is to the left of "good"; and ''here what'' is shewn can be ''said'' by another proposition. But this only applies to that ''part'' of what is shewn which is arbitrary. The ''logical'' properties which it shews are not arbitrary, and that it has these cannot be said in any proposition. | N.B. In any ordinary proposition, e.g., "Moore good", this ''shews'' and does not say that "''Moore''" is to the left of "good"; and ''here what'' is shewn can be ''said'' by another proposition. But this only applies to that ''part'' of what is shewn which is arbitrary. The ''logical'' properties which it shews are not arbitrary, and that it has these cannot be said in any proposition. | ||
When we say of a proposition of [the] form "aRb" that what symbolizes is that "R" is between "a" and "b", it must be remembered that in fact the proposition is capable of further analysis because a, R, and b are not ''simples | When we say of a proposition of [the] form "aRb" that what symbolizes is that "R" is between "a" and "b", it must be remembered that in fact the proposition is capable of further analysis because a, R, and b are not ''simples''. But what seems certain is that when we have analysed it we shall in the end come to propositions of the same form in respect of the fact that they do consist in one thing being between two others. | ||
How can we talk of the general form of a proposition, without knowing any unanalysable propositions in which particular names and relations occur? What justifies us in doing this is that though we don't know any unanalysable propositions of this kind, yet we can understand what is meant by a proposition of the form (∃x, y, R) . xRy (which is unanalysable), even though we know no proposition of the form xRy. | How can we talk of the general form of a proposition, without knowing any unanalysable propositions in which particular names and relations occur? What justifies us in doing this is that though we don't know any unanalysable propositions of this kind, yet we can understand what is meant by a proposition of the form (∃x, y, R) . xRy (which is unanalysable), even though we know no proposition of the form xRy. | ||
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:(2) means: (∃x, ''ψξ'') . ''φ''A = ''ψ''x . ''φ''x.<!--<ref>''ξ'' is Frege's mark of an ''Argumentstelle'', to show that ''ψ'' is a ''Funktionsbuchstabe''. [''Edd''.]</ref>--> | :(2) means: (∃x, ''ψξ'') . ''φ''A = ''ψ''x . ''φ''x.<!--<ref>''ξ'' is Frege's mark of an ''Argumentstelle'', to show that ''ψ'' is a ''Funktionsbuchstabe''. [''Edd''.]</ref>--> | ||
''Use of logical propositions | ''Use of logical propositions''. You may have one so complicated that you cannot, by looking at it, see that it is a tautology; but you have shewn that it can be derived by certain operations from certain other propositions according to our rule for constructing tautologies; and hence you are enabled to see that one thing follows from another, when you would not have been able to see it otherwise. E.g., if our tautology is of [the] form p ⊃ q you can see that q follows from p; and so on. | ||
Th ''Bedeutung'' of a proposition is the fact that corresponds to it, e.g., if our proposition be "aRb", if it's true, the corresponding fact would be the fact aRb, if false, the fact ~aRb. ''But'' both "the fact aRb" and "the fact ~aRb" are incomplete symbols, which must be analysed. | Th ''Bedeutung'' of a proposition is the fact that corresponds to it, e.g., if our proposition be "aRb", if it's true, the corresponding fact would be the fact aRb, if false, the fact ~aRb. ''But'' both "the fact aRb" and "the fact ~aRb" are incomplete symbols, which must be analysed. | ||
That a proposition has a relation (in wide sense) to Reality, other than that of ''Bedeutung | That a proposition has a relation (in wide sense) to Reality, other than that of ''Bedeutung'', is shewn by the fact that you can understand it when you don't know the ''Bedeutung'', i.e. don't know whether it is true or false. Let us express this by saying "It has ''sense''" (''Sinn''). | ||
In analysing ''Bedeutung | 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 {{small caps|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 {{small caps|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).) | ||
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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. | ||
From this it results that "true" and "false" are not accidental properties of a proposition, such that, when it has meaning, we can say it is also true or false: on the contrary, to have meaning ''means'' to be true or false: the being true or false actually constitutes the relation of the proposition to reality, which we mean by saying that it has meaning (''Sinn'') | From this it results that "true" and "false" are not accidental properties of a proposition, such that, when it has meaning, we can say it is also true or false: on the contrary, to have meaning ''means'' to be true or false: the being true or false actually constitutes the relation of the proposition to reality, which we mean by saying that it has meaning (''Sinn''). | ||
There seems at first sight to be a certain ambiguity in what is meant by saying that a proposition is "true", owing to the fact that it seems as if, in the case of different propositions, the way in which they correspond to the facts to which they correspond is quite different. But what is really common to all cases is that they must have ''the general form of a proposition | There seems at first sight to be a certain ambiguity in what is meant by saying that a proposition is "true", owing to the fact that it seems as if, in the case of different propositions, the way in which they correspond to the facts to which they correspond is quite different. But what is really common to all cases is that they must have ''the general form of a proposition''. In giving the general form of a proposition you are explaining what kind of ways of putting together the symbols of things and relations will correspond to (be analogous to) the things having those relations in reality. In doing thus you are saying what is meant by saying that a proposition is true; and you must do it once for all. To say "This proposition ''has sense''" means '"This proposition is true" means ... .' ("p" is true = "p" . p. Def. : only instead of "p" we must here introduce the general form of a proposition.)<!--<ref>The reader should remember that according to Wittgenstein '"p"' is not a name but a description of the fact constituting the proposition. See above, p. 109. [''Edd''.]</ref>--> | ||
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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 | 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. | ||
Logical constants can't be made into variables: because in them ''what'' symbolizes is ''not'' the same; all symbols for which a variable can be substituted symbolize in the ''same'' way. | Logical constants can't be made into variables: because in them ''what'' symbolizes is ''not'' the same; all symbols for which a variable can be substituted symbolize in the ''same'' way. | ||
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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 | 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 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 ''φ''x and ''φ''p 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 ~x is meaningless, is simply that we have given no meaning to the symbol ~''ξ''. I.e. whereas ''φ''x and ''φ''p 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, 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 | 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., ''ψ''x 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. | ''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., ''ψ''x 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. | ||
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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 | 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. | ||
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, and universality (the three fundamental constants) simultaneously. | 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, and universality (the three fundamental constants) simultaneously. | ||