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

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The ''variable proposition'' p ⊃ p is not identical with the ''variable proposition'' ~(p . ~p). The corresponding universals ''would'' be identical. The variable proposition ~(p . ~p) shews that out of ~ (p.q) you get a tautology by substituting ~p for q, whereas the other does not shew this.

It's very important to realize that when you have two different relations (a,b)R, (c,d)S this does ''not'' establish a correlation between a and c, and b and d, or a and d, and b and c: there is no correlation whatsoever thus established. Of course, in the case of two pairs of terms united by the ''same'' relation, there is a correlation. This shews that the theory which held that a relational fact contained the terms and relations united by a ''copula'' () is untrue; for if this were so there would be a correspondence between the terms of different relations.

It's very important to realize that when you have two different relations (a,b)R, (c,d)S this does ''not'' establish a correlation between a and c, and b and d, or a and d, and b and c: there is no correlation whatsoever thus established. Of course, in the case of two pairs of terms united by the ''same'' relation, there is a correlation. This shews that the theory which held that a relational fact contained the terms and relations united by a ''copula'' (ε<sub>2</sub>) is untrue; for if this were so there would be a correspondence between the terms of different relations.

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<references />

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 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.]

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.

Logical functions all presuppose one another. Just as we can see ~p has no sense, if p has none; so we can also say p has none if ~p has none. The case is quite different with φa, and a; since here a has a meaning independently of φa, though φa presupposes it.

The logical constants seem to be complex-symbols, but on the other hand, they can be interchanged with one another. They are not therefore really complex; what symbolizes is simply the general way in which they are combined.

The combination of symbols in a tautology cannot possibly correspond to any one particular combination of their meanings—it corresponds to every possible combination; and therefore what symbolizes can't be the connexion of the symbols.

From the fact that I ''see'' that one spot is to the left of another, or that one colour is darker than another, it seems to follow that it ''is'' so; and if so, this can only be if there is an ''internal'' relation between the two; and we might express this by saying that the ''form'' of the latter is part of the ''form'' of the former. We might thus give a sense to the assertion that logical laws are ''forms'' of thought and space and time ''forms'' of intuition.

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.]<references />

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 The ''variable proposition'' p ⊃ p is not identical with the ''variable proposition'' ~(p . ~p). The corresponding universals ''would'' be identical. The variable proposition ~(p . ~p) shews that out of ~ (p.q)  you get a tautology by substituting ~p for q, whereas  the other  does  not shew this.
-It's very important to realize that when you have two different relations (a,b)R, (c,d)S this  does  ''not'' establish  a correlation between a and c, and b and d, or a and d, and b and c: there is no correlation whatsoever thus established. Of course, in the case of two pairs of terms united by the ''same'' relation, there is a correlation. This shews that the theory which held that a relational fact contained the terms and relations  united  by a  ''copula'' () is  untrue;  for if  this  were  so  there would be a correspondence between the terms of different relations.
+It's very important to realize that when you have two different relations (a,b)R, (c,d)S this  does  ''not'' establish  a correlation between a and c, and b and d, or a and d, and b and c: there is no correlation whatsoever thus established. Of course, in the case of two pairs of terms united by the ''same'' relation, there is a correlation. This shews that the theory which held that a relational fact contained the terms and relations  united  by a  ''copula'' (ε<sub>2</sub>) is  untrue;  for if  this  were  so  there would be a correspondence between the terms of different relations.
-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<references />
+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 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.]
+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.
+{{Small line separator}}
+Logical functions all presuppose one another. Just as we can see ~p has no sense, if p has none; so we can also say p has none if ~p has none. The case is quite different with φa, and a; since here a has a meaning independently of φa, though φa presupposes it.
+The logical constants seem to be complex-symbols, but on the other hand, they can be interchanged with one another. They are not therefore really complex; what symbolizes is simply the general way in which they are combined.
+The combination of symbols in a tautology cannot possibly correspond to any one particular combination of their meanings—it corresponds to every possible combination; and therefore what symbolizes can't be the connexion of the symbols.
+From the fact that I ''see'' that one spot is to the left of another, or that one colour is darker than another, it seems to follow that it ''is'' so; and if so, this can only be if there is an ''internal'' relation between the two; and we might express this by saying that the ''form'' of the latter is part of the ''form'' of the former. We might thus give a sense to the assertion that logical laws are ''forms'' of thought and space and time ''forms'' of intuition.
+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.]<references />