Bertrand Russell Quotes 366
|*1 I have discussed this subject in Principles of Mathematics, Chap. V, and sect. 476. The theory there advocated is very nearly the same as Frege's, and is quite different from the theory to be advocated in what follows. [BR]|
|*2 More exactly, a propositional function. [BR]|
|*3 The second of these can be defined by means of the first, if we take it to mean, `It is not true that ``C(x) is false'' is always true'. [BR]|
|*4 I shall sometimes use, instead of this complicated phrase, the phrase `C(x) is not always false', or `C(x) is sometimes true', supposed defined to mean the same as the complicated phrase. [BR]|
` ``I met x, and x is human'' is not always false'.Generally, defining the class of men as the class of objects having the predicate human, we say that:
`C(a man)' means ` ``C(x) and x is human'' is not always false'.This leaves `a man', by itself, wholly destitute of meaning, but gives a meaning to every proposition in whose verbal expression `a man' occurs.
|*5 As has been ably argued in Mr. Bradley's Logic, Book I, Chap. II. [BR]|
`All men are mortal' means ` ``If x is human, x is mortal'' is always true.'This is what is expressed in symbolic logic by saying that `all men are mortal' means ` ``x is human'' implies ``x is mortal'' for all values of x'. More generally, we say:
`C(all men)' means ` ``If x is human, then C(x) is true'' is always true'.Similarly
`C(no men)' means ` ``If x is human, then C(x) is false'' is always true'.
`C(some men)' will mean the same as `C(a man*6)', and
`C(a man)' means `It is false that ``C(x) and x is human'' is always false'.
`C(every man)' will mean the same as `C(all men)'.
|*6 Psychologically, `C(a man)' has a suggestion of only one, and `C(some men)' has a suggestion of more than one; but we may neglect these suggestions in a preliminary sketch. [BR]|
Thus `the father of Charles II was executed' becomes: `It is not always false of x that x begat Charles II and that x was executed and that ``if y begat Charles II, y is identical with x'' is always true of y'.This may seem a somewhat incredible interpretation; but I am not at present giving reasons, I am merely stating the theory.
`It is not always false of x that ``if y begat Charles II, y is identical with x'' is always true of y',which is what is expressed in common language by `Charles II had one father and no more'. Consequently if this condition fails, every proposition of the form `C(the father of Charles II)' is false. Thus e.g. every proposition of the form `C(the present King of France)' is false. This is a great advantage to the present theory. I shall show later that it is not contrary to the law of contradiction, as might be at first supposed.
|*7 See Untersuchungen zur Gegnstandstheorie und Psychologie (Leipzig, 1904) the first three articles (by Meinong, Ameseder and Mally respectively). [BR]|
|*8 See his `Ueber Sinn und Bedeutung,' Zeitschrift fur Phil. und Phil. Kritik, Vol. 100. [BR]|
|*9 Frege distinguishes the two elements of meaning and denotation everywhere, and not only in complex denoting phrases. Thus it is the meanings of the constituents of a denoting complex that enter into its meaning, not their denotation. In the proposition `Mont Blanc is over 1,000 meters high', it is, according to him, the meaning of `Mont Blanc', not the actual mountain, that is a constituent of the meaning of the proposition. [BR]|
|*10 In this theory, we shall say that the denoting phrase expresses a meaning; and we shall say both of the phrase and of the meaning that they denote a denotation. In the other theory, which I advocate, there is no meaning, and only sometimes a denotation. [BR]|
|*11 I use these as synonyms. [BR]|
The center of mass of the solar system is a point, not a denoting complex;Or again,
`The center of mass of the solar system' is a denoting complex, not a point.
The first line of Gray's Elegy states a proposition.Thus taking any denoting phrase, say C, we wish to consider the relation between C and `C', where the difference of the two is of the kind exemplified in the above two instances.
`The first line of Gray's Elegy' does not state a proposition.
C = `the first line of Gray's Elegy', andthe denotation of C = The curfew tolls the knell of parting day. But what we meant to have as the denotation was `the first line of Gray's Elegy'. Thus we have failed to get what we wanted.
`C has property phi' means `one and only one term has the property F, and that one has the property phi'.*12
|*12 This is the abbreviated, not the stricter, interpretation. [BR]|
`There is an entity which is now King of France and is not bald',but is true if it means
`It is false that there is an entity which is now King of France and is bald'.That is, `the King of France is not bald' is false if the occurrence of `the King of France' is primary, and true if it is secondary. Thus all propositions in which `the King of France' has a primary occurrence are false: the denials of such propositions are true, but in them `the King of France' has a secondary occurrence. Thus we escape the conclusion that the King of France has a wig.
|*13 The propositions from which such entities are derived are not identical either with these entities or with the propositions that these entities have being. [BR]|
`There is one and only one entity x which is most perfect; that one has all perfections; existence is a perfection; therefore that one exists.'As a proof, this fails for want of a proof of the premiss `there is one and only one entity x which is most perfect'.*14
|*14 The argument can be made to prove validly that all members of the class of most perfect Beings exist; it can also be proved formally that this class cannot have more than one member; but, taking the definition of perfection as possession of all positive predicates, it can be proved almost equally formally that the class does not have even one member. [BR]|
|*15 I quote Robert Charles Marsh's introduction to this paper in Logic and Knowledge: G. E. Moore has pointed out that Russell's `shortest statement' at the close of the paper is faulty because of the ambiguity of the verb `to write'. `Scott is the author of Waverley' does not, therefore, have the same meaning as `Scott wrote Waverley', since Scott (like blind Milton) may be the author of the work without being the person who literally wrote it for the first time. Russell has accepted this correction `with equanimity'. The right to feel patronizing about this slip is reserved by law to those who have done as much for philosophy as Russell and Moore.|