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For want of the apparatus of propositional functions, many logicians have been driven to the conclusion that there are unreal objects. It is argued, … - Bertrand Russell
" "For want of the apparatus of propositional functions, many logicians have been driven to the conclusion that there are unreal objects. It is argued, e.g., by Meinong, that we can speak about "the golden mountain," "the round square," and so on; we can make true propositions of which these are the subjects; hence they must have some kind of logical being, since otherwise the propositions in which they occur would be meaningless. In such theories, it seems to me, there is a failure of that feeling for reality which ought to be preserved even in the most abstract studies. Logic, I should maintain, must no more admit a unicorn than zoology can; for logic is concerned with the real world just as truly as zoology, though with its more abstract and general features.
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About Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell (May 18, 1872 – February 2, 1970) was a British philosopher, logician, mathematician, historian, and social critic. In 1950, he was awarded a Nobel Prize in Literature.
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Birth Name:
Bertrand Arthur William Russell
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Bertrand Russell, 3rd Earl Russell
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Bertrand Russell, Earl Russell
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Bertrand Arthur William Russell, 3rd Earl Russell
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Russell
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Additional quotes by Bertrand Russell
When, in youth, I learned what was called "philosophy" ... no one ever mentioned to me the question of "meaning." Later, I became acquainted with Lady Welby's work on the subject, but failed to take it seriously. I imagined that logic could be pursued by taking it for granted that symbols were always, so to speak, transparent, and in no way distorted the objects they were supposed to "mean." Purely logical problems have gradually led me further and further from this point of view. Beginning with the question whether the class of all those classes which are not members of themselves is, or is not, a member of itself; continuing with the problem whether the man who says "I am lying" is lying or speaking the truth; passing through the riddle "is the present King of France bald or not bald, or is the law of excluded middle false?" I have now come to believe that the order of words in time or space is an ineradicable part of much of their significance – in fact, that the reason they can express space-time occurrences is that they are space-time occurrences, so that a logic independent of the accidental nature of spacetime becomes an idle dream. These conclusions are unpleasant to my vanity, but pleasant to my love of philosophical activity: until vitality fails, there is no reason to be wedded to one's past theories. (p. 114)
Pure Mathematics is the class of all propositions of the form "p implies q," where p and q are propositions containing one or more variables, the same in the two propositions, and neither p nor q contains any constants except logical constants. And logical constants are all notions definable in terms of the following: Implication, the relation of a term to a class of which it is a member, the notion of such that, the notion of relation, and such further notions as may be involved in the general notion of propositions of the above form. In addition to these, mathematics uses a notion which is not a constituent of the propositions which it considers, namely the notion of truth.
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