Bertrand Russell
(05/18/1872-02/02/1970)
To deal with Russell's philosophy about concepts, lets look first closer two paradoxes: the paradox of the liar and the paradox about classes.
The paradox of the liar is almost as old as the philosophy. Russell restates it as follows: Suppose a man says "I'm lying" then, if what he says is true, he is lying, i.e. what he says is not true, and if what he says is not true then also he is lying, i.e. what he says is true. Such familiar paradoxes had usually been passed by as mere ingenuities; but the paradox of "the class of all classes" could not be so lightly regarded and the same was true about other paradoxes which had raised their head in mathematics and logics.
Not surprisingly, other logicians attempted to avoid paradoxes without a resource to the ramified theory of types.
The best known of these attempts is contained in F.P. Ramsay's essay on "The
Foundation of Mathematics" and in the second edition of "The Principles of
Mathematics" Russell accepts Ramsay's solution. According to Ramsay, Russell has
grouped together paradoxes which are quite different in character - those which (like the
paradox of classes) arise within an attempt to construct a logical system and those which
(like the paradox of the liar) are "linguistic" or "semantic" in their
origin, i.e. which arise only when we try to talk about that system. The simple
theory of types, Ramsay argues - following Peano - suffices to resolve paradoxes of the
first sort and they are the only ones which really matter to the logician as such.
Paradoxes of the second type can be removed by clearing up ambiguities; they depend upon
the ambiguity of everyday words like "means", "names" or "defines". Thus the ramified
theory of types is in neither case necessary and the much-despised "axiom of
reducibility" can be abandoned.
Then the effect of Russell's theory of types is that, like Moore's account of an "analysis", it encouraged the view that linguistic inquiries, one sort or another, have an special importance to the philosopher. The same effect, even more obviously, flowed from Russel's theory of denoting and the discussion of this "logical constant" will lead us into the heart of Russell's philosophy.
