Introduction to Mathematical PhilosophyRussell, Bertrand
Philosophy
Introduction to Mathematical Philosophy
Russell, Bertrand
Mathematics -- Philosophy
"Who did you meet?" "I met a man." "That is a very
indefinite description." We are therefore not departing from
usage in our terminology. Our question is: What do I really
assert when I assert "I met a man"? Let us assume, for the
moment, that my assertion is true, and that in fact I met Jones.
It is clear that what I assert is not "I met Jones." I may say
"I met a man, but it was not Jones"; in that case, though I lie,
I do not contradict myself, as I should do if when I say I met a
[Pg 167]
man I really mean that I met Jones. It is clear also that the
person to whom I am speaking can understand what I say, even
if he is a foreigner and has never heard of Jones.
But we may go further: not only Jones, but no actual man,
enters into my statement. This becomes obvious when the statement
is false, since then there is no more reason why Jones
should be supposed to enter into the proposition than why anyone
else should. Indeed the statement would remain significant,
though it could not possibly be true, even if there were no man
at all. "I met a unicorn" or "I met a sea-serpent" is a
perfectly significant assertion, if we know what it would be to
be a unicorn or a sea-serpent, i.e. what is the definition of these
fabulous monsters. Thus it is only what we may call the concept
that enters into the proposition. In the case of "unicorn,"
for example, there is only the concept: there is not also, somewhere
among the shades, something unreal which may be called
"a unicorn." Therefore, since it is significant (though false)
to say "I met a unicorn," it is clear that this proposition, rightly
analysed, does not contain a constituent "a unicorn," though
it does contain the concept "unicorn."
The question of "unreality," which confronts us at this
point, is a very important one. Misled by grammar, the great
majority of those logicians who have dealt with this question
have dealt with it on mistaken lines. They have regarded
grammatical form as a surer guide in analysis than, in fact,
it is. And they have not known what differences in grammatical
form are important. "I met Jones" and "I met a
man" would count traditionally as propositions of the same form,
but in actual fact they are of quite different forms: the first
names an actual person, Jones; while the second involves a
propositional function, and becomes, when made explicit: "The
function 'I met and is human' is sometimes true." (It
will be remembered that we adopted the convention of using
"sometimes" as not implying more than once.) This proposition
is obviously not of the form "I met ," which accounts
[Pg 168]
for the existence of the proposition "I met a unicorn" in spite
of the fact that there is no such thing as "a unicorn."
Public-domain text, read in full here on John Shaqi.
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