Franz Brentano_The True and the Evident.pdf

92 Appendix 1: On the General Validity of Truth and the Basic Mistakes
but we learn the multiplication tables, which are, again, laws, such as “7×7=49”, telling
what factors have what product. One could even be taught the Pythagorean theorem for a
mathematics of the continuum and in abstraction from its specific spatial character. What
is the point of this? Only that such knowledge is required for calculating and measuring;
without it any attempt at measurement would be certain to fail. 6
Every art, to the extent that it is theory and not practice, teaches laws. It goes beyond
the spheres of the particular sciences, though in different degrees. A considerable part of
the laws of mathematics have the character of the laws just mentioned—i.e., “7×7=49”,
and the Pythagorean theorem (considered in abstraction from space). And just what is this
character? I answer without reservation: that of the principle of contradiction. We would
have a contradiction if there were any 7 which when multiplied by 7 were not to equal 49,
or if the square of the hypotenuse of a right-angled triangle were not to equal the squares
of the other two sides. 7
Surely it would also be contradictory to suppose that the tone colour of the vowel a
might not have the overtones which Helmholtz has established. This particular example
shows how much the indistinctness of apperception tends to veil such contradictions. We
find many more such veils if we enter the sphere of the theory of numbers and the theory
of continuity. There are certain large numbers which we cannot even think of in the strict
sense; for we think, not of these numbers themselves, but only of their surrogates. And what
are we to say of the parts, and of the inner and outer boundaries, of an infinitely divisible
continuum? Small wonder, then, that the imperfection of our powers of conception and
apperception necessitates the invention of all kinds of ancillary methods. What might well
be an immediately enlightening truth 8 is something which we come to know only by way
of a roundabout procedure. Hence the art of calculation and measurement, which is such an
important and impressive part of logic that it takes up entire textbooks in its own right. And
hence, too, the results of all those analyses which lead to the discovery of contradictions in
particular cases and which serve as aids for further procedures.
But though I cannot believe that the art of logic along with that of measurement draws
its truths from any single discipline, I do not hesitate to maintain, now as earlier, that
among the theoretical disciplines psychology stands in closest relation to it. 9
What is the general law of contradiction, after all, but this: that whoever (explicitly
or implicitly) affirms and denies the same thing, i.e., whoever contradicts himself, thinks
absurdly? 10
And the very thing that gives rise to the search for methods of explication is certainly
psychological—for what is it but the indistinctness of certain apperceptions and our
inability to group certain things in a distinct concept?
But you fear that such a conception would make the validity of the truths of logic and
mathematics conditional on our own make-up. You believe that the laws of thinking which
hold for us might be different from those that would hold for other thinking beings. What
would be evident for us might not be evident for them, or indeed the contradiction of what
is evident for us might be evident for them.
You are certainly right in emphatically rejecting any theory which would thus demolish
the concept of knowledge and truth. But you are mistaken if you think that, in giving
psychology this position in relation to logic, one has no way of avoiding such an error.