Conatus: REVISED EDITION by Tom Wallace - HTML preview

C O N A T U S

An analytic statement is a statement that is true because of the meaning of the words. Since it is based on logic, it can be a priori, that is, not derived from observation — so this marks it out as rational rather than empirical. Analytic truth is regarded as necessarily as opposed to contingently true. Readers will note, of course, the correlation here with the necessary and contingent types of truth discussed above. ‘All bachelors are unmarried’ is true because of the meaning of the words, but we saw this to be only trivially true.

Nevertheless, there are some statements that are so self-obviously true that they are considered to be analytic truths. We might consider the principles of logic to be necessarily true. Logic, on the other hand, has to be built on prior assumptions. What is derived from first principles is still not guaranteed to also be true. The same may be said of the five axioms on which geometry is based, and there are axioms also for mathematics.

It is said about analytic truth that it does not provide us with new knowledge. This is a reflection of what is discussed above, in that even if we accept the idea that an analytic truth is indeed an absolute necessary truth, even so, what might be derived from it need not itself be true.

As we’ve seen, mathematics is described as a formal system of truth. (Note, and as discussed in the previous chapter, ‘formal’ is used here in the mysterian sense of ‘form’ — that is, giving structure to the world, and potentially, giving essence. The same word — form — can be used

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