On common-sense axioms beyond simple tautologies

"If nothing is self-evident, nothing can be proved." - C.S. Lewis

Some claim that the only self-evident statements are tautologies. They are suspicious of "tautologies" because they appear to be cheap word tricks. In Adler's words: "You put the truth in by defining your words, and then pull it out as if you were surprised to find it there."

But that's not always the case. There are common-sense statements that are also self-evident. A statement like is axiomatic or self-evident in the sense that its opposite is immediately seen to be false. They have the status of being both indemonstrable and undeniable truths.

And since they are based on common experience and common-sense, they don't belong to an organized body of knowledge (philosophy, mathematics, science, or history).

The example that Mortimer Adler provide is this: "The whole is greater than its parts."

"The statement, 'The whole is greater than its parts,' expresses our understanding of things as they are and of their relationships, which would be the same no matter what words we used or how we set up our linguistic conventions. Finite quantitative wholes exist and they have definite finite parts; for example, this page can be cut in half or in quarters. Now, as we understand a finite whole (that is, any finite whole) and as we understand a definite part of a finite whole, we understand the whole to be greater than the part, or the part to be less than the whole. So far is this from being a mere verbal matter that we cannot define the meaning of the words “whole” and “part”; these words express primitive or indefinable notions. As we are unable to define them separately, all we can do is express our understanding of whole and part by a statement of how wholes and parts are related." - Mortimer Adler