Topics Knowledge

Question All knowledge starts with axioms. Axioms are based on beliefs. Therefore, all derived "knowledge" is nothing more than a belief. Is this a correct conclusion? Thank you very much, Kobe

Accepted:
March 10, 2007

Comments

Hi Kobe: There are a lot of interesting issues packed into your question. Let me try to unpack a couple of them. Philosophers tend to think that knowledge just is a special kind of belief, e.g., a belief that is true and that one is justified in holding. So for most philosophers to conclude that knowledge is nothing more than a belief isn't that worrisome. What is more worrisome is whether knowledge is nothing more than "mere opinion" or "unjustified belief". This may be what you have in mind.

But then the question is why you think that the argument you give leads to the conclusion that knowledge is nothing more than mere opinion. To begin, most philosophers think that we have lots of knowledge that is not based on axioms. For example, when I believe that there is a pencil on my desk based on my perception of the pencil, this belief counts as knowledge even though it wasn't derived from an axiom.

The domain where it is more plausible that knowledge is axiomatic is in logic and math (though even here it is contested). Then your question might be interpreted as something like this: if knowledge of derived truths in a system depends on knowledge of the axioms, then how do we gain knowledge of the axioms? Either knowledge of the axioms is not based on anything, in which case it doesn't seem like it should count as knowledge. Or knowledge of the axioms is based on something other than axioms. But the axioms are supposed to be the source of justification and anything other than the axiom would be less justified than the axioms are supposed to be. So axioms cannot be justified and cannot count as knowledge. And if they aren't knowledge, nothing derived from them is either.

Interestingly, this is an argument that even Aristotle worried about. (See e.g., his Metaphysics Book IV, Ch. 4.) Some philosophers have thought that axioms were self-justifying; others have thought that they are true by definition; others have thought we know them with a kind of intellectual perception (just as we know the pencil is on my desk by virtue of perceiving it...like this but with the "mind's eye"). Aristotle seems to have thought that axioms (or first principles, i.e., the assumptions we all must make) could only be established by showing that one who failed to accept them couldn't really engage in thought or rational debate at all. So, for example, he thought that someone who rejected the Law of Non-Contradiction couldn't say anything meaningful at all and shouldn't be taken seriously in rational inquiry.

This sort of argument -- attempting to show that an "axiom" is presupposed by thought and so must be assumed by a thinking being -- has a substantial history in philosophy. You can even understand Descartes' famous "I think, therefore I am" this way. On this reading, the "I am" is established as a presupposition of any thought, so cannot be (coherently) denied by a thinking being. Similarly, Kant thought that there were a variety of claims that could be established this way.

A valuable question to ask, however, when you are thinking about the problem is whether it is possible for beliefs to be justified without being justified by another belief. If it is possible, then the argument starts to seem less worrisome.

Question All knowledge starts with axioms. Axioms are based on beliefs. Therefore, all derived "knowledge" is nothing more than a belief. Is this a correct conclusion? Thank you very much, Kobe Accepted:March 10, 2007

Question All knowledge starts with axioms. Axioms are based on beliefs. Therefore, all derived "knowledge" is nothing more than a belief. Is this a correct conclusion? Thank you very much, Kobe

Accepted:
March 10, 2007