Posted: Jun 04, 2011 7:05 am
Cito di Pense wrote:Sweenith wrote:Cito di Pense wrote:
Self-evident is not the same as necessary. Necessity is the result of deduction, and hence is not a priori.
Postulates are not the same as axioms. A postulate might be something you have decided to try to prove, otherwise, axioms and postulates would be the same. Why have two words if there is only one concept. Parsimony demands it.
Agreed, something can be necessary without being self-evident (also, something can be self-evident without being necessary).
And while it's true that the conclusion of a valid deductive argument follows necessarily from the premises (meaning if the premises are true, then the conclusion can't fail to be true), that doesn't mean that the conclusion as such is a necessary truth (the conclusion, along with its premises, could be contingently true). Moreover, a proposition is either necessarily or contingently true regardless of whether we arrive at that proposition via deduction (ex: it would still have been true that 2 and 2 makes 4 even if we had never deduced it).
In any case, a priori knowledge doesn't mean "not the result of deduction," it just means that it doesn't depend on empirical or experiential evidence. So even if it were granted that necessity is always only the result of deduction, it still wouldn't follow that necessity cannot be a priori.
You're bullshitting me. Or else you are putting way more into 'necessary' than it can carry. It's just a word in the English language.
All I mean by "necessary" is this: a proposition or statement is necessary if and only if it's impossible for it to be false (like "2+2=4" or "All squares have four sides"). On the other hand, there are certain facts that could have been otherwise than they are, such as the fact that I live in Chicago, or the fact that my computer monitor is to the left of my can of diet Dr. Pepper—the universe might have been organized in such a way that I ended up in Japan, say, or that my monitor was to the right of the can instead of the left—these facts are not necessary, because it was possible for them not to be the case.
Some statement that is not self-evident, and not deduced, and not evident by empiricism? We need examples. Inquiring minds want to know.
First off, what I said was that a priori knowledge doesn't have to be knowledge that's not the result of deduction - i.e., a priori knowledge may or may not be deduced. Secondly, what I said was that a priori knowledge doesn't depend on empirical evidence, not that it couldn't be learned empirically (it may or may not). So I never said anything about a statement that's not deduced and not evidenced empirically.
take for example, "3 x 2 = 6"; let's suppose a child grasps the truth of this statement by observing collections of apples that have fallen from the tree and reflecting on their numerical relations to one another; then he would have learned this via empirical means, right? but, the knowledge he acquires doesn't depend on the apples he was looking at: once he grasps the necessary mathematical truth behind them, he no longer needs the apples to ground or justify his knowledge. That's what I mean when I say that a priori knowledge is independent of empirical experience.
I could grant that there is a priori knowledge, but that it is contingent on not being shown the door, not being handed your hat. That door-showing and hat-handing is the province of science. You could presently claim as a priori knowledge that there are other intelligent species in the universe besides human. Pending a definition of 'intelligent'. Or you could claim that there are no intelligent species, including the human. Pending blah blah blah.
Hmm I don't quite follow. I don't see how "there are other intelligent species in the universe other than humans" or "there are no intelligent species in the universe" could be known a priori, because the truth of either one depends upon the sorts of physical entities which exist in the universe, and facts like that can only be known from observation. Additionally, that fact—(that there are intelligent beings in the universe)—is contingent, and could have been different; as such, it's not necessarily true, and thus (absent of being a "synthetic a priori" truth), can't be known a priori.