Quote:
Originally Posted by reason
Induction is not deduction, by definition.
Deduction: the logical content of the conclusion is a subset of the logical content of the premises.
Induction: the logical content of the premises is a proper subset of the logical content of the conclusion. The set relation between the logical contents is reversed, and therefore, if induction was deductive, then there would be no induction, only deduction. However, inductive arguments are invalid, that is, the conclusion of an inductive inference can be false even when the premises are true, whereas deductive inferences are valid, that is, the conclusion must be true if the premises are true. In other words, there is a distinct, and important, difference between inductive and deductive inferences, which is qualitive and nontrivial.
I have spent way too long thinking about this, btw. |
Grr. I must not have explained this correctly.
I know the definitions of induction and deduction. I've taken like 5 classes that have gone over this stuff. (I've also spent way too long thinking about this. And knowing you, I doubt we're gonna end up disagreeing; I just have trouble wording things in such an INTP way for you to understand right away.)
What I'm saying is that induction is actually a deductive process. "New" information that comes from the inductive process is not actually new. It's just restating the premises or some subset of the premises. The premises are hidden, though... they're not formally listed. But they're still there.
When you say, "the sun has risen every day, therefore it will rise tomorrow", that's induction. But really, you are making the same argument in a deductive way if you included the right premises. Like, if you include "things that I've noticed happen everyday will happen tomorrow with X likelihood", and "things that are some threshold of likely can be thought of as true", etc. it would be a deductive argument.
The real difference between induction and deduction is formality. Induction is less formal, because there are a bunch of hidden premises, and the premises are a bit more vague.
But reasoning has to be deductive. We are biological computers. There's no such thing as coming up with "new" information. Our minds are programs instantiated on the hardware of the brain. And computers are only capable of deduction.
Are you a determinist (you gotta be)? It's not like any atom that makes up our body can decide not to follow the laws of physics. If you think of each atom as a function, then you can think of the body as interactions between trillions of these functions. And functions are not capable of induction, or anything "new".
Each conclusion is come to via deduction if you think of every past state of our brain as a premise.
Do you see what I'm saying now?
EDIT:
Quote:
Originally Posted by reason
if induction was deductive, then there would be no induction, only deduction.
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This is exactly my point.