Gib wrote:I suppose so. If every dog I've ever seen has four legs, and I conclude that ALL dogs have four legs, the hidden assumption is that all the dogs I've seen are perfectly representative of all dogs.

That's the gist (: But of course, in reality, the actual assumptions are probably different. For one, I believe they are observer-independent, so no assumptions of the form "If all I see is cats, then there are only cats". They are more like "If 50% most of the animals in New York are cats, then 50% all of the animals in US outside of New York are also cats".

And there's the question of how broad vs how deep the "forest" of human thought is. A forest is made out of a number of trees. Breadth indicates how many axioms (i.e. random guesses) there are (and also how many trees) whereas depth indicates how much deduction there is (the height of trees.) A forest that is very broad has a lot of specific axioms whereas one that is very deep has few but very general axioms (perhaps only one axiom from which everything else is derived.)

I don't know. I'm pretty sure I'm right that deduction is conventionally defined as logically necessary reasoning and induction as involving leaps, but maybe I've misunderstood the definitions all these years.

You didn't misunderstand, that's pretty much it.

I'll respond to the rest of your post at another time.

EDIT:

On the other hand, it's possible to use an inductive argument to represent a thought process that cannot be represented with a pure deductive argument. This seems to refute my statement that every inductive argument has an equivalent deductive argument.

It's not too difficult to think of an inference that involves a degree of randomness. For example:

1) If most men in New York are black, then all men outside of New York are also black.

2) Most men in New York are black.

3) Socrates is a man and he lives in Athens (so he's outside of New York.)

4) Therefore, Socrates is black.

Number 4 requires an arbitrary decision to be made because Socrates can also be white -- he's not necessarily black. On the other hand, one has to take into account that such a conclusion, albeit arbitrary, in no way contradicts the stated premises. So while not strictly a deductive argument, it's pretty damn close to being one.

So my claim has now to be demoted to something like "In practice, most, if not all, inductive arguments represent thought processes that can also be represented by deductive arguments". I can also add "And those that do not are still largely deductive".