Dear Colleagues,
Here’s a basic (and possibly wrong-headed) question. Probably, if I were a better student of logic and/or epistemology, I would see the answer, but at the moment I don’t.
Why do we even recognize a category of inductive inferences (or, as some would have it, inductive standards of inference)? Why not treat all inferences as deductive, but with some sort of probabilistic qualification built into the conclusions of some of those deductive inferences?
That is, instead of characterizing such inferences in these terms …
1. This is a fair, six-faced, cubical die and I shall roll it in the normal way.
So probably
2. I shall not roll a “6.”
3. The first 999 crows I saw were black
So probably
4. The next crow I see will be black.
… why not characterize them in the following terms?
1. This is a fair, six-faced, cubical die and I shall roll it in the normal way.
Therefore (certainly):
2*. Probably, I shall not roll a “6.”
3. The first 999 crows I saw were black
Therefore (“certainly”):
4*. Probably, the next crow I see will be black.
Of course, I see that there’s a difference between the above arguments and standard deductive arguments such as:
5. If Fluffy is a vixen, then Fluffy is a female.
6. Fluffy is a vixen.
Therefore,
7. Fluffy is a female.
But that difference could be expressed in terms of the presence or absence of a probability qualifier in the conclusion, and not in terms of a fundamentally different kind of inference.
So I repeat my question: why do we allow for two kinds of inference, instead of only one?