By 'deductive inference,' I mean inferences where the premises entail the conclusion, and one is led to accept the conclusion on the basis of the believed premises. (I'll limit this to inference in belief, although I think there's a broader important notion that is neutral on the attitude in question.) I'll use 'ampliative reasoning' to refer to reasoning that is not deductive; where one concludes something that goes 'above and beyond' what was given in the premises.
Suppose I see that Herman has an iPhone, and come to believe on this basis that Herman has an object. It is very natural in this instance to represent my reasoning deductively:
Herman has an iPhone.
Therefore, Herman has an object.
(I don't much mind if you want to include a tacit premise to the effect that iPhones are objects. Put it in or leave it out, as you like.)
Some reasoning, however, is commonly thought to be ampliative. Just which cases are like this is a matter of some controversy. One might think that ordinary perceptual judgments are like that:
It appears to me as if I have pocket kings.
Therefore, I have pocket kings.
Or maybe standard cases of induction are like that:
Torfinn got angry the last twenty times someone mentioned two-dimensionalism.
Therefore, Torfinn will get angry the next time someone mentions two-dimensionalism.
I think there's generally thought to be a strong intuitive sense in which it is correct to formalize these arguments as ampliative, rather than deductive. But I just don't see it. These ampliative bits of reasoning are easily recast as deductive ones. One way to do this is to add to each a tacit premise at least as strong as the material conditional from original premise to conclusion. Another way is to take the inferences as being run against the background assumption that such a bridging principle holds. (I'm not sure how different these two ways are.) Either way, I'm trying to make sense of the intuitive idea that, in inferring Q from P, one demonstrates one's commitment to the material conditional P > Q. One cannot conclude that Q on the basis of P while regarding it as an open question whether it might be the case that P and ~Q.
Insisting that all reasoning is deductive will, I think, get us out of some messy problems. (Without going into detail here, I'm thinking about closure iterations, easy knowledge, and bootstrapping.) There must be some reason it's not the obvious choice, but I don't see what it is. What reason do we have to avoid positing tacit premises like these?