Suppose someone makes the following inference, and you have to decide whether they count as being justified in accepting the conclusion.
3 is odd
3 is prime
Intuitively, one wants to say: if they are making the inference "x is odd ---> x is prime" then the answer is no, but if they are making the inference "3 is F ---> 3 is prime" then they are. So how do we tell/what determines what inference they are making?
a. phenomenology: Is the answer to this question a matter of how the subject feels when making the transition above? But, let me stipulate that this is a psychologically basic inference for them in the sense that they don't consciously think of any rule before making it (on pain of regress there have to be some inferences which have this status for us, if we make any inferences at all). So all they experience is saying to themselves with confidence and conviction "3 is odd" and then, a moment later "3 is prime".
b.what other inferences they would make: Or maybe what matters is, whether they tend to accept other things, that are instances of the bad inference procedure, but not the good one (e.g. would they say "15 is odd" and then, a moment later, "15 is prime")?
But it will always be the case that a person is disposed to accept some bad, and some good, particular inferences. So, how do we carve up the space of different inferences they are willing to make into different "kinds" of inference?
How do we decide that e.g. being willing to infer `15 is odd'...`15 is prime', counts against being justified in inferring `3 is odd'...`3 is prime', but being willing to infer `3 is greater than 2'...`the number of gods is greater than 2', does not?
c. neuroscience: Well, maybe the workings of the brain will be best described by carving it up into different mechanisms which produce different classes of inferences. So, maybe we need to look at the class of inferences which are made via the workings of the *same brain mechanism* that lead the person to say "3 is odd...3 is prime"? But we know almost nothing about how brain-functioning is best individuated into different `processes'. So, if this were right, it would seem that we aren't yet in a position to evaluate claims about justification, even in normal cases.
d. just saying there's a brute primitive division of inferences into natural kinds: Ok, this is the best I can come up with, but it's certainly not very attractive.
p.s. I realize this is kindof like the generality problem for reliablism. But this problem seems to apply to everyone who accepts that we can be justified in making some logical/mathematical inferences.