Show-Me the Argument

Conservatism is often defined as follows:

(C) If S believes that p, then, in the absence of defeaters, S thereby has at least some degree of justification for believing that p.

I will now give a rough characterization of the distinction between propositional and doxastic justification for p. For S to have propositional justification for her belief that p is for her to have reasons for her belief that p. This does not imply that S bases her belief on those reasons; S might believe that p on a whim or she might not even believe p at all. However, if S has propositional justification for p and S bases her belief that p on her propositional justification, then S has doxastic justification for p. These considerations show that propositional justification for a belief alone does not make a belief have any positive epistemic status. Sally might have great reasons for believing that there has been an increase in global warming (say, the testimony of reliable scientists she knows), but if her belief is based solely on the results of her ouija ball, then her belief has little positive epistemic status. However, if she bases her belief on the testimony of those scientists, then the belief will have positive epistemic status; it will be doxastically justified. (more…)

In an earlier post, http://philosophy.missouri.edu/show-me/?p=138#more-138, I followed Plantinga in arguing that our memorial beliefs constitute cases of knowledge without evidence.  I still think this is right, but I’m going to try to pull from a new set of cases.

Some of my knowledge is inferred from other beliefs; this is the case for my knowledge that the lights at my apartment are currently turned off (which is based on my knowledge that I turned out all the lights when I left and that no one has been there since).  Call this sort of evidence propositional evidence.  My perceptual knowledge, however, is noninferentially believed; the evidence here will be constituted at least partly by my sensory experiences and not by other beliefs, e.g., the experience of being appeared to redly or the tactile experience of touching a hard round ball.  Call this sort of evidence sensory evidence.  (For more careful explication of these points, see http://philosophy.missouri.edu/show-me/?p=128#more-128.)

But consider my knowledge that 5+2=7 or that I was in California recently.  The evidence for these beliefs is neither propositional nor sensory.  The suggestion for what constitutes evidence for these beliefs is that they seem true to me.  Upon considering the propositions, they seem true, and so I believe them.  I disputed this in the above linked posts, but I will grant the point.

The mental state of its seeming to me that 5+2=7 or that I was in California recently must not just be mere phenomenal reflection on the belief itself.  Otherwise, evidence would be entailed by belief, and so it would be trivially the case that knowledge entails evidence.  If seemings are to count as evidence, they must be something beyond mere belief.
Now consider my knowledge that I believe that 5+2=7 or that I believe that I was in California recently.  Upon considering these propositions, I immediately know them.  While it is plausible that I know that 5+2=7 on the basis of its seeming true to me, it’s less clear that I know that I believe that 5+2=7 on the basis of its seeming true to me.  Or so I am suggesting.  What do ya’ll think?