If somebody asks me why I believe something, I may be able to give logical justification for my belief. On the other hand, I may be unable to do this, but nonetheless hold that my belief stands on solid ground. In the latter case it would appear that either I am irrational in holding my belief, or that I have some kind of justification for my belief which I am unable to express adequately. Are there cases in which I can rationally believe something, and yet be unable to express an adequate logical justification for that belief?
I suggest that there are such cases. To give a simple case, suppose that I believe “I enjoy The Beatles.” If somebody asked me why I hold this belief, my justification would appear circular and logically inadequate. I could give reasons such as, “on this date I enjoyed this song,” and enumerate many such facts. But this would appear to be merely reiterating the very belief that I am justifying, only in a more detailed fashion. If I was asked to prove that on this date I enjoyed this song, I could not do so, and would probably dismiss my questioner as unreasonable in requiring this type of justification.
It seems that there are certain assertions which we can make, which nobody expects us to justify. These include reports of our subjective experiences. “I am happy,” “I am in pain,” or “I enjoy The Beatles” are examples of such assertions. Rational people make this type of assertion without justification, and accept this type of assertion from others without expecting justification.
We have evidence for these assertions, but this evidence is unshared. If I assert that I am happy, I am making this assertion based on evidence which is available only to me and which I cannot share. This evidence is my subjective experience of being happy.
Let us call an assertion based on unshared evidence a “bare assertion.” Assertions of religious beliefs are frequently bare assertions.
For instance, I believe that:
(H.1) All is one.
I do not believe (H.1) on logical grounds; indeed, it is arguable that (H.1) is not even logically meaningful. My basis for believing (H.1) is that I have had many spiritual experiences whose content was to the effect that (H.1). These spiritual experiences are unshared, and so (H.1) is a bare assertion.
If mathematicalism is true, then all unshared evidence is in principle shareable. Under mathematicalism, every experience and mental state is a mathematical pattern, and this pattern can therefore in principle be captured and shared somehow.
If mathematicalism is false, then there may exist evidence that is in principle unshareable. The distinction is, however, perhaps somewhat academic, in that there is no important operational difference between evidence that is unshared and unshareable by any currently available means, and evidence that is unshared and unshareable by any means.
Beliefs based on unshared evidence form a difficulty in two ways. First, it is difficult to say whether or not these beliefs are rational. The person holding the evidence seems obviously the only person qualified to evaluate the belief, but besides being uniquely qualified they are also uniquely unqualified, due to the bias which they have as a result of the fact of holding the evidence. It may be the case, then, that nobody exists who is qualified to evaluate the rationality of these beliefs.
There is a second difficulty with beliefs based on unshared evidence, which is that which arises when there are disagreements. It is unclear how to resolve these disagreements. For instance, consider:
(H.2) Jesus Christ is our Lord and Savior.
People who believe (H.2) usually do so on the basis of the unshared evidence of religious experience. People who disbelieve (H.2) usually do so on the basis of the lack of any evidence for (H.2), and possible counterevidence. The resolution of this debate is very problematic, but only because some of the relevant evidence is unshared. If all of the evidence were shared, then the debate would probably be resolved.