Fallis claims that such gaps are not unusual and that at least some of the time proofs containing them are accepted by mathematicians in a justificatory context.
(Much of this work traces back to Pólya (1945).) A background issue in all of these debates concerns the extent to which each particular non-deductive method plays an essential role in the justificatory practices of mathematics.
This asymmetry between the justificatory potential of religious and secular reasons, it is further claimed, should shape the political practice of religious believers.
While public reason liberals need not share Gaus's epistemology of justificatory reasons, the right account cannot be too far off, for any public reason liberal must accept that citizens can be rational to comply with reasons that others systematically reject and so, in some way or another, different individuals must be epistemically justified in affirming very different reasons.
The coherentist might hope to reply to this problem by claiming that there is still a justificatory web: the belief is a memory belief and one might believe that most of one's memory beliefs are true; therefore, this belief is likely to be true and is hence justified.
The lesson, the reliabilist will tell us, is that the justificatory status of a memory belief is, in standard cases, partially a function of the belief's justificatory status at an earlier time.
To motivate idealization, consider how the public justification fares if it declines to idealize, or endorses justificatory populism.
On the other hand, public justificatory arguments are meant to have an impact on the individuals whom they target and, in particular, to give them motives as well as reasons for conformity to the demands they are subject to (Macedo 1990 makes these points especially forcefully).
Suppose Albert and Betty are the only members of the justificatory constituency and suppose there are no shared reasons that would justify accepting X.
Equal distribution is therefore not merely one among many alternatives, but rather the inevitable starting point that must be assumed insofar as one takes the justificatory claims of all to be of equal weight.
This justificatory procedure is all the more needed the less evident — indeed the more unclear or controversial — it is if what is at stake is actually suffering, distress, an objective need.
