Despite the limitations of “S knows that p” epistemology, it may be worthwhile to examine some basic “S knows that p" propositions in order to try to clarify the relations between epistemic ground, justification, and warrant. Such an examination may also help to delineate some of the controversies regarding the relations between epistemic ground, justification, and warrant. Thus, some basic “S believes that p” or "S knows that p" propositions are:
1. Even if there is sufficient reason (or there are sufficient grounds) for S to believe that p, p may still be false. (Although it may be argued, to the contrary, that if there are sufficient grounds for S to believe that p, then p must be true.)
2. If there is sufficient reason (or there are sufficient grounds) for S to believe that p, then S may be justified in believing that p. (Although it may be argued, to the contrary, that the justification for a belief cannot be provided solely by the grounds for that belief, and that a belief must not only have sufficient grounds, but also be true in order to be justified.)
3. If S believes that p, but p is false, then S’s belief is unwarranted. (Although it may be argued, to the contrary, that warrant may be defined in such a way that all warranted beliefs do not necessarily have to be true. For example, Kent Bach (1996) explains that one way of defining warrant may be to say that warranted beliefs are those beliefs that, if true, are not accidentally true.1)
4. S’s believing p at a given time t may be justified on the basis of the evidence available to S at t, but that act of belief may turn out to be unwarranted if the evidence available to S at t is incomplete or contradicted by further evidence that may or may not have been available to S at t. (Although it may be argued, to the contrary, that S was not justified in believing p at t if that act of belief is later found to be unwarranted or to have been based on insufficient evidence that p.)
5. If S has sufficient grounds for believing that p, then that belief may be justified.
6. A sufficient reason or ground for a belief may constitute (or be taken as) a sufficient justification for that belief.
7. The grounds for a belief may provide the justification for that belief. (Although in order for S herself to feel justified in believing p, S herself may have to judge the grounds for believing p to be sufficient.)
8. S’s belief that p may, in fact, be fully or merely partially justified or warranted.
9. If S’s belief that p is, in fact, fully justified or warranted, then that belief takes fully into account, and is fully supported by, the evidence that p (if an evidentialist theory of justification or warrant is proposed or accepted).
10. The reasons or grounds for S’s believing that p at t may be logical, epistemic, moral, religious, and/or psychological.
11. As shown by Edmund Gettier (1963), in cases where S believes that p, and S’s belief happens accidentally to be true and to be justified because of circumstances unknown to S, that belief, although true and justified, cannot properly be said to constitute knowledge that p.2
12. If S believes that p, then that belief is warranted if (1) it is justified, (2) p actually holds, and (3) the justification for the belief cannot be questioned or refuted by the kinds of arguments provided by Gettier cases.3 However, it may be argued that there may always be exceptions to this set of conditions, involving warranted beliefs not covered by this theory or by some other similar theory of warrant.
13. If S knows that p and also knows that q, then S knows that p (and that q). However, from S’s knowing that p and that q, it does not follow that S knows that p and q. That is to say, from S’s knowing that p and q hold independently, it does not follow that S knows that p and q hold conjointly (nor does it follow that p and q actually do hold conjointly).
14. Prop. 13 may be stated negatively as: If S does not know that p and also does not know that q, then p knows neither that p nor that q.
15. From S’s knowing that p, it does not follow that either S knows that p or S knows that q (because both consequents could hold). Nor does it follow that S knows that p or q (because from S's knowing that p, it does not follow that S knows that p or q hold disjunctively, nor does it follow that they actually do hold disjunctively).
1Kent Bach, “Accidental Truth and Would-be Knowledge,” Philosophical Quarterly, 198 (1996), 183-190. Online at http://online.sfsu.edu/kbach/accidtruth.html.
2Edmund Gettier, “Is Justified True Belief Knowledge?” in Analysis, 23 (1963), 121-123.
3Fred Dretske, “Gettier and Justified True Belief: Fifty Years On,” in The Philosophers Magazine (July 9, 2013), online at http://philosophypress.co.uk/?p=1171.
Alston, William P. “The Deontological Conception of Epistemic Justification,” in Philosophical Perspectives, Vol. 2, Epistemology (1988), pp. 257-299.
Merricks, Trenton. “Warrant Entails Truth,” in Philosophy and Phenomenological Research, 55 (1995): 841-855.
Merricks, Trenton. “More on Warrant’s Entailing Truth,” in Philosophy and Phenomenological Research, 57 (1997), 627-631.
Ryan, Sharon. “Does Warrant Entail Truth?” in Philosophy and Phenomenological Research, Vol. LVI, No. 1, March 1996, pp. 183-192.
Zagzebski, Linda. “The Inescapability of Gettier Problems,” in The Philosophical Quarterly, Vol. 44, No. 174, (Jan., 1994), pp. 65-73.