Condition 4a is an internalist constraint that requires S to have at least some minimal reasons (or intuitions) for a belief on occasions when S is questioned by a truth-seeking objector. Reasons are often needed to show that one has some non-arbitrary basis for a belief, and that one's belief isn't just a guess or based upon spurious reasons. In cases where holding a belief has some pragmatic or theoretical importance, S should have strong reasons (i.e., evidence, premises) to support p, and S should be able to rule-out the logical and physical possibilities that would make p doubtful or false. If there are actual undermining factors present, and if S is aware of them, then S should be able to resolve any possibilities that imply ~p with a high degree of probabilistic and psychological certainty. This pragmatic condition suggests that there is a normative and contextual component to personal justification, and that it is persons (and not some independent objective criteria) that determine how much evidence is 'sufficient.' The standards for 'strong evidence' will vary by context (e.g., depending upon how important it is for S to know p, as opposed to merely believing p). The conscientious truth-seeker will evaluate what kinds of evidence, how much evidence, and what sorts of reasoning are sufficient for p to be believed.

S's psychological certainty about having strong enough evidence for believing p, by itself, is not enough to satisfy condition 4a. The strength of S's reasons for believing p may be challenged by other persons. If there are facts that would (or should) undermine S's belief, critical objectors will often press these issues.

Condition 4a is consistent with the doctrine of 'fallibilism' which posits S can know p, but that S's strong reasons for believing p do not guarantee the truth of p. Although 4a requires S to have 'strong evidence' to believe p this requirement is not as strong as infallibilism which claims that in order to know p, S must know that counter-possibilities (implying not-p) are false. In order for condition 4a to be satisfied, S does not need to rule-out every possibility that is known to be incompatible with p. Instead it is assumed that S can know p, based on assumption against counter-possibilities that S takes for granted, without knowing them to be true.

With non-human animals, condition 4a does not apply, since animals do not debate the applicability of their reasons for their beliefs. Some animals are capable of acting upon evidence and knowing, but without a self-conscious inspection of their justifying reasons.

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