inferential knowledge a kind of ‘indirect’ knowledge, namely, knowledge based on or resulting from inference. Assuming that knowledge is at least true, justified belief, inferential knowledge is constituted by a belief that is justified because it is inferred from certain other beliefs. The knowledge that 7 equals 7 seems non-inferential. We do not infer from anything that 7 equals 7 – it is obvious and self-evident. The knowledge that 7 is the cube root of 343, in contrast, seems inferential. We cannot know this without inferring it from something else, such as the result obtained when multiplying 7 times 7 times 7.
Two sorts of inferential relations may be distinguished. ‘I inferred that someone died because the flag is at half-mast’ may be true because yesterday I acquired the belief about the flag, which caused me to acquire the further belief that someone died. ‘I inferentially believe that someone died because the flag is at halfmast’ may be true now because I retain the belief that someone died and it remains based on my belief about the flag. My belief that someone died is thus either episodically or structurally inferential. The episodic process is an occurrent, causal relation among belief acquisitions. The structural basing relation may involve the retention of beliefs, and need not be occurrent. (Some reserve ‘inference’ for the episodic relation.) An inferential belief acquired on one basis may later be held on a different basis, as when I forget I saw a flag at half-mast but continue to believe someone died because of news reports.
That ‘How do you know?’ and ‘Prove it!’ always seem pertinent suggests that all knowledge is inferential, a version of the coherence theory. The well-known regress argument seems to show, however, that not all knowledge can be inferential, which is a version of foundationalism. For if S knows something inferentially, S must infer it correctly from premises S knows to be true. The question whether those premises are also known inferentially begins either an infinite regress of inferences (which is humanly impossible) or a circle of justification (which could not constitute good reasoning). Which sources of knowledge are non-inferential remains an issue even assuming foundationalism. When we see that an apple is red, e.g., our knowledge is based in some manner on the way the apple looks. ‘How do you know it is red?’ can be answered: ‘By the way it looks.’ This answer seems correct, moreover, only if an inference from the way the apple looks to its being red would be warranted. Nevertheless, perceptual beliefs are formed so automatically that talk of inference seems inappropriate. In addition, inference as a process whereby beliefs are acquired as a result of holding other beliefs may be distinguished from inference as a state in which one belief is sustained on the basis of others. Knowledge that is inferential in one way need not be inferential in the other. See also FOUNDATIONALISM , INFERENCE , PRACTICAL REASONIN. W.A.D.