The foregoing complicated set of definitions permits us to reduce knowledge to a simple formula. Knowledge is undefeated justified acceptance. The reduction is easily effected. We began in the first chapter with the following definition of knowledge:
DK. S knows that p if and only if (i) S accepts that p, (ii) it is true that p, (iii) S is completely justified in accepting that p, and (iv) S is completely justified in accepting that p in a way that is not defeated by any false statement.
We then undertook to analyze conditions (iii) and (iv) by means of a complicated set of definitions. The first definition specifies the system, the acceptance system, with which something must cohere to yield justification.
-147-D1. A system X is an acceptance system of S if and only if X contains just statements of the form, S accepts that p, attributing to S just those things that S accepts with the objective of accepting that p if and only if p.
The second definition expresses the idea that justification is coherence with a system.
D2. S is justified in accepting p at t on the basis of system X of S at t if and only if p coheres with X of S at t.
The next definitions articulate the idea that coherence with a system means that all skeptical objections, competitors, can be met because they are either beaten or neutralized on the basis of the system.
D3. S is justified in accepting p at t on the basis of system X of S at t if and only if all competitors of p are beaten or neutralized for S on X at t.
D4. c competes with p for S on X at t if and only if it is more reasonable for S to accept that p on the assumption that c is false than on the assumption that c is true, on the basis of X at t.
D5. p beats c for S on X at t if and only if c competes with p for S on X at t, and it is more reasonable for S to accept p than to accept c on X at t.
D6. n neutralizes c as a competitor of p for S on X at t if and only if c competes with p for S on X at t, the conjunction of c and n does not compete with p for S on X at t, and it is as reasonable for S to accept the conjunction of c and n as to accept c alone on X at t.
We thus arrive at a definition of personal justification.
D7. S is personally justified in accepting that p at t if and only if S is
justified in accepting that p on the basis of the acceptance system of S at t.
To proceed beyond personal justification to complete justification, we require a notion
of justification based on that part of the acceptance system that remains when all errors have been eliminated, the verific system. This kind of justification is called verific justification. The next three definitions accomplish this and result in a definition of complete justification as the combination of personal and verific justification.
-148-D8. A system V is a verific system of S at t if and only if V is a subsystem of the acceptance system of S at t resulting from eliminating all statements of the form, S accepts that p, when p is false. (V is a member of the
ultrasystem of S.)
D9. S is verifically justified in accepting that p at t if and only if S is justified in accepting that p on the basis of the verific system of S at t.
D10. S is completely justified in accepting that p at t if and only if S is personally justified in accepting p at t and S is verifically justified in accepting p at t.
Finally, we require a definition of undefeated justification which amounts to
justification on the basis of those systems resulting from the corrections of errors in the acceptance system by either elimination of the acceptance of the error or
replacement by the acceptance of denial of the error.
D11. S is justified in accepting that p at t in a way that is undefeated if and only if S is justified in accepting p at t on the basis of every system that is a member of the ultrasystem of S at t.
D12. A system M is a member of the ultrasystem of S at t if and only if
either M is the acceptance system of S at t or results from eliminating one or more statements of the form, 'S accepts that q,' when q is false, replacing one or more statements of the form, 'S accepts that q,' with a statement of the form, 'S accepts that not q' when q is false, or any combination of such eliminations and replacements in the acceptance system of S at t with the constraint that if q logically entails r which is false and also accepted, then 'S accepts that r' must also be eliminated or replaced just as 'S accepts that q' was.
Needless to say, the attempt to analyze justification and undefeated justification in terms of acceptance, reasonableness, and truth has yielded a complicated analysis. As is often the case, however, thorough analysis enables us to find the underlying
simplicity. We are now in a position to provide an elegant reduction of the original analysis of knowledge (DK). Knowledge reduces to undefeated justification, a just reward for our arduous analytical efforts.
The reduction of knowledge to undefeated justified acceptance is a consequence of our explication of condition (iv). This condition implies the other three. It is easiest to see that undefeated justification implies complete justification. The verific system is one of the members of the
-149-ultrasystem and, therefore, if a person is justified in accepting that p on the basis of every member of the ultrasystem as our definition of undefeated justification requires, the person is justified in accepting that p on the basis of the verific system. Thus, if a person's justification for accepting that p is undefeated, then the person is verifically and completely justified in accepting that p. Undefeated justified acceptance obviously implies acceptance, and the implication of the truth condition is trivial. If a person accepts that p and it is false that p, then any justification the person has for accepting p will be defeated. The reason for this is that if it is false that p, then the skeptic in the ultra justification game may require the claimant to replace acceptance of p with acceptance of the denial of p and the claimant will lose the game starting with the claim that p. This is equivalent to saying that if a person accepts that p when p is false, then some member of the ultrasystem containing acceptance of the denial of p will defeat the person's justification for accepting p. Hence, condition (iv), the
defeasibility condition of (DK), our original definition of knowledge, logically implies the other three conditions, and knowledge is reduced to undefeated justification.
The reduction is a formal feature of the theory. The substance of it is the coherence theory of justification in which personal justification results from coherence with an acceptance system, just as other necessary kinds of justification, verific, complete, and undefeated, result from modifications of the acceptance system. The soul of the theory is personal acceptance. This is entirely an internal matter. One is personally justified in accepting something because what one accepts informs one that such
acceptance is a trustworthy guide to truth. Even the conclusions that one accepts from perception and inference must cohere with one's background information articulated in an acceptance system to insure that they are trustworthy. Without such insurance, one may possess information but lack knowledge, for, the trustworthiness of
perception and inference is not a necessary a priori truth. When they prove
trustworthy, this is the result of the nature of our faculties, the circumstances we find ourselves in and, most importantly, our background information about the
circumstances in which our faculties are worthy of our trust. The soul of personal justification requires a body of truth to provide knowledge, however. A truth
connection between an acceptance system and worldly fact is essential. There must be a match between what one accepts as a trustworthy guide to truth and what really is a trustworthy guide to truth. The match must be close enough to sustain justification when error is eliminated or replaced with truth.
Given the importance of the trustworthiness of acceptance in yielding undefeated
justification and knowledge, the theory might be regarded as a form of reliabilism, but, given that the acceptance of our
trust-
-150-worthiness yields, in the normal case, justification of its own acceptance, the theory might as well be called foundational coherentism. To obtain knowledge we need the right mix of internal and external factors. Our theory may appear dialectically
promiscuous, but fidelity to a single approach is epistemic puritanism. The simple theory, though ever seductive, is usually the mistress of error. The queen of truth is a more complicated woman but of better philosophical parts.