Abstract
“Knowledge” is an honorific intended to distinguish sources of information that are approved from those that are not and also to distinguish full beliefs that are prized from full beliefs that are despised. These are two distinct functions. The function of sources of information is quite different from the function of states of full belief. We should not expect that the characterization of knowledge in the two cases should be the same or that conflict between the two can be settled by appeal to “our ordinary” concept of knowledge. (There is no such thing.)
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- 1.
My first effort to elaborate the conception of knowledge and its relation to full belief discussed here appeared in Levi (1983) versions of which were read at several places in the early 1970s. The final version was submitted for publication in 1975 but did not appear until 1983. In 1976, I published another version of the same ideas. The first three chapters of Levi (1980) are a more leisurely and carefully elaborated statement of the same general conception. More recent statements of this view are found in Levi (1991, 2004, ch. 1).
- 2.
The full belief that h is to be distinguished from the state of full belief K of which it is a consequence. Both the full belief that h and the state of full belief K are potential states of full belief. The set of potential states of full belief K is a Boolean Algebra. I shall suppose that K is an atomic algebra. W is the set of atoms. I assume that the Algebra is closed under meets of subsets of K of cardinality of W. The members of K are thus the power set of W. K is the set of states of full belief that an inquirer may coherently adopt at some given time. I do not mean to impose any conceptual bound on W. If X wishes to consider potential states that are more specific than the elements of W, I assume that X may move to a space of potential states of full belief more fine grained than K. But I shall retain the restriction that the new set of potential states like the old one is an atomic algebra. The atoms in K are, thus, not to be confused with conceptual counterparts of possible worlds. There are no possible worlds immune to splitting. Thus, subsets of W are not to be confused with propositions understood as sets of possible worlds. If one wishes, one can think of subsets of W as doxastic propositions in K. Or one can think of the joins of such subsets (which are potential states of full belief) as doxastic propositions in K. X’s full belief that h is full belief in the truth of a doxastic proposition understood as a potential state of full belief that h. X’s full belief that h could be the potential state of full belief K that is X’s current state of full belief. But as a general rule it is a potential state of full belief that is weaker than K. Hence, I do not think of X’s full belief that h as a state. A fortiori it is not a mental state. Consider, however, the set of full beliefs to which X is committed at a given time. This is the set of all consequences of X’s state of full belief K and may be used to characterize that state.
- 3.
In Levi (1980), I took X’s state of knowledge at t to be X’s standard for serious possibility rather than beginning by taking X’s state of full belief at t to be X’s standard for serious possibility. I pointed out then as I have done here that from X’s point of view at t, the two characterizations coincide. I also pointed out that X distinguishes between Y’s knowledge and Y’s full beliefs at any time or X’s knowledge and X’s full beliefs at times other than t. This raises the question as to whether from X’s point of view at t, Y’s standard for serious possibility at t’ is Y’s state of full belief or Y’s state of knowledge at t’. This question was not explicitly addressed but was discussed in Levi (1979) reprinted in Levi (1984, p. 153). The view taken is substantially the one adopted here.
- 4.
Notice that if X judges that h is probable to a degree other than 0 or 1, X is in suspense as to whether it is true or false that h. The converse, it should be emphasized, does not hold. X may judge that h carries probability 1 and yet be in suspense as to whether h is true or false. In that case, X has partial belief that h. When X is absolutely certain that h, X has full belief. Probability 1 in that event does not represent a degree of partial belief. X has ruled out as impossible the truth of ~h. If X assigns probability 1 and remains in suspense, X has not ruled out the possibility of the truth of ~h any more than X does if X assigns probability less than 1 and greater than 0. (Of course, probability 0 carries the same ambiguity between full and partial belief as probability 1 in dual form.) The difference between full belief and partial belief is no mere matter of degree.
- 5.
Let different agents hold conflicting probability judgments, value judgments, modal judgments or conditional modal judgments. In order that any one of the parties to the dispute may maintain that there is a true answer to the issue under dispute and that beliefs contradicting this answer are false, that agent should presuppose that the following conditions hold:
-
(i)
Suspending judgment concerning the issue under dispute should be a rationally coherent attitude to adopt.
-
(ii)
Judging the alternative views to be serious possibilities of truth should be a rationally coherent attitude.
-
(iii)
Assigning credal probabilities to the alternative views should be rationally coherent.
In the case of probability judgment, Savage’s argument (Savage 1974, p. 58) (as reconstructed in Levi, 1979 to relate to the truth-value bearing status of probability judgments satisfying these three requirements) may be sketched as follows:
Let X suspend judgment between the probability that h being r and being s. Suppose X judges it probable to degree x that the value is r and 1−x that it is s. \(p(h/p(h) = r)\) should equal r. where p represents X’s current probability. (This is an instance of Van Fraassen’s (1984) “Reflection Principle” in the “synchronic” case, the only case where the principle has any merit as a norm of rationality. See Levi 1987.) It then follows from the calculus of probabilities that \(p(h) = xr + (1 - x)s\). If \(x = 1,\;p(h) = r\) counter to assumption. If \(x = 0,\;p(h) = s\) again counter to assumption. If x is positive but less than 1, x is some real value distinct from r and s – again counter to assumption. If we allow indeterminacy in probability judgment so that we recognize a range of values for x to be permissible, there will be a corresponding range of permissible values for p(h). But no matter what the interval may be it does not cohere with suspending judgment just between r and s. The supposition that X has suspended judgment concerning the true probability has led to absurdity in every case and should be rejected. So credal probability judgments cannot be truth-valued.
-
(i)
- 6.
We should be careful to distinguish between providing necessary and sufficient truth conditions for “it is possible that h according to X” and “it is possible that h” in terms of consistency with the information available to X (who may be a single inquirer or community agent.) In his excellent paper on possibility (Hacking, 1967, p. 148), Hacking defines what he calls epistemic possibility according to X. (Strictly speaking, Hacking speaks of “epistemic possibility within a community of speakers”. I replace “within a community of speakers” by “according to X”.) But it becomes fairly clear that his target is to supply truth conditions for “It is possible that h”). This shift has provided an excuse for subsequent commentators to explore contextualist or relativist accounts of truth conditions for so-called “epistemic modals”. A good example is De Rose (1992). On the view I favor, however, when we drop the relativity to the agent X, there are no truth conditions to account for.
- 7.
I classify if-sentences according to V.H. Dudman’s (1983, 1984, 1985) proposals and maintain that both “pure indicatives” (Dudman’s hypotheticals) and subjunctive and future indicative conditionals (Dudman’s conditionals) lack truth values. Gibbard’s classification (1981) more or less resembles Dudman’s but Gibbard regards the subjunctive and future conditionals to have truth-values and to be capable of being judged probabilistically – which I deny (see Levi 1997, 2.7.) This disagreement is closely related to Gärdenfors’s argument for abandoning the Ramsey Test for subjunctive and future conditionals (Gärdenfors 1986, 1988) and my response to that argument (Levi 1988, 1997, ch. 3–4).
- 8.
- 9.
For the record, I still stand by Levi (1967b, 1969) adjusted to accommodate my adopting a clear commitment to full belief as the standard for serious possibility as explaining acceptance as evidence. R.C. Jeffrey’s alleged refutation of my views in (Jeffrey, 1970) seems to me to concede the main points I was making and illustrating in the examples I discussed that he so roundly criticized. As Jeffrey writes: “To judge the soundness of a shift from p to p’ we must not only look at the two belief functions and their differences; we must also inquire into the forces which prompted the change – the dynamics of the change (Jeffrey 1970, p. 178). I take it that to judge a change sound, one would need to know the forces that prompt the change. But to ascertain this, one would have to acquire full beliefs. And this undercuts the probabilist program that Jeffrey was promoting. It seems to me that Spohn has to address a similar issue.
- 10.
Prominent among them is L.J. Cohen’s distinction between belief and acceptance that focuses attention on belief as a disposition to what I should call a fit of doxastic conviction and acceptance as a decision (Cohen 1992). The distinction he makes may be compared to the distinction I draw between beliefs as performances and beliefs as commitments. That is to say, some of the concerns Cohen has in making the distinction are common to my concerns in adopting the contrast I propose. These concerns are not directly relevant to the discussion in section 3.
- 11.
Erik Olsson (2003) rightly objected that X cannot evaluate the informational values of the three options and take the decision between (1), (2) and (3) in the state of inconsistent conflict K⊥ that results after the recalcitrant experience takes place. For this reason, I suggested (2003) that X anticipate the serious possibility of such conflict by providing a procedure for handling such issues before they arise.
- 12.
There is an exception to this observation. If one is a Messianic Realist like Popper or like Peirce sometimes appears to be, one might argue that X should be concerned to minimize risk of error as assessed according to X’s prior point of view. If the ink bottle is fully believed to be present, X might then think that precommitting to the view that it is absent is deliberately courting error. Messianic Realism would support Unger’s claim that if one is absolutely certain, one should never give up the conviction. I have discussed and argued against Messianic Realism in Levi (1980, 1991). In any case, the fault for dogmatism could in that case be placed on the shoulders of Messianic Realism rather than absolute certainty.
- 13.
All of these ideas are to be distinguished from claims of infallibility for persons or for their testimony as in the idea that the Pope is infallible when speaking ex cathedra. This conception of infallibility relates to sources of information. A source of information need not be infallible even on topics concerning which the source is approved in order to be a source of knowledge.
- 14.
For illustrative purposes, I take it that minimal rationality requires that X’s state of full belief or the set of X’s full beliefs at a given time should be consistent, it should contain all the consequences of X’s state of full belief, that X should fully believe that X fully believes that h if and only if X fully believes that h, that X should fully believe that X does not fully believe that h if and only if X does not fully believe that h and that X should be opinionated as to whether X fully believes that h or does not do so.. Insofar as X’s state of full belief is representable by a set of sentences in a regimented language DML with a belief operator Bxt, every such set is a deductively closed set satisfying the axioms of an S5 modal propositional system (see Levi 1997, ch. 5 for further elaboration).
- 15.
These remarks summarize my reaction to Cohen’s ideas concerning his distinction between belief and acceptance (Cohen 1992).
- 16.
These four ways of changing doxastic commitment are considered in Levi (1980, 1991, 2004).
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Levi, I. (2010). Knowledge as True Belief. In: Olsson, E., Enqvist, S. (eds) Belief Revision meets Philosophy of Science. Logic, Epistemology, and the Unity of Science, vol 21. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9609-8_12
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