The Value of Knowledge Wolfgang Spohn Workshop Full and Partial Belief TiLPS, Oct. 20-22, 2014
Table of Contents The Issue A Brief Word on the Gettier Business Modal Theories of Knowledge Nozick’s Sensitivity Analysis (2) Pritchard’s Safety Analysis Freitag’s Normality Analysis A Discontent with Modal Theories (2) The Epistemic Interpretation of Conditionals The “Circumstances are Such That” Reading of Conditionals The Sensitivity Analysis Epistemically Interpreted (2) The Other Analyses Epistemically Interpreted Returning to the Surplus Value of Knowledge The Surplus Value of Knowledge (4) Oct.%21,%2014% The%Value%of%Knowledge% 2%
The Issue There is a well-known traditional account of the value of knowledge: Knowledge has practical value; it enables us to better reach our aims. Or in formal decision-theoretic terms: the expected value or utility of cost-free relevant true information is always positive (Savage 1954). Theorems of this kind are usually subsumed under the heading “the value of knowledge” (Skyrms 1990). However, strictly speaking, they only explain the value of true belief. There is a more recent discussion in epistemology about the value of knowl- edge asking: what is the surplus value of knowledge over and above the value of (justified) true belief? Clearly, this question presupposes an account of what knowledge is. So, it is also a Gettier-induced question. The threat behind it is: if we can’t find a good answer, we need not care about knowledge and can in particular forget about all this Gettier business. Oct.%21,%2014% The%Value%of%Knowledge% 3%
A Brief Word on the Gettier Business As is well-known this business arose from Gettier’s criticism [which we also find, e.g., in Russell and in 8 th century Indian philosophy (Dharmottara)] of the traditional JTB analysis that knowledge is justified true belief. Knowledge is not just that, but something more, which we are well advised to scrutinize. My only criticism of the obsessive scrutiny is that we have for- gotten how unclear the necessary JTB conditions are: ! What is the relevant notion of truth involved here? (Don’t say the correspondistic one only because you don’t know what else to say.) What at all is belief? (This is a very deep question, and it is surprising ! how little clarity there is in the relevant literature.) ! What is justification? (The relevant literature is shamefully missing clear accounts of that.) ( I tend to say that, from a rationalistic per- spective, all beliefs are justified. If a belief were not at least subjective- ly justified, I would be irrational to hold it. However, this remark does not absolve us from saying what justification is. ) Oct.%21,%2014% The%Value%of%Knowledge% 4%
Modal Theories of Knowledge The last remark only suggests that we won’t find a surplus value of knowl- edge over true belief within the JTB analysis. So we must attend to what “something more” might mean. Let us focus on the so-called modal theories of knowledge, for which a useful and very general scheme may be provided (cf. Freitag 2013). The scheme is this: x knows that p iff: (1) In the actual world @ p holds as well as that x believes that p , (2) The material implication “if x believes that p , then p ” – in short: B x ( p ) ⟶ p – is true in each world of the so-called warranty set K , to which the actual world @ may or must belong. They idea here is that, if x knows that p , her belief in p is guaranteed to be true, or is necessarily true (where that guarantee or necessity is not ab- solute, but restricted to the warranty set K – which is a dummy so far). Oct.%21,%2014% The%Value%of%Knowledge% 5%
Nozick‘s Sensitivity Analysis I The warranty set K may be interpreted in various ways. One possibility is the sensitivity analysis of Nozick (1981) (which is close to Goldman’s (1967) causal analysis). According to it a condition beyond JTB for x's knowing that p is (where � stands for the conditional, however it is to be interpreted – see below): (3) if p had not been the case, x would not have believed that p – formally: ¬ p � ¬B x ( p ) . According to the received Stalnaker/Lewis truth conditions of counterfactuals, (3) says that the warranty set K consists of the non- p -worlds closest or most similar to the actual world @ and all worlds at least as close than those the non- p -worlds (in which p is true). In all those worlds, (3) re- quires, ¬ p ⟶ ¬B x ( p ), i.e., B x ( p ) ⟶ p must be true. Oct.%21,%2014% The%Value%of%Knowledge% 6%
Nozick‘s Sensitivity Analysis II Nozick adds a second condition, often considered less important, which he expresses as a factive subjunctive conditional and which I try to capture thus (the intention, or hope, is here that “since” is less causally loaded than “because”): (4) since p has been the case, x believes that p – formally: p � B x ( p ) . According to the received semantics this means that in all closest p- worlds B x p is true as well. Thus, according to scheme (2), clause (4) does not add any further truth guarantee to (3), since p and hence the material implication B x ( p ) ⟶ p is true in all (closest) p- worlds, anyway. And if Centering is assumed in the semantics of � , (4) adds nothing to (1). Oct.%21,%2014% The%Value%of%Knowledge% 7%
Pritchard‘s Safety Analysis Pritchard (2005) states his so-called safety analysis also with the help of a factive subjunctive conditional, which I again try to capture with “since”: (5) since x believes that p , p is (has been) the case – formally: B x ( p ) � p . According to the received semantics this means that in all closest B x ( p ) - worlds p is true as well. Hence, according the received semantics and assuming Weak Centering, but avoiding Centering (otherwise (5) would be trivial), (5) assumes the warranty set K to be the set of all worlds closest to actuality (in which B x ( p ) ⟶ p is true, whether or not x believes that p in them). Oct.%21,%2014% The%Value%of%Knowledge% 8%
Freitag‘s Normality Analysis According to Freitag (2013) the warranty set K consists in all normal worlds in which the material implication B x ( p ) ⟶ p is true. So knowledge is a belief the truth of which is normally guaranteed. We cannot generally presup- pose that the actual world is normal, i.e., that Weak Centering holds if the similarity order is interpreted as a normality order. Hence, Freitag must explicitly assume that the actual world is normal, i.e., that @ is in K (this explains the ambiguity in (2)). So, according to his analysis, knowledge requires: (6) if x believes that p , then p is (normally) the case – formally: B x ( p ) � p (though with a different interpretation of � than in (5)). This is also a natural reading of indicative conditionals. Oct.%21,%2014% The%Value%of%Knowledge% 9%
A Discontent with Modal Theories I Now my interest is not to discuss niceties of those three variants of modal theories of knowledge. Nor is my interest to discuss whether other ac- counts also fall under the scheme (2). Let it suffice that we have a repre- sentative sample of quite plausible accounts of knowledge. My concern is rather that all three variants heavily rely on the conditional idiom (and partially even on an awkward factive version of the conditional idiom). The conditional idiom is fundamental and ubiquitous; it is philoso- phically essential not only in accounts of knowledge, but almost every- where. But it is still so ill understood that it is careless to simply assume it as the basis of any philosophical analysis. Thus, it is a problem for the knowledge theorist as well and not only for the conditional theorist. Oct.%21,%2014% The%Value%of%Knowledge% 10%
A Discontent with Modal Theories II One big problem is that the conditional idiom is so confusingly multifarious that it does not seem to admit of a unified account – whence the multitude of accounts. Another big problem is that the very graphic geometry of similarity spheres – on which the received semantics for subjunctive (not indicative) condi- tionals is based – hides how poorly we understand the similarity or closeness involved here. Our relevant intuitions exclusively derive from our intuitions which conditionals to accept. The same concern applies to Freitag’s normality analysis. Normal conditions are a special case of ceteris paribus conditions, and that’s a hornets’ nest as well; philosophers of science are quarreling for decades about an ap- propriate analysis. Oct.%21,%2014% The%Value%of%Knowledge% 11%
The Epistemic Interpretation of Conditionals I cannot discuss now conditionals (and normal conditions) in general. (I did so in Spohn (2013).) Let me only say: ! that in my view the best approach to conditionals is to see them as expressing conditional belief and features thereof, ! that we should hence turn to accounts of conditional belief like AGM belief revision theory or, much better, ranking theory (see Spohn (2012), where the ill-understood similarity orderings find an intelligible subjective ! correlate in entrenchment orderings or cardinal ranking functions. This seems to be a well explored strategy. But it is not. I seem to appeal to un- derstand conditionals via the familiar Ramsey test (according to which condi- tionals indeed simply express conditional belief). However, conditi-nals go far beyond the Ramsey test; they can be used to express other features of conditional belief beyond conditional belief itself. And this is not well ex- plored. The relevant feature for us is this: Oct.%21,%2014% The%Value%of%Knowledge% 12%
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