spohn, value of knowledge - tilburg university · knowledge has practical value; it enables us to...

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)

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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.


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 8th 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.)


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:

Bx(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).


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 � ¬Bx(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 ⟶ ¬Bx(p), i.e., Bx(p) ⟶ p must be true.


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 � Bx(p) . According to the received semantics this means that in all closest p-worlds

Bxp 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 Bx(p) ⟶ p is true in all (closest) p-worlds, anyway. And if Centering is assumed in the semantics of �, (4) adds nothing to (1).


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:

Bx(p) � p . According to the received semantics this means that in all closest Bx(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 Bx(p) ⟶ p is true, whether or not x believes that p in them).


Freitag‘s Normality Analysis

According to Freitag (2013) the warranty set K consists in all normal worlds in which the material implication Bx(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:

Bx(p) � p (though with a different interpretation of � than in (5)). This is also a natural reading of indicative conditionals.


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.


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.


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:


The „Circumstances are Such That“ Reading of Conditionals

According to the Ramsey test, what I do by uttering a conditional p � q is to express my conditional belief in q given p, B(q | p).

Another and in my view more plausible reading is that I thereby express my (unconditional) belief that the circumstances are such that I can maintain my conditional belief, or, more precisely: that I believe s, B(s), where s is the disjunction s1 � … � sn of all maximal circumstances si under which I believe in q given p, i.e., B(q | p � si) (where maximality is relative to some contextually given more or less fine-grained partition of circumstances).

This entails that B(q | p � s) and, only (!) given some further conditions, the latter entails B(q | p), i.e., the Ramsey test.

I call this the “circumstances are such that” reading of conditionals. A special case is the most wide-spread causal reading of conditionals (which is, in fact, a “history is such that” reading).


The Sensitivity Analysis Epistemically Interpreted I

Let’s apply this, for instance, to Nozick’s sensitivity analysis (3). According to the epistemic interpretation we are not after the truth condition of a knowledge ascription, but rather after which beliefs a ascriber z ex-presses by ascribing knowledge to the subject x.

According to Nozick, if z ascribes to x knowledge of p, z thereby claims: p, Bx(p), and ¬p � ¬Bx(p). And according to the “circumstances are such that” reading of �, z thereby expresses Bz(p), Bz(Bx(p)), Bz(b3), and Bz(¬Bx(p) | ¬p � b3) – where b3 may be called the knowledge background, or rather the knowledge ascription background, which is defined in the same way as the disjunction s of maximal circumstances on the previous slide. (The subscript “3” refers to Nozick’s condition (3).)


The Sensitivity Analysis Epistemically Interpreted II

The knowledge background b3 is an objective proposition which is true or false, but it is subjectively defined relative to the conditional beliefs of z. z takes it to be true, but she may be wrong, of course.

The knowledge background b3 is characterized by a peculiar stability, which consists in the fact that any additional information c, as long as it is logi-cally compatible with b3, does not change the relevant conditional belief of z, i.e., for any such c we have Bz(¬Bx(p) | ¬p � b3 � c).

This does not hold generally. In general, a conditional belief is not preserved under additional logically compatible information. The reason why the background b3 has this stability property lies in its definition as a disjunc-tion of maximal circumstances. This stability will prove important for my argument below.


The Other Analyses Epistemically Interpreted

Similarly, Nozick’s condition (4) translates into the condition that the ascriber z claims that p � Bx(p) and thus has some background b4, for which Bz(b4) and Bz(Bx(p) | p � b4).

Furthermore, Pritchard’s condition (5) translates into the condition that the ascriber z claims that Bx(p) � p and thus has some background b5, for which Bz(b5) and Bz(p | Bx(p) � b5).

Finally, Freitag’s normality analysis yields something similar in an epistemic interpretation of normal conditions. Condition (6) then translates into the condition that the ascriber z claims that Bx(p) → p under normal condi-tions and thereby expresses Bz(b6) and Bz(p | Bx(p) � b6) for some dis-junction b6 of maximal normal (≈ not unexpected) conditions.

The backgrounds b3 – b6 may differ (because Nozick, Pritchard, and Freitag subtly differ). But all of them have the stability mentioned. And it would be an instructive exercise to find conditions under which they fall in one.


Returning to the Surplus Value of Knowledge

Plato‘s Meno is often interpreted as offering a stability theory of knowledge: “True opinions are … a fine thing and altogether good in their effects so long as

they stay with one. … they are not worth much until one ties them down by reasoning out the explanation … then … they become items of knowledge, and … permanent. And that’s what makes knowledge more valuable than right opinion, and the way knowledge differs from right opinion is by being tied down.”

This resembles the JTB analysis often associated with the Theaitetos, but goes beyond it by adding the stability idea. However, reasons as such don’t help. As I said, in a rationalistic perspectives beliefs always come with reasons. And in general, reasons come and go and may be as unstable as beliefs.

So, how can the stability idea be understood within the framework I have deve-loped? (Rott (2004) was the first to pursue this idea in the belief revision framework.)


The Surplus Value of Knowledge I

If an (empirical) proposition is true, we will eventually find reasons for taking it to be true in Peirce’s ideal limit of inquiry (which is extremely counter-factual in various ways). (We may leave it open whether we can thereby define a notion of truth, though I tend to think so.)

So, if I now believe p, I take p to be true – this is one and the same. Hence I also believe that this belief will survive in the ideal limit of inquiry. It is my everyday experience, though, that I have to give up and revise my beliefs, although, when I believe p, I at the same time believe that this will not happen to my belief in p. However, once I should have given up my belief in p, I likewise do not expect it to return.

The same is true from the ascriber’s perspective. If she ascribes me a true be-lief, she simply shares my belief, we may both be wrong, and her belief is subject to the same dynamic instabilities as mine.


The Surplus Value of Knowledge II

How do things stand if the ascriber z ascribes me (= x) knowledge of p? Of course, she may be wrong again. However, there is still a difference:

First, she again shares my belief; i.e.: Bz(p) and Bz(Bx(p)). She does more, however. She also believes in the knowledge ascription back-

ground b (where I now neglect the differentiation by indices); i.e.: Bz(b). And given this background, she believes Bx(p) given p and/or ¬Bx(p) given ¬p, or perhaps more neutrally, that p is a reason or positively relevant for Bx(p) in the sense that her degree of belief in Bx(p) is higher given p than given ¬p.

Moreover, this reason relation or positive relevance between p and Bx(p) is stable in the sense that no information logically compatible with b can change anything about it.


The Surplus Value of Knowledge III

This puts the ascriber into a better position: If she simply takes p to be true (and be-lieves that I do so, too), she does have some reason for that, but maybe a wrong reason; and she also believes that eventually, in the ideal limit, there will be true reasons for maintaining the belief in p.

However, if she ascribes knowledge of p to me, then she has a specific (conditional) reason for p, namely Bx(p), that I believe in p, and moreover this reason will persist, at least as long as her background b is not defeated.

This improves the warrant which the ascriber has for the truth of my belief. If the ascriber merely believes p (perhaps because she trusts me), this belief may be undermined by any reason against p. However, if she thinks that I know p, then not any reason against p will undermine her belief in p. Rather, the entire back-ground b would have to be defeated, before anything could count against p.

(It is a general advantage of explanations that they provide stable reasons in this sense, and the ascriber has some particular explanation for my belief, if she ascribes knowledge to me.)


The Surplus Value of Knowledge IV The final move is: The very same holds within the first-person perspective. I

myself can distinguish between believing p and believing to know p. Well, almost the same: I cannot presently take the third-person perspective on

myself. I am conscious of the fact that I presently believe that p. And this conscious fact bears no justificatory relations; all possible reasons pertain only to the content p and not to that fact that I now believe that p.

However, concerning my past (and my future) beliefs I can very well take the third-person perspective. And then I need not take each of my previously acquired beliefs to be knowledge, precisely because I need not believe in the knowledge background required for the belief to be knowledge. This is how I can distinguish between believing p and believing to know p.

But if I believe in the relevant knowledge background for p, then my belief in p is, as described, more stable than the mere belief in p. This, I take it, is the surplus value of knowledge for me.


Many thanks

For your attention!


Bibliography

Freitag, Wolfgang (2013), I know. Modal Epistemology and Scepticism, Mentis, Münster. Goldman, Alvin I. (1967), “A Causal Theory of Knowing”, Journal of Philosophy 64, 357-372. Nozick, Robert (1981), Philosophical Explanations, Harvard University Press, Cambridge, Mass. Pritchard, Duncan (2005), Epistemic Luck, Oxford, Oxford University Press. Rott, H. (2004), „Stability, Strength and Sensitivity: Converting Belief into Knowledge“, Erkenntnis,

61, 469-493. Savage, Leonard J. (1954), The Foundations of Statistics, New York: Wiley, 2nd ed.: Dover 1972. Skyrms, Brian (1990), The Dynamics of Rational Deliberation, Cambridge, Mass.: MIT Press. Spohn, Wolfgang (2012), The Laws of Belief. Ranking Theory and its Philosophical Applications,

Oxford University Press, Oxford. Spohn, Wolfgang (2013), “A Ranking-Theoretic Approach to Conditionals”, Cognitive Science 37,

1074-1106.


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