Contextualism

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Contextualism and Knowability

February 27, 2009 in Epistemology, Logic | Comments closed

I have been thinking about Fitch’s paradox again, and it seems to me that a very generic contextualist solution is available. The knowledge operator is said to be a three place relation, Katp, between (1) an agent, (2) a time, and (3) a proposition. The contextualist argument modifies this relation to include context in some way. In other words, context governs shifting standards in play when attributing knowledge. This modification, then, may be represented by adding an index to the knowledge operator, something like an ordered pair, <f,n>, representing a set of standards ‘n’ relative to an information state ‘f’. In other words, we have a factual component representing the information a particular context makes accessible, and a normative component which supervenes on the factual component.1 Abbreviating this pair as ‘c’, we have the knowledge operator now represented as a four-place relation Katcp. Given this generic representation of context, the variable ‘c’ may shift in two directions, either (a) the standards in play may be strengthened or weakened or (b) the information-state of the agent may change. While a change in information-state will tend to shift the epistemic standards in play, it is not necessary that these two variables shift in tandem, for there are many examples of context shifting due to the introduction of new information that does not specifically undermine particular knowledge claims.2

Given this framework, a preliminary objection could be made that there is no operator to shift the context, but I think that the recent to-do about competent deduction closure schemas presents an efficient method for introducing such an operator. That is to say, when one is in a position-to-know some proposition, whatever operator is introduced to show a deduction being made would be sufficient to shift the context ‘c’. This is due to the introduction of new information–the move from evidence to knowledge–which could potentially raise or lower the supervenient standards.3

Now for the paradox of knowability. To be brief4, the core of the paradox lies in a reductio ad absurdum:

(1) K(p & ~Kp) Assumption
(2) Kp & K(~Kp) (1), K-Closure
(3) Kp & ~Kp (3), K-Factive

Where (2) follows from (1) given that knowledge distributes over conjunction, and (3) follows from (2) provided that knowledge is logically stronger than truth. Now, a competent deduction closure schema would modify the move from (1) to (2), limiting the conjuncts in (2) to just the set of some agents evidence, where said agent would have to preform a competent deduction on her evidence in order to infer the contradiction in (3). Given the preceding framework, however, this deduction would shift the context parameter between the left-hand-side and right-hand-side of (3):

(1) Kc(p & ~Kcp) Assumption
(2) Ep & E(~Kcp) (1), CD-Closure
(3) Kc’p & Kc’(~Kcp) (2), Competent Deduction
(4) Kc’p & ~Kcp (3), K-Factive

Here (2) notes that some agent is in a position to know the conjuncts of (1), but the move from (2) to (3), the deduction itself, shifts the context. New information is introduced. In other words, if knowledge is closed under position-to-know, then there is a relationship between the information one has access to in any given context and the potential extensions of said information, but once one does in fact extend said information the information-state denoted by ‘f’ in ‘c’ has changed.

  1. I should note here that I am oversimplifying things by characterizing ‘f’ as factual, for I would think that the information accessible given any context would consist not only of facts, but also the salient possibilities of error, the set of presuppositions in play, and possibly many other components which would be relevant to the supervenient norms. ↩
  2. This is going to localize knowledge in much the same way Jonathan Schaffer’s contrastive account does, and I have to say that I have benefited greatly from my antecedent work on his contrastivism. Additionally, I have to thank Jonathan Kvanvig for the many conversations regarding the issues involved in the paradox of knowability as well, for without his teaching I would not have the grasp I do on the intricacies of this particular problem. ↩
  3. I have to thank Ryan Wasserman here for pointing out that the position-to-know closure schema might be available to do some extra work regarding a solution to this paradox. ↩
  4. Given that this is just a blog, I am here summarizing the germ of an idea on which I intend to capitalize in a more formal manner in the weeks to come. For additional information on this paradox, see my posts here and here, or the SEP entry here. ↩

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Upcoming Conferences

January 17, 2009 in Epistemology, Logic, Philosophy of Language | Comments closed

Two interesting conferences in the works:

Workshop: “Epistemology, Context, Formalism”

Focusing on a very interesting and underdeveloped area of research, with an incredible keynote lineup (as seen on Certain Doubts):

  • Context and Epistemology. In the last decades epistemology has seen a major “linguistic turn”, through the increased reliance, in contemporary debates, on syntactic, semantic and pragmatic “evidence” about ordinary (uses of) linguistic constructions in terms of “know”, most notably as a result of the flourishing discussions over the epistemological relevance of various notions of context (of inquiry, of attribution, of assessment, etc.).
  • Epistemology and Logic. In addition to its “linguistic turn” epistemology has also seen a “logical turn”, through the recently revived and rising conviction that discussions in mainstream epistemology may benefit from formal epistemology (epistemic logic, formal learning theory, belief revision, and so on) which, however, has had close to nothing to say about context (modulo a few exceptions).
  • Logic and Context. While well-known approaches to context can be found in natural language semantics and pragmatics, the only logics of context properly speaking are to be found in theoretical computer science where, however, the main logical treatments of context owe nothing or so to philosophy (again, modulo a few exceptions).

CFP: “New Directions in the Theory of Presupposition”

As seen on Kai von Fintel’s blog, the description provides an excellent summary and list of references in the current areas of research:

The last ten years has seen a wealth of new developments on the topic of presupposition and, in particular, the projection problem for presupposition. While there had been considerable interest in the seventies in developing entirely pragmatic accounts of presupposition triggering and projection (Wilson, 1974, Stalnaker 1977, Grice, 1981), these accounts had generally not been sufficiently developed to match the dynamic accounts developed in the eighties in predictive power. Recent work, such as that of Schlenker (2006, 2008), however, has shown that broadly pragmatic accounts can also have considerable predictive power. In addition, trivalent approaches based on such techniques as supervaluations and the Strong Kleene connectives, which were dismissed by many long ago, have recently attracted new interest (Beaver and Krahmer, 2001, George, 2008, Fox, 2008) and have been shown capable of handling many empirical issues in presupposition projection. Thus there is no longer a clear consensus on how we should explain presupposition projection. In addition, experimental work has raised interesting questions about what the basic facts of presupposition projection are and suggests that real empirical work is needed to determine some of the subtleties (Chemla 2007). There has also been renewed interest in the triggering problem (Simons, 2001, Abusch, 2002) which naturally links up to the projection problem, as well as recent theoretical work on foundational issues such as the notion of common ground and accommodation (Beaver and Zeevat, 2004, von Fintel, 2001, 2006, Stalnaker, 2002). The purpose of this workshop is to bring together researchers on presupposition to discuss these new developments and connect some of the different theoretical and empirical questions, which are too often considered in isolation.

We invite submission of abstracts from linguists, philosophers, and cognitive scientists, addressing formal or foundational issues about theories of presupposition, or offering new empirical perspectives that bear on them. We especially encourage papers that address questions about the explanatory depth of different theories or the triggering problem, or introduce new forms of experimental or empirical evidence relevant to adjudicating between theories of presupposition.

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Schaffer on Evidence

January 11, 2009 in Epistemology | 2 comments

In what follows I will point to a problem in Jonathan Schaffer’s conception of evidence given his contrastive epistemology. I will outline Schaffer’s substantive epistemic conditions, followed by an argument which points to certain implications of Schaffer’s theses amounting to an account of evidence which is factive. This factivity of evidence is problematic, however, as the conditions on evidence are weaker than those on knowledge.

Schaffer provides several substantive theses for his contrastive execution of the contextualist proposal that knowledge is the elimination of relevant alternatives. Specifically, Schaffer proposes three necessary and sufficient conditions for knowledge:

(K) Kspq iff:

  1. p,
  2. S has proof that p rather than q,
  3. S is certain that p rather than q on the basis of (2).1

The first condition states that knowledge is factive, or logically stronger than truth. In this case, then, the entailment Kspq→p holds. The second condition is Schaffer’s interpretation of a justification condition, one which he calls restricted infallibilism about evidence. Proof, so defined by Schaffer, is conclusive evidence, evidence defined in terms of Lewisian elimination:

(Elim) possibility p is eliminated for S (at t) iff p is inconsistent  with S’s total experience e (at t). S has conclusive evidence that p rather than q, on this interpretation, iff q is eliminated for S.2

This infallibilism is restricted, however, in terms of the context partition ∏, where the space of eliminable possibilities are just those ‘live options’ relevant to the conversation. The final condition is that of belief with the addition of a basing clause, what Schaffer terms restricted indubitabilism about belief. One’s belief must be indubitable in that one must be certain, or lack any doubt, of p’s truth. Further, it must be properly based, which is a causation-rationality hybrid:

(Base) S’s proof must be a rationalizing, non-deviant cause of S’s certainty.3

This condition is restricted in the same fashion as (K.2), where the space of possibilities open to doubt are just those members of the context partition ∏, the possible answers to the question under discussion.

Given that Schaffer relies on a position-to-know closure schema4, it would behoove him to sharpen his definition of evidence. Evidence is defined as the ternary relation Espq, which consists in both the elimination of the alternatives q to p and some positive support for p. I assume, from his brief discussion, that evidence also imports all those contrastive qualities previously discussed of knowledge concerning the contrast variable q, and that elimination is defined as previously noted in (K.2) and (Elim). These provisions prompt an additional question, however, as to Schaffer’s commitment to the factivity of evidence. Due to the wording of (K.2) and (Elim), proof of p rather than q consists in S having conclusive evidence, a restricted infalliblism about evidence. This definition needs clarification, as conclusivity could break in one of two directions:

  1. Evidence could be conclusive in the objective sense, which would clearly amount to the truth of p, or
  2. Evidence could be considered conclusive in the subjective sense, which might be considered as some high level of credence obtained by S.

We must remember here that Schaffer considers evidence as the elimination of salient relevant alternatives to p, and what must be conclusive is not so much the truth of p directly, but the elimination of the context parameter q. Further, there must be some unspecified level of positive support for p. Evidence would then seem to provide support for p indirectly, through the infallible elimination of salient alternatives q.

The use of the term infallible here would seem to point to (1) rather than (2), for if one were to be wrong about one’s elimination of q in the objective sense, one could not consider one’s evidence infallible. If the term used were perhaps a restricted dogmatism about evidence, then perhaps (2) might be tenable. Differently put, (2) would seem to be a misled view of evidence for reasons regarding the level of credence necessary to be committed to the proof of one’s evidence. If the level of credence necessary for proof is to be considered the subjective probability of 1, then one would be committed to a level sufficient to that for which one might rationally bet one’s life on one’s evidence. It is quite difficult to find many contingent propositions that a rational human being would bet one’s life on. As such, to be committed to the proof of the evidence of contingent propositions to the point that it is conclusive would be taking a quite dogmatic stance on one’s evidence.

Given this, it would seem that (1) would be the more appropriate stance considering Schaffer’s comments on evidence. To be clear, however, it is not that the evidence for p is infallible; rather, it is the evidence against q, as the evidence for p may be minimal at best. As such, (1) may be restated as the necessary condition:

  1. S has evidence for p if S has established the falsity q.

This condition would commit Schaffer to the inference rule Epq→~q.

This entailment is unsettling. For, if we are to assume, given Schaffer’s contrastive modification of evidence, that p and q are pairwise exclusive for the evidence relation as they are for the knowledge relation5, the further entailment must hold: Epq→((p & ~q) v (~p & q)). Putting these together, by conditional proof, provides: Epq→p6. And thus evidence is factive. This is a troubling result, as Schaffer does not stipulate the necessity for much, if any, positive support for p. As such, the truth of some proposition p may be obtained simply by the elimination of all salient relevant alternatives to p. The question must be posed to Schaffer, then, regarding the status of contexts in which all but one alternative is eliminable but actuality is not salient. In cases such as these it would seem that one’s evidence would entail the truth of p, even if p is false.

For example, suppose that in a fit of passion, a man, Jim, stabs another, Bob, in an obviously critical fashion, in the midst of a crowded room. The room is populated by both witnesses to the scene as well as police officers. The officers, true to their role, capture Jim and begin interviewing witnesses as to the question of the perpetrator of Jim’s murder. Evidence amounts quickly intimating Jim to the point of the elimination of all salient alternatives to the participants of this particular context. Unbeknownst to anyone in this circumstance, however, Bob has some undiagnosed heart problems; specifically, his health is such that a blood clot stopped his heart just milliseconds before the knife hit, rendering the knife wound epiphenomenal to Bob’s death. As such, direct perceptual evidence of Jim’s attack provides the elimination of those possible alternatives that some other perpetrator might have stabbed Bob, and Bob’s lack of vital signs provide direct evidence of his death. Coupling these pieces of evidence allows for the elimination of all those alternatives to Bob’s murderer other than Jim, with the possibility of Bob dieing of natural causes outside the epistemic range of those involved. This situation, then, provides all that is needed to imply the truth of the proposition p: {Jim is Bob’s murderer}, even though the truth of p diverges from actuality.

Initially, a stipulation along the lines of Lewis’s rule of actuality might seem fitting, where actuality is always relevant, but this rule fails to draw out how exactly actuality would be taken into account in a case such as that of Jim and Bob. In such cases, it would seem the agents within the context would be afflicted by some form of presupposition failure, giving the actuality rule an ad hoc flavor. Further, the way in which the question might be presented within the context could eliminate actuality as a viable member of the answer partition—this could be provided for in the previous example by noting that the police interrogating witnesses provide a lineup and state the question explicitly. When the question is posed in this way, the rule of actuality would contradict a previous stipulation of Schaffer’s, that when the question under discussion has some explicit possible answers, the answers countenanced must be set to the explicit values.7

  1. Schaffer, Contrastive Knowledge (2005), p. 255 ↩
  2. Schaffer, Contrastive Knowledge (2005), p. 255, p. 255 fn. 2, additionally, see Lewis, Elusive Knowledge (1996) ↩
  3. Schaffer, Contrastive Knowledge (2005), p. 255 fn. 3 ↩
  4. Cf. Schaffer, Closure, Contrast, and Answer (2007) ↩
  5. Schaffer, Contrastive Knowledge (2005), p. 239 fn. 5 ↩
  6. Proof. Assume Epq for the purposes of a conditional proof. ((p & ~q) v (~p & q)) is implicated by pairwise exclusion. Assume (p & ~q) for the purposes of v-elim, obtaining p by &-elim on (p & ~q). Assume (~p & q) for the purposes of v-elim, obtaining p by explosion given q by &-elim and ~q by the implication in (1) above. Discharging the v-elim provides p, further discharging the conditional proof provides Epq→p. ↩
  7. Cf. Schaffer, Closure, Contrast, and Answer (2007), p. 251 fn. 19 ↩

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