Epistemology

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Whats Next? (Epistemic Parity)

October 21, 2009 in Epistemology | No comments

So in my last post I did a bit of negative work, but I do think that Independence is something to be maintained if possible. In the very least it prevents question-begging and bootstrapping from occurring, and while it might be possible to develop some kind of theory which deals with these worries independently, independence cuts quite cleanly on these issues. So, in the next few posts I plan on a bit more negative work and then some positive stuff (hopefully). First, I would like to look at personal information with a bit of a magnifying glass. I don’t think any way of cashing this notion out is going to do what we want with respect to epistemic parity judgments1. In particular, I think either the appeal to personal information as a symmetry breaker will either violate independence itself or will need to be incorporated universally. If it is incorporated universally, however, we will be in a position where we evaluate ourselves as epistemic peers with those who have access to more first-order evidence than we do (since we have access to internal evidence as a counterweight)2.

After these arguments, I will look at one or two possible positive theses. First, I think that perhaps we can get out of the evidence assymetry problem mentioned above by conditionalizing on the reliability of the testimony and jettisoning the evidence equality assumption altogether, but this program is going to need some chisholming, as we are going to have a generality problem looming regarding the process type or reference class we are specifying. Second, perhaps in conjunction with the first, we might move from a naive view of the disagreement with respect to a proposition p or ~p to a contrast class3. Given that in cases of disagreement we can individuate a particular question under discussion, we can determine a set of relevant possible alternatives to conditionalize on, and in this manner we can cut out the hard cases without violating independence.

  1. Now, a distinction should be made here. If we are rejecting independence and adopting a steadfast view, personal information might have some other use. But I think this might be problematic for similar reasons to those I will forward. ↩
  2. Tim Sundell brought this point up in conversation. ↩
  3. This kind of move was made relative to an analysis of knowledge by Jonathan Schaffer, and the suggestion that it might apply fruitfully to disagreement was made by Fabrizio Cariani. ↩

Epistemic Parity

October 20, 2009 in Epistemology | No comments

The literature on the Epistemology of Disagreement has been primarily characterized by two opposing views: the steadfast and conciliatory. The steadfast view proposes that, in the context of peer disagreement, certain factors allow one to hold one’s ground. That is to say, the evidence provided by peer disagreement is weak—not something that would generally require belief revision. The conciliatory position, on the other hand, places great weight on the evidence provided by the fact that two epistemic peers disagree. The conciliationist bases the particular weight given to peer disagreement on the principle that if epistemic parity is indeed maintained, one should have no reason to discount one’s peer. Provided this, the question remains as to how one might certify an epistemic peer in such a way as to prevent question-begging downgrades based on the content of the disagreement itself. Given this problem, the conciliationist requires a regulatory principle: independence. This principle certifies that the evaluation of an epistemic peer should take place antecedently to the disagreement in order to prevent such downgrades of parity. It will be the purpose of this paper to argue that the current conciliationist resolution to certain hard cases of disagreement either violates or trivializes this principle. To establish these results, I will (1) outline the principle in full detail, (2) provide an example case in which independence becomes problematic, (3) detail the arguments provided to resolve this case in which independence is purportedly maintained, (4) argue that these results either violate independence outright or force modifications to the principle in such a way that it becomes epistemically vacuous, and (5) develop some possible alterations available to the conciliationist that might salvage the independence principle.

The most recent concilliationist formulation of independence is provided by David Christensen (draft, 2008), the principle is stated thus:

Independence. In evaluating the epistemic credentials of another’s expressed belief about P, in order to determine how (or whether) to modify my own belief about P, I should do so in a way that doesn’t rely on the reasoning behind my initial belief about P.1

It is important to note here that independence as stated provides a necessary condition on epistemic parity: parity must be established independently of one’s reasoning about the content of the disagreement. In order to establish independence of this nature, Adam Elga (2006) provides necessary and sufficient conditions on epistemic parity thus:

A counts B as an epistemic peer with respect to an about-to-be judged claim if and only if S thinks that, conditional on A and B disagreeing about the claim, A and B are equally likely to be mistaken.2

These conditions specify that parity must be established antecedently to the disagreement, and such parity is represented by the equality:3

(EP) Pr(A is right whether p | A and B disagree whether p) = Pr(B is right whether p | A and B disagree whether p)4

Given this characterization, nothing has yet been said regarding the factors upon which such a parity evaluation must stand. Christensen, however, has recently provided two tentative requirements:

(A)  One’s dispute-independent assessment of her epistemic credentials yields high estimates for:

  1. The likelihood that her expressed disagreement is sincere,
  2. Her degree of informedness, and
  3. The likelihood of her having reasoned correctly from the evidence she has;

and,

(B) The reasons for one’s assessments of (a)-(c) are strong.5

Given these requirements, (PH) can be reformulated thus:

(EP’) Pr(A is right whether p | A is sincere & A is well informed with respect to p & A is basing her reasoning on her evidence) = Pr(B is right whether p | B is sincere & B is well informed with respect to p & B is basing her reasoning on her evidence)

So, if one has antecedently judged that one’s interlocutor satisfies (PH’), and such a judgment satisfies condition (B), which is just to say that one is doxastically justified in one’s assessment of (EP’), one is then in a position to split-the-difference when a disagreement with respect to p arises6.

Given the preceding characterization of the conciliatory position, I will now outline a (very familiar) case that serves to problematize the position:

Splitting the Check. Suppose that I am going to dinner with my friend. We often dine together, and she has never given me reason to doubt her abilities to perform mathematical calculations on the fly. We often split the bill, and on this occasion we have decided to do just that. On previous occasions, we have come to agreement over the price of our shares, and my friend has a very good track record with respect to splitting the check. On this occasion, however, I come to the conclusion that the split is $43, and she comes to the conclusion that the split is $430.7

Given this case, and provided that there are no antecedent consideration relative to the context of disagreement that would cause me to downgrade my compatriots status as an epistemic peer, such as the consumption of a few bottles of wine, it would appear that (PH’) would easily be established pre-disagreement. Further, given the track record we have relative to this kind of occasion, it is conceivable that I am in fact justified in my assessment. But this seems to be a case where my compatriot is clearly in error. And we can fill out the background information of this case to extenuate this error: consider, for example, that no item on the menu is priced higher than $25, and we have not been overindulgent and ordered multiple meals. Given these considerations, it would seem that the conciliationist would require me to lower my credence in the proposition that the split is $43. Neither Elga nor Christensen sit comfortably with this result.

In hard cases such as this, the conciliationist appeals to counterfactual considerations in order to break the peerhood symmetry. The basic line is that, while the original probability function in the right-hand-side of (EP’) provides an equality, there is a possible alternative probability function PrC(B is right whether p | B is sincere & B is well informed with respect to p & B is basing her reasoning on her evidence & B is malfunctioning cognitively) that does not satisfy this equality. Given that were I to conditionalize in this way, I would not consider B my epistemic peer, it is clear that in cases where my compatriot’s answer is in fact crazy, I should downgrade her peerhood status.8 Christensen makes this move by an appeal to personal information, a concept introduced by Lackey (forthcoming), where it is observed that one has access to additional evidence about “the normal functioning of one’s own cognitive faculties.”9 Christensen further extends this kind of information to include information regarding your estimation of the sincerity of your judgement. These considerations lead to the ability to asses the various aspects of the conditionalization relative to the contextual information available after the disagreement has occurred, and given these considerations, were these circumstances to arise, I would again be able to downgrade the peerhood status of my compatriot by instantiating a different probability function than that of my original parity judgment.10

Both Elga and Christensen claim that this kind of downgrading is independent of the content of the disagreement. This is an odd claim. Looking diachronically at the Splitting the Check case, it would seem that we have the following temporal ordering of events:

t0: A and B agree to split the check, and calculate their respective answers to the question whether p. Given the information available, A and B then make a parity judgment relative to (EP’).

t1: A proposes that the split is $43, and B proposes that the split is $430.

t2: Given the new information available, and realizing that something has gone horribly awry, A makes a judgment to the effect that B’s peerhood status with respect to A is downgraded.

Now, given that t1 represents the content of the disagreement, it is difficult to see how a judgment made by A at t2 is independent of the said content. For without the new information introduced by t1, there would be no reason to change B’s parity status. Claiming that the information upon which A made a parity judgment is purely contextual, and thus not relevant to the content, does not help either, for any relevant contextual pre-disagreement information would be exhausted in the initial parity judgment. Any additional information would have to be inferred from the content of the disagreement, and an inference based on the content of the disagreement fails to satisfy the condition in Independence such that one’s reasoning be independent of the reasoning behind one’s initial belief that p. For the content of the disagreement is based on one’s initial reasoning about p, and the reasoning involved in t3 is based on the content of disagreement. It is simply one step removed.

Even if we were to grant that independence is not violated in this case, what would prevent one from, by parity of reasoning, making a counterfactual judgment such that an alternative, equality violating, probability function is introduced: PrQB(B is right whether p | B is sincere & B is well informed with respect to p & B is basing her reasoning on her evidence & B is mistaken whether p). It would seem that, in any case of disagreement, one could simply appeal post-disagreement to a probability function such as this in order to downgrade the status of one’s peer. If the purpose of Independence were to prevent question-begging maneuvers such as this, it would seem that it has ceased to function as a regulatory principle. Thus, it seems that either the conciliationist has violated independence by a chain of reasoning based indirectly on the initial reasoning about the question whether p, or the regulatory function of the principle itself has been trivialized.11

How, then, should we consider the claim made both by Christensen and Elga that the line of reasoning adopted in the above case is independent of the reasoning about the disagreement? It looks initially like this kind of counterfactual consideration could possibly be some kind of safety or sensitivity constraint on one’s epistemic parity judgment, and, if so, taking into consideration the above constraints, we might have some necessary and sufficient conditions for judgments of epistemic parity like this:

(JEP) S judges S’ an epistemic peer iff

(1) (EP’) is satisfied,

(2) S is justified in (1),

(3) S bases S’s (1)-Judgment on (2), and

(4) If S’ were not an epistemic peer of S, S would not judge S’ to be an epistemic peer.

Now, in this case (4) is a sensitivity requirement. In other words, S’s judgment of epistemic parity must align with what is in fact the case regarding S’. So, in the Splitting the Check case, S would violate (4) if S did not pick up on some symmetry breaking contextual information that violates (1) prior to the disagreement occurring. (JEP) looks like it accomplishes that which the conciliationist is attempting with his response to the Splitting the Check case, but I think it is going to end out too strong. The force of the previous case is just that there is no antecedent information, contextual or otherwise, that breaks the symmetry. It is only post-disagreement that one finds that there is some problem with S’. Thus, (4) looks to be too easy to violate. In any normal case of disagreement, where (1), (2), and (3) are satisfied, there will be possible worlds in which S’ has some sort of hidden cognitive malfunction which delivers illicit answers to the question under discussion.

Given the preceding considerations, perhaps (JEP) might benefit from a safety condition:

(4′) If S were to judge S’ to be an epistemic peer, S’ would be an epistemic peer of S.

If satisfaction of (EP’) is our definition of epistemic peer, however, then it looks like we run into problems similar to the sensitivity constraint. To be clear, the reasoning in (1) comes antecedently to the disagreement. In all of those cases where there is some hidden form of cognitive malfunction, the state of information previous to the disagreement is such that S would evaluate S’ correctly relative to (EP’). It is only after the judgment that the additional information becomes available, and it is only relative to this information-state that the safety constraint would become substantive. But this is not the point at which the parity judgment takes place.

In conclusion, I have developed some conditions on epistemic parity and epistemic parity judgments amenable to the conciliationist, but it is not initially clear how these judgments successfully navigate the hard cases of disagreement in a way that does not violate or trivialize Independence.

 

  1. Cf. Christensen, David (manuscript). ↩
  2. Elga, Adam (2006) p. 13 fn. 21. ↩
  3. I have to thank Fabrizio Cariani for making this point initially in Jennifer Lackey’s Epistemology Seminar. ↩
  4. Here ‘Pr’ is cast in terms of credence. ↩
  5. Christensen, David (Manuscript) p. 27. ↩
  6. I am glossing (B) here a bit, for Christensen does not specifically note that one must have good reasons. ↩
  7. This case is due in its original formulation to Christensen (2007). ↩
  8. Cf. Elga (2006) p.19. ↩
  9. Lackey, Jennifer (forthcoming) p. 14. ↩
  10. Cf. Christensen (manuscript) p. 14-15. ↩
  11. This general kind of argument has been made by Lackey, from what I understand, in correspondence with Christensen. ↩

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The Amherst Lecture in Philosophy

October 20, 2009 in Epistemology | No comments

The Amherst Lecture in Philosophy has published Lecture 4: “Probability and Danger”, Timothy Williamson.

Abstract: What is the epistemological structure of situations where many small risks amount to a large one? Lottery and preface paradoxes and puzzles about quantum-mechanical blips threaten the idea that competent deduction is a way of extending our knowledge (MPC). Seemingly, every- day knowledge involves small risks, and competently deducing the conjunction of many such truths from them yields a conclusion too risky to constitute knowledge. But the dilemma be- tween scepticism and abandoning MPC is false. In extreme cases, objectively improbable truths are known. Safety is modal, not probabilistic, in structure, with closure and factiveness conditions. It is modelled using closeness of worlds. Safety is analogous to knowledge. It suggests an interpretation of possible worlds semantics for epistemic logic. To avoid logical omniscience, a relation of epistemic counterparthood between formulas is introduced. This supports a safety conception of knowledge and formalizes how extending knowledge by deduction depends on logical competence.

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Finkish Epistemic Peers

June 29, 2009 in Epistemology | No comments

My recent trip to Chicago was a success, and I had a great time at the Disagreement Conference1. While there were many excellent presentations–with Roger White, Sherri Roush, and Branden Fitelson’s presentations (in order of appearance) being my favorites–, I have one persistent worry that I noticed unaddressed throughout the conference. In other words, when considering the epistemic significance of disagreement, the presenters tended to bracket the considerations by excluding those who were not considered epistemic peers in some form or fashion. This kind of bracketing took many different forms, from considering the general reliability of the testimonial reports of the agent to whether the agent was epistemically virtuous. The worry I have is this: when considering whether one is an epistemic peer, it would seem that the primary method of analysis is that of attributing a dispositional property, and when attributing such a property, one tends to run into the problems of the conditional fallacy. In what follows I will take an unrefined notion of epistemic peerhood, requiring only that it be considered some form of dispositional property of an agent, and look at several possible sharpenings of a familiar thought experiment in the disagreement literature which will serve to develop some problems for such a dispositional analysis.

A dispositional analysis of epistemic peerhood can be stated thus:

P. Necessarily, a subject S is considered an epistemic peer iff were S to be in some context of disagreement, some dispositional property M would emerge.

The dispositional property involved here will differ with the particulars of the theory in question. To simplify the exposition, I will consider the manifestation property of peerhood to be reliability of testimonial reporting relative to the kind of dispute in question.

Now, for the example, I will use the classical disagreement over a restaurant bill:

Suppose agent A and agent B are splitting the bill at a restaurant. Both agents see the price of the bill, and, on the basis of some quick mental math, come to the conclusion that a certain amount is owed. Agent A asserts that the amount owed is $42, while agent B asserts that the amount owed is $45.

In this case both A and B have access to a shared set of evidence, the cost of the bill, and, given that the numbers do not match, they are in a context of disagreement. To demonstrait the finkishness of epistemic peerhood, it will not be necessary to stipulate which member of the disagreement is correct, but we will consider A to have both sound mathematical reasoning abilities and to be a generally reliable purveyor of testimonial knowledge. In what follows, I will provide three separate cases in which B’s disposition to be A’s epistemic peer is finked. First, B’s disposition will be masked, and then two separate cases of dispositional mimicking will be considered.

For the first case, suppose B is generally reliable in mathematical calculations, has no problems with mental math, and in fact preforms calculations of the sort required for splitting the bill every day without error. Further, B is able to record her calculations reliably in her mathematics notebook. It just so happens, however, that due to randomly occurring crippling social anxiety, the majority of the time B is interacting with other people, her mathematical acuity diminishes severely. When this social anxiety occurs, B can only provide approximate yet unreliable guesses when considering mathematical problems such as that provided above. Further, it just so happens that in all actual cases of disagreement, B has been beset by said social anxiety.

For the second case, suppose that B is actually an incompetent mathematician, such that even the most simple arithmetic problems are incomprehensible. B has, however, survived thus far by a series of incredibly lucky random guesses. B has never mentioned to her so-called peers that she is incompetent, and has a demonstrably better than average track record in producing solutions to arithmetic problems in cases of disagreement.

In the final case, suppose that B is a pathological liar, and while her mathematical abilities are functioning properly, she is not a reliable purveyor of testimony. As it so happens, however, in all previous contexts of disagreement she has based her lies on false beliefs due to accidental error, and the majority of the testimony itself has been true.

Thus, in the first case, while B has the disposition transmit reliable testimony regarding her mathematical calculations, it just so happens that in contexts of disagreement she fails to do so. In the second case, while B does not have the disposition to transmit reliable mathematical testimony, she has so far been succesfull and reliable in such transmission. And finally, in the third case, while B has the disposition to transmit unreliable testimony, she has heretofore been unsuccesfull in her endeavors.

  1. I have to thank Jennifer Lackey, Alvin Goldman, and David Christensen for putting on such an impressive event, and while my reference class may be somewhat small, I can say I have not yet been to a better conference. ↩

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Knowability and Transmission Failure

March 15, 2009 in Epistemology | No comments

I have been reading a bit on epistemic circularity recently, and it struck me that there might be a non-transmission of warrant argument available to the anti-realist regarding the Paradox of Knowability1. In what follows I will sketch Martin Davies’ limitation principle and his notions of R-defeat and a question-settling context, and then point out how the transmission of warrant might fail for the paradox given an anti-realist position.

In Martin Davies’ Hempel Lectures2 he provides a general principle of limitation on the transmission of warrant from the premises of a valid argument to its conclusion:

Epistemic warrant cannot be transmitted from the premises, P1, . . . , Pn, of a valid argument to its conclusion Q if the warrants for believing the premises are constituted by putatively warranting elements, w1, . . . , wn, and, for one of the premises, Pi, someone who (i) accepted all the putatively warranting elements, w1, . . ., wn. [sic] in themselves, and (ii) accepted all the premises save Pi as so warranted, but (iii) doubted the conclusion Q would be directly rationally committed to a belief that would R-defeat the warrant for Pi that is constituted by wi.3

The concept of R-defeat, or rational defeat, of a warrant is the idea that if one were to accept the warrants governing the premises of a palpably valid argument, yet doubt the truth of the conclusion, one would be rationally required to adopt a belief that cannot be rationally combined with the acceptance of a prima facie warranting element of a particular premise in said argument.  The holding of such a belief in such a context would effectively remove the warranting element of the premise in question, and thus one could not settle the question as to whether the argument is sound by a failure of transmission. This context is termed a question settling context, a context where the conclusion of a purported argument is considered open pro tem.

Given these considerations, let us now take a look at the Paradox of Knowability. This particular paradox results from the commitment of the anti-realist that there is some weak epistemic connection to truth. This connection is formulated as a modal weakening of the consequent of the position held by the Kantian idealist: from ‘p→Kp’ to ‘p→◊Kp’. The argument itself collapses the latter position into the former, and a charge that the position has been reduced to absurdity is leveled. Now, it must be noted, the collapse from weak verificationism to naive idealism is not itself absurd, although the idealist position is not terrible defensible, so why is it that this result is deemed absurd by the realist? It would seem the realist would have to sneak a negation of the idealist position into the premises in order to generate a full blooded absurdity result, and that is exactly what has been done. Consider the Fitch proposition which generates the paradox, that there is an unknown truth: p & ~Kp. This proposition is equivalent4 to ‘~~(p & ~Kp)’ and thus ‘~(p→Kp)’, exactly what is needed to generate the absurdity of the weaker verificationist position given the collapse.

The anti-realist might provisionally accept some warrant for the negation of the naive idealist position in contexts where the epistemic connection to truth is not in question, but I would think that once this connection is made salient, the anti-realist might withhold judgement on the position of the naive idealist rather than accepting its negation. Judgement thus being withheld, the warrant for the Fitch proposition would suffer R-defeat, thus blocking the transmission of warrant to the collapse of the verificationist position.

Note: As I got deeper into the literature, I decided that working out the details of this position would require a bit of work on inferentialism. I have moved away from this specific position, but something interesting regarding Cohen’s problem of easy knowledge has subsequently developed through my research. More on that soon.

  1. For an explanation of the paradox, see the SEP entry here. For additional thoughts on the subject, see my posts here, here, and here. ↩
  2. Princeton University, 2003. Cf. here, here, and here. ↩
  3. Lecture 3, page 2. ↩
  4. This is a classical equivalence, in an intuitionistic framework–or any other which rejects excluded middle–it would amount to a one-way entailment. ↩

Erkenntnis: Conditionals and Ranking Functions

March 8, 2009 in Epistemology, Logic | Comments closed

Erkenntnis Vol 70, Number 2/March, 2009 is currently open access. Editors Franz Huber, Erik Swanson, and Jonathan Weisberg put together this issue from the proceedings of the first Formal Epistemology Festival in Konstanz, Germany. The issue focuses on conditionals and ranking functions, with contributions from philosophers such as Timothy Williamson, Robert Stalnaker, and Alan Hájek.

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Plato: Criterion Problems

March 1, 2009 in Epistemology | Comments closed

In preparation for my Plato seminar tomorrow, I have been reading over book 6 and 7 of The Republic. I noticed that in the early passages of Book 7 Socrates admits to an assumption with unfortunate implications. Proceeding his initial exposition of the Cave parable, Socrates qualifies the conclusions drawn in the final section of Book 6:

If you identify the upward path and the view of things above with the ascent of the soul to the realm of understanding, then you will have caught my drift — my surmise — which is what you wanted to hear. Whether it is really true, perhaps god only knows. My own view, for what it’s worth, is that in the realm of what can be known the thing seen last, and seen with great difficulty, is the form or character of the good. But when it is seen, the conclusion must be that it turns out to be the cause of all that is right and good for everything. (517b)

Thus, the truth of Socrates’ first principle, the Good, is no more than an assumption. This assumption is a troubling one, given his preceding explanation of the divided line, particularly his distinction between thinking and understanding, as given by the contrasting examples of philosophic and scientific inquiry. To elucidate this contrast, Socrates first provides an example of thinking, where one “is compelled to work from assumptions, proceeding to an end-point, rather than back to an origin or first principle. (510b)” By way of analogy, Socrates characterizes the methods of the geometers:

When people are doing things like geometry and arithmetic, there are some things they take for granted in their respective disciplines. Odd and even, figures and the three types of angle. That sort of thing. Taking these as known, they make them into assumptions. They see no need to justify them either to themselves or to anyone else. They regard them as plain to anyone. Starting from these, they then go through the rest of their argument, and finally reach, by agreed steps, that which they set out to investigate. (510c)

This methodology moves from the realm of the doxa to the realm the forms, but since they “use assumptions as first principles” (511d) and treat their models as images rather than forms, they relegate their inquiry to the domain of belief and conjecture. Given that the faculties of reason are a tool of mathematics, however, the geometers reach the first part of the second section, that of thinking, the “halfway house between opinion and understanding. (511d)” This differs from the philosophic mode of inquiry, which “goes from an assumption to an origin or first principle which is free from assumptions. (510b)” The philosopher, then, does not proceed from the doxa, but from the dialectic alone:

Finally, by the other section of the line representing the objects of understanding you must take me to mean what reason itself grasps by the power of dialectic, when it uses assumptions not as first principles, but as true “bases” — points to take off from, entry-points — until it gets to what is free from assumptions, and arrives at the origin or first principle of everything. This it seizes hold of, then turns round and follows the things which follow from this first principle, and so makes its way down to an end-point. It makes no use at all of any object of the senses, but only of pure forms — working through them and towards them. And it ends in forms. (511bc)

Here we land in some trouble. Socrates states that for one to gain access to the realm of understanding, one must proceed from assumptions to that which lacks assumptions–a first principle–by the dialectic alone. Now, Plato began his dialectic with an inquiry into the nature of justice, and moved from justice to knowledge or understanding. It is his premises regarding these concepts that entail his first principle, and by assuming the truth of his first principle he seems to be affirming the consequent.

Socrates is running into the problem of the criterion. The power of the dialectic can only establish the validity of his argument, not its soundness. To establish the truth of his premises he faces a choice, he must either (a) descend into the realm of the doxa or (b) justify a circular form of reasoning. Given (a) Socrates is in no better a position than the geometers, and would thus be relegated to the halfway house between opinion and understanding. The alternative, on the other hand, is a more interesting matter. That is to say, if Socrates’ arguments are enthymematic, in that they presuppose his first principle, G, and if G entails his conclusions regarding knowledge, justice, and the like and these conclusions jointly entail his first principle, then the truth of G establishes the soundness of his arguments. Circular, but not viciously so. A problem remains, unfortunately, for the truth of G is only assumed, not established, and it seems the only method by which Socrates might establish this assumption is, again, either (a) by a descent into the realm of the doxa or (b) by an appeal to the agreement of his interlocutors. Unfortunately, given this strategy Socrates has simply passed the buck, for (a) lands him back in his halfway house and (b) simply widens the circle.

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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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Zagzebski on Virtue Acquisition

February 17, 2009 in Epistemology | Comments closed

Today we began studying Sosa’s Epistemology in Professor Kvanvig’s Epistemology seminar. We finished Zagzebski’s Virtues of the Mind last week, and as I made my way through it I noticed some potential problems regarding her views on the acquisition of virtues. In the book Zagzebski outlines a  motivation-based virtue theory, which includes an account of intellectual virtues for the purpose of an epistemic application. In what follows I will first provide some groundwork, outlining the internal component of a virtue in terms of a dispositional motivation, the external component of a virtue, where virtue is defined as a success term based on a reliability constraint, and the standards for virtue possession. After the ground has been cleared, I will propose a potential regress which faces her account as antecedently developed.

Virtue is defined by Zagzebski in terms of one’s motivations, where a motivation is a “persistant tendency to be moved by a motive of a certain kind.”1 A motive is, in other words, a low-level, action directing emotion. The particular virtues are based on these dispositional motivations, with each virtue taking a particular motivation as its source. This motivation-based account of virtue has both general and specific consequences. That is to say, the motivational component of a virtue will provide impetus for the agent to develop certain skills needed to carry out one’s goals, with the particular consequences of driving one to find out certain non-moral facts about particular circumstances, dependent upon the ends required by the motivational component of the virtue. These internal conditions lead directly into the external aspect of a virtue, where virtue is defined in terms of success.2 The success component of a virtue is independent of the motivation component, and it provides that reliable success in attaining the ends of the motivational component is a necessary condition for virtue possession. Reliability is given in terms of truth conduciveness, but this link may be either direct or indirect. For directly truth conducive virtues I will asume that the reliability component is cashed out in terms of reliably generating true beliefs. Indirect truth conduciveness, however, is given a somewhat vague definition, in that Zagzebski “suggest[s] that we may legitimately call a trait or procedure truth conducive if it is a necessary condition for advancing knowledge in some area even though it generates very few true beliefs and even if a high percentage of the beliefs formed as the result of this trait or procedure are false.”3

Zagzebski adds to this account of intellectual virtues that they are acquired “through the imitation of virtuous persons and practice in acting virtuously.”4 This launches an immediate regress:

(1) Person A acquires virtue V through imitation of person B.

(2) Person B acquires virtue V through imitation of person C.

(3) Person C … D.

(4) Ad Infinitum.

This is not the end of the matter, however. The previous regress may be sharpened through appropriate supplementation to more accurately account for the way in which a virtue is acquired:

(1) Person A assesses virtue V in person B, as B exhibits behavior X in appropriate situations (a1, a2, …, an), and therefore person A acquires virtue V through imitation of person B.

(2) Person B assesses virtue V in person C, as C exhibits behavior X in appropriate situations (b1, b2, …, bn), and therefore person B acquires virtue V through imitation of person C.

(3) Person C … D.

(4) Ad Infinitum.

Now, with this more accurate sketch of the acquisition regress involved, the question may be posed as to how one assesses behavior in appropriate situations. This behavior is to be considered successfull if it is to exhibit the virtue involved, and the success must be reliable. Reliability, however, is a vague concept. Given this, and the previous distinction between directly and indirectly reliable virtues, it would seem that any given directly reliable virtue may be reduced to an indirectly reliable virtue provided a slight modification of the previous regress:

(1) Person A assesses virtue V in person B, as B exhibits behavior X in appropriate situations (a1, a2, …, an) with degree of success P1, and therefore person A acquires virtue V through imitation of person B.

(2) Person B assesses virtue V in person C, as C exhibits behavior X in appropriate situations (b1, b2, …, bn) with degree of success P2=(P1-1), and therefore person B acquires virtue V through imitation of person C.

(3) Person C assesses virtue V in person D, as D exhibits behavior X in appropriate situations (c1, c2, …, cn) with degree of success P3=(P2-1), and therefore person B acquires virtue V through imitation of person D.

(4) Ad Infinitum.

Here we have it. Given any directly reliable virtue, with an arbitrarily high degree of success, as the route is traveled through iterations of virtue acquisition success approaches 0.

  1. Zagzebski (1996), p. 132 ↩
  2. Cf. Zagzebski (1996), p. 100 and p. 134 ↩
  3. Zagzebski (1996), p. 182 ↩
  4. Zagzebski (1996) p. 157-158 ↩

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Second Formal Epistemology Festival: Causal Decision Theory and Scoring Rules

February 13, 2009 in Epistemology, General, Logic | Comments closed

University of Michigan, Ann Arbor
May 29–31, 2009

This is the second of three small, thematically focused events in formal epistemology, organized by Franz Huber (Konstanz), Eric Swanson (Michigan), and Jonathan Weisberg (Toronto). This year’s festivities coincide with the 10th anniversary of the publication of James Joyce’s The Foundations of Causal Decision Theory. Confirmed participants include John Collins, Branden Fitelson, Allan Gibbard, Chris Hitchcock, James Joyce, Sarah Moss, and the organizers.

Submissions of papers on topics related to causal decision theory, scoring rules, or both are welcome. Please send a pdf prepared for blind reviewing to <ericsw AT umich DOT edu>.

Deadline for submissions: March 22, 2009.
Notification of acceptances: April 5, 2009.

See here for more information.

* From Franz Huber via Philosop

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