Pietroski and Semantic Architecture

February 3, 2010 in Logic, Philosophy of Language | No comments

I am currently working on Paul Pietroski’s Events and Semantic Architecture, and after reading the first chapter, I am a bit puzzled by a few things he says as to in what the underlying structure of a semantic theory should consist. As I am still working through the beginning sections of the book, I would just like to get clear on a few things he says here, as well as some potential pitfalls that I hope to see him address as I get further into the work. The main concern is related to his criticisms and responses to how one should go about assigning semantic content to expressions. The traditional picture as developed by Montague in the 70s assigns semantic content to an expression through a set of compositional axioms which provide expressions particular interpretation functions, and these functions take as input either entities or functions from entities to truth values and map them either to truth values or further functions from entities to truth values. Pietroski would like us to reject this framework, and there are two particular reasons for this rejection that I would like to examine in some detail. First, he argues for an event semantics that replaces function application with concatenation through conjunction and existential closure over events. Now, this is a fairly prevalent alternate framework currently, and his departure would not be so spectacular were it not for his further commitment to the replacement of the set theoretic foundations of the functionist programme with a kind of property evaluation model. In what follows I first flag some remarks by Pietroski which provide the most significant departures from the functionist programme, then I note that the actual implementation of his programme retains some very similar moving parts to that of the model that he is attacking.

To begin, note that Pietroski defines the `Semantic Value’ of an expression as a set of semantic properties which serve to explain the way in which competent speakers evaluate said expression: “to say that expression Σ has the Value(s) it has is just to say that Σ has certain semantic properties , and is thus evaluated in a certain way by competent speakers.”1 So, rather than a particular expression having as its semantic content an intension or extension, it has a set of properties which cause a particular mode of evaluation. Now, given this view, he goes on to specify some notation such that the semantic value of an expression φ as Val(x,φ), which relates the particular θ-role of an expression to an event in the most basic cases. This move by Pietroski is interesting in that it draws a tight connection between the psychological aspects of meaning with that of an expressions semantic content. So the semantic properties in question are actually relational properties between the thematic role of an expression and an event, and this relational property supervenes on the (potential?) evaluation of speakers of the language.

At this point we have lost one nice thing about the functionist view: compositionality. Given that the semantic content of certain expressions could just be functions from functions to functions, the function application account allows for basic compositionality without the need for any additional machinery. Pietroski, on the other hand, has to posit two additional principles in order to get the individual expressions that comprise a particular sentence in a language to compose. These are (1) concatenation is conjunction and (2) existential closure. I bracket existential closure for the moment, as the details involved here come later in the book, and instead limit my comments to how certain criticisms Pietroski levels against the function application view interact with his view of semantic content coupled with (1).

The first step in problematizing this account is to note Pietroski’s view on vagueness and its relation to natural language semantics. The argument runs by first citing Benaceraff and then noting that vagueness exists in natural language to the preliminary conclusion that there is no fact of the matter as to whether there are precise extensions of vague predicates:

If `{x: x is bald}’ specifies a set, there is a set that it specifies. So given this set and some others that `{x: x is bald}’ might specify, for all we know, there is a fact of the matter as to which set it does specify. But given some individuals who are (intuitively) neither clearly bald nor clearly not bald, many sets are equally good–and equally bad–candidates for being the alleged set of bald things. There seems to be no fact of the matter as to which of these is the alleged set. So perhaps we should conclude that `{x: x is bald}’ does not specify any set. [...] In my view, there is no fact of the matter about which of the candidates is specified by `{x: x is bald}’.2

Now, putting aside the many ways in which the literature has gone about fixing up this problem, if we just grant Pietroski this claim, and his further conclusion that “the apparent fact of vagueness creates a difficulty for even stating Functionist axioms that actually assign values to predicates of natural language.”3, then a problem surfaces for the positive account Pietroski is sketching simply due to the apparent dearth of formal methods now available.

The problem in question relates to his account of concatenation as conjunction. The general strategy is Davidsonian, and it is one that I am amenable to. The problem, however, is that without the mathematical tools of analysis that Pietroski seems to be denying the linguist access too, the particular methods involved in composing lexical strings by conjunction becomes a somewhat magical process. Differently put, conjunction is a form of function application. Pietroski seems to assent to this:

Conjunctivists do not deny that concatenation corresponds to a function, since predicate-conjunction can obviously be so described: ||^|| = λo.v iff ∃F∃G[o=<F,G> & v=λo'.t iff F(o')=t & G(o')=t]. One can also encode Functionism in terms of assigning a semantic value to concatenation: ||Π^α||=||^||(<||Π||,||α||>); where ||^||=λo.v iff ∃F∃x[o=<F,x> & F(x)=v], and `F’ ranges over functions from individuals to truth-values (and `o‘ ranges over ordered pairs of functions and elements to the relevant domains).4

Now, given his preceding rejection of the possibility of even stating functionist axioms for a natural language semantics, he owes an explanation of how conjunction works, if this particular strategy fails. But the only account he gives is precisely that which he later denies. So it looks like Pietroski owes us an explanation of concatenation as conjunction, where conjunction is not a boolean operation as it is standardly conceived yet still provides equivalent results.


Update 2/7/2010

Through correspondence with Pietroski, I have cleared up the primary concern which I raised in this post. It appears that when Pietroski was writing this book he put some of the terminology in such a way (due to external pressures) as to cause me to have some misleading assumptions. That is to say, Pietroski’s arguments are more coherently taken to be suggesting a move away from model theoretic semantics on the whole. The problem I was having is that, assuming we are doing MTS, I don’t see how you can specify the meaning of `&’ in your recursive definition of the model without function application. But Pietroski would rather think of the job of natural language semantics as illuminating a conceptual model (in the Chomskian vein), where formal tools are used for the purposes of illumination and clarity. Given this shift, he would like to say that we can just take conjunction as basic, and then use plural quantification to directly refer to objects in the world, circumventing the mathematical representation via sets.

  1. p. 30 fn. 1 ↩
  2. p. 61 ↩
  3. p. 64 ↩
  4. p. 49 ↩

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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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Knowability Paradox Updates

October 18, 2009 in Uncategorized | No comments

Joe Salerno has posted an update regarding the new Synthese special edition on Knowability which is becoming available in their online first collection. This new volume follows the release of his edited work on Knowability, which came out in August. I am reworking a paper I wrote previously on the topic, and I will be posting that here in the coming weeks.

I have not been very active here lately, and I intend on changing that fact. I am currently pulling together some thoughts on the Epistemology of Disagreement, and I should have some preliminary material up here soon related to the significance and methodology of epistemic parity judgments, so stay tuned!

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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Episteme Conference: The Epistemological Significance of Disagreement

June 23, 2009 in Uncategorized | No comments

Sorry I have not been posting recently, but I have been busy finishing out some papers for upcoming conference deadlines. But good news! I will be in Chicago over the next few days to catch the Episteme Conference at my new home. I am sure I will have something interesting to say about this, so stay tuned.

Rational Inconsistent Beliefs

June 8, 2009 in Uncategorized | No comments

Suppose rational belief is closed under competent deduction:

(RBC) Necessarily, if S has a rational belief that p, and p entails q, then S is a competent deduction away from a rational belief that q, maintaining her belief that p throughout.

Given this moderate closure schema, which seems somewhat plausible, considering what seems to be a close link between rationality and deduction, it is possible to come to rationally believe a set of inconsistent propositions, by deduction alone.

Consider the preface paradox: An author publishes a book. It is rational for the author to believe that the conjunction of the propositions in this book are false, given reflection on her fallible nature, etc.:

(1) RB(~(p1&p2&…&pn))

Now, further suppose that the author then begins looking through the book, or reflecting on each proposition individually. Now for each p1,…,pn it is not a stretch to consider that the author rationally believe the proposition, as there is a good chance that the individual proposition countenanced is not that which makes the conjunction false, and the author stands behind her work. But we can take this further. Suppose for each p1,…,pn the possibility of error were raised. For example, someone–perhaps the author herself–were to point out that the editor is known for transposition errors, spelling mistakes, etc., and it would be beneficial to double check whether the proposition in question were true. In each of these cases, the author could, by disjunctive addition, come to the deductive conclusion that there is no editing mistake present 1:

(2) p1 v ~EM(p1)

(3) ~~(p1 v ~EM(p1))

(4) ~(~p1 & ~~EM(p1))

(5) ~(~p1 & EM(p1))

Thus, by (2)-(5), we have the conclusion that it is not the case that not p1 and there is an editing mistake regarding p1. This argument can be repeated for each p2,…,pn, with the result that, not only does it seem initially plausible that each of p1,…,pn are rational to accept individually, they are in fact robustly rational beliefs, immune to the possibility of error. At this point we now have:

(6) RB(p1) & … & RB(pn) & RB(~(p1 & … & pn))

If rational belief is aggregative, or closed under conjunction, then we have rational inconsistent beliefs:

(7) RB((p1 & … & pn) & ~(p1 & … & pn))

We can make this a bit uncomfortable for the author previous to the commitment to belief aggregation, however. For suppose that once the author had iterated through all of her beliefs, someone pointed out to her that she rationally believed the negation of the conjunction of her beliefs, and the iteration she just preformed committed her to rationally believing each proposition within the conjunction individually, which is inconsistent–one of her beliefs must not be rational. Given this, she could first prove that it is rational to believe the negation of the conjunction in the face of a series of rational beliefs in each conjunct:

(8) RB(~(p1&p2&…&pn)) v ~(RB(p1) & … & RB(pn))

…

(9) ~(~RB(~(p1&p2&…&pn)) & (RB(p1) & … & RB(pn)))

Then she could prove that it is rational to believe each conjunct in the face of the negation of the conjunction:

(10(1-n)) RB(p(1-n)) v ~RB(~(p1&p2&…&pn))

…

(11(1-n)) ~(~RB(p(1-n)) & RB(~(p1&p2&…&pn)))

If we wanted to take this a step further, and assume aggregation, by stopping one step short of the full-out contradiction:

(12) RB(p1&p2&…&pn) & RB(~(p1&p2&…&pn))

She could prove that it is rational to have a rational belief in both the conjunction and the negation of the conjunction:

(13)  RB(p1&p2&…&pn) v ~RB(~(p1&p2&…&pn))

…

(14) ~(~RB(p1&p2&…&pn) & RB(~(p1&p2&…&pn)))

——-

(15) RB(~(p1&p2&…&pn)) v ~RB(p1&p2&…&pn)

…

(16) ~(~RB(~(p1&p2&…&pn)) & RB(p1&p2&…&pn))

So, not only can you have inconsistent rational beliefs, but you can have rational beliefs that your inconsistent beliefs are rational.


  1. This is Cohen’s Easy Knowledge deduction ↩

Mereological Nihilism (contd.)

May 5, 2009 in Uncategorized | No comments

I have been thinking a bit more about the (B) theorist1 in my previous post. It looks as if allowing the content of one’s propositions to be determined by one’s intentions can leave one open for liar sentence analogs. Consider this sentence: ‘I am intending with this utterance to express a proposition different from the one determined by the sentence which I am expressing.’ In this case, if p1 is that which we would normally assign to the sentence, the proposition expressed is different, p2, and p1≠p2. On the other hand, p2 then becomes the proposition assigned to the sentence which he expressed, thus making it not in fact the proposition intended. An easy response would be that utterances like this have no propositional content, but I think this is somewhat embarrassing for the (B) theorist.

If we take the no-content view seriously we then allow one’s underlying theoretical commitments to dictate when a proposition is actually expressed by a sentence. What would happen, then, if someone who held a theoretical view that propositions were not dictated by one’s intentions were to utter the liar-analogous sentence? If the sentence expressed a proposition in this case, then we would have weird cases where someone who wavered between the two views would on some occasions express propositional content with a particular sentence and on other occasions not. If, on the other hand, the (B) theorist were to hold that propositions are dicated by intentions generally, and one who does not hold this view would express no content on liar-analogous utterances as well, then it would seem that any percieved gap between the (B) theorist and the (A) theorist would close, as the (B) theorist would be passing the buck, simply positing a wide-ranging error-theory on a different level.

  1. Lets not get confused here with the philosophy of time. I probably should have picked different letters, but I think the difference in substance suffices to differentiate the positions ↩

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Mereological Nihilism

May 4, 2009 in Uncategorized | No comments

Over the course of the last semester, I have had the chance to have morning coffee with Dr. Kvanvig and Ryan Byerly. During the last few weeks, we have had some interesting conversations on mereological nihilism, specifically regarding what exactly is expressed when a purported nihilist engages in conversation with the folk. It seems that there are two general views on what kind of proposition is expressed when making utterances regarding things such as chairs and tables: either (A) the nihilist would propose that the propositions expressed in folk-contexts are in fact propositions quantifying over some form of simples, attributing a wide-ranging error theory, or (B) the nihilst would propose that the propositions she asserts are of the (A) form, but when one does not have such a theoretical view undergirding one’s assertion, one is simply quantifying over the composites.

I find the (B) line of argument troubling, as it seems to presuppose that one may intentionally manipulate the proposition one expresses. Language is a social phenomenon. The (B) view here seems to imply that, rather than a shared language, we, as speakers, are all speaking individual idiolect which happen to share a surface form and structure in such a way as to accidentally match up such that we manage to understand one another. This is risky business. I do not see how any proper semantics could be developed on such a view, for it would be quite possible that two subjects might seem to communicate (as the surface structure of their idiolect align), yet their intentions fundamentally diverge in their communication-acts. To provide an example, suppose my idiolect is bisimilar to that of a random strangers in all respects, except for the directions left and right. I have these reversed. I get out of a taxi in Chicago, and ask said stranger for some directions to a particular building I am interested in. The stranger, knowing nothing of Chicago, provides a random set of directions, which, according to his idiolect, happen to be completely wrong. But as I have the directions ‘left’ and ‘right’ reversed, the set I interpret from his utterances happen to be correct. I go off on my merry way following the directions I received and manage to successfully make it to the building in question. The question remains however, as to the semantic value of ‘left’ and ‘right’ in this example (assuming that the semantics is compositional, which is pretty standard these days).


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