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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!

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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Philosophers’ Carnival 89

April 12, 2009 in Uncategorized | No comments

Welcome to the 89th installment of the Philosophers’ Carnival.

Starting with some metaethics, Philosophy, et cetera provides both a potential objection to Parfit’s Triviality Objection and a guest post by Jeff Sebo: ‘What is Constructivism?’. Following in tune, The Space of Reasons challenges a certain theory of desire with an over-intellectualization, in part 1 of The “Guise of the Good” Theory of Desires. Additionally, The Ends of Thought provides some insight on Intentionality and the Object of Moral Perception: Ricoeur’s Challenge, and Uncommon Priors finishes out the section, posing the question: Is it possible to err in judgments of fashion?

Following this issue’s series in ethics, we have Philosophengang concerned with characterizing A phenomenology of dread, while Possibly Philosophy introduces a puzzle concerning Size and Modality and Matters of Substance highlights The Age of Hyperintensionality.

The Arché Methodology Project has seen some action in the past few weeks, with posts on Methodology and Epistemology and A Plea for Case Studies by Brian Weatherson, with Jonathan Ichikawa following in suit, providing A Case Study: Stalnaker on conditionals.

Finally, in the philosophy-related news, Certain Doubts has moved to a new location, so update your bookmarks! That’s all for this time, and, as always, there were far too many submissions to include in a single carnival, so I had to be selective. The next issue will be held at Go Grue! on May 04, 2009.

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Philosophers’ Carnival

March 23, 2009 in Uncategorized | No comments

The new philosophers’ carnival is here. I will be hosting the next one, scheduled for April 13, 2009. I have already had a few submissions, so if you have one, send it my way.