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Friday, December 15, 2006


I will be travelling for the next few weeks. Lemmings will be fairly quiet during that time.

Sharvy's Theory of Descriptions

I've posted a new draft of my paper "Sharvy's Theory of Definite Descriptions Revisited" on my webpage. Comments are more than welcome.

New Metaphysics Blog

The grad students at UB have started a new group blog, Ungrounded Dispositions. It is devoted to metaphysics and related matters and is well worth checking out.

Tuesday, December 12, 2006

2D and Context-Sensitive Predicates

Lots of predicates are claimed to be context-sensitive. Familiar examples include 'know', 'come', 'go', 'nearby', 'local', 'left', 'right', 'tall', and 'rich'. Here I shall mostly be concerned with a different group of predicates which may or may not turn out to be context-sensitive, namely predicates such as 'is the brightest object in the evening sky'. At first glance predicates like this one seem to be context-sensitive. After all, nothing can be the brightest without being the brightest to someone. Besides your evening sky isn't my evening sky. So, a good guess is that this sort of predicate is context-sensitive. This would mean that its 2-intension would vary across contexts. So, for some speakers, its extension may include Venus. For others not. But how then do we account for its 1-intension (its Fregean sense). One possibility is to take the predicate's 1-extension at a scenario to be relative to speakers. The idea is simple enough: scenarios are worlds with or without a centered individual. What counts as the brightest in the evening sky will be relative to the individual in the center (I am pretty sure I have seen this account of the predicate in David Chalmers' work, but when I went back to look I couldn't find the place).

But this sort of approach comes at a cost. For the individual in the center is also the 1-extension of 'I'. So, it would seem that I can know the following things on a priori grounds: 'Hesperus and I both exist iff Hesperus is the brightest object in the evening sky', 'if Hesperus and I both exist, then I am not blind', and 'If Hesperus and I both exist, then I am not a zombie'. Let's run the argument for the first case. 'Hesperus' (suppose) was acquired via the description 'the brightest object in the evening sky'. Now, suppose the scenario has no center, then the left-hand side is false. But so is the right-hand side. For there is no brightest object if the centered individual is not there to observe it. Suppose scenarios have centers. Then the left-hand side is true just when the right-hand side is. But now if these conditionals are true at all scenarios, then by definition one is in a position to know them on a priori grounds. But these conditionals do not seem a priori.

What to do? Well, we can simply reject the supposition that 'is the brightest object in the evening sky' is context-sensitive. Ignoring 'the evening sky' part of the predicate, there is a simple way of accounting for such predicates as expressing dispositional properties. x is the brightest object in the evening sky iff x would appear as the brightest in the evening sky to a standard observer under standard circumstances. This will get around the problem. But there is something odd about this. 'Bright', 'red', 'blue', and so on, no doubt express dispositional properties. It is easy to imagine what 'standard conditions' means here. It means something like 'normal lighting conditions, no obstructions, no evil deceivers, etc.'. But standard conditions do not usually include information about location. What would a normal or standard location be anyway? To account for the 'the evening sky' part it thus seems that we need to contextualize after all. Perhaps a mixed approach will do. On a mixed approach, 'x is the brightest object in the evening sky' is true at a scenario iff x is the brightest object to a standard observer located at the center under standard conditions. Even though we appeal to the center here, we do not run into trouble, as the analysans is a modal claim.

Monday, December 11, 2006

More Links

David Chalmers has some links to posts on consciousness and two-dimensionalism, including some posts on Lemmings.

As Brian Weatherson points out, the new Philosophical Perspectives is out. I just received my copy in the mail today. It is packed with very interesting-looking articles (not counting my own). Like Brian I look forward to reading these when we get passed this semester and the upcoming APA.

I should mention James Beebe's post on blind refereeing over at Certain Doubts again. I think this issue is extremely important, as publication is the only way up from the mud for many unestablished but promising young philosophers.

I note that Carrie Jenkins has a new book on knowledge and arithmetic coming out with Oxford University Press. It looks super-interesting.

Thursday, December 07, 2006

Around the Blogosphere

Noam Chomsky turned 78 today. (Language Log)

David Chalmers reviews Phenomenal Concepts and Phenomenal Knowledge: New Essays on Consciousness and Physicalism, edited by Torin Alter and Sven Walter.

You can read about temporary and accidental intrinsics over at Knowability.

"Is Blind Review Threatened by Online Works in Progress?", James Beebe asks.

Can you submit a legal brief in Seussian verse? Brian Weatherson has the answer.

Not just Philosophers, Mathematicians too

Philosophers sometimes work on idiosyncratic problems which members of award and grant committees fail to see the value of. What about this for a grant proposal? "I would like to spend the next two semesters examining whether one can construct a feasible version of Lewis' (1968) counterpart theory but without postulate P2". I would immediately give money to this project but for obvious reasons I do not recommand that you submit it as your next grant proposal (unless you know I am on the committee). Speaking of failure to see the value of others' projects, here are some projects in mathematics which I bet many grant committees would turn down (or would have turned down). The projects are described in more detail here.

In 1896 Hadamard and de la Vallee Poussin proved that the chance that a random number nearby some large number n is prime is about 1 / ln(n), where ln(n) denotes the natural logarithm of n.

In 1930, L.G. Schnirelmann proved that every even number n greater than or identical to 4 can be written as the sum of at most 300,000 primes (this is my favorite).

In 2002 Liu Ming-Chit and Wang Tian-Ze proved that every odd number n greater than 2 x 10^{1346} is the sum of three primes. Meanwhile Oliveira e Silva is running a distributed computer search that has verified the weak Goldbach conjecture, viz. that all odd numbers greater than 9 are the sum of three odd primes, up to n > 4 x 10^{17}. So the gap is closing. Perhaps in a few years (with the faster computers the future will bring) the gap will close, and the conjecture will be proven (if the grant committees are willing to chip in).

Email Subscriptions

I've finally gotten around to adding an email subscription option for Lemmings. You can find it at the bottom of the sidebar.

Wednesday, December 06, 2006

Another 2D Puzzle

Here is another one of those can't-see-the-flaw-but-don't-believe-the-conclusion-style arguments:

Initial definitions:
[] ----- it is metaphysically necessary that
<> ----- It is metaphysically possible that
Apriori ----- It is a priori that
EP ----- It is epistemically possible that (or 'it is compatible with what is a priori that')
'Julius' ----- name (in the semantic sense) but known a priori to refer to the actual inventor of the zip.

Principle A:
(As proposed in the comment section here -- DJC's last comment): "the outermost operator determines which intension(s) of the immediately embedded sentence to look at", e.g., '(Apriori, actually p) iff (Apriori p)'.

By A, we have:
(1) Apriori []p <--> Apriori Apriori(p) [Apriori tells box to look at 1-intension]
(2) []Apriori(p) <--> [][]p [box tells a priori to look at 2-intension]
(3) []EP(p) <--> []<>p [box tells EP to look at 2-intension]

Metaphysical modality is governed by S5 (which includes):

[]p --> [][]p
<>p --> []<>p

So, we get (by 1-3):
[]p --> []Apriori (p)
<>p --> []EP (p)

Substituting in:

[]Water is H20 --> [](Apriori (water is H20))
<>Julius is not the inventor of the zip --> [](EP(Julius is not the inventor ...))

But that seems wrong. It doesn't seem that it is necessarily a priori that water is H20. Nor does it seem that it is necessary that it is epistemically possible that Julius is not the inventor of the zip (given that it is not epistemically possible that he is not).

Tuesday, December 05, 2006

Justices Weigh Race School Admissions

From Truthout:

Supreme Court deliberations are private, but yesterday's oral arguments on whether it is constitutional to allow school systems to use race in making school assignments became as much a public debate between the divided justices as a questioning of lawyers. The ultimate decision is likely to be one of the most defining of the court headed by the new chief justice, John G. Roberts Jr., and a powerful statement about where the nation stands more than 50 years after Brown v. Board of Education demanded an end to segregated schools.

Saturday, December 02, 2006

Frances on Trick Socks and Religious Experience

What are trick socks and what do they have to do with religious experience? Bryan Frances argues that if you see what appears to be blue socks, and you continue to believe that the socks are blue, in spite of being told by reliable witnesses that they are really green, then it is plausible to think that your belief is blameworthy. But then if you "see" what appears to be God but you are told by reliable witnesses that what you "saw" was really something else, then, by analogy, your continued belief that you "saw" God is blameworthy. So, the blue socks case seems to suggest that to have religious beliefs of a certain kind may be epistemically irresponsible.

UPDATE: Bryan Frances has posted another excellent post on trick socks and religious experience over at Knowability, partially in response to Colleen Keating, Trent Dougherty, and other commentators.