Saturday, November 13, 2010

We have moved!

Go check the new bLOGOS here!

Thursday, October 21, 2010

On Properties of Sets of Properties

If I understood it right, part of the core of Zalta's LOGOS Colloquium today was the thesis that his abstract objects were not mere sets of properties. I wasn't completely clear about exactly his reasons for this, but he mentioned the contention that sets can not exemplify any of its members. Apologies in advance if I am missing something basic, but is this really so? Take P to be the property of being a set mentioned at The bLOGOS and consider its singleton. Isn't it both the case that P is a member of {P} and that {P} exemplifies P? No?

Monday, April 05, 2010

Are King's propositions too fine-grained?

Jeffrey King is well-known for his account of propositions as worldly entities, as facts consisting of objects, properties and relations. The fact that King claims is a propositions is of the following sort: there is a language containing some expressions that stand in certain sentential relations (basically, the way they got syntactically combined) , with each expression having as semantic value an object, a property or a relation. (This is the basic set-up, he adds more bells and whistles on top of that.) One main advantage of King's view is the ability to solve a major problem for unstructured views of propositions (especially for the propositions-as-possible-worlds view): namely, accounting for necessary truths (or falsehoods) in a way that doesn't make them all equivalent. Since King's propositions inherit their structures from the sentential relations that bind together the words in the sentences expressing those propositions, each proposition (including necessary ones) will have a different structure, closely related to the sentence used to express it. A related problem that is nicely solved in King's framework are the different puzzles arising from embeddings under propositional attitude verbs: for example, the propositions expressed by the sentences "Annie ran 20 kilometres" and "Annie run 12.43 miles" are different, and that accounts for Bill's (who's ignorant about lenght measures) believing one and not the other. It thus seems that on King's account propositions have enought structure as to count as different when we want them to count as such.
This is all nice and good. The question now is: doesn't this positive feature of King's view turn on closer inspection into a negative one? For, as it has been pointed out, it could be that now propositions are too fine-grained. For King claims that not only the propositions expressed by "Annie ran 20 kilometres" and "Annie ran 12.43 miles" are different (which might be easier to accept), but also, for example, that the propositions expressed by the sentences "1=2" and "2=1" are different. This might very well strike some as being utterly counterintuitive.
King is aware of the counterintuitiveness of his claim, and therefore tries to alleviate the worry. To this effect, he asks the reader to compare the propositions expressed by the sentences above with those expressed by the following ones: "1<2" and "2<1". Do these sentences express different propositions? They clearly do. But notice now that what makes the latter sentences express different propositions is just the different order of their constituents. But if that's the case, why shouldn't we accept that "1=2" and "2=1" also express different propositions? Our reluctance to do so is traced down by King to one peculiar feature of the relation that the equality sign stands for: namely, its transitivity. It's true that equality is transitive, King says, but that is just a feature of that particular relation, and it shouldn't bear on the issue whether the same propositions is expressed or not by sentences that differ only in the order of their constituents. I find the explanation involving the peculiaity of equality convincing, but I also understand that one could still feel that one's intuitions about the identity of propositions have not being attended to. To be sure, King has a shot at dispensing with those intuitions; usual motives are invoked - their unreliability, them tracing other kinds of content than propositional content, etc. But this seems to me problematic, at least for the following reason: if King has to give up intuitions at some point, the defendant of the unstructured propositions view could do the same. The set of intuitions given up by each camp will be different, of course, but what becomes unclear is whether King can still claim the advantage he thinks his view has over the unstructured propositions view. So, the questions to be answered are: Do you believe that King has a problem here - are his propositions too fine-grained? Do you find his explanation in the case of the propositions expressed by "1=2" and "2=1" correct? What do you think about his dismissal of (some) intuitions? [This post is a late semi-transcription of a discussion that took place at a reading group in Paris, and the points raised here were originally raised by Michael Murez and Adrian Briciu.]