gdp's Comments

consequently.org : Testing, testing, 1, 2, 3. | consequently.org | news

Sun, 19 Jun 2011 12:54:02 +0000

Well, in the paper I explain why I don't think that the two-dimensional semantics, in which points are pairs of worlds, is fundamental. It's interesting that the hypersequent system gives you the same logic.

But I don't understand question 2: truth (in general) is defined at pairs of worlds. Necessary A is true at <w,v> iff A is true at <w,v'> for every world v'. This includes v, so if Necessary A holds at <w,v> then A holds at <w,v> too.

consequently.org :

Mon, 14 Mar 2011 19:50:04 +0000

I haven't decided on licensing yet. I'm still in discussions with a potential publisher, and it will be up to what we can both agree on.

consequently.org : Testing, testing, 1, 2, 3. | consequently.org | news

Wed, 19 Jan 2011 11:31:03 +0000

Well, Jeff Horty couldn't make it from Florida, due to the blizzards in Boston. (Once your flight from Florida is bumped, you're not getting another one for a week, apparently. They are that overbooked.) But Johan and I made it from the easier-to-get-to-Boston starting points of Amsterdam and Hong Kong respectively, and we had a decent enough crowd. I waved my arms a lot and said things like 'soundness and completeness theorems are there for a reason' and 'equal rights for proofs along with models' and 'proof theory can play a semantic role, too' while motivating a sequent calculus for 2D modal logic, saying nice things about Nuel's treatment of tonk, and occasionally muttering darker words about 'normative pragmatics' and sounding like I was some of the other people from the Pittsburgh area. Whether that added up to anything I'll leave for other people to tell. At least Jon Cogburn got something out of the session, and others seemed to like it too.

JvB told jokes, was very dynamic (in both senses of the words) and was much more radical than me, saying logic should include all forms of cognitive dynamics. He was great and I'm not doing what he said justice, but I came first and I then suffered from post-talk ennui, which is never a good time for me to absorb someone else's talk.

consequently.org : Testing, testing, 1, 2, 3. | consequently.org | news

Sat, 4 Dec 2010 23:14:02 +0000

Nobody from Bulgaria has invited me yet. I'd love to visit.

consequently.org : Testing, testing, 1, 2, 3. | consequently.org | news

Wed, 24 Nov 2010 01:53:05 +0000

I’ll try to keep everyone informed. I’ll try posting here in between talks and catching up with people. Are you making your way across to the APA? The closest I’ll get to Calgary is somewhere in high up, between LA and Boston, I’m afraid. This is a very quick visit.

consequently.org : Time Flies | consequently.org | news

Tue, 20 Oct 2009 04:54:04 +0000

Allen's already there. I hope your paths cross soon.

consequently.org : Always More... | consequently.org | news

Tue, 13 Oct 2009 11:52:14 +0000

That's an interesting point. The cardinality objection is a slightly
different one to this problem, however. Even if we maintain a cap on
the size of worlds (or limit worlds in some other way), if # is
definable, not every set of worlds can count as a proposition.

consequently.org :

Thu, 13 Aug 2009 21:00:13 +0000

Thanks, Andrzej! I'll be sure to add these references. They're really helpful.

consequently.org : Always More... | consequently.org | news

Wed, 29 Jul 2009 01:03:07 +0000

Hi Laureano:

Yes, that definition of #A is badly worded. The intention is this:
take the sentences equivalent to A. For each sentence in this set,
take the sentence letters not occurring in that sentence. (This is
clearly non-empty, since none of the sentences contain every sentence
letter.) Then take the first sentence letter in that list.

That's what I meant to write, and my wording is bungled. Changing the
any to some correct the wording too.

I hope that helps.

consequently.org : Rumfitt on Multiple Conclusions, Part 2 | consequently.org | news

Wed, 15 Jul 2009 05:06:05 +0000

You're right, that is a possible response. I don't want to say that
any bit of an argument is itself an argument (imagine stopping mid-
sentence.)

But I would want to say that if stopping at some point gives
you something with a recognisable structure (as these cases admit),
and something whose validity can be interpreted in a perspicuous way
(as happens in these cases), where this can play a role in the general
account of argument structures (as it can in here), then there's
something going for it.

consequently.org : Little Snippets of News | consequently.org | news

Thu, 18 Jun 2009 05:26:04 +0000

Alas, IntenseDebate doesn't provide a way to import old comments -- at
least they don't yet. I hope they will one day.

consequently.org : Rumfitt on Multiple Conclusions, Part 1 | consequently.org | news

Sun, 7 Jun 2009 23:02:21 +0000

We have a winner: yes, it's from he inimitable Dav Pilkey, and the Captain Underpants stories. A prize will be winging its way to Colin (wherever he is, between UConn + St Andrews these days.) As to the nature of the clash between accepting/rejecting (or asserting/denying). When pressed, I say more about why we'd go in for accepting/rejecting in the first place, and how having something whose job it is to normatively stand against accepting (or asserting) is just the ticket in certain circumstances. The story Huw Price tells in "Why 'Not'?" is in the right ballpark.

consequently.org : Rumfitt on Multiple Conclusions, Part 2 | consequently.org | news

Tue, 2 Jun 2009 15:29:08 +0000

Thanks, Ole. That's helpful to point out. I wasn't thinking of the use/mention point explicitly when writing Multiple Conclusions, but it's nice to know that this all works out.

consequently.org : Rumfitt on Multiple Conclusions, Part 1 | consequently.org | news

Tue, 2 Jun 2009 09:47:05 +0000

I'd prefer if you introduced yourself, and if you commented on the
substance of the post. But of course, if you come up with the answer
to the quiz question before June 8, you get the prize.

consequently.org : Problems for Naïve Property Theories | consequently.org | news

Mon, 1 Jun 2009 20:06:06 +0000

Thanks Frode! That clarifies things for me.

--
Greg Restall

consequently.org : Problems for Naïve Property Theories | consequently.org | news

Mon, 25 May 2009 11:54:03 +0000

I wasn't particularly worried, except that some non-classical theories (especially those without contraction) use different accounts of ordered pairs, as different definitions have different properties... Anyway, I agree that the Cantini construction (which I now see, when looking it up, goes back to Gilmore, who I should have added to Visser, Woodruff and Kripke) is very neat. It's not clear to me that this is a counterexample to my [=I], as it's not just we can have [=I] without extensionality. I haven’t checked all the proof yet. Can we get a derivation _using logic alone_ from x in a to x in b and vice versa? Cantini doesn’t claim that, from my reading. But regardless, it's clear to me that in this construction we must have a failure of [=I] somewhere, as in this model, the other conditions are all satisfied, or so it seems to me. The question is whether, in this model, what we’ve got are properties in the sense Field, Priest, or other folks are after.

consequently.org : Problems for Naïve Property Theories | consequently.org | news

Mon, 25 May 2009 11:16:46 +0000

Hmmm. This is a nice argument. But I deny [Fact 2]. I don’t think that if F(A & B) = F(A & C). In particular, I take it that (for true A) the fact that (A & A) is the same thing as the fact that (A & T), for a trivial truth T entailed by absolutely everything, for they're both the fact that A. However, the fact that A isn’t the same as the fact that T. But in general, I’m more than happy to admit really finely grained theories of properties for which [=E] fails. It's just really surprising then that a naïve theory of these cannot then have the fine grain 'quotiented out' by logical equivalence—at the cost of triviality. That’s just weird. I go on a bit about this in the note on Field's book, as [=E] is what he rejects too.

consequently.org : Problems for Naïve Property Theories | consequently.org | news

Mon, 25 May 2009 04:39:39 +0000

Thanks, Frode! This is the spot that all of these iterative constructions (which are generalisations of Kripke/Woodruff/Visser/etc. model-making techniques) break the argument. I'll have to re-check Cantini's book to see what he has to say. This construction (to get strong fixed points, like A(x,y) being the instantiation graph of some property) is a little tricky. It's not immediately clear to me what principles about pairing are needed in the proof (I'll need to check the book for the detail, I suppose). It seems to take a little bit of work to have constructions of the form D = <(x,f): φ(x,f)>, where we're choosing pairs satisfying some condition. You can define that, I suppose, by setting D = <y: (∃x)(∃f)(y=(x,f) & φ(x,f))>, but checking that this does what you want means figuring out the detail of exactly how conjunction, the existential quantifier and pairing work.

consequently.org : Problems for Naïve Property Theories | consequently.org | news

Sun, 24 May 2009 12:25:45 +0000

As I posted on your blog, that's a super version of the paradox. It applies to properties as well as classes. Think of subsethood as a strength ordering on properties — you've made no commitment to that strength ordering being related to identity. I love it.

consequently.org : Problems for Naïve Property Theories | consequently.org | news

Sat, 23 May 2009 12:17:17 +0000

These are tricky issues, of course. But personally, I don't think that substituting co-referential rigid designators preserves quite enough semantic value to do the job in this context, and that's one way to avoid the slingshot trivialising things. All that's needed for [=E] to bite the property theorist is logical deduction, nothing more. You may think that a=b (and that "a" and "b" are rigid designators) without thinking that the deduction from Fa to Fb is logically valid. So I'm quite prepared to say that co-referential rigid designators might have different semantic values in the sense salient for analysing this deduction. (In models of 2D modal logic, for example, co-referential rigid desginators have the same denotation in each row, but not further afield in a model.) So there, the semantic value for the two names will differ, at least in this richer sense. (The thought behind the worry about opacity, however, wasn't primarily one about models. It was just the thought that if from Fa one could deduce Ga, and vice versa, then there's nothing more to having the property F than there is to having the property G — that they're the same property, since they’re logically indistinguishable.)