The Arche Weblog

Basic Knowledge Workshop

noreply@blogger.com (Marcus Rossberg) — Mon, 13 Nov 2006 18:44:00 +0000

On 24-25 November, 2005, Arché will hold a Pilot Basic Knowledge Workshop. Speakers and respondents are:

Corine Besson, Jessica Brown, Martin Davies, Philip Ebert, Patrick Greenough, Lars Gundersen, John Hawthorne, Carrie Jenkins, Duncan Pritchard, Jason Stanley, Timothy Williamson and Elia Zardini.

More information can be found here.

Arché Graduate Conference

noreply@blogger.com (Marcus Rossberg) — Mon, 13 Nov 2006 18:30:00 +0000

The 3rd Arché Graduate Conference is taking place 17-19 November, 2006.

There will be eight talks by graduate students with staff responses. The keynote speakers are Graham Priest, Diana Raffman, and Jason Stanley.

More details and registration here.

Words for RelativismS

noreply@blogger.com (Dan López de Sa) — Fri, 10 Nov 2006 01:08:00 +0000

I have just come back from participating in the Arché's final Vagueness Workshop. It has been a great fun—jetlag and loads of killing objections to my paper notwithstanding ;-)!

In two or three occasions there, the issue as to which might be the appropriate taxonomy of contexutalist/relativist positions in recent debates arose, including the issue as to which might be appropriate descriptive labels for the taxons. I’d like to post specifically on the latter here. In some papers I have suggested the following taxonomy, taking as basic the datum of apparent faultless disagreement from Crispin, and (some of) the jargon from Lewis-MacFarlane.

Are appearances to be endorsed?

No → (1) Non-Relativism

Yes → Is the content of the relevant sentence in the different contexts the same?

No → (2) Indexical Contextualism

Yes → Is the index determined by the different contexts the same?

No → (3) Non-Indexical Contextualism

Yes → (4) Radical Relativism

(Couple of quick remarks: Admittedly, an ‘hermeneutic’ view on which the content of sentence depends on the perspective from which it is assessed is set aside. How to locate ‘subject-sensitive invariantism’ is a delicate issue: in my view here might be some versions of the view falling under (2) and some falling under (3)—and perhaps some falling under (1) or (4).)

Regardless of the details, some people might more or less agree with the taxons, and still dispute the labels. Some concerns I have sympathy with:

· Re (1): it is purely negative. In some debates, ‘realist’ might do, and in some debates, ‘(insensitive) invariantism’ might, but they seem to lack the desirable ‘trans-debate’ generality.

· Re (2)-(3): In some debates, particularly concerning knowledge attributions and epistemic modals, ‘contexualism’ is reserved specifically for (2), which also has in its favor that the relevant expressions need not be, according to (2), strictly speaking indexicals. But this leaves (3) without appropriate label, which I think should ideally convey the shared moderate character of (2) and (3) vis-à-vis (4).

· Re (4): ‘Radical’ is overused in taxonomies, and the view is commonly referred to as ‘Truth Relativism’ or ‘Relativism about Truth.’ True enough, but—unless one keeps in mind a suitable explicit stipulation—these latter labels could be fairly used for any of the relativistic (2), (3) and (4) options: after all, all of them endorse the appearances that none of the judgers are thereby judging something that is not true!

Any views?

(Cross-posted at bleb.)

'Faultless Disagrement'?

noreply@blogger.com (Dan López de Sa) — Thu, 31 Aug 2006 17:21:00 +0000

One of the issues we have sometimes discussed at the Relativism Seminar is faultless disagreement. The notion comes, I take it, from Crispin’s discourse failing to exert cognitive command, but I don’t remember if the phrase occurs already in Truth & Objectivity.

In any case, I was thinking it would be appropriate to characterize it terms along the lines of: there are possible contrasting variation in judgements about issues in the domain that does not involve fault in any of the participants. If something like this is adopted, then the appearance of faultless disagreement seems to be a (neutral) datum for relativists and non-relativists alike: different relativisms (moderate and radical, indexical and non-indexical) offer different accounts of how to endorse such appearances, whereas realist, insensitive invariantist alternatives try to explain such appearances away.

(Of course, as Elia has observed, crucial work should be done by 'contrasting' in the suggested characterization—otherwise judgements expressible by ‘I am tired’ and ‘I am not tired’ would qualify. For my own elaboration, see this paper.)

Some other people (see for instance Max’ ‘Faultless Disagreement’) require further that there be a single content or proposition which is contrastingly judged. According to this more restricted sense, it seems to me, it can no longer be just taken for granted that there seems to be faultless disagreement, nor all versions of relativism would endorse the appearances – notably, indexical versions would not. These I take to favor the more liberal usage I suggested.

Any thoughts?

Worlds and Times Enough or Locations?

noreply@blogger.com (Dan López de Sa) — Wed, 16 Aug 2006 20:00:00 +0000

Last year we discussed Andy Egan’s ‘Second-Order Predication and the Metaphysics of Properties’ (AJP 82 (2004), 48–67), at the Metaphysics Reading Group in a couple of sessions.

In the paper, it is argued that properties should be identified with functions from worlds to extensions, as a way of solving the following problem: If properties are sets of (possible) instances, things that exist in more than one world can’t have any of their properties contingently. Properties like being green exists in more than one world, but have some properties contingently: being somebody’s favourite property.

Then, although more tentatively, it is argued that properties should be identified with functions from worlds and times to extensions, as a way of solving the following problem: If properties are functions from worlds to extensions, then things without temporal parts can’t have any of their properties at some but not other times. Properties like being bent don’t have temporal parts, but have some properties at some but not other times: being coinstantiated with being hungry.

I think I am generally sympathetic, but I was concerned that the same kind of reasoning would also motivate that properties should be identified with functions from worlds and times and places (or locations, for short) to extensions. After all, (i) “Second-order predication” of properties such as having many instances around seem to pose similar problems to the world-time proposal, by being possibly true at some places but not others; (ii) there seem to be parallel cases of spatially self-locating attitudes; and (iii) the response to Lewis' concern seems similarly effective as to defend the world-time-place proposal from the charge that these are relations rather than properties.

Any views?

Names can be connotative!

noreply@blogger.com (Aidan) — Thu, 29 Jun 2006 12:14:00 +0000

I hereby propose Arche move from its current home in St Andrews to the more fittingly titled City of Truth and Consequences, in New Mexico.

Alternatively, we could rename St Andrews to make it more Arche-friendly. Suggestions welcome.

A plea for information about "actually".

noreply@blogger.com (Robbie Williams) — Wed, 31 May 2006 16:34:00 +0000

I believe that "Actually(p)" is often taken to be a logical consequence of "p". A number of questions:

(a) is this a standard view? Who disagrees? Who agrees?
(b) what are the central papers I should be looking at if I want to think about this claim?
(c) is the claim that this is a logical consequence *argued for* anywhere (as opposed, e.g. to just deriving it in a system where we've laid down a syncategoramic axiom for an actually operator).
(d) does anything philosophically interesting turn on whether or not this is validity?

(The reason I'm interested is that I've recently been thinking about anologies between "determinately" for the supervaluationist and "actually" for the modal logician, and the result above is the analogue of "p|=Def(p)".)

Epistemic Norms

noreply@blogger.com (Carrie Jenkins) — Wed, 03 May 2006 08:59:00 +0000

Does anyone know if the following combination of views has been defended?

1. Epistemically normative statements are made true by/express objective facts
2. These are naturalistically respectable facts (having to do with e.g. truth or probable truth given evidential position etc.)
3. This does not mean epistemically normative statements are equivalent in sense to statements which are explicitly about truth, probable truth etc.

(Cf. the corresponding view in ethics, that moral statements are made true by/express objective facts about e.g. the maximization of utility, but do not have the same sense as statements explicitly about the maximization of utility.)

Any pointers would be much appreciated!

Vixens and Vixens*

noreply@blogger.com (Dan López de Sa) — Wed, 26 Apr 2006 10:50:00 +0000

Last weekend we benefited in Newtonmore from a very enjoyable Arché Reading Party. Thanks again to Doug and Paul for organizing this!

There, Carrie presented the paper ‘Experience, Concepts and Modal Knowledge,’ where she extends the ideas in her 'Knowledge and Arithmetic' as to cover modal issues, by substantiating the contention that structural relations between concepts can lead to a correct understanding of the structural relations between those features of the world to which the concepts correspond.

The worry I had is the following. In discussion, it was clear that, for Carrie, the relevant relations between the properties of being a fox, being female, being a vixen—as opposed to the induced relations between their extensions —all hold within the actual world. Now consider the property of being a vixen*, which is had by something in the actual world iff it is a vixen in the actual world, but is also had in some counterfactual situation by things by things that are male fox in those. Presumably, the contrasting relations between the properties of being a fox, being female, being a vixen* also hold within the actual world. Now it seems then crucial for Carrie’s project that our concept vixen fits (refers to, signifies) the property of being a vixen as opposed to the property of being a vixen*.

But in virtue of what is this the case? One option seems to be that there are some facts about the concept itself in virtue of which this holds—perhaps manifesting in intuitions about how to describe using 'vixen’ certain 'vixen’-free described scenarios, in the sort of way made familiar by recent two-dimensional literature. But this seems close to the “Carnapian” alternative that Carrie was officially opposing. One other option is that there are some empirical facts settling the issue. But this in turn seems to be what motivated Craig’s concern, given that presumably these empirical facts would concern the properties only through their instances, which by assumption being a vixen and being a vixen* actually share. Thus they seem not to discriminate between the two coextensive different properties. The worry is, in a nutshell, that is not clear what else could do the job—nor how to pursue Carrie’s project without something of the sort.

Modality Conference Registration Open

noreply@blogger.com (Carrie Jenkins) — Mon, 24 Apr 2006 16:18:00 +0000

Registration is now open for the Arche conference on the Metaphysics and Epistemology of Modality taking place in St Andrews on 7-9 June 2006. The registration form is available online from the conference webpage.

Bombscare

noreply@blogger.com (Aidan) — Thu, 20 Apr 2006 01:52:00 +0000

With all the conference stuff that was going on this weekend, I forgot to ask Jason Stanley what he thought of the following case. Recall that Stanley holds the following views; IRI about knowledge (and most other epistemic notions), plus know-how is a species of know-that. According to the first thesis, whether or not a subject's true belief counts as knowledge is partly determined by the direness of being wrong, given the subject's practical interests ('The more you care, the less you know' as Stanley is reported to have put the view). According to the latter, having know-how isn't to be analysed as having a capacity or an ability of some sort, but rather as possession of a type of propositional knowledge (albeit under a 'practical mode of presentation').

In a very recent paper, Jonathan Schaffer has argued that IRI is incompatible with a certain natural and compelling picture of the 'social role of the expert'. The basic idea is that experts 'serve as a reservoir of knowledge' of a particular field, but for experts to have this status requires a certain stability; it cannot be the case that their possession of knowledge of the relevant body of information can 'fluctuate as the stakes rise and fall'.

Schaffer's point inspired the case I want to raise here. A bomb-disposal expert is presumably someone who knows how to diffuse and dispose of a bomb. But bomb-disposal seems like a risky-business; the consequences of getting something wrong are surely about as dire as we can imagine, supposing (as seems likely) that such an expert doesn't want to be blown to pieces. So according to IRI, a bomb-disposal expert diffusing a bomb doesn't know how to diffuse a bomb. (One might dispute whether the stakes really are high enough to force this conclusion. But throughout the literature on these issues, we are invited to conclude that losing a bet, being late for an important meeting, or failing to have enough money in your bank-account to cover a critical bill are consequences dire enough to defeat relevant knowledge attributions; getting blown up by a bomb seems sufficiently unpleasant too).

So like Schaffer, I feel there's a case to be made that IRI about knowledge does some violence to our intuitive picture of expertise and experts. And given Stanley's other committments, it's not even an option to say that although the bomb-disposal expert loses various items of propositional knowledge, he retains some relevant know-how. (It is still an option to say that he retains some relevant set of abilities or capacities, but I expect (and hope!) that others will share my intuition that this does not sufficiently mitigate the conclusion that a bomb-disposal expert diffusing a bomb doesn't know how to diffuse a bomb).

Basic Knowledge Workshop: Call For Graduate Papers

noreply@blogger.com (Carrie Jenkins) — Tue, 28 Mar 2006 15:00:00 +0000

An Arché workshop on Basic Knowledge will take place on 24-25 November 2006. Speakers will include Jason Stanley, Duncan Pritchard, Jessica Brown and Timothy Williamson. There will be a slot for a graduate student paper. Graduate students, and those who obtained their PhDs within the last twelve months, are invited to submit papers of not more than 5000 words. Please send submissions as email attachments in Word or similar format (no pdf files please) to Carrie Jenkins. Suitable topics include: Sceptical Paradox, Transmission and/or Closure, Non-Evidential Warrant, Internalism and Externalism, and A Priori Knowledge. Particularly welcome are papers which open up new areas of enquiry within these fields, and/or highlight directions in which further research is needed. Travel and subsistence will be covered by Arche for the author of the selected paper.

Status Belli

noreply@blogger.com (Carrie Jenkins) — Fri, 17 Mar 2006 17:28:00 +0000

The final Arché Abstraction Workshop, informally titled 'Status Belli', will take place in St Andrews on 8-10 December. Details will be posted on TWiki as they become available.

What Price Bivalence?

noreply@blogger.com (Aidan) — Mon, 13 Mar 2006 01:05:00 +0000

In a talk I've been giving various places recently, I've argued that Delia Graff's theory of vagueness, like other theories which hold onto bivalence, runs into trouble with the forced-march Sorites. Here's the worry in brief. Graff explains our ignorance of where the boundary in a given series lies with the following similarity constraint:

'..if two things are saliently similar [in the relevant respect], then it cannot be that one is in the extension of a vague predicate, or in its anti-extension, while the other is not.' (2000: 57)

The idea is that whenever one is evaluting a pair of items in a suitably constructed Sorites series, both will be saliently similar, and so either both are in the extension of the predicate in question or both are in the anti-extension; the boundary is never where we are looking for it. This also gives an explanation of why we are liable to find Sorites reasoning compelling despite its invalidity (something critics have complained is entirely missing from Williamson-brand Epistemicism, though it's a central concern in Sorensen's Vagueness and Contradiction).

But now imagine a subject shown the items in a Sorites series in order, and asked of each whether it is in the extension of the relevant predicate or the anti-extension. Given the way the series has been constructed, she can neither competently judge all of the items to be in the extension, nor all of the items to be in the anti-extension. So at some point she must 'jump'; that is, judge some item n to be in the extension, yet judge item n + 1 (differing only marginally in the relevant respects from n) to be in the anti-extension. But by the similarity constraint, the boundary in known not to lie between n and n + 1, so how can her judgements be viewed as competent?

As Derek Ball, Geoff Georgi and Crispin Wright all rightly pointed out to me in various discussions, Graff has an answer to that question ready. It's essentially that of Diana Raffman in 'Vagueness without Paradox' (1994); when the subject judges n to be in the extension, n + 1 is too, but when the subject jumps, the boundary shifts so that now both n and n + 1 are in the anti-extension. So the subject's judgements can be seen as competent, yet the similarity constraint is never violated. As Raffman writes (1994: 57):

'There are shifts - events that occur - but these are best viewed as Gestalt like changes of “perspective” or “anchor,” not as boundary crossings - at least not if by ‘boundary’ you mean something that installs a simultaneous and/or fixed category difference between adjacent patches.'

It's clear that my original objection fails to engage with this kind of response, but I've been wondering how it's actually meant to work, given Graff's committment to bivalence - I've reached the conclusion that it doesn't. In presenting the forced-march above, I assumed that the subject only had two available responses. But we should be able to drop this assumption and allow the subject to respond as she likes (see for example Raffman 1994: 45-6). Suppose the subject judges n to be in the extension; then n + 1 is also in the extension. Now suppose when confronted with n + 1, the subjects responds 'I don't know', or 'There's no fact of the matter', or 'It's neither in the extension nor the anti-extension'. How does a shift in the location of the boundary such that both items are now in the anti-extension help to ensure that the subject says something competent? The problem is this; the boundary is supposed to shift so as to accomodate the speakers judgements - that's how we can see the subject who jumps in the face of the forced-march as doing something competent - but while there are a number of judgements a subject might return, the endorser of bivalence only recognises binary options for accomodating them.

(In a recent Analysis note ('How to understand contextualism about vagueness', 2005) Raffman explicitly considers what would happen on her earlier view when a subject switches from judging items to lie in the extension of the relevant predicate to judging them to be borderline. But the issues I raise above don't get into sight, simply because in a parenthetical remark she assumes '[f]or the sake of argument only' that we're working in a three-valued logic (246). With the assumption in place the subject's judgements can be accomodated, but that doesn't help us see how the trick is to be pulled whilst retaining bivalence.)

Grundgesetze Translation Project website

noreply@blogger.com (Marcus Rossberg) — Sun, 12 Mar 2006 17:02:00 +0000

The Grundgesetze Translation Project website is online now.

Go to the Arché website and click on "Projects" in the column on the left hand side to find it.

Executive Directorship Available

noreply@blogger.com (Carrie Jenkins) — Fri, 10 Mar 2006 09:58:00 +0000

Anyone who wants my job can now read the advertisement for it at jobs.ac.uk.

Arche papers online

noreply@blogger.com (Carrie Jenkins) — Wed, 08 Mar 2006 10:34:00 +0000

Just an announcement: many of Crispin Wright's papers are now available online, from the 'outcomes' section of the Arche website. These pages also have links to many other online papers, including work in progress. (Arche members/associates/network members: if you would like your work to be included, just send me a link or a file!)

Could a priori knowledge be subject-sensitive?

noreply@blogger.com (Aidan) — Fri, 03 Mar 2006 18:16:00 +0000

Here's a question that arose out of reading Thomas Crisp's recent Analysis note, 'Hawthorne on Knowledge and Practical Reasoning'.

According to Delia Graff's theory of vagueness ('Shifting Sands', 2000), contextualism gets something important wrong, and something important right. Contra the contextualist, vague predicates like 'heap' and 'bald' express the same property throughout their respective suitably constructed Sorites series. Yet changes in the practical interests of a subject making judgements with such predicates determine shifts in their extensions (shifts not attributable to changes in the relevant comparison class, etc), and the resulting picture of the semantics of such expressions i. invalidates Sorites reasoning, ii. explains why we find such reasoning intuitively compelling, and iii. does not require us to give up classical logic or semantics. So the contextualist has something like the right idea, but the hope is Graff's theory delivers the same package whilst neatly avoiding some familiar problems with contextualist approaches.

Now, while the extension of a vague predicate is sensitive to the practical interests of the relevant subject, there are restrictions on such boundary-shifting; just as admissible sharpenings for a supervaluationist must respect the clear polar cases, Graff suggests that on her view the interests of a subject can never determine that the boundary shifts so that, to take an extreme case, a man with no hairs on his head is in the anti-extension of 'bald'. There's something very reasonable about this requirement, but last summer I remember Carrie, Robbie, and other people around the Vagueness project wondering whether Graff really needs or is entitled to it.

Crisp's note suggested to me that there might be a similar issue for interest-relative invariantism (IRI) about knowledge, as defended in Hawthorne and Stanley's recent monographs. According to IRI, contextualism about knowledge gets something important wrong, and something important right. Contra the contextualist, the property expressed in knowledge ascriptions is invariant. Yet changes in the practical interests of a subject determine shifts in whether or not their true beliefs count as knowledge (even keeping their evidence fixed). So whether or not a subject's true belief counts as knowledge depends on non-epistemic (at least as traditionally conceived) features of their circumstances, such as how high the stakes are regarding the possibility that they're wrong.

The parallel question to the one we might want to ask the boundary-shifter about vagueness is this; could it ever be the case that the consequences of being wrong about the truth of a proposition are so disasterous that knowledge attributions are defeated, despite the proposition enjoying some (putatively) priviledged epistemic status (apriority or analyticity, for example)? Crisp's paper suggests that without some Chisholming, Hawthorne's formulation of IRI does indeed allow this possibility. Is there a neat way to avoid such a committment, or is it just a consequence of IRI (unless we do some special-pleading regarding a priori knowledge)? If it is a genuine committment, is that a particuarly bad result? There certainly seems something somewhat counter-intuitive about it, but are there materials for an objection?

Vagueness & supervenience

noreply@blogger.com (Elizabeth) — Fri, 24 Feb 2006 14:21:00 +0000

Okay, so I sent this out as an e-mail to the vagueness list, but Darth Jenkins made me post it here too. She has brought peace to her new empire.

I'm currently working on a paper ('Ontic Vagueness Without Supervenience') whereI make the claim that ontic vagueness, if there is such a thing, is an ontological kind irreducible to other, precise ontological kinds. So if you've only got ontic vagueness at the supervenient level, you've got non-reductivesupervenience. Which is weird.

Anyway, I've got my reasons for why I think this in the ontic case, but I'm wondering if there's space here to make analogy with the semantic case. Is anyone tempted by the view that semantic vagueness is irreducible to precise linguistic components? I.e., if you've got vagueness at, say, the sentence level, that vagueness can only be explained (if it's explained at all) in virtue of the vagueness of that sentence's components -- you either say that vagueness in compounds isn't reducible (or just doesn't supervene at all), or you say that it's reducible to component vague things ('vagueness all the way down'). If anyone knows of work on this type of thing, can you point me in thedirection of some references? Thanks! (And pardon my ignorance, if I'm missing something obvious.)
Cheers, Elizabeth

The doubtful Frege?

noreply@blogger.com (Philip) — Mon, 13 Feb 2006 11:13:00 +0000

There is a recent discussion about a passage in Frege's Foreword to his Grundgesetze concerning the status of Basic Law V (e.g. Burge, Jeshion or Shapiro). The passage reads (in the Furth translation):

"If we find everything in order, then we have accurate knowledge of the grounds upon which each individual theorem is based. A dispute can arise, so far as I can see, only with regard to my Basic Law concerning courses-of-values (V), which logicians perhaps have not yet expressly enunciated and yet is what people have in mind, for example, where they speak of the extension of concepts. I hold that it is a law of pure logic. In any event the place is pointed out where the decision must be made." (Frege, 1964, pp. 3-4)

Some commentators interpret this section as conceding that Basic Law V is not obvious or self-evident. We are wondering how to understand this claim and suggest four ways of interpreting Frege's (alleged) doubts about Basic Law V.

(1) Frege had doubts about the truth of Basic Law V.

This interpretation seems highly unlikely in the light of the last passage of his Foreword where he writes: "As a refutation ... I can only recognize someone's actually demonstrating ... that my principles lead to manifestly false conclusions. But no one will be able to do that." (Frege, 1964, p. 25)

(2) Frege had doubts as to whether Basic Law V is self-evident.

This would entail that a logical law - since Frege considers Basic Law V to be one - can be non-self-evident. The question is whether being self-evident is a necessary epistemic property for a basic axiom in a Logicist project. If not, then how did Frege conceive of Logicism from the epistemic point of view? If yes, then Frege could not have claimed to have established Logicism.

(3) Frege has no doubts but allows rational doubt about the logical status of Basic Law V.

The thought is that Frege concedes to his opponents that they can entertain rational doubts and that further dispute might arise as to whether Basic Law V is a genuine logical principle. He, however, is convinces that it is true and logically so, and merely formalises what is implicit in the contemporary logicians' practice.
Frege could still hold - on this interpretation - that everything that is logical is also self-evident.

(4) Frege speculates about unrational doubts other logicians might have.

Frege raises the point that no-one before him has explicitly stated Basic Law V although it is commonly implicitly used. This unfamilarity with the explicit formulation might trigger doubts. However, they are not only unfounded but also not rational.

Any thoughts?

Philip & Marcus

noreply@blogger.com (Robbie Williams) — Wed, 08 Feb 2006 18:04:00 +0000

I thought I would cross-post something that I put up elsewhere: really appreciate comments and suggestions.

Here's something I came across when I was last up in St Andrews visiting the lovely people at Arche. While thinking about stuff presented at a vagueness workshop by (among others) Achille Varzi, Greg Restall and Dominic Hyde, I suddenly realized something disturbing about super- and sub-valuationists notions of "local validity".

(Local validity is important because everyone accepts that *it* is not revisionary of classical consequence. The substantial question is whether *global* validity is revisionary.)

It's easiest to appreciate the worry in the dual "subvaluationist" setting. Take a standard sorites argument, taking you from Fa, through loads of conditional premises, to the repugnant conclusion Fz. Now the standard subvaluationist line is that though every premise is (sub-)true, the reasoning is invalid (*global* subvaluational consequence departs from classical consequence on multi-premise reasoning of just this sort.)

But local validity matches classical validity even on multi-premise reasoning (details are e.g. in the paper Achille Varzi presented to Arche). Problem! We've got a valid argument with true premises, whose conclusion is absurd (and in particular, it's not true: even a dialethist can't accept it). It really doesn't come much worse than that.

You can reconstruct the same problem for a supervaluationist using local validity, if you take multi-conclusion logic seriously. And you should. It addresses this question: if you've established that a load of propositions fail to be true, what can you conclude? If the conclusions C follow from the premises A, then if each of the conclusions are "rejectable" (fails to be true) one of the premises is rejectable (fails to be true).

Take a sorites series a, b, c,....,z and consider the following set of formulae: {Fa&~Fb; Fb&~Fc; ....;Fy&~Fz}. In a classical multi-conclusion setting, the premises {Fa, ~Fz} entail this set of conclusions. The result therefore carries over to a supervaluationist setting under local validity (but - crucially - not with global validity).

Now, each of the conclusions is really bad (only an epistemicist could buy into any one of them). For the supervaluationist, they're each rejectable. So one of the premises must be rejectable too. But of course, neither is.

Either way, this seems to me pretty devastating for "local validity" fans. (NB: I chatted about this to Achille Varzi, and he's put forward a response in the footnotes of the paper mentioned above. I don't think it works, but it raises some really nice questions about what we want a notion of consequence for.)

Upper-Hume and Upper-V

noreply@blogger.com (Roy T Cook) — Tue, 07 Feb 2006 21:14:00 +0000

Question: Some of you math-ers might remember that a few months ago Crispin and I sent a few things out regarding the status of what we called Upper-V and Upper-Hume (I believe these are Crispin's terms). Basically, these are the third-order versions of V and HP, i.e. the principles that provide numbers (or extensions) for each concept holding of concepts holding of objects. It turns out that these are mathematically quite interesting (well, Upper-Hume is - Upper-V is just as inconsistent as V). Does anyone know of anyone who has published anything on this? The reason I ask is that I have been invited to write a paper on the Bad Company objection, and I am planning on looking at the non-conservativeness of Upper-Hume in order to suggest that the problem is worse than we might have thought. Basically, I just want to make sure that I am not reinventing the wheel.

PS: Has anyone figured out whether I am a neo-fregean or not? (I haven't) I seem to alternate between papers that defend the view and criticisms of it. Its kind of frustrating being a philosopher of math who doesn't have a definite philosophy of math.

noreply@blogger.com (Robbie Williams) — Fri, 03 Feb 2006 18:30:00 +0000

Here's something I've been trying to figure out over the last few days.

Suppose you go for the "two object" solution to statue/clay puzzles. So you think because Goliath (the statue) and Lump (the piece of clay) have different modal/temporal properties, they must be distinct. Nevertheless, they are co-located.

Usually at this point, people start worrying about what metaphysical relation holds between them, in virtue of which they can be co-located. But what exactly are we trying to explain here? Why not say that they are merely colocated? What would we be unable to explain about the case?

Here's a subsidiary question: if you do have reasons to believe that Goliath and Lump are related by a special constitution relation, do your reasons for thinking so give you reason to think that it's necessary that any duplicate of Goliath+Lump are constitution-related (i.e. is constitution an external relation: intrinsic to the pair Goliath+Lump)?