Search Results for: Absolute Generality

Absolute Generality 25: Indefinitely extensible concepts, "big" and "small"

The Shapiro/Wright paper is a high point in the Absolute Generality collection. For a start, First, they focus on Dummettian considerations. I’ve already urged here that considerations against the possibility of absolutely general quantification based on Skolemite worries, or on … Continue reading

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Absolute Generality 24: Parsons concluded

I’ve commented at length on the central, load-bearing, section of Parson’s paper. The concluding five and a bit pages I found less engaging. There are some comments on a paper by Rayo and Williamson which I might take up when … Continue reading

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Absolute Generality 23: Parsons on the Williamson argument again

Let’s start by presenting a Williamson-style argument in a slightly different way. On an interpretative truth-theory for a language L, as we said, we’ll have a clause for a monadic L-predicate P along the lines of ‘for all o, P … Continue reading

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Absolute Generality 22: Parsons on varieties of Russell’s paradox

Parsons, however, doesn’t think that the principal problems about quantifying over everything arise from a supposed commitment to metaphysical realism but are “logical difficulties … [which] arise from considering how sentences or discourses containing quantifiers are interpreted. This apparently innocent … Continue reading

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Absolute Generality 21: Parsons on metaphysical realism

It is a pleasure, as always, to turn to a paper by Charles Parsons (a long time ago, his “Frege’s Theory of Numbers” was one of the papers that grabbed me when I very first started philosophy and it helped … Continue reading

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Absolute Generality 20: Linnebo on sets, properties, etc.

And having said that I would write about Linnebo’s paper next, I find myself rather regretting that promise, and this will have to be a non-comment! Linnebo begins by announcing that the “strongest argument against the coherence of unrestricted generalization” … Continue reading

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Absolute Generality 19: Lavine on McGee’s argument

There are still over twenty pages of Lavine’s paper remaining. Since, to be frank, Lavine doesn’t write with a light touch or Lewisian clarity, these are unnecessarily hard going. But having got this far, I suppose we might as well … Continue reading

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Absolute Generality 18: More on schematic generality

In a subsection entitled ‘Schemes are not reducible to quantification’, Lavine writes Schematic letters and quantifiable variables have different inferential roles. If n is a schematic letter then one can infer S0 ≠ 0 from Sn ≠ 0, but that … Continue reading

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Absolute Generality 17: Schematic generality

In Sec. 7 of his paper, Lavine argues that there is a distinct way of expressing generality, using “schemes” to declare that ‘any instance [has a certain property], where “any” is to be sharply distinguished from “every”‘ (compare Russell’s 1908 … Continue reading

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Absolute Generality 16: Lavine on the problems, continued

(3) “The third objection to everything is technical and a bit difficult to state, and in addition it is relatively easily countered,” so Lavine is brief. I will be too. Start with the thought that there can be subject areas … Continue reading

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Absolute Generality 15: Lavine on the problems

Shaughan Lavine’s is one of two fifty-page papers in Absolute Generality (I’m not sure that the editors’ relaxed attitude to overlong papers does either the authors or the readers a great service, but there it is). In fact, the paper … Continue reading

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Absolute Generality 14: A rule for ‘everything’

The final section of McGee’s paper is called “A rule for “everything”‘. He argues that “the semantic values of the quantifiers are fixed by the rules of inference”. The claim rests on noting that (i) two universal quantifiers governed by … Continue reading

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Absolute Generality 13: Skepticism about the quantifiers in particular

In Sec. 2 of his paper, McGee reviews a number of grounds that might be offered for skepticism about absolutely unrestricted quantification. But he doesn’t take the classic indefinite extensibility argument very seriously — indeed he doesn’t even mention Dummett, … Continue reading

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Absolute Generality 12: McGee on semantic scepticism

I was intending to look at the papers in Absolute Generality in the order in which they are printed. But Glanzberg’s piece is followed by a long one by Shaughan Lavine which is in significant part a discussion of Vann … Continue reading

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Absolute Generality 11: Indefinitely expanding?

I mentioned that Glanzberg’s paper focuses on Williamson’s version of Russell’s paradox for interpretations. I can’t say that I find that version very illuminating, but there it is. But it does shape Glanzberg’s discussion, and he tells the story about … Continue reading

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Absolute Generality 10: Expanding background domains

Having tried twice and miserably failed to explain to a sullenly sceptical Hungarian girl that you don’t make an espresso macchiato by filling up the cup to the top with hot milk, I was perhaps not in the optimal mood … Continue reading

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Absolute Generality 9: Restricting quantifiers

Section 3 of Glanzberg’s paper gives an overview of the ways in explicit and common-or-garden-contextual restrictions on quantifiers work (as background to a discussion in later sections about how “background domains” are fixed). This section isn’t intended to be more … Continue reading

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Absolute Generality 8: Glanzberg on contextualism

According to Michael Glanzberg’s “Context and Unrestricted Quantification”, quantifiers always have to be understood as ranging over some contextually given domain; and paradoxes like Russell’s show that, ‘for any given context, there is a distinct context which provides a wider … Continue reading

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Absolute Generality again

A while ago I made a start here on blogviewing Absolute Generality, edited by Augustín Rayo and Gabriel Uzquiano (OUP, 2006): but I only had a chance to comment on two papers before the chaos of term and other commitments … Continue reading

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Absolute Generality 7: Hellman on talking donkeys

The final section of Hellman’s paper is called ‘Making do with “less”‘, and concerns strategies that the sceptic about the coherence of absolutely general quantification can use to makes sense of (true!) assertions like ‘there are no talking donkeys’ or … Continue reading

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Absolute Generality 6: Hellman on ontologies

Hellman’s second line of argument against absolutely general quantification rests — according to the title of Section 4 of his paper — on the multiplicity of ‘factually equivalent ontologies’. The claim is that ‘The same underlying factual situation [can be] … Continue reading

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Absolute Generality 5: Hellman on extensibility

In the next section of his paper, Hellman expounds a version of the Dummett indefinite extensibility argument. You know the sort of thing! ‘Take some ordinals; then, whatever we start with, there’s an operation which gives us a new ordinal … Continue reading

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Absolute Generality 4: Hellman on the problem

I’ll return to the second paper in the Absolute Generality collection, Michael Glanzberg’s ‘Context and unrestricted quantification’, in due course: but as it happens I’ve just read Geoffrey Hellman’s ‘Against “Absolutely Everything”‘, so I’ll comment on that while it is … Continue reading

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Absolute Generality 3: Postulational modality

Well, I think I’m going to have to admit defeat. I’ve tried reading Fine’s paper for the third time and I’m still stumped by his positive claims about ‘postulational modality’. The defender of indefinite extensibility thinks that ‘whatever interpretation [of … Continue reading

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Absolute Generality 2: Showing and saying

Suppose I think that there is something problematic about absolutely general quantification. So I try to say “You can’t quantify over absolutely everything”. But either that “everything” is absolutely general, and I’ve illustrated how you can quantify over absolutely everything … Continue reading

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Absolute Generality 1: Kit Fine and the All in One Principle

OK, time to make a start on blogviewing Absolute Generality, edited by Augustín Rayo and Gabriel Uzquiano (OUP, 2006). As in the Church’s Thesis volume, the editors take the easy line of printing the papers in alphabetical order by the … Continue reading

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Absolutely Generality again: new readers start here!

Back in December, I was blogging about the Rayo/Uzquiano volume Absolute Generality. Then other things intervened. But it is time, at last, to get back to reading the rest of the volume. So far, I’ve said something about the papers … Continue reading

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Begriffsschrift and absolutely unrestricted quantification

We owe to Frege in Begriffsschrift our modern practice of taking unrestricted quantification (in one sense)  as basic. I mean, he taught us how to rephrase restricted quantifications by using unrestricted quantifiers plus connectives in the now familiar way, so that … Continue reading

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Notes, handouts, papers, talks

This page lists various notes, handouts, papers, and so on from the last few years. Many of these pieces are also linked to from other pages here or from old blog postings. They are of very varying levels of sophistication, … Continue reading

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Postcard from Siena – 1

We have decamped back to Siena for the better part of a month. Or rather to a small village about 15km to the east. Siena is already bustling with tourists, but here things are very quiet. From one window, a … Continue reading

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Philosophy of Religion 14: Miracles?

Those who are getting fed up with me banging on and on about the Murray/Rea Introduction to the Philosophy of Religion and are waiting for some serious stuff can rest easy. This will be the penultimate post on that book. … Continue reading

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Philosophy of Religion 8: Pluralism

No. I’m not giving up my day job. A new logic book project is under way and taking nearly all my attention. When I’m more confident that it is “taking off” and going places, I’ll say more about it here: … Continue reading

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Religion and The Philosophy of Religion

I’ve commented here a couple of times about some daft newspapers columns about matters of religion and science (see here and here). And — quite unexpectedly — I’ve found myself contributing a number of responses on religion as a newbie … Continue reading

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Forthcoming attractions …

And what happened to my “blogview” of Absolute Generality? Good question! I’ve been a bit snowed under. But I plan to get back to that — at long last — next week, finishing looking at the papers in the book, … Continue reading

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Blog roll … and thanks to Monica Vitti

I’ve added a link alongside to Tim Gower’s blog (thanks to Carrie Jenkins for recommending it), and I’ve removed links to a couple of seemingly dormant blogs. I’m a bit staggered to find that the number visitors to this blog … Continue reading

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Eat your heart out again

As a bit of a break from absolute generality, I’ve just started reading Melvin Fitting’s short book Incompleteness in the Land of Sets. I’ll write some comments here when I’ve finished it (which shouldn’t take long, as there are just … Continue reading

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Forthcoming attractions …

Well, having perhaps rather foolishly said I was thinking about blogging on the Absolute Generality collection edited by Agustin Rayo and Gabriel Uzquiano, I’ve been asked to review it for the Bulletin of Symbolic Logic. So that decides the matter: … Continue reading

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Normal service will be soon resumed …

The last tripos meeting today, and as always justice was of course done. I wish. (Oh, roll on the day when we stop having to place students in artificially bounded classes — first, upper second, etc. — and just rank-order … Continue reading

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Shapiro Varieties of Logic

Shapiro: Varieties of Logic Stewart Shapiro’s very readable short book Varieties of Logic (OUP, 2014) exhibits the author’s characteristic virtues of great clarity and a lot of learning carried lightly. I found it, though, to be uncharacteristically disappointing. Perhaps that’s because for me, … Continue reading

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Quick book note: Stewart Shapiro’s Varieties of Logic

Stewart Shapiro’s very readable short book Varieties of Logic (OUP, 2014) exhibits the author’s characteristic virtues of great clarity and a lot of learning carried lightly. I found it, though, to be uncharacteristically disappointing. Perhaps that’s because for me, in some key respects, … Continue reading

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