Thursday, June 29, 2006
Weir to Glasgow
News that I've been hoping to hear has just gone up on Leiter Reports. Alan Weir, currently at Queen's University Belfast, has just accepted a Professorship in our home city. Alan works mainly in philosophy of maths and logic, but also in language, mind and epistemology. I hope his work starts to receive more attention as a result of the move. In particular, he's defended the view that the Russell paradox is to be blamed on the background logic rather than the axioms of Naive Set Theory. Even those (like myself) who incline towards orthodoxy on this issue should recognise Alan's work as a challenge that has as yet gone unanswered. (The few reactions I have seen in print have usually simply pointed out that the revisions that need to be made to logic to block the derivation of the contradiction are severe. I've yet to be convinced that we can in good philosophical conscience dismiss Alan's challenges on those grounds.)
Labels: Links
Tuesday, June 27, 2006
Truth or Consequences
I googled 'Truth or Consequences', looking for a Festschrift in honour of Nuel Belnap, and instead discovered the City of Truth or Consequences. What the hell?
There's a section of the website where they tell you how the city got its name. Still makes no damn sense though.
Oh well, snakes on a plane...
There's a section of the website where they tell you how the city got its name. Still makes no damn sense though.
Oh well, snakes on a plane...
Labels: Links
Sunday, June 25, 2006
Congratulations........
.....to those of my masters class who graduated on Wednesday, and to Simon Robertson, Brian McElwee, and the first class of Arche students (Ross, Philip, Marcus, Robbie and Nikolaj) for graduating with their PhDs.
Back of the net.
Back of the net.
Labels: Links
Sunday, June 11, 2006
Tales of the Inexpressible
When Jason Stanley was here for the UT Grad Conference in April, I took the chance to talk to him about his draft 'Philosophy of Language in the Twentieth Century'. Now, I haven't managed to finish the paper, but it's an impressive survey of a stupidly large field, and Stanley manages to include nice accounts of the contributions made by Tarski and Carnap and other figures who we all acknowledge as a vital part of the story of our subject, but who often get somewhat glossed over in these kinds of overview pieces.
However, one figure who is really noticeably absent is the later Wittgenstein. Moreover, Stanley's assessment of the contribution of the Tractatus to 20th Century philosophy is surprisingly negative:
'The Tractatus impeded progress in philosophy, because it led philosophers (in particular the Logical Positivists) to expend their energies in the pursuit of developing and honing a criterion of meaningfulness, and using the criterion to argue that traditional philosophical theses failed to satisfy it, and were hence meaningless [...]. ' (p10)
Now, Stanley doesn't deny that the Tractatus did some good; in particular, he notes that the connections the early Wittgenstein saw between modality and meaning turned out to yield insights when studied more systematically by later philosophers (p10). But my own assessment of the Tractatus is overall much more upbeat, and I wanted to say a little bit about why.
Firstly, and most germane to Stanley's topic, the Tractatus contains one of the earliest and clearest statements of the thought that the meaning of a sentence is its truth-conditions:
4.024 'To understand a proposition means to know what is the case, if it is true.
(One can therefore understand it without knowing whether it is true or not.)
One understands it if one understands its constituent parts.'
Stanley takes the idea that the proper form a theory of meaning should be truth-conditional to have been 'extraordinarily fruitful, perhaps the most fruitful insight in the long history of the study of meaning' (p18). As David Wiggins presents the history of that insight (in 'Meaning and Truth Conditions: From Frege's Grand Design to Davidson's' in the Hale and Wright Blackwell Companion), the Tractatus marks the first important development of the idea after Frege. From this perspective, the Tractatus should be a integral part of Stanley's story.
I also have a more positive view of the saying/showing distinction. It would be hard not to agree that it provided inspiration for some philosophical wild-goose chases (though I'm not sure how to assess the claim that such failed projects were a symptom of philosophical progress being impeded). On the other hand, I think the distinction led to some geniune insights in maths and logic. Wittgenstein originally introduced the distinction to offer a response to Lewis Carroll-style worries about the system of logic in Principia Mathematica. Those concerns are evident on the first page of the Notes on Logic (1913), where Wittgenstein writes that '[d]eductions only proceed according to the laws of deduction but these laws cannot justify the deduction.' (Notebooks 1914-18: p108). We find the saying/showing distinction first unveiled as the solution to this problem in the opening sentence of the Notes dictated to Moore in Norway in 1914:
'Logical so-called propositions shew [the] logical properties of language and therefore [the] Universe, but say nothing.' (Notebooks: p108).
That one can infer B from A and A -> B is not to be justified by appeal to a further rule of inference. Rather, anyone who understands the symbols involved can see that B follows from these premises. This difficult thought received its mature statement in 5.132 of the Tractatus:
'If p follows from q, I can conclude from q to p; infer p from q.
The method of inference is to be understood from the two propositions alone.
Only they can justify the inference.
Laws of inference, which - as in Frege and Russell - are to justify the conclusions, are senseless and would be superfluous.'
Tricky stuff. But the passage forms part of a pretty deep critique of the universalist conception of logic coming from Frege and Russell. The issue here is not just how inference is to be justified, though that's obviously a central and important part of Wittgenstein's concerns. In the background here is the issue of how the logical propositions are to be demarcated. For the universalist the mark of the logical is unrestricted validity and their self-evidence; from his earliest recorded philosophical remarks it is clear that Wittgenstein is starkly opposed to universalism. Logic 'must turn out to be a totally different kind than any other science' (Letter to Russell 1912, Notebooks: p120).
I should get to the point. The saying/showing distinction is the centrepiece of Wittgenstein's critique of the universalist conception of logic, and this critique had a number of really interesting and important consequences. For example, it provided grounds on which Wittgenstein could check Russell's tendency to claim that the axioms he needed to adopt to try to get his logicism to fly were logical; a crucial moment in the history of set theory, and its demarcation from logic.
Of course, as I noted above Stanley doesn't claim that the Tractatus didn't have positive influence. But here I wanted to say a little about why I disagree with his overall assessment; the Tractatus certainly has its flaws, particularly stylistic flaws, but ultimately I think it was an impressive, at times poignant, and overall beneficial contribution to 20th Century Philosophy. In any case, I strongly recommend reading Stanley's paper; I've learned a lot from it, and from thinking through these points of disagreement.
However, one figure who is really noticeably absent is the later Wittgenstein. Moreover, Stanley's assessment of the contribution of the Tractatus to 20th Century philosophy is surprisingly negative:
'The Tractatus impeded progress in philosophy, because it led philosophers (in particular the Logical Positivists) to expend their energies in the pursuit of developing and honing a criterion of meaningfulness, and using the criterion to argue that traditional philosophical theses failed to satisfy it, and were hence meaningless [...]. ' (p10)
Now, Stanley doesn't deny that the Tractatus did some good; in particular, he notes that the connections the early Wittgenstein saw between modality and meaning turned out to yield insights when studied more systematically by later philosophers (p10). But my own assessment of the Tractatus is overall much more upbeat, and I wanted to say a little bit about why.
Firstly, and most germane to Stanley's topic, the Tractatus contains one of the earliest and clearest statements of the thought that the meaning of a sentence is its truth-conditions:
4.024 'To understand a proposition means to know what is the case, if it is true.
(One can therefore understand it without knowing whether it is true or not.)
One understands it if one understands its constituent parts.'
Stanley takes the idea that the proper form a theory of meaning should be truth-conditional to have been 'extraordinarily fruitful, perhaps the most fruitful insight in the long history of the study of meaning' (p18). As David Wiggins presents the history of that insight (in 'Meaning and Truth Conditions: From Frege's Grand Design to Davidson's' in the Hale and Wright Blackwell Companion), the Tractatus marks the first important development of the idea after Frege. From this perspective, the Tractatus should be a integral part of Stanley's story.
I also have a more positive view of the saying/showing distinction. It would be hard not to agree that it provided inspiration for some philosophical wild-goose chases (though I'm not sure how to assess the claim that such failed projects were a symptom of philosophical progress being impeded). On the other hand, I think the distinction led to some geniune insights in maths and logic. Wittgenstein originally introduced the distinction to offer a response to Lewis Carroll-style worries about the system of logic in Principia Mathematica. Those concerns are evident on the first page of the Notes on Logic (1913), where Wittgenstein writes that '[d]eductions only proceed according to the laws of deduction but these laws cannot justify the deduction.' (Notebooks 1914-18: p108). We find the saying/showing distinction first unveiled as the solution to this problem in the opening sentence of the Notes dictated to Moore in Norway in 1914:
'Logical so-called propositions shew [the] logical properties of language and therefore [the] Universe, but say nothing.' (Notebooks: p108).
That one can infer B from A and A -> B is not to be justified by appeal to a further rule of inference. Rather, anyone who understands the symbols involved can see that B follows from these premises. This difficult thought received its mature statement in 5.132 of the Tractatus:
'If p follows from q, I can conclude from q to p; infer p from q.
The method of inference is to be understood from the two propositions alone.
Only they can justify the inference.
Laws of inference, which - as in Frege and Russell - are to justify the conclusions, are senseless and would be superfluous.'
Tricky stuff. But the passage forms part of a pretty deep critique of the universalist conception of logic coming from Frege and Russell. The issue here is not just how inference is to be justified, though that's obviously a central and important part of Wittgenstein's concerns. In the background here is the issue of how the logical propositions are to be demarcated. For the universalist the mark of the logical is unrestricted validity and their self-evidence; from his earliest recorded philosophical remarks it is clear that Wittgenstein is starkly opposed to universalism. Logic 'must turn out to be a totally different kind than any other science' (Letter to Russell 1912, Notebooks: p120).
I should get to the point. The saying/showing distinction is the centrepiece of Wittgenstein's critique of the universalist conception of logic, and this critique had a number of really interesting and important consequences. For example, it provided grounds on which Wittgenstein could check Russell's tendency to claim that the axioms he needed to adopt to try to get his logicism to fly were logical; a crucial moment in the history of set theory, and its demarcation from logic.
Of course, as I noted above Stanley doesn't claim that the Tractatus didn't have positive influence. But here I wanted to say a little about why I disagree with his overall assessment; the Tractatus certainly has its flaws, particularly stylistic flaws, but ultimately I think it was an impressive, at times poignant, and overall beneficial contribution to 20th Century Philosophy. In any case, I strongly recommend reading Stanley's paper; I've learned a lot from it, and from thinking through these points of disagreement.
Labels: Jason Stanley, Philosophy of Language, Philosophy of Logic, Wittgenstein
Arche Audit 2006
I effectively ended up taking last week off from posting here, without meaning to. I flew Austin to Glasgow on the 30th of May, and I've spent the last week or so getting over jetlag and slight illness, and attending the Arche audit in St Andrews.
To some extent, the group of people that were salient in Arche when I used to be around has fragmented (albeit in a very healthy way). We had people at the audit who had travelled from Austin, New York, Western Ontario, Spain, Israel and Leeds, and who hadn't all been in a room together for at least a year. The upshot was the Audit felt more like something of a reunion than anything else, and so the atmosphere in the seminars was terrific. It felt like a great example of how fruitful philosophical discussion can take place without becoming a competitive sport.
Mark Sainsbury kicked off the talks by discussing his new work on fictional discourse. In his last book Reference Without Referents (which really deserves to be much more widely read and discussed), Mark tentatively suggested that fictional names can be handled within his theory of reference by the same mechanisms that other seemingly empty proper names can be. In short, Mark adopts a (negative) free logic which allows that names can be meaningful - given axioms within a broadly Davidsonian truth-theoretic semantic framework - even if they have no bearer. The meaning of sentences with empty names as constituents can be determined compositionally but, as the 'negative' in negative free logic suggests, all such sentences will be false; Mark's suggestion in the book was that this account can be extended to fictional discourse, and our disposition to hear sentences like 'Sherlock Holmes is a detective' as true is ascribed to our tendency to conflate truth with fidelity to the stories or to fail to recognise an implicit (and, crucially, intensional) 'according to the fiction' operator prefixing the sentence.
Even in RWR Mark was explicit that this couldn't be the complete story, and so he's been trying to see what further progress can be made. He starts from the thought that the RWR story is ok for sentences like 'Sherlock Holmes is a detective' which are within the fiction so to speak - evaluable for fidelity to the story rather than genuine truth - but cannot be the right account of 'Sherlock Holmes is famous', intended as a claim about the fame of the fictional character created by Conan-Doyle and thus evaluable for genuine truth. The reason is that we accept the latter sentence as true simpliciter, but since 'Sherlock Holmes' doesn't refer to anything, negative free logic incorrectly rules that the sentence is false. In a radical departure from RWR, Mark's new suggestion is that in such occurances fictional names refer to abstract objects. The view that fictional names refer to such entities is hardly novel, but Mark twist is that he doesn't want to extend it to sentences made within the fiction like 'Sherlock Holmes is a detective', since although such an account delivers the same assignment of truth-value as negative free logic (false, since abstract objects can't be detectives), he thinks it puts any reasonable account of the creative and imaginative processes behind fiction beyond our grasp. This is really only the background to Mark's new work, which largely concerns making sense of a range of phenomena now he's adopted this dualistic account of discourse featuring fiction names; anaphora, cross-realm sentences (such as 'Sainsbury admires Sherlock Holmes for being a detective), and other hideously tricky cases. The discussion brought out just how tricky the issues are here, but it's fascinating stuff and I'm looking forward spending some time this coming year working on it.
We also had interesting discussions on the Caesar Problem, Zalta and Linksy's version of neo-logicism, modal realism (Andreas blogs about this talk here), vagueness and omniscience, and Williamson's pessimism regarding the prospects of a reductive analysis of knowledge. The audit closed (for those of us sadly unable to get up for Carrie Jenkins' talk at 9am on the last day) with Kit Fine talking about Frege's Puzzle and related issues in the philosophy of language. In essence, Fine's tactic is to show how Millianism, the thesis that the meaning of a proper name is exhausted by its referent, can avoid committment to the intersubstitutivity of coreferential proper name salva significatione by recognising that there may be semantic relations between proper names flanking the identity sign which are not necessarily known by speakers competent with each of the names taken singularly (that's probably not quite right, but it gives the flavour of the proposal, and Fine has a new monograph on this material coming out soon). Discussion centred on the proposal's compatibility with a plausible principle of compositionality, though Mark and I were also worried about how to extend the solution to Frege's puzzle to failures of intersubstitutability outside identity contexts (these kind of worries are nicely discussed by Wo).
I had some great conversations with various people, though a particular highlight was getting to hear Fine talk about how his views on vagueness have shifted in the 30 years since 'Vagueness, Truth and Logic' over dinner. All in all, the Audit was a great experience once again.
To some extent, the group of people that were salient in Arche when I used to be around has fragmented (albeit in a very healthy way). We had people at the audit who had travelled from Austin, New York, Western Ontario, Spain, Israel and Leeds, and who hadn't all been in a room together for at least a year. The upshot was the Audit felt more like something of a reunion than anything else, and so the atmosphere in the seminars was terrific. It felt like a great example of how fruitful philosophical discussion can take place without becoming a competitive sport.
Mark Sainsbury kicked off the talks by discussing his new work on fictional discourse. In his last book Reference Without Referents (which really deserves to be much more widely read and discussed), Mark tentatively suggested that fictional names can be handled within his theory of reference by the same mechanisms that other seemingly empty proper names can be. In short, Mark adopts a (negative) free logic which allows that names can be meaningful - given axioms within a broadly Davidsonian truth-theoretic semantic framework - even if they have no bearer. The meaning of sentences with empty names as constituents can be determined compositionally but, as the 'negative' in negative free logic suggests, all such sentences will be false; Mark's suggestion in the book was that this account can be extended to fictional discourse, and our disposition to hear sentences like 'Sherlock Holmes is a detective' as true is ascribed to our tendency to conflate truth with fidelity to the stories or to fail to recognise an implicit (and, crucially, intensional) 'according to the fiction' operator prefixing the sentence.
Even in RWR Mark was explicit that this couldn't be the complete story, and so he's been trying to see what further progress can be made. He starts from the thought that the RWR story is ok for sentences like 'Sherlock Holmes is a detective' which are within the fiction so to speak - evaluable for fidelity to the story rather than genuine truth - but cannot be the right account of 'Sherlock Holmes is famous', intended as a claim about the fame of the fictional character created by Conan-Doyle and thus evaluable for genuine truth. The reason is that we accept the latter sentence as true simpliciter, but since 'Sherlock Holmes' doesn't refer to anything, negative free logic incorrectly rules that the sentence is false. In a radical departure from RWR, Mark's new suggestion is that in such occurances fictional names refer to abstract objects. The view that fictional names refer to such entities is hardly novel, but Mark twist is that he doesn't want to extend it to sentences made within the fiction like 'Sherlock Holmes is a detective', since although such an account delivers the same assignment of truth-value as negative free logic (false, since abstract objects can't be detectives), he thinks it puts any reasonable account of the creative and imaginative processes behind fiction beyond our grasp. This is really only the background to Mark's new work, which largely concerns making sense of a range of phenomena now he's adopted this dualistic account of discourse featuring fiction names; anaphora, cross-realm sentences (such as 'Sainsbury admires Sherlock Holmes for being a detective), and other hideously tricky cases. The discussion brought out just how tricky the issues are here, but it's fascinating stuff and I'm looking forward spending some time this coming year working on it.
We also had interesting discussions on the Caesar Problem, Zalta and Linksy's version of neo-logicism, modal realism (Andreas blogs about this talk here), vagueness and omniscience, and Williamson's pessimism regarding the prospects of a reductive analysis of knowledge. The audit closed (for those of us sadly unable to get up for Carrie Jenkins' talk at 9am on the last day) with Kit Fine talking about Frege's Puzzle and related issues in the philosophy of language. In essence, Fine's tactic is to show how Millianism, the thesis that the meaning of a proper name is exhausted by its referent, can avoid committment to the intersubstitutivity of coreferential proper name salva significatione by recognising that there may be semantic relations between proper names flanking the identity sign which are not necessarily known by speakers competent with each of the names taken singularly (that's probably not quite right, but it gives the flavour of the proposal, and Fine has a new monograph on this material coming out soon). Discussion centred on the proposal's compatibility with a plausible principle of compositionality, though Mark and I were also worried about how to extend the solution to Frege's puzzle to failures of intersubstitutability outside identity contexts (these kind of worries are nicely discussed by Wo).
I had some great conversations with various people, though a particular highlight was getting to hear Fine talk about how his views on vagueness have shifted in the 30 years since 'Vagueness, Truth and Logic' over dinner. All in all, the Audit was a great experience once again.
Labels: Conferences, Mark Sainsbury, Philosophy of Language
Thursday, June 01, 2006
Committment Issues
I have a general policy of not using this blog as a place to draw attention to papers I've written, but this post is going to be the first exception. The reason is that I'm feeling guilty because a couple of months ago Doug Ownings (UConn) posted an interesting question about ontological committment, and in particular about how to respond to 'easy' proofs of the existence of numbers, propositions and the like. In the comments I said I'd have something to say on this topic when I had more time, but although it's been in the back of my mind since then, I never delivered the goods.
So here finally is the next best thing, the text of a talk I gave last year in St Andrews, responding to Yablo's 2000 paper 'Apriority and Existence' which is on just this topic. As a paper it suffers from a slight lack of clarity in places, and if I didn't have more pressing committments I'd rewrite sections of it, but what it tries to do is to explain how a contemporary platonist can be discriminating about which a priori arguments for the existence of abstract objects he endorses; so one can hold that there is a sound and a priori argument for the existence of numbers without being committed to what Yablo calls 'over-easy' proofs of propositions or models.
(I've noticed Firefox doesn't like opening pdfs linked from UT pages. IE seems to work fine though.)
So here finally is the next best thing, the text of a talk I gave last year in St Andrews, responding to Yablo's 2000 paper 'Apriority and Existence' which is on just this topic. As a paper it suffers from a slight lack of clarity in places, and if I didn't have more pressing committments I'd rewrite sections of it, but what it tries to do is to explain how a contemporary platonist can be discriminating about which a priori arguments for the existence of abstract objects he endorses; so one can hold that there is a sound and a priori argument for the existence of numbers without being committed to what Yablo calls 'over-easy' proofs of propositions or models.
(I've noticed Firefox doesn't like opening pdfs linked from UT pages. IE seems to work fine though.)
Labels: Links
