Nothing of Consequence

The kink to the book didn't come out properly....

2010-06-07T09:48:33.968+01:00

The kink to the book didn't come out properly. But it's enough to google the title, "Unity, Truth and the Liar", and you'll get there!

Yes, at long last it is out! :-) The readership o...

2010-06-07T09:44:15.133+01:00

Yes, at long last it is out! :-)

The readership of this blog may also be interested in the fact that, much before this translation came out, there has been something of a small industry of papers on Bradwardine's solution to the Liar over the last years, mostly by Stephen himself but also by Greg Restall, Elia Zardini and me. In these papers we try (among other things) to make the relevance of Bradwardine's text more tangible to the modern reader.

There is also a whole book pretty much dedicated to Bradwardine on the Liar:

http://books.google.nl/books?id=uvVNCsZy2-wC&printsec=frontcover&dq=%22Unity,+Truth+and+the+Liar&source=bl&ots=l0g5YUZn2Y&sig=yC4BGCJXkohSjj8IVnlAc_muNkw&hl=nl&ei=VrAMTLLZA5qSOPqM_d8C&sa=X&oi=book_result&ct=result&resnum=2&ved=0CBwQ6AEwAQ#v=onepage&q&f=false

Excellent news. Did we tell you about the paradox ...

2010-06-03T08:51:53.273+01:00

Excellent news. Did we tell you about the paradox reading group. Colin, Dave Ripley, Shawn Standefer, Mike Caie, Mike De, and I have been meeting weekly to discuss parts of your book and Hartry's book. Especially the bits about the argument from Gödel's 2nd incompleteness thm to validity not being truth-preserving. So you should prepare for tons of questions! See you in about a week.

I think that I'll be able to make it to Hartry...

2010-06-02T20:37:16.559+01:00

I think that I'll be able to make it to Hartry's talk. I'll be asleep, but I should be there. (I think that my arrival time works...) In any event, I'll definitely be there for the important talks -- by those Caret and Hjortland fellas. I look forward to them!

See you soon. -Jc

Thanks to both of you!

2010-04-05T20:48:56.513+01:00

Thanks to both of you!

I recommend Suomenlinna, the fortification on the ...

2010-04-05T19:03:42.328+01:00

I recommend Suomenlinna, the fortification on the coast of Helsinki: http://en.wikipedia.org/wiki/Suomenlinna

I would go here: http://www.tripadvisor.com/Attr...

2010-04-03T12:03:06.614+01:00

I would go here:

http://www.tripadvisor.com/Attraction_Review-g189934-d245524-Reviews-Gallen_Kallela_Museum-Helsinki_Southern_Finland.html

Nice to see that people still read my undergrad th...

2010-02-19T20:47:17.007Z

Nice to see that people still read my undergrad thesis!

Wow! This is great. Lloyd Humberstone is one of th...

2010-02-18T16:20:08.653Z

Wow! This is great. Lloyd Humberstone is one of the very, very best philosophical logicians today. (His lectures/talks, in my experience, are always interesting, fun, and models of clarity.) I hope that I overlap with his visit at some stage!

Congratulations! This is really good.

Thanks for the interesting post. It seems that V(L...

2010-02-18T10:59:31.895Z

Thanks for the interesting post.
It seems that V(L(V)) will always include V. If so, absoluteness can be seen as simply a notion of maximality (or closure) of V.
So requiring absoluteness of classes of valuations does not yet provide the intimate connection wanted between consequence or rules and truth functions. (It just rules out all the non-maximal ones.) If you want absoluteness for all V in a system, what you need is a more fine grained notion of consequence (or rules) using, eg, n-sided sequent systems.
Have I got it right?

Hi JC "the subject and predicate supposit fo...

2010-02-17T11:46:23.198Z

Hi JC

"the subject and predicate supposit for the same thing" means roughly that the subject and predicate *stand* for the same thing. Supposition is the key semantic concept in later Latin medieval logic, and a lot has been written on it (including by me!). The main point is that Ockham has something that we could describe as a 'semantic' approach to truth, as opposed to 'metaphysical'. What makes a proposition true is a semantic fact (the fact that its subject and predicate stand for the same thing, in the case of affirmatives), not a metaphysical fact (e.g. the existence of a truth-maker, things being as it describes them to be etc.). If you are up to it, I wrote a fairly short (about 5.000 words) survey on medieval theories of truth, you can find it in my webpage, under 'papers and talks'.

Why is Ockham's solution to the Liar bad? Well, he was one of the so-called 'restringentes', people who thought we should restrict self-reference. Ockham did not want to ban self-reference altogether ('This sentence is in English' would be ok); the trouble with his 'solution' is that it is essentially very ad hoc: self-reference is ok except when it's not! And these are precisely the paradoxical cases. Not much of a solution, really...

Ole: yes, good idea. I'll be there. Catarina:...

2010-02-16T16:29:39.041Z

Ole: yes, good idea. I'll be there.

Catarina: what does he mean by "the subject and predicate supposit for the same thing"?

On Ockham on paradox: what's the allegedly uninteresting view? [From Catarina's quote, I thought for a second that he might be in the Nick (J.J.) Smith ballpark -- where we're forced to say that sometimes either the subject or predicate terms misfire (picking out something other than what they superficially appear to pick out), but I doubt that this is what's going on.]

Hope you're both well!

Jc

JC, here is a quote from Ockham you may like: “Th...

2010-02-16T09:29:00.408Z

JC, here is a quote from Ockham you may like:

“Thus, for the truth of ‘This is an angel’ it is not required that the common term ‘angel’ be really identical with what is posited as the subject, or that it be really in that subject, or anything of this sort. Rather, it is sufficient and necessary that the subject and predicate supposit for the same thing.” (Ockham, 1998; 86).

It is indeed a bit in the spirit of Ockham's razor. Ockham has no trouble dealing with metaphysics and positing metaphysical entities, but he will try not to for as long as he can!

And Ockham on paradoxes is indeed not that interesting, it's not only Stephen's love for Bradwardine guiding his judgment here...

Hi JC, Make sure to come along when you visit in t...

2010-02-16T08:21:35.664Z

Hi JC, Make sure to come along when you visit in the summer! I was hoping we'll read Ockham on paradoxes later on, but Stephen isn't all that impressed with him (being a Bradwardine man and all).

There's certainly at least a superficial conne...

2010-02-16T01:56:14.851Z

There's certainly at least a superficial connection. It'd be interesting to explore this a bit.

Meanwhile, it's notable that the best argument for a transparency view of truth (an expressive-device disquotationalism a la Field or Beall or the like) adverts to Ockham -- or at least his razor.

I wish I could attend the MLG! The medievals were way ahead of my time, at least wrt logical explorations! Enjoy!

Don't worry, Greg, we'll be gentle! :) But...

2010-02-01T19:33:39.680Z

Don't worry, Greg, we'll be gentle! :) But as Ole reported, it will mostly be a general overview of recent debates on logical pluralism, and our own ideas will be developed mainly with the purpose of clarifying these debates for as much as possible.

Tim: Thanks for good questions. Sorry that this go...

2010-02-01T11:41:02.735Z

Tim: Thanks for good questions. Sorry that this got a bit long. I agree that the theoretical nature of the proof-theoretist's constraints is an interesting one. I'll try to say something about that below.

'Are claims about the justification of logical inferences empirical or normative?' Stewart has been pressing us on this question for some time already. I think that the answer is a negotiation between the two. I'll try to explain why.

First, it makes little sense, I think, to let experimental data alone dictate when we are entitled to make certain inferences. We know from extensive testing that people are terrible at abstract reasoning, even when they do (generally) infer correctly in particular instances. I wouldn't let data like that undermine modelling reasoning with general (abstract) laws. In other words, there is a normative issue of correct inference that is independent of the data. (Unless you want to let people's response to, say, the Monty Hall Problem be indicative of correct probabilistic reasoning.)

However, an epistemological story about justification of deduction is something more complicated. I guess this is what Stewart is asking about. The orthodox inferentialist, for example, thinks that there is a connection between separability and our acquisition of logical concepts. This connection in turn underlies the understanding-entitlement link that is crucial to their epistemological story. (This is one of the things Williamson attacks in his book.)

Should our reconstruction of logical reasoning reflect this by including separability (or, say, harmony/conservativeness/cut elimination, or whatever else you think is a crucial formal constraint)? Yes - if you think that it is integral to the justificatory story (like the inferentialist often does). Is that theory then hostage to empirical considerations? Yes, I think so. If it happens to be the case that the connection between separability and concept-acquisition (or between the latter and the understanding-entitlement link) is undermined by experimental psychology or cognitive science, that is pertinent to the credibility of the theory.

Yet, it also appears clear to me that there is more to this type of theorizing than the data. Like in other fields, considerations that are non-empirical might count in favour of a theory as well. Negotiating that boundary is hard, as we know.

I hope this is not simply a way of rejecting Stewart's question. I am, ultimately, tempted to answer it by saying 'empirical', but with the proviso stated above. The critical part is that it being empirical doesn't mean that it answers (only) to data about reasoning patterns, but about a bigger picture about language- and reasoning-modules.

Finally, I absolutely agree that the issue cuts across the two camps. Of course, this is precisely why Stewart asks the question: As a model-theoretician he has struggled with which parts of his models are 'modelling' something, and which are mere artefacts of the formal theory. (See his Vagueness in Context, for example.)

Greg: We'll keep you posted. Hopefully, we'...

2010-02-01T11:01:28.588Z

Greg: We'll keep you posted. Hopefully, we'll have lots of time to discuss it come September!

Bernardo: Don't know the schedule for the school yet, I'm afraid. But I think the school ends at the 22nd.

Very cool. Unfortunately I'll be there only af...

2010-02-01T09:19:07.362Z

Very cool. Unfortunately I'll be there only after the 22nd. Do you have any idea when the official dates will be available? Cheers!

Looks like fun! I wish I could be there, but I'...

2010-02-01T08:43:07.026Z

Looks like fun! I wish I could be there, but I'm sure you'll have a ball.

(Let me know if something comes up I should be worried about.)

Tim, These are indeed the crucial issues to be r...

2010-01-31T16:15:06.781Z

Tim,

These are indeed the crucial issues to be raised. Data from experimental psychology have something to say about disputes in philosophy of logic only insofar as the latter is at least to some extent a descriptive enterprise. But it is not obvious that it is, or that it should be (but it is also not obvious that it shouldn’t be), so the bearing that experimental data can have on these discussions is not a straightforward matter.

This being said, I absolutely agree with you that, while most people would endorse the kind of claim made by Florian (i.e. that it is a strictly normative matter), in practice people often appeal to what *is* the case in our cognition of logic (instead of what *ought* to be the case) as an argument to defend a particular position. (In your words: “Certain kinds of traditional interests for proof theorists seem to depend upon quasi-empirical claims.”) Two cases that spring to mind. (i) The claim often put forward by proponents of the proof-theoretical approach to logical consequence to the effect that their approach does better justice to (gives better insight into) the epistemic aspects of logical cognition. But this is clearly a quasi-empirical claim: do we really process logical cognition in a way that is more similar to the proof-theoretical, rule-based approach? (ii) The debate on single vs. multiple conclusions. Opponents of the multiple-conclusion approach (Rumfitt, Tennant) often appeal to the ‘unnaturalness’ of handling multiple conclusions from a cognitive point of view---again, an empirical claim, but one which is not given empirical corroboration in these discussions.

The real problem for the kind of reply given by Florian (which I do endorse, at least to some extent) is that the obvious question to be asked next is: on the basis of *what* are we to judge whether certain inferential practices are justifiable? What are the criteria? Where do they come from? In other words, it is of course fine to maintain that the justification of inferential practices is a purely normative affair, but we still need a story concerning the source of this normativity---that is, if it is not adequacy to how we actually draw inferences.

My own view on these matters, which still needs to be substantially developed, is that it is going to be a normative story, but one that takes into account the kind of agents we actually are. Something like: this is how our inferential practices should be, but given our actual cognitive make-up and epistemic mechanisms. So empirical data will be relevant for the formulation of the full story, but it will not be a purely descriptive story either. (There is a nice paper by Pelletier et al. on psychologism and the is/ought divide for logic, I think it is called ‘Is logic all in our heads?’) As it turns out, our actual patters of reasoning appear to differ significantly from the canons of logic (as suggested by the experiments in the ‘heuristics and biases’ tradition, and as extensively discussed by e.g. G. Harman, among others), so the is/ought dichotomy is particularly delicate in this case.

Very interesting post! And I've been thinking ...

2010-01-30T12:02:59.814Z

Very interesting post! And I've been thinking about similar things lately.

A couple of weeks ago, Florian was talking about separability, and Stewart Shapiro asked: Are claims about the justification of logical inferences empirical or normative?

Florian's answer was: normative. However we actually come to learn/acquire logic rules and reasoning techniques, the question is whether there is a reconstruction of them which shows that they preserve warrant.

Florian's answer seems right to me. But it raises the further question. How closely must your reconstructions track actual cognitive processes?

Certain kinds of reconstruction may look nothing like the actual processes of concept acquisition (whatever they look like). The question is, why we should think that this matters. If all we wanted to know was whether our practices are justifiable?

In fact, I think there is a risk here. Certain kinds of traditional interests interests for proof theorists seem to depend upon quasi-empirical claims. For example: it is not immediately clear why we should care about issues like separability. The justification often given for separability is that that, in the reconstruction, we'd want to acquire concepts one-by-one. But why must reconstructions have that form?

We might try to justify an interest in separability on other grounds. In particular, it tends to be easier to prove nice results about separable than logics than about non-separable logics. So, in Popperian spirit, we should start with the separable logics, and see how far we can get with them; if we don't get very far, then we should start investigating non-separable logics. (Michael Potter suggested something a little like this, without mentioning Popper.)

The problem with this line of justification is the following. If you want to justify classical logic, and you find that separability is an impediment to that, you can simply (again, in Popperian spirit) drop the requirement of separability.

All of which makes me think a few things.

(1) How many other issues are affected in the same way as separability? For example, why should we insist that our reconstructions must be harmonious, once we've dropped separability?

(2) I think that neither Stewart's question, nor Florian's answer, depend specifically on any stance in the proof v. model theory debate. (As it happens, I think that Florian, you and I all reckon that proof theory and model theory are complementary, but tend to have a softer spot for proof theory.) So there ought to be similar issues for people who favour model theory over proof theory. I'm not yet exactly sure what they would be, but here's one thought. When we ask about truth (in the light of the Liar) and offer a Field-style model-theoretic story, we ought to ask why we should care about that kind of a reconstruction.

(3) Did Florian give the right answer to Stewart's question? I'm pretty sure he did. But I'm wondering if we might be able to find some cunning way to reject Stewart's question.

I'd be very interested to hear your thoughts!

Hey, what happened to my previous comment? Here it...

2010-01-27T19:37:17.437Z

Hey, what happened to my previous comment? Here it is again:

I think the most interesting recent work combining psychology and cognitive science with (philosophy of) logic is done by Keith Stenning and my colleague Michiel van Lambalgen:

http://www.amazon.com/Human-Reasoning-Cognitive-Science-Bradford/dp/0262195836/ref=sr_1_1?ie=UTF8&s=books&qid=1264612561&sr=8-1

Stenning is a cognitive scientist and van Lambalgen is a logician, and the combination yields very interesting results. One of their points is precisely that a better knowledge of logic as it is actually done can contribute to experimental research. They correctly point out in the book that the notion of 'logic' underlying most of the work in the psychology of reasoning tradition is much too narrow.

Also relevant for the interface between philosophy and cognitive science and psychology is the following recent volume:

http://www.amazon.com/Reasoning-Studies-Human-Inference-Foundations/dp/0521612748/ref=pd_sim_b_2

I forgot to mention that Keith Stenning works in E...

2010-01-27T19:10:12.983Z

I forgot to mention that Keith Stenning works in Edinburgh, so it shouldn't be too complicated to bring him over to St. Andrews...

I know Øystein. He comes very often to Buenos Aire...

2010-01-27T03:11:45.138Z

I know Øystein. He comes very often to Buenos Aires. I am very sured his project has a very bright future.