### I've started a new blog

I don't promise higher frequency posting. Coming to a new city, it's easy to find time for blogging. If I get a life, however, productivity might drop. Sounds like a good deal to me.

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Nothing of Consequence

## Friday, March 04, 2011

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I've started a new blog

## Saturday, August 07, 2010

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Mini-course and Workshop on 'Logic or Logics?'

## Thursday, June 10, 2010

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FLC Conference

## Monday, June 07, 2010

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Translation of Thomas Bradwardine's 'Insolubilia'

## Wednesday, June 02, 2010

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FLC Audit

*June 9-11th, 2010*

## Tuesday, June 01, 2010

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Meeting in Honor of Jouko Väänänen's Sixtieth Birthday

*16-18th September, University of Helsinki*

## Tuesday, May 18, 2010

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Workshop

## Thursday, April 22, 2010

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Travel plans disrupted

## Saturday, April 03, 2010

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Helsinki visit

## Friday, March 05, 2010

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Paraconsistent Foundations of Mathematics Blog

## Sunday, February 21, 2010

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3rd FLC Workshop: Propositions, Context, and Consequence

## Thursday, February 18, 2010

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Categoricity and Absoluteness

A blog on the philosophy of logic, philosophy of mathematics and logic proper.

After moving to Munich and LMU I've started a new blog. There will be philosophy and logic, yes, but there will also be other things I'm interested in.

I don't promise higher frequency posting. Coming to a new city, it's easy to find time for blogging. If I get a life, however, productivity might drop. Sounds like a good deal to me.

I don't promise higher frequency posting. Coming to a new city, it's easy to find time for blogging. If I get a life, however, productivity might drop. Sounds like a good deal to me.

Posted by Ole Hjortland at 10:25 a.m. 0 comments

A little ad for our upcoming FLC event in Arché. Lots of great people will be around to talk about logical pluralism, revision of logic and combining logics.

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The members of the Arché Foundations of Logical Consequence project will be holding a Mini-course and Workshop on the theme 'Logic or Logics?' from 27 September - 1 October, 2010. The aim of the Mini-course is to provide intensive graduate-level instruction on the latest thinking about pluralism and revision in logic, followed by a Workshop dedicated to new research on the same theme.

If you are interested please register now at the following link: http://onlineshop.st-andrews.

The speakers for the Mini-course are:

• JC Beall (University of Connecticut)

• Carlos Caleiro (Instituto Superior Técnico, Portugal)

• João Marcos (DIMAp / UFRN, Brazil)

• Graham Priest (University of Melbourne/CUNY)

• Greg Restall (University of Melbourne)

• Gillian Russell (Washington University, St Louis)

• Johan van Benthem (University of Amsterdam)

The speakers for the Workshop are:

• JC Beall (University of Connecticut)

• Colin Caret (Arché, University of St Andrews)

• Roy Cook (University of Minnesota)

• Ole Hjortland (Arché, University of St Andrews)

• Greg Restall (University of Melbourne)

• Penelope Rush (University of Tasmania)

• Gillian Russell (Washington University, St Louis)

• Johan van Benthem (University of Amsterdam)

Further inquiries should be directed to arche@st-andrews.ac.uk

Posted by Ole Hjortland at 11:14 a.m. 0 comments

Labels: Conferences, Logical pluralism, Logical Revisionism

This weekend is our 1st FLC conference. We have an amazing group of invited and contributing speakers, plus a number of other visitors from all over. The full programme with commentators is here.

Posted by Ole Hjortland at 2:28 p.m. 0 comments

I just found out that Stephen Read's edition of Thomas Bradwardine's *Insolubilia* is available. This is the first full translation of Bradwardine's work on paradoxes. (For more on insolubles, see here.) The edition has a long introduction by Stephen Read, comparing Bradwardine's theory both to medieval and contemporary approaches to semantic paradoxes. The text, which contains both the Latin and the English, is based on all thirteen known manuscripts. Highly recommended reading, not only for historians of logic, but for anyone interested in paradoxes.

Posted by Ole Hjortland at 9:25 a.m. 2 comments

Labels: History of Logic, Medieval

Once a year the AHRC-funded projects in Arché have an academic audit. It involves an external auditor who comes to St Andrews to interview project members, and writes a progress report on their work. For the Foundations of Logical Consequence the auditor is Hartry Field. As part of Audit programme the auditor will give a paper next week, and so will the two postdoctoral research fellows in the project, i.e. Colin Caret and yours truly.

Here is the programme:

Wednesday 4-6pm: Hartry Field, "Is There a Problem about Revising Logic?"

Thursday 9-11am: Colin Caret, "Against Model Theory"

Friday 9-11am: Ole Hjortland, "Thrice Denied: Speech acts, categoricity, and the meaning of logical connectives"

More information on the upcoming FLC conference is soon to follow.

Posted by Ole Hjortland at 1:55 p.m. 2 comments

Labels: Audit, Conferences, FLC

The Helsinki Logic Group is organising a conference in honor of Väänänen's 60th birthday. The event is entitled "Set Theory, Model Theory, Generalized Quantifiers and Foundations of Mathematics". There is a great list of invited speakers, and also two tutorials on the 13-15th prior to conference.

Find more information here.

Posted by Ole Hjortland at 5:51 p.m. 0 comments

Labels: Conferences, Model-theory, Set-theory

December 7-8th, 2010

A little plug for an upcoming workshop in Amsterdam entitled: "From cognitive science and psychology to empirically-informed philosophy of logic". Quite a mouthful, but an interesting topic. The list of speakers is below, and the workshop also has a call for papers. More information here. I've already seen Pelletier talk about reasoning and generics, a topic that proved really interesting. Much recommended.

*Confirmed speakers*:

Johan van Benthem: Opening

David Over: "New paradigm phychology of conditionals"

Michiel van Lambalgen: "Logical form in cognitive processes"

Helen de Cruz: "Animal logic, an evolutionary perspective on deductive reasoning"

Rafael Nuñez: "Towards a cognitive science of proof"

Francis Jeffrey Pelletier: "Reasoning with generic information"

Catarina Dutilh Novaes: "Formal languages and the extended mind"

Posted by Ole Hjortland at 11:07 a.m. 0 comments

Labels: Conferences, Logic, Methodology, Psychology

Unfortunately, the air traffic ban in Europe prevented me from attending UNILOG'10 in Estoril, Portugal this week. Colin and I were hoping until the end that we could rebook, but it's been impossible to find another flight. A real shame - I've been to both the former UNILOGs, and I was really looking forward to seeing friends again. The good news is that Catarina, my co-teacher of the logical pluralism tutorial, finally made it to Estoril. She's put together a compressed version of the tutorial, so other attendees will still have the chance to see most of the material.

Also, thanks to the organisers for their tireless effort, despite the unhappy circumstances.

With a bit of volcanic cooperation, however, I * will * be on my way to Helsinki on Monday. As announced some weeks back, I'll be there on staff exchange giving lectures for both undergraduate and postgraduate students.

Posted by Ole Hjortland at 2:41 p.m. 0 comments

Labels: Conferences, Teaching

As I've said earlier, I'll be in Portugal between the 17th and 26th, for the 3rd UNILOG Congress. I thought I'd mention that I'll be moving straight from Lisbon to Helsinki the following week. I'll be there for six days on a Socrates staff exchange (an EU programme) between the University of St Andrews and the University of Helsinki. In other words, it's not a research visit, but a number of guest lectures for the students in Helsinki. I'll get back to you about the details and times when it's settled.

I'm much looking forward to meeting both faculty and students in Helsinki. Any suggestions about what else to do in Helsinki are welcomed.

Posted by Ole Hjortland at 10:32 a.m. 3 comments

Just to note that Zach Weber has set up a blog for the Melbourne based, ARC-funded project:* Paraconsistent Foundations of Mathematics*. Zach Weber is a post doc on the project, working together with Chief Investigators Graham Priest and Greg Restall. In addition, Francesco Berto, from the University of Aberdeen, NIP, is a research associate.

You can read about the aim and background on the blog. If you want the real thing, go look at Zach's PhD thesis *Paradox and Foundation* here.

Posted by Ole Hjortland at 10:57 a.m. 0 comments

March 20-21st, 2010

It's about time to advertise our upcoming *3rd FLC Workshop*, entitled 'Propositions, Context, and Consequence'. This time around the Foundations of Logical Consequence project moves into an area closely connected to the Contextualism & Relativism project. We're having a two day workshop focusing on the *relata of consequence*, *context-sensitivity*, *indexicality*, and more.

The speakers:

Francesco Berto

Catarina Dutilh Novaes

Walter Pedriali

Martin Pleitz

Stewart Shapiro

Hartley Slater

Isidora Stojanovic

Elia Zardini

Programme and more information here.

Posted by Ole Hjortland at 8:00 a.m. 0 comments

Labels: Conferences, Contextualism, Logic, Semantics

There are lots of ways of being a *logical inferentialist*. I've harped on a number of times about *proof-theoretic harmony* and other proof-theoretic constraints that inferentialists favour. In short, these approaches, which mostly concern themselves with finding, in some sense, appropriate pairs of rule-sets (in natural deduction or sequent calculus), are following in the tradition of Nuel Belnap. His was probably the most influential reply to Prior's venomous tonk-paper. Yet, there were a series of other replies, some of which receive little attention in the contemporary debate about proof-theoretic semantics.

People like J.T. Stevenson ("Roundabout the runabout inference-ticket") and Steven Wagner ("Tonk") had---perhaps like Prior himself---little sympathy for proof-theoretic semantics (in its early versions by Popper and Kneale). Both suggested that the real trouble with tonk is its blatant disregard for the underlying truth-conditional semantics (in fact, Stevenson is even looking for truth-*functional* semantics). These replies were mostly ignored in the harmony industry, for two different reasons, I suspect: First, a recourse to Tarski style semantics was precisely what the proof-theoretic semanticists were trying to avoid. Second, even if you thought there was something to the idea that when a set of rules *determine *the meaning of a logical connective, it determines a truth-condition, the above papers offered little or no insight into how to formalise this connection. In fact, both appear to be mostly concerned with classical logic (and boolean values).

Yet, their suggestion comes with some merits. First, inferentialists, although they provide an interesting idea of how *concept-acquisition* works for logical concepts, had more to say about justification of deduction than about the *nature of semantic content*---other than that it's not truth-conditional à la Tarski. Wagner suggests a worthwhile Fregean distinction (I here adopt some terminology from Hodes "On the sense and reference of a logical constant"): Although inference rules are constitutive of the *sense* of a logical connective, the *reference* is not to be identified with the set of inference rules. Rather, the reference is truth-conditional and it is determined by the sense. There is a hope here of having the best of two worlds. On one hand we get a recognised theory of semantic content; on the other hand we can still adopt the inferentialist's thinking about entitlement to inference.

But despite any initial advantages, the problems described above still remain. How precisely does the relation between inference-rules and truth-conditions work? How do the inference rules *carve out* the semanic content? And, importantly, is this simply a way of spelling out a relationship between *classical* inferences and *classical* semantics?

In an attempt to answer these questions I've worked on some technical notions that can help give us the appropriate go-between for the truth-conditions and the inference rules. Standardly, proof-theory and model-theory is kept together by soundness and completeness, but these results tell us little in way of how the rules of the proof-theory determine what the models look like. We can highlight this in a straightforward way. Assume that we have an antecedent idea of some basic semantic concepts, in particular, the difference between our designated and undesignated truth values. However, assume that we have no antecedent notion of the semantic conditions for the logical connectives in question (over and above that they operate on said values). Consider then the example of classical logic, in a standard (single-conclusion) natural deduction system. Carnap showed that such systems are *non-categorical* in the sense that the inference rules are sound and complete with respect to two distinct classes of boolean valuations. (In fact, to an infinite number of different ones, see Hardegree's "Completeness and Super-Valuations".) Of course, only one of these classes is the *admissible* class of classical valuations, in the sense that it can be induced from the atomic assignments via the truth-conditional clauses for connectives. However, the point in the inferentialist context is precisely that these clauses cannot be assumed; they must be *determined* by the proof-theory. In our example, the non-categoricity amounts to a sort of non-uniqueness result for the proof-system at hand (with respect to boolean valuations).

It is natural, then, to think of categoricity as constraint one would like to impose on a proof-system for the rules to determine the truth-conditions. The idea is as follows: If the rules are sound and complete with respect to only one class of valuations, then we have learned something about the semantic content of the connectives; namely that their truth-conditions must respect whatever conditions the class of valuations yields. If we move to a multiple-conclusion system, Shoesmith and Smiley (*Multiple-Conclusion Logic*) showed us that we get precisely this. A classical multiple conclusion system is only sound and complete with respect to the class of classically admissible valuations. We have, in other words, a way of carving up the truth tables for classical connectives looking exclusively at the inference rules. Of course, we do apply some background assumption about what the matrices contain (e.g., the values), but we make no assumption about the semantic content of, say, negation and disjunction.

What about *non-boolean matrices*? Without getting into details, it is crucial that the notion of categoricity at play in Shoesmith and Smiley's work is defined with respect to *partitions* of formulae into those that a valuation takes to 1 and those it takes to 0 (for the boolean values). When we go (finitely) many-valued, on the other hand, the partitions glosses over distinctions that don't cut across the designated/non-designated divide. Put differently, the definitions aren't fine-grained enough. We can learn something about the consequence relation from the inference rules, since consequence (at least normally) is only concerned with *preservation of designated values*. But, the truth-functions contain more detailed information, that can not be coded by proof-systems that can be categorical in the above sense.

What is called for is the more fine-grained notion of *absoluteness*. There is interesting work on this in Dunn and Hardegree's *Algebraic Methods in Philosophical Logic*. Again, without being too precise, absoluteness holds of a class of valuations just in case the logic induced from the class of valuation, itself induces a class of valuation which is identical to the original. I.e., *V* = **V**(**L**(V)), where **V** and **L** are functions such that (a) *L*(*V*) is the class of arguments not refuted by any valuation *v* in *V*; and (b) *V*(*L*) is the class of valuations which refutes no argument in *L*. (A *logic* is meant in the minimum sense of a class of arguments; of course the shape of them, e.g., single- vs multiple-conclusion (premise), will matter.)

Absoluteness is a stronger notion than categoricity. In fact, whereas Shoesmith and Smiley proves that every finitely many-valued logic is categorical with respect to a multiple-conclusion system, the result does not hold for absoluteness. Multiple-conclusion, although sufficient in the boolean case, doesn't hold in general. What is needed, it turns out, are generalisations using *n*-sided sequent systems, where* n* is the number of values in the logic in question. Such systems have been explored in much detail in Richard Zach's *Proof theory of finite-valued logics*.

Posted by Ole Hjortland at 8:00 a.m. 2 comments

Labels: Inferentialism, Many-valued logics, Proof-theory, Semantics

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