Wilfrid Hodges' logic page

Personal

Dr Wilfrid Hodges
Herons Brook
Sticklepath
Okehampton
Devon EX20 2PY
Phone 01837 840154
E-mail my first and last names with a dot between them, at btinternet.com.
My old QMUL website containing corrigenda to textbooks.

Married since 1965 to Helen M. Hodges, Emeritus Professor, Institute of Psychiatry, Kings College, University of London.
Children (all with Facebook pages):

• Sally Watson = Dr Sally Hodges, Tavistock and Portman NHS Foundation Trust;
• Gale Hodges;
• Edwin (Eddy) Hodges.

Directions for reaching me by car are here, and pictures of the house and property are here.

Bibliography and CV

A list of my publications is here. My CV is here.

The lectures below come with two health warnings. First, when I lecture I add explanations and comments; you will have to imagine these. Second, there are some mistakes, some of which are corrected in the published versions indicated.

Arabic logic and semantics

Translations of Ibn Sina

1. 'Ibn Sina and conflict in logic', for a Festschrift. (Revised draft 18 August 2009.) This contains a commented translation of Ibn Sina's commentary on the final section of Aristotle, Peri Hermeneias. Ibn Sina tackles some particularly incomprehensible remarks in Aristotle with the aid of some thoughts about lengths of proofs. There is also a polemical section which seems to be intended to show that metatheorems of logic - in particular those of the kind illustrated by the more recent laws of distribution and interpolation theorems - are just as useful for philosophical argument as the laws of logic itself. If Ibn al-Tayyib is Ibn Sina's target in this passage, it may help to explain why Ibn al-Tayyib came to dislike Ibn Sina so much.

2. 'Ibn Sina on patterns of proofs' (Revised draft 6 October 2009.) Ibn Sina defines two different notions of compound syllogism and studies the relations between them.

3. 'Ibn Sina on analysis: 1. Proof search. Or: Abstract State Machines as a tool for history of logic', for a Festschrift. (Revised draft 6 September 2009.) This contains a commented translation of a section of Ibn Sina's commentary on a couple of paragraphs of Aristotle's Prior Analytics. Ibn Sina seems to be giving his reader a string of 64 exercises to train the reader in a proof search algorithm for syllogisms. I confirm that he is doing this, by extracting from his text all the essential ingredients of an Abstract State Machine for the algorithm.

4. Other commented translations of Ibn Sina's logic will appear here as they become available. Probably the next will be his treatment of reductio ad absurdum. This contains an early form of the rule of arrow-introduction, together with some supporting theory that bears close comparison with Frege. Besides that, I will try to get up on this site translations of passages referred to in the papers already here.

Other items on Arabic logic

1. Lecture on Definitions in Ibn Sina's Jadal, from conference 'The Topics in the Arabic and Latin Traditions', CRASSH, Cambridge 2006.

2. Lecture on Ibn Sina's semantics, Seminar, Department of Philosophy, St Andrews June 07.

3. Lecture on Ibn Sina's syllogistic, Oxford, November 07. This lecture had the strictly limited aim of describing in modern terms a formal system adequate to support what Ibn Sina says about the semantics of predicate syllogisms. After reading more of Ibn Sina I am no longer at all sure that it is adequate; there is evidence that a two-quantifier system is needed. The question is not easy. Ibn Sina's theory of knowledge made it acceptable for him to explain his basic concepts through worked examples rather than definitions; this can be very frustrating for modern interpreters.

4. Sprenger's translation of Risala al-Shamsiyya by al-Qazwini al-Katibi.
   

General history of logic

1. The history of British logic, British Logic Colloquium, Manchester, September 2001. It would be good to have the history of the origins of the BLC written up before too many memories die. I'm not offering to write it, but if I get a chance I will put here some of my old BLC archives. Meanwhile some corrections on this talk: (Page 3) The distinction was certainly noticed before Lukasiewicz, but it came slowly. Already Ibn Sina studies conversions between forms like A and forms like B. The rule of arrow-introduction is explicit in the Port-Royal Logic, though only for one-step inferences. Frege discusses the notion of making and resolving assumptions. (Page 16) As Tim Williamson pointed out, Lewis Carroll should be mentioned here. (Page 17) The word 'quantifier' appears first in De Morgan, as an abbreviation for 'quantifying phrase' - which comes from Hamilton as De Morgan acknowledges.

2. Indirect proofs and proofs from assumptions. I wrote this in 2004 to clarify in my own mind some issues raised by Paolo Mancosu, without any plans to publish it as it is. I still think it is correct in what it covers, but the absence of medieval logicians is unbalanced. In particular Ibn Sina should be discussed alongside the Port-Royal Logic and Frege. Mancosu has seen the paper but not responded.

3. What happened to fallacies?, Indian Logic Circle, Kolkata October 2005.

4. Logic versus theory of language in the late 19th century, Augustus De Morgan Workshop, Kings London November 2000.

5. Tutorial on Tarski and decidable theories, Mumbai 10 January 2005. A fuller version is in the Proceedings.

6. Tarski on Padoa's method, International Conference on Logic, Navya-Nyaya and Applications, Homage to Bimal Krishna Matilal, Kolkata January 2007. A fuller version is in the Proceedings.

7. The history of model theory. This was written for a handbook on the history of mathematical logic (not the more recent Gabbay-Woods many-volume handbook). Before the paper was finished, the terms of reference were changed to ones that I didn't have the time to meet. So after some discussion I withdrew the chapter. Later the handbook itself folded. Anybody wanting to use any of this material in writing a history of early model theory is welcome to do that; if they contact me I might be able to supply some corrections and background.

8. Bill Marsh's unpublished 1966 DPhil thesis on uncountably but not countably categorical theories (included with his permission).

9. My paper 'Detecting the logical content: Burley's "Purity of Logic"' refers to a checklist of consequentiae in Burley's book. That checklist is here.

10. Where Frege is coming from, seminar, Amsterdam March 2009. The talk compares Ibn Sina, Leibniz and Frege on some key issues in logic and semantics, and aims to illuminate Frege by putting him into this context.

11. Why modern logic took so long to arrive, three lectures for Cameleon, March 2009. I trace the development, over the last two thousand years, of (1) relational reasoning, (2) proof rules that discharge assumptions, (3) type-theoretic semantics. There is a collection of texts to accompany the lectures, including eight pages of translation of Ibn Sina.

12. Traditional logic, modern logic and natural language, a paper that looks for the fundamental dividing lines between traditional logic and modern logic. Comparisons between traditional and modern logic tend to be based on an assumption that traditional logicians were aiming to do what modern logicians do, but weren't so good at it. Wouldn't it be better history, and fairer to all concerned, to try to establish what the traditionals themselves thought they were aiming to do? The paper is for a Festschrift, and the present version has the personal references removed.

13. How Boole broke through the top syntactic level. For the meeting History of Modern Algebra: 19th Century and Later, in memory of Maria Panteki, Thessaloniki October 2009. The talk notes that Boole broke with traditional logic by allowing substitutions at any depth in a formula. I discuss why this breakthrough marks a fundamental difference between traditional and modern logic, and how far Boole understood what he was doing in making the advance. Here is a draft of the writeup for the Proceedings.

14. A talk for the 60th birthday of Oleg Belegradek, Istanbul, December 2009. The talk contains a mixture of mathematical and personal reminiscences about how the Kemerovo model theorists (Belegradek and Zilber) came into contact with the British model theorists across the iron curtain.

Semantics in natural language, mathematics, engineering

1. From sentence meanings to full semantics, Mumbai 10 January 2005. A fuller version is in the Proceedings.

2. The interplay of fact and theory in separating syntax from meaning from Esslli 05 Edinburgh.

3. Architectural questions about theories of sentence and word meanings, Bristol October 2006.

4. The mathematical core of Tarski's truth definition, Unilog 2, Xi'an August 2007.

5. Composition of meanings for a workshop at Duesseldorf in 2003.

6. Necessity in mathematics was written for the Proceedings of a conference on Necessity and Contingency. But I can't get any confirmation that the Proceedings will appear. The paper was based on a review of the modal terminology in the first hundred pages of Birkhoff and Mac Lane, A Survey of Modern Algebra. The review contains more material, which I hope to report on soon.

7. Necessity in mathematics II. Slides for a talk at the 'Practice-based Philosophy of Logic and Mathematics' Workshop, Amsterdam, August-September 2009. The talk picks up some ideas from the preceding piece as evidence for the processes involved in understanding a mathematical textbook.

8. Models in science and technology, for a workshop in Delft, April 2004. This was an early stage in the writing of Functional modelling and mathematical models, to appear in a pioneering volume on the philosophy of technology.

9. The model theory of specification, Conference in memory of Sauro Tulipani, Camerino April 2006.

10. Model theory as Peacock's revenge. This is the unpublished original of a paper that appeared in Spanish translation. If retrospective dedications are allowed, I would like to dedicate this original to the memory of Maria Panteki, a learned and generous authority on George Peacock; she died in 2008, long before her time.

Mathematical logic

1. Short model theory course, Johannesburg December 1999.

2. Three tutorials in logic, Tbilisi 6-10 October 2003.

3. Draft of lecture on non-structure, Hattingen July 1999. Chris Laskowski and I gave lectures on non-structure; I reviewed the 'classical' material and Chris introduced more recent work. There was a plan for a joint paper, but it never materialised.

4. Classification over a predicate, Istanbul Bilgi University March 2001. The published version was devoted to the special case of theories of linear orderings. But see also the paper of Rami Grossberg in the same volume. Istanbul is an earthquake zone, and apparently there was an earthquake during my talk, but I never noticed.

5. Model theory of pairs of abelian groups, for St Petersburg July 2005. Here is an archived preprint of the version in press, which includes some nontrivial corrections. Anatoly Yakovlev was in the audience at the talk, and the paper includes his answer to the final Question on relatively categorical pairs of finite abelian groups.

6. Fully abstract valuations for subgames, De Morgan Workshop on Interactive Logic, London November 2005. A fuller version is in the Proceedings.

7. Maze games, proof games and some others, for 'Games in logic, language and computation', Amsterdam September 2005. Here is the PowerPoint. The talk contains some personal opinions about the motivation of game-theoretic modelling.

8. Mathematics of imperfect information, Kings London February 2000.

9. Set-theoretic definability of constructions. This was a report to the British Logic Colloquium in 2007 on the proof (with Saharon Shelah) that there is no formula of set theory which provably in ZFC defines an algebraic closure for each field. The proof is in two papers; one of them has appeared, and the other is in preparation.

Cognitive aspects of logic

1. Some notes I put up for my students at Queen Mary: Psychologists' tips on how and how not to learn. Though I take responsibility for the contents, I checked them with my wife who is a professional psychologist.

2. Some things a logician would like to know about human reasoning, CogSci 2001, Edinburgh August 2001. Another question I put to some cognitive scientists more recently is this: Where logical rules operate at deeper levels of the syntax of the sentences in question, presumably the ease of the inference (judged by speed and accuracy, say) is negatively correlated with the complexity of the sentences. Is there a further effect, that it is correlated negatively with the depth at which the rules operate? (Example inference: Mrs Sterne is the Queen of Bohemia. I met the husband of the person who used to be Mrs Sterne's lifestyle guru. Therefore I met the husband of the person who used to be the lifestyle guru of the Queen of Bohemia.) The reason for the question is historical: It's often claimed that the restriction of aristotelian logic to top-level processing has something to do with natural language reasoning. My suspicion is that this is completely untrue; everyday reasoning tends to use relatively simple sentences, but the rules of first-order logic that operate at deeper levels create no particular problem for natural language reasoning. I've had no answers back yet.

3. Efforts to make mathematics infallible, Workshop on semantic processing, logic and cognition, Tuebingen November 2005.

4. How reasoning depends on representations, two lectures to Centre for Cognitive Science, Jadavpur University, Kolkata, October 2005. The work of Keith Stenning that I discuss here has moved on: see Keith Stenning and Michiel van Lambalgen, Human Reasoning and Cognitive Science, MIT Press, Cambridge Mass. 2008.

Mathematics and music

1. Talk on Pythagoras, QMW Oct 98. A revised version of this talk was given as the Coulter McDowell Annual Lecture at Royal Holloway in 2001. Pythagoras must have been an extraordinary person, but modern scholarship has stripped him of most of his supposed scientific advances. One that is still sometimes attributed to him is the correlation between subdivisions of a vibrating string and points of the musical scale. I argued, relying on the shapes of kitharas and the known techniques for playing them, that this correlation was probably clear to professionals at least a generation before Pythagoras. It would be consistent with what we do know about Pythagoras if he took this known correlation and converted it into some kind of music therapy. (Sad footnote: I tried unsuccessfully to discuss this with the late and much missed David Fowler, who was an expert both on Greek mathematics and on the mathematics of the musical scale. Later I learned that at the time he was already severely ill with the brain tumour that took him not long after.)

2. Some raw material on mathematical and musical beauty, for a meeting of mathematicians and artists organised by Juliette Kennedy in Utrecht, November 2007. For copyright and technical reasons, most of the music itself is missing here. The talk draws on an archive of geometrical patterns in music. Material from the same archive went into my Third Annual Venn Lecture in Hull in 2003, and into two published papers (first), (second), one joint with Robin Wilson. For some years I have hoped to turn the archive into a book, but it is not high priority.

3. Time, Music and Mathematics. Slides for a talk at the Greenwich Observatory, November 2009.

4. The geometry of music, one of a group of lectures on mathematics and music arranged by Robin Wilson at Gresham College to mark his retirement from the post of Professor of Geometry at Gresham. My handout is here. The lecturers were Robin himself and me (November 2009) and Jonathan Cross (December 2009).

IUHPS DLMPS

The website of the IUHPS Division of Logic, Methodology and Philosophy of Science is at http://www.dlmps.org.