Sep 16, 2013 ... Erik Stenius. • Donald Davidson. • Ingemar Hedenius. • Jaakko Hintikka. •
Wilhelm K. Essler. • Saul Kripke. • Dagfinn Føllesdal. • David Kaplan.
THE HÄGERSTRÖM LECTURES 2013
TIMOTHY WILLIAMSON Logic as Metaphysics September 16–20, 2013
FILOSOFISKA INSTITUTIONEN
Logic as Metaphysics Lecture 1: Logic and Dialectic Commentator: Jonas Åkerman (Stockholm) Monday September 16, 2 P.M. – 4 P.M. Auditorium Minus, Gustavianum Abstract: Logic is often cast in the role of a referee between competing scientific or metaphysical theories, and therefore as having no scientific or metaphysical content of its own, on pain of losing its required neutrality. This conception exerts pressure to keep logic as weak as possible. However, it is hopeless because virtually every putative principle of logic ever formulated has been challenged on metaphysical or even scientific grounds. The attempt to finesse the problem by relativizing logic to a dialectical context is unpromising because it makes the science of logic too ad hoc. A different response is to argue that the supposed challenges are purely verbal, because the two sides do not mean the same by their logical symbols. However, such a response is not grounded in plausible principles of interpretation in the way it claims to be. In particular, it is not well-motivated by interpretative charity. Moreover, it is undermined by the way in which meanings are socially determined. In the case of the dispute between classical and intuitionistic logic, a simple technical result excludes a certain sort of peaceful coexistence between the two sides. In short, the appearance of disagreement in logic is veridical.
Lecture 2: Logic as an Abductive Science Commentator: Thomas Ekenberg (Uppsala) Tuesday September 17, 1 P.M. – 3 P.M. Auditorium Minus, Gustavianum Abstract: On an alternative conception of logic to that considered in Lecture 1, logical theories are much more like other scientific theories than is usually thought. Consideration of Tarski’s classic account of logical truth in the setting of higher-order logic shows how to associate with each logic a theory generated by a set of non-metalinguistic universal generalizations that demand scientific investigation. A pragmatic aspect is permitted in the selection of logical constants, since it will depend on the aims of the inquiry at hand. In choosing between logical theories of this sort, no recourse is needed to a transcendental superlogic. Rather, we use a standard abductive methodology, choosing between theories on grounds of simplicity, strength, elegance, unifying power, and consistency with known facts (the relevant notion of consistency here is again immanent, not transcendental; it can just be a matter of not entailing all sentences of the language in the given logic). This methodology may seem to assimilate logic to the natural sciences, in the manner of Quine’s ‘Two Dogmas of Empiricism’. However, as Russell already saw, the abductive methodology plays a significant role in foundational aspects of mathematics, without turning it into a natural science. It is in no more danger of doing so in the case of logic.
Lecture 3: The Problem of Achilles and the Tortoise Commentator: Sara Packalén (Stockholm) Wednesday September 18, 2 P.M. – 4 P.M. Auditorium Minus, Gustavianum Abstract: The account of logic in Lecture 2 focuses on logical truth at the expense of logical consequence. In the light of Lewis Carroll’s classic paper ‘What the Tortoise Said to Achilles’, and in a much more developed way of the tradition of proof theory going back to Gentzen, this may look like a fundamental mistake. Isn’t logic the study of reasoning? However, any such conception involves a psychologization of logic that needs to be opposed, even when the study is qualified as prescriptive rather than descriptive (how we ought to reason rather than how we do reason). By carefully sifting out questions about psychological processes, we can answer recent arguments that seek to reveal some incoherence in the idea of choosing between logics in the manner suggested by Lecture 2. However, there are also essential non-psychological roles that only rules of inference, but not axiom schemas, can play, to which justice must be done.
(Compare a standard axiomatization of classical propositional logic with modus ponens as a rule of inference to an axiomatization in which all tautologies are axioms and there are no further rules of inference.) We can do more justice to those further roles by considering not just logics in isolation, but also their auxiliary role in combination with non-logical theories, such as those of natural science. This extension of the account is fully consistent with the abductive methodology already sketched.
Lecture 4: The Role of Higher-Order Logic Commentator: Matti Eklund (Uppsala) Thursday September 19, 1 P.M. – 3 P.M. Auditorium Minus, Gustavianum + Reception at the Philosophical Department afterwards Abstract: Logical principles, the universal generalizations discussed in Lectures 2 and 3, need to be formulated in a higher-order language, with quantification into any grammatical position in a sentence in which a non-logical constant can occur. For example, quantification into both predicate position and sentence position is needed. We therefore require some way of understanding such quantification. There are objections to any attempt to understand it in set-theoretic, substitutional, set-theoretic, or plural terms. Rather, it should be understood in its own terms, as sui generis, without any attempt to reduce it to something else. This raises the concern that we may be subject to some illusion of understanding. However, the proper response to such a concern is not to make the futile attempt to prove in advance that the higherorder language is intelligible, but rather to continue in the same conjectural, abductive spirit as before. If we are really talking nonsense, that should become evident soon enough. On the most natural way of developing the foregoing conception of logic, the generality is to be understood as absolutely unrestricted, but other aspects of the account may be compatible with a view of it as indefinitely extensible. The popular dichotomy between ontology and ideology will be criticized as embodying a tacit metaphysical bias in favour of first-order logic. On the conception I defend, higher-order logic is incomplete, so the consequences of that incompleteness need to be considered.
Lecture 5: Why Classical Logic? Commentator: Tor Sandqvist (KTH) Friday September 20, 2 P.M. – 4 P.M. Room IV University Main Building Abstract: The conception of logic developed in Lectures 1-4 makes non-classical logics genuine rivals of classical logic, but it also enables us to give an abductive defence of classical logic over its rivals in immanent rather than transcendental terms. Whereas the conception of a logic as a would-be neutral referee militated in favour of a weak logic, and therefore very likely a non-classical one, the conception of it as selected for its abductive virtues, such as simplicity and strength, tends to favour classical logic — not trivially, by some stipulation in its favour, but because classical logic is in fact strikingly simple and strong by comparison with its main rivals. The appropriate notion of comparative strength here is not the formal logical one (on which one theory is stronger than another if the former entails the latter but not vice versa) but rather the more general informal one familiar in philosophy of science (on which of two individually consistent but jointly inconsistent theories, one may be stronger than the other). For example, classical propositional logic is stronger than intuitionistic logic in both senses, but when we add propositional quantifiers and make ¬ ∀ P (P ∨ ¬P) an axiom of the intuitionistic system its classical analogue is stronger in the second sense but not the first (for reasons given in Lecture 1, we may treat translation between the systems homophonically). Similarly, that is the sense in which special relativity is stronger than its negation. The best case for logical deviance comes from examples in which weakening the underlying logic permits us to strengthen some other principle in compensation — for example, a disquotational principle for a truth predicate. However, even there the choice of the non-classical logic involves prioritizing a special science over a more general one in a way that looks methodologically wrong-headed from a scientific point of view (compare sacrificing a principle of fundamental physics in order to retain one of evolutionary biology).
Timothy Williamson will be the thirty seventh Hägerström Lecturer. Previous lecturers have been • Konrad Marc-Wogau
• Richard M. Hare
• Georg Henrik von Wright
• D. Hugh Mellor
• Willard Van Orman Quine
• John Broome
• Patrick Suppes
• Martha C. Nussbaum
• Peter Geach
• Judith Jarvis Thomson
• Alonzo Church
• Hidé Ishiguro
• David Lewis
• Margaret Boden
• Amartya Sen
• Max Cresswell
• Erik Stenius
• Richard Jeffrey
• Donald Davidson
• Christine Korsgaard
• Ingemar Hedenius
• Julia Annas
• Jaakko Hintikka
• Marie McGinn
• Wilhelm K. Essler
• John McDowell
• Saul Kripke
• Ian Hacking
• Dagfinn Føllesdal
• Allan Gibbard
• David Kaplan
• Simon Blackburn
• Sören Halldén
• Bas van Fraassen
• Hilary Putnam
• Michael J. Zimmerman
