Yes or no? Is there such a thing as philosophical logic? Which contrast? The case of determinism Lukasiewicz Thomas M¨uller Prior Thomason What is [email protected] philosophical Department of Philosophy logic? Utrecht University Guangzhou, 12 November 2012 Cultures of Mathematics and Logic 1 Logic today is a multidisciplinary endeavor, spanning a.o. I computer science I linguistics Yes or no? Which contrast? I mathematics The case of I philosophy determinism Lukasiewicz Prior Thomason Logic and philosophy: evolving interrelation What is philosophical I Logic used to be a branch of philosophy (like so much else) logic? I Philosophical questions were a key driving force, e.g. • for ancient and medieval logic • for formal logic in the 20th century I What is the relation between logic and philosophy now? I Specifically: Is there such a thing as philosophical logic? I Several fields of interaction, e.g., determinism 2 Overview Yes or no? Yes or no? Which contrast? The case of determinism Which contrast? Lukasiewicz Prior Thomason What is The case of determinism philosophical logic? Lukasiewicz Prior Thomason What is philosophical logic? 3 NO It's not in the Dictionary of philosophical terms Yes or no? Which contrast? The case of determinism Lukasiewicz Prior Thomason What is philosophical logic? Nor in most other reference works (e.g., SEP) 4 YES Yes or no? Which contrast? The case of determinism There's a successful Journal of philosophical logic Lukasiewicz Prior There's a successful Handbook of philosophical logic Thomason What is philosophical cover image cover image logic? And there's more 5 From the Handbook of philosophical logic \The Handbook of Philosophical Logic is a unique systematic survey of the central areas of philosophical logic. [. .] Written Yes or no? by world authorities in philosophical logic [. .]" Which contrast? The case of determinism \[T]he field of philosophical logic [is] vast and heterogeneous Lukasiewicz Prior with roots in general philosophy, mathematical logic and Thomason theoretical linguistics to cite just a few [. .]" What is philosophical logic? Distinguishes \work done under the term philosophical logic", which also includes work from \related disciplines like the philosophy of science or the philosophy of mathematics", from philosophical logic proper Important canonizing function (2nd edition is much larger) But no definition of the field 6 From the Journal of philosophical logic Aims and scope says: The Journal of Philosophical Logic aims to provide a forum for Yes or no? work at the crossroads of philosophy and logic, old and new, Which contrast? with contributions ranging from conceptual to technical. The case of determinism Accordingly, the Journal invites papers in all of the traditional Lukasiewicz Prior areas of philosophical logic, including but not limited to: various Thomason What is versions of modal, temporal, epistemic, and deontic logic; philosophical constructive logics; relevance and other sub-classical logics; logic? many-valued logics; logics of conditionals; quantum logic; decision theory, inductive logic, logics of belief change, and formal epistemology; defeasible and nonmonotonic logics; formal philosophy of language; vagueness; and theories of truth and validity. In addition to publishing papers on philosophical logic in this familiar sense of the term, the Journal also invites papers on extensions of logic to new areas of application [. .] 7 \Philosophical logic": history (I) Historisches W¨orterbuchder Philosophie has an entry on Yes or no? philosophical logic in the modern era Which contrast? The case of determinism Lukasiewicz Prior Thomason What is philosophical logic? 8 \Philosophical logic": history (II) \Philosophical logic" of 16th cent. ff. criticized as \without insight for deep problems, psychologistic" (Boche´nski) Yes or no? Which contrast? Focus on semiotics, concepts The case of determinism Lukasiewicz Kant: Focus on judgment Prior Thomason I Formal logic, as studying only the pure form of thought | What is philosophical for Kant, completed with Aristotle logic? I Formal issues: identity, non-contradiction I Transcendental logic. Table of categories, necessary kinds of content \Laws of thought", but aim to be non-psychological Not our notion of philosophical logic 9 Which contrast? If there is \philosophical logic", is it philosophical rather than: Yes or no? Which contrast? I symbolic? (as in Journal of symbolic logic) The case of determinism I formal? (as in Notre Dame journal of formal logic) Lukasiewicz Prior I applied? (as in Journal of applied logic) Thomason What is I mathematical? (as in Journal of mathematical logic) philosophical logic? I ...? Many clear non-candidates for the relevant contrast, e.g.: ancient, deontic, epistemic, intuitionistic, modal, paraconsistent, Polish, provability, quantum, relevance, spatial, . 10 Philosophical rather than mathematical \Mathematical logic" nowadays seems clear enough: I Logic as practiced by mathematicians Yes or no? I Canonical subfields: set theory, model theory, recursion Which contrast? theory, . The case of determinism Lukasiewicz I Research on \structural" questions, or triggered by Prior questions in mathematics Thomason What is I Channels back to mainstream mathematics (at least to philosophical logic? some extent) I Technically hard Contrast philosophical logic: I Logic as practiced by philosophers? I No link back to mathematics? (Nowadays?) I Often technically simple 11 Philosophical rather than formal Could it be logic if it's not formal? After all, logic is a formal science if there is one Yes or no? Which contrast? There are courses in \informal logic", or argumentation theory The case of determinism Lukasiewicz If logic is about \telling good arguments from bad", then such Prior Thomason informal logic is logic What is philosophical logic? But I a large part of philosophical logic is formal; I it's not clear that informal logic belongs to philosophy, rather than, e.g., psychology or rhetoric Still, there's a tradition of logics for specific content (not-just-formal logic?) 12 Philosophical formal logic Yes or no? Which contrast? Most of philosophical logic is formal|but \not just formal"? The case of determinism Lukasiewicz Belnap, Notes on the science of logic: Prior Thomason Philosophical logician is interested in what the formalism e.g., What is philosophical of a three-valued logic, means. logic? Is there \content to the form"? Or is form enforced by (philosophical) content? 13 (In)determinism in philosophy Rough idea: Determinism claims that there is just one Yes or no? possibility for the future; indeterminism: more possibilities Which contrast? The case of determinism Lukasiewicz Loose associations for \determinism" / \deterministic": Prior Thomason What is + precision, dependability philosophical + total control logic? − ironclad necessity, preordained − making us helpless − exclusion of control through us 14 (In)determinism and (philosophical) logic Philosophical problems of determinism have led to many Yes or no? developments in (philosophical?) logic Which contrast? The case of determinism Example here: Lukasiewicz Prior Future contingents: claims about the open future Thomason What is philosophical Three episodes from the 20th century: logic? I Lukasiewicz, three-valued logic I Prior, temporal logic I Thomason, supervaluations 15 Determinism and three-valued logic JanLukasiewicz Yes or no? I \On the notion of Which contrast? possibility" (1920): The case of determinism Motivating a 3rd truth Lukasiewicz Prior value via possibility Thomason What is I \On three-valued logic" philosophical (1920): logic? pic Tables for 3-valued connectives I \On determinism" (rectoral address Warsaw, 1922): Use of 3-valued logic for future possibility 16 Lukasiewicz: three-valued logic On determinism (1922) Yes or no? Which contrast? I Determinism: \If A is b at instant t it is true at any The case of determinism instant earlier than t that A is b at instant t" Lukasiewicz Prior I Reference to Aristotle's De interpretatione Thomason What is I \To me, personally, the principle of bivalence does not philosophical appear to be self-evident. [. .] Indeterminate sentences, logic? which ontologically have possibility as their correlate, take the third truth value." I \The logical argument which seems to support determinism falls decisively." 17 Determinism and temporal logic Arthur Prior Yes or no? Which contrast? I Studied ancient and The case of determinism medieval texts Lukasiewicz Prior I John Lock Lectures, Thomason Oxford 1955/56: Time What is philosophical and Modality logic? pic I From Diodorean modality to branching time: Invention of formal temporal logic I Past, Present and Future (1967) 18 Prior: tense (temporal) logic and branching time I Tense logic: \it will be the case that" (F ) and \it was the case that" (P) as sentence-modifying operators Yes or no? Which contrast? I Atomic propositions: present-tensed The case of determinism I \The truth-functional technique seems simply out of place" Lukasiewicz Prior I Suggestion Kripke: possibility via tree-like structures Thomason What is I History: maximal chain in tree philosophical logic? I Main difficulty: Give semantics for future tense F 0 0 • Standard relational, m j= F φ iff ex. m > m, m j= φ • Peircean, m j= F φ iff in every history h through m ex. m0 > m, m0 2 h, s.t. m0 j= φ 0 0 0 • Ockhamist, m=h j= F φ iff ex. m > m, m 2 h, s.t. m j= φ 19 Branching time: moments and histories Yes or no? Which contrast? The case of determinism Lukasiewicz Prior Thomason What is philosophical logic? m m 20 Prior: tense (temporal) logic and branching time I Tense logic: \it will be the case that" (F ) and \it was the case that" (P) as sentence-modifying operators Yes or no? Which contrast? I Atomic propositions: present-tensed The case of determinism I Suggestion Kripke: possibility via tree-like structures Lukasiewicz Prior I History: maximal chain in tree Thomason What is I Main difficulty: Give semantics for F philosophical 0 0 logic? • Standard relational, m j= F φ iff ex. m > m, m j= φ Too many true • Peircean, m j= F φ iff in every history h through m ex.