Logic and Metaphysics B

obligatory courses

(in Polish) Znajomość logiki na poziomie podstawowym, mile widziane zaliczenie logiki II.

Zajęcia tutorialowe (Tutorial part): znajomość logiki pierwszego rzędu i podstaw teorii mnogości (na poziomie kursu Logic II/Logika II), znajomość logiki modalnej (na poziomie kursu Logic and Metaphysics A).

Classroom

The tutorial consists of a lecture part (30 h.) and an exercise part (30 h.).

The aim of the lecture part is to offer a general perspective on the relationships between logic and philosophy. Special attention will be paid to the role played by logical methods in solving problems in metaphysics, such as realism vs. anti-realism with respect to universals, physical world, mind and mathematics, issues of causality, space and time.

The exercise part will be primarily focused on training in formal methods and applications of logic (in particular, modal logic) to philosophy and metaphysics. It will also include reading of philosophical papers, student presentations and discussions.

FROM 2020/2021

The tutorial consists of a lecture part (30 h.) and an exercise part (30 h.).

The aim of the lecture part is to offer a general perspective on the relationships between logic and philosophy. Special attention will be paid to the role played by logical methods in solving problems in metaphysics, such as realism vs. anti-realism with respect to universals, physical world, mind and mathematics, issues of causality, space and time. The lecture will give a brief survey of the uses of logic in metaphysics in the past (ontological argument, Kant’s arguments for realism, McTaggart’s argument for the unreality of time), but the focus will be on contemporary logical methods in metaphysic.

The exercise part will be primarily focused on training in formal methods and applications of logic (in particular, modal logic) to philosophy and metaphysics. Our list of topics includes: modality (basic notions and systems of modal logic, their syntax and semantics), selected applications of modal apparatus (conditionals and counterfactuals, knowledge and beliefs, provability) and non-existence (free logics and their philosophical and semantic applications). Apart from training in formal logic, we will also read and discuss philosophical papers, and students will do short text-based presentations.

FROM 2019/2020

The course will consist of a lecture part (30 h) and tutorial part (30 h). The lecture will focus on the more philosophical-metaphysical aspects of the issues covered, presenting both their historical origins, the basic intuitions behind them and their relationships to problems in other domains (epistemology, philosophy of mind, philosophy of science). The tutorial part will be more technical; its goal will be to introduce the students to the metaphysically relevant aspects of modern formal logic.

Issues to be covered in the lecture part:

(1) Space and time, their nature and structure

(2) Causality and causation

(3) Determinism-indeterminism debate

(4) Modal concepts and modal properties (necessity, possibility, contingency)

(5) Realism vs. antirealism with respect to modality

(6) The status of mathematical and other abstract objects

Topics of the tutorial part:

Below is presented and optimistic version of the programme. It is possible that important details, proofs of theorems or even whole items from the list below will be skipped in the classes.

1. Propositional intuitionistic logic, first-order intuitionistic logic. Kripke semantics for the intuitionistic logic. (2-3 classes).

2. Coding of syntax in arithmetic. Coding of finite sets, definition of provability. Basic properties of the provability predicate. Self-reference in arithmetic: Diagonal Lemma. (2-3 classes).

3. Goedel's Incompleteness Theorems, Tarski's Theorem on undefinability of truth. Rosser's theorem (3 classes).

4. Provability logic, Solovay's Theorem (2 classes).

5. Turing machines, undecidability of the halting problem. Connections with the First Goedel's Theorem. Church's Thesis. (3 classes)

FROM 2020/2021

Benthem van, J., Modal logic for open minds, 2010, manuscript.

Linsky, B. and E. Zalta, “In defense of the simplest quantified modal logic”, Philosophical Perspectives, (Logic and Language) 8, 1994, pp. 431–458.

Edgington, D., “On conditionals”, in D.M. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, Springer, 2001, Volume 14, pp. 127–221.

Stalnaker, R., “A theory of conditionals” in Studies in Logical Theory, American Philosophical Quarterly Monograph Series 2, 1968, Oxford: Blackwell, pp. 98–112.

Lewis, D., Counterfactuals. Oxford: Basil Blackwell, 1973.

Lehman, S., “More free logic”, in Handbook of Philosophical Logic, 2001, Volume 5, pp. 197–259.

Burge, T., “Truth and singular terms”, Nous, 8, 1974, pp. 309-325.

Sainsbury, M. “Referring descriptions”, in M. Reimer, A. Bezuidenhout (eds.), Descriptions and Beyond, Oxford: Oxford University Press, 2004, pp. 369-89.

Lowe, J. E., “A Survey of Metaphysics”, Oxford University Press 2002.

Dummett, M., “The Logical Basis of Metaphysics”, Harvard University Press 1976.

TO 2019/2020

1. James W. Garson, "Modal Logic for Philosophers", Cambridge University Press 2013

2. Rod Girle, "Modal Logic and Philosophy", Routledge 2009

3. Johan van Benthem, "Modal Logic for Open Minds", Center for the Study of Language and Information 2010

4. Paweł Urzyczyn, Morte Heine B. Sorensen (1998), "Lectures on the Curry-Howard Isomorphism", Elsevier Science Publishers

Knowledge: The student is acquainted with topics in contemporary metaphysics and with the principal debates therein. The student has a general orientation in some advanced topics and methods in formal logic and understands their applicability to problems in metaphysics.

Skills: The student is able to give an independent formulation to problems in contemporary metaphysic, and understands how to approach them with logical methods. The student is well prepared for further education and research in the fields of contemporary metaphysics and the applications of logic therein.

Social competence: The student is able to discuss highly abstract philosophical problems in a group, is sensitive to views and arguments of others, understands the importance of clear and disciplined discourse.

FROM 2020/2021

The requirements include: regular presence, a short presentation on a given topic related to the list of readings, and a positive result from the test organized in the second part of the semester. The final grade is calculated based on the outcome of the presentation, tutorial test, and the final exam.

Permissible number of absences: 2

TO 2019/2020

Attendance, active participation, tests and final exam.