MATHEMATICAL LOGIC

The course provides an introduction to formal ontology, starting with the analogy with formal logic. It will address how logical frameworks, broadly construed, are useful to provide rigorous formulations and analyses of several metaphysical questions, and to suggest different solutions. In particular, the course will focus on the logic of parthood, an absolutely central notion of our conceptual system. After a preliminary introduction on the formal mathematical properties of the parthood relation, we will discuss classic questions such as the relation between the matter that constitute an object and the object itself, the problem of atomism and infinite divisibility of matter, the existence of the universe. We will conclude with the discussion of several questions---the nature of extension, the persistence of material things, fundamentality of the universe, monism and pluralism---the require a systematic development of the interaction between the logic of parthood with other central notions, e.g., location and dependence.

The course offers a first introduction to the use and application of sophisticated formal tools to philosophical questions of crucial importance. The course also introduces mathematical theories that are indispensable in contemporary philosophy: order theory, algebraic structures, and measure theory.

Familiarity with sophisticated formal logic, rigorous formulations of central philosophical questions.

Formally, there are no pre-requisites. As far as possible, everything will be introduced in class. A certain familiarity with first order logic---e.g., a course in Logic 1---represents an advantage. Attendance is highly recommended.

Formal Logic, Formal Ontology: The logic and mathematics of parthood

Part I: Formal Development

• Introduction: Formal Logic and Formal Ontology (Reading: Hofweber (2020)).
• Background Logic, and Theory of Order (Reading: Varzi (2016))
• Decomposition Principles (Reading: Varzi (2016))
• Composition Principles 1 (Reading: Varzi (2016))
• Composition Principles 2: Algebraic Structures (Reading: Varzi (2016))

Part II: Metaphysical Issues

• The Composition Questions, Composition and Identity (Reading: Korman and Carmichael (2016)).
• Atomism (Reading: Varzi (2017))
• Universalism and Extensionalism, Heaps and Structures (Reading: Cotnoir (2016))

Part III: Interaction with other (Formal) Notions

• Parthood and Location 1: The Subregion Theory of Parthood (Reading: Markosian (2014))
• Parthood and Location 2: Persistence (Reading: Gilmore (2018), \S1-\S3 and \S6.3.2)
• Parthood, Location and Extension: Extended Simples, Unextended Complexes, Measure Theory (Reading: McDaniel (2007))
• Parthood, Dependence and Fundamentality: Priority Monism (Reading: Schaffer (2010))

Disclaimer: The program is tentative and could be adjusted.

[1] Cotnoir, A. 2016. Does Universalism Entail Extensionalism? Noûs 50 (1):121-132.

[2] Gilmore, C. 2018. Location and Mereology. Stanford Encyclopedia of Philosophy. At: https://plato.stanford.edu/entries/location-mereology/ .

[3] Hofweber, T. 2020. Logic and Ontology. Stanford Encyclopedia of Philosophy. At: https://plato.stanford.edu/entries/logic-ontology/ .

[4] Korman, D. and Carmichael, C. 2016. Composition. In Oxford Handbooks Online. DOI: 10.1093/oxfordhb/9780199935314.013.9

[5] Markosian, N. 2014. A Spatial Approach to Mereology. In Kleinschmidt, S. (ed). Mereology and Location, Oxford, Oxford University Press: 69-90.

[6] McDaniel, K. (2007b). Brutal simples. Oxford Studies in Metaphysics, 3, 233–265.

[7] Schaffer, J. 2010. Monism: The Priority of the Whole. The Philosophical Review 119: 31-76.

[8] Varzi, A. 2017. On Being Ultimately Composed of Atoms. Philosophical Studies, 174: 2891-2900.

[9] Varzi, A. 2016. Mereology. Stanford Encyclopedia of Philosophy. At: https://plato.stanford.edu/entries/mereology/ .

Class participation, discussion.
The exam consists of a written paper on one of the topics of the course. The topic needs to be agreed in advance. Further references on such topic will be suggested. The paper should not exceed 3000 words. Students that submit the paper a month before the scheduled exam will be sent written comments on the draft in advance.

The course is structured around frontal lectures. However active participation (questions, discussion) is highly encouraged.

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