# Formal Methods in Philosophy and Related Disciplines

## Semester 1, 2017

Time
Mondays, 14.00–16.00
Location
Napier 204
Instructor
Antony Eagle

### Overview

This seminar will be an introduction to formal and technical tools that have been of use to philosophers and those doing foundational work in related disciplines (linguistics, mathematics, computer science, and economics). The emphasis will be on introducing the tools and exploring their properties, though some mention of applications will be made, especially in motivational remarks. No prior acquaintance with logic is required, though familiarity with introductory logic (such as that covered in Introduction to Logic, PHIL 1110) could be useful. The seminar is open to Honours, MPhil and PhD students in any discipline. It may also be possible for interested others to audit the class; please contact the instructor.

This course is part of the CaRST program for PGR students at the University of Adelaide.

It is provisionally proposed that assessment will be by weekly exercises, a short paper, and a take home exam, collectively equivalent to 5000 words. More details on assessment can be found below.

The first part of the course, on logic and set theory, will be based on the following freely available text:

This text is under ongoing revision, so students should ensure they look at the most recent version when preparing for a given week. The class is a ‘road test’ for the textbook, so if there are any errors or unclarities that you find, I would greatly appreciate hearing about them. I aim to update the textbook and this website weekly, generally by Wednesday evening.

Material for the remainder of the course will be supplied by the lecturer.

### Class Format

Each week I will set some text to read and some exercises to complete. Details will be in Seminar Schedule below.

This is an honours seminar, not an undergraduate lecture. I do not propose to offer extensive lectures during seminar, though I will be happy to clarify and run through difficult material if that seems warranted. The aim however is to get participants to become familiar with using these methods, not merely passively hearing about them, so class time will be focussed more on practical use in solving set exercises.

Accordingly, I will presuppose that you will have read the assigned material and made an attempt to tackle the set exercises each week. There is not a great deal of reading assigned in terms of page numbers, but you might find it challenging, so be sure to leave plenty of time to read and look at the exercises before class. I hope that the exercises shouldn’t take more than an hour each week for students who have thoroughly read the text.

In class, we will begin by discussing the exercises, and then turn to further issues arising from the material that have not been covered. I will call on students and auditors in the class to volunteer solutions to the exercises; students will be incentivised to prepare and discuss their solutions by the assessment scheme.

### Seminar Schedule

This schedule is subject to change. ‘EDL’ denotes the textbook Elements of Deductive Logic. In the ‘exercises’ column, the bold number indicates the page number in the text, the numbers (and any following letters) after the colon denote which exercises (and components of a multi-part exercise) to attempt.

1 Introduction EDL chs. 0–2.1 13: 1, 2
32: 1abd, 2aceg, 4
2 Set Theory EDL ch. 2.2–3 42: 5c, 17cd
55: 3, 4
3 No meeting: public holiday
4 Sentential Logic I EDL chs. 4–5.3 78: 1, 2, 4, 9, 10
94: 3, 4, 6bdefg, 7abd
5 Sentential Logic II Notes on Tableaux 19: 1, 2ace, 3ab, 5
6 Predicate Logic EDL ch. 7 and ch. 9.1–9.3. 149: 2, 7, 10, 15
178: 2, 5, 9, 12
7 Modal Logic JC Beall and Bas C van Fraassen (2003) ‘Normal Modal Logics’, pp. 51–84 (ch. 5) in their Possibilities and Paradox, OUP. local copy
Some notes on their notation:
1. They use $$A, B,…$$ for variables over sentences, where we use $$\phi,\psi,…$$;
2. they write negation $$¬$$ as $$\sim$$, conditional $$\rightarrow$$ as $$\supset$$ and biconditional $$\leftrightarrow$$ as $$\equiv$$;
3. they use $$\Vdash$$ for entailment (we use $$\vDash$$);
4. they label their truth values 1 and 0, not $$T$$ and $$F$$;
5. they write their valuations $$v(w,A) = 1$$, suppressing mention of the model; we would write $$⟦\phi⟧^{w}_{\mathscr{A}} = T$$, read: ‘$$\phi$$ is true at $$w$$ in $$\mathscr{A}$$’.
55: 2
59: 2, 3(odd)
67: 1, 2, 3, 4
81: 1(odd), 3(even), 5, 6
8 Conditionals
• EDL ch. 10.1.
• David Lewis (1973) ‘Counterfactuals and comparative possibility’, Journal of Philosophical Logic 2: 418–446. doi:10.1007/BF00262950
9 Probability I
• Alan Hájek and Chris Hitchcock (2016) ‘Probability for Everyone—Even Philosophers’, pp. 5–30 in Hájek and Hitchcock (eds.), The Oxford Handbook of Probability and Philosophy, OUP. doi:10.1093/oxfordhb/9780199607617.013.2
• Eagle, Antony (2011) ‘Probability Primer’, pp. 1–24 in Eagle (ed.) Philosophy of Probability: Contemporary Readings, Routledge.
10 Probability II Eagle, Antony (2016) ‘Probability’, pp. 417–39 in Paul Humphreys (ed.), The Oxford Handbook of Philosophy of Science, Oxford: Oxford University Press. doi:10.1093/oxfordhb/9780199368815.013.24 Week 10 questions
11 Evidential Decision Theory Martin Peterson (2009) ‘The Decision Matrix’ (pp. 17–39) and ‘Decisions under risk’ (pp. 64–90) in his An Introduction to Decision Theory CUP.
12 Causal Decision Theory/Mereology TBD

### Assessment

This is not a standard honours course, because of the technical material involved. Accordingly, there are two ‘tracks’ of assessment in this course.

#### Track 1

Assessment on this track will be by the standard honours process: students will submit a 5000 word paper by the common deadline for all semester 1 honours courses: midday, Friday 14 July. Students write on a topic of their choosing relevant to the course material, in consultation with the course instructor. The topic should be confirmed with me by Friday June 16 at the latest. I am happy to discuss potential topics with you and make suggestions about what might be fruitful to look at. (Example topics might be: the role of possible worlds in modal logic; the semantics of natural language conditionals; the nature of logical consequence; the epistemology of set theory; the correct analysis of probability; etc.)

#### Track 2

The second track of assessment recognises that it is not appropriate to assess your grasp on formal technical material by requiring submission of a 5000 word paper. In this track, assessment has three components:

1. Participation (20%): Each week that you turn up to class and volunteer a contribution to class discussion – in particular, by presenting a solution to one of the exercises to the class – you will receive 2 marks, up to a maximum of 20.

2. Take home exam (40%): A take home exam of 1 week duration. The questions will be available commencing at midday on Monday June 5 2017, and exams will be due midday on Monday June 12 2017.

The questions set in the exam will be of a straightforward nature, and the exam will be open book. Students who put in appropriate effort will get results commensurate with that effort. The examiners will take into account the overall profile of the course cohort in determining appropriate final marks.

3. Short Essay (40%): This will be a short essay of 2000–2500 words on the philosophy of logic. It is due at the same time as other honours essays, and should be confirmed with the instructor in the same way as if you were writing a longer essay.

Last updated: 2016–05–09.

###### Week 10 questions
1. Why not just identify chance with frequency?
2. Can chances be thought of – as in the ‘classical theory’ – as the ratio of favourable worlds to possible worlds?
3. Why should we accept that chance is incompatible with determinism?
4. Do we have credences at all; and even if we do, are they probabilistic?
5. Can Bayesians solve the problem of old evidence?
6. How does undermining threaten the Principal Principle? What are our options?