LOGIC AND PHILOSOPHY OF SCIENCE 2

The presence and use of logic is ubiquitous if hidden in the theory and practice of the sciences. The seminar offers a first introduction to logic and its role in the sciences. We will present a first introduction to formal logic---first order predicate logic (with identity), inductive logic, theory of relations, probability theory. We will then address logical questions that are of crucial scientific relevance. For example, we will use formal logic to phrase rigorously the idea that reality is structured in a hierarchy of levels of relative fundamentality described by the special sciences---allegedly ensuring irreducibility and autonomy. As for another example, we will develop a little bit of probability theory that is crucial for the logic of confirmation in science. We will also look at controversial arguments such as the argument from intelligent design, discussing issues about the demarcation of science and pseudo-science.

The seminar represents the first introduction to the use of abstract formal methods that are ubiquitous in the theory and practice of science and philosophy.

Knowledge and familiarity with formal logic, arguably the most crucial instrument to investigate rigorously philosophical questions; application of rigorous formal tools to relevant scientific case studies.

There are no pre-requisites. Everything that is needed will be introduced in class. A certain acquaintance—if not familiarity—with formal languages and theories will be an advantage.

The seminar consists of 15 lectures, 2 hours each, for a total of 30 hours. Readings are in the Bibliography (Testi di Riferimento) Tentative contents include:

1. Introduction. Logic and .... Science (No Reading)

2. Naive Set Theory (Reading: [6], Chapter 1)

3. Arguments, Their Structure, and Propositional Logic 1 (Reading: [3] Chapter 2 and Chapter 3: § 3.1-3.4)

4. Propositional Logic 2: Truth Tables for Formulas and Arguments (Reading: [3] Chapter 3, § 3.5-3.6)

5. Propositional Logic 3: Conclusion and Applications to Science: Foundations of Computer Science, Mechanicism and Falsifiability (Reading: [3] Chapter 3)

6. Predicate Logic 1: Names and Quantifiers (Reading: [3] Chapter 6, § 6.1-6.3)

7. Predicate Logic 2: Model Theoretic Semantics (Reading: [3], Chapter 3, §6.4)

8. Predicate Logic 3: Validity and Applications to Sciences: The Causal Argument, Ontological Commitments of Theories (Reading: [2], §1.1-1.6, and [5])

9. Theory of Relations (Reading:[6] Chapter 2)

10. Theory of Relations (Reading: [6] Chapter 2)

11. Applications to Science: Levels of Reality, Fundamentality of Physics and Autonomy of Special Sciences (Reading: [1])

12. Probability 1 (Reading:[3] Chapter 10)

13. Probability 2 (Reading: [6], Chapter 5)

14. Applications to Science: Inductive Validity, Confirmation, Intelligent Design (Reading: [4] Chapter 12)

15. Preparation for the Exam (No Reading)

[1] Bliss, R. and Priest, G. 2018. The Geography of Fundamentality. In Bliss, R. and Priest, G.(eds) Reality and Its Structure. Oxford: Oxford University Press, pp. 1-34.

[2] Bricker, P. 2014. Ontological Commitment. Stanford Encyclopedia of Philosophy. At https://plato.stanford.edu/entries/ontological-commitment/

[3] Nolt, J., Rohatyn, D., Varzi, A. 1998. Logic (2nd ed.). New York: McGraw Hill.

[4] Priest G. 2017. A Very Short Introduction to Logic. Oxford: Oxford University Press.

[5] Quine, W. v. O, 1948. On What There Is. Review of Metaphysics 2(5): 21-38.

[6] Steinhart, E. 2017. More Precisely. Toronto: Broadview.

The exam consists of a written text at the end of the semester. It will be structured around different questions on different topics of the seminar. The written exams consists of three questions. The first two questions are ``exercise'' style questions whereas the last is an open questions. First two questions are 10 pints each, last question is 15 points. The last session will be entirely dedicated to the preparation of the exam. In fact, an example of possible final exam will be distributed. The written exam lasts two hours.

The seminar will be structured around frontal lectures. However active student participation (e.g., questions, discussion) is highly encouraged.

English

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