We will be reading the following texts:

• Number and Numbers; Alain Badiou.

• Menon; Plato.

• Thinking about mathematics; Stewart Shapiro.

De moment només penjo el pla docent de l'any passat. Here is an academic year calendar of the UB.

The second semester for the graduate courses runs from February 6, 2023 -- May 26, 2023. Lecturer and course coordinator: Joost J. Joosten

The text below shall be updated as we go along in our course.

This is a course of 6 credits which corresponds to 45 contact hours and the students are supposed to dedicate at least 75 more hours of individual work. Since we do three hours a week, this will correspond to 15 weeks.

Official information regarding the course is published at the course pages of the UB. From there, one can redirect to the courses. The lectures will take place in Aula 410 in the Montalegre Building.

The lecture schedule is as follows:

Mondays 11:00 -- 12:00

Tuesdays 11:00 -- 13:00

We strongly advice students to follow the course in the so-called avaluació úinca mode. Here we will have take-home exercises, a mid-term exam and a final exam.

Date and location midterm exam: TBA;

Date and location final exam: TBA.

The distribution of points in the final grade is as follows:

Take-home exercises: 40 %

Midterm exam: 30 %

Final exam: 30 %

Students may also decide --even though we stronly would like to discourage this-- to participate in the so-called avaluació única.

Date and location avaluació única exam: June 9, 2023, 12:00 -- 14:00, Aula 410.

Date and location resit exam: July 6, 2023, 12:00 -- 14:00, Aula 410.

As mentioned, the lecturer is Joost J. Joosten and the best way to contact is by sending an email. You can also come around to see if I'm in: the Montalegre building in Room 4045 with phone number +34 934031939.

There will be no lectures on

April 2 -- April 10;

May 1

June 5

Further, we shall see how giving a constructive reading to the connectives gives rise to a different logic: constructive or intuitionistic logic. Naturally this requires a ontological stance very different from platonism/realism underlying classical logic. If time allows we shall see how contstructive logic can be related both to classical and to modal logic.

• To get an understanding how modalities add a subtle and complex dimension to reasoning;

• See a couple of standard modal logics and reason in them;

• Understand the ontological presupposition that underly constructive reasoning;

• Understand the ontological presupposition that underly classical reasoning;

• Understand the fundamental difference and tension between the two.

• Learn formal reasoning systems in Natural Deduction style;

• Learn formal reasoning systems in Gentzen Deduction style;

• Learn and understand proofs by induction

• Study modal semantics;

• Learning how to apply the soundness theorem to obtain non-derivability results;

• Learning how to apply the completenss theorem to obtain provability without actually exhibiting a concrete proof

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We dwelled on what logic is about, what ontological assumptions are subsumed by classical logic and how this can be challenged and how this is challenged by constructive logic. In the tradition of Brouwer, this is often also known as intuitionistic logic refering the intuition involved in Kant's A priori synthetic knowledge of mathematics. We also discussed how various anomalies plagued foundations of mathematics and logic at the turn of the 19th century.

Examples of Kripke semantics at work.