cod. 03354

Academic year 2013/14
2° year of course - Second semester
Academic discipline
Logica e filosofia della scienza (M-FIL/02)
Storia della filosofia e istituzioni di filosofia
Type of training activity
30 hours
of face-to-face activities
6 credits
course unit
in - - -

Learning objectives

The student is expected to develop a critical eye with regard to mathematical reasoning: is there one objective Logic for Mathematics? Are there more than one? He will also be encouraged to evaluate the significance of mathematical theorems about Logic. More generally, he will learn how mathematical methods can be applied to domains which are less stable than those concerning mathematical objects.



Course unit content

At the beginning of the course, a few lectures will be devoted to the Intuitionistic Philosophy of Mathematics, i.e. an approach to do Mathematics constructively without infinitistic assumptions. Then, Heyting's formalization of Intuitionistic reaoning is introduced followed by an analysis of both algebraic and Kripke-type semantics. By way of a conclusion, the existence of a close connection between the two different semantical systems is established, thereby showing that there is a uniform and accurate representation of the Intuitionist's notion of meaning in a formal language.

Full programme

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1) M. Fitting, Intuitionistic Logic, Model Theory and Forcing, NothHolland 1969.
2) H. Rasiowa & R. Sikorski, The Mathematics of Metamathematics, Warsavia 1963,
3) Notes for Students.

Teaching methods

There will be lectures, exercises will be assigned and corrected in class. The strategy will be to go from the concrete to the abstract, to further confirming examples and to reflect on the significance of the work.

Assessment methods and criteria

The final mark will depend upon the student's performance in an oral exam and the quality of his participation in the comunalwork in class.

Other information

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