Philosophy of Mathematics

Discrimination between belief and knowledge. Empirical and analytic knowledge. Knowledge as justifiable belief.

The problem of the validity of scientific knowledge. Scientific theories and predictions. Neo-positivism (logical positivism, logical empiricism) and the principle of (experimental) verifiability. Popper’s reaction and the Falsification Principle.  

Kuhn’s «Structure of Scientific Revolutions» and the difference mitigation between knowledge at exact sciences and humanities.

The meaning of “Paradigm” and “Normal Science”. The meaning of incommensurability of competing paradigms. The “paradigm shift” as a belief shift.

Lakatos’ restricted view. Hard core and the protective belt of a Research Programme and its role at scientific evolution.

Feyerabend’s opinion on epistemological anarchism (anarchist theory of knowledge), the meaning of “counter-induction” and the opposition to the method.

The problem of progress in Science and its analysis by Laudan.

The meaning of natural selection and its transfer to matters of epistemology. Toulmin’s evolutionary epistemology.

• Kuhn, T. S. (2012). The structure of scientific revolutions. University of Chicago Press.
• Popper, K. (1959). The Logic of Scientific Discovery. London: Hutchinson.