E. Agazzi

György Darvas

Mathematics is often considered as a body of knowledge that is essen tially independent of linguistic formulations, in the sense that, once the content of this knowledge has been grasped, there remains only the problem of professional ability, that of clearly formulating and correctly proving it. However, the question is not so simple, and P. Weingartner's paper (Language and Coding-Dependency of Results in Logic and Mathe matics) deals with some results in logic and mathematics which reveal that certain notions are in general not invariant with respect to different choices of language and of coding processes. Five example are given: 1) The validity of axioms and rules of classical propositional logic depend on the interpretation of sentential variables; 2) The language dependency of verisimilitude; 3) The proof of the weak and strong anti inductivist theorems in Popper's theory of inductive support is not invariant with respect to limitative criteria put on classical logic; 4) The language-dependency of the concept of provability; 5) The language dependency of the existence of ungrounded and paradoxical sentences (in the sense of Kripke). The requirements of logical rigour and consistency are not the only criteria for the acceptance and appreciation of mathematical proposi tions and theories.

Philosophy of Mathematics Today

Anna-Teresa Tymieniecka

In medicine the understanding and interpretation of the complex reality of illness currently refers either to an organismic approach that focuses on the physical or to a 'holistic' approach that takes into account the patient's human sociocultural involvement. Yet as the papers of this collection show, the suffering human person refers ultimately to his/her existential sphere. Hence, praxis is supplemented by still other perspectives for valuation and interpretation: ethical, spiritual, and religious. Can medicine ignore these considerations or push them to the side as being subjective and arbitrary? Phenomenology/philosophy-of-life recognizes all of the above approaches to be essential facets of the Human Condition (Tymieniecka). This approach holds that all the facets of the Human Condition have equal objectivity and legitimacy. It completes the accepted medical outlook and points the way toward a new `medical humanism'.

E. Agazzi

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