Among the main concerns of 20th century philosophy was that of the foundations of mathematics. But usually not recognized is the relevance of the choice of a foundational approach to the other main problems of 20th century philosophy, i.e., the logical structure of language, the nature of scientific theories, and the architecture of the mind. The tools used to deal with the difficulties inherent in such problems have largely relied on set theory and its ''received view''. There are specific issues, in philosophy of language, epistemology and philosophy of mind, where this dependence turns out to be misleading. The same issues suggest the gain in understanding coming from category theory, which is, therefore, more than just the source of a ''non-standard'' approach to the foundations of mathematics. But, even so conceived, it is the very notion of what a foundation has to be that is called into question. The philosophical meaning of mathematics is no longer confined to which first principles are assumed and which ''ontological'' interpretation is given to them in terms of some possibly updated version of logicism, formalism or intuitionism. What is central to any foundational project proper is the role of universal constructions that serve to unify the different branches of mathematics, as already made clear in 1969 by Lawvere. Such universal constructions are best expressed by means of adjoint functors and representability up to isomorphism. In this lies the relevance of a category-theoretic perspective, which leads to wide-ranging consequences. One such is the presence of functorial constraints on the syntax-semantics relationships; another is an intrinsic view of (constructive) logic, as arises in topoi and, subsequently, in more general fibrations. But as soon as theories and their models are described accordingly, a new look at the main problems of 20th century's philosophy becomes possible. The lack of any satisfactory solution to these problems in a purely logical and set-theoretic setting is the result of too circumscribed an approach, such as a static and punctiform view of objects and their elements, and a misconception of geometry and its historical changes before, during, and after the foundational ''crisis'', as if algebraic geometry and synthetic differential geometry -not to mention algebraic topology -were secondary sources for what concerns foundational issues. The objectivity of basic geometrical intuitions also acts against the recent version of structuralism proposed as 'the' philosophy of category theory. On the other hand, the need for a consistent and adequate conceptual framework in facing the difficulties * Text of a talk given at the
This paper discusses the positions of Italian philosopher Giulio Preti (1911?1972) in relation to the quarrel between Analytic and Continental philosophy. Preti?s thought appears as a systematic thought permitting to overcome, through his logical, epistemological and linguistic reflection, the divide between these two approaches. The different features of his philosophy are analyzed here in detail and compared to the main theoretical assumptions of Analytic and Continental philosophy.
What is the structure of a scientific explanation? How many types of explanation are there? Does science really offer explanations? From the traditional model, according to which "explaining" means "finding causes" we have moved on to the deductive-nomological model (D-N), introduced by Hempel and Oppenheim in 1948, according to which the explanation is a logical inference drawn from specific laws and conditions, without any reference to causes. The D-N model was then integrated by statistical-inductive explanations, but the objections made to Salmon's model over recent decades have stimulated proposals for alternatives, including the pragmatic and the "unificationist" models, through to the retrieval of the notion of cause by Salmon himself. This book analyses the epistemological problems relating to the explanation, arriving at the retrieval of the link between explanation and truth that the twentieth century sought to eliminate.
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