151 research outputs found
Solipsism and philosophy of mathematics: intuitionists compared
No full textThis paper will consider L.E.J. Brouwer, A. Heyting and G.F.C. Griss as the first generation of Dutch intuitionists to look at the interrelationship between solipsism and mathematics.
In particular our focus will be on Heyting, on the basis of the existence of some unpublished material (and also some published material difficult to find) revealing of the author's opinion on the subject and hence worthy of attention
Arend Heyting and Phenomenology: is the meeting feasible?
No full textIn the literature one can see the increasing trend of supporting intuitionism through phenomenology. Brouwer’s pupil, Arend Heyting, is said to be a forerunner of this trend, as he used a phenomenological terminology in order to define intuitionist negation, by elaborating the first intuitionist logic. In this paper, the author tries to explore—with reference to the unpublished material stored in the Heyting archive—how much of Heyting’s general thought is compatible with phenomenology. In the conclusion she suggests that Heyting and Husserl, insofar as they both think consciousness must be the very beginning of knowledge, share a same antipsychologistic attitude which coexists with an attempt to overcome solipsism. Yet, the phenomenological concept of degree of evidence cannot be applied to Heyting’s scale of evidence (including small natural numbers, large natural numbers, infinitely proceeding sequences, the universal quantifier), on the one side because it is not clear if the latter is common and shared by all intuitionists, and, on the other side, because the former presupposes a revisable evidence that does not fit to Heyting’s viewpoint. Furthermore, Husserl’s and Heyting’s conceptions of the nature of mathematics and logic and of their relationship are essentially different. From an intuitionist viewpoint mathematics is the domain of evidence, while logic transcribes its regularities. From a phenomenological viewpoint, mathematics remains outside the domain of evidence. Apophantic logic coincides with mathematics (without either of them absorbing the other), but transcendental logic lies at a higher level
Per una nuova didattica. L'argomentazione a scuola: la normativa in vigore e una proposta di curricolo
No full textA rigor di logica
No full textMentre è apprezzata l''affidabilità della logica come garanzia di correttezza del ragionamento, il suo carattere formale, che richiede un faticoso addestramento per familiarizzarsi, è spesso vissuto come un ostacolo insormontabile. Ciò dà origine ad una serie di critiche molto pesanti, che espongo in questo volume a partire dal testo di Andrea Nye ''Words of power'' - che dagli anni Novanta costituisce una raccolta ricca delle obiezioni che sono state sollevate contro la logica - e per le quali propongo varie possibili risposte
From logistiké to logistique: the long travel of a word
No full textThis paper aims to follow some of the key stages that the term logistiké passed through thanks to the double meaning it received since its appearance in ancient Greece: a more technical one (i.e. reckoning) and a more general one (i.e. reflecting, thinking). Taking as a starting point the Pythagorean Archytas, the discussion will take into account Plato’s very influential contribution, its developments, the modern age with a special focus on Leibniz, and the revival of the notion in French in 19th century
Towards a re-evaluation of Julius Koenig's Contribution to Logic
No full textJulius König is famous for his mistaken attempt to demonstrate that the continuum hypothesis was false. It is also known that the only positive result that could have survived from his proof is the paradox which bears his name. Less famous is his 1914 book Neue Grundlagen der Logik, Arithmetik und Mengenlehre. Still, it contains original contributions to logic, like the concept of metatheory and the solution of paradoxes based on the refusal of the law of bivalence. We are going to discover them by analysing the content of the book
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