Lajevardi and Salehi, in “There may be many arithmetical Gödel sentences”, argue against the use of the definite article in the expression “the Gödel sentence”, by claiming that any unsound theory has Gödelian sentences with different truth values. We show that their Theorems 1 and 2 are special cases (modulo Löb's theorem and the first incompleteness theorem) of general observations pertaining to fixed points of any formula, and argue that the false sentences of Lajevardi and Salehi are in fact not (...) Gödel sentences. (shrink)

Lajevardi and Salehi, in “There may be many arithmetical Gödel sentences”, argue against the use of the definite article in the expression “the Gödel sentence”, by claiming that any unsound theory has Gödelian sentences with different truth values. We show that their Theorems 1 and 2 are special cases (modulo Löb's theorem and the first incompleteness theorem) of general observations pertaining to fixed points of any formula, and argue that the false sentences of Lajevardi and Salehi are in fact not (...) Gödel sentences. (shrink)

Lajevardi and Salehi, in “There may be many arithmetical Gödel sentences”, argue against the use of the definite article in the expression “the Gödel sentence”, by claiming that any unsound theory has Gödelian sentences with different truth values. We show that their Theorems 1 and 2 are special cases (modulo Löb's theorem and the first incompleteness theorem) of general observations pertaining to fixed points of any formula, and argue that the false sentences of Lajevardi and Salehi are in fact not (...) Gödel sentences. (shrink)

An intensional logic is presented and suggested as a framework for a formal investigation of learning. The framework allows for discussing and comparing concepts and representations, and makes it possible to view learning processes as iterations of a certain type of functions. It is shown how this framework may be used to shed light on Meno’s paradox, but also on concepts such as Vygotsky’s ZPD and learning trajectories. In the case of mathematics, where there are recent attempts to merge ideas (...) from the philosophy of mathematics with ideas from the philosophy of education, a formal framework such as the one presented here, may constitute a common arena of discussion. (shrink)

Recently Carrie S. Jenkins formulated an epistemology of mathematics, or rather arithmetic, respecting apriorism, empiricism, and realism. Central is an idea of concept grounding. The adequacy of this idea has been questioned e.g. concerning the grounding of the mathematically central concept of set (or class), and of composite concepts. In this paper we present a view of concept formation in mathematics, based on ideas from Carnap, leading to modifications of Jenkins’s epistemology that may solve some problematic issues with her ideas. (...) But we also present some further problems with her view, concerning the role of proof for mathematical knowledge. (shrink)

Attempts have been made to analyse features in mathematics within a social constructivist context. In this paper we critically examine some of those attempts recently made with focus on problems of the objectivity, ontology, necessity, and atemporality of mathematics. Our conclusion is that these attempts fare no better than traditional alternatives, and that they, furthermore, create new problems of their own.

Rorty’s profound and challenging critique of contemporary philosophy is in several ways somewhat unfair. Analytic philosophy can contribute towards ‘wisdom’ in a reasonable sense of the term, though not in Rorty’s narrow sense; and his contrast between ‘sophist’ and ‘sage’, with the latter understood in Plato’s way, is also too constricting. Also, some contemporary ‘analytic’ work in the ‘history of philosophy’, so called, is not invalidated by Rorty’s strictures - especially his implied accusation that we shan’t be interested in the (...) intellectual past if we can’t look down on it. (shrink)

States commit wrongs that demand redress. In her recent book, Avia Pasternak considers the circumstances under which it is legitimate to impose the cost of redress upon the state’s citizens at large. Her answer is that it is legitimate to impose reparative burdens on citizens only when they participate in their state intentionally, specifically, when they intend to play their part in maintaining state institutions. The book thus has revisionary implications for current international legal practice, given reparative burdens are currently (...) imposed upon states no matter their internal relations. The book’s persuasive argument will be of interest not only to scholars of normative political theory and social ontology, but also international legal theorists. That said, its core claim that citizen participation must be ‘genuine’ would benefit from further specification through future scholarship. (shrink)