If the initial segment Σ of Ω is a set, then it has a least strict upper bound S(Σ) ∈ Ω. Thus, for numbers α = S(Σ) and β = S(Σ′), α < β iff α ∈ Σ′; α = β iff Σ = Σ′; S(∅) is the least number 0… (More)

The background of these remarks is that in 1967, in ‘’Constructive reasoning” [27], I sketched an argument that finitist arithmetic coincides with primitive recursive arithmetic, PRA; and in 1981, in… (More)

The volumes of Gödel’s collected papers under review consist almost entirely of a rich selection of his philosophical/scientific correspondence, including English translations face-to-face with the… (More)

Kurt Gödel: Collected Works Volume III [Gödel, 1995] contains a selection from Gödel’s Nachlass; it consists of texts of lectures, notes for lectures and manuscripts of papers that for one reason or… (More)

In this survey of the history of constructivism, more space has been devoted to early developments (up till ca 1965) than to the work of the last few decades. Not only because most of the concepts… (More)