A footnote to The crisis in contemporary mathematics

Abstract

We examine the preparation and context of the paper "The Crisis in Contemporary Mathematics" by Errett Bishop, published 1975 in Historia Mathematica. Bishop tried to moderate the differences between Hilbert and Brouwer with respect to the interpretation of logical connectives and quantifiers. He also commented on Robinson's Non-standard Analysis, fearing that it might lead to what he referred to as 'a debasement of meaning.' The 'debasement' comment can already be found in a draft version of Bishop's lecture, but not in the audio file of the actual lecture of 1974. We elucidate the context of the 'debasement' comment and its relation to Bishop's position vis-a-vis the Law of Excluded Middle.

The Tyszkiewicz Amulet, a Chalcedony Pendant Inscribed with an Incantation on Thorn Bush

“…Nergal became the 'lord of the Netherworld' in the beginning of the second millennium B.C. 15 Thus, based on the text of Ms.A, we propose that the incantation more likely dates to the early Isin period rather than Ur III. 16 Transliteration 3. u 2 sikil u 2 kur 2 !…”

“…Taking into account the connection between i m (line 4) and š u d u m (line 5), it can be suggested that these lines deal with the thorn bush before its use in magicalmedical practices. For the divine sanction needed to allow the use of the thorn bush by the incantation priest (mentioned in lines [12][13][14][15][16][17], see Section 3.…”

“…a-na-ku KUR KUR 2 KUR KUR 2 KUR KUR 2 KUR KUR 2 54 lu-ma-aš-šir-ka 15 The incantation priest says before Šamaš as follows: 16 'You are the thorn bush, the offspring of Enlil. 17 Because of so-and-so, son of so-and-so 18 whose god is soand-so, (whose) goddess is so-and-so, 19 who 21 has been seized 19 by the Namtar demon, the Asakku demon, the liʾbu-disease, 20 the roaming ghost, the wandering ghost (or) 21 the mountain liʾbu-disease.…”

“…This section refers to the status of the thorn bush at a time when it was not yet written on tablets dealing with these practices (line 4) and did not appear in (pharmacological) list(s) that would have revealed its role among magical and healing plants. However, the second part of the Kultmittelbeschwörung (lines [12][13][14][15][16][17] leaves no doubt that the incantation priest is able to use the thorn bush on behalf of Enki, who legitimated him in order to accomplish his ritual practise.…”

Two-Track Depictions of Leibniz’s Fictions

“…Thus, Errett Bishop opposed both the classical development of the real numbers and the use of infinitesimals in teaching calculus [5]. For a discussion, see [9][10][11]31]. 2 Galileo (1564-1642) observed that the natural numbers admit a one-to-one correspondence with their squares.…”