Wittgenstein’s Diagonal Argument: A Variation on Cantor and Turing

Floyd, Juliet

doi:10.1007/978-94-007-4435-6_2

Cited by 37 publications

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“…35-8) and Bhattacharya and Bhattacharya (1981, p. 103-104). 38 Floyd (2012). construction rule stated by Cantor. This framework may be useful for somebody, who does not feel happy in the paradise created by Cantor.…”

Section: Resultsmentioning

confidence: 99%

A Monstrous Inference called Mahāvidyānumāna and Cantor’s Diagonal Argument

Guha

2015

J Indian Philos

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A mahāvidyā inference is used for establishing another inference. Its Reason (hetu) is normally an omnipresent (kevalānvayin) property. Its Target (sādhya) is defined in terms of a general feature that is satisfied by different properties in different cases. It assumes that there is no (relevant) case that has the absence of its Target. The main defect of a mahāvidyā inference μ is a counterbalancing inference (satpratipakṣa) that can be formed by a little modification of μ. The discovery of its counterbalancing inference can invalidate such an inference. This paper will argue that Cantor's diagonal argument too shares some features of the mahāvidyā inference. A diagonal argument has a counterbalanced statement. Its main defect is its counterbalancing inference. Apart from presenting an epistemological perspective that explains the disquiet over Cantor's proof, this paper would show that both the mahāvidyā and diagonal argument formally contain their own invalidators.

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Section: Resultsmentioning

confidence: 99%

A Monstrous Inference called Mahāvidyānumāna and Cantor’s Diagonal Argument

Guha

2015

J Indian Philos

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“…And this command, necessarily, is empty, tautologous, meaninglessly private. It is analogous, as I have argued elsewhere, to drawing a card in a board-game that says, 'Do What You Do' (Floyd, 2012(Floyd, , 2017. It is a 'command' that cannot be followed.…”

Section: Searchingmentioning

confidence: 89%

“…Incidentally, Wittgenstein never saw Turing's paper, but, hearing about it, told Normal Malcolm that he guessed it would be no ‘leg‐pull’. On whether it was or was not, see Floyd, , p. 27, n. 9.…”

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confidence: 99%

Teaching and Learning with Wittgenstein and Turing: Sailing the Seas of Social Media

Floyd¹

2019

Journal of Philosophy of Education

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Results of the Boston University Mellon Sawyer seminar 2016–2019 (http://www.mellophilemerge.com) reveal that social and philosophical drives are increasingly central to our uses of technology, including AI. This raises critical challenges for democracy, especially in a hyper‐connected world where social media shapes human conduct in ways we are only beginning to appreciate. A history of the mutual impact of Turing and Wittgenstein on one another points to the contemporary foundational significance of our artful capacity to embed everyday words in forms of life. Wittgenstein's mature focus on forms of life, interlocutory drift, and rule‐following, with its play between the ‘I’ and the ‘we’, was an informed critical response to Turing's idea of a ‘Turing machine’, his analysis of the very idea of taking a ‘step’ in a formal system. Wittgenstein's characterisations of our drive to evade a responsibility in speech, especially by appealing to ‘machines’ or ‘algorithms’ as pure mathematical objects, are invaluable warnings for us. The enduring importance of mutually‐attuned ‘phraseology’ to education may be formulated as a humanistic challenge to the very ideas of ‘computational foundations’ and ‘Big Data’ in our hyper‐connected world.

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“…The notion ofÜbersichtlichkeit as a developed philosophical idea in connection with mathematical proof derives from Wittgenstein's writings of 1939-40, and, significantly, precisely those manuscripts that were written in the wake of his conversations with Alan Turing in 1937 and 1939 (cf. [24], [26]). Turing personally sent o↵ only five o↵prints of his famous paper "On Computable Numbers, with an application to the Entscheidungsproblem" ( [104]) in the first round, and one was to Wittgenstein, who was then trying to put together the PI.…”

Section: Surveyability (üBersichtlichkeit)mentioning

confidence: 99%

“…Turing, he said, had gotten to "the right perspective" mathematically. 26 Gödel objected, however, to what he took to be a prejudicial assumption of Turing's about our mental lives: that our experiences are discrete or discretizeable.…”

Section: Turing Machines: From Language Games To Social Softwarementioning

confidence: 99%

Parikh and Wittgenstein

Floyd

2017

Outstanding Contributions to Logic

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A survey of Parikh's philosophical appropriations of Wittgensteinian themes, placed into historical context against the backdrop of Turing's famous paper [104], "On computable numbers, with an application to the Entscheidungsproblem" and its connections with Wittgenstein and the foundations of mathematics. Characterizing Parikh's contributions to the interaction between logic and philosophy at its foundations, we argue that his work gives the lie to recent presentations of Wittgenstein's so-called metaphilosophy (e.g., [38]) as a kind of "dead end" quietism. From early work on the idea of a feasibility in arithmetic ([54]) and vagueness ([56]) to his more recent program in social software ([63]), Parikh's work encompasses and touches upon many foundational issues in epistemology, philosophy of logic, philosophy of language, and value theory. But it expresses a unified philosophical point of view. In his most recent work, questions about public and private languages, opportunity spaces, strategic voting, non-monotonic inference and knowledge in literature provide a remarkable series of suggestions about how to present issues of fundamental importance in theoretical computer science as serious philosophical issues.

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Wittgenstein’s Diagonal Argument: A Variation on Cantor and Turing

Cited by 37 publications

References 14 publications

A Monstrous Inference called Mahāvidyānumāna and Cantor’s Diagonal Argument

A Monstrous Inference called Mahāvidyānumāna and Cantor’s Diagonal Argument

Teaching and Learning with Wittgenstein and Turing: Sailing the Seas of Social Media

Parikh and Wittgenstein

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