Cantor's Abstractionism and Hume's Principle

Ternullo, Claudio; Zanetti, Luca

doi:10.1080/01445340.2021.1954471

Cited by 2 publications

(1 citation statement)

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“…Some truths will be left out, and so, by definition, 𝓣 cannot be a set of all truths (Grim,op.cit.,. Non-Cantorian set theories have been proposed, but, as Ternullo and Zanetti (2021) argue, these fail to meet Gödel's (1947) minimal account of abstraction. Now, if omniscience consisted in God's knowing all true propositions, irrespective of tense, this argument would be very damaging to the claim that he possesses itbut, as we have seen, it does not.…”

Section: The Coherence Of 'God' As Defined Herementioning

confidence: 99%

In Defence of the Coherence of the Concept of God.

Blaber¹

2023

Preprint

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This paper will outline an idea of ‘God’ that may be rationally defensible, and will seek to defend it against possible objections. The idea will not, however, be the orthodox one of Trinitarian Christianity, but that of Unitarianism, Judaism and Islam. It will also not seek to defend the idea of God’s omnibenevolence, arguing that the existence of evil and suffering in the world tells against the attribution of that moral quality, at least as understood by humans, to God. The belief that evil and suffering in the world is decisive proof of God’s non-existence will be refuted.

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Section: The Coherence Of 'God' As Defined Herementioning

confidence: 99%

In Defence of the Coherence of the Concept of God.

Blaber¹

2023

Preprint

View full text Add to dashboard Cite

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A Reassessment of Cantorian Abstraction based on the $$\varepsilon $$-operator

Bonatti

2022

Synthese

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Cantor’s abstractionist account of cardinal numbers has been criticized by Frege as a psychological theory of numbers which leads to contradiction. The aim of the paper is to meet these objections by proposing a reassessment of Cantor’s proposal based upon the set theoretic framework of Bourbaki—called BK—which is a First-order set theory extended with Hilbert’s $$\varepsilon $$ ε -operator. Moreover, it is argued that the BK system and the $$\varepsilon $$ ε -operator provide a faithful reconstruction of Cantor’s insights on cardinal numbers. I will introduce first the axiomatic setting of BK and the definition of cardinal numbers by means of the $$\varepsilon $$ ε -operator. Then, after presenting Cantor’s abstractionist theory, I will point out two assumptions concerning the definition of cardinal numbers that are deeply rooted in Cantor’s work. I will claim that these assumptions are supported as well by the BK definition of cardinal numbers, which will be compared to those of Zermelo–von Neumann and Frege–Russell. On the basis of these similarities, I will make use of the BK framework in meeting Frege’s objections to Cantor’s proposal. A key ingredient in the defence of Cantorian abstraction will be played by the role of representative sets, which are arbitrarily denoted by the $$\varepsilon $$ ε -operator in the BK definition of cardinal numbers.

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Cantor's Abstractionism and Hume's Principle

Cited by 2 publications

References 20 publications

In Defence of the Coherence of the Concept of God.

In Defence of the Coherence of the Concept of God.

A Reassessment of Cantorian Abstraction based on the $$\varepsilon $$-operator

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