Comments on “What the Internalist Should Say to the Tortoise”

Wright, Sarah

doi:10.1017/epi.2015.15

Cited by 2 publications

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References 10 publications

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“…For example,Fumerton (2015) suggests an "internalist" interpretation, after which he justifies equally well two opposite conclusions without being able to choose between them; also commented byWright (2015).…”

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What the Tortoise Said to Achilles: Lewis Carroll’s paradox in terms of Hilbert arithmetic

Penchev

2021

SSRN Journal

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Lewis Carroll, both logician and writer, suggested a logical paradox containing furthermore two connotations (connotations or metaphors are inherent in literature rather than in mathematics or logics). The paradox itself refers to implication demonstrating that an intermediate implication can be always inserted in an implication therefore postponing its ultimate conclusion for the next step and those insertions can be iteratively and indefinitely added ad lib, as if ad infinitum. Both connotations clear up links due to the shared formal structure with other well-known mathematical observations: (1) the paradox of Achilles and the Turtle; (2) the transitivity of the relation of equality. Analogically to (1), one can juxtapose the paradox of the Liar (for Lewis Carroll's paradox) and that of the arrow (for "Achilles and the Turtle"), i.e. a logical paradox, on the one hand, and an aporia of motion, on the other hand, suggesting a shared formal structure of both, which can be called "ontological", on which basis "motion" studied by physics and "conclusion" studied by logic can be unified being able to bridge logic and physics philosophically in a Hegelian manner: even more, the bridge can be continued to mathematics in virtue of (2), which forces the equality (for its property of transitivity) of any two quantities to be postponed analogically ad lib and ad infinitum. The paper shows that Hilbert arithmetic underlies naturally Lewis Carroll's paradox admitting at least three interpretations linked to each other by it: mathematical, physical and logical. Thus, it can be considered as both generalization and solution of his paradox therefore naturally unifying the completeness of quantum mechanics (i.e. the absence of hidden variables) and eventual completeness of mathematics as the same and isomorphic to the completeness of propositional logic in relation to set theory as a first-order logic (in the sense of Gödel (1930)'s completeness theorems).

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What the Tortoise Said to Achilles: Lewis Carroll’s paradox in terms of Hilbert arithmetic

Penchev

2021

SSRN Journal

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show abstract

mentioning

confidence: 99%

What the Tortoise Said to Achilles: Lewis Carroll’s Paradox in Terms of Hilbert Arithmetic

Пенчев¹

2021

Preprint

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Lewis Carroll, both logician and writer, suggested a logical paradox containing furthermore two connotations (connotations or metaphors are inherent in literature rather than in mathematics or logics). The paradox itself refers to implication demonstrating that an intermediate implication can be always inserted in an implication therefore postponing its ultimate conclusion for the next step and those insertions can be iteratively and indefinitely added ad lib, as if ad infinitum. Both connotations clear up links due to the shared formal structure with other well-known mathematical observations: (1) the paradox of Achilles and the Turtle; (2) the transitivity of the relation of equality. Analogically to (1), one can juxtapose the paradox of the Liar (for Lewis Carroll’s paradox) and that of the arrow (for “Achilles and the Turtle”), i.e. a logical paradox, on the one hand, and an aporia of motion, on the other hand, suggesting a shared formal structure of both, which can be called “ontological”, on which basis “motion” studied by physics and “conclusion” studied by logic can be unified being able to bridge logic and physics philosophically in a Hegelian manner: even more, the bridge can be continued to mathematics in virtue of (2), which forces the equality (for its property of transitivity) of any two quantities to be postponed analogically ad lib and ad infinitum. The paper shows that Hilbert arithmetic underlies naturally Lewis Carroll’s paradox admitting at least three interpretations linked to each other by it: mathematical, physical and logical. Thus, it can be considered as both generalization and solution of his paradox therefore naturally unifying the completeness of quantum mechanics (i.e. the absence of hidden variables) and eventual completeness of mathematics as the same and isomorphic to the completeness of propositional logic in relation to set theory as a first-order logic (in the sense of Gödel (1930)’s completeness theorems).

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Comments on “What the Internalist Should Say to the Tortoise”

Abstract: Richard Fumerton has provided two possible responses that the internalist might make to the “Tortoise problem.” I argue that the second of these two responses is preferable, and I suggest one way that it might be strengthened.

Cited by 2 publications

References 10 publications

What the Tortoise Said to Achilles: Lewis Carroll’s paradox in terms of Hilbert arithmetic

What the Tortoise Said to Achilles: Lewis Carroll’s paradox in terms of Hilbert arithmetic

What the Tortoise Said to Achilles: Lewis Carroll’s Paradox in Terms of Hilbert Arithmetic

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