What The Tortoise Has To Say About Diachronic Rationality

Valaris, Markos

doi:10.1111/papq.12172

Cited by 4 publications

(3 citation statements)

References 30 publications

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“…There is a complex debate about the metaphysics of inferences-do they extend in time, e.g (Hlobil 2015;Valaris 2016…”

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confidence: 99%

Should Intro Ethics Make You a Better Person?

Nieswandt¹

2022

Teleological Structures in Human Life

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There is a common demand that moral theory be 'practical', voiced both in-and outside of philosophy. Neo-Humeans, Kantian constitutivists and Aristotelian naturalists have all advocated the idea that my knowledge that I ought to do something must lead me to actually do it-an idea sometimes called the "practicality requirement" for moral theory. Some university administrators apply this idea in practice, when they force students who violate the code of conduct to complete classes in moral theory, hoping that the knowledge obtained there would lead the student not to reoffend. I argue that the practicality requirement rests on a false understanding of the relation both between knowledge and motivation, focusing my critique on recent Aristotelian proposals.

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“…There is a complex debate about the metaphysics of inferences-do they extend in time, e.g (Hlobil 2015;Valaris 2016…”

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confidence: 99%

Should Intro Ethics Make You a Better Person?

Nieswandt¹

2022

Teleological Structures in Human Life

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“…Valaris (2017) justifies "that there are diachronic norms of epistemic rationality -namely, norms of good reasoning" (the author's italic) meaning a necessary mental jump from the premises to the conclusion corresponding to different ("diachronic") moments of time.…”

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confidence: 99%

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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“…Valaris (2017) justifies "that there are diachronic norms of epistemic rationalitynamely, norms of good reasoning" (the author's italic) meaning a necessary mental jump from the premises to the conclusion corresponding to different ("diachronic") moments of time.Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 31 December 2021…”

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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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What The Tortoise Has To Say About Diachronic Rationality

Cited by 4 publications

References 30 publications

Should Intro Ethics Make You a Better Person?

Should Intro Ethics Make You a Better Person?

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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