### Abstract

We criticize the claim made by Čiurlionis, namely that mathematical solutions to Zeno's aporia are unsatisfactory, as they rely on "a false conditional premise". First, the rules of formal logic do not forbid deriving true statements from false statements, so even if mathematical solutions rely on a false premise this does not guarantee the falsity of their conclusion. Second, the truth value of the antecedent of the conditional depends on an empirical fact, so even granted that the consequent is false, the conditional statement should be viewed as contingent. Third, and most important, the statement in the consequent admits of two interpretations: a strict qualitative interpretation of identity of space-time points, which makes the statement nomologically necessarily false but irrelevant to the Zeno's aporia; and a looser mathematical quantitative interpretation of the identity of space-time points, which makes the statement relevant but not only contingently false. We conclude that there is no reason to accept the claim that this conditional statement is false and that Čiurlionis takes a wrong path in his attempt to resolve Zeno's aporias.

Original language | Lithuanian |
---|---|

Pages (from-to) | 113-125 |

Number of pages | 13 |

Journal | Problemos |

Volume | 70 |

Publication status | Published - 2006 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Philosophy

### Cite this

*Problemos*,

*70*, 113-125.

**Apie "klaidingacombining ogonek implikacinecombining ogonek prielaidacombining ogonek".** / Dagys, Jonas; Briedis, Mindaugas.

Research output: Contribution to journal › Article

*Problemos*, vol. 70, pp. 113-125.

}

TY - JOUR

T1 - Apie "klaidingacombining ogonek implikacinecombining ogonek prielaidacombining ogonek"

AU - Dagys, Jonas

AU - Briedis, Mindaugas

PY - 2006

Y1 - 2006

N2 - We criticize the claim made by Čiurlionis, namely that mathematical solutions to Zeno's aporia are unsatisfactory, as they rely on "a false conditional premise". First, the rules of formal logic do not forbid deriving true statements from false statements, so even if mathematical solutions rely on a false premise this does not guarantee the falsity of their conclusion. Second, the truth value of the antecedent of the conditional depends on an empirical fact, so even granted that the consequent is false, the conditional statement should be viewed as contingent. Third, and most important, the statement in the consequent admits of two interpretations: a strict qualitative interpretation of identity of space-time points, which makes the statement nomologically necessarily false but irrelevant to the Zeno's aporia; and a looser mathematical quantitative interpretation of the identity of space-time points, which makes the statement relevant but not only contingently false. We conclude that there is no reason to accept the claim that this conditional statement is false and that Čiurlionis takes a wrong path in his attempt to resolve Zeno's aporias.

AB - We criticize the claim made by Čiurlionis, namely that mathematical solutions to Zeno's aporia are unsatisfactory, as they rely on "a false conditional premise". First, the rules of formal logic do not forbid deriving true statements from false statements, so even if mathematical solutions rely on a false premise this does not guarantee the falsity of their conclusion. Second, the truth value of the antecedent of the conditional depends on an empirical fact, so even granted that the consequent is false, the conditional statement should be viewed as contingent. Third, and most important, the statement in the consequent admits of two interpretations: a strict qualitative interpretation of identity of space-time points, which makes the statement nomologically necessarily false but irrelevant to the Zeno's aporia; and a looser mathematical quantitative interpretation of the identity of space-time points, which makes the statement relevant but not only contingently false. We conclude that there is no reason to accept the claim that this conditional statement is false and that Čiurlionis takes a wrong path in his attempt to resolve Zeno's aporias.

KW - Achilles and tortoise aporia

KW - Identity conditions

KW - Solutions of aporias

UR - http://www.scopus.com/inward/record.url?scp=61249191206&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=61249191206&partnerID=8YFLogxK

M3 - Article

VL - 70

SP - 113

EP - 125

JO - Problemos

JF - Problemos

SN - 1392-1126

ER -