FOM: Aristotel's "Infinitum Actu Non Datur" Thesis

Stephen G Simpson simpson at
Mon Feb 15 15:35:12 EST 1999

 > From: Alexander Zenkin <alexzen at>
 > Subject: FOM: Aristotel's "Infinitum Actu Non Datur" Thesis
 > Date: Thu, 11 Feb 1999 00:41:58 +0300
 > Can anybody tell me where does Aristotel state his famous thesis
 > "Infinitum Actu Non Datur" and how does he substantiate it ? (
 > Please, with references and short citations since, unfortunately, I
 > myself have not a possibility to attend a library now).

Chapter I section 13 of H. G. Apostle's book `Aristotle's Philosophy
of Mathematics', pages 67-80, is entitled `The Infinite'.  Here
H. G. Apostle pulls together all the relevant passages from
Aristotle's writings, including 46 footnotes giving Bekker page
citations.  Most of the citations are to the Physics and the
Metaphysics.  The arguments that Aristotle presents are many-sided and
very acute.  He carefully considers and refutes the arguments of other
thinkers such as Democritus, Plato, Antiphon, and Zeno.  The flavor of
it is like this: `There are five main arguments for the belief in the
existence of the infinite ...' (203b15-30).

-- Steve Simpson

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