Publication

Sources of delusion in 'Analytica Posteriora 1.5'

Hasper, P. S., 2006, In : Phronesis-A journal for ancient philosophy. 51, 3, p. 252-284 33 p.

Research output: Contribution to journalArticleAcademicpeer-review

APA

Hasper, P. S. (2006). Sources of delusion in 'Analytica Posteriora 1.5'. Phronesis-A journal for ancient philosophy, 51(3), 252-284.

Author

Hasper, Pieter Sjoerd. / Sources of delusion in 'Analytica Posteriora 1.5'. In: Phronesis-A journal for ancient philosophy. 2006 ; Vol. 51, No. 3. pp. 252-284.

Harvard

Hasper, PS 2006, 'Sources of delusion in 'Analytica Posteriora 1.5'' Phronesis-A journal for ancient philosophy, vol. 51, no. 3, pp. 252-284.

Standard

Sources of delusion in 'Analytica Posteriora 1.5'. / Hasper, Pieter Sjoerd.

In: Phronesis-A journal for ancient philosophy, Vol. 51, No. 3, 2006, p. 252-284.

Research output: Contribution to journalArticleAcademicpeer-review

Vancouver

Hasper PS. Sources of delusion in 'Analytica Posteriora 1.5'. Phronesis-A journal for ancient philosophy. 2006;51(3):252-284.


BibTeX

@article{109ca15643774c7fa5f7d2e9843722cc,
title = "Sources of delusion in 'Analytica Posteriora 1.5'",
abstract = "Aristotle's philosophically most explicit and sophisticated account of the concept of a (primary-)universal proof is found, not in Analytica Posteriora 1.4, where he introduces the notion, but in 1.5. In 1.4 Aristotle merely says that a universal proof must be of something arbitrary as well as of something primary and seems to explain primacy in extensional terms, as concerning the largest possible domain. In 1.5 Aristotle improves upon this account after considering three ways in which we may delude ourselves into thinking we have a primary-universal proof. These three sources of delusion are shown to concern situations in which our arguments do establish the desired conclusion for the largest possible domain, but still fail to be real primary-universal proofs. Presupposing the concept of what may be called an immediate proof, in which something is proved of an arbitrary individual, Aristotle in response now demands that a proof be immediate of the primary thing itself and goes on to sketch a framework in which an intensional criterion for primacy can be formulated.For the most part this article is a comprehensive and detailed commentary on Aristotle's very concise exposition in 1.5. One important result is that the famous passage 74a17-25 referring to two ways of proving the alternation of proportions cannot be used as evidence for the development of pre-Euclidean mathematics.",
author = "Hasper, {Pieter Sjoerd}",
year = "2006",
language = "English",
volume = "51",
pages = "252--284",
journal = "Phronesis",
issn = "0031-8868",
publisher = "BRILL ACADEMIC PUBLISHERS",
number = "3",

}

RIS

TY - JOUR

T1 - Sources of delusion in 'Analytica Posteriora 1.5'

AU - Hasper, Pieter Sjoerd

PY - 2006

Y1 - 2006

N2 - Aristotle's philosophically most explicit and sophisticated account of the concept of a (primary-)universal proof is found, not in Analytica Posteriora 1.4, where he introduces the notion, but in 1.5. In 1.4 Aristotle merely says that a universal proof must be of something arbitrary as well as of something primary and seems to explain primacy in extensional terms, as concerning the largest possible domain. In 1.5 Aristotle improves upon this account after considering three ways in which we may delude ourselves into thinking we have a primary-universal proof. These three sources of delusion are shown to concern situations in which our arguments do establish the desired conclusion for the largest possible domain, but still fail to be real primary-universal proofs. Presupposing the concept of what may be called an immediate proof, in which something is proved of an arbitrary individual, Aristotle in response now demands that a proof be immediate of the primary thing itself and goes on to sketch a framework in which an intensional criterion for primacy can be formulated.For the most part this article is a comprehensive and detailed commentary on Aristotle's very concise exposition in 1.5. One important result is that the famous passage 74a17-25 referring to two ways of proving the alternation of proportions cannot be used as evidence for the development of pre-Euclidean mathematics.

AB - Aristotle's philosophically most explicit and sophisticated account of the concept of a (primary-)universal proof is found, not in Analytica Posteriora 1.4, where he introduces the notion, but in 1.5. In 1.4 Aristotle merely says that a universal proof must be of something arbitrary as well as of something primary and seems to explain primacy in extensional terms, as concerning the largest possible domain. In 1.5 Aristotle improves upon this account after considering three ways in which we may delude ourselves into thinking we have a primary-universal proof. These three sources of delusion are shown to concern situations in which our arguments do establish the desired conclusion for the largest possible domain, but still fail to be real primary-universal proofs. Presupposing the concept of what may be called an immediate proof, in which something is proved of an arbitrary individual, Aristotle in response now demands that a proof be immediate of the primary thing itself and goes on to sketch a framework in which an intensional criterion for primacy can be formulated.For the most part this article is a comprehensive and detailed commentary on Aristotle's very concise exposition in 1.5. One important result is that the famous passage 74a17-25 referring to two ways of proving the alternation of proportions cannot be used as evidence for the development of pre-Euclidean mathematics.

M3 - Article

VL - 51

SP - 252

EP - 284

JO - Phronesis

JF - Phronesis

SN - 0031-8868

IS - 3

ER -

ID: 4481394