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    Lefèvre used mathematics to clarify and exemplify Aristot... — Carmelics
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    Lefèvre used mathematics to clarify and exemplify Aristotelian physical concepts rather than to make natural philosophy mathematical.

    Philosophy of LanguageTruth & Knowledge
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    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.The qualities of heat and cold in his example are not reimagined as mathematical objects but remain within Aristotelian natural philosophy.
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    • 2.The point of the example is to defend Aristotle's account of contraries, not to undermine it.
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    • 3.Like his predecessors, Lefèvre applied mathematical reasoning in service of Aristotelian physics.
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Quantifying intensive qualities like heat on a mathematical scale structurally transforms them into measurable magnitudes, regardless of stated intent.
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    • 2.The Merton School calculators showed that applying proportional reasoning to qualities implicitly mathematizes natural philosophy, even within Aristotelian frameworks.
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    • 3.Lefèvre's adoption of latitude-of-forms vocabulary borrows tools whose internal logic subverts qualitative Aristotelian ontology from within.
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    Reason against 2 of 2
    ?
    • 1.The distinction between 'using mathematics to clarify' and 'making natural philosophy mathematical' collapses when the mathematical structure determines the valid inferences.
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    • 2.Philosophers like Dear and Mahoney have argued that pedagogical mathematization in Renaissance Aristotelianism was a transitional form of genuine mathematization, not merely illustration.
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    Topics

    Philosophy of LanguageTruth & Knowledge

    Notable Defenders

    AristotleancientReferenced for his category of substance
    AristotleancientCategories; Physics IV.10, 219b5–10
    AristotleancientOn the Soul III.5
    AristotleancientLefèvre 1502a: 124r
    AristotleancientCategories
    AristotleancientPhysics, On the Heavens, Parva naturalia, On the Soul
    AristotleancientNicomachean Ethics
    AristotleancientAs cited in Beatus Rhenanus's course notes
    Aristotleancient
    AristotleancientPolitics; Economics
    Boethiusancient
    Chrysippusancient
    Horaceancient
    OvidancientMetamorphoses 15.367–36
    PlatoancientLaws; Republic
    PorphyryancientAuthor of the Isagoge, on which Lefèvre wrote notes
    Pseudo-Dionysius the Areopagiteancient
    Pythagorasancient
    Themistiusancientfifth-century paraphrast
    Themistiusancient
    ThemistiusancientParaphrases of Aristotle
    VirgilancientAeneid 3.214–218
    Augustin RenaudetcontemporaryRenaudet 1953: 131
    Cesare VasolicontemporaryVasoli 1959: 226, 233
    Christopher CelenzacontemporaryCelenza 2010
    Eckhard KesslercontemporaryKessler 1999
    GuerlaccontemporaryGuerlac 1979: 31
    Albert the Greatmedieval
    Averroesmedieval
    Boethiusmedieval
    George of TrebizondmedievalDialectica, published by Lefèvre 1508
    Heymeric de CampomedievalProblemata inter Albertum Magnum et Sanctum Thomam, Cologne, 1496
    Jacques Lefèvre d'ÉtaplesmedievalCommentary on Aristotle's Categories
    Jacques Lefèvre d'Étaplesmedieval
    Jacques Lefèvre d'ÉtaplesmedievalOosterhoff 2018: 77–85
    Lefèvre d'Étaplesmedieval1502a: 344v
    Lorenzo VallamedievalHumanist logical tradition
    Nicholas of Cusamedieval
    Peter of SpainmedievalAuthor of Summule logicales
    Peter of SpainmedievalSummule logicales
    Peter of SpainmedievalSummule logicales
    Ramon Lullmedieval
    Rudolph AgricolamedievalHumanist logical tradition
    Thomas Aquinasmedieval
    Thomas Bradwardinemedieval
    William of Moerbekemedieval
    Angelo Polizianomodern
    Beatus RhenanusmodernStudent of Lefèvre whose notes recorded his views; Renaudet 1953: 131
    Beatus RhenanusmodernCahier d'étudiant, Bibliothèque humaniste de Sélestat, MS 50, 253r
    Carl von PrantlmodernPrantl 1870: 4:278–280
    Ermolao BarbaromodernDionisotti 1955
    Ermolao Barbaromodern
    Ermolao Barbaromodern
    Ermolao BarbaromodernTranslations of Themistius's Paraphrases of Aristotle
    Jacques Lefèvre d'ÉtaplesmodernIntroductory Dialogue on Difficult Physics, 1502a: 128v
    Jacques Lefèvre d'ÉtaplesmodernLefèvre 1510: 2r
    Jacques Lefèvre d'ÉtaplesmodernSubject of the passage; held ambiguous position on nominalism, sought via media
    Jacques Lefèvre d'ÉtaplesmodernLefèvre 1502a: 124r
    Jacques Lefèvre d'ÉtaplesmodernLefèvre 1496b, 1508
    Jacques Lefèvre d'Étaplesmodern
    Jacques Lefèvre d'ÉtaplesmodernLefèvre 1505b
    Jacques Lefèvre d'Étaplesmodern1492 paraphrases of the Physics, On the Heavens, the Parva naturalia, and On the Soul
    Jacques Lefèvre d'Étaplesmodernnotae on NE III.10, in 1497: d7v
    Jacques Lefèvre d'Étaplesmodern1496b: a1v; 1503 edition of Aristotle's logical works
    Jacques Lefèvre d'ÉtaplesmodernHecatonomiae (1506)
    Juan Luis VivesmodernHumanist logical tradition
    Lefèvre d'ÉtaplesmodernNotes on Aristotle's Categories, 1503a: 23v
    Lorenzo VallamodernNauta 2009
    Marsilio FicinomodernTranslations of Plato's Laws and Republic
    Peter RamusmodernHumanist logical tradition
    Rudolph AgricolamodernNauta 2009

    Related

    Lefèvre's adoption of latitude-of-forms vocabulary borrows tools whose internal ...Like his predecessors, Lefèvre applied mathematical reasoning in service of Aris...Philosophers like Dear and Mahoney have argued that pedagogical mathematization ...Quantifying intensive qualities like heat on a mathematical scale structurally t...
    +4 moreShow less
    The Merton School calculators showed that applying proportional reasoning to qua...The distinction between 'using mathematics to clarify' and 'making natural philo...

    Source

    AI-extracted1/3 agreementValid
    SEP: lefevre-etaples
    View source passageHide passage
    But (x) is impossible. The new maximum (x) would be greater than the previous maximum (k), which is absurd—a maximum cannot be increased. Therefore, he concludes, the amount of contraries is limited by the absolute maximum degrees of the quality measured. Qualities and their contraries, consequently, cannot be intensified in the same object beyond this maximum limit. There are undeniable quantitative features to this argument, comparable to the geometrical intuitions that animated fourteenth-cen
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

    The point of the example is to defend Aristotle's account of contraries, not to ...
    The qualities of heat and cold in his example are not reimagined as mathematical...
    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit