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Holdouts clung to demonstrative proof in science and theology against the rising tide of probability.
Ibn Kammuna boldly claims to have formulated the the first demonstrative proof for the soul's eternity a parte ante.
The falâsifa are convinced, al-Ghazâlî complains at the beginning of the Incoherence, that their way of knowing by "demonstrative proof" (burhân) is superior to theological knowledge drawn from revelation and its rational interpretation.
Some philosophers construe evidence in terms of demonstrative proof, others in terms of objective and/or subjective probability, and others simply in terms of anything that belief is responsive to (see the entry on evidence).
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This is science, after all, and demonstrative proofs are neither possible nor required.
It is more relevant to note that Ibn Daud criticizes the emanation-theory of the philosophers by claiming that there are no demonstrative proofs for it.
In general, Falaquera repeatedly states that he views the Torah as a source of truth, and that its teachings are in accord with the true teachings of philosophy and science for which there are demonstrative proofs.
Mullā Ṣadrā makes extensive use of logical analyses and demonstrative proofs, which rest on what he calls "illuminative principle" (qā'idah ishraqiyyah); that is, what has entered the heart (al-varidāt al-qalbiyyah), or "Divinely realized knowledge" (taḥqīq 'arshī).
The third grade of justice thus relies on two central tenets of Leibniz's metaphysics, for which he believes there are demonstrative proofs; indeed, he believes he provides such proofs (PE, "Principles of Nature and Grace, Based on Reason," §4, §8; PE, "Monadology," §4, §38).
It is certainly possible that, at the upper bounds of human capacity, one may find an individual blessed with "an intense purity and an intense connection to the supernal sources" such that he can intuit all or most of what humans are capable of knowing, "not by means of an uncertain tradition, but by means of middle terms and demonstrative proofs".
Aristotle's account of proof as demonstrative argument fits very well to the structure of ancient geometry as axiomatized in Euclid.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com