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For the hypothesis that each of these discoveries was destined to find expression, even if the genius of Kelvin had not obtained, there is the best of traditional proof: each was in fact made by others.
Both demonstrate that the materiality of an alleged falsehood was not a mere afterthought but rather one of the primary reasons for allowing traditional proof of reliance to be brushed aside at certification.
Jones then fired a warning if the United States Anti-Doping Agency prohibited her from going to the Athens Olympics based on information coming out of the federal investigation of Balco, rather than the traditional proof of a failed drug test.
Instead, it relieved plaintiffs from providing traditional proof of reliance, explaining that "causation is adequately established in the impersonal stock exchange context by proof of purchase and of the materiality of misrepresentations, without direct proof of reliance". Id., at 906 (emphasis added).
However, this does not mean that the solution is not unique, but that there are no mathematical bases to be sure of this assumption according to traditional proof proposed in the literature.
The improvement of Bolzano's version of this traditional proof consists in Bolzano's explicitly mentioning premise (2) as indispensable for the deduction (WL I, 145, 151; cf. also WL IV, 282 f ., thus making clear that the proof would not go through if this premise were not accepted.
Similar(53)
–Should computer-assisted proofs receive lower status than traditional proofs?
Even in traditional proofs, reviewers rarely check every step, instead focusing mostly on the major points.
Hardy finds it difficult to grasp the methods of his friend, who doesn't use traditional proofs to solve his problems.
In a new policy, The Annals has decided that computer-assisted proofs have merit, but the journal will accord them a lower status than traditional proofs, regarding them more like laboratory experiments that provide supporting evidence.
In this respect the skeptical philosophers had been right to criticize the traditional proofs of the existence of God or of the immortality of the soul as so much empty dogmatism.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com