To effect this sort of reduction, Aristotle relies upon a series of meta-theorems, some of which he proves and others of which he merely reports (though it turns out that they do all indeed admit of proofs).
This particular deduction is perfect because its validity needs no proof, and perhaps because it admits of no proof either: any proof would seem to rely ultimately upon the intuitive validity of this sort of argument.
Lord Ellenborough stated that The discussion which has taken place here, and the consideration which has been given to the facts alleged, most conclusively show that this is not a case that can admit of no denial or proof to the contrary; under these circumstances, however obnoxious I am myself to the trial by battle, it is the mode of trial which we, in our judicial character, are bound to award.
We are plainly in the same territory as Reid's account: "there are principles common to [philosophers and the vulgar], which need no proof, and which do not admit of direct proof", and these common principles "are the foundation of all reasoning and science" (Reid 2002).
Though the truth or the applicability of these principles does not admit of direct proof, they are consistently confirmed by experience and, Maritain holds, cannot be denied without contradiction (Preface to Metaphysics, p. 90).
In the first place this phase of the Government's case is subject to the admitted infirmities of proof by imputation.
But he admits that proof is in the eye of the beholder.
Still, IOC president Jacques Rogge told Prime Minister David Cameron earlier this week that he was "happy" with the way London had gone about its work, but he admitted that "the proof of the pudding will be in the eating".
NBH Pratt admits 'no proof of bullying by Brown'.
There is a necessarily crude calculus with large parameter (e.g., residual operators are just bounded on L2), but the calculus admits the proof of Garding inequalities and enables us to symmetrize and sometimes even diagonalize the singular systems being considered by microlocalizing simultaneously in both slow and fast variables.
It therefore is plain that the burden of proof was dealt with and carried in a manner which does not admit of criticism by the defendant.
