The above derivation is an illustrative example of Bolzano's importation of proof methods from mathematics — such as the methods of indirect proof and of mathematical induction — into philosophy.
There classical logic is only available by means of some rule of indirect proof, which, at least to some extent, destroys the symmetry of the reasoning principles (see section 3.5).
As proof-of-principle, we evaluated the indirect detection of fLuc protein fused to a V5 or 3flag tag after locoregional overexpression in the mouse striatum.
In dealing with counterfactual hypotheses of indirect proofs mentioned above, Averroes and Thomas Aquinas made use of the idea of abstract possibilities which did not imply the idea of alternative domains.
Łukasiewicz takes this propositional basis to be occasionally invoked by Aristotle, for instance in the treatment of indirect proofs, but for the most part left as tacit, and he therefore regards it as legitimate to criticise Aristotle (unlike the Stoics) for not explicitly formulating the underlying propositional logic.
And while he characterized what he did know about as "damning," he said that instead of irrefutable proof, investigators had an array of indirect evidence that they argue strongly implicates Dr. Ivins in the attacks, which killed 5 people and sickened 17 others.
Detecting gravitational waves has long been a goal of astrophysicists; a Nobel prize was handed out in 1993 for indirect proof of their existence.
They have never been seen directly, though an indirect proof of their existence, based on studying a pair of collapsed stars, was rewarded with the 1993 Nobel prize in physics.
For nonviral gene delivery particles (lipid- or polymer-based), indirect proof of nuclear entry during mitosis is provided.
No magnetic nanoparticles were observed on the surface of the nanospheres, which is an indirect proof of polymer encapsulation.
