What could it mean to say that a mathematical proposition was true if there was no possibility of proving it?
The case pits the value of finality in criminal cases against the possibility of proving an inmate's innocence long after trials and appeals are concluded.
His recent cases include advising a law firm on the possibility of proving authorship of a handwritten, unwitnessed will of a 90-year-old Holocaust survivor who spoke Yiddish.
Whatever one says about the possibility of proving the existence of an object purely with conceptual truths, many philosophers have maintained that at least logic has to be neutral about what there is.
Some of them doubted the possibility of proving that there are only ten categories of reality, while some went so far as to reduce them to two (Ockham) or three (Buridan).
Frege seems to have been sceptical about the possibility of proving logical invalidity and independence precisely because he saw that such proofs would not be possible without a principled demarcation of logical constants, which he did not see how to provide (Frege 1906, 429; and for discussion, Ricketts 1997).
Just as "one can recognize that ["logical propositions"] are true from the symbol alone" (6.113), "the possibility of proving" mathematical propositions means that we can perceive their correctness without having to compare "what they express" with facts (6.2321; cf. (RFM App. III, §4)).
So with the possibility of proving his innocence off the table, the trial which could last until June centers on whether Tsarnaev should be put to death or sentenced to life in prison without the possibility of parole.
That way, on the rare occasion that an innocent person is wrongfully convicted, there remains the possibility of proving that person's innocence while that person is still alive.
That is what is fundamentally compelling about a game of chance: the possibility of getting lucky, of proving to yourself that you are, in fact, blessed by fate.
