Textual analysis using pure logic

I have been having an amusing conversation with 'Nishadani' on his Wikipedia talk page. Nishadani is one of those tireless defenders of orthodoxy on Wikipedia, fighting the battle against (in his case) all sorts of interesting theories that 'the man from Stratford' did not write the plays published in his name. There is more about the whole issue on Wikipedia here, although the article misses the interesting fact that the great mathematician Georg Cantor (the transfinite man) spent much time and money trying to prove that Bacon was the author of the Shakespeare plays. He writes (to Dedekind, 28 July 1899)

The big question was whether, besides the alephs, there are also other powers of
sets; for two years now I have been in possession of a proof that there are no
others; so that, for example, the arithmetic linear continuum (the totality of
all real numbers) has a determinate aleph as its cardinal number.
The Bacon-Shakespeare question, on the other hand, is for me completely
finished; it cost me a great deal of time and money; to pursue it further I
should have to make much greater sacrifices, travel to England, study the
archives there, etc. With warm greetings to you and your sister [etc.]

It's interesting because Cantor made one of the greatest contributions to mathematicians and logic in the whole history of the subject (e.g Godel's proof and much else ultimately depends on the insights of Cantor's elegant diagonal argument), and yet here he is spending 'much time and money' on something generally regarded as, well, a bit cranky.

But enough of that. The aim of this post to is show 'Nishadani' and his like that we can prove the falsity of Baconian, Oxfordian Marlovian theories etc. etc., without any tedious recourse to textual analysis, biography or any other such un-philosophical considerations. We can prove it by pure logic. Let ‘Shakespeare’ denote whoever it was that wrote the plays attributed to the man of that name.

1. Shakespeare and Bacon were one and the same person.
2. There is no doubt as to whether Shakespeare wrote The Tempest
3. There is some doubt as to whether Bacon wrote The Tempest
4. If a=b and Fa then Fb (Indiscernibility of identicals)

Since the four propositions are aporetic, i.e. jointly yield a contradiction, one of the premisses must be false. The first is a mere assumption. Clearly the second is true: obviously the man who wrote the 'Shakespeare' plays called himself 'Shakespeare', just as 'Nishadani' calls himself 'Nishadani'. That is pure logic. The third is true - there wouldn't be so much arguing and gnashing of teeth on Wikipedia if there were no doubt at all. And the fourth (from Leibniz) is beyond all doubt. If Shakespeare and De Vere (or Marlow or whoever) were one and the same person, and De Vere was accused of pederasty, then so was Shakespeare. If De Vere died in 1604 (or whenever) then so did Shakespeare, assuming the identity.

But all four imply a contradiction. By substitution of 'Bacon' for 'Shakespeare' in proposition (2), and by indiscernibility of identicals (4), we have

(*) There is no doubt as to whether Bacon wrote The Tempest

But this proposition contradicts (3) above. It cannot be true that there is some doubt that Bacon wrote the Tempest (even a tiny bit of doubt) and that there is no doubt. Contradiction. Therefore the weakest of the four propositions above must be rejected, namely that Bacon and Shakespeare were the same person.

So forget the historical and textual crap. By purely logical and philosophical methods we can clarify all manner of difficult questions like this.