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Eliezer_Yudkowsky comments on How to Convince Me That 2 + 2 = 3 - Less Wrong
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SS0 isn't a free variable like "x", it is, in any given model of arithmetic, the unique object related by the successor relation to the unique object related by the successor relation to the unique object which is not related by the successor relation to any object, which is how mathematicians say "Two".
Although as a mathmo myself I should point out that, to save time, we usually pronounce it "Two". :)
I am quite familiar with TNT. However either you are talking about models of arithmetic based on peano axioms, in which case e.g. SS0 + SS0 = SSS0 simply cannot be true, for it contradicts these axioms and if both the peano axioms and said equation were true, you wouldn't have a model of arithmetics; or (what I'm assuming) you are actually talking about non-peano arithmetics, in which case there is no compelling reason why any equation of this kind should generally be true anyway.
On another note, it seems that bayesianism is heavily based on peano arithmetic, so refuting peano arithmetic by means of bayesianism seems like refuting bayesianism rather than refuting peano arithmetic, at least to me.