As much as I understand what the thread creator is getting at, it's an overvaluation of the probabilistic nature of the universe to assume 1 + 1 = Invalid, which is what I have a serious problem with. It's a nonsensical claim, and if you want to get your point about an uncertain universe across it's probably best to use another example.
Every formal theory, axiom etc of mathematics is by definition, a language. Everything that can be described or conceived, including every structure or process is isomorphic to a description or definition in language. For example, if you can grasp or perceive some conceptualization, you can name it and give it a definition as well.
Every sentient creature, i.e. you, constantly affirm the linguistic structure of reality by exploiting this isomorphism to make even a single perception. Cognition and perception are languages on their own as well.
Basically, what I'm saying here is that every perception you make only confirms that you're wrong and that this discussion is semantic nonsense. 1+1 = 2 is simply an extrapolation of the perceived universe onto a definition in language. Language and mathematics are something you depend on to make and evaluate even a single perception. To reject this idea you have to reject reality itself.
Arguing about whether or not the universe is unstructured and probabilistic is completely unrelated to 1+1 = 2. On one hand, we have a formal language system that maps a concept onto a definition in language, which is what 1+1 = 2 is. On the other hand, we're arguing that the universe is sometimes unpredictable, in which the vast majority of people here are replying with 'Well, no ****', because the two are unrelated concepts.
If you're still not getting it, this is equivalent to claiming that the following picture is not necessarily an apple, because the universe is unpredictable, despite the fact our language has defined it as such:
http://pocketnow.com/html/portal/new...resh-apple.jpg
So really, there's no debate here. It has been said before, so it's basically kicking the dead horse, but if you have new ideas to discuss it's probably best to put them into a new thread or something that doesn't have a crap title.
Sadly, this is the only thriving thread in CT right now XD