So here I am making good on a promise to expand on a previous post about the weakness (hence flexibility) of natural languages versus the consistency (hence brittleness) of non-natural ones such as metalanguages that try to account for natural ones.
The anxiety that drives us to create metalanguages is based on an anxiety about paradoxes and inconsistencies in natural language. Fueled by the belief that these paradoxes can be eliminated.
One well known example of the inconsistencies of natural language is the sentence
(1) This sentence is false.
This is the Liar paradox. Many philosophers are anxious to work around the fact that (1) is both true and untrue simultaneously (p ∧ ¬p), violating the law of non-contradiction (LNC).
Logicians have tended to produce “higher level” accounts of truth to work around statements such as (1). Unfortunately, like a virus, (1) can mutate to adapt to the new conditions. All that happens is that the metalanguages become more brittle than the natural language, because they are more rigid. For example, consider the extended Liar:
(2) is not True.
Okay, maybe this one is neither true nor false, but valueless. So consider this one:
If (2) is not True, then “(2) is not True” is True.
And so on. By trying to get rid of the contradiction, some philosophers make it much worse.
Problems with LNC are of particular import to speculative realism, since Meillassoux and others are anxious to adhere to it. They claim that true violations of LNC would entail divine beings.
Meillassoux's reasoning about this begs the question. It goes something like this: “Reason cannot countenance divine beings. In order not to allow for divine beings, LNC must hold. Therefore, LNC holds.”
One reason for this question begging might be the too rigid bright line Meillassoux draws between reason and belief. By adhering to a rigid definition of reason, Meillassoux's argument becomes brittle. Any true contradiction could break it.
I suspect that contradictoriness is a symptom of some recalcitrance of reality, such as object withdrawal. On my view, it's easier to side with Lacan, who argues that “there is no metalanguage.” But to hold this well you have to allow for (some) contradictions.
Contradictoriness also applies to set theory, which is a major plank of Meillassoux's speculative realism and Badiou's Maoism. To be continued.