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.
4 comments:
I've an idea about our capacity for metalanguage that I've been meaning to work on, but have never gotten around to it. It follows from one of the many curiosities (well, not so curious) about the nervou system. The brain has several regions for analyzing sound. Music and language share some of these, but differ in others. And then there's the perception of, shall we say, ordinary sounds, sounds that aren't music nor speech, but could be anything else -- though I wonder about the perception of animal vocalizations. The sound of language is, in some sense, 'transparent' to the brain's speech regions. They deal with speech sounds, but don't put them before us as objects of perception. Rather, they are with us, or perhaps behind us, as vehicles of perception. And so we are ordinarily unaware of speech as such.
But what happens when we listen to a foreign tongue? Our speech receptors can't parse the input, can't treat it as the transparent vehicle of thought and perception. And so it becomes an object, out there, to be perceived perhaps by the brain regions that perceive those ordinary sounds, or perhaps those ordinary cries. In this way language becomes an object of our thought. It is there for us to think about it. And so we naturally become meta to it. But not in they turning your eyeballs back on themselves kind of way that we sometimes think of when we conceptualize going meta.
Oh, wait a minute, it turns out that I did do something with this idea after all. Here's an old post on it.
Hi Tim,
I wonder if you've read any work by Graham Priest. His work on veridical contradictions could be of interest to you. Check out his book *Beyond the Limits of Thought* (Oxford University Press, 2002) if you haven't already. In that work, he outlines the formal structure of paradoxes at the limits of expressibility, knowability, iterability, etc. He calls it the Inclosure Schema. I suppose you'll find or at least suspect a "brittleness" in Priest's work, but he's at least worth mentioning. For one thing, Priest shows how the Liar's paradox is only a specific case of more a general paradox at the limits of cognition, a point which might add to your discussion. You may also be interested in his chapter (in the same book) on Nagarjuna, written with Jay Garfield, as well as his attempts to understand Heidegger and Derrida in terms of dialetheism.
I'm not trained in analytic philosophy, so I can't go too deep on the subjects you've broached here. I will say that I tend to agree that the will to metalanguage is often based on anxiety. Priest may be clever, but a certain anxiety may indeed be motivating him. That said, I think that Priest and anyone else endeavoring in good faith to think "dialetheism" deserves a place in the conversation. For my part, I can't deny that anxiety has been an important part of my own philosophical development. Perhaps your use of the word "us" in that sentence indicates that the same is true for you. Anyway, if you're familiar with dialetheism I'd love to hear your thoughts on it.
Cheers,
-A
Yes indeed I have Aaron. In fact Graham and I hung out recently in Melbourne. He is positive about OOO. I shall read your comment carefully and probably post directly on it.
The great pre-modern systems of thought stressed knowledge as adequation of mind to thing (Veritas est adequatio intellectus ad rem). Language was the instrumentality of adequation, especially,as it developed, formal language. The hidden assumption was that the object of language (reality)was itself consistent (God the geometer didnt, maybe couldnt, contradict Himself). The paradoxical character of "natural" languages was seen as their flaw (a holdover of Platonism). Formal languages were to be preferred because, qua consistent, they would serve to adequate thought to a reality taken to be itself consitent. One challenge of the paradoxical findings of the metatheory of formal languages in the 20th century is that it might be taken to suggest that reality is itself not consistent and that is why "natural" language serves to adequate to it so well. (This assumes that adequation is still a good theory, which is these days, by and large, not as popular position to hold as once it was.)
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