‘Meaningless’?
I’ve had many conversations about the semantic paradoxes (in particular, the Liar). And by far, the most common response is that “the paradoxes are meaningless”. I can see why this view is attractive, but I’ve yet to hear anyone convincingly say why.
Most of the time, the explanation is pretty awfully circular: “They’re meaningless because they don’t make any sense” or “They can’t have a truth value” or “They are meaningless because they are paradoxical”. But what we want is a theory which explains why paradoxical sentences are paradoxical. It doesn’t help much to quarantine all the troublesome sentences in some catch-all category without further explanation (can we say ad hoc?).
That’s why I like Grelling’s paradox. It’s pretty straightforward, and to my mind it undercuts some of the intuitions that lead to meaningless response. Here it is:
Let an adjective A be homological iff the sentence “`A‘ is A” is true. An adjective is heterological if and only if it it’s not homological. Now, consider the following sentence:
- `Heterological’ is heterological.
What truth-value should (1) receive? Per usual with paradoxes (1) is true iff (1) is false.
The nice part about this paradox, is that there’s no self-reference going on. The concepts involved are circular in some fashion, but it should be pretty clear that they aren’t problematic on that front. Both ‘homological’ and ‘heterological’ have extensions that are straightforward to grasp. For example ’short’ is a short word, ‘monosyllabic’ has more than one syllable. It doesn’t take much to see that the concepts make clear sense, and could even be meaningfully put to use in English.
So one might ask: how is it that (1) could be meaningless while “‘Short’ is short” seems perfectly fine. Perhaps, one would be willing, despite appearances, to contend that “‘Short’ is short” is meaningless. Or perhaps, one might maintain that there is no predicate which expresses what it common to all such sentences.
All of these responses could be developed, I’m sure. The point is that, when you think a bit about Grelling’s paradox, they all seem undermotivated. Anyway, I like to think that any theory of paradox, if it is going to be a theory will have to tell us why paradoxical sentences are meaningless. More importantly, the ‘meaningless’ view will have to do so in a way that doesn’t rule out too many non-paradoxical sentences we think are meaningful.
I don’t think this is quite what you were looking for–the author doesn’t discuss Grelling’s Paradox, for example–but I think it’s close enough that you might find it interesting. It’s a paper by N.J.J. Smith called “Semantic Regularity and the Liar Paradox”. You can find it here, in a longer and a shorter version:
http://www.personal.usyd.edu.au/~njjsmith/papers/
Here’s the abstract:
“I argue that the Liar paradox forces us to abandon the principle of Semantic Regularity, which says that there are perfectly reliable, principled relationships between our behaviour, mental states and physical environment on the one hand, and what we mean by our utterances on the other hand. Relinquishing Semantic Regularity opens the way to a solution to the Liar which
is one hundred percent classical, and which does not generate a strengthened Liar paradox or revenge problem; it also yields solutions to semantic indeterminacy arguments such as those of Quine, Davidson, Putnam and Kripkenstein, to the problem of empty names, and to a recalcitrant problem in the literature on vagueness, the problem of false precision.”
Thanks for the reference Jason. I have a copy of that particular monist volume because it’s filled with some good papers on Truth studies (including ones on pluralism). So, I’ve actually already had a look at Smith’s paper previously.
His solution is not exactly the “meaningless” solution I was hinting at. He suggests we treat wff as mathematical objects, like sets, and not mere syntactical strings of marks on a page. This allows him to propose a “non-existence” solution to the semantic paradoxes by claiming that such wff qua mathematical objects don’t exist. In the case of `heterological’, the meaningless-response would say: there is a predicate `heterological’ but it’s meaningless. Smith’s response is that there simply is no linguistic expression `heterological’.
The idea is philosophically parallel to mathematicians standard resolutions of Russell’s set paradox. The main difference is that mathematicians already have a fairly intuitive conception of a set (the ‘iterative’ conception) which independently motivates the non-existence of a Russell set. In the case of wffs,, it’s not clear that philosophers have such an alternative conception. (Although, to Smith’s credit he does a lot of work to motivate it, including solving some problems in phil. lang. unrelated to semantic paradox.)
I’ve seen N.J.J. Smith’s work before. (He wrote a really interesting paper on modal mereology based on continuum-many-valued logic.
The nice part about this paradox, is that there’s no self-reference going on.
That’s not really true; the self-reference is just obscured. “Heterological” and “homological” are, on a strict theory of types, meta-adjectives that describe primary adjectives. Note that short and monosyllabic do not suffer from this sort of embedded self-reference: they describe their own orthographic characteristics, not their own semantic characteristics. A strict theory of types is not violated in the latter cases because the connection between the semantic characteristics are not entailed by the orthographic characteristics.
Grelling’s paradox seems like a pure pseudo-problem.
To the ‘Barefoot Bum’:
Thanks for the comments.
I’m not sure you’re right about this, if by type theory you mean something along the lines of a Montague-style semantics for natural language. If our language has the expressive resources to represent its own semantics, then the adjectives can be named as objects in our domain. So, by quoting a term, adjectives can apply to terms in the same way they apply to any other object in the domain. This means that there’s no need to raise the semantic type of ‘heterological’, or treat it as a meta-adjective. Lots of semantic types have been proposed for adjectives, but heterological should get whatever type all the others get.
As to the distinction between orthological vs. semantic. This is interesting, but I’m not sure how much to make of it. Perhaps the paradoxical generating features turns on the fact that the term comments on its own semantics. But there must be plenty of unproblematic/non-paradoxical examples of this. Here’s one: homological. No paradox there (sans negation).
Anyway, it’s not obvious to me (or lots of others doing philosophy of language, for that matter) that Grelling’s paradox is a pure pseudo-problem.