Tuesday, September 29, 2009

What Calling The LNC "Metaphysical" Won't Get You A Free Pass On

[It's been recently forcefully pointed out to me that a regular, predictable schedule here would be good. Accordingly, I'm going to try to update every Monday and Wednesday for the foreseeable future. We'll see how that goes.]

So I just saw this extremely interesting article by Tuomas E. Tahko, "The Law Of Non-Contradiction As A Metaphysical Principle." (Thanks to William Shultz for the pointer.) From a quick skim, it looks like Tahko is making a useful distinction between the LNC understood just as a logical formula that says that for any sentence, the negation of the conjunction of that sentence and its negation is true, and something more like what I like to call "monaletheism" (a helpful term coined by Ryan Lake), a distinction often run together when the debate about dialetheism is casually referred to as a debate about the Law of Non-Contradiction. After all, the dialetheist can embrace the LNC in the former sense, as long as they're willing to commit to a secondary true contradiction, (P & ~P) & ~(P & ~P) for every simple contradiction (P & ~P) that they are committed to. Moreover, IIRC, the LNC is actually a logical truth in Graham Priest's favored logic LP (Logic of Paradox), and in a talk I saw in Melbourne, Koji Tanaka said that this was a feature of all of the paraconsistent logics that Koji liked. So this seems like a worthwhile distinction to make. As far as Tahko's favored way of expressing it....meh. I more or less agree with Quine on issues of ontological commitment, confirmational holism and the like, so I'm a bit skeptical about how much light is shed on the status of a given truth when we slap the "metaphysical" label on it, but Tahko's explication of what he's getting at with the label seems more or less unobjectionable to me:

"At its simplest, the metaphysical interpretation of LNC amounts to this: the entities of the mind-independent reality are plausibly governed by some sort of principles...as to what kind of properties a certain kind of entity can and cannot have, and further, some of these properties are mutually exclusive. For instance, a particle cannot both have and not have a charge at the same time, or an object cannot be both green and red all over at the same time. It seems that reality just is such that it conforms to the law of noncontradiction. For instance, a particle cannot both have and not have a charge at the same time, or an object cannot be both green and red all over at the same time."

The general spirit of this passage resonates nicely for me with what Frege seems to be getting at when he says that: "[l]ogic is concerned with the laws of truth, not of holding something to be true, not with the question of how men think, but with the question of how men must think if they are not to miss the truth." So far, so good.* What I have a problem with, in Tahko's presentation, comes shortly after that definition:

"Another thing to note before we proceed is that semantic paradoxes such as the Liar do not threaten LNC as a metaphysical principle. Any arbitrariness or vagueness over language has no bearing on LNC understood as a metaphysical principle. A counterexample to the metaphysical version of LNC could only be a true contradiction in the world."

I don't think this works. First of all, I'm deeply skeptical about the idea that the Liar Paradox has much of anything to do with vagueness. Take a typical Liar sentence:

# The sentence marked by the number sign is false.

No one, reading this sentence, has the slightest doubt about what sentence is being referred to, or about what it is to say of any sentence that it is false. Moreover, "true" and "false" certainly seem pre-philosophically to be mutually exclusive properties of sentences, certainly no less mutually exclusive than "red" and "green" as the colors of the entire visible surface of an object. So, unless sentences are not, for some reason, part of "the world" (which is certainly a strange thought, since they certainly *seem* to have an independent existence), then it looks like the LNC-as-a-"metaphysical"-principle as Tahko defines it should apply to the truth-and-falsehood of sentences as well as the redness-and-greenness of visible surfaces.

And what work is "arbitrariness" doing here? Of course, you could argue (as many people do) that any claim that "ungrounded" sentences like the Liar (or its non-paradoxical twin, the Truth-Teller) is either true or false is in some sense arbitrary, but if that line of thought gets you to the result that such sentences are "neither true nor false," you run into familiar problems with Strengthened Liar sentences, like:

$ The sentence marked with the dollar sign is not true.

...and the problem for the orthodox logical/metaphysical position on entities having some properties and not others, and some such combinations of properties being generally impossible, rears its ugly head once more. So, to sum up my objection to Tahko's move for side-stepping the semantic paradoxes, it seems to me that:

(a) Sentences are part of the world,
(b) Different semantic statuses of sentences seem to mutually exclude each other in the same way as e.g. different charges of particles or different colors of visible surfaces, and to equally be the sort of thing that the LNC-as-a-metaphysical-principle-as-defined-by-Tahko would pretty much have to apply to, &
(c) If the problem posed for logical orthodoxy by the Liar has anything to do with either vagueness or arbitrariness, it's far from obvious, and, at first blush, it's not clear how mention of either clarifies why the Liar isn't a problem for the-LNC-as-a-metaphysical-principle.

So, any thoughts out there? Is there a good way of glossing Tahko's discussion that makes his quick dismissal of the Liar more plausible than it sounds to me right now? Let me know what you think.

*Obviously, agreeing with Frege about *that* much is an entirely different matter from agreeing with him that logical truths are "analytic," or are about a metaphysically different sort of reality than other kinds of truths, or anything of the kind. Also, this description of what "logic is concerned with" on the relevant level of analysis shouldn't be taken as ruling out the possibility (unforeseen by Frege, as far as I know) that logical systems can fail to accurately model the way things really are but still be interesting and instrumentally useful tools for formal reasoning about various subjects.


Tuomas said...

Thanks for you comments on my paper Ben!

I admit that I didn't want to go into the details of the Liar Paradox in this paper, even though there would no doubt be interesting things to say about it. However, I do think that it's not essential for my purposes and still think that semantic paradoxes will not undermine LNC understood in the metaphysical sense.

I agree that sentences are a part of the world, as I think that language is, but they are certainly not part of the world in the same manner as, for instance, electrons are; we could say that they are abstract objects. Now, in the paper I say that I am quite happy with so called linguistic dialetheism, which Liars and other semantic paradoxes would seem to imply.

If you like, we could put it like this: one part of the world, namely semantic objects, is paradoxical. However, they are certainly not part of the *physical* world. It's hardly a surprise that a human construction such as language is paradoxical, but it seems to me that this is at least to some extent strictly due to lazyness: we haven't defined language as accurately as we could, because in most cases we don't need to.

I should add that I didn't mean to suggest that the Liar is a problem of vagueness, although I admit that it might seem so from the text. I had in mind primarily Priest's examples such as being in a room or being outside a room. This is where (linguistic) vagueness comes in: should we choose to do so, we could remove vagueness of this type very easily, it all depends on how we choose to define 'being in a room'. And now for the key point: when a metaphysical realist talks about *the world*, he generally means *the mind-independent world*. Because language is clearly not mind-independent, it is not included in the world in this sense. I am primarily interested in whether LNC applies to the *mind-independent world*, and semantic paradoxes seem to have no bearing on this.

By the way, it's "Tahko" rather than "Takho".

Ben said...


Sorry about the spelling mistake. It's been corrected.

It's actually not yet clear to me what useful sense of "mind-independent" there is in which language doesn't count. Languages are certainly the result of human human thought and activity, but once brought into existence, have at least a somewhat independent existence, yes? This is what I take Priest to be getting at in one of the best bits of rhetoric in 'In Contradiction', when he says that, "Even though our conceptualisation/linguistic structure is, in a sense, a human product, it does not follow that we have complete control over what we produce. (This, after all, is the moral of Frankenstein, and, in a much more horrific way, of Capital.)"

In terms of the distinction between what Mares calls "semantic dialetheism" and what he calls "metaphysical dialetheism" and attributes to Priest, if I'm remembering correctly from Mares' article in the LNC anthology, he says that the semantic dialetheist isn't committed to the view that the most accurate overall description of the world would be inconsistent. The sort of objection I'm trying to push, basically, is this:

If you're willing to accept semantic but not metaphysical dialetheism, at least if you accept that dividing line between the two (which, of course, might be a bad way to express it...who knows), do you think that the most accurate overall description of the world (which might be expressed in some new, more consistent language) would include some contradictions about the meaning of certain sentences of English?

Tuomas said...

Thanks Ben.

Well, whether language is a part of the world or not and in what sense seems to be an ancillary issue here, but my use of 'mind-independent' in the sense that it excludes language shouldn't be particularly controversial; 'independent' here refers to something like 'ontologically independent' and the fact that we don't have complete control over language does not make it mind-independent in this sense. At any rate, I could just use *physical* world instead of *mind-independent* world.

Anyway, I'm perfectly happy to say that language, whatever its status is in the world, has elements that are paradoxical or contradictory. But this is hardly news.

What would be news is if the physical world, or world minus language, would be contradictory, but I have not seen any convincing arguments for this. My main concern in the paper was to show that Priest (or Zeno) have not put forward such arguments either.

I'm not entirely happy with the notion of 'the most accurate overall description of the world'. But if it is allowed that this description can be expressed in some new, consistent language, then I would imagine that it would not include any contradictions. Concerning the meaning of certain sentences of English, i.e. the contradictory ones, it would perhaps say that they are meaningless. But I'm not very concerned about this. After all, language is only a tiny part of this description, and contradictions just a fraction of that. I'm concerned about whether the primary subject matter of metaphysics is consistent, and that would still seem to be the case.

I linked to your post from my blog (http://ttahko.net/blog/), I hope that's ok.

tim said...

Hi Ben and Tuomas

I was directed here by Tuomas' link on facebook.

I think the discussion between the two of you brings to the fore the following: Isn't logic (and LNC) a bit more *general* than any metaphysical principle? From your paper, I see you discussing the principle:

1. (for all F)(forall x)~(Fx & ~Fx)

Where F ranges over physical properties (e.g. "having a charge"). Well, I certainly think that principle 1 is true. But that's also because I think that the following is never false:

2. ~(P & ~P)

Moreover 1 follows immediately from 2. But 2 is of much wider scope than 2 and not, apparently, metaphysical. So I can't possibly agree with your conclusion that LNC is a metaphysical principle.

I take it that's what Ben was getting at in his criticism?

That said, I agree with Tuomas that Priest has not found any good counterexamples to 1 (and so has found no good counterexamples to 2).

William said...

Tim, what do you mean when you say "metaphysical principle" ?

tim said...

William: good question.

I take it that Tuomas' idea is that we are meant to think of LNC as a constraint on states of affairs in the world. That is, what things there are and what properties they have. (Whereas I think LNC has much broader scope than that.)

Am I right, Tuomas?

(I should say that I am somewhat sceptical of the idea that there's anything distinctive about metaphysics. However, I think I can bracket *that* disagreement between Tuomas and myself.)

William said...

Tim, so you're sympathetic to the view that there is nothing distinctive about metaphysics from the empirical sciences?

tim said...

William: I'm sympathetic to the claim that metaphysics *shouldn't* go much beyond science+maths. Lots of contemporary metaphysics (as practicised by self-described metaphysicians) has nothing to do with science or maths, and I tend to be sceptical about that. However, my views on the relationship between metaphysics and science have nothing to do (so far as I can tell) with Tuomas' paper on LNC. So I'll shut up.

Tuomas said...

Tim, thanks for you input.

You're right in that I am interested in the sort of reading of LNC which is something like your (1), and in some sense (2) certainly is more general. But ultimately I think that (1) precedes (2), that is, I believe that (2) was only formulated because something like (1) appeared to be true. Accordingly, the order of explanation here is from the world to the laws of logic. It seems to me that Aristotle's discussion of these matters also suggests something similar, although I'll have to take another look at that.

If we bite the bullet in regard to semantic paradoxes, then I think that (2) in the most general possible sense is not true. I've said that I'm prepared to do this, although I wouldn't mind a solution to the Liar which avoids this. However, as I see it, the interesting content of LNC is certainly expressed with (1) (although restricting it just to physical properties might not be necessary).

In some sense we've just got two different readings of LNC here, we might call (2) strengthened LNC. But like I said, I think that (1) is more fundamental, and (2) is simply a generalisation of that metaphysical principle, which might or might not be true. Perhaps this is also the dividing line between semantic and metaphysical dialetheism.

tim said...

I assumed you were operating with (1), from what you say on p.34, quoting Aristotle 1984: 1005b19 –20. Just out of curiosity, what about e.g.:

(3) it cannot be the case that there both is an F and that there is no F.

I suppose that (3) is (paraconsistently) entailed by schema (2) but not (paraconsistently) by (1). Is it "metaphysical" or "logical"?

Tuomas said...

That's a good point Tim, I think I would want to say that (3) is metaphysical as well. However, if we view existence as a property, controversial as it is, then (3) is entailed by (1). I'm not saying that this is necessarily the case, but I think there are some good reasons to treat existence in this way. Alternatively I might have to say that the metaphysical interpretation of LNC is wider than just (1), even if not as general as (2).

Ben said...


First of all, of course, link from wherever you want. You don't have to ask.

Second, I certainly agree with you that Priest's case for "Zeno's Principle" and the contradiction theory of change is unconvincing for a variety of reasons. (I blogged about that a while back--http://blogandnot-blog.blogspot.com/2009/07/graham-priests-theory-of-change.html )

Third, I think there might be an important distinction being run together with the talk of mind-dependence. Whatever one thinks about the relationship between mental states and languages, it seems to me that certain sorts of contradictions even *about mental states* might be the sort of contradictions your version of the-LNC-understood-metaphysically is meant to rule out.

IIRC, at some point in your paper, you have a formulation something like the following: the sorts of true contradictions that don't bother you much are merely true-in-a-language or true-in-a-model, not really true in the world (i.e. true simpliciter). (If I'm misremembering here, let me know.) It seems like we can make a closely related distinction about beliefs--it seems obviously true that some people have inconsistent beliefs, but it's not obvious that there are true inconsistencies *about* people's beliefs. (This would, right, be the distinction between B(P) & B(~P) on the one hand and B(P) and ~B(P) on the other.) For example, Graham Priest certainly believes that the Russell Set is a member of itself and that it isn't a member of itself, and even most of his most ardent critics wouldn't argue with *that* claim (about his beliefs). On the other hand, if it were true that Priest believed that the Russell Set was a member of itself *and* it was not true that Priest believed that the Russell Set was a member of itself...i.e. he simultaneously had and lacked precisely the same psychological state in precisely the same sense....then *that* would be a true contradiction about something that (despite being about mental states) we might want in a really strong sense to call part of a "mind-independent" reality, i.e. a reality that is the way it is regardless of what any of us think about it.

(Now, the psychological claim that someone could simultaneously believe something and fail to believe it sounds absurd, but it seems to me that this is exactly the result that's at stake in Kripke's Pierre Paradox.)

Similarly, with the Strengthened Liar particularly, it seems like the danger of Liar reasoning is that it could show us not that some model portrayed something as being both true and false, but that some entity (the Strengthened Liar sentence) has a certain property (being true) and that it fails to have that property. At the very least, that seems to threaten Tim's principle (3).

Tuomas said...


Cheers, I'll try to keep this short. I'm a bit uneasy about extending the metaphysical LNC to beliefs, as we are dealing with mental states here (and as you say, people seem to have contradictory beliefs, especially children and the mentally ill). You may be right about the Russell Set case though, it sounds like something to which it would be nice to apply LNC to. But I'm not convinced that Kripke's puzzle is a good counterexample to that, for one thing, it doesn't seem to me that it satisfies the requirement of having 'precisely the same psychological state in precisely the same sense', as you put it.

As for the Strengthened Liar, I'm not entirely happy about applying the analogy here: it seems to me that sentences cannot be distinguished from the model in which they appear. That is, I don't think that the Strengthened Liar has any independent existence outside the model of the English language, in which case we would still be talking about what a certain model portrays as being true or false -- hence something outside the intended scope of the metaphysical LNC.

Ben said...


Just to clarify: I'm not saying that these things are serious problems for your view (which isn't that far off from mine in many ways), or that there aren't good clean consistent solutions. I'm just pushing the narrower point that they do pose challenges (even if defeatable ones) even to your favored version of the LNC.

Tuomas said...

Sure Ben, I appreciate your comments, I certainly hadn't considered all these points, but I'll try to keep them in mind in future work. I'm trying to work on something on the notion of logical truth at the moment, maybe I'll consult you about that...