Monday, June 4, 2012

Mailbag Monday: Dialetheism

Mailbag Monday: A weekly segment that covers readers' questions and concerns about all things Philosophy, Bro, and Philosophy Bro that don't quite fit anywhere else. Send your questions to philosophybro@gmail.com with 'Mailbag Monday' in the subject line.
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Matthew writes,

I was wondering if you could explain Dialetheism for me. That shit is confusing. How can a contradiction be true?

Right, so, for those of you playing along at home, dialetheism is (roughly) the belief that there are true contradictions, or dialetheias - for some p, both p and not-p are true. Which means that, whatever p is, you could ask, "Hey, bro, uh... p?" and I could legitimately respond "Yes! Also, no."

And of course, at first blush that sounds fucking crazy. How can a thing be true and false at the same time? If you're a Randian, you are perhaps stomping your foot here and just insisting that contradictions can't be true, and that's all there is to it. (Also, if you're a Randian you should know that I'm going to be presenting two sides to an issue here, so get out while you can.)

It turns out, some sentences just don't fit neatly into the true/false paradigm. Sentences like the Liar's Paradox: "This sentence is false." What do you do with something like that? Is it false? Well then it's true, so suck it. Maybe instead you want to say it's true? Well if it's true, then it's false, so also suck it.

And now maybe you're like, "Well gosh, this is embarrassing. Okay, well, you've put me on the spot here, Bro, but can we just say it's neither?" I mean, we totally can say that, sure, and in fact for millenia we did just say that. No one really knew what to do about those paradoxes and they tried to sweep them under the rug like, "Huh! Aren't you an amusing little trick of language? Well, scurry off, we're trying to say true or false things here!" But they just won't go away. And then you get something like this sentence:
This sentence is either false or neither true nor false.

If that sentence is true, then you get either "true and false" or "true and not true or false"; and if it's false then you get "true and false", and you're right back where you started.

If that last bit confused you, don't worry about it. The important thing is, you can't just add new possibilities and get out of the paradox. No matter how many levels up you try to go, someone's going to find a way to stick you with a sentence that is both true and not true. Now you could try to just keep saying, "Oh, well, if we go one level up in language we see that that sentence doesn't make sense!" But really, you're building these arbitrary metalanguages and they're not doing anything except getting you out of this one problem. And you can never build enough. A dialetheist is going to roll his eyes at you and say, "Just... will you just let it be true and false, for fuckssake?"

But of course, allowing there to be contradictions opens up a whole new goddamn can of worms, which is my least favorite kind of can to open, and also my most favorite (see what I did there? Right, I know, fuck me.) For starters, it blows classical logic all to hell. It turns out that in classical logic, if you can prove a contradiction, you can prove literally whatever you want. Which, spoiler alert, is bad. We don't need people running around like, "The Liar's Paradox! Therefore, it follows that NASCAR is a sport!" See how that could get out of hand quickly? So if you accept dialetheism, you have to develop some new logical systems to make it work out. And that work is being done! Dialetheism is actually a pretty recent development, and it's some of the coolest stuff being done right now in philosophy.

One problem dialetheism faces is deciding which sentences get to be true and false. Obviously no one wants to make every contradiction true. But now, when someone says, "Well, I think p" you can't be sure they don't also think not-p. What do you do with that? WHERE DOES THE MADNESS STOP?! The obvious candidates are the Liar's Paradox and related statements - the tricky, self-referential bullshit, really. Those are statements that more or less force you to admit they're true and false, because they can't be one without the other and there's no neat solution in 'neither.' Graham Priest, maybe the most influential dialetheist still working in the field, has suggested - reminded us, really - that you should accept those statements that you have good evidence for, which he takes to be pretty limiting - you have good evidence that the Liar's Paradox is both true and false; on the other hand, you have lots of evidence that Elvis is dead, almost no evidence that he is not dead, and definitely no evidence that he both is and is not dead. So you don't have good reason to believe that "Elvis is dead" is both true and false. It looks like very few statements will turn out to be dialetheias on an evidence based view. Priest also suggests early on that transition states, like when you pass from one room to another, might give us dialetheias - it is true that I am in the room and also that I am not in the room. I'm halfway! These seem less obviously dialetheias to me - "You're inside and not inside so contradictions can be true!" seems like the kind of bullshit that would make Wittgenstein want to put his head through a goddamn wall.

So we have this hilarious image, an impetuous child angrily stomping her foot and screeching, "Contradictions CAN'T be true! They just can't!" But really, that's more or less all we have. Aristotle called the Law of Non-Contradiction the most basic law of reason, period, but that was just his way of gesturing and saying, "Well, I mean, obviously." He actually gave some reasons, but none of them were super-convincing. It was more like everyone wanted it to be true, so when Aristotle gave some bullshit argument they were like, "Oh, yeah, good enough. Okay. NEXT!" (If there's enough demand for it, I can summarize that text and/or Priest's two-millenia-late response.) And can you blame anyone for wanting that to be true? That seems pretty reasonable to me - you'd want some things to be true, and others to be false, and never the 'twain shall meet. When someone says "Hey dude, there are no velociraptors coming," you don't want to have to worry, "...but what if there also are velociraptors coming?" So it's no surprise that Aristotle got away with just sort ofs claiming contradictions are false for so long - we all think like that, which is why shit like the Liar's Paradox is so goddamn irritating. I mean, Thomas Aquinas thought that even God Almighty Himself couldn't make contradictions happen. When you think about how many annoyingly obvious things philosophers do question, it's a testament to how entrenched in our thought non-contradiction really is, that it took two millenia for someone to go, "Uh, guys? Are we sure about this?"

But eventually, someone did. So, here we are. So the short answer to your question, Matthew, might just be "Well, it turns out there just are true contradictions. Sorry for partying."
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For more on dialetheism, the SEP page is really good if you've got the time - it is a technical introduction, but it is minimally technical.

19 comments:

  1. Awesome post!

    And please, please, pretty please, I'd love to see Aristotle and Priest on the ring. Like what you did with Socrates the other day. That was _so_ epic.

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  2. There are distinct "brands" of dialethism--for instance, the "deflationist" or "spandrels of truth" type advocated by J.C. Beall, and the more more "robust" (realist) type advocated by Graham Priest. It's also important to note that logicians can favor paraconsistent logics (logics in which ex falso quolibet, aka "principle of explosion," everything follows from a contradiction, is blocked) without further commitment to dialethism (the view that there are some true contradictions). It's important to be aware that a number of options are available, even within non-classical logic.

    There have been interesting interviews with Beall and Priest recently:
    http://www.3ammagazine.com/3am/logically-speaking/
    http://www.3ammagazine.com/3am/spandrels-of-truth/
    I hope folks have some fun with non-classical (deviant) logic! It's worthwhile considering, even if one's intuitions remain "classical."

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  3. Hilarious post, also yes to Aristotle-Priest dialogue. Was curious if you are a XKCD fan, PB, judging by your use of velociraptors in the example. JC Beall taught me for a semester; a great, funny lecturer.

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  4. Philosophy Bro,

    Your writing is very entertaining and you provide a great intro to the topic!

    But, why can't I just say that the person (sincerely) uttering the sentence "This sentence is false" is confused? I mean, it seems to amount to some kind of radical skepticism, which is admittedly immune to disproof (but, I think it was Putnam who said "Doubt requires as much justification as belief" while summarizing what he and his contemporaries found attractive about pragmatism)

    Here we are, chugging along just fine, and someone comes along and says something can be true and false at the same time, like, literally. Why should I believe them? The fact that they can wrap that enigmatic belief into a sentence where I can't see it ("This sentence is false") doesn't mean I can't smell it... I say the burden is on them, and I ask in reply, "What on earth does that sentence mean?" While I may have an incentive to be smarmy and coy, I sincerely do not know what the sentence means... it seems like gibberish.

    (I'm open to being shown the light, Broseph! I mean, dude-man, the fact that so many people have tripped out about this for so long makes me wonder if I'm being facile, but still though ...)

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  5. I fear I may have ignored the fine distinctions between nonsense, gibberish, and what not. If so, I throw myself at the mercy of the court... Plug in the best word, please.

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  6. This is probably my inner Bertrand Russel speaking: But why not just take the view that the Liar's Paradox, and other's like it, are just gibberish?

    Negation as failure and autoepistemic logic and such.

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  7. I'm with Jeffers on this one. Granted, I haven't had much exposure to dialetheist literature – until recently I wasn't even aware it was a "thing" among any reputable philosophers – but it certainly seems like an awfully bizarre claim based on a few strange statements that already seem rather more like (possibly meaningless) linguistic confusions than logical conundrums. On that note I'm surprised you didn't give much attention to the legion of traditional responses/resolutions to the Liar's Paradox. Kripke, Gödel, Tarski, Barwise and Etchemendy, Langan, Prior – all have written some fairly interesting and occasionally quite convincing solutions to the thing, usually covered at the beginning of any Symbolic Logic 101 course.

    What gives, bro?

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    1. Mostly, that just wasn't the question. If I do a post exclusively on the Liar's Paradox, I'll have a chance to cover more of those.

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  9. Claims like...

    "It turns out, some sentences just don't fit neatly into the true/false paradigm. Sentences like the Liar's Paradox: "This sentence is false." What do you do with something like that? Is it false? Well then it's true, so suck it. Maybe instead you want to say it's true? Well if it's true, then it's false, so also suck it. "

    ...certainly seem to represent the dialetheist position as hinging on sentences like the Liar's Paradox. Does there remain (in your opinion) any compelling argument for dialetheism if these few "self-contradictory" sentences are shown to be not so contradictory at all, or outright linguistic bullshit?
    Because, if note, if such sentences are the core motive for the dialetheist position, I'm not sure how that "wasn't the question." But I may have misunderstood that contingency.

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  10. The Liar Paradox is nothing more than clever word play. "This sentence is false" is meaningless for there is no sentence that it is referring to.

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  11. Can we just say, "most sentences are for describing reality" and "no sentence that is not either false or true describes reality"? So we can form these funky contradictions, but we can only form them in a sort of _abstract space_, and we can't connect them up to anything that matters, like velociraptors. So we'd basically isolate them as a linguistic quirk and say "Meanwhile, while we're over here talking about reality, we don't need to bother with them." Would that work as a compromise?

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  12. Giraffes, Elephants, Baboons!June 12, 2012 at 5:31 PM

    @FeepingCreature / others who seem to see the Liar's Paradox as mere linguistics, or something to sweep under the rug: I don't think that's a valid response, because self-reference is a perfectly valid thing to use in speech. Even if you want to outlaw the specific formulation of the Paradox where a single sentence refers to itself, what about "The following sentence is false. The previous sentence is true."? True, you could disregard that type of formulation by disregarding sentences that refer to other sentences at all, but then you'd have to disallow people saying things about other people saying/thinking things, etc., and what you're left with, it seems to me, is not really what we would call human language. As I see it, at least, self-reference (or reference to others' speech/thought, which can always lead to indirect self-reference) is a pretty integral part of the way humans think and communicate.

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    1. Godel Escher Bach, right?

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    2. Weell..

      I don't think the Liar's Paradox can be deductively or "once and for all" disproven. But I do think we should think seriously about who holds the burden here. A sort of everyday chin-stroking session would reveal that we use "true" and "false" either to describe the world, or certain states of affairs. Other than that, perhaps we use it to refer to certain a priori impressions or beliefs (e.g. 2+2=4).

      It's not that self-reference is outlawed, or that I have a card up my sleeve that allows me to (QED) dismiss the Liar's Paradox, but as I alluded to earlier, I am unmoved by the example of the Liar's Paradox and sentences such as "This sentence is false," and can see no reason to be moved or impressed. I grant that it's fun and trippy or what-not, but given the attention that has been paid to this issue, I'm left confused - I just don't get what all the fuss is over.

      I mean, even your example "The following sentence is false. The previous sentence is true." can be interpreted as nonsense because it is underwritten by the principle "things can be true and false, in the same way, and at the same time, such that a genuine contradiction can be true." And well, I can see no reason to believe that. I don't have a knock-down general rule that would be perfectly inclusive (neither over nor under), rather, I suggest we look at how we normally use the words "true" and "false." If the Liar's Paradox and similar examples do not conform to our typical usage, then why shouldn't we feel comfortable simply shrugging and moving on?

      Genuinely Curious..

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    3. Guilty as charged--Hofstadter's a big influence of mine. Which doesn't mean I would necessarily disagree with a counterargument.

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  13. I think you are wrong to say that there "are true contradictions". Contradictions are a third group: there are true statements, false statements and contradictory statements. Accepting "contradictory" as a third truth value is very different to contradictions being true.

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