Saturday, November 13, 2004

True Contradictions

In a previous post I suggested that there might exist true contradictions. At least, I was not willing to rule out the possibility. Now I'm reconsidering my position. In order to do so, I want to consider the question: what would it mean for a true contradiction to exist? (How would the world have to be for us to describe it in such a way?) And to answer this I think we will need to delve into even murkier waters, addressing that perennial favourite, 'What is truth?'

I won't pretend to know all the answers to those questions. But I'm hoping that by exploring them here, I can sort out my thoughts a bit, and perhaps come to a better understanding of them. (This is one of those unplanned, 'off the top of my head' posts, where I'm making it up as I go along. You'll just have to bear with me. I should also mention that I'm woefully ignorant of the philosophical literature on this topic. Comments are especially welcome from those who know more about this stuff!)

Truth and Reality
I've always been a fan of the good old 'correspondence theory' of truth. A proposition is true if it corresponds to reality, and false otherwise. Fairly common-sensical stuff, it seems. Well, until you start to dwell on it a bit longer. For what, exactly, is the nature of this 'correspondence'? I understand this in terms of representations. A proposition represents some state of affairs. A proposition is true if the representation is an accurate one - that is, if the 'state of affairs' it describes actually exists in reality.

But here's the tricky thing: representations are incomplete. As discussed here, reality in its entirety is too much for us to deal with. To avoid information overload, we must abstract away the details and focus on just a few properties we deem 'important'. A single 'something' can be analysed in many different ways, all of which capture different aspects of it, and all of which we may wish to deem 'true'. Using the analytic knife, there is no limit to the ways in which we can cut up our handful of sand.

So there's no simple one-one correspondence here. A representation may highlight some aspect of reality, but it never fully captures "the whole thing". This makes me wonder if there is a problem with my above suggestion that a represented state of affairs can actually exist as reality. The represented SoA is ambiguous, vague and incomplete; what exists is not. Perhaps we can say that the SoA is a part of reality, and we need not be concerned about its incompleteness. But I think there is a more fruitful path we can take, and that is to admit that although no representation can perfectly describe reality, nevertheless some can describe it well enough for our purposes. Down this road lies Pragmatism, but let's see how far we can comfortably travel.

True or False?
By this view, something is true if it describes reality accurately enough for our purposes, and false otherwise. The standards required to fulfill that 'enough' will vary according to context. I could truly describe someone as 100kg, while their boxing coach - mindful of a tournment open only to those under 101kg - would consider my statement false, because they're actually closer to 102kg. There's not really any conflict here, it just depends what level of accuracy you're after. We can dispel the appearance of relativism by specifying the missing parameter: in this case, the degree of 'rounding' involved.

True and False?
Could there ever be a case of a true contradiction - that is, a sentence for which, once all the parameters are specified, we would still consider it both true and false?

I previously suggested that there might be. One reason for thinking this would be if we thought of truth as an independently-existing property which attaches to propositions. For if you think of falsity likewise (rather than as the mere absence of truth), then it would seem that we could attach both these properties at once. It may not be our usual way of thinking about things, but it could be done, and sense can be made of it all by way of paraconsistent logics. It's not entirely unmotivated either, since it's one way to resolve the notorious Liar Paradox.

But this may no longer hold up if we instead understand truth and reality in the way I described above. If representations are always incomplete approximations of reality, then you can never have a sentence with "all the parameters specified". We can always add more detail. So why would we ever stick with a contradiction?

It's just not useful to say that something is both true and false - both 'accurate enough' and yet not. If there's a real dispute over whether a representation is accurate enough, then that would seem to indicate that we're using the wrong representation. We should pull out our knives and make another cut.

Conclusion:
I guess what I'm really saying here is that if we ever found ourselves in a situation which we were tempted to describe in contradictory terms, then we should redescribe it in such a way that the contradiction goes away. Truth isn't something magical that exists out there in the world (though it is dependent upon physical reality - I'm not a total relativist!). Instead, it's something we apply to judge our models of the world. It's a property of our representations, not of concrete objects. So, since truth and falsity don't exist 'out there' in the world, nor do contradictions. Contradictions are merely properties of bad descriptions. Bad descriptions are not useful; they are not 'accurate enough for our purposes'. So, by this view, a contradiction cannot be true.

16 comments:

  1. It is what human beings SAY that is true and false; and they agree in the language they use. That is not agreement in opinions but in form of life.
    -- Wittgenstein, 'Philosophical Investigations', paragraph 241

    80. The truth of my statements is the test of my understanding of these statements.
    81. That is to say: if I make certain false statements, it becomes uncertain whether I understand them.
    -- Wittgentstein, 'On Certainty' 

    Posted by Roy Sablosky

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  2. Im probably not explaining anything new here but

    Presumably it is never possible for you to say the absolute truth (unless you hedge with lots of maybe's) because you can never perfectly represent reality you can only approximate it.

    Not lying is damn near impossible – not just in general but in most sentences.
    You will say “the cup is on the table” but you can take it down to all sorts of levels the lowest of which disputes the very existence of a unit called a “cup” and only assigns at best a probability that it is where you say it is (assuming you can even trust your own senses). Not only does a representation only cover an aspect it may be describing the reality from a perspective that is technically false and only superficially true. In this case your representation is not even a part of reality.

    So this

    “By this view, something is true if it describes reality accurately enough for our purposes, and false otherwise.”

    Does indeed make a reasonable definition but of course is designed for the specific purpose of having a useful definition between true and false and not an “absolute” difference and in later analysis we must not confuse them.

    You have a pragmatic problem with your discussion of revealing the degree of rounding involved since you never know even the degree of rounding perfectly. Each time you get more accurate another unknown variable will emerge. At its smallest analysis there will be an entirely unsolvable unknown variable (the uncertainty principle! heh)
     

    Posted by geniusNZ

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  3. "It is what human beings SAY that is true and false"
    Yeah, I like that quote - thanks Roy!

    Genius, I'm not sure I follow your comment about rounding. Suppose we know the number we're after is greater than 2.35 but less than 2.45. Then surely we can know perfectly well that the number we're after is 2.4 (rounded to one decimal place)? 

    Posted by Richard

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  4. the point is how do you KNOW it is between 2.35 and 2.45. I am really thinking of statistical sample situations but i will take yours for example - here there is a weighing of a boxer and it is your rounding as a reporter that matters but even then the more correct answer is “to the best of my recall I saw the weighing machine indicate the point just above the number 101” then you are free to define how good your recall is (?) and how far “a little bit” is (maybe .5? but how do you know that?). And so it goes if one is in the search for perfect truth.
    Yeah I'm a nit picker. 

    Posted by geniusNZ

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  5. Hmm, well, while I do enjoy a good discussion of radical skepticism (have a look through my posts here), I do think it tends to be counterproductive to bring up such objections when discussing other matters.

    It's also worth noting the distinction between metaphysical and epistemological inquiry. In this post I was focussing on the question of what it is for something to BE true, regardless of whether we can KNOW it to be such. I think this is an important distinction. But I suppose a Pragmatist would disagree. 

    Posted by Richard

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  6. yes as I said I was feeling like a nit picker there.

    Well quantum mechanics would say that it can't be true - you can only have a probability of it being true and in fact the probability is reality (the photon REALLY IS in two places at the same time).
    Having said that there is no problem at all if you are just saying "can it be true enough for our purposes and the purposes of anyone we are likely to meet - in which case - yes sure. 

    Posted by GeniusNZ

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  7. The point being that as you define your point more accuratly you slowly reduce the possibility for someone to be confused by it or to find a technical error in it. It tends towards - but never reaches zero. 

    Posted by geniusNZ

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  8. I guess what I'm really saying here is that if we ever found ourselves in a situation which we were tempted to describe in contradictory terms, then we should redescribe it in such a way that the contradiction goes away.But what makes you think that it might not actually be truer to describe it in its contradictory state? True, we would never ascertain such knowledge but given that we can change our focus or context to describe any given thing in almost any given way then there might be occasions whereby it is useful to keep a contradictory description because it more aptly encapsulates the thing we are describing. I think we are big enough to handle it.

    We resort to oversimplification when we can say that it is both ‘true’ & ‘false’ that “the sun is rising”. In fact given the consensual nature of truth in our application of it, is it not more accurate to say that all statements are inherently contradictory in nature and that contradiction is removed by allowing the majority of people to be satisfied with a given context and proclaim the statement as ‘true’ or ‘false’.
     

    Posted by Illusive Mind

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  9. hmm .. sounds good IM. 

    Posted by geniusnz

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  10. "there might be occasions whereby it is useful to keep a contradictory description"

    I'm not convinced. Can you think of any examples?

    My thought here is that when we make an assertion, we do so to provide information. When you talk to someone, there's an unspoken agreement that what you have to say is worth the bother of them listening to (this is the cornerstone of 'relevance theory' in semantics/pragmatics). But what does a contradiction tell us? You may reason that if something is true you'll go with Plan A, if false fall back on Plan B, but what if it's both? What are you supposed to do with such information? It strikes me as useless.

    But I'd certainly be interested to hear counterexamples. 

    Posted by Richard

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  11. The contradiction may be required to explain other parts of the information with sufficient parsamony - or for some other suhc reason - at times tht may be the best you can do. 

    Posted by geniusnz

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  12. If removing certain information and or context from or surrounding a particular claim constructs truth and falsity, then contradictions can always be found upon further scrutiny.

    As such, to provide a contradictory account could mean in most cases giving the most amount of information and evidence without bias or prejudice, very useful indeed.

    Of course I'm not talking about a scientific or a legal context where our aim is to emphasize a particular view, however perhaps in history it is useful to say that King 'x' was both a hero and not a hero.

    Speaking in this manner reveals that all there is in the world is information, not truth. So in many cases it may be better to reproduce as much of that information as possible.
     

    Posted by Illusive Mind

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  13. Although I can see where you're coming from, I still disagree that a contradiction would ever be the most useful way of describing a state of affairs. Rather than saying "King X was both a hero and not a hero", it would be more informative to clarify the situation in such a way that the contradiction disappears. That is, you could specify the respects in which the King's actions were heroic, whilst contrasting this with his cold, ruthless character (say). This makes the contradiction go away, and I think it is obvious that it is a more informative and more useful way of looking at it.

    In general, I think you have it backwards when you say contradictions result from "further scrutiny". Rather, they arise from a lack of analysis, when more depth or detail is required.

    Again, I find the "analytic knife" metaphor useful here. The world is a handful of sand, and we can carve it up in arbitrarily many different ways. Some of those ways will lead to what we call "contradictions" - which I argue is symptomatic of a bad description. Instead, we should make divisions that clarify nuanced differences and highlight the salient information so we can act on it. I still don't think a contradiction would ever best serve our purposes in this respect. 

    Posted by Richard

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  14. It would seem - Illusive mind wants to gather more information and you want to apply more analysis to that information.
    So Ilusive mind wil kep producing contradictions and you will keep solving them. So contradictions are both a lack of analysis AND a result of having moe information.
    If we want a practical answer however I think illusives task will get easier and yours harder. 

    Posted by geniusnz

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  15. I think that the metaphor of the analytic knife applies to this discussion itself. We can cut it in such a way that we are searching for contradictions or eliminating contradictions but still ending up with the same sand in our hands.

    I would admit that in a number of cases it is beneficial to limit contradictory information, if designing a nuclear reactor or constructing a new theorem or arguing a case in court we want to somehow provide the best account we can to support a particular version of information, however accurate that might be.

    It might also be worth conceding that it makes no sense to search for contradictions (sounds Derridian) in the case of a priori claims. We want one plus one to equal two otherwise we can’t construct a system that works, however accurate that system might be in describing information that doesn’t abide by those same rules.

    However, when we are not trying to construct a version of the world, but attempting to sift through the sand and understand the complexities of a subject’s contradictions need not be frowned upon. I’ll use history as an example only because it is so often a place riddled with contradictory claims.

    [b] Rather than saying "King X was both a hero and not a hero", it would be more informative to clarify the situation in such a way that the contradiction disappears.[/b]
    I of course think it is more informative to provide the detail behind the claim. I think that you can look at it as having the contradiction disappear or not.

    You could say that in the eyes of his own people King X was a hero for vanquishing the enemy but also showing mercy, but in the eyes of the enemy, no mercy was shown and none of his actions were heroic. Is it true that it was a hero or not? I think that eliminating the contradiction by changing the syntax is playing games, and simplifying the matter into a mathematical form is a mistake, because it is an inaccurate representation of the complexities of the given subject.

    If the king is on trial and you are the prosecutor, then yes it is more useful to simplify and institute a bias.

    [b]In general, I think you have it backwards when you say contradictions result from "further scrutiny". Rather, they arise from a lack of analysis, when more depth or detail is required.[/b]
    If we return to the analytic knife for a moment. Truth is constructing by cutting pieces of sand a way in such a way that they are simple and even elegant, but if we consider that the exact opposite truth can be cut from the same sand then the uncut heap is inherently contradictory. Closer examination means going beyond the neat pieces of sand into the messy perplexing vortex, and I think gives the open minded observer a fuller understanding and comprehension.

    [b]contradictions are both a lack of analysis AND a result of having more information.[/b]
    Yes we can produce contradiction through both means. I think this is a good point. Just because something might be contradictory doesn’t mean it is more detailed.
     

    Posted by illusive_mind

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  16. Instead, it's something we apply to judge our models of the world.

    -Is this something we REALLY do? If it is or isn't, what you say is false.

    Contradictions are merely properties of bad descriptions.
    Bad descriptions are not useful; they are not 'accurate enough for our purposes'.

    -(Graham Priest quote from SEP)

    Consider Bohr’s theory of the atom. According to this, an electron orbits the nucleus of the atom without radiating energy. However, according to Maxwell’s equations, which formed an integral part of the theory, an electron which is accelerating in orbit must radiate energy. Hence Bohr’s account of the behaviour of the atom was inconsistent. Yet, patently, not everything concerning the behavior of electrons was inferred from it. Hence, whatever inference mechanism it was that underlay it, this must have been paraconsistent.

    So, by this view, a contradiction cannot be true.

    -If the above quoted is true, then your conclusion is false.

    ReplyDelete

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