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.
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.