To be and not to be: an introduction to dialetheism

Is there such a thing as a true contradiction? The view that there is, dubbed ‘dialetheism’ by Graham Priest and Richard Routley, is increasingly finding itself a topic of much philosophical discussion. Indeed, whilst most people – and most philosophers, for that matter – instinctively recoil at such a seemingly outlandish idea, the position has, as Priest suggests, “been gaining, if not acceptance, the respect of other parties in the debate”.

The orthodox belief that something cannot be both true and false can be traced back millennia but finds its first real defence in Aristotle, who named the law ‘the principle of non-contradiction’ (or PNC) and went as far as to brand it “the most certain of all principles”. Yet, despite his confidence, it’s not clear that it is in fact so certain; whilst most philosophers since have been happy to give Aristotle the last word on the issue, his defence of the PNC isn’t all that convincing. And whilst some may think that the principle is not in need of defence any more than mathematical truths (e.g., 2+2=4), there seem to be a variety of cases in which this intuition is tested. The following example, for instance, has become central to the debate in recent years but was actually first advanced by Eubulides almost two and a half thousand years ago:

The liar’s paradox: “This sentence is false”. Is it?

According to classical logic (and the PNC) there are two viable answers: yes, or no – true, or false. Yet, if the sentence is true, then it is false – and if it is false, then it is true. It could be neither true nor false, but the example can always be adapted to make room for this possibility:

The liar’s paradox reformulated: “This sentence is either false or neither true nor false”. Now what?

Essentially, we’re back to the start. The new version of the paradox leaves us with two possibilities; the sentence is either false or neither true nor false. Either way, the proposition is not true, but then – as in the original case – it must be. This gets a bit confusing, but the fact of the matter is that one cannot escape the paradox that easily.

So why not accept dialetheism? It may seem strange, but why not allow the odd sentence to be both true and false? Well, if dialetheism is true, then classical logic goes out the window; within the classical framework, if you can prove a contradiction then you can prove absolutely anything – which is obviously undesirable. What’s more, if we can have true contradictions (dialetheia) in cases like the liar’s paradox, then why should we not expect to find them out in ‘the real world’? Whilst this seems highly implausible, there are in fact cases of ‘real world’ dialetheia that are often touted. Transition states, for instance, are frequently discussed with reference to dialetheism. When I leave my house, there must be a time (t) before which I am inside and after which I am outside. But where am I at exactly t? Inside or outside? Perhaps I’m both.

Such an approach to transition states may provide a solution to another of Eubulides’s paradoxes:

The Sorites paradox: I have a heap of sand. It seems that the removal of one grain will not result in the heap no longer qualifying as such. But if this is the case, then the removal of a single grain should never make a difference to the sand’s status as a heap, even when I only have one or two or three grains left. Is this right?

Some philosophers have suggested that, whilst one end of the spectrum clearly constitutes a heap, and the other doesn’t, the middle states can be thought of as both heaps and not heaps. This might seem pretty ridiculous, but perhaps it’s the only non-arbitrary resolution. Certainly, assigning a fixed quantity which qualifies something as a heap is not going to work – our common understanding of a heap of sand requires hundreds of thousands of grains but we wouldn’t, for example, wish to say the same of a heap of rocks. Dialetheism may account for the in-between states as our piles grow.

The problem with these cases is as follows: even if we are to accept dialetheism, how do we know which sentences are both true and false? How do we spot dialetheia? Priest argues that this isn’t an issue; as always, we should simply accept that for which we have good evidence. Whilst we have a serious indication that the liar’s paradox is dialethic in nature, we don’t have any reason to believe that the Earth is both spherical and flat – in fact, we know the latter to be false (and only false!).

The issue however is that, if accepted, dialetheism may become too tempting a solution to seemingly intractable problems: “I can’t figure out if this is true or false… eh… it’s probably both!”. Allowing for dialetheia, is it the case that everything that seems contradictory is actually contradictory (and acceptably so)? Is the whole notion of a paradox therefore misplaced? And can we even conceive of contradictions anyway? Or perceive them in the ‘outside world’? All of these questions remain, and work is being done in order to formulate a consistent – or perhaps perfectly inconsistent – doctrine of dialetheism.



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