Are there non-semantic dialetheia
Well, some may say, OK, I accept that 'This sentence is false' is a dialetheia, but that's just semantic, the real world doesn't have things that are both true and not true'.
It seems a reasonable point. There are a few problems with it:
- This is a question for logic itself, does logic apply in the 'real' world, or is it simply semantic playing with symbols? This is a philosophical question that's not just a consequence of dialetheism. - What does it mean for logic to apply to reality? How would you know?
There are some answers, maths depends on logic, physics depends on maths, and aerodynamics works, aeroplanes fly. So it follows that logic works in the real world. Well, up to a point, there's a lot going on in those steps and there could be simply luck or coincidence. The real world might be quite different, but in a way that still leaves it looking as if this is the case --- and so forth.
So it's a bit of a muddy area to begin with. It is, though, a good challenge. Is there evidence, in the way the world works, for there being any dialetheia?
Here are a few possibilities:
X has mass: Is X a wave? No. ~W(x) X diffracts: is X a wave? Yes. W(x) ∃x, x is real, W(X) ⋀ ~W(x). ∴ Wave/Particle duality is a #dialetheia
Relativity: Fred & Joe, twins. Fred & Joe same age? Yes, same birthday (p). Fred -> Mars & back -> Fred younger (~p) ∴ p ⋀~p #dialetheia
You can see an objection here, that this is just a matter of semantics. What we mean when we say 'A is older than B' is two different things, that usually coincide: 1. A was born before B and 2. A has been alive longer than B.
This means that all relativity reveals is that they don't always coincide. In the case of Fred and Joe, Fred is older than Joe in sense 1 but Fred is younger than Joe in sense 2. Which means it's not a dialetheia because there are two propositions P and Q, normally, if P then Q so for any person x, P(x),Q(x). However, in the case of relativistic travel you can have P(x).~Q(x).
So this doesn't work - but I think it's an instructive case. Maybe all apparent physical dialethiea are like this. If you look at the first example, wave/particle duality, that would seem not to be the case. The properties of a particle and the properties of a wave are, in most senses, incompatible with each other. So for something to be both is a real inconsistency.
Again, though, this can be argued to be a failing simply in our understanding. Now we know we were wrong, particles and waves are compatible, in fact real objects can all be described in terms of both. Well, yes, you certainly can say that, but, aren't you, in fact, acknowledging that this is a dialethiea in the real world? Once dialethiea are found, then they will, presumably, just like this, be incorporated into our understanding of the physical world.
But does that mean that they're not actually dialethiea any more? Well, it's an interesting question.
Euclidean and non-Euclidean geometry
Euclid: p: ∑ int. ∠ Δ=180° p ⊂ T Einstein: p: ∑ int. ∠ Δ≠180° p ⊂ F Euclid right? Yes Einstein right? Yes p ⊂ T ∩ F ∴ p ⋀~p #dialetheia
OK, you may argue that this is just semantics because maths is semantics, a set of tautologies, in fact. However, it is possible to measure triangles in the real world and find that some are Euclidean and some non-Euclicean.
So we revise geometry to suit and admit both.
Isn't that, though, precisely because this is a dialethiea in the real world that we've accommodated to?