Dialetheism

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Dialetheism

Are you a dialetheist? - take the survey

Survey of attitudes to dialetheism

There are more things in heaven and earth, Horatio, Than are dreamt of in your philosophy. - Hamlet, William Shakespeare'

A dialetheia is a sentence p that is both true and has it's negation ~p true.

or

∃ p s.t. p ⋀ ~p

Alternatively:

T ⋂ F ≠ ∅     [where T = {all true sentences} and F = {all false sentences}]

What it is all about

What's Interesting about dialetheism - some perspective

It's a reasonable question; 'Why would anybody be interested in dialetheism?'

As usual, with matters philosophical and fairly common with matters logical, there are quite a few possible reasons. Here are mine:

  • It's amazing, and to me fascinating, that Aristotle's view has remained, pretty well unchallenged, for well over 2000 years.
  • The implications for understanding truth are huge - getting closer to an answer to Pontius Pilate's famous question: 'What is truth?'.
  • It appeals to the radical in me, because it is radical, getting down to the radix, or root, that feeds logic and thus maths, physics and much of the physical world.
  • It is liberating. I've found my mind far more open to alternatives, even if they're not dialetheas, than before. It helped me to gain a new excitement in reality to see, after all this time, a new way of looking.
  • It makes such intuitive sense. Despite us having been taught that accepting a dialethea is the route to madness in logic, we do, in fact, often accept them in day-to-day life.
  • There's a new world to be explored - in the Platonic world we've not before glimpsed this new world, hidden as it was behind the iron gate of the law of non-contradiction.... more an invisibility cloaking device concealing the fact it was even blocking a world.
  • It is also encouraging because it is so hated by mathematicians and doubted by philosophers - in a quite visceral way. Understandable because it rips away what's been seen as a foundational hook into understanding the universe. This shows its power.
  • It's interesting, too, how attacks on it have been so feeble, to date, anyway. Usually what are presented as attacks are, in fact attacks on straw men, not dialetheism itself. This reveals how radical it is, though it is extremely simple, it is also very difficult for some people to understand, even trained logicians and mathematicians grapple to grok just what it means. The profound simplicity is its complexity.
  • The dichotomy has helped Western civilization develop. No doubt about that. It's also hindered its development. It's time that we grew up and understood that the dialectic is only one possible framework. The world is not just divided into binary opposites. A contradiction might reveal more options, rather than closing the discussion.
  • It shows that Gödel's incompleteness theorems are not alone in demonstrating how peculiar the platonic realms actually are. It was surprising, 'shocking' is more the word, to find that systems as rich as Arithmetic, inevitably, cannot be complete and consistent. There are statements that are true, but not provable within the system. Now we know that a similarly startling fact applies to the very much simpler world of logic.
  • Most of all, though, beyond all the above, what excites me is the thought of how many other fascinating worlds are hidden behind similar assumptions, just waiting for the mind brave enough to think the previous unthinkable and ignore orthodoxy.

Plato's Sunglasses

title=The world is Black & White! I can see it. Either P or ~P - never both
If you are stuck in Plato's cave and can only see through glasses blackened by the 'law' of the excluded middle
- then you can never see the world revealed by dialethism.