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Jane asked:
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What does philosophy of contradiction mean?
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What does dialetheism mean?
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============
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Dialetheism is the view that there are true contradictions. Dialetheism opposes the so-called Law of
Non-Contradiction: for any A, it is impossible for both A and A to be true — which has been nearly
universally accepted since the time of Aristotle — though some, Hegel for one, have doubted it. The
view is perhaps most associated with Graham Priest.
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A logic is paraconsistent if it is not "explosive". An inference relation is explosive if a contradiction
entails everything (for all A, if A and not-A then B, for any B). It is paraconsistent if and only if it is
non-explosive — as Priest points out the Dialetheist will be believe that deductively valid inference is
paraconsistent but the paraconsistent logician need not believe in dialetheia (that is, true
contradictions). Also, the dialetheist need not believe that all contradictions are true (the view that all
contradictions are true is called trivialism).
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Why should anyone believe that there can be true contradictions? Well, the main argument for
dialetheism begins from the paradoxes of self-reference — viz. the liar paradox and Russell's
paradox. In turn, the liar paradox asks us to account for the sentence 'this sentence is not-true' and
Russell's paradox concerns the set of all sets that is not a member of itself. The paradoxical nature of
both is clear. In the liar paradox, if the sentence is true, then its false. But if its false, then its true. So
its both either way! In Russell's paradox, the basic question is is the set of all sets a member of itself?
It must be otherwise it cant be the set of all sets, but how can a set {a} be a member of itself? Though
many have argued that the paradoxes of self-reference are open to solution, the solutions themselves
do ask us to say very strange things about the nature of reference and set-theory — so maybe
Dialtheism can get us off the hook.
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Dialetheism is a technical topic and as such I wont expand much because to much will be left unsaid .
As such, all I can do is refer you to Priest's online synopsis of Dialetheism at
http://plato.stanford.edu/entries/dialetheism. Please be aware that you do need to have a good grasp
of logic when coming to read about Dialethism, as often much is taken for granted. If you have any
questions then feel free to email me.
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Rich Woodward
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