Dialetheism
From Logic
Dialetheism is the view that there are true contradictions, or dialetheia. More specifically, dialetheists believe that for some sentence or proposition P, both P and its negation, not-P are true. Dialetheism is not itself a formal logic, but to endorse dialetheism without accepting some version of paraconsistent logic is to accept everything at all, namely trivialism. Graham Priest, of the University of Melbourne and the CUNY Graduate Center, is dialetheism's most prominent contemporary champion. He defines Dialetheism as the view that there are true contradictions. (Reference: "Dialetheism, logical consequence and hierarchy" and Whittle, Bruno. "Dialetheism, logical consequence and hierarchy." Analysis Vol. 64 Issue 4 (2004): 318-326.)
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Motivations
The motivations for dialetheism might be split into several groups:
- Formal semantic concerns brought about by such puzzles as the Liar and Russell's paradoxes. From the premises of classical logic and naïve set theory one can derive outright contradictions, a result that is traditionally frowned upon. The classical response to this problem is to revise the axioms of set theory in order to make them consistent. Dialetheists respond to the problem by accepting the contradictions as true.
- It might be argued that our actual thinking is dialetheic. In other words, it is not completely prima facie implausible that we might affirm both a proposition and its negation. Freud noted that to the unconscious both a wish and its negation could exist, simultaneously. Freud pointed to our dreamlife as evidence - where contradictions freely roam.
- Graham Priest argues in Beyond the Limits of Thought that dialetheia arise at the borders of expressibility, in a number of philosophical contexts other than formal semantics.
Formal consequences
It is important to recognize the formal ramifications, to mathematics, of accepting a contradiction as sound. Using some commonly accepted and intuitively plausible rules of logic, we can easily show that the formula P & ¬P implies everything; taking a contradiction as a premise, we can prove any A.
1) P v ~P By assumption (the law of noncontradiction which is axiomatic)
2) P By (1) and conjunction elimination
3) P v A By (2) and disjunction introduction
(4) ~P By (1) and conjunction elimination
(5) A By (3), (4), and disjunctive syllogism
(This is often called the principle of explosion, since the truth of a contradiction makes the number of theorems in a system "explode".) Any system in which any formula is provable is trivial and uninformative; this is the motivation for solving the semantic paradoxes. Dialethesists solve this problem by rejecting the principle of explosion, and, along with it, at least one of the more basic principles that lead to it, e.g. disjunctive syllogism or transitivity of entailment, or disjunction introduction.
Advantages
The proponents of dialetheism mainly advocate its ability to avoid problems faced by other more orthodox resolutions as a consequence of their appeals to hierarchies. Graham Priest once wrote "the whole point of the dialetheic solution to the semantic paradoxes is to get rid of the distinction between object language and meta-language". <ref name="Dialetheism, logical consequence and hierarchy" />
Criticisms
One important criticism of dialetheism is that it fails to capture something crucial about negation and, consequently, disagreement. Imagine John's utterance of P. Sally's typical way of disagreeing with John is a consequent utterance of ¬P. Yet, if we accept dialetheism, Sally's so uttering does not prevent her from also accepting P; after all, P may be a dialetheia and therefore it and its negation are both true. The absoluteness of disagreement is lost. The dialetheist can respond by saying that disagreement can be displayed by uttering "¬P and, furthermore, P is not a dialetheia". Again, though, the dialetheist's own theory is his Achilles' heel: the most obvious codification of "P is not a dialetheia" is ¬(P & ¬P). But what if this itself is a dialetheia as well? One dialetheist response is to offer a distinction between assertion and rejection. This distinction might be cashed out in terms of the traditional distinction between logical qualities, or as a distinction between two illocutionary speech acts: assertion and rejection. Another criticism is that Dialetheism cannot describe logical consequences because of its inability to describe hierarchies.<ref name="Dialetheism, logical consequence and hierarchy" />
Works cited
- Frege, Gottlob. "Negation." Logical Investigations. Trans. P. Geach and R. H Stoothoff. New Haven, Conn.: Yale University Press, 1977. 31-53.
- Parsons, Terence. "Assertion, Denial, and the Liar Paradox." Journal of Philosophical Logic 13 (1984): 137-152.
- Parsons, Terence. "True Contradictions." Canadian Journal of Philosophy 20 (1990): 335-354.
- Priest, Graham. In Contradiction. Dordrecht: Martinus Nijhoff (1987).
- Priest, Graham. "What Is So Bad About Contradictions?" Journal of Philosophy 95 (1998): 410-426.
References
External links
- Graham Priest. Dialetheism. In the Stanford Encyclopedia of Philosophy, 2004.
