2

In the usual propositional logic, proving a contradiction means that one can prove any other proposition; this on the face of it , and when one turns it over is quite strange - and there are modern paraconsistent logics that attempt to circumvent this.

Does Aristotelian logic, as Aristotle used it, suffer from the same problem?

3

There are few "propositional" laws used in Aristotle's logic.

One of the methods of proof used by A. in deriving figures form the basic ones is reductio (anagein) through the impossible (dia to adunaton), i.e. the principle of indirect proof.

An early use of Consequentia mirabilis has been found; see William Kneale, Aristotle and the Consequentia Mirabilis (1957), in the lost Protrepticus.

But it seems that an explicit use of Ex falso (sequitur) quodlibet is not present into his logical works.

Of course, the rejection of contradictions is the "firmest" principle of A.' logic and metaphysics.

An aristotelian locus that seemingly involves "explosion", but in the context of metaphysics and not logic, is Metaph, IV.4, 1007b19–on :

Again, if all contradictories are true of the same subject at the same time, evidently all things will be one. For the same thing will be a trireme, a wall, and a man, if it is equally possible to affirm and to deny anything of anything [...].


See Aristotle on Non-contradiction : Dialetheism and Paraconsistency for a proposed "paraconsistent" interpretation of some passages found in A.'s works.


According to Ernest Addison Moody, Truth and Consequence in Medieval Logic (1953), page 90, in Buridan, Consequentiae, (Book I, ch.8, rule 7) we have:

"Ad omnem copulativam ex duabus contradictoriis constitutam sequi quamlibet aliam, etiam consequentia formali"

that we can translate as :

p ∧ ¬ p ⊢ q

See Medieval Theories of Consequence for an overview:

Buridan's treatise on consequence and the treatises inspired by it, most notably Albert of Saxony's (a chapter of his Perutilis logica) and Marsilius of Inghen's treatise on consequence. There is also the interesting commentary on the Prior Analyics formerly attributed to Scotus which is thought to have been composed before or in any case independently of Buridan's treatise. [...] This tradition can be referred to as the Parisian/continental tradition on consequences.

  • Thanks for the response; it does beg the question how did the PNC come about in logic, the wiki article referenced doesn't say; also, The article on dialectism in A mentions that the sygollistic is reported as being paraconsistent in the prior analytics - though it doesn't say why, or in what sense. – Mozibur Ullah Jan 1 '16 at 14:19
  • There are passages I've noted too in A's metaphysics which curiously sounds he's using some kind non-traditional onto-logic. – Mozibur Ullah Jan 1 '16 at 14:22

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