User:Peter Damian/Law of excluded middle draft

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Sources.

Principle of bivalence

 * Cicero, Acad. pri., ii "Fundamentum dialecticae est, quidquid enuntietur (id autem appellant axioma) aut verum esse aut falsum"; De fato 21 "Itaque contendit omnes nervos Chrysippus ut persuadeat omne axioma aut verum esse aut falsum"
 * Aristotle: "In the case of that which is or which has taken place, propositions, whether positive or negative, must be true or false. " (De Interpretatione 9).
 * According to Boethius (Commentary on the Perihermenias) the Stoics criticised Aristotle for denying the principle (Meiser p.208) "Putaverunt autem quidam, quorum Stoici quoque sunt, Aristotelem dicere in futuro contingentes nec veras esse nec falsas. Quod enim dixit nihil se magis ad esse habere quam ad non esse, hoc putaverunt tamquam nihil eas interesset falsas an veras putari. Neque veras enim neque falsas esse arbitrati sunt. Sed falso. Non enim hoc Aristoteles dicit, quod utraeque nec verae nec falsae sunt sed quod una quidem ipsarum quaelibet aut vera aut falsa est, non tamen quemadmodum in praeteritis definite nec quemadmodum in praesentibus sed enuntiativarum vocum duplicem quodammodo esse naturam, quarum quaedam essent non modo in quibus verum et falsum inveniretur sed in quibus una etiam esset definite vera, falsa altera definite, in aliis vero una quidem vera, altera falsa sed indefinite et commutabiliter et hoc per suam naturam, non ad nostram ignorantiam atque notitiam. "
 * Leibniz Nouv. Ess. iv 2 ~1 calls the Principle of Contradiction, that "A proposition is either true or false but not both", which contains two assertions: (1) that that a proposition can’t be both true and false at once (the Principle of Contradiction; (2) that it can’t happen that a proposition is neither true nor false (principle of bivalence)

Law of Excluded Middle

 * Aristotle:
 * 'it is necessary in every case either to affirm or to deny' ''Metaphysics B 2 (996b26-30)
 * 'it is not possible that there should be anything between the two parts of a contradiction, but it is necessary either to affirm or deny one thing of any other thing' Ibid G 7 (1011b 26-7)
 * "in the case of a pair of contradictories, either when the subject is universal and the propositions are of a universal character, or when it is individual, as has been said,' one of the two must be true and the other false" (De Interpretatione 9, see also chapter 7).
 * Wolff "Inter contradictoria non dari medium; propositionum contradictoriarum altera necessario vera" (Log. ~532) ,
 * Baumgarten: "omne possibile aut est A aut non A" (Metaphysics 10)
 * Hegel "Everything is essentially different; or as it is also expressed, - Of two contradictory attributes only the one belongs to anything and there is no third" (Log. ~41)

Future contingents

 * In Defence of the Thin Red Line: A Case for Ockhamism