آيا اصل طرد شق ثالث يك شرط سلبي براي حقيقت است؟

Is the Law of Excluded Middle a negative condition for truth?

كانت منطق را به دو حوزه كلي منطق عمومي و منطق استعلايي تقسيم مي­كند. منطق عمومي نسبت به اعيان خنثي است و صرفا قواعد انسجام خود انديشه و از اين رو صرفا شرايط سلبي حقيقت را بيان مي­كند. اما آيا اصل طرد شق ثالث كه مي­گويد از بين يك گزاره و نفي آن يكي درست است يك شرط صرفا سلبي براي حقيقت است؟ در اين مقاله نشان مي­دهيم كه چنين نيست. در اين راستا هم به لحاظ تاريخي به برهان كانتور اشاره مي­كنيم و هم به تحليل ماهيت اين اصل با استفاده از پديده­شناسي استعلايي مي­پردازيم. با مقايسة ديدگاه­هاي مهم ارائه شده دربارة اين اصل يعني ديدگاه­هاي هوسرل، براوئر و هيتينگ، و همچنين از خلال تحليل قصدي ادات نفي از آن رو كه در اصل طرد شق ثالث فراخوانده مي­شود، نسبت اين اصل با منطق صوري را مورد بحث قرار مي­دهيم.

Kant divides logic into two main fields: general logic and transcendental logic. General logic abstracts altogether from objects; and it concerns only the rules of self-consistence of thoughts. Thus it contains merely the negative criteria of truth. On the other hand, Kant considers general logic in its Aristotelian formalization as finished and complete. This logic grants the law of excluded middle, which says for any proposition either it or its negation is true. But is such a law a merely negative condition for truth? In this paper we show that it is not. In this respect we mention historical issues raised by Cantor’s proof and more importantly discuss about the phenomenological nature of this law. We will show that the positive use of this law brings forth a challenge for the Kantian viewpoint. We explain the possible ways to confront this challenge. By means of a compression between the main views developed in regard to this law, namely those of Husserl, Brouwer and Heyting, we will explore the phenomenological status of this law. We will show that on the basis of Husserl's analyses in Formal and Transcendental Logic and in Experience and Judgment, about the nature of valid judgments and that of negation, the law of excluded middle is not generally valid.