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Вынуждение как истинностная процедура

Вынуждение как истинностная процедура

Abstract

The main concern of the article is discovery of a method of forcing introduced by an American mathematician Paul Cohen as an effective technique in logic that has found wide application in the theory of proof, moreover, has strictly ontological consequences. The very possibility of its implementation indicates that the being is organized in such a way as to allow us to, provided a certain set of conditions being met, to “force” some nonsolvable propositions to become true. Although all truths are to be produced by a subject, at the same time they still belong to the world subject’s actions cannot “force” the truth of any proposition he wants, but only of those which are nonsolvable within the ontology in question. By making decision, unconditioned from the point of view of that world he lives in, and being irrationally confident in reality of the event, “faithful subject” is capable to change the world.

В статье обосновывается идея того, что метод форсинга, открытый американским математиком Полом Коэном, не только стал чрезвычайно эффективной логической техникой и широко применяется в теории доказательств, но имеет еще и сугубо онтологические следствия. Сама возможность его реализации указывает нам на такое устройство бытия, при котором мы при соблюдении ряда условий способны «заставить» некоторые неразрешимые утверждения стать истинными. Несмотря на то что все истины производятся Субъектом, они остаются при этом истинами мира — действия Субъекта «вынуждают к истине» именно неразрешимые в онтологии, а не любые суждения. Принимая ничем не мотивированное с точки зрения того мира, в котором он живет, решение и продолжая иррационально верить в то, что событие все же имело место, «верный субъект» тем самым изменяет мир.

Keywords

ТЕОРИЯ МНОЖЕСТВ, КОНТИНУУМ-ГИПОТЕЗА, ФОРСИНГ, АКСИОМАТИЧЕСКОЕ РЕШЕНИЕ, СУБЪЕКТ, СОБЫТИЕ

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    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
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    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Average
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average