excluded middle


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excluded middle

n
(Logic) logic the principle that every proposition is either true or false, so that there is no third truth-value and no statements lack truth-value
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Among their topics are methodological triangulation in empirical philosophy (of mathematics), the beauty (?) of mathematical proofs, an empirical study on the admissibility of graphical inferences in mathematical proofs, new foundations for fuzzy set theory, what is not obvious about obvious: a data-driven approach to the philosophy of logic, and folk judgements about conditional excluded middle. (Ringgold, Inc., Portland, OR)
When reading their books, I became familiar with words and concepts like epistemology, ontology, a posteriori, Helenization, the law of noncontradiction, and the excluded middle.
There seems to be something missing with development in Africa, however, which I have linked to what Meyers calls the "excluded middle."
In classical dialectics, the excluded middle law is the third of the three classic laws of thought.
The people who clamor for the approval of the BBL in the name of peace commit the fallacy of the excluded middle. They think of the BBL as the only alternative to war, when there is another way to peace.
We also need Paul Hiebert-type critical realist approaches that are self-aware of Western "excluded middle" assumptions (that rule out spiritual realities within a middle tier between God and this worldly, scientifically observable phenomena).
But this statement breaks Aristotle's Law of the Excluded Middle, where "A and Not A" is a contradiction.
And the more conventional by complication the beginning of the demonstration by such axioms taken as principles, the less acceptable, by simplification, is the understanding that all the propositional tautologies emerge from the formula of the excluded middle, as all antilogies proliferate the violation of the principle of non-contradiction --we are thus hinting at the decisional method by normalizing prepositional phrases, according to which the truth of the statement of the form "([p.sub.1] [disjunction] [logical not][p.sub.1] [disjunction] ...) & ....
The classical logic is based on three axioms: the axiom of identity which states that "A is A"; the axiom of noncontradiction which states that "A is not non-A"; and the axiom of the excluded middle which states that no third term "T" exists which is simultaneously "A" and "non-A" (Nicolescu, 2005, p.
For instance, the quantum superposition principle is contrary to the Aristotelian law of the excluded middle, since one can superpose two states with opposite properties (e.g., spin directions).
Our setting is Bishop's constructive mathematics ([3], [4], [5], [6], [8] and [15]), mathematics developed with Constructive logic (or Intuitionistic logic) - logic without the Law of Excluded Middle P [disjunction][logical not]P.