Article ID: CBB305574148

Internal Negation and the Principles of Non-Contradiction and of Excluded Middle in Aristotle (2020)

unapi

It has long been recognized that negation in Aristotle’s term logic differs syntactically from negation in classical logic: modern external negation attaches to propositions fully formed, whereas Aristotelian internal negation forms propositions from sentential constituents. Still, modern external negation is used to render Aristotelian internal negation, as may be seen in formalizations of Aristotle’s semantic principles of non-contradiction and of excluded middle. These principles govern the distribution of truth values among pairs of contradictory propositions, and Aristotelian contradictories always consist of an affirmation and a denial. So how should we formalize a false denial? In the literature, we find that a false denial is formalized by means of two negation signs attached to a one-place predicate. However, it can be shown that this rendering leads to an incorrect picture of Aristotle’s principles. In this paper, I propose a solution to this technical problem by devising a formal notation especially for Aristotelian propositions in which internal negation is differentiated from external negation. I will also analyze both principles, each of which has two logically equivalent forms, a positive and a negative one. The fact that Aristotle’s principles are distinct and complementary is reflected in my new formalizations.

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Authors & Contributors
Loner, David
Tarantino, Piero
Wood, Rega
Tuominen, Miira
Rochberg, Francesca
Rijk, Lambertus Marie de
Concepts
Philosophy
Logic
Epistemology
Mathematics
Ethics
Arab/Islamic world, civilization and culture
Time Periods
Ancient
Medieval
20th century
6th century
Places
Greece
Rome (Italy)
Middle and Near East
Byzantium
United States
Mesopotamia
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