The Philosophical Debate On Consistency
In classical logic Aristotle's three laws, namely, the excluded middle (p or ¬p), non-contradiction ¬ (p ∧ ¬p) and identity (p iff p), are regarded as the same, due to the inter-definition of the connectives. Moreover, traditionally contradictoriness (the presence of contradictions in a theory or in a body of knowledge) and triviality (the fact that such a theory entails all possible consequences) are assumed inseparable, granted that negation is available. These views may be philosophically challenged, precisely on the grounds that they fail to distinguish between contradictoriness and other forms of inconsistency.
On the other hand, it is possible to derive triviality from the 'conflict' between consistency and contradictions, once these notions have been properly distinguished. The very notions of consistency and inconsistency may be furthermore internalized at the object language level.
Read more about this topic: Paraconsistent Logic
Famous quotes containing the words debate and/or consistency:
“Like man and wife who nightly keep
Inconsequent debate in sleep
As they dream side by side.”
—Robert Graves (1895–1985)
“All religions have honored the beggar. For he proves that in a matter at the same time as prosaic and holy, banal and regenerative as the giving of alms, intellect and morality, consistency and principles are miserably inadequate.”
—Walter Benjamin (1892–1940)