Principle of explosion
From Logic
(Difference between revisions)
| Line 3: | Line 3: | ||
Here is the proof: | Here is the proof: | ||
| - | 1) P v ~P By assumption (the law of noncontradiction which is axiomatic) | + | 1) P v ~P By assumption (the law of noncontradiction which is axiomatic)<BR> |
| - | 2) P By (1) and conjunction elimination | + | 2) P By (1) and conjunction elimination<BR> |
| - | 3) P v A By (2) and disjunction introduction | + | 3) P v A By (2) and disjunction introduction<BR> |
| - | (4) ~P By (1) and conjunction elimination | + | (4) ~P By (1) and conjunction elimination<BR> |
(5) A By (3), (4), and disjunctive syllogism | (5) A By (3), (4), and disjunctive syllogism | ||
| - | + | <P> | |
Supporters of paraconsistent logic typically disagree with (3), holding that there are contradictory views (such as those found in quantum mechanics) that do not necessarily hold that contradictions must 'explode". | Supporters of paraconsistent logic typically disagree with (3), holding that there are contradictory views (such as those found in quantum mechanics) that do not necessarily hold that contradictions must 'explode". | ||
Current revision as of 02:06, 16 May 2009
The principle of explosion is the rule of classical logic that states that anything follows from a contradiction -
Here is the proof:
1) P v ~P By assumption (the law of noncontradiction which is axiomatic)
2) P By (1) and conjunction elimination
3) P v A By (2) and disjunction introduction
(4) ~P By (1) and conjunction elimination
(5) A By (3), (4), and disjunctive syllogism
Supporters of paraconsistent logic typically disagree with (3), holding that there are contradictory views (such as those found in quantum mechanics) that do not necessarily hold that contradictions must 'explode".
