Soundness
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A logical argument is sound if and only if
A proof procedure (e.g. natural deduction) for a logic is sound if it proves only valid formulas (also tautologies). Formally: a system is sound when if "
", then also "
".
[edit] Sound arguments
Suppose we have a sound argument (in this case a syllogism):
- All men are mortal.
- Socrates is a man.
- Therefore, Socrates is mortal.
The argument is valid (because the conclusion is true based on the premises, that is, that the conclusion follows the premises) and since the premises are in fact true, the argument is sound.
The following argument is valid but not sound:
- All animals can fly.
- Pigs are animals.
- Therefore, pigs can fly.
Since the first premise is actually false, the argument, though valid, is not sound.
[edit] References
- Irving Copi. Symbolic Logic, Vol. 5, Macmillian Publishing Co., 1979.
- Boolos, Burgess, Jeffrey. Computability and Logic, Vol. 4, Cambridge, 2002.
- de:Korrektheit (Logik)
- is:Rétt röksemdafærsla
- uk:Правильність
| This page uses content from the English-language version of Wikipedia. The original article was at Soundness. The list of authors can be seen in the page history. As with Psychology Wiki, the text of Wikipedia is available under the GNU Free Documentation License. |
