Soundness

From Wikipedia, the free encyclopedia

(Redirected from Unsound)
Jump to: navigation, search

A logical argument is sound if and only if

  1. the argument is valid
  2. all of its premises are true.

A proof procedure (e.g. natural deduction) of a logical system is sound if it proves only valid formulas (also tautologies). In notation, a logical system is sound if X_1,\ldots,X_n \vdash Y implies X_1,\ldots,X_n \models Y.

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.

  • Irving Copi. Symbolic Logic, Vol. 5, Macmillian Publishing Co., 1979.
  • Boolos, Burgess, Jeffrey. Computability and Logic, Vol. 4, Cambridge, 2002.
 Logic Portal
 This logic-related article is a stub. You can help Wikipedia by expanding it.
Retrieved from "http://en.wikipedia.org/wiki/Soundness"
Advanced Search
Included Web Search Engines


Safe Search

close

Top Matching Results

Occasionally Search.com will highlight specialized results that are based on the context of your query. Examples of specialized results include specific links to news, images, or video.

Top Matching Results may highlight information from other Search.com pages, content from the CNET Network of sites, or third party content. The listings are based purely on relevance. Search.com does not receive payment for listings in this section but our partners that provide this data may get paid for listing these products.

Sponsored Links

This section contains paid listings which have been purchased by companies that want to have their sites appear for specific search terms and related content. These listings are administered, sorted and maintained by a third party and are not endorsed by Search.com.

Search Results

Search.com sends your search query to several search engines at one time and integrates the results into one list which has been sorted by relevance using Search.com's proprietary algorithm. You can customize the list of search engines included in your metasearch from the preferences.

The search engines that are used in your metasearch may allow companies to pay to have their Web sites included within the results. To view the Paid Inclusion policy for a specific search engine, please visit their Web site. Search.com does not accept payment or share revenue with any search engine partner for listings in this section.