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To my knowledge truth preservation is a property of a valid deductive argument, but I can't really find a definition of it. I feel like mine is lacking, but here is my tentative definition:

"Truth preservation is a property of a valid deductive argument that ensures the truth in the premises is involved/transferred in/to the conclusion".

Thanks.

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    You are right; I would prefer the term "transferred to" in your definition.
    – Jo Wehler
    Commented Nov 6, 2015 at 20:35
  • @JoWehler, thanks. Is truth preservation merely a property present in deductive arguments?
    – seeker
    Commented Nov 6, 2015 at 20:36
  • I know the term only from expressions like "deductive arguments are truth preserving".
    – Jo Wehler
    Commented Nov 6, 2015 at 20:38

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Not quite. An argument is called truth preserving if it does not produce false conclusions given true premises. Valid, or logically valid, arguments are those where the conclusion is a logical consequence of the premises. There are different definitions of logical consequence that lead to different definitions of validity. In particular, on some definitions it is possible to have truth preserving arguments that are invalid because the notion of validity is restrictive.

For instance, the argument Gödel gave for the truth of his sentence is invalid, if logical consequence is defined as deductive provability, but it is truth preserving. Under the semantic notion of logical consequence valid arguments are exactly the truth preserving ones, but in complex theories there may be no effective way to find out if a given argument is semantically valid.

See logical truth and logical consequence.

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