Sound, Valid, True: Difference between revisions
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{{trope}} |
{{trope}} |
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== "Sound," "Valid" and "True" == |
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In logic, "sound", "valid", and "true" ''are not synonymous''. The premises and conclusion can be "true" or "false"; the chain of reasoning itself can be "valid" or "invalid"; the argument as a whole is either "sound" or "unsound". |
In logic, "sound", "valid", and "true" ''are not synonymous''. The premises and conclusion can be "true" or "false"; the chain of reasoning itself can be "valid" or "invalid"; the argument as a whole is either "sound" or "unsound". |
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A perfect (deductive) argument. It is true and valid, and therefore sound. In other words, the argument must be based on accurate information and not contain any errors in logic. |
A perfect (deductive) argument. It is true and valid, and therefore sound. In other words, the argument must be based on accurate information and not contain any errors in logic. |
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== Strength and Cogency: Inductive logic == |
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Of course, the above only refers to deductive logic. When it comes to induction, things get a bit more dicey. (Literally.) |
Of course, the above only refers to deductive logic. When it comes to induction, things get a bit more dicey. (Literally.) |
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Therefore, Brahim is Muslim. }} |
Therefore, Brahim is Muslim. }} |
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This is what is called a ''strong'' inductive argument: more likely to be true than false. It's invalid: we only know that Brahim is Moroccan<ref>And male -- from his name -- but let's ignore that</ref> |
This is what is called a ''strong'' inductive argument: more likely to be true than false. It's invalid: we only know that Brahim is Moroccan.<ref>And male -- from his name -- but let's ignore that</ref> Brahim could be one of the 1.1% of Moroccans who are Christian, or one of the 0.2% of Moroccans who are Jewish. Nevertheless, it is highly likely, given no data about Brahim other than that he is Moroccan, that Brahim is in fact Muslim. If Brahim is in fact Muslim, then the argument becomes ''cogent'': not only strong, but true. |
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Theoretically, the dividing line between strong and weak inductive arguments is at 50%: at anything above 50%, the argument is strong. This can be a bit counterintuitive: |
Theoretically, the dividing line between strong and weak inductive arguments is at 50%: at anything above 50%, the argument is strong. This can be a bit counterintuitive: |
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