What kinds of questions and topics are not decided by logical analysis?

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Because logic deals not with facts per se, but relationships among propositions, it cannot be used to analyze simple assertions. For example, if you state "the moon is made of green cheese", you cannot use logic to prove or disprove the assertion because it is a simple statement of a singular fact about some external reality. Similarly, you can use logic to analyze the syllogism:

All men are mortal.

Socrates is a man.

Therefore Socrates is mortal.

 Logic would be of no use in analyzing Socrates' probable natural lifespan. Instead, you would need to do a medical examination of Socrates or apply some form of statistical analysis.

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