Logic

A way of knowing that is highly reliable is logic, which is the foundation for mathematics. Among other things, logic presents rules for how to tell whether something is true or false, and it is extremely useful. However, logic in and of itself, with no reference to the real world, is not complete. It is logically correct to say, "All cows are brown. Bossy is not brown. Therefore Bossy is not a cow." The problem with the statement is the truth of the premise that all cows are brown, when many are not. To know that the proposition about cows is empirically wrong even if logically true requires reference to the real world outside the logical structure of the three sentences. To say, "All wood has carbon atoms. My computer chip has no carbon atoms. Therefore my computer chip is not made of wood" is both logically and empirically true.

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