Is Axiomatic Deduction Knowledge? (Also, how the categorical syllogism works!)

Cogita!

To answer the question  the definitions of axiom, knowledge, deduction, and induction must first be understood.

According to the Oxford English Dictionary Online:

an axiom is “A statement or proposition which is regarded as being established, accepted, or self-evidently true;”

knowledge is defined as “True, justified belief; certain understanding, as opposed to opinion;”

deduction is “The inference of particular instances by reference to a general law or principle [an axiom];” and induction is ” The inference of a general law from particular instances.” 

In science the general rule for what is scientific knowledge is whether a theory is experimentally testable and falsifiable. However, not all knowledge is scientific, nor should it be. Under an experimental testability definition of (scientific) knowledge axiomatic deduction is not (scientific) knowledge, because axioms are not strictly testable.   However, under this confining definition of (scientific) knowledge, in which only inductive, experimentally testable things are knowledge, pure…

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