What is deductive reasoning?

In logic and in math, reasoning from known quantities proceeds in two directions:  Deductive reason goes inward from the known to what can be assumed because it is in the same subset: “All X is Y, therefore X1 is Y” (All mammals have four limbs; therefore, veterans have four limbs.) This logic goes from the general to the specific.

Inductive reasoning goes outward from what is known to what can be speculated:  “Everyone who has ever walked in this door has been wearing a hat; therefore, the next person to walk in this door will be wearing a hat.” This logic goes from the specific to the general.

While from these examples it would appear that inductive reasoning is less reliable, it is the kind of reasoning that moves science forward.  “The last 1,000,000 objects fell at 32 ft. per second per second; therefore the next object will fall at 32 ft. per second per second.”  The uncertainty lies in the signifiers:  How are we defining “mammal”?  Does it include amputees?  And is the next object in the same gravitational field, or are we on the moon now?

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