Deduction is reasoning from premises to conclusions that are logically entailed by the premises. In other words, it is sound reasoning; if we are able to deduce a conclusion from a set of premises, it must be true whenever the premises are true.
All men are mortal. Socrates is a man. Therefore, Socrates is mortal.
It is noteworthy that there are patterns of reasoning that are sometimes useful but do not satisfy this strict criterion. There is inductive reasoning, abductive reasoning, reasoning by analogy, and so forth.
Induction is reasoning from the particular to the general. The example shown below illustrates this. If we see enough cases in which something is true and we never see a case in which it is false, we tend to conclude that it is always true.
I have seen 1000 black ravens. I have never seen a raven that is not black. Therefore, every raven is black.
Now try red Hondas.
Induction is the basis for Science. Deduction is the subject matter of Logic. Science aspires to discover new knowledge. Logic aspires to derive conclusions implied by things we know or assume to be true.
Abduction is reasoning from effects to possible causes. Many things can cause an observed result. We often tend to infer a cause even when our enumeration of possible causes is incomplete.
If there is no fuel, the car will not start. If there is no spark, the car will not start. There is spark. The car will not start. Therefore, there is no fuel.
What if the car is in a vacuum chamber?
Reasoning by analogy is reasoning in which we infer a conclusion based on similarity of two situations, as in the following example.
The flow in a pipe is proportional to its diameter. Wires are like pipes. Therefore, the current in a wire is proportional to diameter.
Now try price.
Of all types of reasoning, deduction is the only one that guarantees its conclusions in all cases, it produces only those conclusions that are logically entailed by one's premises.
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