Reason is the mental capacity humans have to draw conclusions based on observable evidence or based on the premises of an argument.
Philosophy is largely a study of human reason and some works, such as Immanuel Kant's [1724-1804] "Critique of Pure Reason" spend hundreds of pages examining the nature of human reason, its structure, and its limits.
Reasoning, the use of reason, can either be inductive or deductive.
Reason is, in my opinion, the highest ability
of human beings, and should be used a lot more.
Unfortunately, it seems to me, that if
we did all actually use reason, we would abolish, or at least alleviate, those great institutions
like war, religion, famine, suffering, and poverty.
Induction is reasoning from specific facts to general principlies and is the method by which empirical science proceeds. For example, scientists have consistently observed, through various experiments, that the speed of light is about 300,000 kilometers per second.
Therefore, using inductive reasoning, scientists have theorized that the speed of light is constant throughout all space and time. But, nothing can be proven with any certainty using induction because it is possible that the speed of light could be different at some time or place in the universe that has not been tested.
Because we can not currently test the speed of light billions of years in the past or future, induction is more a method of assumption than reasoning.
It should be noted that it can not be validly stated that "the speed of light is probably the same speed everywhere and for all time".
Rather, a more correct statement would be "the speed of light has been the same speed everywhere and at every time we have tested it and we assume this will be true for all places and times we test it, though we have no reason for this assumption.".
Deduction is reasoning from general principles to specific instances and is the method studied by logic. Deduction does not require observation because all of the information required to reason deductively is contained in the premises of a deductive argument.
The premises of an argument are the assumed first statements that can possibly lead to a valid conclusion. For example, the premise "All black cats are nice" and the premise "Pandora is a black cat" will lead to valid conclusion that "Pandora is a nice cat".
In chess, a player could usefully use both inductive and deductive reasoning. Inductively, one could reason that an opposing player will make similar opening moves and that she or he will have similar reactions to situations in the game that she or he experienced in the past.
But, it should be noted, this is only a useful assumption and, one that can be damaging if incorrect.
Deductive reasoning allows for the logical analysis of the pieces and their possible interactions. A player could assume the questionable premise, "All cornered kings are soon checkmated" and attempt to avoid the conclusion by not allowing her or his king to meet the condition of being cornered.
This is because if it is true that "All cornered kings are soon checkmated" and it is true that "My king is cornered" then it necessarily implies that "My king will soon be checkmated".