These words refer to the act of exact, objective thinking that deals with provable fact and abides by the rules of logic in tracing premises to conclusions. Reasoning is the most inclusive and informal of the words here, indicating any attempt to draw conclusions by the use of valid methods of thought while remaining impartial and admitting for consideration only unbiased data. Ratiocination is a more formal word for the same concept, but it may occasionally suggest a mind moving from one conclusion to another in a long, complex, even tortuous, process: a cogent and convincing piece of reasoning demonstrating the common origin of man; a process of ratiocination that led him to several unpleasant conclusions.

An inference is, much more specifically, the movement from premises to conclusion; consequently reasoning may be side to be the attempt to make valid inferences, and ratiocination the puzzling out of a chain of inferences. If deduction is used in reaching an inference, reasoning proceeds from general premises regarded as proved or true and reaches a particular, specific conclusion.

• All men are mortal; I am a man; therefore, I am mortal.

Induction is the opposite process in which reasoning collects all the particulars that relate to a problem and draws a general conclusion that explains their behaviour.

• Every man whom he knew of had died, sooner or later. Therefore, all men are mortal.

The laws of science, such as the law of gravity, are first inductions from particulars. Once these laws are considered valid, they become the basis for any amount of deductions provided that these are derived according to the rules of logic.