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An argument is an attempt to justify (establish as true) one assertion (belief, statement, claim, proposition, "sentence," etc.), called the conclusion, on the basis of one or more others, called premise(s). Differently put: an argument is an attempt to convince someone of the truth of a conclusion on the basis of one or more premises (or 'reasons'). Or: in an argument we infer a conclusion from one or more premises (the inference consisting in this passing from the premises to the conclusion). It follows from this definition of 'argument' that any argument makes at least two assertions: the conclusion and at least one premise.
Suppose someone wonders whether it is true that Socrates was a mortal being. (For simplicity, let's say 'is a mortal being,' or simply 'is mortal.') We might try to convince that person (or perhaps ourselves) of the truth of that assertion by this argument (A1):
Socrates is a human being.
\ Socrates is mortal. ('\' and the line mean 'therefore.')
Deduction and induction are the two basic types of inference (argumentation, reasoning, attempts at justification, etc.) A deductive argument claims that its conclusion is necessitated by the premise(s); an inductive argument claims that its conclusion is made probable by the premise(s). Consider this argument (B): 'Whenever the sun shines, it is warm outside. The sun is shining; hence presumably it is warm outside.' Now contrast this argument with another one (C): 'When the sun is out, it is usually warm outside. The sun is shining; hence presumably it is warm outside.' The conclusion in both arguments (B and C) is 'It is warm outside.' However: In B the conclusion is necessitated by the premises, i.e., if the premises are true, then the conclusion must also be true (in the sense that asserting the premises while denying the conclusion would result in a contradiction). In C, by contrast, the conclusion is merely made probable by the premises: if the premises are true, then the conclusion is probably also true. Note that words like 'presumably' introducing the conclusion occur even in deductive arguments (to express the arguer's surprise or perhaps hesitation about the necessity); and words like 'must' similarly occur in the conclusion even of inductive arguments (to express the arguer's strong conviction, based on very high probability).
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