Deductive reasoning, also called Deductive logic, is reasoning which constructs or evaluates deductive arguments. Deductive arguments are attempts to show that a conclusion necessarily follows from a set of premises. A deductive argument is valid if the conclusion does follow necessarily from the premises, i.e., if the conclusion must be true provided that the premises are true. A deductive argument is sound if its premises are true. Deductive arguments are valid or invalid, sound or unsound, but are never true or false.
An example of a deductive argument:
The first premise states that all objects classified as 'men' have the attribute 'mortal'. The second premise states that 'Socrates' is classified as a man- a member of the set 'men'. The conclusion states that 'Socrates' must be mortal because he inherits this attribute from his classification as a man. Deductive reasoning is sometimes contrasted with inductive reasoning.
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Deductive arguments are generally evaluated in terms of their validity and soundness. An argument is valid if it is impossible both for its premises to be true and its conclusion to be false. An argument can be valid even though the premises are false.
This is an example of a valid argument. The first premise is false, yet the conclusion is still valid.
This argument is valid but not sound. For a deductive argument to be considered sound the argument must not only be valid, but the premises must be true as well.
A theory of deductive reasoning known as categorical or term logic was developed by Aristotle, but was superseded by propositional (sentential) logic and predicate logic.
Deductive reasoning can be contrasted with inductive reasoning. In cases of inductive reasoning, it is possible for the conclusion to be false even though the premises are true.
Philosopher David Hume presented grounds to doubt deduction by questioning induction. Hume's problem of induction starts by suggesting that the use of even the simplest forms of induction simply cannot be justified by inductive reasoning itself. Moreover, induction cannot be justified by deduction either. Therefore, induction cannot be justified rationally. Consequentially, if induction is not yet justified, then deduction seems to be left to rationally justify itself - an objectionable conclusion to Hume.
Hume did not provide a strictly rational solution per se. He simply explained that we cannot help but induce, but that it is lucky that we do so. Certainly we must appeal to first principles of some kind, including laws of thought.
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