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multiple minor edits, some presentational edits, and some objective additions.
A '''deduction''' in [[formal logic]] is a way of proving a proposition. It is used most often in geometry, but also has its place in philosophy and law. It is often unused in science as it requires that one have certainty of truth of both the major and minor premises--something science is unwilling to make claims about.
A '''deduction''' in [[formal logic]] is a way of proving a proposition. Specifically, when a conclusion is inferred from premises or facts, it is said to "follow" (''like the water downstream to the spring source''), from previously stated propositions via certain logical rules.
Deduction is used most often in geometry, but also has its place in philosophy and law. Deduction is often un-used in science, as deduction requires that one have certainty of truth of both the major and minor premises--something science is unwilling to make claims about.
The most famous rule goes as follows:
The normal contrast to deduction is [[induction]], whereby the two are posed as distinct opposites. However, they are not so distinct as to be alien to each other. Rather, induction and deduction have a single common root from which they necessarily are operationally distinguished: the mind. So, in regard to formal logic in this root sense, a merely mechanical or electronic simulator of genuine mental operations does not possess either any actual deductive or actual inductive logic.
The most famous formal deductive rule goes as follows:
#A is true.
#A is true.
F implies T, True
F implies T, True
The final two are rooted in the fact that the consequent following from an antecedent that is not true says nothing about the truth or falsity of the statement, it must be assumed to be true.
The final two are rooted in the fact that the consequent following from an antecedent that is not true says nothing about the truth or falsity of the statement, it must be ''assumed'' to be true.
Aristotle codified the rules of syllogistic deduction two millenia ago in [[Ancient Greece]]. He created 256 forms of syllogisms relating to groups of things. For example, an AAA1 syllogism:
Aristotle codified the rules of syllogistic deduction two millenia ago in [[Ancient Greece]]. He created 256 forms of syllogisms relating to groups of things. For example, an AAA1 syllogism: