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== Deduction and Induction ==

== Deduction and Induction ==

Deductive logic is characterized by certainty: in a valid argument, when the premises are true, the conclusion '''must''' be true.  Inductive logic is famously less certain; in a good inductive argument, even when the premises are true, it is still possible for the conclusion to be false.  [[David Hume]]'s 18th-century critique of induction remains a very pressing problem for disciplines like [[science]] which rely on inductive reasoning.

Deductive logic is characterized by certainty: in a valid argument, when the premises are true, the conclusion '''must''' be true. The certainty, however, comes at a price.  Take a classic argument of deductive logic:

 

 

The conclusion is "contained" in the premises.  In a sense the conclusion is "known" before it is elucidated.  The conclusion, "Socrates is mortal" is also less informative than the premises which imply not just that Socrates is mortal but that a lot of other beings (anyone for whom the term "is a man" applies) are also mortal.  As a result deductive logic is not thought to add to knowledge, merely to clarify it.

 

Inductive logic is ampliative, but is famously less certain.  In a good inductive argument, even when the premises are true, it is still possible for the conclusion to be false.  A classic example of an inductive argument is:

 

 

Before the discovery of Australia the premise was true someone following inductive logic would have reached the conclusion.  Given the existence of black swans in Australia, however, that conclusion is false.  [[David Hume]]'s 18th-century critique of induction remains a very pressing problem for disciplines like [[science]] which are commonly held to rely on inductive reasoning.

== Uses of logic in other disciplines ==

== Uses of logic in other disciplines ==