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Informal proofs with identity
All of the arguments we will deal with will either be valid or invalid.
Accordingly, we
need to develop methods of demonstrating
logical consequence
(the fact that a given
conclusion follows necessarily from a given set of premises) and
logical
nonconsequence
(the fact that a given conclusion does not follow necessarily from a
given set of premises).
Remember, if the conclusion of an argument
does
follow
necessarily from its premises, then the argument is valid; if the conclusion
does not
follow necessarily from the premises, then the argument is invalid.
While demonstrating that an argument is invalid requires finding a circumstance in which
the premises are true and the conclusion false (i.e., a
counterexample
), how might we
demonstrate that an argument is valid?
Proofs
In formal logic, a proof is a stepbystep demonstration that a given conclusion does
indeed follow necessarily from a given set of premises.
Proofs allow us to use
intermediate steps that establish connections among the premises that will be helpful in
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This note was uploaded on 02/10/2011 for the course PHIL 110 taught by Professor ? during the Spring '06 term at South Carolina.
 Spring '06
 ?

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