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Phil notes continued

21.

Symmetric If A bears the relation to B, then B must bear the same relation to A

Non-symmetric if A bears the relation to B, then B may or may not bear the same

relation to A

Asymmetric If A bears the relation to B, then B cannot bear the same relation to A

22.

Ree!i"e Anythin# ca$able of bearin# this relation to somethin# else must also

bear the relation to itself

Non-ree!i"e If a thin# can bear this relation to somethin# else, then it may ormay not bear the relation to itself

Irree!i"e No ob%ect could bear the relation to itself &e!. A is taller than A'

2(.

Proof A series of "alid inferences leadin# to a conclusion

)ormat

Inference Proof

1 If P then *2 Not *( P or R ++ So, R Not P 1,2 modus tollens R (, disjunctive syllogism

A!ioms Statements are acce$ted ithout any $roof because they are ob"iously

true

/heorems A form of $roof ere statements are deri"ed from a!ioms

2.

Reductio ad absurdum A ty$e of $roof hich shos a statement has some absurd

conse0uence hich in some conte!ts is somethin# e no to be false

- Also non as reductio

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Proof by contradiction Be#ins by assumin# the o$$osite of hat e ant to $ro"e,

and then shos that this assum$tion leads to a contradiction, a ay to use a

necessary falsehood.

2.onditional $roof