Philosophy

Front 1

Sentence Logic

Back 1

a type of logic where letters stand for simple sentences, which are then combined and altered in various ways to make other sentences.

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Connectives and Operatoes

Back 2

symbols used in sentence logic

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V

Back 3

or (inclusive)

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&

Back 4

and

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^

Back 5

and

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~

Back 6

not

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-->

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if, then

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=

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if and only if

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Modus Ponens

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mode that affirms by affirming
1) p --> q
2) p
_______
3) q

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Hypothetical Syllogism

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1) p --> q
2) q --> r
_______
3) p --> r

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Addition

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1) p
2) q
_______
3) p & q

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Modus Tollens

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mode that affirms by denying
1) p --> q
2) ~q
_______
3) ~p

Front 13

Disjunctive Elimination

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1) p V q
2) ~p
_______
3) q

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Constructive Dilemma

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1) p --> t
2) q --> t
3) q V p
_______
3) t

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Fallacy of affirming the consequent

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1) p --> q
2) q
_______
3) p

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p --> q
What is p?
What is q?

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p = sufficient condition, antecdent
q = necessary condition, consequent

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conditional

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any sentence of the form "if, then" is a conditional sentence

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contrapositive

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every conditional sentence has its contrapositive, which is just another way of writing it, and it has the same meaning and truth value

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truth value

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in classical logic every (indicative) sentence has one ot two truth values, true or false.

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reductio ad absurdum

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(reduction to the absurd)
an agrument in which p is disproven by assuming p to be true and then showing the absurd consequences that would follow

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7 Miscellaneous steps

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1) the order of the premises does not affect validity, though some are easier to underrstand than others
2)use any letters you like and as many as you need
3)the negation of a conditional, p --> q to ~(p --> q) ot (p --> q)
4)when analyzing agruments, may need to string togther two or more agruments
5) generalization can be expressed as conditionals: if c is an x then c is a y.
6)conditionals can be complex (q & r) --> (s V p)
7)tenses are not always neat, you may need to fudge

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proposition

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the meaning of an indicative sentence

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agrument

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a proposition, along with some reasons fro accepting that proposition

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premise

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a proposition expressing a reason, or part of a reason, for accepting some conclusion

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conclusion

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the propostitione for which reasons are offered

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valid

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an agruement is valid when, if its premises are true, its conclusion cannot be false. in a valid agrument, that conclusion follows those premises.

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sound

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an agruments is sound whne it is valid and has true premises

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5 tips for agruments analsis

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1)identify conclusion
2)identrify main reason for conclusion
3)identify any aupplementary reasons necessary for either making the agrument a decent one or representing the clear sense of the author
4)check to see if you have all and only the necessary premises
5)check the agrument for validity and for soundness

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philosophy

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cirtical thinking about fundamental questions

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foundational questions

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1) important - b/c it matters how we anwser
2) basic - cannot be readily anwsered by appealing to another discipline

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critical thinking

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1) logical
2) aware of presuppositions
3) willing to be streched, tested, and revise

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constructive dilemma

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the agruments splits, yet either direction taken results in the same conclusion

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interpretation of clarity

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attribute to them the best agrument that is consistent w/ faithfulness. in interpreting an agruemnts assume that they ar enot a fool.

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tautology

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true be definition