SYMBOLIC LOGIC - California State University, Sacramento



SYMBOLIC LOGIC

SENTENTIAL LOGIC: VALID ARGUMENT FORMS

NOTE: ONLY VALID ARGUMENTS ARE DERIVABLE BY SUBSTITUTION FROM VALID ARGUMENT FORMS.

• To be valid, an argument must be derivable from at least one valid argument form.

• We can show all the following argument forms to be truth-table valid.

• This means that the form of each of the following argument forms is valid.

• This means that any argument we can derive by substitution of sentence letters for sentence variables in these argument forms is also valid.

MODUS PONENS MODUS TOLLENS

p כ q p כ q

p ~q

q ~p

premise 1 premise 2 conclusion premise 1 premise 2 conclusion

p q p כ q p q p כ q ~q ~p

T T T T T T F F

T F F T F F T F

F T T F T T F T

F F T F F T T T

HYPOTHETIC SYLLOGISM

p כ q

q כ r

p כ r

premise 1 premise 2 conclusion

p q r p כ q q כ r p כ r

T T T

T T F

T F T

T F F

F T T

F T F

F F T

F F F

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