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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