Modus Ponens
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In sentential logic (also known as propositional calculus or sentential
calculus) the representation of modus ponens is:
(P→Q)∧P→ Q
where
→ is the symbol for logical implication and
∧ is the symbol for logical conjunction.
Substituting words for the logical operators, this reads as:
if P implies Q and P, then Q
where P and Q are both sentences incorporating assertions. The predicates (including the conditional statement and the antecedent) and the consequent are frequently laid out line by line and enumerated.
1. P→Q
2. P
————
3. Q
Example.
Let P be the sentence 'If it is raining' and Q be the sentence 'There will be clouds overhead'. Then modus ponens will involve the two sentences in conjunction and the first sentence, as the predicates, with sentence Q as the consequent.
'If it is raining, there will be clouds overhead'
'It is raining'
—————————————————
'There will be clouds overhead'
P is called the sufficient condition, and Q the necessary condition. These assignations are based on the intuitive logical implications of each sentence. That it is raining is enough information, or a sufficient condition, to imply that there are clouds overhead. That there are clouds overhead is a necessary condition for it to be raining.
Editor(s): Long, B.
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