Modus Ponens - Grade: A PDF

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Modus Ponens...

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Modus Ponens Modus ponens is widely considered to be a valid and simple form of argumentation, which proves “If P then Q.” If we determine that the first premise (P) is true and the conclusion of the “If P then Q” statement is also true, then by the rule of modus ponens, the second premise (Q) can be inferred to be true as well. For example, consider the argument “If it is not raining tomorrow, then I will meet you at the park.” If it happens not to be raining tomorrow and the overall “If….then” statement is deemed to be true, then one could infer that I would meet them at the park. Although modus ponens is used universally and regarded as valid, the proof from which the validity is derived cannot be produced without originally considering modus ponens to be valid. Even though, modus ponens can only be verified in this manner, it shouldn’t be considered an invalid form of argument because many theorems in science rely on a similar logic. One of the attributes that makes modus ponens a valid method of argument is the fact that “If… then” is a truth functional connective. Truth functional connectives are words that connect two or more prepositions and the validity of the newly formed preposition depends solely on the validity of the individual prepositions. For this reason, modus ponens can be used to make valid arguments using truth tables. One can determine that modus ponens is a truth functional connective by starting with the assumption that “If P then Q” is true. From there premises (Q) can be negated to give a new statement “If P then ~Q (~ = not),” which must be false since the modus ponens statement a line above was true. If this statement is then negated the ending result is the inverse ~ (If P then ~ Q), which has the exact same truth value as our original statement “If P then Q”. This means the “~ (If P then ~ Q)” follows from “If P then Q.” If we then start with the statement “~ (If P then ~ Q)” we can see its meaning is logically equivalent to “If P then Q” because ~ (If P then ~ Q) says if true premises were plugged in for both P and Q the overall “If…

then” statement would also be true. So we find that “If P then Q” also follows from“~ (If P then ~ Q).” For these reasons the two statements are true in precisely the same situations. Constructing truth tables for the “If P then Q” and “~ (If P then ~ Q)” produce identical truth tables that can be seen on the final page (the last columns are the same). This occurrence shows that the validity of the overall statement combined by “If and then” is solely determined by the individual prepositions. To prove that modus ponens is a valid method of argumentation, we should use the “If P then Q” truth table. From modus ponens we know that the antecedent (P) and the “If P then Q” are both true. On the truth table the only instance of this is in the first row and therefore this is the only row that could be valid. The other three rows have one or both being false and therefore cannot be valid. In the first row, the consequent (Q) happens also to be true, making all three parts true and thus valid. For this reason Q can always be inferred to be true using modus ponens and shows that all modus ponens arguments are always valid. Modus ponens is a valid method of argumentation based on the truth tables, but can only be proved using the assumption that the “If….then” statement is valid first. Without this assumption we would be unable to validate modus ponens. For some people, this might cause people to have a harder time accepting that modus ponens is in fact valid, but many natural phenomenon and theorems in science and mathematics fields rely on similar logic. For these reasons, modus ponens shouldn’t be considered an invalid method.

If P then Q

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If P then Q

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~ (If P then ~ Q) P

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~Q

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~ (If P then ~ Q)

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