Syllogisms/Modus Ponens/Modus Tollens

We learned in class today the differences between syllogisms, modus ponens, and modus tollens. All three are used in deductive logic.



SYLLOGISMS!

A syllogisms is the bringing together of two statements to arrive at a conclusion. Thus, there are a total of three statements involved in a syllogism. Of the two statements, one is a general statement, while the second is a specific factual statements that pertains to the gerneral statement. The general statements is the "major premise" and the specific factual statement is the "minor premise". The resulting assertion that brings these two premises together is called the "conclusion". Each of the premises has one term in common with the conclusion: in a major premise, it is the predicate, or major term, of the conclusion, and in a minor premise, it is the subject, or minor term, of the conclusion. It should follow these formulas: A=B, B=C, A=C. For example:



B = A
Major premise: All elephants are loud.

C = B
Minor premise: Lucy is an elephant.

C = A
Conclusion: Lucy is loud.



MODUS PONENS!

Modus Ponens is a form of deductive reasoning where "if p, then q" or "if not p, then not q" situations are involved. In a situation given that "if p, then q" is valid, and if the p is a positive premise, then q must also be a positive premise(if p, then q/p/therefore, q). Modus ponens can be used in the negative, as well, so that if p is a negative premise, then q is also a negative premise (if not p, then not q/not p/therefore, not q).

Ex. of "if p, then q"
p q
If it rains, then we will go to Toys R Us.
p: It is raining.
q: Therefore, we will go to Toys R Us.

Ex. of "if not p, then not q"
p q
If he won't clean his room, then he won't get his allowance.
p: He didn't clean his room.
q: Therefore, he won't get his allowance.


MODUS TOLLENS!

Modus Tollens is a form of deductive reasoning where if the statement "if p, then q" is valid, and q is a negative premise, then p must be a negative premise, as well. If there is "Not q", then therefore there is "Not p", such that if p, then q/not q/therefore, not p. So, if premise p is true, then premise q is also true. But given that premise q is false, premise p will be false.

p q
If she eats her vegetables, she will grow taller.
q: She has not grown taller.
p: Therefore, she did not eat her vegetables.