Deductive Reasoning

SYLLOGISMS, MODUS PONENS, AND MODUS TOLLENS

A Syllogism consist of three statements and two terms in each statement. The first statement is known as the major premise, which is more general, where as the second statement is the minor premise, which is more specific, and then the conclusion states the result with an original term of the first statement along with a different term from the second statement.

For example:

minor premise: All humans need food.
major premise: Greg is a human.
conclusion: Therefore, Greg needs food.

A modus ponen is very similar to a syllogism in a way that they both have three statements, each of which containing two terms, however, modus ponens contain all positive statements.
The rule for this is:

If p, then q.
p.
Therefore q.

An example of a modus ponen is:

If it rains, then I will wear a sweatshirt.
It rains.
Therefore, I will wear a sweatshirt.

Along with syllogisms and modus ponens, a modus tollen also has three statements with two terms each, however, all three statements are negative. The rule for this is:

If not p, then not q.
Not p.
Therefore, not q.

An example a modus tollen is:

If Myles is good at basketball, then he will play in the game.
Myles is not good at basketball.
Therefore, Myles will not play in the game.