"Syllogisms" are useful building blocks for deductive arguments.
DEFINITION: A "Syllogism" is a deductive argument with two premises leading to a conclusion (McCall, 1952).
For example, a famous syllogism from Aristotle:
PREMISE: All men are mortal.
PREMISE: Socrates is a man.
CONCLUSION: Therefore, Socrates is mortal.
Even arguments that may seem simpler than syllogisms can often be expressed more clearly as syllogisms. Our example, "The sun always comes up in the morning. Therefore, the sun will come up tomorrow," actually skips one step in the reasoning. The full argument is a syllogism:
PREMISE: The sun always comes up in the morning.
PREMISE: Tomorrow there will be a morning.
CONCLUSION: Therefore, the sun will come up tomorrow.
Syllogisms can also involve somewhat more complex premises like conditional (if...then) statements. For example:
PREMISE: If I go to college, then it's likely that I will get a high-paying job.
PREMISE: I am going to college.
CONCLUSION: Therefore, it's likely that I will get a high-paying job.
Some syllogisms have specific names. The last syllogism about going to college is of a specific form called "modus ponens" (Layman, 2005). Modus ponens has the general form:
PREMISE: If A then B.
PREMISE: A is true.
CONCLUSION: Therefore, B is also true.
In the previous syllogism, "A" signifies "if I go to college" and "B" signifies "it's likely that I will get a high-paying job."
Clearly, modus ponens is useful for making predictions. For example, consider that A is some cause and B is some outcome. If we know that the cause is present, then we can successfully predict the outcome.
However, one problem for research scientists is that we often don't know if A is truly the cause of something or not! If we aren't sure if first premise of modus ponens is true, then modus ponens won't help us much.
(Or, to express the previous statements in the form of modus ponens:
PREMISE: If we aren't sure if the first premise of modus ponens is true, then modus ponens won't help us much.
PREMISE: Research scientists often aren't sure of the first premise of modus ponens.
CONCLUSION: Therefore, modus ponens won't help us much).
Arguably the most important syllogism for science is called "modus tollens" (Layman, 2005). Modus tollens takes the form:
PREMISE 1: If A then B.
PREMISE 2: B is NOT true.
CONCLUSION: Therefore, A is also NOT true.
Modus tollens is important because it allows us to soundly REJECT hypotheses (Popper, 1962). For example, if we hypothesize that green M&Ms make you smarter, we could conduct an experiment:
PREMISE 1: If P then C If any person eats green M&Ms, they will get smarter.
PREMISE 2: C is NOT true I ate green M&Ms but I am NOT smarter.
CONCLUSION: Conclude NOT P Therefore, we REJECT the hypothesis that any person who eats green M&Ms gets smarter
Modus tollens allows us to use data to reject hypotheses. If we can reject the hypothesis that green M&Ms make everyone who eats them smarter, then we've learned something. Perhaps green M&Ms have some other influence (or none at all).
Modus tollens is a fundamental syllogism for much scientific reasoning. In future sections, we will see how we can use Modus tollens to test both general, explanatory hypotheses and specific predictions.
Modus tollens can also be applied to non-scientific areas such as how we see our society. For example, consider the syllogism:
PREMISE 1: If P then C Everyone who works hard and plays by the rules will be financially rewarded.
PREMISE 2: C is NOT true Many people work hard and play by the rules but do NOT make a lot of money.
CONCLUSION: Conclude NOT P Working hard and playing by the rules is not sufficient for financial reward.
Although we would very much like for premise P to be true, and for hard work to always be rewarded, hard work and playing by the rules are not enough for many people to earn lots of money. Many other factors such as generational wealth, educational inequalities, structural and personal racism and sexism, regional opportunities, etc. clearly have an enormous impact on financial earnings.
Valid syllogisms are simple and modular. Simple and modular arguments can help us construct more complex arguments. Both modus ponens and modus tollens are valid syllogisms if expressed correctly. Therefore syllogisms such as modus ponens and modus tollens can help construct more complex arguments from simple, modular components.