# SYLLOGISMS

### "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 of the first premise of

*modus ponens*, 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 of the first premise of *modus ponens*, 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 a __more important__ syllogism for science is called "*modus tollens*" (Layman, 2005). *Modus tollens* takes the form:

__PREMISE__: If A then B.

__PREMISE__: 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__: We hypothesize that everyone who eats green M&Ms gets smarter.

__PREMISE__: I ate green M&Ms but I am NOT smarter.

__CONCLUSION__: Therefore, we REJECT the hypothesis that everyone 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).

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.