Identifying Four Common Syllogisms

Euler diagram
An Euler diagram to illustrate the inclusivity and exclusivity of various political and geographical divisions within the British Isles

Week 4, Lecture 1

Learning Objectives

    1. Identify four common syllogisms
    2. Identify common informal fallacies

Here I offer the last section on philosophy’s methodology. In our previous lecture we identified the two categories of reasoning (deductive and inductive) and we discussed ways of evaluating the quality of arguments: are they valid, invalid, and do they have sound reasoning?

In this lecture I will present you some common valid argument forms and, more importantly, the common informal fallacies.

I will emphasize the informal fallacies because it is important for us to recognize these patterns of thinking so that we do not fall into these patterns of thinking ourselves.

Common valid deductive argument forms

Categorical syllogism: “A syllogism is an argument form that consists of two supporting premises and a conclusion. In a categorical syllogism, the premises and conclusion are all categorical statements—that is, statements about a category of things.”

Premise: All A (men) are B (mortal).
Premise: P is A (Paul is a man).
Conclusion: Therefore, P is B (Paul is mortal).

Modus Ponens: this phrase means “affirming the antecedent.” An antecedent is the first part of a hypothetical statement (so the words immediately following if). The second part of an hypothetical statement (the words immediately after then) is called the consequent.

Premise: If A (I have prepared thoroughly), then B (I will do well).
Premise: A is the case (I have prepared thoroughly).
Conclusion: Therefore, B (I will do well).

Modus Tollens: this phrase means “denying the consequence.” Like the modus ponens situation, we are dealing with an if/then proposition, but in this syllogism, the conditions of the consequent are denied in the second premise:

Premise: If A (Larry is a really good friend), then B (he will remember my birthday).
Premise: Not A (Larry didn’t remember my birthday)
Conclusion: Therefore, not A (Larry doesn’t really care about me)

Disjunctive syllogism: in this context disjunctive means presenting alternatives. With this kind of syllogism the second premise denies one of the alternatives and the conclusion affirms the remaining option.

Premise: Either A (I left my wallet in El Segundo) or B (I lost my wallet).
Premise: Not A (my wallet is not at that diner in El Segundo).
Conclusion: Therefore B (I lost my wallet).

Click here to continue the lecture and move on to informal fallacies.