Note: This supplementary page is for enrichment/informational purposes. It provides a few examples of deductive argument forms. Some will receive focus in upcoming course content.

Categorical Syllogisms make claims about groups of things or categories.  We will study categorical syllogisms in depth in Module 3.  An example:

All cats are mammals.
All leopards are cats.
/∴ All leopards are mammals.

Disjunctive Syllogisms have a disjunctive (either-or) proposition as a premise.  An example:

Felix is either a dog or a cat.
Felix is not a dog.
/∴Felix is a cat.

Hypothetical Syllogisms have at least one premise that is a conditional (i.e. hypothetical) “if-then” statement. We will look in depth at conditional statements in Unit 4. For now, keep in mind that:

  • The ‘if’ part of the statement (the precipitating factor) is known as the “antecedent.”
  • The ‘then’ part of the statement (the resulting factor) is known as the “consequent.”

In a pure hypothetical (conditional) syllogism, all propositions, including the conclusion, are hypothetical propositions.  An example:

If it rains tonight, then the game will be canceled.
If the game is canceled, then we’ll go to the movies.
/∴If it rains tonight, then we’ll go to the movies.

Any argument in this pure hypothetical syllogism form is valid:

If A, then B.
If B, then C.
/∴If A, then C.

Modus Ponens is a type of hypothetical (conditional) syllogism.  One premise is a conditional (if-then) proposition, and another premise affirms that the antecedent of the hypothetical premise is, in fact, the case. The conclusion then claims the truth of the consequent.  An example:

If Socrates is a man, then Socrates is mortal.
Socrates is a man.
/∴Socrates is mortal.

Any argument in this modus ponens form is a valid argument:

If A then C.
A.______
/∴C

Modus Tollens is a type of hypothetical (conditional) syllogism, One premise is a conditional (if-then) proposition. The other premise denies (indicates untruth of) the consequent of the hypothetical premise. The conclusion then claims that the antecedent is not the case (that is, denies it.)  An example:

If Socrates is immortal, then Socrates cannot die.
Socrates died.
/∴Socrates is not immortal.

Any argument in this modus tollens form is a valid argument:

if A then C.
not C.____
/∴ not A

Arguments based on Mathematics do not have a precise “form” but they guarantee conclusions with certainty. Here’s a simple example of a math-based argument:

Thirty-seven runners started the race.
Thirty runners have finished.
/∴ Seven runners remain unaccounted for.