The third part of logic concerns the third act of the intellect, i.e., reasoning, the process of acquiring new knowledge from prior known truths expressed in true judgments. The ideal of reasoning is the categorical syllogism wherein the necessary truth of a universal conclusion is established, indeed caused, by the truth of more universal premises, arranged in valid figures. As we will see below, the goal of such categorical, i.e., demonstrative, syllogisms is what Thomas Aquinas understood to be scientia, or science. What follows is a very abbreviated presentation of Aristotle and Thomas’s logic of argumentation and reasoning, really just the highlights of what is a very complex and sophisticated system, especially as that system was developed and elaborated upon by logicians in the Middle Ages. Omitted here are the principles and rules of syllogism, the reduction of syllogisms to the perfect (first) figure, fallacies, and much more that can be found in a comprehensive introduction to traditional or Aristotelian logic, of which there are many fine published presentations
Categorical Syllogism
Aristotle discovered that one can make sound inferences from true statements based on the form in which they are expressed. Thus, by presupposing the truth of certain statements expressed in certain (what are known as valid) forms, one can infer (and be confident in knowing) the truth of other statements. The inference and the resultant knowledge are guaranteed by the form of language in which the ideas are expressed. The inference, however, depends on one having some prior (true) knowledge.
Aristotle called this way of expressing argumentation the syllogism, and every such syllogistic argument consists of three universal propositions of the sort we discussed above: A, E, I, and O. The two propositions that express what is already known are the premises, and they lead the mind to some new knowledge which the mind infers from them to draw the third proposition, the conclusion. Some further terminology:
- Major premise contains Predicate of the conclusion.
- Minor premise contains Subject of the conclusion
- The Middle term links Subject and Predicate
All M is P. All rational animals are able to laugh.
All S is M. All humans are rational animals.
.: All S is P Therefore, all humans are able to laugh.
A syllogism should represent an order of judgment that proceeds from the more universal knowledge expressed in the premises to the less universal, new knowledge expressed in the conclusion. A more complete presentation of Aristotelian-Thomistic logic would explore and explain the principles and rules of demonstrative syllogisms, and precisely how the middle term links the conclusion’s subject and predicate through the premises of valid syllogistic forms, but for the purposes of this Overview, let us merely list which Figures, and which Moods (quality (Affirmative/Negative) and quantity (Universal/Particular) (i.e., A, E, I, O) of their premises and conclusions) express valid inferences.
There are three valid Figures of syllogisms, differentiated according to whether the Middle term is in the premises as their subject or predicate. Thus,
I. II. III.
M is P P is M M is P
S is M S is M M is S
.: S is P .: S is P .: S is P
* For the reasons why there is no valid fourth figure, consult an introduction to traditional logic.
The Perfect Syllogism: The First Figure
In demonstrative arguments in the First Figure, one can most clearly see that the conclusion depends on the truth of the premises, and the fact that the subject term is related to the predicate term. The middle term provides the reason that the predicate is true of the subject. In the example above, rationality is the link between humans and the ability to laugh. That is, a person can laugh because she is rational. The Middle Term is the cause of the knowledge of conclusion for it states the reason or cause for the subject of the conclusion having the predicate it does.
The first figure is called the perfect figure, because in this disposition of terms, the middle term is middle in universality and has the middle position in the premises. As subject of the major premise and predicate of the minor premise, the middle term clearly stands between the major and minor extremes. In this figure, the position of the major extreme is the position of greatest universality and that of the minor the position of least universality. The first figure is thus the figure most evident to us.[1]
The Form of a syllogism refers to its Mood, the quality (Affirmative/Negative) and quantity (Universal/Particular) of its premises (A, E, I, O) and Figure. The following are an exhaustive list of the valid forms within each Figure as designated by the Latin mnemonic “words” medieval logicians devised for this purpose. The vowels of the mnemonic words specify the valid quantity/quality of the premises and conclusion (Mood) in each Figure.
Figure I – Barbara, Celarent, Darii, Ferio
M is P A – All M is P All rational things can laugh.
S is M A – All S is M All humans are rational.
.: S is P A – .: All S is P Therefore, all humans can laugh.
E – No M is P
A – All S is M
E – .: No S is P
A – All M is P
I – Some S is M
I – .: Some S is P
E – No M is P
I – Some S is M
O – .: Some S is not P
Figure II – Cesare, Camestres, Festino, Baroco
P is M E – No P is M
S is M A – All S is M
.: S is P E – .: No S is P
A – All P is M
E – No S is M
E – .: No S is P
E – No P is M
I – Some S is M
O – .: Some S is not P
A – All P is M
O – Some S is not M
O – .: Some S is not P
Figure III – Darapti, Felapton, Disamis, Datisi, Bocardo, Ferison
M is P A – All M is P
M is S A – All M is S
.: S is P I – .: Some S is P
E – No M is P
A – All M is S
O – .: Some S is not P
I – Some M is P
A – All M is S
I – .: Some S is P
A – All M is P
I – Some M is S
I – .: Some S is P
O – Some M is not P
A – All M is S
O – .: Some S is not P
E – No M is P
I – Some M is S
O – .: Some S is not P
Hypothetical Syllogisms
Sometimes categorical arguments can be expressed as hypothetical expressions in the form of if …, then …. For instance, if it is raining, then the ground is wet. This sort of logic expressed as the relationship between propositions is the basis of modern logic. These sorts of arguments symbolize whole propositions (not just subject, predicate, and middle terms) with the use of lowercase letters p, q, r, s, etc. Thus, “If p, then q.” Here, p represents the antecedent, and q, the consequent. There are certain valid forms of argument in propositional logic which were known to medieval logicians, that were treated as complex versions of categorical syllogisms, so it would be helpful to also be familiar with them.
Modus Ponens, or affirming the antecedent:
If p, then q. If it is raining, then the ground is wet.
p It is raining.
.: q. Therefore, the ground is wet.
Modus Tollens, or denying the consequent:
If p, then q. If it is raining, then the ground is wet.
Not q. The ground is not wet.
.: Not p. Therefore, it is not raining.
Dilemma, or process of elimination:
Either p or q. Either he has an alibi, or he committed the murder.
Not p. He does not have an alibi.
.:q Therefore, he committed the murder.
[1] John A. Oesterle, Logic: The Art of Defining and Reasoning (Prentice-Hall 1952), p. 120.
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Updated January 18, 2025
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