Deductive Reasoning and Aristotelian Logic
Deductive Reasoning
Deductive reasoning involves deriving specific conclusions from general principles. Aristotle, in his Posterior Analytics, explored both inductive and deductive reasoning but emphasized deduction for scientific knowledge. He believed that understanding causes is crucial, prioritizing the analysis of deductive reasoning, particularly the categorical syllogism.
Deductive reasoning aims to extract a particular truth from a universal one. Three main types exist:
- Categorical
- Hypothetical
- Disjunctive
Each type depends on the relationship used as a starting point.
| Type | Example |
|---|---|
| Categorical | All humans are mortal. People from Madrid are human. Therefore, people from Madrid are mortal. |
| Hypothetical | If you pass, you go on vacation. You passed. Therefore, you go on vacation. |
| Disjunctive | This path goes north or south. It goes north. Therefore, it does not go south. |
The Syllogism
A syllogism is a categorical deductive argument with three propositions (premises and conclusion) and three terms. The major premise is the most general statement. The minor premise is less general. The conclusion follows from the major premise via the minor premise.
The predicate of the conclusion (P) appears in the major premise. The subject of the conclusion (S) appears in the minor premise. The middle term (M) appears in both premises but not the conclusion.
Aristotelian Logic
Aristotelian logic posits a direct correspondence between thought and reality. The categories of the mind reflect objective categories of reality. This gives thought an ontological dimension. Traditional Aristotelian logic focuses on concepts, particularly predicates and categories, as well as judgments and reasoning forms, especially the categorical syllogism, as tools for scientific knowledge.
Concepts
A concept is the intellectual representation of an object, distinct from sensations, perceptions, or memories. Concepts have two key properties: comprehension (essential characteristics) and extension (the set of objects to which the concept applies).
Aristotle’s Categories and Topics outline ten fundamental categories, distinguishing between substance (what exists in itself) and accidents (what exists in another being, in substance).
Judgments
Relating two concepts forms a judgment. A judgment is affirmative if the relationship holds and negative if it doesn’t. The subject is what is affirmed or denied, and the predicate is what is affirmed or denied of the subject.
Aristotle distinguishes between the matter (the concepts) and the form (the relationship) of a judgment. He represents the subject as ‘S’ and the predicate as ‘P’. “John is tall” becomes “S is P,” and “John is not tall” becomes “S is not P.”
Judgments, like concepts, are mental acts expressed by propositions (grammatical sentences). Different propositions can express the same judgment, and the same proposition can represent different judgments depending on the context.