Chapter 7: The Simple Syllogism
“The syllogism is the act of reasoning by which the mind perceives that from the relation of two propositions (called premises) having one term in common there necessarily emerges a new, third proposition (called the conclusion) in which the common term, called the middle term (M), does not appear.”
The syllogism itself is neither true nor false; it is valid or invalid.
In pages 132 and 133 there are rules of the syllogism and formal fallacies.
Enthymeme: is a syllogism logically abridged by the omission of one proposition, either the major premise, the minor premise, or the conclusion. In page 142 – 143, the author writes about the importance of this device. A sorites is a chain of enthymemes.
This chapter explains in greater detail the simple syllogism along with other forms derived from it. It explains the rules for using along with some examples.
The syllogism itself is neither true nor false; it is valid or invalid.
In pages 132 and 133 there are rules of the syllogism and formal fallacies.
Enthymeme: is a syllogism logically abridged by the omission of one proposition, either the major premise, the minor premise, or the conclusion. In page 142 – 143, the author writes about the importance of this device. A sorites is a chain of enthymemes.
This chapter explains in greater detail the simple syllogism along with other forms derived from it. It explains the rules for using along with some examples.
Chapter 8: Relations of Hypothetical and Disjunctive Propositions
Hypothetical Proposition: one that asserts the dependence of one proposition on another (if, unless, if not, provided that). The proposition which depends on the other is the consequent; the one on which it depends is the antecedent. It expresses a relation of propositions, a conditional relation of dependence and limitation.
Disjunctive Proposition: one that asserts that of two or more suppositions, one is true. It is an either…or proposition.
Both have special characteristics, in particular, truth or falsity, and quality. They also have all the relations that simple propositions have, and the rules governing these relations are practically the same.
The Hypothetical Syllogism: can be pure hypothetical syllogism or mixed hypothetical syllogism.
The Disjunctive Syllogism: the moods can be ponendo tollens, and tollendo ponens.
The Dilemma: is a syllogism which has for its minor premise a disjunctive proposition, for its major premise a compound hypothetical proposition, and for its conclusion either a simple or a disjunctive proposition. It has four moods: simple constructive, complex constructive, simple destructive, and complex destructive.
Disjunctive Proposition: one that asserts that of two or more suppositions, one is true. It is an either…or proposition.
Both have special characteristics, in particular, truth or falsity, and quality. They also have all the relations that simple propositions have, and the rules governing these relations are practically the same.
The Hypothetical Syllogism: can be pure hypothetical syllogism or mixed hypothetical syllogism.
The Disjunctive Syllogism: the moods can be ponendo tollens, and tollendo ponens.
The Dilemma: is a syllogism which has for its minor premise a disjunctive proposition, for its major premise a compound hypothetical proposition, and for its conclusion either a simple or a disjunctive proposition. It has four moods: simple constructive, complex constructive, simple destructive, and complex destructive.