PAPER NO. 75
REASON AND ARGUMENT
- By reason is meant the laws of thought, or logic: identity: a is a; excluded middle: either a or non-a; non-contradiction: not both a and non-a (same time, same respect). These laws are natural laws.
- Reason is used as a test for meaning primarily and as a test for truth only secondarily. If a law of thought is violated, then there is no meaning. Wherever there is meaning, reason is being used.
- Reason is used to form concepts, judgments (propositions) and arguments (inferences).
- In a concept the mind grasps the essential nature of a thing. A concept is expressed by a word or term. A definition expresses the meaning of a word or the concept expressed in the word. The essence of a class of things is the set of qualities that all members and only members always have. Word, definition, meaning, concept and essence are closely related. In all of the above a is distinguished from non-a by reason (law of identity). Concepts are logically ordered from the most basic to less basic.
- In a simple judgment two concepts are joined by affirmation or separated by negation. In a compound judgment two propositions are joined by “or,” “if/then,” or “and.” Simple judgments are either true or false and are expressed by propositions.
The four forms of propositions differ by quantity (all/some) and quality (is/is not):
All S is P universal affirmative (A)
No S is P universal negative (E)
Some S is P particular affirmative (I)
Some S is not P particular negative (O)
These are related in the square of opposition (see the PDF Version).
Contradictions (A/O; E/I): differ in quantity and quality; both cannot be true; both cannot be false.
Contraries (A/E): may both be false; both cannot be true.
Subcontraries (I/O): may both be true; both cannot be false.
Subalterns (A/I; E/O): if the universal is true the particular is true, but not reversed.
The meaning of a proposition is made clear by analyzing its concepts and its form. To oppose a position the contradictory of the position must be established.
- The following apply to deductive arguments only:
An argument uses premises (reasons) to support a conclusion (the point being proven).
An argument is valid if the premises logically support the conclusion.
An argument is sound if it is valid and the premises are true (needed for rational belief).
The following argument or syllogism forms are commonly used:
Categorical syllogism: two concepts related to a third are related to each other.
All S is M / All M is P / ∴All S is P (S and P being related to M can be related to each other)
Hypothetical syllogism: if a cause is present, so is the effect; if no effect, then no cause.
If P then Q / P / ∴Q and If P then Q / not Q / ∴not P (These are the only valid forms of this argument)
Disjunctive syllogism: either A or non-A / it is not A / ∴it must be non-A
Reductio ad absurdum: proof by showing that the contradiction leads to an absurdity.
All these argument forms rely on the laws of thought (reason) in order to infer valid conclusions.
- For any rationally held belief, reasons can be given in support of the belief (conclusion). The alternative to the use of reason ultimately is meaninglessness (spiritual death).
This paper was originally developed for an Introduction to Philosophy course.
