Hypothetical Propositions

JUDGMENTS & PROPOSITIONS

The Hypothetical Propositions

The Supposition

is a mental structure that has the subject-copula-predicate form but is not asserted to represent a reality

it is a merely possible judgment after a supposition has been construed

in the mind, it may be judged to be true in a sense of

representing a fact or reality or to be false in the sense of not

corresponding to reality

The Hypothetical Proposition1. comprises two or more suppositions

dependent (conditioned) on each other in regard to their truth of falsity

2. through the unifying conjunctions (if, either-or, not-both-and), serving as a copula, the proposition expresses a judgment concerning the truth of one or all of these suppositions

3. the three kinds of hypotheticals are the; disjunctive, conjunctive, and conditional propositions

The Disjunctive Propositions

the disjunctive (either-or) proposition asserts the truth of an undetermined one (or of at least) of the two or more suppositions called alternatives

if none of the stated alternatives is true, the proposition is false


The expression of alternatives takes the form of; complete suppositions contracted form of

alternative subjects having the same predicate

of alternative predicates having the same subject

A special case of the contracted disjunctive is the divisive proposition, which states a logical division

Examples: Either this labor dispute

is settled by arbitration, or a strike is unavoidable.

Either the Republicans or the Democrats will win this election.

He must either register or forfeit the right to vote.

Simultaneous quantities are either lines, surfaces, or solids


The enumeration of alternatives; either all the

possible alternatives must be mentioned,

or all the possible alternatives except those which are definitely known to be non-actual

Examples: The strikers will

either win or lose or accept a compromise.

This man is either a communist or a fellow traveler with communists.


Exclusive or inexclusive alternatives they are exclusive

when only one is or can be true

they are inexclusive when at least one, possibly more than one is true they are called

improper disjunctives and are rarely used

Examples: Either some

fertilizer is applied, or no good crop can be obtained.

This student of high scholastic standing is either very talented or very diligent.


The purpose of a disjunctive proposition is to express two or more hypotheses (suppositions) within which the truth must lie.

Upon the evidence obtained through investigation, we substitute for the usual (proper) disjunctive proposition with exclusive alternatives a categorical statement of the true alternative

The Conjunctive Proposition

asserts that its two suppositions or alternatives cannot be or not true at the same time in the sense of representing simultaneous realities

if the two suppositions can be true at the same time, the proposition is false

the suppositions are commonly contracted into; one statement of two subjects having the

same predicate, or a statement of two predicates having the

same subject

The Conjunctive Proposition

Examples: He cannot be both a senator and a member of the

President’s Cabinet. Full moon and an eclipse of the sun cannot

simultaneously occur. He is not both a physician and a chiropractor. That a person habitually tell lies, and that he should

not thereby destroy confidence in his statements, is impossible.

False conjunctive: You cannot be deeply interested in worldly affairs

and strive to be a saint.

The Conditional Proposition

the conditional (if) proposition comprises two suppositions called the antecedent (condition, protasis) and the consequent (apodosis)

asserts that the truth of the antecedent implies the truth of the consequent

when the truth of the antecedent does not involve the truth of the consequent, the proposition is false

the mood of the verbs used in the contrary-to-fact conditional shows that the possibilities referred to are known to be unrealized


Examples: If the barometer falls, atmospheric pressure is

decreasing. If an immigrant is not a citizen, he is not entitled to

vote. If God is holy, He hates sin. If it does not rain, the game will be played.Contrary-to-fact conditional: If this earth were a paradise, all men would be happy.False conditional: If Plato is an Athenian, he is a philosopher.


since in a true conditional the truth of the antecedent involves the truth of the consequent, we conclude in the conditional syllogism from the known truth of the former to the truth of the latter

Example:If the barometer is falls, atmospheric pressure is decreasing.The barometer is falling.Therefore atmospheric pressure is decreasing.


Two types of antecedents or conditions:1. A dispensable (sine qua) antecedent is one of

several conditions from the truth of which the truth of the consequent can be inferred.

If he studies logic, he trains his mind. If he studies natural science, he trains his mind. If he studies mathematics, he trains his mind.

2. An indispensable (sine qua non) antecedent is the only condition from the truth of which the truth of the consequent can be inferred.

If this triangle is equilateral, it is equiangular.

Conversion of One Type to Another Type of Proposition

as a rule a given judgment is most naturally expressed in only one of the four forms of proposition: categorical, disjunctive, conjunctive, conditional

some judgments, however, may be stated equally well, or nearly as well, in all four types.

Example:Categorical: An equilateral triangle is equiangular.Disjunctive: A triangle is either equilateral, or else it is

not equiangular.Conjunctive: A triangle cannot be equilateral and not be

equiangular.Conditional: If a triangle is equilateral, it is equiangular.

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Hypothetical Propositions