hypothetical syllogism

The second Idea is based on the hypothetical syllogism.

This would appear to conform to what is known, in formal logic, as hypothetical syllogism.

The hypothetical syllogism rule may be written in sequent notation:

Schopenhauer said that all three Ideas (God, soul, and universe) might be derived from the hypothetical syllogism.

He wrote on the hypothetical syllogism and on the propositional calculus, which were both part of the Stoic logical tradition.

Each of these two principles is an instance of a valid argument form known as universal hypothetical syllogism in first-order predicate logic.

In classical logic, hypothetical syllogism is a valid argument form which is a syllogism having a conditional statement for one or both of its premises.

Hypothetical syllogism is closely related to modus ponens and sometimes thought of as "double modus ponens."

Hypothetical syllogism is one of the rules in classical logic that is not always accepted in certain systems of non-classical logic.

Avicenna's system of logic was responsible for the introduction of hypothetical syllogism, temporal modal logic and inductive logic.

Some examples of valid argument forms are modus ponens, modus tollens, disjunctive syllogism, hypothetical syllogism and dilemma.

Types of syllogism to which it applies include statistical syllogism, hypothetical syllogism, and categorical syllogism, all of which must have exactly three terms.

As is common with fallacious undistributed middle arguments, it can also be seen as the fallacy of affirming the consequent when restated as an equivalent hypothetical syllogism:

Thus Theophrastus invented five moods of syllogism in the first figure, in addition to the four invented by Aristotle, and stated with additional accuracy the rules of hypothetical syllogisms.

Hypothetical syllogism is closely related and similar to disjunctive syllogism, in that it is also type of syllogism, and also the name of a rule of inference.

In propositional logic, hypothetical syllogism is the name of a valid rule of inference (often abbreviated HS and sometimes also called the chain argument, chain rule, or the principle of transitivity of implication).

The assertorical speaks of logical reality or truth; as, for example, in a hypothetical syllogism, the antecedens presents itself in a problematical form in the major, in an assertorical form in the minor, and it shows that the proposition is in harmony with the laws of the understanding.

The earlier Megarian dialecticians - Diodorus Cronus and Philo - had done work in this field, and the pupils of Aristotle - Theophrastus and Eudemus - had investigated hypothetical syllogisms, but it was Chrysippus who developed these principles into a coherent system of propositional logic.