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(Valid) Inferences

This category contains articles with valid logical inferences, in particular from propositional logic.

1. (Material) Conditionals

Modus ponens Modus tollens
Premise 1 A → B
(If A, then B)
A → B
(If A, then B)
Premise 2 A ⌐B (not B)
Conclusion B ⌐A (not A)
Type Conditional Conditional

There are also more specific forms that are derived from these two moduses, for example:

2. Conjunctions and Disjunctions

Modus ponendo tollens Modus tollendo ponens
Premise 1 ⌐(A ∧ B)
(not both, A and B)
A ∨ B
(A or [incl.] B)
Premise 2 A B ⌐A (not A) ⌐B (not B)
Conclusion ⌐B (not B) ⌐A (not A) B A
Type Conjunction Disjunction

3. Syllogisms

Syllogisms are forms of logical inferences that infer a new proposition from two premises containing a total of three terms. There are 24 valid syllogisms which can be grouped into four categories by their basic forms:

In addition, the Sorites (polysyllogism) can also be seen as a more general form of the Modus Barbara.

About this site

Ad Hominem Info is a project to explain and categorize the most common systematic fallacies and fallacies. On this page, you will find a background article that briefly explains an important logical concept, which may be needed to better understand another article in this area.
For more information, please see the main category „logic

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