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Of the many and varied argument forms that can possibly be constructed, only very few are valid argument forms. In order to evaluate these forms, statements are put into logical form . Logical form replaces any sentences or ideas with letters to remove any bias from content and allow one to evaluate the argument without any bias due to its ...
categorical syllogism A form of deductive reasoning in Aristotelian logic consisting of three categorical propositions that involve three terms and deduce a conclusion from two premises. category In mathematics and logic, a collection of objects and morphisms between them that satisfies certain axioms, fundamental to category theory. category ...
The corresponding conditional of a valid argument is a logical truth and the negation of its corresponding conditional is a contradiction. The conclusion is a necessary consequence of its premises. An argument that is not valid is said to be "invalid". An example of a valid (and sound) argument is given by the following well-known syllogism:
The study of arguments using categorical statements (i.e., syllogisms) forms an important branch of deductive reasoning that began with the Ancient Greeks. The Ancient Greeks such as Aristotle identified four primary distinct types of categorical proposition and gave them standard forms (now often called A, E, I, and O).
A syllogism (Ancient Greek: συλλογισμός, syllogismos, 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true.
Types of syllogism to which it applies include statistical syllogism, hypothetical syllogism, and categorical syllogism, all of which must have exactly three terms. Because it applies to the argument's form, as opposed to the argument's content, it is classified as a formal fallacy.
For example, the argument, "All young girls wear skirts; Julie is a young girl; therefore, Julie wears skirts" is valid logically, but is not sound because the first premise isn't true. The syllogism is a form of deductive reasoning in which two statements reach a logical conclusion. With this reasoning, one statement could be "Every A is B ...
Categorical data analysis; Categorical distribution, a probability distribution; Categorical logic, a branch of category theory within mathematics with notable connections to theoretical computer science; Categorical syllogism, a kind of logical argument; Categorical proposition, a part of deductive reasoning; Categorization; Categorical perception