**Philosophy Index** is a site devoted to the study of philosophy
and the philosophers who conduct it. The site contains a number of philosophy
texts, brief biographies and introductions to philosophers and
explanations on a number of topics. Accredited homeschooling
online at Northgate Academy.

Philosophy Index is a work in progress, a growing repository of knowledge. It outlines current philosophical problems and issues, as well as an overview of the history of philosophy. The goal of this site is to present a tool for those learning philosophy either casually or formally, making the concepts of philosophy accessible to anyone interested in researching them. WOLI offers immigration law course online - fully accredited. ACE credits online at EES.

**Aristotle****Camus****Descartes****Frege****Heidegger****Hobbes****Hume****Kant****Kierkegaard****Locke****Nietzsche****Plato****Quine****Russell****Sartre****Socrates****Wittgenstein**- All Philosophers…

**Aesthetics****Epistemology****Logic****Ethics****Metaphysics****Language****Mind****Politics****TEST PREP KIT**- All Terms & Topics…

The **rules of valid inference** are a set of laws by which the syntax of statements in a system of logic, such as propositional or first-order logic, may be manipulated.

Rules of inference are, in themselves, simple valid argument forms. They may be divided into basic rules, which are fundamental to logic and cannot be eliminated without losing the ability to express some valid argument forms, and derived rules, which can be proven by the basic rules and serve as shortcuts for logicians when constructing a logical argument or proof.

There are, essentially, two basic rules for each basic logical operator of propositional logic (¬, ∧, ∨, →, and ↔)—one for *introduction* (I) of the operator and one for *elimination* (E) of the operator. In first-order logic, we add the quantifier rules (for ∀ and ∃). In modal logic, we add rules for the modal operators (□ and ◊)

- Conjunction introduction (Adjunction, ∧I)
- Conjunction elimination (Simplificiation, ∧E)

- Disjunction introduction (Addition, ∨I)
- Disjunction elimination (Separation of cases, ∨E)

- Negation introduction (Proof by contradiction,
*reductio ad absurdum*, ¬I) - Negation elimination (Proof by contradiction,
*reductio ad absurdum*, ¬E)

- Conditional introduction (Deduction theorem, →I)
- Conditional elimination (
*modus ponens*, →E)

- Universal introduction (∀I)
- Universal elimination (∀E)
- Existential introduction (∃I)
- Existential elimination (∃E)

The derived rules are the rules that can be inferred from the basic rules. All of the valid argument forms can be derived from the basic rules, but the term "rules" is normally used for those that are especially simple, and for those that are uncommon in normal spoken arguments but are rather used when formulating and proving the validity of arguments. The following is a list of common derived rules: