Conjunction { Philosophy Index }

Philosophy Index

Philosophy Index

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.

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Conjunction

Conjunction is a truth-functional operator in logic which is equivalent to the word “and”.

If P is known and Q is known, we may say P and Q, or formally:

P ∧ Q

This may be read as “P and Q” or “it is the case that both P and Q”.

In symbolic logic, the conjunction symbol ( ∧ ) is used to symbolize a conjunction. The ampersand ( & ) or the word AND, and in some cases, a dot ( · ), are used in some logical systems. For consistency, this site will always use the ∧ symbol.

Truth values

The following table illustrates the possible truth values of P ∧ Q, given each possible valuation of its terms, P and Q. Note that P ∧ Q is true if, and only if, P is true, and Q is true.

P Q P ∧ Q
T T T
T F F
F T F
F F F

English conjunctions

The conjunction is normally associated with the English word “and”. However, many other words function as conjunctions in English. For instance, the following words and phrases may also take the form of a conjunction:

Some of these phrases may seem to lose some information when translated into symbolic logic. For instance, the phrase “John isn't a lawyer, but he is a paralegal” may be symbolized as ¬L & P, if L means “John is a lawyer” and P means “John is a paralegal”. The choice of the English word “but” is meant to show contrast between the two propositions, rather than simply say that both are the case.