Logic (from the Ancient Greek: λογική, translit. logikḗ), is the systematic study of the form of valid inference, and the most general laws of truth. A valid inference is one where there is a specific relation of logical support between the assumptions of the inference and its conclusion. In ordinary discourse, inferences may be signified by words such as therefore, hence, ergo, and so on.
There is no universal agreement as to the exact scope and subject matter of logic (see § Rival conceptions, below), but it has traditionally included the classification of arguments, the systematic exposition of the 'logical form' common to all valid arguments, the study of proof and inference, including paradoxes and fallacies, and the study of syntax and semantics. Historically, logic has been studied in philosophy (since ancient times) and mathematics (since the mid-19th century), and recently logic has been studied in computer science, linguistics, psychology, and other fields.
In the formal languages
used in mathematical logic
and computer science
, a well-formed formula
or simply formula
(often abbreviated wff
, pronounced "wiff" or "wuff") is an idea
which is expressed using the symbols
and formation rules
(also called the formal grammar
) of a particular formal language. To say that a string
is a wff with respect to a given formal grammar
is equivalent to saying that
belongs to the language generated by
. A formal language can be identified with the set of its wffs.
Bertrand Arthur William Russell, 3rd Earl Russell OM FRS
(18 May 1872 – 2 February 1970), was a British philosopher
and advocate for social reform.
A prolific writer, he was also a populariser of philosophy and a commentator on a large variety of topics, ranging from very serious issues to those much less so. Continuing a family tradition in political affairs, he was a prominent anti-war activist, championing free trade between nations and anti-imperialism.