propositions into account, like predicates and quantifiers. Extended logics accept the basic intuitions
behind classical logic and apply it to other fields, such as metaphysics, ethics, and epistemology. Deviant
logics, on the other hand, reject certain classical intuitions and provide alternative explanations of the
basic laws of logic.
The word "logic" originates from the Greek word logos, which has a variety of translations, such as
reason, discourse, or language.[4] Logic is traditionally defined as the study of the laws of thought or
correct reasoning,[5] and is usually understood in terms of inferences or arguments. Reasoning is the
activity of drawing inferences. Arguments are the outward expression of inferences.[6] An argument is a
set of premises together with a conclusion. Logic is interested in whether arguments are correct, i.e.
whether their premises support the conclusion.[7] These general characterizations apply to logic in the
widest sense, i.e., to both formal and informal logic since they are both concerned with assessing the
correctness of arguments.[8] Formal logic is the traditionally dominant field, and some logicians restrict
logic to formal logic.[9]
Formal logic is also known as symbolic logic and is widely used in mathematical logic. It uses a formal
approach to study reasoning: it replaces concrete expressions with abstract symbols to examine the
logical form of arguments independent of their concrete content. In this sense, it is topic-neutral since it is
only concerned with the abstract structure of arguments and not with their concrete content.[10]
Formal logic is interested in deductively valid arguments, for which the truth of their premises ensures
the truth of their conclusion. This means that it is impossible for the premises to be true and the
conclusion to be false.[11] For valid arguments, the logical structure of the premises and the conclusion
follows a pattern called a rule of inference.[12] For example, modus ponens is a rule of inference
according to which all arguments of the form "(1) p, (2) if p then q, (3) therefore q" are valid, independent
of what the terms p and q stand for.[13] In this sense, formal logic can be defined as the science of valid
inferences. An alternative definition sees logic as the study of logical truths.[14] A proposition is logically
true if its truth depends only on the logical vocabulary used in it. This means that it is true in all possible
worlds and under all interpretations of its non-logical terms, like the claim "either it is raining, or it is
not".[15] These two definitions of formal logic are not identical, but they are closely related. For example,
if the inference from p to q is deductively valid then the claim "if p then q" is a logical truth.[16]
Formal logic uses formal languages to express and analyze arguments.[17] They normally have a very
limited vocabulary and exact syntactic rules. These rules specify how their symbols can be combined to
construct sentences, so-called well-formed formulas.[18] This simplicity and exactness of formal logic
make it capable of formulating precise rules of inference. They determine whether a given argument is
valid.[19] Because of the reliance on formal language, natural language arguments cannot be studied
directly. Instead, they need to be translated into formal language before their validity can be assessed.[20]
The term "logic" can also be used in a slightly different sense as a countable noun. In this sense, a logic is
a logical formal system. Distinct logics differ from each other concerning the rules of inference they
accept as valid and the formal languages used to express them.[21] Starting in the late 19th century, many
Definition
Formal logic