Conjunction (AND) is one of the
basic operations of Boolean logic. It
can be electronically implemented in
several ways, for example, by using
two transistors.
sentence would be true or false. One of its central methodological
assumptions is the principle of compositionality. It states that the
meaning of a complex expression is determined by the meanings
of its parts and how they are combined. For example, the meaning
of the verb phrase "walk and sing" depends on the meanings of the
individual expressions "walk" and "sing". Many theories in formal
semantics rely on model theory. This means that they employ set
theory to construct a model and then interpret the meanings of
expression in relation to the elements in this model. For example,
the term "walk" may be interpreted as the set of all individuals in
the model that share the property of walking. Early influential
theorists in this field were Richard Montague and Barbara Partee,
who focused their analysis on the English language.[173]
The epistemology of logic studies how one knows that an
argument is valid or that a proposition is logically true.[174] This
includes questions like how to justify that modus ponens is a valid
rule of inference or that contradictions are false.[175] The
traditionally dominant view is that this form of logical
understanding belongs to knowledge a priori.[176] In this regard, it
is often argued that the mind has a special faculty to examine relations between pure ideas and that this
faculty is also responsible for apprehending logical truths.[177] A similar approach understands the rules
of logic in terms of linguistic conventions. On this view, the laws of logic are trivial since they are true by
definition: they just express the meanings of the logical vocabulary.[178]
Some theorists, like Hilary Putnam and Penelope Maddy, object to the view that logic is knowable a
priori. They hold instead that logical truths depend on the empirical world. This is usually combined with
the claim that the laws of logic express universal regularities found in the structural features of the world.
According to this view, they may be explored by studying general patterns of the fundamental sciences.
For example, it has been argued that certain insights of quantum mechanics refute the principle of
distributivity in classical logic, which states that the formula  is equivalent to
. This claim can be used as an empirical argument for the thesis that quantum logic
is the correct logical system and should replace classical logic.[179]
Logic was developed independently in several cultures during antiquity. One major early contributor was
Aristotle, who developed term logic in his Organon and Prior Analytics.[183] He was responsible for the
introduction of the hypothetical syllogism[184] and temporal modal logic.[185] Further innovations include
inductive logic[186] as well as the discussion of new logical concepts such as terms, predicables,
syllogisms, and propositions. Aristotelian logic was highly regarded in classical and medieval times, both
in Europe and the Middle East. It remained in wide use in the West until the early 19th century.[187] It has
now been superseded by later work, though many of its key insights are still present in modern systems of
logic.[188]
Epistemology of logic
History