Deductive reasoning is the mental process of drawing deductive
inference
Inferences are steps in reasoning, moving from premises to logical consequences; etymologically, the word '' infer'' means to "carry forward". Inference is theoretically traditionally divided into deduction and induction, a distinction that in ...
s. An inference is deductively
valid
Validity or Valid may refer to:
Science/mathematics/statistics:
* Validity (logic), a property of a logical argument
* Scientific:
** Internal validity, the validity of causal inferences within scientific studies, usually based on experiments
** ...
if its conclusion follows logically from its
premises, i.e. if it is impossible for the premises to be true and the conclusion to be false. For example, the inference from the premises "all men are mortal" and "Socrates is a man" to the conclusion "Socrates is mortal" is deductively valid. An argument is ''
sound'' if it is ''valid'' and all its premises are true. Some theorists define deduction in terms of the intentions of the author: they have to intend for the premises to offer deductive support to the conclusion. With the help of this modification, it is possible to distinguish valid from invalid deductive reasoning: it is invalid if the author's belief about the deductive support is false, but even invalid deductive reasoning is a form of deductive reasoning.
Psychology is interested in deductive reasoning as a psychological process, i.e. how people ''actually'' draw inferences.
Logic, on the other hand, focuses on the deductive relation of
logical consequence
Logical consequence (also entailment) is a fundamental concept in logic, which describes the relationship between statements that hold true when one statement logically ''follows from'' one or more statements. A valid logical argument is on ...
between the premises and the conclusion or how people ''should'' draw inferences. There are different ways of conceptualizing this relation. According to the
semantic
Semantics (from grc, σημαντικός ''sēmantikós'', "significant") is the study of reference, meaning, or truth. The term can be used to refer to subfields of several distinct disciplines, including philosophy, linguistics and comput ...
approach, an argument is deductively valid if and only if there is no possible
interpretation
Interpretation may refer to:
Culture
* Aesthetic interpretation, an explanation of the meaning of a work of art
* Allegorical interpretation, an approach that assumes a text should not be interpreted literally
* Dramatic Interpretation, an event ...
of this argument where its pr