Logic is the
formal science of using
reason and is considered a branch of both
philosophy and
mathematics and to a lesser extent
computer science. Logic investigates and classifies the structure of statements and arguments, both through the study of
formal systems of inference and the study of arguments in
natural language. The scope of logic can therefore be very large, ranging from core topics such as the study of
fallacies and
paradoxes, to specialized analyses of reasoning such as
probability, correct reasoning, and arguments involving
causality. One of the aims of logic is to identify the correct (or
valid) and incorrect (or
fallacious)
inferences. Logicians study the criteria for the evaluation of
arguments.
Fallacy (
list) – incorrect argumentation in reasoning resulting in a misconception or presumption. By accident or design, fallacies may exploit emotional triggers in the listener or interlocutor (appeal to emotion), or take advantage of social relationships between people (e.g. argument from authority). Fallacious arguments are often structured using rhetorical patterns that obscure any logical argument. Fallacies can be used to win arguments regardless of the merits. There are dozens of types of fallacies.
Formal logic
Formal logic – Mathematical logic, symbolic logic and formal logic are largely, if not completely synonymous. The essential feature of this field is the use of
formal languages to express the ideas whose logical validity is being studied.
Computability theory – branch of mathematical logic that originated in the 1930s with the study of computable functions and
Turing degrees. The field has grown to include the study of generalized computability and definability. The basic questions addressed by recursion theory are "What does it mean for a function from the natural numbers to themselves to be computable?" and "How can noncomputable functions be classified into a hierarchy based on their level of noncomputability?". The answers to these questions have led to a rich theory that is still being actively researched.