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In ordinary language, logic is the reasoning used to reach a conclusion from a set of assumptions. More formally, logic is the study of inference—the process whereby new assertions are produced from already established ones. As such, of particular concern in logic is the structure of inference—the formal relations between the newly produced assertions and the previously established ones, where "formal" means that the relations are independent of the assertions themselves. Just as important is the investigation of validity of inference, including various possible definitions of validity and practical conditions for its determination. It is thus seen that logic plays an important role in epistemology in that it provides a mechanism for extension of knowledge.

As a byproduct, logic provides prescriptions for reasoning, that is, how people—as well as other intelligent beings, machines, and systems—ought to reason. However, such prescriptions are not essential to logic itself; rather, they are an application. How people actually reason is usually studied in other fields, including cognitive psychology.

Traditionally, logic is studied as a branch of philosophy. Since the mid- 1800s logic has been commonly studied in mathematics, and, even more recently, in computer science. As a science, logic investigates and classifies the structure of statements and arguments and devises schemata by which these are codified. The scope of logic can therefore be very large, including reasoning about probability and causality. Also studied in logic are the structure of fallacious arguments and paradoxes. The ancient Greeks divided dialecticSocial philosophy Broadly speaking, a dialectic is an exchange of propositions (theses) and counter-propositions (antitheses) resulting in a synthesis of the opposing assertions, or at least a qualitative transformation in the direction of the dialogue. into logic and rhetoricRhetoric (from Greek ρητωρ, rhetor "orator") is one of the three original liberal arts or trivium (the other members are dialectic and grammar). While it has meant many different things during its 2500-year history, it is generally d. Rhetoric, concerned with persuasive arguments, would currently be seen as contrasted with logic, in some sense; as is dialectic in most of its acquired meanings.

1 Scope of logic

As it has developed, many distinctions have been introduced into logic. These distinctions serve to help formalize different forms of logic as a science. Here are some of the more important distinctions.

1.1 Deductive and inductive reasoning

Originally, logic consisted only of deductive reasoningDeductive reasoning is the process of reaching a conclusion that is guaranteed to follow, if the evidence provided is true and the reasoning used to reach the conclusion is correct. The conclusion also must be based only on the evidence previously provide which concerns what follows universally from given premises. However it is important to note that inductive reasoning—the study of deriving a reliable generalization from observations—has sometimes been included in the study of logic. Correspondingly, we must distinguish between deductive validity and inductive validity. An inference is deductively valid if and only if there is no possible situation in which all the premises are true and the conclusion false. The notion of deductive validity can be rigorously stated for systems of formal logic in terms well-understood notions of semanticsIn general, semantics (from the Greek semantikos or "significant meaning," derived from sema sign) is the study of meaning, in some sense of that term. Semantics is often opposed to syntax, in which case the former pertains to what something means while t. Inductive validity on the other hand requires us to define reliable generalization of some set of observations. The task of providing this definition may be approached in various ways, some less formal than others; some of these definitions may use mathematical models of probability. For the most part our discussion of logic deals only with deductive logic.



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Topics: Logic, Scope Of Logic, Deductive And Inductive Reasoning...

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