Logic

[Insert Header]

[Insert Picture]

1. WHAT IS LOGIC?

????

Logic is the systematic study of the form of valid inference, and the most general laws of truth. A valid inference is one where there is a specific relation of logical support between the assumptions of the inference and its conclusion. In ordinary discourse, inferences may be signified by words such as therefore, thus, hence, ergo, and so on.

There is no universal agreement as to the exact scope and subject matter of logic (see § Rival conceptions, below), but it has traditionally included the classification of arguments, the systematic exposition of the ‘logical form’ common to all valid arguments, the study of proof and inference, including paradoxes and fallacies, and the study of syntax and semantics. Historically, logic has been studied in philosophy (since ancient times) and mathematics (since the mid-19th century), and recently logic has been studied in cognitive science (encompasses computer science, linguistics, philosophy and psychology).

The concept of logical form is central to logic. The validity of an argument is determined by its logical form, not by its content. Traditional Aristotelian syllogistic logic and modern symbolic logic are examples of formal logic.

  • Informal logic is the study of natural language arguments. The study of fallacies is an important branch of informal logic. Since much informal argument is not strictly speaking deductive, on some conceptions of logic, informal logic is not logic at all. See § Rival conceptions below.
  • Formal logic is the study of inference with purely formal content. An inference possesses a purely formal content if it can be expressed as a particular application of a wholly abstract rule, that is, a rule that is not about any particular thing or property. The works of Aristotle contain the earliest known formal study of logic. Modern formal logic follows and expands on Aristotle. In many definitions of logic, logical inference and inference with purely formal content are the same. This does not render the notion of informal logic vacuous, because no formal logic captures all of the nuances of natural language.
  • Symbolic logic is the study of symbolic abstractions that capture the formal features of logical inference. Symbolic logic is often divided into two main branches: propositional logic and predicate logic.
  • Mathematical logic is an extension of symbolic logic into other areas, in particular to the study of model theory, proof theory, set theory, and computability theory.

2. WHAT IS THE ESSENTIAL DIALECTIC OF LOGIC?

The Essential Dialectic of Logic is:

{Noncontradiction-Identity ⇆ Identity-Noncontradiction ⇅ Noncontradiction-Noncontradiction} ↻ Identity-Identity

3. WHAT IS THE COMPLETE DIALECTIC OF LOGIC?

The Complete Dialectic of Logic is:

{Identity ⇆ Noncontradiction ⇅ Excluded-Middle} ↻ Sufficient-Reason

????

4. WHAT IS THE EQUIVALENT DIALECTIC OF LOGIC?

The Equivalent Dialectic of Logic is:

{Mathematics ⇆ Logic ⇅ Ontotheology} ↻ Reality

????