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Logic
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Logic is the study of the principles of valid demonstration and inference. It is a branch of philosophy, a part of the classical trinity of grammar, logic, and rhetoric.
Logic concerns the structure of statements and arguments in formal systems of inference and natural language. Topics include:
- Validity
- Fallacies and Paradoxes
- Reasoning using probability
- Arguments involving causality
Logic is also commonly used today in argumentation theory.
Nature
Form is central to logic, complicating exposition that "formal" in "formal logic" is commonly used in an ambiguous manner.
- Informal Logic: study of natural language arguments
- Formal Logic: study of inference with purely formal content where that content is made explicit
- Symbolic Logic: study of symbolic abstractions that capture the formal features of logical inference
- Mathematical Logic: extension of symbolic logic into other areas
"Formal logic" is often used as a synonym for symbolic logic. Informal logic is understood to mean any logical investigation that does not involve symbolic abstraction. In the broader sense, formal logic is old, dating back more than two thousand years, while symbolic logic is only about a century old.
Properties of Logical Systems
- Consistency: none of the theorems of the system contradict one another
- Soundness: the system's rules of proof will never allow a false inference from a true premise (if a system is sound and its axioms are true, then its theorems are also guaranteed to be true)
- Completeness: there are no true sentences in the system that cannot be proved in the system
Not all systems can achieve all three virtues.
Rival Conceptions of Logic
Logic arose from a concern with correctness of argumentation. Modern logicians normally wish to ensure that logic studies just those arguments that arise from appropriately general form of inference. Others argue that logic should be conceived as the science of judgment. On this conception, the valid inferences of logic follow from the structural features of judgments or thoughts.
Deductive and Inductive Reasoning
Deductive reasoning concerns what follows necessarily from given premises. Inductive reasoning is the process of deriving a reliable generalization from observations and has sometimes been included in the study of logic.
Topics in Logic
- Syllogistic Logic
- Analysis of the judgments into propositions consisting of two terms that are related to one of a fixed number of relations
- Expression of inferences by means of syllogisms that consisted of two propositions sharing a common term as premise
- Conclusion which was a proposition involving the two unrelated terms from the premises
- Predicate Logic
- Allows sentences to be analyzed into subject and argument in several different ways
- Logicians able to give an account of quantifiers general to express all arguments occurring in natural language
- Modal Logic
- Deals with the phenomenon that sub-parts of a sentence may have their semantics modified by special verbs or modal particles
- Affects the circumstances in which we take an assertion to be satisfied
- Deduction and Reasoning
- Distinguishing good from bad arguments
- Mathematical Logic
- Application of the techniques of formal logic to mathematics and mathematical reasoning
- Application of mathematical techniques to the representation and analysis of formal logic
- Philosophical Logic
- Deals with formal descriptions of natural language
- A continuation of the traditional discipline that was called "logic" before the invention of mathematical logic
- Greater concern with the connection between natural language and logic
- Argumentation Theory
- Study and research of informal logic, fallacies, and critical questions as they relate to every day and practical situations
External Links
Relevant discussion threads on AboveTopSecret.com
