Logic
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Logic | |
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| Type | Formal and philosophical discipline |
| Field | Philosophy; Mathematics |
| Core idea | Study of valid reasoning, inference, and formal structure of arguments |
| Assumptions | Relations between propositions can be formally analyzed; validity can be distinguished from truth |
| Status | Established field |
| Related | Reasoning; Inference; Argument; Rationality |
Logic is a discipline concerned with the principles of valid reasoning and inference. It studies the formal structures that determine whether conclusions follow from premises, independently of the specific content of those premises.
Logic plays a foundational role in philosophy, mathematics, computer science, and formal aspects of linguistics, providing tools for analyzing arguments, proofs, and systems of reasoning.
Core idea
At its core, logic investigates the conditions under which reasoning is valid. A valid argument is one in which, if the premises are true, the conclusion must also be true.
Validity is distinct from truth: a logically valid argument may have false premises, and a true conclusion may be reached through invalid reasoning.
Logical form
Logic focuses on logical form rather than subject matter. By abstracting away from content, logical analysis reveals patterns of inference that apply across diverse domains.
This abstraction allows logical principles to be applied universally, regardless of the topic under consideration.
Deductive logic
Deductive logic studies inferences where conclusions follow necessarily from premises. Classical examples include syllogisms and formal proofs.
Deductive systems aim to provide clear criteria for validity and consistency.
Non-deductive logic
Not all reasoning is deductive. Non-deductive logics address forms of reasoning that involve uncertainty, plausibility, or degrees of support.
These approaches overlap with probabilistic and defeasible reasoning, extending logical analysis beyond necessity.
Formal systems
Logic is often developed through formal systems consisting of symbols, rules of formation, and rules of inference. Formal systems allow reasoning to be made explicit, precise, and mechanically checkable.
Such systems are central to mathematics and computer science.
Logic and reasoning
Logic provides normative standards for reasoning. It specifies how conclusions ought to follow from premises, rather than how agents in fact reason.
This distinction highlights the difference between logical validity and psychological processes.
Logic and inference
Logical analysis clarifies the structure of inference by distinguishing valid from invalid steps. It also helps identify hidden assumptions and ambiguities in arguments.
Inference that violates logical principles may still be persuasive but lacks formal justification.
Limits and scope
Logic does not determine the truth of premises or supply empirical content. Its scope is limited to evaluating the relationships between propositions.
Some forms of reasoning resist formalization, leading to debates about the boundaries of logical analysis.
Status
Logic is a well-established discipline with multiple systems and interpretations. Its enduring role is to clarify the structure of reasoning and provide standards for evaluating arguments across contexts.