- "Logic is the study of correct reasoning."
The study of reasoning and argumentation.
Propositional logic: The study of logical relationships between statements that are either true or false.
Predicate logic: The study of logical relationships between statements that contain variables.
Modal logic: The study of logical relationships between statements involving possibility, necessity, and contingency.
Induction and deduction: The two primary methods of logical reasoning.
Truth tables: A graphical method used to analyze the logical relationships between a set of propositions.
Syllogisms: Arguments that contain two premises and a conclusion.
Categorical propositions: Propositions that relate two classes or categories.
Inference rules: Rules that allow one to derive logical consequences from a set of premises.
Fallacies: Common errors in logical reasoning.
Scientific method: A systematic approach to inquiry based on observation and experimentation.
Critical thinking: The ability to analyze and evaluate arguments and evidence.
Deductive reasoning: Reasoning that moves from general premises to specific conclusions.
Inductive reasoning: Reasoning that moves from specific observations to general conclusions.
Philosophy of science: The study of the nature, methodology, and limits of scientific inquiry.
Epistemology: The study of knowledge and belief.
Classical logic: This is the most traditional form of logic, which is based on the principles of aristotelian logic. This type of logic uses the syllogism, which involves deductive reasoning to form a conclusion.
Symbolic logic: This type of logic utilizes symbols to represent logical propositions, making it a useful tool for mathematical and scientific applications.
Modal logic: This type of logic is used to analyze the meaning of words such as "possible" and "necessary". Modal logic can be used to examine the nature of knowledge and the limitations of our understanding of the world.
Fuzzy logic: This type of logic involves degrees of truth, rather than strict binary true/false statements. Fuzzy logic is often used to solve problems where there is ambiguity or imprecision.
Intuitionistic logic: This type of logic places importance on the role of the individual and the subjective experience in the process of reasoning. It emphasizes the role of intuition and rejects classical logic's reliance on strict deduction.
Deontic logic: This type of logic deals with ethical and moral obligations, distinguishing between what is allowed, prohibited, or required. It is often used to develop codes of conduct or ethical frameworks.
Epistemic logic: This type of logic examines knowledge and the processes by which we acquire it. It emphasizes the importance of evidence and justification for beliefs.
Temporal logic: This type of logic focuses on time and temporal relationships, analyzing propositions in terms of their truth conditions over different time periods.
Non-monotonic logic: This type of logic deals with uncertain, complex, or incomplete information, in which new information can change the previously established conclusion.
Inductive logic: This type of logic starts with known premises and derives conclusions that are likely or probable, rather than certain. It is often used in scientific and statistical reasoning.
- "Formal logic is the science of deductively valid inferences or logical truths. It studies how conclusions follow from premises due to the structure of arguments alone, independent of their topic and content."
- "Informal logic is associated with informal fallacies, critical thinking, and argumentation theory."
- "Informal logic examines arguments expressed in natural language, while formal logic uses formal language."
- "When used as a countable noun, the term 'a logic' refers to a logical formal system that articulates a proof system."
- "Logic plays a central role in many fields, such as philosophy, mathematics, computer science, and linguistics."
- "Arguments consist of a set of premises together with a conclusion."
- "Premises and conclusions express propositions or claims that can be true or false."
- "An important feature of propositions is their internal structure."
- "Complex propositions are made up of simpler propositions linked by logical vocabulary like 'and' or 'if...then'."
- "The truth of a proposition usually depends on the meanings of all of its parts."
- "Logically true propositions are true only because of their logical structure, independent of the specific meanings of the individual parts."
- "An argument is correct if its premises support its conclusion."
- "Deductive arguments have the strongest form of support: if their premises are true, then their conclusion must also be true."
- "Ampliative arguments arrive at genuinely new information not found in the premises."
- "They are divided into inductive and abductive arguments."
- "Inductive arguments are statistical generalizations, like inferring that all ravens are black based on many individual observations of black ravens."
- "Abductive arguments are inferences to the best explanation, for example, when a doctor concludes that a patient has a certain disease which explains the symptoms they suffer."
- "Arguments that fall short of the standards of correct reasoning often embody fallacies."
- "Systems of logic are theoretical frameworks for assessing the correctness of arguments."