- "Logic is the study of correct reasoning."
The study of reasoning, arguments, and the principles of valid and sound inference.
Definition of Logic: Logic is the branch of philosophy concerned with reasoning and argumentation, specifically the study of validity, inference, and truth.
Basic Concepts of Logic: This includes the principles of identity, non-contradiction, and excluded middle, as well as the idea of propositions, premises, and conclusions.
Formal and Informal Logic: Formal logic deals with the symbolic representation of arguments, which can be checked for validity using mathematical rules, whereas informal logic can deal with the content and structure of arguments.
Deductive Reasoning: This refers to the process of drawing logical conclusions from a set of premises using valid arguments.
Inductive Reasoning: This concerns drawing general conclusions from specific observations or data and is used for scientific and empirical investigations.
Modus Ponens and Modus Tollens: These are common forms of deductive reasoning.
Syllogisms: These are deductive arguments composed of three statements, where two premises lead to a conclusion.
Fallacies: These are arguments that seem plausible but do not actually follow logically or are based on false premises.
Propositional Calculus: This refers to the study of propositions and logical operators, such as "and," "or," "not," and "if-then.".
Predicate Calculus: This deals with the study of quantified variables, such as "for all" and "there exists.".
Modal Logic: This extends traditional logic to include concepts of possibility and necessity.
Formal Systems: These are mathematical systems used to represent reasoning and argumentation.
Metatheory: This involves studying the structure of formal systems and their limits.
Fuzzy Logic: This is a type of logic where variables can have partial truths or values, rather than just true or false.
Intuitionistic Logic: This is a type of logic that rejects the notion of excluded middle, and cannot prove every proposition.
Deontic Logic: This deals with concepts of obligation and permission.
Temporal Logic: This deals with concepts of time and ordering.
Epistemology: This is the branch of philosophy concerned with knowledge, beliefs, and theories.
Ontology: This is the branch of philosophy concerned with the nature of existence and reality.
Ethics: This is the branch of philosophy dealing with moral principles and values.
Propositional Logic: It is concerned with relationships among propositions, sentences, or statements. It deals with logical relationships between propositions that involve logical operators such as AND, OR, and NOT.
Predicate Logic: This type of logic is based on the idea of predicates and their corresponding subjects. It involves relationships between predicates and subjects to make logical statements.
Modal Logic: It examines the relationships between statements and the ways in which they can be true or false. It asks whether a statement is necessarily true or true only under certain conditions.
Deontic Logic: This type of logic is concerned with rules and principles of obligation, permission, and prohibition. It aims to establish what is right or wrong, what is permissible or impermissible, and what should or should not be done.
Epistemic Logic: It is concerned with knowledge, belief, and truth. It aims to study how knowledge and belief are related and how truth can be established.
Fuzzy Logic: It is concerned with reasoning that is approximate rather than precise. It deals with degrees of truth rather than absolute truth.
Non-monotonic Logic: It is concerned with reasoning that is not based on fixed rules or principles. It involves the use of default assumptions and revision of beliefs.
Intuitionistic Logic: It is a type of non-classical logic that rejects the principle of excluded middle, which states that a proposition must either be true or false. It is concerned with constructive reasoning, where proofs are seen as construction processes.
Paraconsistent Logic: It is a type of logic that allows for contradictions. It is based on the idea that contradictions can coexist in a coherent way.
Quantum Logic: It is a type of logic that is based on the principles of quantum mechanics. It deals with the logical properties of quantum systems, such as superposition, entanglement, and uncertainty.
- "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."