- "Logic is the study of correct reasoning."
Deals with reasoning and argumentation.
Propositions: Statements expressing a complete thought or idea that can be true or false.
Arguments: A series of propositions which are intended to provide support for a conclusion.
Deductive Reasoning: A process of reasoning where the truth of the conclusion can be inferred from the premises.
Inductive Reasoning: A process of reasoning where the truth of the conclusion is probable based on the premises, but not necessarily logically certain.
Validity: An argument is valid if, assuming the premises to be true, the conclusion must also be true.
Soundness: An argument is sound if it is valid and all of its premises are true.
Logic Symbols and Notations: Symbols and notations used to represent logical statements and their relationships.
Logical Fallacies: Mistakes or errors in reasoning that can lead to invalid or unsound arguments.
Propositional Logic: A branch of logic that deals with the logical relationships between propositions.
Predicate Logic: A branch of logic that deals with the logical relationships between subjects, predicates, and objects.
Truth Tables: Tables used to determine the truth value of compound propositions.
Inference Rules: Patterns of logical reasoning used to derive conclusions from premises.
Syllogisms: Deductive arguments that consist of two premises and a conclusion.
Categorical Logic: A branch of logic that deals with the logical relationships between categories.
Modal Logic: A branch of logic that deals with the logical relationships between propositions and different modalities such as possibility and necessity.
Aristotelian Logic: Also known as traditional or classical logic, it is the most well-known type of logic. It is based on the work of Aristotle and focuses on reasoning and deducing conclusions from premises.
Modal Logic: A type of logic that deals with possibility and necessity. It is used to determine whether a statement is true or false based on the level of certainty or probability associated with it.
Propositional Logic: This type of logic deals with propositions or statements that can either be true or false. It is used to construct logical arguments and reason about the truth or falsity of statements.
Predicate Logic: This type of logic deals with predicates or properties that can be applied to objects or individuals. It is used to construct logical arguments about relationships between objects and predicates.
Intuitionistic Logic: A type of logic that emphasizes the constructive nature of mathematical proof. It is based on the idea that not all statements can be proven or negated, and that some statements can be neither true nor false.
Deontic Logic: A type of logic that deals with obligations, permissions, and prohibitions. It is used to reason about ethical and moral dilemmas.
Fuzzy Logic: A type of logic that deals with uncertainty and vagueness. It is used to reason about situations where there are degrees of truth or many possible answers.
Paraconsistent Logic: A type of logic that allows for contradictions to coexist without leading to absurdities. It is used to reason about situations where there may be inconsistent information or beliefs.
Relevance Logic: A type of logic that focuses on the relevance of premises to conclusions. It is used to reason about situations where there may be irrelevant information or premises.
Non-classical Logics: These are various types of logics that are not traditional or classical logic. They include many different kinds, such as temporal logic, epistemic logic, and quantum logic.
- "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."