- "Logic is the study of correct reasoning."
The study of reasoning and argumentation.
Propositions and their truth values: A proposition is a statement that can be either true or false.
Validity and soundness: Validity refers to the logical structure of an argument, while soundness refers to the truth of the premises and the validity of the argument.
Logical connectives: Logical connectives are words used to join simple statements together to form compound statements.
Truth tables: A truth table is a table used to determine the truth value of complex propositions based on the truth values of their component propositions.
Propositional logic: Propositional logic is the study of logical relationships between propositions.
Predicate logic: Predicate logic is the logic of relations and attributes, which considers how predicates can be combined to form more complex statements.
First-order logic: First-order logic is a more advanced version of predicate logic that allows for quantifiers and variables.
Arguments and their structures: An argument is a group of statements that are presented as reasons or evidence for a conclusion.
Deductive reasoning: Deductive reasoning is a form of reasoning in which a conclusion is reached based on logically valid premises.
Inductive reasoning: Inductive reasoning is a form of reasoning that involves generalizing from specific observations to make broader claims.
Fallacies: A fallacy is an error in reasoning that results in a false or misleading conclusion.
Modal logic: Modal logic involves the use of modalities such as possibility, necessity, and contingency.
Sets and set theory: Sets and set theory study the properties of sets, which are collections of objects.
Recursion theory: Recursion theory is a branch of mathematical logic that studies the concept of computability and its associated properties.
Model theory: Model theory is concerned with the study of mathematical structures as models of formal languages, and their relation to logical systems.
Classical logic: Is the most widely used and traditional type of logic, which focuses on the principles of validity and entailsment.
Modal logic: Is focused on concepts of possibility and necessity.
Deontic logic: Is focused on concepts of obligation and permission.
Temporal logic: Is focused on concepts of past, present, and future events.
Epistemic logic: Is focused on concepts of knowledge, belief, and truth.
Paraconsistent logic: Is focused on the concept of contradictions that can be true in some contexts.
Fuzzy logic: Is focused on the idea of representing degrees of truth rather than just true or false.
Intuitionistic logic: Is focused on the concept of constructive proof and doesn't accept the law of the excluded middle.
Relevance logic: Is focused on concepts of relevance and entailment.
Non-monotonic logic: Is focused on the idea of reasoning with incomplete or uncertain information.
- "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."