- "Logic is the study of correct reasoning."
The study of reasoning and argumentation.
Propositional Logic: Propositional logic deals with propositions, which can either be true or false. This type of logic focuses on the relationship between these propositions.
Predicate Logic: Predicate logic extends propositional logic to include variables, quantifiers, and predicates. It is used in mathematics and computer science to make precise statements.
Modal Logic: Modal logic is concerned with the use of modalities, such as possibility and necessity, to express statements about the world.
Boolean Algebra: Boolean algebra is a branch of algebraic logic that deals with variables that can only have two values, true or false. It is used in digital electronics and computer science.
Inference: Inference is the process of drawing conclusions from premises. It is a central concept in logic, and is used in mathematics, philosophy, and computer science.
Deductive Reasoning: Deductive reasoning is a type of reasoning where the conclusion follows necessarily from the premises. It is used in logic, mathematics, and philosophy to construct proofs.
Inductive Reasoning: Inductive reasoning is a type of reasoning where the conclusion is probable based on the evidence at hand. It is used in science to make predictions and draw conclusions based on observations.
Formal Proof: A formal proof is a step-by-step demonstration of the truth of a statement or theorem in a formal language. It is used in mathematics and logic to establish the validity of arguments.
Set Theory: Set theory is the branch of mathematics that deals with sets and their properties. It is used in various areas of mathematics and logic.
Recursion Theory: Recursion theory is the study of the computability of functions and the sets that they generate. It is used in computer science and mathematical 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."