"Logical reasoning is a mental activity that aims to arrive at a conclusion in a rigorous way."
The process of using a specific methodology to arrive at a valid conclusion based on available information.
Deductive reasoning: The process of drawing specific conclusions based on general principles or premises.
Inductive reasoning: The process of drawing general conclusions based on specific observations or experiences.
Conditionals: Statements that describe a relationship between two propositions, such as "if-then" statements.
The fallacies of reasoning: Common mistakes that people make when reasoning, such as ad hominem attacks, slippery slopes, and straw man arguments.
Syllogisms: Logical arguments that consist of three parts: a major premise, a minor premise, and a conclusion.
Decision making frameworks: Structured processes for analyzing and making decisions, such as the decision matrix or cost-benefit analysis.
Cognitive biases: The various ways in which our thoughts and decision making processes can be influenced by our emotions, beliefs, or other factors.
Problem-solving: The process of analyzing and identifying solutions to a particular problem.
Argumentation and debate: The ability to construct and present logical arguments, as well as to evaluate the arguments of others.
Game theory: The study of decision making in strategic situations, as well as the mathematical models used to analyze those situations.
Critical thinking: The ability to evaluate information and arguments objectively, and to arrive at reasoned conclusions based on evidence.
Bayesian reasoning: The application of probability theory to logical reasoning, particularly in the fields of statistics and machine learning.
Fuzzy logic: A system for reasoning that allows for uncertainty and imprecision in language and data.
Causal reasoning: The process of identifying cause-and-effect relationships between events or phenomena.
Ethics: The study of moral principles and values, and their role in decision making.
Deductive reasoning: This involves starting with a general premise and using it to reach a specific conclusion. Deductive reasoning follows the rule of validity, which means that if the premises are true, the conclusion must also be true. For example, "All humans are mortal. Socrates is a human. Therefore, Socrates is mortal.".
Inductive reasoning: This involves making generalizations based on specific observations or evidence. Inductive reasoning follows the rule of probability, which means that if the premises are true, the conclusion is likely to be true. For example, "Every crow I have seen is black. Therefore, all crows are black.".
Abductive reasoning: This involves starting with an incomplete set of observations and using them to form a hypothesis that would explain the observations. Abductive reasoning involves identifying the simplest and most likely explanation for an observation even if it is incomplete. For example, if there is smoke coming from a room, it is abductive reasoning to assume there is a fire in the room.
Analogical reasoning: This involves using similarities between two objects or events to make predictions or decisions about one based on what is known about the other. For example, a physician might use the analogy of a car engine to explain how the human heart works.
Casual reasoning: This involves the process of identifying a cause and effect relationship between two events or variables. Casual reasoning involves identifying the cause and effect relationship between two events or variables. For example, smoking leads to an increased risk of lung cancer.
Counterfactual reasoning: This involves considering what might have happened if a past event had been different. Counterfactual reasoning involves exploring alternative possibilities and hypothetical scenarios. For example, what would have happened if World War II ended differently.
Conditional reasoning: This involves reasoning with if-then statements or propositions. Conditional reasoning involves drawing conclusions based on hypothetical or conditional situations. For example, if I study hard, then I will get an A on the test.
Syllogistic reasoning: This involves a form of deductive reasoning that involves two premises and a conclusion. The two premises are connected by a logical quantifier such as "all," "some," or "none." The conclusion follows from the premises in a valid manner. For example, "All cats are animals. All animals have fur. Therefore, all cats have fur.".
Fuzzy logic: This involves reasoning that deals with imprecise information or uncertainty. Fuzzy logic involves estimating likelihoods and probabilities rather than precise values. For example, a person might describe an object as being "kind of big" or "sort of heavy.".
Modal logic: This involves reasoning that deals with modalities such as possibility, necessity, or contingency. Modal logic involves specifying the conditions under which a statement is true or false. For example, "It is possible that it will rain tomorrow.".
"The premises and the conclusion are propositions, i.e. true or false claims about what is the case."
"The main discipline studying logical reasoning is called logic."
"Deductive reasoning offers the strongest support: the premises ensure the conclusion, meaning that it is impossible for the conclusion to be false if all the premises are true."
"For example: all men are mortal; Socrates is a man; therefore, Socrates is mortal."
"Deductive reasoning plays a central role in formal logic and mathematics."
"Non-deductive reasoning is often understood in terms of probability."
"The premises make their conclusion rationally convincing without ensuring its truth. This is often understood in terms of probability: the premises make it more likely that the conclusion is true..."
"Inductive reasoning is a form of generalization that infers a universal law from a pattern found in many individual cases."
"Abductive reasoning, also known as 'inference to the best explanation', starts from an observation and reasons to the fact explaining this observation."
"Analogical reasoning compares two similar systems. It observes that one of them has a feature and concludes that the other one also has this feature."
"Arguments that fall short of the standards of logical reasoning are called fallacies."
"For formal fallacies, like affirming the consequent, the error lies in the logical form of the argument."
"For informal fallacies, like false dilemmas, the source of the faulty reasoning is usually found in the content or the context of the argument."
"Some theorists understand logical reasoning in a wide sense that is roughly equivalent to critical thinking."
"In this regard, it encompasses cognitive skills besides the ability to draw conclusions from premises."
"Examples are skills to generate and evaluate reasons and to assess the reliability of information."
"Further factors are to seek new information, to avoid inconsistencies, and to consider the advantages and disadvantages of different courses of action before making a decision."
"The premises ensure the conclusion, meaning that it is impossible for the conclusion to be false if all the premises are true."
"Logical reasoning is norm-governed in the sense that it aims to formulate correct arguments that any rational person would find convincing."