"Deductive reasoning is the mental process of drawing deductive inferences."
The process of reasoning from general principles to specific cases.
Basic Concepts in Deduction: This includes an overview of what deduction is and its role in reasoning.
Propositional Calculus: This involves analyzing propositional expressions in the form of logical operators such as "AND," "OR," and "NOT" to determine their logical validity.
Predicate Logic: A more complex form of logical analysis that involves analyzing propositions involving quantifiers and variables.
Categorical Logic: A type of deduction that involves analyzing categorical propositions, such as those involving "all," "some," and "none.".
Deductive Arguments: An explanation and evaluation of the structure of deductive arguments and what defines a sound and valid deduction.
Fallacies: Common logical fallacies that can occur in reasoning or argumentation.
The Nature of Truth: An overview of the concept of truth in relation to deductive reasoning, including the correspondence theory and coherence theory of truth.
Inductive Reasoning: An introduction to inductive reasoning and how it differs from deductive reasoning.
Syllogisms: An analysis of basic forms of syllogism, involving the relationship between premises and the conclusion, and the different types of syllogisms.
Modal Logic: The study of modal terms such as "possibly," "necessarily" and their role in deductive reasoning.
Inductive Deduction: An inference based on observation of common patterns in a collection of individual instances.
Abductive Deduction: An inference on the probable explanation for an observation.
Hypothetico-Deductive: Predicting and verifying implications of hypotheses and theories.
Logical Deduction: Deriving a conclusion from premises that are necessarily true.
Analogical Deduction: Drawing a conclusion from similarities between things that are otherwise different.
Pragmatic Deduction: Using knowledge to make sound and reasonable predictions and decisions.
Deductive Reasoning: Arrival of a conclusion from premises that are known to be true.
Casual Deduction: Inferring causes from observed phenomena.
Moral Deduction: Deriving the moral implications of a given situation.
Deductive Inference: Deriving a conclusion from premises that are known to be true.
Defeasible Deduction: Acknowledging that the conclusion may not always be true since some premises may be defeated.
Fuzzy Deduction: Using vague or uncertain information to arrive at a conclusion.
Bayesian Deduction: An approach to probability that uses a priori information to revise probabilities.
Indefinable Deduction: Unknown premises that can’t be quantified with certainty.
Natural Deduction: A method of proof using derivation trees.
"An inference is deductively valid if its conclusion follows logically from its premises."
"For example, the inference from the premises 'all men are mortal' and 'Socrates is a man' to the conclusion 'Socrates is mortal' is deductively valid."
"An argument is sound if it is valid and all its premises are true."
"It is invalid if the author's belief about the deductive support is false, but even invalid deductive reasoning is a form of deductive reasoning."
"Psychology is interested in deductive reasoning as a psychological process, i.e. how people actually draw inferences. Logic, on the other hand, focuses on the deductive relation of logical consequence between the premises and the conclusion or how people should draw inferences."
"According to the semantic approach, an argument is deductively valid if and only if there is no possible interpretation of this argument where its premises are true and its conclusion is false. The syntactic approach, on the other hand, holds that an argument is deductively valid if and only if its conclusion can be deduced from its premises using a valid rule of inference."
"A rule of inference is a schema of drawing a conclusion from a set of premises based only on their logical form."
"Various rules of inference, like the modus ponens and the modus tollens exist."
"Invalid deductive arguments, which do not follow a rule of inference, are called formal fallacies."
"Deductive reasoning contrasts with non-deductive or ampliative reasoning. For ampliative arguments, like inductive or abductive arguments, the premises offer weaker support to their conclusion."
"One topic concerns the factors determining whether people draw valid or invalid deductive inferences."
"People are more successful for arguments of the form modus ponens than for modus tollens."
"People are more likely to believe that an argument is valid if the claim made in its conclusion is plausible."
"People tend to perform better for realistic and concrete cases than for abstract cases."
"Mental logic theories hold that deductive reasoning is a language-like process that happens through the manipulation of representations using rules of inference."
"Mental model theories claim that deductive reasoning involves models of possible states of the world without the medium of language or rules of inference."
"According to dual-process theories of reasoning, there are two qualitatively different cognitive systems responsible for reasoning."
"Epistemology, probability logic, and philosophy are some of the fields that are concerned with deductive reasoning."
"Natural deduction is a type of proof system based on simple and self-evident rules of inference."