"Deductive reasoning is the mental process of drawing deductive inferences."
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.
Propositional Logic: Deals with the relationship between propositions or statements using logical operators such as "and," "or," "not," "if-then," and "if and only if.".
Quantificational Logic: Focuses on the elaboration of the basic structure of deduction, introducing quantifiers such as "all," "none," and "some.".
Inductive Reasoning: Logic that involves making inferences from specific observations to general conclusions.
Argumentation Theory: The study of argumentation and its use in determining the merits of ideas, beliefs, or assertions.
Syllogisms: A logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions.
Fallacies: Refers to errors in reasoning, logical glitches, or mistakes due to a lack of evidence or weakness in the argument.
Modal Logic: A type of logic that deals with the concept of necessity, possibility, and truth.
Predicate Logic: A formal logic that deals with quantifiers, predicates, and variables.
Epistemology: The study of knowledge, its nature, and its limits, and how knowledge is acquired.
Metaphysics: The study of the fundamental nature of reality, including the relationship between mind and matter, substance and attribute, cause and effect, and potentiality and actuality.
Categorical Syllogism: This type of deductive reasoning begins with two premises and draws a conclusion based on those premises. The conclusion is typically in the form of “All A is B,” “No A is B,” “Some A is B,” or “Some A is not B,” where A and B are categories.
Hypothetical Syllogism: This type of deductive reasoning involves drawing a conclusion from two conditional statements. The conclusion assumes the “if-then” nature of each statement.
Disjunctive Syllogism: This type of deductive reasoning involves a conclusion drawn from two possible options. It assumes that one of the two options is true, but not both.
Modus Ponens: This type of deductive reasoning involves affirming the antecedent of a conditional statement to draw a conclusion. In other words, if you know “if A then B,” and you find out that A is true, then you can deduce that B is also true.
Modus Tollens: This type of deductive reasoning involves denying the consequent of a conditional statement to draw a conclusion. In other words, if you know “if A then B,” and you find out that B is false, then you can deduce that A is also false.
"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."