Deductive reasoning is the process of drawing valid inferences. An inference is valid if its conclusion follows logically from its premises, meaning that it is impossible for the premises to be true and the conclusion to be false.
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. Some theorists define deduction in terms of the intentions of the author: they have to intend for the premises to offer deductive support to the conclusion. With the help of this modification, it is possible to distinguish valid from invalid deductive reasoning: 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.
Logic studies what conditions an argument is valid under. According to the semantic approach, an argument is valid if there is no possible interpretation of the argument whereby its premises are true and its conclusion is false. The syntactic approach, by contrast, focuses on rules of inference, that is, schemas of drawing a conclusion from a set of premises based only on their logical form. There are various rules of inference, such as modus ponens and modus tollens. Invalid deductive arguments, which do not follow a rule of inference, are called formal fallacies. Rules of inference are definitory rules and contrast with strategic rules, which specify what inferences one needs to draw in order to arrive at an intended conclusion.
Deductive reasoning contrasts with non-deductive or ampliative reasoning. For ampliative arguments, such as inductive or abductive arguments, the premises offer weaker support to their conclusion: they indicate that it is most likely, but they do not guarantee its truth. They make up for this drawback with their ability to provide genuinely new information (that is, information not already found in the premises), unlike deductive arguments.
Cognitive psychology investigates the mental processes responsible for deductive reasoning. One of its topics concerns the factors determining whether people draw valid or invalid deductive inferences. One such factor is the form of the argument: for example, people draw valid inferences more successfully for arguments of the form modus ponens than of the form modus tollens. Another factor is the content of the arguments: people are more likely to believe that an argument is valid if the claim made in its conclusion is plausible. A general finding is that people tend to perform better for realistic and concrete cases than for abstract cases. Psychological theories of deductive reasoning aim to explain these findings by providing an account of the underlying psychological processes. 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, on the other hand, 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.
The problem of deduction is relevant to various fields and issues. Epistemology tries to understand how justification is transferred from the belief in the premises to the belief in the conclusion in the process of deductive reasoning. Probability logic studies how the probability of the premises of an inference affects the probability of its conclusion. The controversial thesis of deductivism denies that there are other correct forms of inference besides deduction. Natural deduction is a type of proof system based on simple and self-evident rules of inference. In philosophy, the geometrical method is a way of philosophizing that starts from a small set of self-evident axioms and tries to build a comprehensive logical system using deductive reasoning.
and 27 Related for: Deductive reasoning information
Deductivereasoning is the process of drawing valid inferences. An inference is valid if its conclusion follows logically from its premises, meaning that...
with the inductive reasoning other than deductivereasoning (such as mathematical induction), where the conclusion of a deductive argument is certain...
Sanders Peirce held that the most important division of kinds of deductivereasoning is that between corollarial and theorematic. He argued that while...
is being built on deductively. A theory being assumed as true and subsequently built on is a common example of deductivereasoning. Theory building on...
reasoning to produce logically valid arguments and true conclusions. Reasoning may be subdivided into forms of logical reasoning, such as deductive reasoning...
sub-classifications in deductivereasoning, inductive reasoning and abductive reasoning. ‘Deductivereasoning is a basic form of valid reasoning, commencing with...
ideas, "might be a powerful tool to improve reasoning." This approach stresses the idea that "deductivereasoning is not only about getting the 'right' answer...
philosophy of logic, defeasible reasoning is a kind of provisional reasoning that is rationally compelling, though not deductively valid. It usually occurs when...
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical...
patterns to get the Zoombinis to the next level. Similarly, with the deductivereasoning sub-games, these exercises discourage random guessing by giving only...
formal fallacy, deductive fallacy, logical fallacy or non sequitur (/ˌnɒn ˈsɛkwɪtər/; Latin for 'it does not follow') is a pattern of reasoning rendered invalid...
Wason in 1966. It is one of the most famous tasks in the study of deductivereasoning. An example of the puzzle is: You are shown a set of four cards placed...
beginning in the latter half of the 19th century. Abductive reasoning, unlike deductivereasoning, yields a plausible conclusion but does not definitively...
later does not .: 439 In opposition, deductivereasoning is a basic form of valid reasoning. In this reasoning process a person starts with a known claim...
evidence. Types of reasoning can be divided into deductive and non-deductivereasoning. Deductivereasoning is governed by certain rules of inference, which...
the structure of a deductive argument that renders the argument invalid, while an informal fallacy originates in an error in reasoning other than an improper...
information. Analytical reasoning involves breaking down large problems into smaller components and using deductivereasoning with no specialised knowledge...
Many reasoning systems employ deductivereasoning to draw inferences from available knowledge. These inference engines support forward reasoning or backward...
logic. Deductivereasoning concerns the logical consequence of given premises. On a narrow conception of logic, logic concerns just deductivereasoning, although...
'conclusion, inference') is a kind of logical argument that applies deductivereasoning to arrive at a conclusion based on two propositions that are asserted...
automatic, in complex situations advanced reasoning is necessary. Types of causal reasoning include: Deductivereasoning implies a general rule; an event is...
that of a rational form of discourse that relies on inductive and deductivereasoning. Aristotle first systematized the usage of the word, making it one...
specialised, but they also overlap or interact with each other. Deductivereasoning, on the other hand, has been shown to be related to either visual...
In logic and deductivereasoning, an argument is sound if it is both valid in form and has no false premises. Soundness has a related meaning in mathematical...
has been (or could be) formally defined, and with which one may do deductivereasoning and mathematical proofs. Typically, a mathematical object can be...