Deductive reasoning is the mental process of drawing deductive inferences. An inference is deductively valid if its conclusion follows logically from its premises, i.e. if 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. 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. There are different ways of conceptualizing this relation. 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. There are various rules of inference, like the modus ponens and the 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 to 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, like inductive or abductive arguments, the premises offer weaker support to their conclusion: they make it more likely but they do not guarantee its truth. They make up for this drawback by being able to provide genuinely new 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 factor is the form of the argument: for example, people are more successful for arguments of the form modus ponens than for modus tollens. Another 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 deductive reasoning 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. (Wikipedia).
Geometry - Ch. 2: Reasoning and Proofs (13 of 46) What is Deductive Reasoning?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is deductive reasoning. Sometime known as deductive logic or leading to a deductive conclusion. It is reasoning from one or more statements to reach a logical conclusion. And I will expla
From playlist GEOMETRY CH 2 PROOFS & REASONING
http://www.teachastronomy.com/ Deduction is a way of combining observations or statements made in science logically. Deduction provides a very strong way of connecting observations with a conclusion. Typically we start with premises and combine them to draw conclusions. For example, if
From playlist 01. Fundamentals of Science and Astronomy
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Logical Reasoning: Become A Better Thinker
Logical thinking is also known as analytical reasoning, critical thinking or abstract thinking. It is an important trait, especially among developers in the software development industry. Without the logic, they would not understand how the software works, nor would they produce a clean co
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Introduction to Deductive Reasoning
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From playlist Introduction to Proof
Logic: The Structure of Reason
As a tool for characterizing rational thought, logic cuts across many philosophical disciplines and lies at the core of mathematics and computer science. Drawing on Aristotle’s Organon, Russell’s Principia Mathematica, and other central works, this program tracks the evolution of logic, be
From playlist Logic & Philosophy of Mathematics
A Deductive Perspective Toward Equation Solving
In this video, we take a deductive perspective toward the process of equation solving. Thanks for watching! Comment below with questions, and make sure to like / subscribe! Instagram: https://www.instagram.com/braingainzofficial
From playlist Proofs
Geometry - Ch. 2: Reasoning and Proofs (14 of 46) Applying Deductive Reasoning: Ex. 1
Visit http://ilectureonline.com for more math and science lectures! In this video I will use deductive reasoning to find out if x is an odd number if the following algebraic expressions are even: x+2, 2x-1, 3x+2, and 3x+1. (Example 1) Next video in this series can be seen at: https://you
From playlist GEOMETRY CH 2 PROOFS & REASONING
HSC Science Extension Module 1 Induction and Deduction
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From playlist Y12 Sci Ex Mod 1 Foundations of Scientific Thinking
Foundations - Seminar 6 - Discharging hypotheses and Curry-Howard
Daniel Murfet discusses the introduction and elimination rule for implication in natural deduction, the way in which undischarged hypotheses are managed, the "identity" of natural deductions (which deductions count as "the same") and how all of this feeds into the Curry-Howard (CH) corresp
From playlist Foundations seminar
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This is the first main video on a series of videos: How to do mathematical proofs. This video focuses on the basics of mathematical logic, specifically, the distinction between deductive and inductive reasoning, and examples of premises, propositions, and whatnot. The course is structured
From playlist How to do Mathematical Proofs
1. Ch. 1 (Part 1/3) Introduction to Logic, Philosophy 10, UC San Diego - BSLIF
Video lecture corresponding to _Basic Sentential Logic and Informal Fallacies_, Introduction, and Chapter 1, Part 1 of 3. This is for the class Introduction to Logic, Philosophy 10, UC San Diego.
From playlist UC San Diego: PHIL 10 - Introduction to Logic | CosmoLearning.org Philosophy
Reasoning | Introductory Astronomy Course 1.04
Welcome to Astronomy: Exploring Time and Space, a course from Professor Impey, a University Distinguished Professor of Astronomy at the University of Arizona. Learn about the foundations of astronomy in this free online course here on YouTube. This video is part of module 1, Science and Hi
From playlist Introductory Astronomy Module 1: Science and History
Billy Price and Will Troiani present a series of seminars on foundations of mathematics. In this seminar Billy introduces natural deduction as a proof system. You can join this seminar from anywhere, on any device, at https://www.metauni.org. This video was filmed in Deprecation (https:/
From playlist Foundations seminar
Lecture 8: Risk Preferences II
MIT 14.13 Psychology and Economics, Spring 2020 Instructor: Prof. Frank Schilbach View the complete course: https://ocw.mit.edu/14-13S20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63Z979ri_UXXk_1zrvrF77Q This lecture continues the discussion of risk preferences, an
From playlist MIT 14.13 Psychology and Economics, Spring 2020
Difference between inductive and deductive reasoning | Precalculus | Khan Academy
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/algebra-home/alg-series-and-induction/alg-deductive-and-inductive-reasoning/v/deductive-reasoning-1 Deductive Reasoning 1 Watch the next lesson: https://www.khana
From playlist Sequences, series and induction | Precalculus | Khan Academy
Inference: A Logical-Philosophical Perspective with Alexander Paseau
In this talk, Professor Alexander Paseau, Faculty of Philosophy, University of Oxford, will describe some of his work on inference within mathematics and more generally. Inferences can be usefully divided into deductive or non-deductive. Formal logic studies deductive inference, the obviou
From playlist Franke Program in Science and the Humanities
Introduction to Mathematical Induction (1 of 2: Two Different kinds of Logic)
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From playlist Introduction to Proof by Mathematical Induction