Logical truth is one of the most fundamental concepts in logic. Broadly speaking, a logical truth is a statement which is true regardless of the truth or falsity of its constituent propositions. In other words, a logical truth is a statement which is not only true, but one which is true under all interpretations of its logical components (other than its logical constants). Thus, logical truths such as "if p, then p" can be considered tautologies. Logical truths are thought to be the simplest case of statements which are analytically true (or in other words, true by definition). All of philosophical logic can be thought of as providing accounts of the nature of logical truth, as well as logical consequence. Logical truths are generally considered to be necessarily true. This is to say that they are such that no situation could arise in which they could fail to be true. The view that logical statements are necessarily true is sometimes treated as equivalent to saying that logical truths are true in all possible worlds. However, the question of whether any statements are necessarily true remains the subject of continued debate. Treating logical truths, analytic truths, and necessary truths as equivalent, logical truths can be contrasted with facts (which can also be called contingent claims or synthetic claims). Contingent truths are true in this world, but could have turned out otherwise (in other words, they are false in at least one possible world). Logically true propositions such as "If p and q, then p" and "All married people are married" are logical truths because they are true due to their internal structure and not because of any facts of the world (whereas "All married people are happy", even if it were true, could not be true solely in virtue of its logical structure). Rationalist philosophers have suggested that the existence of logical truths cannot be explained by empiricism, because they hold that it is impossible to account for our knowledge of logical truths on empiricist grounds. Empiricists commonly respond to this objection by arguing that logical truths (which they usually deem to be mere tautologies), are analytic and thus do not purport to describe the world. The latter view was notably defended by the logical positivists in the early 20th century. (Wikipedia).
This video focuses on how to write the converse of a conditional statement. In particular, this video shows how to flip the hypothesis and conclusion of a conditional statement. The concepts of truth value and logical equivalence are explored as well. Your feedback and requests are encour
From playlist Geometry
How to determine the truth of a statement using a truth table
👉 Learn how to determine the truth or false of a conditional statement. A conditional statement is an if-then statement connecting a hypothesis (p) and the conclusion (q). If the hypothesis of a statement is represented by p and the conclusion is represented by q, then the conditional stat
From playlist Conditional Statements
How to determine the truth of a statement using a truth table
👉 Learn how to determine the truth or false of a conditional statement. A conditional statement is an if-then statement connecting a hypothesis (p) and the conclusion (q). If the hypothesis of a statement is represented by p and the conclusion is represented by q, then the conditional stat
From playlist Conditional Statements
How to determine the truth table from a statement and determine its validity
👉 Learn how to determine the truth or false of a conditional statement. A conditional statement is an if-then statement connecting a hypothesis (p) and the conclusion (q). If the hypothesis of a statement is represented by p and the conclusion is represented by q, then the conditional stat
From playlist Conditional Statements
Understanding Logical Statements 1
U12_L1_T2_we1 Understanding Logical Statements 1
From playlist Algebra I Worked Examples
An introduction to the general types of logic statements
From playlist Geometry
Truth Tables and Logical Equivalence
From playlist e. Sets and Logic
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
CCSS What are truth tables and how can we create them for conditional statements
👉 Learn how to determine the truth or false of a conditional statement. A conditional statement is an if-then statement connecting a hypothesis (p) and the conclusion (q). If the hypothesis of a statement is represented by p and the conclusion is represented by q, then the conditional stat
From playlist Conditional Statements
Basic Methods: We define tautology and contradiction and consider the conditions of logical equivalence and implication. Examples include DeMorgan's Laws for logic, modus ponens, and the Law of the Excluded Middle. As a final note, we introduce the Substitution Rules.
From playlist Math Major Basics
This E-Lecture discusses the machinery of propositional logic and its limitations. It includes a detailed treatment of the logical connectives and their truth-values.
From playlist VLC103 - The Nature of Meaning
Inference: A Logical-Philosophical Perspective - Moderated Conversation w/ A.C. Paseau and Gila Sher
Inference: Â A Logical-Philosophical Perspective. Moderated Conversation with Gila Sher, Department of Philosophy, University of California, San Diego on the talk by Alexander Paseau, Faculty of Philosophy, University of Oxford. The Franke Program in Science and the Humanities Understandi
From playlist Franke Program in Science and the Humanities
MATH 0100 | Episode 1 | Propositions and Combinational Logic
Let's learn about facts and logic! The proposition kind, of course. Made for SoME1: https://www.3blue1brown.com/blog/some1
From playlist Summer of Math Exposition Youtube Videos
Fundamentals of Mathematics - Lecture 02: Propositional Calculus and De Morgan's Laws
Course page: http://www.uvm.edu/~tdupuy/logic/Math52-Fall2017.html videography - Eric Melton, UVM handouts - David Zureick-Brown, Emory
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What are the basics of mathematical logic? | Intro to Math Structures VS1.1
So you want to prove things? Where do you start if you haven't ever written a proof before? In most cases, a course on discrete mathematics or mathematical structures is where someone writes their first proof and that starts with propositional calculus. In this video section, we go through
From playlist The CHALKboard 2022
Knights, Knaves, and Propositional Logic [Discrete Math Class]
This video is not like my normal uploads. This is a supplemental video from one of my courses that I made in case students had to quarantine. I decided that it might be of general interest for people wanting to learn about propositional logic (mathematical propositions, logical connectives
From playlist Discrete Mathematics Course
This computer science video follows on from the video that introduces logic gates. It covers creating truth tables for combinations of simple logic gates, including a mention of some well used combinations. Combinations of logic gates manipulate pulses of electricity, and because these pu
From playlist Logic Gates
Chapter 8 - Logic (intro) - IB Math Studies (Math SL)
Hello and welcome to What Da Math This video is an introduction to logic from Chapter 8 of Haese edition of IB Math Studies book. In this and other chapter 8 videos we will focus on truth tables, deductive reasoning and logic, conjunction, disjunction, negation and exclusive disjunction.
From playlist IB Math Studies Chapter 8
The Ultimate Guide to Propositional Logic for Discrete Mathematics
This is the ultimate guide to propositional logic in discrete mathematics. We cover propositions, truth tables, connectives, syntax, semantics, logical equivalence, translating english to logic, and even logic inferences and logical deductions. 00:00 Propositions 02:47 Connectives 05:13 W
From playlist Discrete Math 1
Determining the truth of a conditional statement
👉 Learn how to determine the truth or false of a conditional statement. A conditional statement is an if-then statement connecting a hypothesis (p) and the conclusion (q). If the hypothesis of a statement is represented by p and the conclusion is represented by q, then the conditional stat
From playlist Conditional Statements