Michael's Education: November 2010. LESSON 3 d Inference is a process by which a conclusion is drawn from a valid sequence and relationship of premises. Kinds of inference 1. Inductive inference. A form of reasoning that proceeds from particular premises to a general conclusion. 2. Types of Induction 1. 1. Ex.: A school is a School. 2. Ex.: A school is either a school or not a school 3. Be at the same time or respect. Ex.: A school cannot be a school and not a school at the same time. 4. Ex.: A school is a place of learning. 2. 2 kinds of Empirical Induction 1. Example: Since Dr. 2. Example: Since 80 % of survey respondents said that they preferred LRT to Jeepny as mode of transportation, we conclude that LRT is preferred as a mode of transportation by the public. 1. 1. It is the process of drawing conclusions from the implication of a statement and its Opposing categorical statements.
Kinds of Immediate Inferences 1. 2. 2. Syllogisms are verbal expressions of arguments that are products of reasoning or inferential thinking. 1. 2. 1. The Logic Cafe. Logic.
Proofs. Philosophicallexicon.com. Propositional Logic [Internet Encyclopedia of Philosophy] Propositional logic, also known as sentential logic and statement logic, is the branch of logic that studies ways of joining and/or modifying entire propositions, statements or sentences to form more complicated propositions, statements or sentences, as well as the logical relationships and properties that are derived from these methods of combining or altering statements.
In propositional logic, the simplest statements are considered as indivisible units, and hence, propositional logic does not study those logical properties and relations that depend upon parts of statements that are not themselves statements on their own, such as the subject and predicate of a statement. Table of Contents 1. Introduction A statement can be defined as a declarative sentence, or part of a sentence, that is capable of having a truth-value, such as being true or false. George W. Sometimes, a statement can contain one or more other statements as parts. George W. 2. 3. A. The Joy Of Logic, Wingspan Productions, BBC Four | Prime Focus. The Joy Of Logic, Wingspan Productions, BBC Four Wingspan returned to Prime Focus for post production on another sharp, witty and mind-expanding programme ‘The Joy of Logic’. The online edit was completed by Katie Kemp in Avid Symphony.
Enzo Cannatella mixed the audio in protools HDX. A lot of sound effects were added, especially for the animated effects, helping to bring them to life and increase viewer understanding. Enzo said “Although the subject is rather complicated, it is told in a fun way, so it was important that the sound reflected that.” This foray into the world of logic with Computer Scientist Dave Cliff takes viewers on a roller-coaster ride through philosophy, maths, science and technology, considering that today's generation of logical computing machines could be smarter than us. See BBC Four listings here.
Translating Ordinary Language Claims. Ordinary Language Claims Arguments like the ones below can't be tested using Venn diagrams until they are "translated" or formatted into categorical standard form syllogisms: His dogs go everywhere he goes, so he goes everywhere they do. Requirements for Successful Translation In order to use Venn diagrams to test arguments like these, you must first be able to translate individual ordinary language claims into categorical standard form claims.
Your text lists ten types of claims to watch for, but we can simplify this scheme by thinking about the basic requirements of any successful translation from one language into another. One requirement for a successful translation is that the result meet the grammatical and syntactical rules of the language into which you translate. 1. a subject term: a plural noun or pronoun 2. a predicate term: a plural noun or pronoun 3. a quantifier: "Some," "No," or "All" 4. a copula: "are" or "are not" (the latter never occurring after a universal quantifier)
"Translation Tips"
Catagorical. Propositional. Learning Logic at Home. By Nathaniel Bluedorn (Revised May 2008.) When I was 13, my parents were in a dilemma. They wanted to teach logic and thinking skills to me and my brother and sisters, but they did not know how. In the years since the, my parents did find logic books and videos. Some were excellent. Some were hard to use. For learning at home, I think a logic textbook needs to be: Self-teaching - most parents never learned logic themselves, but self-teaching materials will help them learn it along with their children.
You can read our reviews of logic books and materials that are on the market and check out our list of logic resources available online. Pre-Logic for Children Under Age 13 Before age 13, I think children can benefit from pre-logic mind exercises. Pre-logic activities are optional. Logic Activities Games and everyday activities may develop your child's powers for thinking. A natural way to stimulate a child's mind is simply to converse with him. Building Thinking Skills Age 13 and Older.
Disjunctive not-both xor syllogism. Presentations/teaching. Random. Logic Matters | Logic, enthusiasms, sceptical thoughts, and a little LaTeX geekery. The Self-Paced Logic Project: Study guides. To give a sense of the content of the course as taught in 2002, here are the study guides for all six units. Unit 1: Starting an Argument The study guides are meant to enable you to predict what the test on the unit will look like, to practice the sorts of questions that will be on it, and to know how the different parts are weighted.
It gives pointers on how to study and practice for each section. If you use the study guides, you should never be surprised by what's on a test. Technical definitions. (3 questions, 20% of the final grade.) Unit 2: Testing Validity Validity seems like hocus-pocus until you understand the notion of logical form and learn how to test "whether a logical form has any substitution instances in which all the premises are true but the conclusion false". Warning: the test for Unit 2 will take considerably more time than that for Unit 1! Logical forms and substitution instances. (8 questions, 10.9% of final grade). New in this unit: actual test items. Teach Yourself Logic: A Study Guide, and other book notes. Most philosophy departments, and many maths departments too, teach little or no serious logic, despite the centrality of the subject.
Many students will therefore need to teach themselves, either solo or by organizing study groups. But what to read? Students need annotated reading lists for self-study, giving advice about the available texts. The Teach Yourself Logic Study Guide, linked below, aims to provide the needed advice by suggesting some stand-out books on various areas of mathematical logic. The main Guide and its Appendix are in PDF form, designed for on-screen reading. Teach Yourself Logic 2105: A Study Guide (PDF, iv + 94 pp.) If the Guide’s length makes it sound daunting, there are also some supplementary webpages which might help ease your way in: About the Guide Is the Guide for you?
And here are some additional webpages: It goes without saying, of course, that all constructive comments and suggestions continue to be most warmly welcomed.
Aristotle: Logic [Internet Encyclopedia of Philosophy] Aristotelian logic, after a great and early triumph, consolidated its position of influence to rule over the philosophical world throughout the Middle Ages up until the 19th Century. All that changed in a hurry when modern logicians embraced a new kind of mathematical logic and pushed out what they regarded as the antiquated and clunky method of syllogisms.
Although Aristotle’s very rich and expansive account of logic differs in key ways from modern approaches, it is more than a historical curiosity. It provides an alternative way of approaching logic and continues to provide critical insights into contemporary issues and concerns. The main thrust of this article is to explain Aristotle’s logical system as a whole while correcting some prominent misconceptions that persist in the popular understanding and even in some of the specialized literature. Table of Contents 1. Ancient commentators regarded logic as a widely-applicable instrument or method for careful thinking. 2. 3. 4. 1. 2.
Logic Module. SoftOption ® | Instructional publishing for logicians. How to read logical notation. Propositonal Connectives The first set of symbols we are going to introduce you to are called propositional connectives because they combine with one proposition, or combine two propositons, to make a new one. That sounds more complicated than it is. Let me explain. A proposition is simply what is expressed by any ordinary English indicative sentence, like "The cat is on the mat". The simplest case we can consider is when you add the words "It is not the case that …" to "The cat is on the mat" to make a new proposition, "It is not the case that the cat is on the mat". Logicians call this operation negation, and, letting P stand for "The cat is on the mat", "It is not the case that the cat is on the mat" is normally symbolised in one of the four following ways: The above would be read in English as "It's not the case that P", or, more simply, "Not P".
The next four connectives are ones which join two propositions to make a new one. The above would be read in English as "P and Q". PrinterFriendlyViewPack. Table of logic symbols. 11 Recent IPOs At Risk Of Running Out Of CashHis logic compels me to dig in and look at which companies are most vulnerable to a shutdown in capital markets. I've compiled a list of companies that went public in 2013 ... A number of companies on this table have already had to reduce their sales ... The “Proper” Glassware: DON'T Be An IdiotI do know that several of the reps requested that I not tell customers my conclusions, as they felt that the company's reputation precluded having some logic-resistant weasel like me out there counter-pointing their mountains of scientific evidence.
To ... Lois Tilton reviews Short Fiction, late SeptemberLogic belatedly makes him realize this young woman is in fact the natural he was sent to find. But nothing in this universe is that ... Edith looks into the nearest one; inside is a narrow bed, a little table and two chairs. Will Common-Core Testing Platforms Impede Math Tasks? Are Europe's Horrid Crimes Forgiven? Logic 101 - Part 1 - Assertion-Level Logic. Chapter 10: Logic. Gallery For > Symbolic Notation Logic. Symbolic Logic — Sage Reference Manual v6.3: Symbolic Logic. Logic, Truth and Language. Vignette 17Logic, Truth and Language Logic is an indispensable part of our daily lives, just as it is an indispensable part of mathematics.
Whenever we present a reasoned argument on some topic, and whenever we present a proof of a mathematical fact, we are using logic. In both cases, the logic being used follows exactly the same structures. When used in mathematics, the structure of a logical argument is relatively easy to discern, but when embedded in ordinary language, the logic may not be so readily identifiable. Symbolic Logic The use of a symbolic language to represent logical arguments, mathematical or otherwise, can often clarify the logic involved, and help you to determine whether the argument is valid or not. Compound statements can be built from simple statements, by connecting them with various logical connectives. For instance, if P and Q are statements, then the compound statement "P implies Q" would be denoted , while the statement "P and Q" would be denoted Truth Tables is:
Symbolic logic : Carroll, Lewis, 1832-1898. The Age of the Universe, Part 1. The Bible implicitly teaches Why is it that so many scientists choose to ignore the recorded history of the Bible, and instead believe in a vastly inflated age of the universe? The age of the universe is a point of dispute between the Bible and the opinion of the majority of astronomers today. The Bible implicitly teaches us about the age of the universe. In other words, it gives us sufficient information so that we can compute approximately how long ago God created the universe. The Bible teaches that the entire universe was created in six earth-rotation days (Exodus 20:11 ). Many people today would scoff at this claim. Circular reasoning One answer is circular reasoning: many scientists believe the world is old because they believe most other scientists think the world is old.
Many times, the circular reasoning can be cross-disciplinary. The evolution connection The imaginary vast ages are invoked to make these seemingly miraculous leaps feasible. The big-bang connection. Hardegree - Philosophy 110. Symbolic Logic. Symbolic logic is the method of representing logical expressions through the use of symbols and variables, rather than in ordinary language. This has the benefit of removing the ambiguity that normally accompanies ordinary languages, such as English, and allows easier operation. There are many systems of symbolic logic, such as classical propositional logic, first-order logic and modal logic.
Each may have seperate symbols, or exclude the use of certain symbols. Logical Symbols The following table presents several logical symbols, their name and meaning, and any relevant notes. The name of the symbol (under “meaning” links to a page explaining the symbol or term and its use). Note that different symbols have been used by different logicians and systems of logic. Propositions, Variables and Non-Logical Symbols The use of variables in logic varies depending on the system and the author of the logic being presented. Unurthed. Eight diagrams by Lewis Carroll (of Alice’s Adventures in Wonderland) from his 1897 Symbolic Logic, in which Carroll presents a symbolic method of representing propositions and visually deriving the logical outcomes of syllogisms, fallacies, and soriteses. “First, let us suppose that the above [Biliteral] Diagram is an enclosure assigned to a certain Class of Things, which we have selected as our ‘Universe of Discourse,’ or, more briefly, as our ‘Univ’.
“Secondly, let us suppose that we have selected a certain Adjunct, which we may call x, and have divided the large Class, to which we have assigned the whole Diagram, into the two smaller Classes whose Differentiæ are x and not-x (which we may call x’), and that we have assigned the North Half of the Diagram to the one (which we may call… the x-Class), and the South Half to the other (which we may call… the x’-Class). By this formula we can visually represent the following propositions (p34, 35): If “Univ. How to read logical notation. LOGIC: Informal, Symbolic and Inductive - CHHANDA CHAKRABORTI. Introduction to Symbolic Logic. Module: Basic logic. The term "logic" is often used in many different ways. It is sometimes understood broadly as the systematic study of the principles of good reasoning. As such logic is not very different from critical thinking. But sometimes "logic" is understood more narrowly as what we might call "deductive logic".
Roughly speaking, deductive logic is mainly about the consistency of statements and beliefs, as well as the validity of arguments. These are the topics we shall investigate in the following modules. Tutorials in this module Modules on formal logic Formal logic is the study of logic using special symbols and clearly-defined rules of reasoning. Other logic modules Further reading See this page from Joe Lau for a list of textbooks on formal logic.Entries on logic in the Stanford Encyclopedia of Philosophy - These are articles that discuss some of the main issues in the philosophy of logic. Philosophy at RBJones.com. How to Read and Understand Philosophy. Philosophical Disquisitions: Mizrahi on The Argument from Natural Inequality (Part One) Philosophy 101. Category:Philosophy. Stanford Encyclopedia of Philosophy. Philosophy Research Guide | PCC Library. VORTEX Portal.