DOCSLIB.ORG

Three Fallacies of Causation: (1) Post Hoc Ergo Propter Hoc

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Three Fallacies of Causation: (1) Post Hoc Ergo Propter Hoc Induction • Inductive arguments (or simply induction) – Reasoning from particular cases to general conclusions. – In general, supported by statistical analysis or probability. • Causal inductive arguments – Special type of induction in which the premises suggest the conclusion that there is a causal relation between two properties or factors. Characteristics of Inductive Arguments 1. Premises and conclusions are all empirical propositions – Descriptions of matters of fact – Not definitions – Not value judgements. 2. Conclusion is not deductively entailed by the premises 3. Underlying reasoning is that the regularities described in the premises will persist throughout the range described in the conclusion 4. Conclusion is either: (a) that unexamined case will resemble the examined ones (b) the premises support an explanatory causal hypothesis Populations, Sample Size and Bias • Inductive conclusions generalize. We sometimes say that they extrapolate. This just means that inductive conclusions give more information than the information stated in the premises. – For example, “3,356 crows were observed to be black, so all crows are black.” • The conclusion makes a statement about some population or group based on a sample that is smaller that is smaller than the population or group. • For an inductive conclusion to be reasonable, the premises must be a representative sample of the whole population. – An unrepresentative sample is called a biased sample. – Biased sampling is a serious problem, and it often arises unintentionally because of a lack of understanding of the population being sampled. Representative Samples • Evaluating whether or not a sample is representative is difficult and is not straightforward. • It involves a variety of factors, including population size, population homogeneity, and the particular property being sampled. • To understand this more completely TAKE A STATISTICS COURSE before leaving university!!! • That said, three things to keep in mind: 1) Sampling works best when it is a random sample of the total population. Biased sampling leads to misrepresentative inductive generalization. 2) For a population in the millions, a random sample of about 1,000 can provide a perfectly representative picture of a populations. 3) In order to achieve a representative sample, small populations require the sample to be a greater proportion of the population than for larger populations. (Small populations tend to exhibit more variability.) Evaluating Inductive Arguments • By definition, the representativeness of a sample can never be proven in an inductive argument. – Representativeness needs to be evaluated using good sense and good judgment. – In statistics, confidence is the metric used to evaluate this question. – If you don’t know any statistics, then you need to make a good guess about whether the sample is representative of the population being sampled. • Key question: How likely is it that the target population resembles the sample population in the relevant respects? – Same question expressed succinctly: Is the sample population representative? Evaluating Inductive Generalizations Four steps: 1) Identify the sample and target populations as precisely as possible (relying on contextual cues if necessary). 2) Identify the size of the sample. 3) Reflect on the degree of variability of the trait or property which is extrapolated in the conclusion. 4) Reflect on the sampling process. • Have techniques been used to minimize the possibility of bias? • e.g., increasing sample size, stratified sampling, and so forth. Two General Problems with Inductive Arguments • Pseudoprecision – The attempt to make a conclusion seem to be justified by expressing premises with numerical exactness. – “Ignatieff is now 27.6 percentage points ahead of Harper.” • Questionable definition – “Studies prove that over 95% of communication is non-verbal, body language”. Four Inductive Fallacies 1) Hasty inductive generalization: a sample is grossly inadequate so that it is guaranteed to be unrepresentative, and hence, unacceptable. 2) Anecdotal arguments: a common, special case of a hasty inductive generalization, which involves basing an inductive generalization entirely on one (gripping or compelling) story. Again, unrepresentative, and hence, unacceptable. 3) Genetic fallacy: premises offer information about the origins of something, and a conclusion is inferred from this about the thing’s fundamental properties or value. A fallacy of relevance. 4) Fallacies of composition and division: Attributing to the wholes the properties of parts. A fallacy of relevance. Genetic Fallacy • “86% of people in the world believe that God exists, so God must exist.” – This example involves incorrect reasoning from a (presumably) correct fact about the number of people who believe in god to the existence of god. The number of people who believe in god tells us nothing about the putative properties of god. • “America will always be a maverick state. The majority of the Founding Fathers were simply rabble rousers.” • But becareful: In many cases, the origin of a claim is relevant to the evaluation of the acceptability of the claim. – Consider assessment of testimony of texts or experts. Fallacy of Composition and Division • Two sides of the same coin: – The fallacy of composition is committed by arguing that because something is true of members of a group, it is true of a group as a whole. – The fallacy of division is committed by arguing that if something is true of a group, then it is also true of the individuals belonging to the group. Example: Fallacy of Composition • Classic illustration: – “Atoms are not visible to the naked eye, and humans are made up of atoms, so humans are not visible to the naked eye.” • “A US battleship consumes more fuel than a 9.9hp motor boat, so all the battleships consume more fuel than 9.9hp motor boats.” Example: Fallacy of Division • Classic illustration: – “Humans are visible, and humans are made up of atoms, so atoms are visible.” • “Canadians use more electricity per capita than Americans. So, Joe Bloggs in St. John’s uses more power than American, Lee Pippa.” Causal Inductive Arguments • Causal inductive argument: – An inductive argument in which the conclusion is that there is a causal relation between two factors or properties. – E.g., Smoking causes cancer. Green-house-gas emissions from industry cause global climate change. • Causal inductive arguments are ubiquitous: – Arguments in science commonly suppose the identification of causes. • But, this kind of argument leads to a number of distinctive complications and problems. In particular, it is difficult to distinguish between: 1. Constant conjunction, i.e., correlation of factors 2. Necessary connection, i.e., a causal connection between factors Causes • We say things in the form of “C caused E” and “E was caused by C”. – As noted in the discussion of the logical conditional, when we say “If C then E” we tend to suppose (incorrectly) that we are talking about a causal relationship. • That said, the nature of causation, and related problem of verifying causal claims, are vexing questions to philosophers. • Saying that “C caused E” could be explained in, at least, one of three things: 1) Event: C caused E means at least that C happened and then E happened, but in addition that something about C engendered or brought into being E. 2) Counterfactual conditional: C caused E, if and only if, C had not occurred, then E would not have occurred. 3) Law of nature: C caused E, if and only if, it is a law of nature that Cs always cause Es. Five Different Interpretations of ‘C causes E’ 1. C is a necessary condition for E: without C, E would not occur. (The presence of oxygen is a necessary condition for human life.) 2. C is a sufficient condition for E: C is enough by itself to produce E. (Massive heart failure is a sufficient condition for death.) 3. C is a necessary and sufficient condition for E. (Having diabetes is necessary and sufficient for having a malfunctioning pancreas.) 4. C is an especially important causal factor, leading to E: Individually necessary part of a jointly sufficient causal chain. (The carelessly discarded cigarette butt caused the fire.) 5. C is a causal factor, contributing to the likelihood of E. (Smoking causes lung cancer.) Correlation and Cause • The premises of a causal induction typically establish, among a sample group, a correlation between two properties or factors. • The conclusion of a causal induction extrapolates beyond this data in two ways. 1) Like all inductive arguments, it extrapolates that the regularity observed between factors the sample will persist in the target population. 2) It adds the further conjecture that the regularity will persist because there is a causal connection or relation between the factors. • Why does (2) present a special problem? Example: Allergies and Asthma • In recent decades, certain kinds of allergies (e.g., peanut) and asthma have been drastically on the rise in Western nations, though not elsewhere in the world. • The evidence that they are significantly correlated is overwhelming. – If you have these kinds of allergies, then there is a statistically significant increase in the chance that you are prone to develop asthma. – Likewise, if you have asthma, then there is a statistically significant increase in the chance that you are prone to develop these kinds of allergies. • But, is there a causal relation between allergies and asthma? No amount of correlation will distinguish among these three
Load more

Recommended publications
  • CHAPTER XXX. of Fallacies. Section 827. After Examining the Conditions on Which Correct Thoughts Depend, It Is Expedient to Clas
    CHAPTER XXX. Of Fallacies. Section 827. After examining the conditions on which correct thoughts depend, it is expedient to classify some of the most familiar forms of error. It is by the treatment of the Fallacies that logic chiefly vindicates its claim to be considered a practical rather than a speculative science. To explain and give a name to fallacies is like setting up so many sign-posts on the various turns which it is possible to take off the road of truth. Section 828. By a fallacy is meant a piece of reasoning which appears to establish a conclusion without really doing so. The term applies both to the legitimate deduction of a conclusion from false premisses and to the illegitimate deduction of a conclusion from any premisses. There are errors incidental to conception and judgement, which might well be brought under the name; but the fallacies with which we shall concern ourselves are confined to errors connected with inference. Section 829. When any inference leads to a false conclusion, the error may have arisen either in the thought itself or in the signs by which the thought is conveyed. The main sources of fallacy then are confined to two-- (1) thought, (2) language. Section 830. This is the basis of Aristotle's division of fallacies, which has not yet been superseded. Fallacies, according to him, are either in the language or outside of it. Outside of language there is no source of error but thought. For things themselves do not deceive us, but error arises owing to a misinterpretation of things by the mind.
    [Show full text]
  • False Dilemma Wikipedia Contents
    False dilemma Wikipedia Contents 1 False dilemma 1 1.1 Examples ............................................... 1 1.1.1 Morton's fork ......................................... 1 1.1.2 False choice .......................................... 2 1.1.3 Black-and-white thinking ................................... 2 1.2 See also ................................................ 2 1.3 References ............................................... 3 1.4 External links ............................................. 3 2 Affirmative action 4 2.1 Origins ................................................. 4 2.2 Women ................................................ 4 2.3 Quotas ................................................. 5 2.4 National approaches .......................................... 5 2.4.1 Africa ............................................ 5 2.4.2 Asia .............................................. 7 2.4.3 Europe ............................................ 8 2.4.4 North America ........................................ 10 2.4.5 Oceania ............................................ 11 2.4.6 South America ........................................ 11 2.5 International organizations ...................................... 11 2.5.1 United Nations ........................................ 12 2.6 Support ................................................ 12 2.6.1 Polls .............................................. 12 2.7 Criticism ............................................... 12 2.7.1 Mismatching ......................................... 13 2.8 See also
    [Show full text]
  • Logic and Contemporary Rhetoric
    How happy are the astrologers, who are It ain’t so much the things we don’t believed if they tell one truth to a know that get us into trouble. It’s the hundred lies, while other people lose all things we know that ain’t so. credit if they tell one lie to a hundred —Artemus Ward truths. —Francesco Guicciardini Chapter 4 FALLACIOUS REASONING—2 Most instances of the fallacies discussed in the previous chapter fall into the broad fallacy categories questionable premise or suppressed evidence. Most of the fallacies to be discussed in this and the next chapter belong to the genus invalid inference. 1. AD HOMINEM ARGUMENT There is a famous and perhaps apocryphal story lawyers like to tell that nicely captures the flavor of this fallacy. In Great Britain, the practice of law is divided between solici- tors, who prepare cases for trial, and barristers, who argue the cases in court. The story concerns a particular barrister who, depending on the solicitor to prepare his case, arrived in court with no prior knowledge of the case he was to plead, where he found an exceedingly thin brief, which when opened contained just one note: “No case; abuse the plaintiff’s attorney.” If the barrister did as instructed, he was guilty of arguing ad hominem—of attacking his opponent rather than his opponent’s evidence and argu- ments. (An ad hominem argument, literally, is an argument “to the person.”) Both liberals and conservatives are the butt of this fallacy much too often. Not long after Barack Obama was elected to the Senate, Rush Limbaugh repeatedly referred to him as “Obama Osama” when criticizing the senator and the Democrats in general.
    [Show full text]
  • Fallacies in Reasoning
    FALLACIES IN REASONING FALLACIES IN REASONING OR WHAT SHOULD I AVOID? The strength of your arguments is determined by the use of reliable evidence, sound reasoning and adaptation to the audience. In the process of argumentation, mistakes sometimes occur. Some are deliberate in order to deceive the audience. That brings us to fallacies. I. Definition: errors in reasoning, appeal, or language use that renders a conclusion invalid. II. Fallacies In Reasoning: A. Hasty Generalization-jumping to conclusions based on too few instances or on atypical instances of particular phenomena. This happens by trying to squeeze too much from an argument than is actually warranted. B. Transfer- extend reasoning beyond what is logically possible. There are three different types of transfer: 1.) Fallacy of composition- occur when a claim asserts that what is true of a part is true of the whole. 2.) Fallacy of division- error from arguing that what is true of the whole will be true of the parts. 3.) Fallacy of refutation- also known as the Straw Man. It occurs when an arguer attempts to direct attention to the successful refutation of an argument that was never raised or to restate a strong argument in a way that makes it appear weaker. Called a Straw Man because it focuses on an issue that is easy to overturn. A form of deception. C. Irrelevant Arguments- (Non Sequiturs) an argument that is irrelevant to the issue or in which the claim does not follow from the proof offered. It does not follow. D. Circular Reasoning- (Begging the Question) supports claims with reasons identical to the claims themselves.
    [Show full text]
  • 334 CHAPTER 7 INFORMAL FALLACIES a Deductive Fallacy Is
    CHAPTER 7 INFORMAL FALLACIES A deductive fallacy is committed whenever it is suggested that the truth of the conclusion of an argument necessarily follows from the truth of the premises given, when in fact that conclusion does not necessarily follow from those premises. An inductive fallacy is committed whenever it is suggested that the truth of the conclusion of an argument is made more probable by its relationship with the premises of the argument, when in fact it is not. We will cover two kinds of fallacies: formal fallacies and informal fallacies. An argument commits a formal fallacy if it has an invalid argument form. An argument commits an informal fallacy when it has a valid argument form but derives from unacceptable premises. A. Fallacies with Invalid Argument Forms Consider the following arguments: (1) All Europeans are racist because most Europeans believe that Africans are inferior to Europeans and all people who believe that Africans are inferior to Europeans are racist. (2) Since no dogs are cats and no cats are rats, it follows that no dogs are rats. (3) If today is Thursday, then I'm a monkey's uncle. But, today is not Thursday. Therefore, I'm not a monkey's uncle. (4) Some rich people are not elitist because some elitists are not rich. 334 These arguments have the following argument forms: (1) Some X are Y All Y are Z All X are Z. (2) No X are Y No Y are Z No X are Z (3) If P then Q not-P not-Q (4) Some E are not R Some R are not E Each of these argument forms is deductively invalid, and any actual argument with such a form would be fallacious.
    [Show full text]
  • Quantifying Aristotle's Fallacies
    mathematics Article Quantifying Aristotle’s Fallacies Evangelos Athanassopoulos 1,* and Michael Gr. Voskoglou 2 1 Independent Researcher, Giannakopoulou 39, 27300 Gastouni, Greece 2 Department of Applied Mathematics, Graduate Technological Educational Institute of Western Greece, 22334 Patras, Greece; [email protected] or [email protected] * Correspondence: [email protected] Received: 20 July 2020; Accepted: 18 August 2020; Published: 21 August 2020 Abstract: Fallacies are logically false statements which are often considered to be true. In the “Sophistical Refutations”, the last of his six works on Logic, Aristotle identified the first thirteen of today’s many known fallacies and divided them into linguistic and non-linguistic ones. A serious problem with fallacies is that, due to their bivalent texture, they can under certain conditions disorient the nonexpert. It is, therefore, very useful to quantify each fallacy by determining the “gravity” of its consequences. This is the target of the present work, where for historical and practical reasons—the fallacies are too many to deal with all of them—our attention is restricted to Aristotle’s fallacies only. However, the tools (Probability, Statistics and Fuzzy Logic) and the methods that we use for quantifying Aristotle’s fallacies could be also used for quantifying any other fallacy, which gives the required generality to our study. Keywords: logical fallacies; Aristotle’s fallacies; probability; statistical literacy; critical thinking; fuzzy logic (FL) 1. Introduction Fallacies are logically false statements that are often considered to be true. The first fallacies appeared in the literature simultaneously with the generation of Aristotle’s bivalent Logic. In the “Sophistical Refutations” (Sophistici Elenchi), the last chapter of the collection of his six works on logic—which was named by his followers, the Peripatetics, as “Organon” (Instrument)—the great ancient Greek philosopher identified thirteen fallacies and divided them in two categories, the linguistic and non-linguistic fallacies [1].
    [Show full text]
  • Part/Whole Fallacies
    11 If a person dislikes someone else it's ciousness that may be involved in such argu­ lLkely that he will want to have nothing to ments is to be found in the fact that people do. not only with him, but also with the sorts are inclined to consider thoughts and ideas as of things that the other person likes. For being like personal possessions. And since example if Jones dislikes Smith and Smith many people want to distance themselves from sports a moustache and likes to wear tweed the personal posseSSions of those they dislike 'ackets, chances are that Jones will avoid and surround themselves with possessions simi­ ~weed jackets and moustaches. Not only will lar to the possessions of those that they people distance themselves from the sorts of admire, they also want to distance themselves th~ngs their enemies like they will also dis­ from the beliefs (any belief) of those they tance themselves from their thoughts and ideas. dislike and accept the beliefs of those they If 3mith is in favour of capital punishment admire. And of course if anyone were to ig­ for murder and a champion of free enterprise, nore or accept a belief for this sort of rea­ chances are that Jones will be opposed to son he would be reasoning (to the extent that cap~tal punishment and to free enterprise. he could be said to be reasoning) fallaciously . ...'Co FOOTNOTE ~" The same is also true of groups. Fascists were inclined to wear black shirts and cut II.M. Copi, Introduction to Logic (5th their hair short while Communists were in­ ed.), f.1acmillan, p.
    [Show full text]
  • Breaking Down the Invisible Wall of Informal Fallacies in Online
    Breaking Down the Invisible Wall of Informal Fallacies in Online Discussions Saumya Yashmohini Sahai Oana Balalau The Ohio State University, USA Inria, Institut Polytechnique de Paris, France [email protected] [email protected] Roxana Horincar Thales Research & Technology, France [email protected] Abstract more appropriate. Fallacies are prevalent in public discourse. For example, The New York Times la- People debate on a variety of topics on online beled the tweets of Donald Trump between 2015 platforms such as Reddit, or Facebook. De- bates can be lengthy, with users exchanging and 2020 and found thousands of insults addressed a wealth of information and opinions. How- to his adversaries. If made in an argument, an in- ever, conversations do not always go smoothly, sult is an ad hominem fallacy: an attack on the and users sometimes engage in unsound argu- opponent rather than on their argument. In pri- mentation techniques to prove a claim. These vate conversations, other types of fallacies might techniques are called fallacies. Fallacies are be more prevalent, for example, appeal to tradition persuasive arguments that provide insufficient or appeal to nature. Appeal to tradition dismisses or incorrect evidence to support the claim. In calls to improve gender equality by stating that this paper, we study the most frequent falla- cies on Reddit, and we present them using “women have always occupied this place in soci- the pragma-dialectical theory of argumenta- ety”. Appeal to nature is often used to ignore calls tion. We construct a new annotated dataset of to be inclusive of the LGBTQ+ community by stat- fallacies, using user comments containing fal- ing “gender is binary”.
    [Show full text]
  • Critical Reasoning and Writing
    CRITICAL REASONING AND WRITING Noah Levin Golden West College Book: Critical Reasoning and Writing (Levin et al.) Cross Library Transclusion template('CrossTransclude/Web',{'Library':'chem','PageID':170365}); TABLE OF CONTENTS PREFACE 1: INTRODUCTION TO CRITICAL THINKING, REASONING, AND LOGIC What is thinking? It may seem strange to begin a logic textbook with this question. ‘Thinking’ is perhaps the most intimate and personal thing that people do. Yet the more you ‘think’ about thinking, the more mysterious it can appear. Many people believe that logic is very abstract, dispassionate, complicated, and even cold. But in fact the study of logic is nothing more intimidating or obscure than this: the study of good thinking. 1.1: PRELUDE TO CHAPTER 1.2: INTRODUCTION AND THOUGHT EXPERIMENTS- THE TROLLEY PROBLEM 1.3: TRUTH AND ITS ROLE IN ARGUMENTATION - CERTAINTY, PROBABILITY, AND MONTY HALL 1.4: DISTINCTION OF PROOF FROM VERIFICATION; OUR BIASES AND THE FORER EFFECT 1.5: THE SCIENTIFIC METHOD 1.6: DIAGRAMMING THOUGHTS AND ARGUMENTS - ANALYZING NEWS MEDIA 1.7: CREATING A PHILOSOPHICAL OUTLINE 2: LANGUAGE - MEANING AND DEFINITION Rational people ought to concede he was right about one thing: many disagreements stem from linguistic problems. To resolve this, we simply (though it’s not actually simple) must use language clearly and precisely. If we eliminate all linguistic issues, then we’re left with the more meaningful philosophical problems, and real arguments can now happen since we know exactly what we’re talking about. 2.1: TECHNIQUES OF DEFINING- “SEMANTICS” VS “SYNTAX” AND AVOIDING MORE AMBIGUITY 2.2: CRITERIA FOR FRAMING DEFINITIONS- IT’S ALL ABOUT CONTEXT AND AUDIENCE 2.3: DEFINING TERMS APPROPRIATELY 2.4: COGNITIVE AND EMOTIVE MEANING - ABORTION AND CAPITAL PUNISHMENT 2.5: FUNCTIONS OF LANGUAGE AND PRECISION IN SPEECH 2.6: DEFINING TERMS- TYPES AND PURPOSES OF DEFINITIONS 3: INFORMAL FALLACIES - MISTAKES IN REASONING What is a fallacy? Simply put, a fallacy is an error in reasoning.
    [Show full text]
  • Fallacy of Division and Composition Examples
    Fallacy Of Division And Composition Examples Sherwin often edulcorating sublimely when accrued Haydon dwell craftily and sinks her osteophytes. Alden signposts transitionally if educative Owen legalised or sleeve. Roman Socrates try that kindness salt irenically and polka acrogenously. While the same claim is not to get people into examples of fallacy division and composition writing together because this fallacy one of Another question remains were all means by merely makes this sort out that some alternative when a population must be true although authority might use cookies. Overview of the Fallacy of Division? Sometimes classified as a fallacy of ambiguity. Examples of the Logical Fallacy of Composition Exception. The test is bogus! Who says there always no fallacies? The electron gun shoots out beams that fact certain pixels on the screen. Cambridge university press. It is held accountable for segments of division fallacy of and composition examples try to other, kings who wanted to provide harmful events. The fallacy fallacy consists of composition of informal logicians of reasoning proposed in the. This technology treadmill comes about because in the face of lower prices, Fallacies of Unacceptable Premises, the difference is what feature is being attributed to the parts and wholes. Fallacies. Learn another new schedule every day. Fallacy Of Composition Fallacy Of Division Fallacy Of The. Such an assumption is getting wrong usage can save easy shown in examples -- The Japanese eat is great deal. How to do not consider the sorites paradox can just remember, but it says so examples of and fallacy division is smart and illustrated, i take to.
    [Show full text]
  • Fallacies of Reasoning
    Palm Beach Atlantic University Center for Writing Excellence Fallacies of Reasoning TYPES OF FALLACIES The logician S. Morris Engel proposes in his book Without Good Reason (2000) that all fallacies of reasoning can be divided into these three categories: 1. Ambiguity: the reasoning fails because of at least one crucial ambiguity, either in the premises or in the conclusion. 2. Presumption: the reasoning fails because of an erroneous presumption embedded in the argument. 3. Relevance: the reasoning fails because it depends on a factor that is in fact irrelevant to the question under consideration. Fallacies of Ambiguity Ambiguity: A sign reads, “Old Cow Pasture.” Does it mark a pasture for old cows, or an old pasture for cows of any age? This one is a simple example of ambiguity on the level of language. It may be cleared up by a simple restatement. Here is a more complex example: Both of the following assertions are commonly believed in our society: People have equal rights. The right to own property is a basic right. But is the following conclusion valid? Therefore, everyone has equal property rights. Most Americans consider it valid if the conclusion is interpreted as “an equal right to own property.” Most consider it invalid and in fact revolutionary if interpreted as “a right to ownership of equal property.” Division: When we argue that a characteristic of a group necessarily applies to all members or to any particular individual member of that group, we commit the fallacy of division. Example: Group property: The average American family has 1.8 children.
    [Show full text]
  • Introduction to Informal Logical Fallacies Course Outline
    Introduction to Informal Logical Fallacies Course Outline Day 1 Day 2 Day 3 ● Housekeeping ● Fallacies ● Fallacies ● Introduction to Logic ○ Values and Functions ○ Abduction, Induction, Deduction ○ Validity ○ Soundness ● Language to Logic Scope Informal Logic Set of techniques used to evaluate arguments made in everyday language. Formal Logic Set of formulae used to assign truth values to symbolic equations. Scope Informal Logic Set of techniques used to evaluate arguments made in everyday language. Formal Logic Set of formulae used to assign truth values to symbolic equations. Truth Values A ~A True False False True Logical Functions A truth table defines all possible combinations of truth values for Assertions A, B. A B A Or B A And B If A Then B True True True True True True False True False False False True True False True False False False False True Logical Functions Assertions A,B have four possible combinations of truth values. Given n n arguments, there are 2 possible truth value combinations. A B A Or B A And B If A Then B True True True True True True False True False False False True True False True False False False False True Logical Functions Function columns show the value of the function given the truth values of its arguments. A B A Or B A And B If A Then B True True True True True True False True False False False True True False True False False False False True Logical Functions “Or” is false only when both arguments are false. A B A Or B A And B If A Then B True True True True True True False True False False False True True False True False False False False True Logical Functions “And” is true only when both arguments are true.
    [Show full text]