Thinking Well - Lavin - Edition 4.0 PDF Textbook

Thinking Well A Creative Commons Logic and Critical Thinking Textbook Authored and Edited by Andrew Lavin With pages from Matthew J. Van Cleave’s Introduction to Logic and Critical Thinking and Matthew Knachel’s Fundamental Methods of Logic and Jason Southworth and Chris Swoyer’s Critical Reasoning: A User’s Manual and inserts on Truth and Intellectual Vices by Michael Fitzpatrick Edition 3.2.3 – Spring, 2022 Licensed under a Creative Commons Attribution 4.0 International License This text made possible by an Open Educational Resources Grant through Butte College and the Textbook Affordability Project at CSU, Chico. 2 This textbook’s first edition was funded by grants from Butte College and CSU, Chico. Since then, I have continued to put unfunded work into improving it. This text is free and always will be, but if you are using it and enjoying it, a donation would be much appreciated and would help fund future improvements to this free resource. Please consider a donation of somewhere around $5 from each reader to support the project. To reiterate, though, this is a free textbook and no donation is necessary. Places to send donations: Paypal: [email protected] Venmo: @Lavin-Andrew 3 Table of Contents Table of Contents..................................................................................................................................................... 4 Chapter 1 - Basic Concepts................................................................................................................................ 10 1.1 Vital Course Concepts............................................................................................................................. 11 1.1.1 Rhetoric vs. Reasoning..................................................................................................................... 12 1.1.2 Propositions........................................................................................................................................ 13 1.1.3 Complex Propositions...................................................................................................................... 13 1.1.4 Inferences or Arguments................................................................................................................. 15 1.1.5 Premises and Conclusions............................................................................................................... 16 1.1.6 Factual Claims and Inferential Claims........................................................................................ 20 1.1.7 On Truth.............................................................................................................................................. 22 1.1.8 The Principle of Charity.................................................................................................................. 25 1.2 Kinds of Inferences................................................................................................................................... 26 1.2.1 Validity............................................................................................................................................... 27 1.2.2 Truth, Validity, Soundness.............................................................................................................. 28 1.2.3 Truth, Strength, Cogency................................................................................................................ 29 Chapter 1 - Key Terms................................................................................................................................... 30 1.3 Chapter One Exercises............................................................................................................................ 31 1.3.1 Rhetoric vs. Reasoning..................................................................................................................... 31 1.3.2 Propositions vs. Non-Propositions................................................................................................. 31 1.3.3 Breaking down complex propositions......................................................................................... 31 1.3.4 Argument or Non-Argument?........................................................................................................ 32 1.3.5 Premise and Conclusion Indicators............................................................................................... 33 1.3.6 Factual Claims and Inferential Claims........................................................................................ 33 1.3.7 Charitable Interpretations............................................................................................................. 33 Chapter 2 - Language, Meaning, and Definition......................................................................................... 35 2.1 Breakdown of meaning:.......................................................................................................................... 35 2.1.1 Vagueness.......................................................................................................................................... 36 2.1.2 Ambiguity........................................................................................................................................... 36 2.2 How does meaning work? Definition and Concepts........................................................................ 37 2.2.1 Intension and Extension................................................................................................................... 38 2.2.2 Types of Definitions......................................................................................................................... 40 2.2.3 Fallacy of Equivocation.................................................................................................................. 42 2.3 Necessary and Sufficient Conditions................................................................................................... 45 2.3.1 Necessary Conditions...................................................................................................................... 45 4 2.3.2 Sufficient Conditions........................................................................................................................ 46 2.3.3 Necessary and Sufficient Conditions........................................................................................... 47 2.3.4 Neither................................................................................................................................................ 48 2.3.5 Background Assumptions................................................................................................................ 48 2.3.6 Who Cares?....................................................................................................................................... 48 Chapter 2 - Key Terms................................................................................................................................... 50 2.4 Chapter Two Exercises............................................................................................................................ 50 2.4.1 Vagueness vs Ambiguity................................................................................................................ 50 2.4.2 Intensional Meaning and Extensional Meaning........................................................................ 51 2.4.3 Types of Definitions......................................................................................................................... 51 2.4.4 Fallacy of Equivocation.................................................................................................................. 52 2.4.5 Necessary and Sufficient Conditions........................................................................................... 52 Chapter 3 - Argument Mapping....................................................................................................................... 53 3.1 The Basics.................................................................................................................................................... 53 3.1.1 Conjoint vs. Independent Support................................................................................................ 54 3.1.2 Terminology....................................................................................................................................... 58 3.1.3 Examples............................................................................................................................................ 62 3.2 Missing Assumptions................................................................................................................................. 65 3.2.1 Identifying Hidden Assumptions................................................................................................... 65 3.2.2 Mapping Hidden Assumptions...................................................................................................... 68 3.3 Objections................................................................................................................................................... 70 3.4 More Complex Arguments..................................................................................................................... 71 3.5 Argument Mapping Conclusion............................................................................................................. 74 3.6 Beginning to Evaluate Arguments......................................................................................................... 74 Chapter 3 Key Terms...................................................................................................................................... 77 3.7 Chapter Three Exercises......................................................................................................................... 77 3.7.1 Conjoint vs Independent Support................................................................................................. 78 3.7.2 Terminology....................................................................................................................................... 78 3.7.3 Simple Argument Maps.................................................................................................................. 79 3.7.4 More Complex Argument Maps................................................................................................... 80 3.7.5 Even More Complex Argument Maps......................................................................................... 80 3.7.6 Hidden Assumptions......................................................................................................................... 81 3.7.7 Mapping Hidden Assumptions...................................................................................................... 82 3.7.8 Identifying Types of Objections................................................................................................... 82 3.7.9 Mapping Objections........................................................................................................................ 83 3.7.10 Hidden Assumptions and Objections........................................................................................ 84 5 Chapter 4 – Intellectual Virtues and Vices..................................................................................................... 85 4.0 Note for Instructors................................................................................................................................... 85 4.1 What are Virtues and Vices?................................................................................................................ 85 4.2 Some Intellectual Virtues......................................................................................................................... 86 4.2.1 Curiosity.............................................................................................................................................. 86 4.2.2 Intellectual Honesty.......................................................................................................................... 87 4.2.3 Intellectual Humility.......................................................................................................................... 87 4.2.4 Charity................................................................................................................................................ 89 4.3 Some Intellectual Vices............................................................................................................................ 89 4.3.1 Vices of Relevance........................................................................................................................... 90 4.3.2 Vices of Presumption..................................................................................................................... 104 4.6 Chapter Four Exercises.......................................................................................................................... 108 4.5.1 Vices of Relevance......................................................................................................................... 108 4.5.3 Vices of Presumption..................................................................................................................... 109 4.5.4 General Vices................................................................................................................................. 109 Chapter 5a - What is Logic?........................................................................................................................... 112 5a.1 Core Concepts.................................................................................................................................. 113 Chapter 5b - Categorical Logic..................................................................................................................... 115 5b.1 The Basics............................................................................................................................................... 115 5b.1.1 Standard Form............................................................................................................................. 115 5b.1.2 Quality and Quantity................................................................................................................. 117 5b.1.3 Square of Opposition................................................................................................................. 117 5b.2 Venn Diagrams..................................................................................................................................... 118 5b.2.1 Using Venn Diagrams for Inferences...................................................................................... 121 5b.2.2 Conversion, Obversion, Contraposition.................................................................................. 123 5b.3 Categorical Syllogisms....................................................................................................................... 124 5b.4 Proving the validity of immediate inferences............................................................................... 132 5b.4.1 Square of Opposition................................................................................................................. 132 5b.4.2 Other Immediate Inferences..................................................................................................... 135 5b.5 Key Terms............................................................................................................................................... 137 Chapter 6 - Propositional Logic...................................................................................................................... 138 6.1 Logical Entailment................................................................................................................................... 138 6.2 Propositions and their Connectors...................................................................................................... 139 6.2.1 “And” AKA Conjunction................................................................................................................. 141 6.2.2 “Not” AKA Negation..................................................................................................................... 143 6.2.3 “Or” AKA Disjunction..................................................................................................................... 144 6 6.2.4 “If…then…” AKA Implication AKA Hypothetical AKA Conditional.................................. 145 6.2.5 “If and only if…” AKA Equivalence.......................................................................................... 147 6.2.6 Logical Words and Operators Summary................................................................................ 148 6.3 More Thoughts on Symbolization....................................................................................................... 149 6.3.1 The Grammar of Propositional Logic........................................................................................ 149 6.3.2 Tricky Conditionals......................................................................................................................... 151 6.3.3 Necessary and Sufficient Conditions......................................................................................... 153 6.3.4 Tricky Ands, Nots, and Nors........................................................................................................ 154 6.3.5 Exclusive vs. Inclusive “Or”........................................................................................................... 155 6.3.6 Framing Words............................................................................................................................... 156 6.4 Logical Operators as Truth Functions................................................................................................ 161 6.4.1 What’s a Truth Function?.............................................................................................................. 161 6.4.2 What’s a Truth Table?.................................................................................................................. 163 6.4.3 Definitions of Logical Operators................................................................................................ 164 6.4.4 Computing Truth Values................................................................................................................ 165 6.5 Logical Analysis using Truth Tables.................................................................................................... 169 6.5.1 Building a Truth Table................................................................................................................... 170 6.5.2 Solving a Truth Table.................................................................................................................... 174 6.5.3 Analyzing a Truth Table............................................................................................................... 178 6.5.4 The Reverse Truth Table Method............................................................................................... 181 Chapter 6 Conclusion............................................................................................................................... 186 6.6 Chapter Six Exercises............................................................................................................................ 186 6.6.1 Basic Symbolization....................................................................................................................... 186 6.6.2 More Complex Symbolization.................................................................................................... 187 6.6.3 Framing Words............................................................................................................................... 187 6.6.4 Main Operators.............................................................................................................................. 188 6.6.5 Computing Truth Values................................................................................................................ 188 6.6.6 Truth Tables Classify..................................................................................................................... 189 6.6.7 Truth Tables Compare.................................................................................................................. 189 6.6.8 Truth Tables Validity..................................................................................................................... 189 Chapter 7 - Natural Deduction....................................................................................................................... 190 7.1 What is it?................................................................................................................................................ 190 7.2 Basic Rules of Implication...................................................................................................................... 193 7.2.1 How to read the rules of implication........................................................................................ 193 7.3 More Rules of Implication..................................................................................................................... 202 7.4 Rules of Replacement............................................................................................................................ 207 7 7.5 More Rules................................................................................................................................................ 213 7.6 Why Learn Natural Deduction?.......................................................................................................... 215 7.7 Conversational Implicature................................................................................................................... 215 7.8 Chapter Seven Exercises...................................................................................................................... 218 7.8.1 Identifying Instances of the Rules............................................................................................... 218 7.8.2 Using the First 4 Rules................................................................................................................... 218 7.8.3 Using the First 8 Rules................................................................................................................... 219 7.8.4 Using all of the Rules of Implication and Replacement........................................................ 219 Chapter 8 - Inductive Reasoning: hypothetical, causal, statistical, and others................................... 221 8.1 Hypothetical Reasoning........................................................................................................................ 221 8.1.1 The Logic of Hypothetical Reasoning........................................................................................ 223 8.1.2 Abductive Reasoning..................................................................................................................... 225 8.1.3 Confirmation Bias........................................................................................................................... 226 8.2 Causal Reasoning................................................................................................................................... 227 8.3 Statistical Generalization..................................................................................................................... 228 8.3.1 Selection Bias.................................................................................................................................. 229 8.3.2 Selective Reporting........................................................................................................................ 231 8.4 Analogical Reasoning............................................................................................................................ 231 8.5 Fallacies of Induction............................................................................................................................. 240 8.5.1 Appeal to Ignorance..................................................................................................................... 240 8.5.2 Slippery Slope................................................................................................................................ 243 8.5.3 Texas Sharpshooter....................................................................................................................... 244 8.5.4 False Cause...................................................................................................................................... 247 8.5.5 Hasty Generalization.................................................................................................................... 248 8.6 Chapter 8 Exercises............................................................................................................................... 249 8.6.1 Fallacies of Induction..................................................................................................................... 249 Chapter 9 - Ethical Reasoning and Evaluation............................................................................................ 251 9.1 Ethics vs. Morality................................................................................................................................... 251 9.2 Universalism vs. Relativism.................................................................................................................... 251 9.3 Three Basic Systems of Morality......................................................................................................... 252 9.3.1 Aristotelian Ethics or more broadly “Virtue Ethics”................................................................ 254 9.3.2 Deontology/Kantianism................................................................................................................ 255 9.3.3 Consequentialism/Utilitarianism................................................................................................. 257 9.4 Levels of Evaluation............................................................................................................................... 257 9.4.1 Material evaluation....................................................................................................................... 258 9.4.2 Agential evaluation....................................................................................................................... 258 8 9.4.3 Structural evaluation..................................................................................................................... 258 9.4.4 A few upshots.................................................................................................................................. 260 Chapter 10 - Mental Heuristics and Biases................................................................................................. 261 10.1 Classical Economics.............................................................................................................................. 261 10.2 Heuristics................................................................................................................................................. 262 10.2.1 Representativeness...................................................................................................................... 263 10.2.3 Anchoring and Adjustment......................................................................................................... 265 10.2.2 Availability.................................................................................................................................... 265 10.2.4 Availability and Online Algorithm Bubbles.......................................................................... 266 10.2.5 Upshots........................................................................................................................................... 267 Chapter 11 – Identifying Good Sources of Information.......................................................................... 269 11.1 Sources of Information........................................................................................................................ 269 Does it have a real author?.................................................................................................................... 269 Is it biased?................................................................................................................................................. 269 Is it thoughtful and honest?...................................................................................................................... 270 Who funded it?.......................................................................................................................................... 271 Does it try to get you to distrust “the others”?................................................................................... 271 11.2 Specific Stories or Information......................................................................................................... 271 Is it Current? Is it Local?............................................................................................................................ 271 What are others saying about it?......................................................................................................... 271 Is it Plausible?............................................................................................................................................. 272 Is it convenient?.......................................................................................................................................... 272 Is it possible that it’s a Deepfake?........................................................................................................ 272 11.3 Sources for this chapter...................................................................................................................... 272 Reading and Guides................................................................................................................................ 272 Relevant Podcast Episodes..................................................................................................................... 273 Conclusion – Intellectual Honesty, Intellectual Humility, and Charity..................................................... 274 9 Chapter 1 - Basic Concepts The most important thing we do as human beings is learn how to think. This is important in two senses of the word: it’s important to human beings because it is the most distinctively unique fact about our species—we think rationally and abstractly—but it’s also important because it the most wide reaching capacity we have—it touches virtually all aspects of our lives. Having a heart that pumps blood or a body capable of certain physical activities might be more fundamental meaning more crucial to simply surviving, but thinking underlies a broad range of activities without which we would be living less than full human lives. The common title of this course is “Logic and Critical Thinking.” So, we can think about the course as having two main components: the study of formal logic and the study of the tools and strategies of critical thinking. This text is structured in a bit of a “sandwich”. Units on critical thinking and then formal logic, and then units on more critical thinking topics. First, Logic. We’ll define logic more fully later, Oh no! Not math! I’m no good at math. but for now: logic is a sort of reasoning that is mathematical in its precision and proofs. It’s like Don’t worry, dear student. Logic is more math with words and concepts, in a sense. straightforward than a lot of the complex concepts that get discussed in math classes. Logic is formal in that it is the science of the Even better, all of logic can be broken down structure of reasoning rather than the content. into simple, step-by-step processes that a Logic isn’t—for example—interested in whether computer can do. You just need to follow the you’re reasoning about puppies, unicorns, or steps carefully and you’ll be guaranteed the international trade agreements; it is instead right answer every time. There’s no magic to interested in how you’re reasoning about these it, no special skills or abilities needed. You things and about the patterns or structures you just need to follow directions carefully and adhere to in your reasoning. Some patterns of put a bit of work into it. reasoning are good in that they can help us truly demonstrate or prove our conclusions, whereas others are not good in that even if the conclusion is true, it will be an accident that we happen to believe what is true—we won’t believe what is true because the argument guided us there. Next, let’s get a bit of a definition of critical thinking going. Critical thinking is primarily the ability to think carefully about thinking and reasoning—to have the ability to criticize your own reasoning. ‘Criticize’ here isn’t meant in the sense of being mean or talking down or making fun of. Instead, I mean the word in the sense of, for example, how a coach might take a critical stance toward her players’ skills—he throws high every time, she doesn’t lead with her foot, they ride too forward in the saddle, etc. ‘Critical’ here means something more like ‘reflective’ or ‘careful’ or ‘attention to potential errors’. So to engage in critical thinking is to engage in self-critical, self-reflective, self-aware thinking and reasoning—thinking and reasoning aimed at self-improvement, at truth, and at careful, deliberate, proper patterns of reasoning. There are many definitions of what critical thinking is, but here’re my thoughts: 10 Separating the thinker from the position: being able to discuss a position without attacking or judging the person holding the position, without getting caught up in our own attachment to the position or its antithesis, and without having our identities Active curiosity and wrapped up in a particular viewpoint or creative thinking: opinion. Knowing oneself not believing that things are simple and settled, enough to avoid biases being willing to go the and errors of thought: next step and think being aware of the flawed about all of the possible patterns of reasoning we’re Critical thinking disposed to engage in, positions and arguments before settling into a consists of at least being aware of cognitive position. these features biases and mental heuristics (rough rules that work well enough to survive but don’t work in many cases) that Understanding we’re prone as a species to argumentation, reasons, and have, all in the interest of evidence: counteracting these biases thinking carefully about and flaws. thinking, about arguments and positions Intellectual honesty, humility, and charity: very important: being honest about what we know and how we know it, what evidence we have and what questions are not yet settled; being humble in recognizing the vast number of things we don’t yet know or understand and in recognizing how very difficult it is to truly know anything at all and so recognizing that the standards are high and we most of the time don’t meet them (and that’s okay); and being charitable or having the disposition to attribute the best intentions and most sophisticated positions and arguments that we can imagine to our opponents in arguments. As you can see, being a critical thinker involves training yourself to have a lot of good habits and dispositions. It involves developing rational virtues so that when the time comes to think about something complex, you are naturally disposed to think well. It doesn’t happen overnight and it certainly doesn’t come for free—no one is born with it. We all need to train ourselves and educate ourselves to stay guarded against errors in reasoning. 1.1 Vital Course Concepts Have you ever been in a conversation with someone and found that they were mischaracterizing what you were saying, bombarding you with seemingly unrelated information, giving up on reasoning at all and instead simply blustering? It feels like you want to figure out what is true and really try to understand the issue you’re discussing, but the person you’re talking to just wants to make some talking points or get a few shots in before plugging their ears and singing to 11 themselves. Like having the discussion, to them, is just a game that they want to win at any cost. I’ve been there, loads of times. Not fun. 1.1.1 Rhetoric vs. Reasoning In ancient Greece one of the most famous Western philosophers of all time—Socrates—noticed that there were different ways that people came to believe what they believe. Some people listened to the poets, the oracles, the playwrights, etc. for truth. They looked to Tradition to find out what they should believe, how they should act, what reality was like, etc. Think Homer: they read the Iliad and the Odyssey and took life lessons from its pages. Others found that by manipulating those around them they could come to win arguments reliably. They found that discussions were sort of like jousting matches in that the person who won the argument was usually the person who was the quickest wit and had the best tools at their disposal. They didn’t care about what was true, or good, or right. They only cared about winning and about Rhetoric. They were the lawyers and politicians of their day (not to say that there aren’t good, honest, principled lawyers and politicians). They were called Sophists. Socrates himself preferred a different route he called Dialectic, where a person made a claim and then others asked critical questions about their claim or position until they found themselves confused and unsure of what to believe. This process of breaking down our presuppositions helped us move past false confidence. The closer we move toward what was called aporia—a state of “impasse” where we’re not sure which direction to take— the more we’re able to consider what the truth is about from all of the baggage we carry from our childhood, from previous conversations, from popular media, etc. Sophists are interested in good rhetoric. Good rhetoric is important. In fact, we have whole courses and sometimes whole departments devoted to good rhetoric. We need to find ways of expressing our ideas in a way that gets the right reaction from our intended audiences. Philosophers, like Socrates, are interested in good reasoning or argumentation. We philosophers (and I count myself among them) care about rhetoric only to the extent that we’re not misleading our audiences or turning them off of our position without good reason. We want to explore what the best reasons are for accepting or rejecting different positions. We don’t want to win an argument if we’re wrong. We’re ready and willing to revise our beliefs if we find out that we don’t have good reason for accepting them. With this in mind, we can posit a distinction between rhetoric and reasoning. Two things you’ll be worried about to different degrees in different situations. Sometimes you’ll care a lot about how your audience will receive your arguments and other times you’ll care more about simply getting it right. Rhetoric: Is primarily concerned with the impact of an argument or piece of writing or speech or the like. How effectively is it producing the effect I want in my audience? Reasoning: is concerned with insight, discovery, truth, and understanding. The goal isn’t to produce a certain impact in the audience, but instead to collectively discover what the best position on a given question is or what the objective merits and demerits of an argument or position are. 12 This is a course about argumentation and reasoning, we’ll be interested in Rhetoric only insofar as it gets in the way of good, honest, clear argumentation. (That isn’t to say that rhetoric always gets in the way. Sometimes, in fact, good rhetoric can amplify good reasoning. Good reasoning is dry and inaccessible without good rhetoric!) 1.1.2 Propositions So we’re interested in how arguments work. What makes them tick? What makes the good ones good and the bad ones bad? How can I make a series of statements and then think that I’ve “proven” or “demonstrated” a further statement? In order to understand arguments, we’ll have to start with the fundamental building blocks: propositions or statements: Propositions are statements that can be true or false. This is the fundamental concept of the course. Take the time to understand it clearly. If a statement can be true or false, then it’s a proposition. Note that a sentence and a proposition aren’t the same thing. Not all sentences are propositions. When we reason, we make statements or consider statements and then we back those statements up with reasons and evidence, draw out the implications and consequences of those statements and so on. There’s a technical distinction between a statement and a proposition, but we will use them interchangeably here. For our purposes, a statement and a proposition are the same thing. Some sentences don’t express propositions at all. This means that they can’t be true or false. You can’t disagree with them, you can’t argue about whether they’re right or wrong, you can’t question them. Not because they’re indubitable (un-doubt-able), but simply because it wouldn’t make any sense to disagree with them! If I said, “Can we please go out to dinner tonight?” you can’t respond with disagreement, saying “I don’t know about that claim, it doesn’t sound right to me.” I haven’t made a statement, so you can’t say I’ve stated something false. Similarly, if you say “wash your hands before dinner” I can’t respond with “that’s false.” It wouldn’t make any sense. These types of sentences don’t express propositions. They’re non-propositions. Non-Propositions: Sentences that aren’t statements about matters of fact (or fiction). They don’t make a claim that can be true or false. They: Exhort: Let’s go get drinks! Let us go hiking on Tuesday! Command: Go to the store later to buy me some cheese. Don’t do that. Plead/Request: Would you please stop that? Please read me a bedtime story! Question: What is the capital of the UAE? How much do the pineapples cost? Perform: I hereby adjourn this meeting! I pronounce you husband and wife! 1.1.3 Complex Propositions Okay, back to propositions. Sometimes propositions are simple, and sometimes they are complex. Meaning sometimes they can be broken down into simpler propositions and sometimes they’re already as simple as they could be. 13 Simple Propositions have no internal logical structure, meaning whether they are true or false doesn’t depend on whether a part of them is true or false. They are simply true or false on their own. – The GDP of the United States is $5. – The Sky is Blue. – Freedom should be the highest value of the state for its citizens. – Harry Potter wears glasses. Complex Propositions have internal logical structure, meaning they are composed of simple propositions. Whether they are true or false depends on whether their parts are true or false. – The GDP of the United States is either $5 or it is $12. – True if the GDP is $5 or if the GDP is $12 – The Sky is Blue, but it doesn’t look blue to me right now. – True if the Sky is blue and if it doesn’t look blue to me right now. – If freedom should be the highest value of the state for its citizens, then we should promote it in our laws and policies. – True if it can’t be that “freedom should be the highest value of the state for its citizens” is true while “we should promote freedom in our laws and policies” is false. In short, each proposition is either a simple proposition or a combination of simple propositions. Simple propositions are true or false just based on how the world is, whereas complex propositions are true or false just based on whether or not the simple propositions that make them up are true or false. I am an elephant …is a false proposition if I say or think it. It’s false because of the way the world is—I am not in fact an elephant. I am an elephant or I am a human …is a true complex proposition if I say or think it. The way “or” propositions work is that only one of the simple propositions needs to be true. The left proposition “I am an elephant” is false, but the right one “I am a human” is true. So, since complex propositions depend on their parts for their truth values, the complex proposition as a whole is true! We can learn to break propositions down into parts. This is an important skill to grasp so that you can understand all of the separate claims someone is making in a single sentence. People often make a host of claims in a single sentence, and you’ll want to be able to separate them. Breaking down complex propositions usually involves identifying the little sentences that make up a complex sentence. So instead of saying “Bobby doesn’t want to play basketball, but he does want to play videogames.” I notice that the “but” connects two independent thought: Bobby doesn’t want to play basketball. Bobby wants to play videogames. “Either you know everything there is to know, or I’m a monkey’s uncle and you’re not as smart as I thought you were.” Breaks down into three separate propositions since there’s an “either…or…” and also an “and”. Breaking down Propositions: separate out the statements that can be independently true or false. It’s a bit tricky and interpretive, but we’re just trying to grasp the basic concept here. 14 We’ll get into this more later in the course, but for now it’s good to have some facility with the basic idea: some propositions don’t have parts that can be true or false independently, while others do. We use words like ‘and’, ‘or’, ‘Either…or…’, ‘but’, and ‘if…then…’ to identify multiple independent propositions. Marcos is taking four courses this semester and working in his parents’ store 20 hours a week. o Marcos is taking four courses this semester. o Marcos is working in his parents’ store 20 hour a week this semester. Frankie, Johnny, and Luigi went to dinner o Frankie went to dinner. o Johnny went to dinner. o Luigi went to dinner. Karen is smart but not very motivated to do well in school or to try to find a job that uses her talents. o Karen is smart o Karen is not very motivated to do well in school. o Karen is not very motivated to try to find a job that uses her talents. Okay, so now we know that there’s an important difference between sentences which express propositions and those that do not. We also know that some sentences express multiple simple propositions and some express only one simple proposition. We’ve hopefully got a good grasp on what a proposition is at this point. 1.1.4 Inferences or Arguments The topic of the course is the argument or inference. What’s that? An Inference or Argument is any purportedly rational movement from evidence or premises to a conclusion Any time you’re being asked to accept one claim on the basis of or because of any number of other claims, you’ve got an inference/argument. “I believe x, because of y, z, and w” or “Because a, b and c, we have to believe that d.” The following is from Knachel, Fundamental Methods of Logic, CC-BY 4.0 Int’l If we’re reasoning by making claims and backing them up with reasons, then the claim that’s being backed up is the conclusion of an argument; the reasons given to support it are the argument’s premises. If we’re reasoning by drawing an inference from a set of statements, then the inference we draw is the conclusion of an argument, and the statements from which its drawn are the premises. We include the parenthetical hedge—“supposed to be”—in the definition to make room for bad arguments. Remember, in Logic, we’re evaluating reasoning. Arguments can be good or bad, logically correct or incorrect. A bad argument, very roughly speaking, is one where the premises fail to support the conclusion; a good argument’s premises actually do support the conclusion. To support the conclusion means, again very roughly, to give one good reasons for believing it. This highlights the rhetorical purpose of arguments: we use arguments when we’re disputing controversial issues; they aim to persuade people, to convince them to believe their 15 conclusion.3 As we said, in logic, we don’t judge arguments based on whether or not they succeed in this goal—there are logically bad arguments that are nevertheless quite persuasive. Rather, the logical enterprise is to identify the kinds of reasons that ought to be persuasive (even if they sometimes aren’t). So you’ve got some support for a conclusion and then that conclusion. The relationship between that support and that conclusion is supposed to be rational—we’re supposed to believe that the support we’re given proves or demonstrates or gives us reason to believe the conclusion. Less abstractly, here’s an example: Bob Marley wrote “One Love” Bob Marley sang the best rendition of “Don’t Worry, Be Happy” Bob Marley wrote “Three Little Birds” Bob Marley wrote “No Woman No Cry” Bob Marley wrote “Buffalo Soldier” So Bob Marley is the greatest musician of all time We’re being asked to believe a number of things here. First, we’re supposed to believe that Marley wrote each of these songs. We’re also being asked to believe that his version of “Don’t Worry, Be Happy” is the best version ever. Finally, and most importantly, we’re being asked to believe that because all of these things are true, it follows that Bob Marley is the greatest musician of all time. This isn’t a very good argument. It’s not being very good has nothing to do with the conclusion. I love Bob Marley and I do think he has written some of the best songs of all time, but I don’t think that these premises entail this conclusion. That is, even if we accept all of these premise, we need not accept the conclusion. “Oh yeah?” someone can reasonably reply, “those are all amazing songs, yes. And I don’t dispute that Marley wrote them, but none of them is as good as Bohemian Rhapsody. Queen is therefore better and Bob Marley cannot be the greatest musician of all time.” There’s no inconsistency with believing that this argument uses good premises to support a possibly-true conclusion, but doesn’t really demonstrate that conclusion using those premise. We can believe the conclusion is true without accepting that the argument supports the conclusion. 1.1.5 Premises and Conclusions All arguments have a common anatomy: All Poodles have curly hair Premises Some humans have curly hair Therefore, some Poodles are humans Conclusion There may be many premises, but they’re all supposed to be statements (propositions) which support or demonstrate the conclusion—whether directly or indirectly. A premise is a proposition which lends credence to the conclusion. It’s supposed to be a group of statements that, if you accept that they’re true, make it the case that you rationally must (or, weaker, should) accept the 16 conclusion. That’s not the case above in our Bob Marley argument. Here’s an argument where it is true: All Roses are Red All Red Things are Ugly All Roses are Ugly If it is in fact true that all roses are red and if it is in fact true that all red things are ugly, then it follows with absolute certainty that all roses are ugly. Try to accept the premises and reject the conclusion. Can’t do it. It’s impossible. Here are all of the Roses: And here are all of the Red Things: Red Things Roses Roses According to the first premise, all of the roses are red things. Notice how all of the roses fit inside all of the red things? That’s a graphical way of representing the claim that there are no roses outside of the category of red things. If you’re looking for a rose, you’re looking for a red thing. No non-red roses. All roses are red. Here are all of the Ugly Things: Ugly Things Red Things Roses According to the second premise, all of the red things are ugly things. See how they all fit inside the circle? Well, if the roses are in the red things circle and the red things circle is in the ugly things circle, it follows that the roses circle is in the ugly things circle. That make sense? Notice how we probably don’t want to accept the conclusion here. Most of us are on board with roses. We think that roses are beautiful or at least that they’re not ugly. So we don’t like this argument. But we can’t, when rejecting an argument, reject the conclusion directly. Why? Well, because the premises are supposed to be proving the conclusion. If the premises are true, then the conclusion must be true. We have to, therefore, reject one of the premises here. The second premise is clearly false. There are lots of pretty and red things. Red roses for instance. Furthermore, not all roses are red! The two premises were false in this case. If, however, you thought both premises were true, you’d have to accept the conclusion as well. Imagine your two friends are dating. If you want to invite one of them to hang out in a group setting, both of them will generally want to come. All of a sudden, they’re a package deal, right? 17 They have a relationship with one another such that if you take one, you have to take the other as well. That’s sort of how premises and conclusions work. They have a logical relationship with one another such that if you think the premises are true, you must also think that the conclusion is true. They’re a package deal. The previous argument illustrates the point that arguments sometimes are bad. There are sometimes reasons to reject an argument (mind you, not to decide that its conclusion is false, but instead to decide that it didn’t demonstrate its conclusion). Arguments can go wrong in only two ways: 1. Bad Inferential Structure: every argument with the same structure as this argument is bad (invalid or weak). The premises don’t in fact demonstrate or maybe even support the conclusion. In other words: we can accept the premises as true without being compelled to accept the conclusion. There’s something wrong with this argument’s general structure. 2. False Premise(s): this particular argument has a premise/assumption that is false. There’s something wrong with this argument’s particular content. The following is from Matthew J. Van Cleave’s Introduction to Logic and Critical Thinking, version 1.4, pp. 2-3 Creative Commons Attribution 4.0 International License. So, to reiterate: all arguments are composed of premises and conclusions, which are both types of statements. The premises of the argument provide a reason for thinking that the conclusion is true. And arguments typically involve more than one premise. A standard way of capturing the structure of an argument is by numbering the premises and conclusion. For example, recall Sally’s argument against abortion: Abortion is morally wrong because it is wrong to take the life of an innocent human being, and a fetus is an innocent human being. We could capture the structure of that argument like this: 1. It is morally wrong to take the life of an innocent human being 2. A fetus is an innocent human being 3. Therefore, abortion is morally wrong By convention, the last numbered statement (also denoted by the “therefore”) is the conclusion and the earlier numbered statements are the premises. This is what we call putting an argument into standard argument form. We can now give a more precise definition of an argument. An argument is a set of statements, some of which (the premises) attempt to provide a reason for thinking that some other statement (the conclusion) is true. Although arguments are typically given in order to convince or persuade someone of the conclusion, the argument itself is independent of one’s attempt to use it to convince or persuade. For example, I have just given 18 you this argument not in an attempt to convince you that abortion is morally wrong, but as an illustration of what an argument is. Later on in this chapter and in this book we will learn some techniques of evaluating arguments, but for now the goal is to learn to identify an argument, including its premises and conclusion(s). It is important to be able to identify arguments and understand their structure, whether or not you agree with conclusion of the argument. How do we identify Premises and Conclusions? Good question! First, we can sometimes identify premises and conclusions simply by recognizing the role they play in an argument. Here’s an argument, for example: Migratory butterflies are facing strain or possible extinction due to the overdevelopment of lands along their migration routes. In developing the routes, humans have tended to remove milkweed, which is a central food source for migratory butterflies. There are two claims here. One seems to support the other one and not the other way around. Which one seems like the claim being supported here? Which one seems like it’s doing the supporting? Good! Right-o, chum. See how the first sentence raises a question and the second sentence answers it? “What’s the relationship between developing land and migratory butterflies?” or simply “Why should we believe that?” The second question answers these questions: we should believe the first sentence because developing means removing milkweed, which is a food source for butterflies. Second, we can recognize conclusions and premises by identifying certain words being used: these are called conclusion indicators and premise indicators. If one of these words is used, typically that means that you’ve spotted a conclusion or a premise (depending on the indicator). Conclusion Indicators all have the general sense of “I’ve told you some things or I’m about to tell you some things, now here’s what I want you to believe.” They have a conclusive feel to them. Here are some especially common ones: Therefore So It follows that Hence Thus Entails that We may conclude that Implies that Wherefore As a result Premise indicators, on the other hand, have the general sense of “from this fact I’m going to infer something else”. Here are some common premise indicators: Because For Given That In that As Since As indicated by Here’s an example argument that I’ve packed with Indicators: In that the legislature has not approved it, and given that it is unconstitutional for me to do it on my own, I must conclude that there is no legal way for me to complete the project using only executive orders and the budgetary authority given to the executive branch. Furthermore, as indicated by the general lack of public support for the plan, it follows that I will be acting in line with the popular 19 will on this issue. Therefore, I must not allocate money to make Fridays “free pizza days” since to do so would be a great abuse of executive power. 1.1.6 Factual Claims and Inferential Claims Each argument makes two different sorts of claims, as we saw with the Bob Marley example above. There are a number of independent factual claims: claims about what is in fact the case or about what the world is like. There is also a somewhat hidden claim that the premises presented compel us to accept the conclusion presented—that there’s a good inference from these premises to that conclusion. Facts and Inferences argument makes two sets of claims: The Factual claims are in the premises: the arguer is claiming that all of the premises are true. The Inferential claim is often implied. The arguer is also claiming that the premises give conclusive support to the conclusion. Remember that these are the two ways an argument can break down: it can make a false factual claim (a premise can be false) or its premises can fail to support its conclusion (the implicit inferential claim can be false). So since we couldn’t possibly find an argument with the same general structure as the previous argument that has true premises, but a false conclusion, we conclude that the structure of that argument was deductively valid. We went through the steps to show that the argument is valid. We demonstrated it with the circles above (these are called “Euler 1 Diagrams”). Here’s the 0F structure without the particular content: All s are s All s are s All s are s So now we have the same types of propositions in the same order, but we’re no longer just talking about roses and red things and ugly things. Any argument with this form will be valid: you won’t be able to reject the conclusion if you accept the premises. This is what it means to have good inferential structure if you’re a deductive argument. We’ll get into the difference between deductive and inductive arguments later. Here’s an invalid inferential structure: All s are s All s are s All s are s How do we know it’s invalid? Well, easy. We find an example of an argument with the same argument form such that the premises are true and the conclusion is false. How about this example? 1 Pronounced “Oiler” because it’s German. 20 All Guavas are Fruits All Strawberries are Fruits All Guavas are Strawberries Guavas and Strawberries are two different sorts of fruit, but that doesn’t mean that they’re the same thing! Let’s check out what the Euler Diagram looks like: Fruits Strawberries Guavas See how strawberries and guavas don’t need to overlap at all to make the premises true? But the conclusion says that they totally overlap. So the premises do not entail the conclusion. We can accept the premises without accepting the conclusion. We only need this one counterexample to show that this argument structure is invalid. What does it mean to have a false premise? Pretty simple. Each premise makes a statement about how the world is. The world either is or isn’t that way, so each premise either is or isn’t true. Any argument with a false premise isn’t a good argument. All of the premises must be true for an argument to have successfully demonstrated its conclusion. Parts of any argument: The Conclusion is the claim that the whole argument is intended to support or demonstrate or prove. It’s the reason we make an argument: to support or demonstrate the conclusion. The Premises are the claims, evidence, ideas, etc. that are intended to support the conclusion They are the assumptions we are asked to take on board. If they are true, then the conclusion either must be or is likely true as well. 21 Here’s a heuristic or rough rule that can sometimes help you identify premises and conclusions. If you are told a premise, you’ll likely not understand why you were told it until you see that it fits into an argument. If you are told a conclusion, you’ll likely wonder what reason the person has for thinking it’s true. The conclusion is the “point” of bringing up the premises: to demonstrate that the conclusion is true. The premises are reasons we have for believing the conclusion. Premises make you ask: Okay, but what Conclusions make you ask: Okay, but why does that mean? What’s the point? Why tell would anyone believe that? Give me me that? reasons or evidence for accepting that Hey, did you know that the US claim. spends more on researching a new The Portland Trail Blazers are by fighter jet than it would on making far the more cohesive basketball college tuition free for everyone? team in the NBA this season. Okay… where are you going with Wait, why do you say that? What’s this? your evidence? 1.1.7 On Truth The following section was written by Michael Fitzpatrick A guiding assumption of this textbook is that truth is our aim when evaluating particular arguments and their conclusions. But what is truth, and why is it so important? After all, many people today seem to think that truth is just whatever a person believes, or that truth doesn’t matter as much as other values such as economic success, political pragmatism, or self-fulfillment. Contrary to these trends, this textbook affirms that thinking well flows out of the nature and value of truth, and that the value of truth should guide how we think. The name ‘truth’ gathers together our human concerns about accuracy and sincerity, to use the two underlying notions proposed by Bernard Williams in his book Truth and Truthfulness. When asserting propositions, adopting beliefs, creating blueprints, drawing maps, giving directions, following cooking recipes, or even just trying to see how much taller a teenager on a growth spurt is since last year, what we’re aiming at is an accurate understanding of our world and our projects in the world. Accuracy is a more or less concept, one we apply for instance in the game of darts. When throwing at a dart board, we aim for the bull’s-eye, and we are more or less accurate depending on how close we get to the target. But truth is not simply about accuracy; it also concerns sincerity, that dimension of representing ourselves and others and our world in ways that are genuine, faithful, trustworthy, and can be taken as presented. When we ask a friend for directions to the gas station, we’re not just depending on the accuracy of their instructions, but also their sincerity in not wanting to deceive us and in wanting to be someone who is trustworthy. 22 Truth understood as the interplay of accuracy and sincerity describes a fundamental way human beings exist. To interact truthfully in the world is to experience ourselves, our neighbors, and our environment as it really is, not as we wish it to be. The mode of truth highlights our capacity to receive new information from sources other than ourselves. Truth is, as Martin Heidegger suggests, “uncovering,” the unconcealing of what is with us in the world, seen for its own sake. In his book Kant and the Platypus, Umberto Eco suggests that truth involves our encounter with “lines of resistance” in the world, ways in which reality pushes back against our concepts and perceptions. In a particularly pregnant passage, Eco describes reality as a continuum with definite shape, As if to say that in the magma of the continuum there are lines of resistance and possibilities of flow, as in the grain of wood or marble, which make it easier to cut in one direction than in another. It is like beef or veal: in different cultures the cuts vary, and so the names of certain dishes are not always easy to translate from one language to another. And yet it would be very difficult to conceive of a cut that offered at the same moment the tip of the nose and the tail. If the continuum has a grain, unexpected and mysterious as it may be, then we cannot say all we want to say. Being may not be comparable to a one-way street but to a network of multilane freeways along which one can travel in more than one direction; but despite this some roads will nevertheless remain dead ends. There are things that cannot be done (or said). (53) Truth names the lines of resistance contouring what we can say, believe, do, experience, and imagine. Resistance does not entail impossibility; we are capable of astonishing creativity that can be used to distort reality, whether by lying to others, creating elaborate conspiracy theories, or engaging in our own self-deception. The point is not that we cannot do these things, but that to do them we have to overcome the resistance of reality. When we are sincere people seeking to aim accurately, we are letting ourselves be shaped by the “frictions” we experience as beings in the world. The foregoing portrait of truth helps to uncover the value truth has and its indispensable role in human life. Truth is both intrinsically and instrumentally valuable: something is intrinsically valuable when it is a end in itself, and instrumentally valuable when it is a means to a end. Truth, like justice and goodness, is both. Truth is also essential to other values humans hold, as well as to a healthy psychological life. We’ll cover each of these in turn. 1. Truth has intrinsic value because it satisfies our curiosity and wonder at existence. To be human is to explore and discover. We try to figure out how electrons can be both a wave and a particle; what creatures live in the darkest regions of the oceans; why whales are mammals that evolved back into the sea; and what the heck is a platypus anyway?! We even investigate the mystery of our selves—from our ingrained irrationality to our capacity for language to our religious tendencies to the enigma of consciousness, we humans want to understand who we are. As we explore our own identities and values, we discover what is true about us, which means we transcend our own fantasies, illusions, and folk stories about who we are. 23 2. Truth also has instrumental value for protecting ourselves against manipulation by other people. Consider this: you are not free to believe whatever you want. What I mean is, you can’t just will yourself to believe something. Try it – will yourself right now to believe that there is a pink elephant in the room with you. No matter how hard you try, you can’t just decide to believe it (at least not sincerely; you could say you believe it and not mean it). But you can decide to get others to believe something that is false or dangerous. You can trick or manipulate them into believing falsehoods, as a practical joke or to take advantage of them. But if you can do this to others... they can do it to you too. If our beliefs are not guided by what is true, then we are vulnerable to other people influencing our beliefs according to what they want us to believe. Politicians do it all the time. 3. Truth is essential to being a responsible, ethical human being. We are not just physical beings governed by the laws of physics; we have responsibilities to ourselves and others. We need to care for our younger siblings, pay our credit card bills on time, not cheat on our sweethearts, and stand up for those less fortunate than ourselves. But meeting these responsibilities requires a reasonably accurate portrait of the world. If we don’t know the truth about other people—their needs and their hopes and their fears—or the truth about the material situation we all find ourselves in, then we can’t meet our responsibilities. Knowing what my sister needs from me requires knowing my sister, knowing the truth not only about her needs but how best to meet them given the resources I have. Action presupposes truth. 4. Finally, truth is essential to a healthy human psychological life. Bernard Williams, in his essay “Deciding to believe,” describes a man who knows his son is dead but does not want to believe it. Suppose the man decides to undertake some act of self-deception so that he no longer believes his son is dead. The problem is that there are other true beliefs the man probably has about the world that imply his son is dead (for instance, that his son never sends letters or comes for a visit). Williams writes, The man gets rid of this belief about his son, and then there is some belief which strongly implies that his son is dead, and that has to be got rid of. Then there is sanother belief which could lead his thoughts in the undesired direction, and that has to be got rid of. It might be that a project of this kind tended in the end to involve total destruction of the world of reality, to lead to paranoia. Perhaps this is one reason why we have a strongly internalised objection to it. If we are not going to destroy all the evidence—all consciousness of the evidence—we have to have a project for steering ourselves through the world so as to avoid the embarrassing evidence. That sort of project is the project of the man who is deceiving himself, and he must really know what is true; for if he did not really know what was true, he would not be able to steer around the contrary and conflicting evidence. (151, from Problems of the Self) The attempt to deceive ourselves into believing one false belief seems to lead to a life of real paranoia and psychological breakdown, as well as the incoherence of needing to know what is true in order to avoid what is true. Of course, believing true beliefs can also lead to psychological upheaval. The realization that Nazi Germany had engaged in extensive crimes against humanity and undertook a holocaust against Jewish and disabled peoples was enormously difficult for 24 many German citizens to accept, and required tremendous revision in their beliefs about themselves, their communities, and their cultural identity. Yet upheaval by true beliefs is externally motivated, coming not from an internal paranoia or avoidance of reality, but from the “lines of resistance” and “uncovering” of reality we described above on the nature of truth. However difficult those truths may be to accept, they are more likely to lead to psychological stability in the long-term than, say, a holocaust denier who has to spend the rest of their lives refuting evidence and testimony about what really happened. There are more reasons beyond these to value the pursuit of truth, but hopefully this provides a sense of why this class is focused on how to reason as well as humanly possible so as to live along the grain of the universe. 1.1.8 The Principle of Charity Okay, Andrew’s back. Now let’s talk about a really important habit to get into. A sort of norm for reasoning well: Always interpret your opponent/interlocuter’s position or argument so as to make it as strong or defensible as possible. There are three reasons for this: one having to do with our goals in having reasoned discussions; another having to do with simple strategy if you are indeed interested in winning a debate; and finally one moral reason for following the principle of charity. If you’re interested not in winning, but in understanding, then of course it doesn’t help to argue against the weakest version of someone’s position or the weakest justification available for someone’s position. For instance, if you want to understand the moral issue of abortion, then arguing with someone who makes a super weak version of an argument for or against abortion rights won’t really help you understand the issues at play in the moral debate. You might win the debate on that day, but you won’t have understood the issue with any more clarity. When you disarm your conversant by letting them know that you understand their position and why someone might believe it, you open the door to more honest and open dialogue that allows for more understanding of each other’s viewpoints. Even if you are interested in winning and you just want the most effective strategy for winning a debate, the principle of charity is still your best bet. Here’s an example of what not to do: My opponent has argued against the idea that immigration is a fundamental human right. She must mean that even amnesty-seekers don’t have the moral right to immigrate away from immediate threats to life and limb. That position is totally ridiculous. This isn’t very interesting. When you’re arguing, you want your opponent to be the hardest version of themselves to critique so that when you do critique them, your critique is the most interesting critique available. Think about how much more interesting it is if someone actually bolsters their opponent’s position by providing justifications for their position and then showing that their position is still wrong. That’s the kind of debate take-down I want to see. My opponent has argued against immigration as a fundamental human right by appeal to simple scarcity: there’s not enough to go around. This, I’m afraid is 25 simply false. There is more than enough to go around if we’re willing to redistribute resources effectively. Nevermind that, though, since there’s a stronger justification for my opponent’s position: that states have the fundamental right of sovereignty, which includes controlling traffic across their borders. This, we might think, is essential to what it means to be a state. This is a very interesting argument, but it still fails to convince me. Even if states have a right to border regulation, it doesn’t follow that individual human beings don’t still have a right to immigrate to where the greatest promise of prosperity is. Isn’t this interesting? Wouldn’t you rather be in dialogue with this person or listen to a debate they’re in than someone who only attacks the weakest interpretation of their opponent’s position? You don’t want your critique to be against a straw figure version of their argument (the easiest- to-refute version) because all they have to do is revise their position slightly and they can side- step your critique. You’ve set them up to make your critique null and void by simply clarifying their position as the stronger version. This is also a good principle for living your life. You want to always attribute the most virtuous intentions to others and to the actions of others. This makes us easier to be around, more fun to converse with, and more empathetic and understanding people. It’s therefore a moral imperative that we treat each other with charity. After all, don’t you want to be given the benefit of the doubt? We want to interpret each other’s actions and arguments as being as rational as possible so that we are in the best standing rationally speaking. We want to attribute the best, most rational intentions allowable by our evidence to those around us so that if we have a problem with what they’re doing, we at least have given them the benefit of the doubt and are more likely to correctly characterize what they’re up to. We want to ascribe the most defensible and reasonable arguments and claims to people with whom we disagree because we certainly don’t want to spend our time critiquing an argument or position that isn’t theirs! We want to focus our energy on the best position or argument they have available to them because we are interested in finding out what the best thing to believe is—what’s true. We aren’t interested in winning for the sake of winning. 1.2 Kinds of Inferences Let’s look at two different inferences: Inference i: The sign says only 3 more miles to the coast, I suppose we’re getting close! Inference d: The definition of a scab is a union member who works during a strike, Manny is a union member who is working during a strike, so Manny is a scab. Notice how even if we accept the premise of inference i, we need not accept the conclusion. Ten gazillion different things could make the sign inaccurate. Maybe the coast moved due to erosion or seismic activity, maybe the sign was stolen from its intended location and moved 10 miles inland, maybe the sign was a practical joke in the first place. Who knows? 26 For inference d, though, it’s not so open-ended. We have a definition and the claim that an individual meets that definition. If the definition of x is d and a is d, then a is an x. If we disagree with the conclusion, we either have to reject the definition, or the description of Manny. We can’t add new information to change the conclusion. Even if Manny is a good guy, or an alien in disguise, or a really pro-union guy, or supporting three kids and a wife with cancer, he’s still a scab if that is in fact the definition of a scab and if that is in fact a true description of Manny. Harsh, but certainly true if the premises are true. The point of comparing inferences I and d is to see that there are two fundamentally different sorts of inference. We call an inference inductive if the support the premises provide for the conclusion is less than certain—if the premises don’t guarantee the conclusion. We call an inference deductive if the premises provide conclusive support for the conclusion—if they guarantee the conclusion or make the conclusion certain. Deductive arguments are mathematical arguments like proofs and the like, logical arguments, arguments from definition, etc. If the premises are true and the argumentative structure is good, then the conclusion must be true. Inductive arguments are arguments from analogy, arguments from qualified authority, causal inferences, scientific hypothetical reasoning, extrapolations from samples, and so on. Even if the argumentative structure is great, the truth of the premises only even makes the conclusion probably true at best. There’s a third kind of argument where we select the best explanation from all of the available plausible explanations. We won’t spend time on it, but it’s worth noting its existence. It’s sometimes called “abduction.” Kinds of Inference Deduction: arguments where the premises guarantee or necessitate the conclusion – Mathematical Arguments, Logical Arguments, Arguments from Definition Induction: arguments where the premises make the conclusion probable. – Analogies, Authority, Causal Inferences, Scientific Reasoning, Extrapolations, etc. Inference to the Best Explanation or Abduction: arguments where the best available explanation is chosen as the correct explanation. 1.2.1 Validity Remember that truth is a property of propositions. That is, only propositions can be true or false. Arguments can never be true or false. It simply doesn’t make any sense to claim that an argument is true or false. Okay, let’s talk about deductive arguments for a hot minute. Deductive argumentative structures are either valid or invalid. An invalid argument structure is one where the premises don’t guarantee the truth of the conclusion, but they should, given the type of argument involved. For instance, if it’s a mathematical argument, then it’s premises should guarantee its conclusion so it’s deductive. But if its premises don’t in fact guarantee its conclusion, then its an invalid deductive argument. 27 A valid argument structure is an argument structure where the premises guarantee the conclusion. That is, if the premises are true, the conclusion follows necessarily. It’s impossible for the premises to be true and the conclusion false. If 2+2=3, and 6-3=3, then necessarily, beyond any doubt, 2+2=6-3. No ifs, ands, or buts about it. It’s impossible for that conclusion to be false without at least one of those premises being false as well. All true premises and a valid argument means the conclusion must be true. Keep in mind that validity is about structures. So the previous paragraph’s arithmetical argument has the structure a+b=c, d+e=c, therefore a+b=d+e. Anything we sub in for the letters, if we create two true premises, will necessitate a true conclusion. What’s a valid argument that has true premises? That’s called a sound argument. Soundness is about both structure and truth: you have to have a good structure and true premises to be a sound argument. An unsound argument, conversely, is an argument that either is invalid or has at least one false premise. 1.2.2 Truth, Validity, Soundness What’s Truth? A proposition makes a statement about the world and the world either is or isn’t the way the proposition describes it to be. One proposition claims that the Gross Domestic Product of the United States of America is approximately $14 Trillion. To find out whether this is true or false, go figure out what the GDP of the US is. Is it approximately $14 Trillion? Another proposition claims that there’s a brown cat on the front porch of your house. Is this true? To find out, just go look at the world: is there in fact a cat on your front porch? Is it a brown cat? The propositions that make up an argument (the premises and the conclusion) are all either true or false. As with all things in philosophy, there is a lot more to say about the complexities here. Some of the earliest philosophy in the Western philosophical tradition is philosophy of logic or language. Aristotle, for instance, asked whether it’s true or false that there will be a sea battle tomorrow. Isn’t it contingent? Aren’t there lots of indeterminant factors involved in determining whether or not a sea battle will in fact take place? If so, it seems like that proposition is neither true nor false yet. So not every proposition is either true or false. We need not, though, deal with such issues. We can proceed as if every proposition is determinately either true or false. Remember: Validity is a property of argument structure: it means “this structure is such that if the premises of any argument with this structure are true, then the conclusion of that argument must be true.” It means: arguments of this structure will never have all true premises and a false conclusion. The structure guarantees the truth of the conclusion given the truth of the premises. Almost like the structure carries the truth of the premises directly to the conclusion without fail. A reliable one-way transporter of truth. A sound argument is an argument that has a valid structure but then also has true premises. If an argument is sound, and if validity means the conclusion must be true if the premises are true, then the conclusion must be true, then what do we know about the truth of the conclusion of any sound argument? Yes! You’re so smart: the conclusion of any sound argument is guaranteed to be true. 28 Truth, Validity, Soundness Truth: propositions are either true or false Validity: good deductive argument structure: True premises make the conclusion necessarily true. (if not, it’s an Invalid structure) Soundness: Valid deductive argument, all True premises. (If not, it’s an Unsound argument) All True Valid Sound Premises Structure Argument 1.2.3 Truth, Strength, Cogency Switching over to inductive arguments, we find an analogous set of properties. Again, inductive arguments are made up of propositions, which can be true or false. The biggest difference is that even good inductive arguments only offer probabilistic support for their conclusions. Meaning accepting all of the premises doesn’t necessitate that one accept the conclusion, it merely gives one more or less strong reason for accepting the conclusion. So the argumentative structure of an inductive argument isn’t either good or bad, it’s a matter of degree (and often a matter of what the actual content is). An inductive argument can therefore offer stronger or weaker inductive support for its conclusion. “Cogent” and “uncogent” are the words we use in place of “sound” and “unsound” for inductive arguments since inductive arguments cannot be sound or unsound. Cogent, therefore, means all true premises and the premises give strong inductive support for the conclusion. Consider these two arguments: I saw a I saw the Sun rise in the East every day black cat of my life and everyone I know reports Therefore all the same and history books and ancient cats are astronomers report the same, so the Sun black will rise in the East tomorrow. Notice how the argument on the left provides pretty weak support for the conclusion. I can believe that the speaker in fact saw a black cat and still think that’s a bad reason for concluding that all cats are black. The right argument, though, is much stronger. There’s much more evidence and the nature of the evidence makes the conclusion much more probable given the truth of all of the premises. 29 Truth, Strength, Cogency Truth: propositions are true or false Strength: Inductive argument: true premises make conclusion probably true. Cogency: Strong inductive argument, all True premises. All True Strong Cogent Premises Inductive Argument Support Again, inductive arguments are collections of propositions (the premises and the conclusion(s) are all propositions. And each of these propositions might be either true or false depending on whether it accurately describes reality. Note: An inductive argument cannot be valid. Why? Because a valid argument guarantees the truth of the conclusion. But an inductive argument only justifies its conclusion to some level of probability. Chapter 1 - Key Terms Deduction Rhetoric Induction Reasoning Truth Propositions Soundness Non-Propositions Validity Inferences/Arguments Strength Non-Inferences Cogency

Thinking Well - Lavin - Edition 4.0 PDF Textbook

Document Details

Tags

Related

Summary

Full Transcript

Upgrade to continue