Reasoning Right Effective and Defective Arguments Reasoning Right Part of the Hands-On, Heads-Up Philosophy Series

Introducing the Principles of Inference through Practical Exercises instructor’s edition Reasoning Right Effective and defective arguments Reasoning Right part of the hands-on, heads-up philosophy series — printing 1.2 Table of Contents | Table of Contents 1 Expressions 1 Reasoning 1 using arguments to express inferences Deduction 3 standards for valid deductive arguments Transformation 6 rephrasing into equivalent expressions Induction 8 standards for strong inductive arguments Fallacies 10 formal and informal defective arguments Non-Inference 22 statements not connected by inference 2 Exercise Sessions 30 iv | | Preface 1.1 Going Where? 1.2 Getting There Humanities > Philosophy > Reasoning. Reasoning Right is a exercise book. You—or That’s the typical classifcation. The truth is, a group of you—form the Court of Reason. Each however, that reasoning is an essential vehicle session, you are given a variety of passages. for all disciplines. Well, perhaps language is the (You might fnd a few of your own arguments, vehicle, reasoning is the driver, and the subject at least in the roster of fallacies.) Judge whether matter is riding shotgun. Anyway, without rea- a passage is an argument, a fallacy, or neither soning it is rather diffcult to advocate or object by applying the principles of inference. If you to a claim in any subject, whether politics or wish, start with a passage and go looking for the arts. So what you have here are handouts an inference rule that fts. Conversely, get to for aspiring politicians, art critics, or anyone know the rules of inference to begin with, then interested in the nature of argument and the consider the passages. Possibly you will end up principles of inference. doing a bit of both. Use the principles to classify passages as Along the way you will bump into Smith effective arguments, defective arguments, or and Wilson, fctitious characters who lend not inferences at all. But don’t stop there! Apply their surnames to save us from awkward vari- the principles to claims heard in commercials, ables such as ‘Mr X’ and ‘Ms Y’. However, the in discussions with other people, even in think- Smith and Wilson of one passage are unrelat- ing through your own point of view. Just be ed to their namesakes in any other passage. In careful not to become a pest, citing the Latin other words, each passage stands on its own. name when pointing out a fallacy in the expres- As an exercise book, Reasoning Right leaves sion of a peer or parent. Keep a sense of humor. scholarship to other resources. Numerous Paraphrase passages until you get a sense of lists of fallacies and not a few introductions to whether or not they make sense. And always logic can be found online and are suggested to be willing to share the secret of your newfound supplement the present material or for further powers of logical discernment. investigation into the world of Reasoning Right. vi | | Expressions 1 Reasoning 1.2 We communicate our reasoning by means of arguments; the argument expresses an inference. 1.1 Reasoning is making inferences. An argument is a group of statements that An inference is connecting information have an inferential relationship. That means to make a decision (reasoning from evidence some statements (called the premises) provide to conclusion) or consider whether there are reason to believe one of the other statements reasons to support a particular belief or claim (called the conclusion). The premises sup- (reasoning from conclusion to evidence). port the conclusion. If there is no inferential A detective inspects the clues to fgure out relationship among the statements, then the who is the culprit passage might still be informative (e.g., an A doctor checks symptoms in order to make example or explanation) or persuasive (e.g., a a diagnosis command or wish), but the passage would not be an argument. A lawyer cites evidence to support a client’s claim of innocence A statement isn’t the same as a sentence. Some sentences express a command or request, A meteorologist examines weather current such as ‘leave the cat alone’ or ‘please pass the conditions for a forecast pepper’. Some sentences ask a question, such as ‘what does it cost?’ or ‘where is the wash- room?’. Other sentences declare an idea or opinion, such as ‘I believe in magic’ or ‘Pluto is a planet’. A statement is that which a declarative sentence asserts and it is either true or false. ‘All humans have genes’ is a true statement; ‘pigs can fy’ is false statement. ‘Je t’aime’, ‘I love you’, and ‘I am in love with you’ express the same statement The term “proposition” will be used as a synonym for “statement”. 2 | Expressions 1.3 Premises “give reason” by having a formal or All insects have six legs, so all wasps have six relevant connection to the conclusion. legs [Unstated premise: all wasps are insects ] In a valid deductive argument the prem- Your editorial is racist and racism is wrong ises have a formal connection to the conclu- [Unstated conclusion: your editorial is wrong ] sion. That is, the structure of the argument fts Unfortunately, enthymemes can conceal one of the recognized forms or patterns to be false claims. For example: boy applies body discussed later. In a deductive argument, true spray [minor premise]; boy gets adoring girls premises guarantee that the conclusion is true. [conclusion]. This omits the false premise: Squares are rectangles; rectangles are quad- body spray gets adoring girls. To evaluate an rilaterals; so squares are quadrilaterals enthymeme, frst state the implied parts, then All humans have genes; I am human; there- determine whether it has the proper structure fore, I have genes of a syllogism. In a strong inductive argument the prem- Darling, I’m sorry Busy people tend to forget ises support – but don’t guarantee – that the such things as anniversaries [I did not saying conclusion is true. The strength of an inductive that I am busy, but you may presume as much argument depends not on its form or struc- if it excuses me for forgetting the anniversary ] ture, but on the relevance of the premises to I hope to repay you soon My late aunt said the conclusion. she would leave a reward to everyone who had It rained yesterday and it rained today, so it looked after her [I actually neglected my aunt, will likely rain tomorrow but will allow you to presume that I looked after her ] You were seen feeing the scene of the crime and the stolen jewels were found in your apart- Yes, I am rather late One simply cannot de- ment, so you are likely the thief pend on buses and trains any more [I walked from around the corner, but you may go ahead 1.4 In everyday arguments, parts are often taken and think that I took a bus or train ] for granted and so they are not stated. I am not happy with Smith for mayor One It is unlikely that you’ll hear “the mower can never be happy with those who cheat on is running; running requires fuel; therefore, their taxes [I have no evidence that Smith is the mower has fuel.” More likely, the argument a tax cheat, but you may presume as much if it would be abbreviated to “there must still be sways your vote ] fuel in the mower since it started.” An argument in which some part is understood, but unstated is called an enthymeme. Enthymemes are useful shorthand when the implied asser- tion is so obvious that stating it would be dull or mechanical. Expressions | 3 The type of reasoning to which we are ac- 2 Deduction customed in our daily lives is typically the fa- miliar, short arguments like syllogisms. Even 2.1 Logical form makes the structure of a statement more clear. then we abbreviate them into enthymemes. For instance: I like you, so I will give you a discount The logical form of a statement shows on the subscription; You’ve got your hands full, its structure using connectives (not, and, or, so let me hold the door; We have to arrive on if-then, is equivalent to) with capital letters time, so we can’t stop for lunch. representing the parts to be connected. Paren- theses are used for grouping indicators and ∴ 1.5 Statements can be connected into more com- is shorthand for ‘therefore’. plex statements with: not, and, or, if-then. The statement ‘the light is on or the light is A simple statement asserts a fact, such as off’ has the form: A or B ‘fre requires oxygen’. The truth value of a statement depends on the truth value of its simple The statement ‘the baby is a boy or the baby statements and how they are connected. is a girl’ also has the form: A or B Negation (not): ~A is read ‘not A’ or ‘it is not To reduce parentheses, connectives have true that A’ or ‘A is not true’. When A is true ~A the following order of priority, from highest is false and when A is false ~A is true. to lowest: negation (not), conjunction (and), disjunction (or), implication (if-then), equiva- Conjunction (and): A & B is read ‘A and B’ lence (if and only if ). So A | B & ~C ⊃ D means or ‘it is true that A and B’. A and B are called the same as (A | (B & (~C))) ⊃ D. conjuncts. A & B is true only when A is true and B is true; otherwise A & B is false. 2.2 An argument is valid if it has one of the deductive forms.

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