Critical Thinking I Course Review Exclusions • the following topics will not be on the exam, so you can leave them out of your preparation. 1. Conductive arguments 2. Categorical Syllogisms • All other topics listed in the course outline will be drawn upon for the exam. Format • The final exam will consist of 7 sections. • The first section will be a series of multiple choice questions. • The other 6 sections will be short answer questions in which you will be asked to use the various methods we have learned for evaluating, testing and assessing arguments of various kinds. Good luck and happy studying. Chapter 1 An argument is: a set of claims in which one or more of them – the premises – are put forward so as to offer reasons for another claim, the conclusion. (1) Arguments in the sense defined are about providing justification for some belief or other. Chapter 1 Conditional sentences are referred to as if/then sentences and cannot be broken into two part. They are one entire sentence. A conditional sentence is one that links several conditions, specifying that IF one condition holds, anther will as well. Conditionals are often found in arguments, but the NEVER express an argument. Chapter 1 Things to review: (1)Argument (2)Conclusion (3)Conditional Statement (4)Explanation (5)Indicator words (6)Nonargument (7)Opinion (8)Premise Chapter 2 Before we can evaluate an argument, we need to understand just what the argument in question is. We need to know what the premises and conclusion are and how the premises are supposed to support the conclusion. Standardizing an argument is to set out its premises and conclusion in clear statements with the premises preceding the conclusion like so: Premise 1 Premise 2… Premise N Therefore, Conclusion Chapter 2 Number the premises and conclusions so that it makes it easy to refer to them by a name: the number. So we can talk about (1) or premise (1) without having to rewrite the entire premise. Standardizing arguments gives us a clear view of where the arguer is going and forces us to look carefully at what the arguer has said. Here is an argument in standard form. (1) If Chuck is in Atlanta, then Chuck is in Georgia. (2) Chuck is not in Georgia. Therefore, (3) Chuck is not in Atlanta. This simple argument is in a clear, standard form. Chapter 2 Arguments often proceed in stages. Sometimes a premise in one argument is a conclusion of another argument. This phenomena happens in what are called subarguments. A subargument is a subordinate argument that is a component of a larger argument, called the whole argument. Figure 2.2 shows the logical relationship of this kind of case. From page 25. Chapter 2 In figure 2.2, statement (2) represented by the circled ‘2’ is the conclusion of a subargument and may be called the subconclusion. But (2) is also a premise in the main argument. The main argument is (2) and (3) to (4), and when we add the main argument with the subargument we get what we call the whole argument. Subarguments are necessary and useful, because sometimes you need to justify a premises with another subargument. In figure 2.2, (4) is also called the main conclusion. Chapter 2 Standardizing an argument is not always a simple matter. Questions, commands, repetition, background and side remarks, jokes, wandering off topic, and so on, can all show up in arguments. These elements of colloquial writing and speech are eliminated when we put the argument in standardized form. The point of standardized form is clarity of the reasoning involved in the argument. Chapter 2 10 General Strategies for Standardizing Arguments (1)Read and understand the passage (2)Make sure the passage contains an argument (3)Identify the conclusion, premises, and any subarguments (4)Omit irrelevant material or side remarks (5)Omit material already used (don’t repeat information) (6)Omit personal phrases like “in my hunble opinion” (7)Number the premises and conclusion and standardize the argument (8)Make premises complete indicative sentences without pronouns (9)Check for subarguments in premises and conclusions (10)Check your argument against the passage for errors or omissions See page 31 for fuller guidelines. Chapter 4 The ARG conditions are: (1) Acceptable premises – it is reasonable for the person receiving the argument to believe the premises to be true (2) Relevant premises – premises are relevant to the conclusion (3) Good grounds – the premises support the conclusion and make it reasonable to believe the conclusion Chapter 4 These are a test of the cogency of an argument. This means that the cogency of an argument requires acceptable premises, relevant premises, and good grounds for adopting the conclusion. Chapter 4 Deductive entailment Often referred to as simply validity, deductive entailment is a tight logical relation where, when the premises are true, the conclusion must be true. Consider the following argument: Only members are allowed into the club. Andrew was not allowed in. So, Andrew is not a member of the club. If the premises are true, then conclusion has to be true. Chapter 4 For deductively valid arguments it is never possible for the conclusion to be false when all the premises are true. Another way to say this is that when the premises are true, the conclusion must be true. Validity does not come in degrees. Deductive arguments are either valid or they are not valid. Deductively valid arguments satisfy both the R and the G conditions for cogency of arguments. Chapter 4 Inductive support Inductive support is evidence (as opposed to reasons) that support the conclusion in a manner less certain than that of deductively valid arguments. Typically inductive argument rely on regularities in the world to make reasonable predictions and are thus called amplitive, they go beyond what is known for certain to what we can reasonably know based on available evidence. Chapter 4 One kind of inductive argument is a generalization about an entire population based on an observed sub group of that population. If all the people I meet from Hamilton are football fans, and I meet Sue from Hamilton, then there is good reason for me to think that she is a football fan (depending on how many people I have observed from Hamilton). Inductive arguments with all true premises don’t guarantee the truth of the conclusion the way deductively valid arguments do. Chapter 4 Using the ARG conditions to evaluate arguments. Start with the A condition (are the premises acceptable?) If so, then move to the R condition (are the premises relevant to the conclusion?) If so, then move on to the G condition (do the premises provide good grounds for accepting the conclusion?) If ARG are satisfied, then we have a cogent argument. Chapter 4 Failing the (A) Condition If the premises are not acceptable (and there are lots of reasons this might happen), then the argument fails the (A) condition. Premises that are clearly false, contain persuasive definitions, or are disputable based on common knowledge are examples as to why premises might not be acceptable. See example pages 95-6. Chapter 4 Failing the (R) Condition If an argument has acceptable premises, we can then ask if the premises are relevant to the conclusion. If for some reason, they are not relevant to the conclusion, then the argument is not cogent. If the argument fails the (R) condition, we do not have to move on and test for (G) since we know the argument is not cogent. See example on pages 97-8. Chapter 4 Failing the (G) Condition If an argument satisfies both the (A) and (R) conditions, we can move on to the (G) condition. If the premises of an argument are true and relevant to the conclusion, the next question is about grounding. Do these relevant, well supported premises actually support the conclusion. If so, then we have a cogent argument. If not, then we don’t. See example on pages 98-9. Chapter 4 Cogency, Soundness, and Validity Deductive entailment (validity) satisfies the (R) and (G) requirements completely. Sound arguments have all true premises and thus satisfy (A). But there are other arguments that are cogent, but not sound because they are either not valid or have premises that are rationally acceptable, but not true. We spent time on soundness in Chs 7 and 8. (108) Chapter 4 Evaluating and Constructing Arguments When an argument is offered, there are three possible ways to respond to an argument: (1) Reasoned acceptance -- ARG are accepted (2) Reasoned rejection -- one or more of ARG are not accepted (3) Suspended judgment -- for various reason you might suspend judgment on the argument See pages 109-10 Chapter 5 Acceptable premises are important because even if you have the best, most elegant reasoning possible, if the premises are not acceptable, then the reasoning does not matter. What does it mean to say that the premises of an argument are rationally acceptable? How might we show that they are? Here are seven ways to show premises are acceptable: Chapter 5 When premises are acceptable: (i)Before you begin we need to make an important philosophical point. Govier refers to 'acceptable' and ‘unacceptable' premises. She doesn't want to refer to 'truth' or 'falsity' or have you say: 'Such and such is true' because whether something is 'true' or 'false' is independent of whether or not anyone KNOWS or BELIEVES it to be true or false. Think about it. (ii) It is either True or False that there is someone named Deanna sitting in a Cafe' in Graz Austria right now. But is this reasonable to believe? How can you KNOW it if you aren't there right now? Or how about whether there is life after death? It's either true or false, but how do we determine which it is? Acceptability is a much better concept to start with since it puts this more epistemologically complex concept of 'what is truth?‘ aside for now ("epistemology" is a branch of philosophy dealing with different theories of knowledge). Chapter 5 Premises are acceptable if: (1)They are supported by a cogent subargument. This means that if the conclusion of a cogent subargument is a premise in another argument, then there is every reason to accept it as a premises. (2) The premises are supported elsewhere. Elsewhere there could be another cogent argument that the author or some other author has already established as cogent. Chapter 5 (3) The premise is know a priori to be true. A priori statements are the kind of things a person could know independent of experience or before experiences. It is contrasted with the term a posteriori. Statements that are knowable a posteriori require experience. Chapter 5 (4) A premise is acceptable if it is a matter of common knowledge. If just about everyone knows or understands that a premise is true, then the premise is acceptable. Chapter 5 When it comes to common knowledge we have to be careful because common knowledge can change given the times and what kind of events are occurring in the world. Chapter 5 (5) Testimony -- under some conditions, a claim is acceptable on the basis of a person’s testimony. There are three main factors that will undermine our acceptance of testimony as reliable. (i) The claims made are implausible (ii) The person making the claim or other source is unreliable (iii) The content of the claim goes beyond the experiences or competency of the testifier A lot of things give rise to when and how we accept testimony and how to govern its acceptability. Chapter 5 (6) Appeal to a proper authority Sometimes we have to take the word of a recognized authority with respect to the acceptability of a premise. If a logic professor told you that a particular argument was deductively valid, you can trust that because she is a proper authority on the validity of arguments. This same logic professor, however, may not be an authority on the exports of the state of Florida, and cannot explain if an income tax would increase tax revenue or not. Authorities must be proper to make premises acceptable. Chapter 5 (7) The last method of accepting premises is different from the rest. We say that we accept a premise provisionally or conditionally. You might find an argument to pass both the (R) and (G) conditions for cogency, but are uncertain about the acceptability of the premises. You can provisionally accept the premises and thus provisionally accept the conclusion and cogency of the argument. Chapter 5 Summary of the acceptability conditions: A premise in an argument is acceptable if any one of the following conditions is satisfied: (1)It is supported by a cogent subargument. (2)It is supported elsewhere by the arguer or other person, and this fact is noted. (3)It is know a priori to be true. (4)It is a matter of common knowledge. (5)It is supported by appropriate testimony. (6)It is supported by an appropriate appeal to authority. (7)The premise is not know to be rationally acceptable, but can be accepted provisionally for the purpose of the argument. Chapter 5 Summary of Unacceptable Conditions (1)One or more premises are refutable on the basis of common knowledge, a priori knowledge, or reliable knowledge from testimony or authority. (2)One or more premises are a priori false. (3)Several premises, taken together, produce a contradiction, so that the premises are explicitly or implicitly inconsistent. (4)One or more premises are vague or ambiguous to such an extent that it is not possible to determine what sort of evidence would establish them as acceptable or unacceptable. (5)One or more premises would not be rationally acceptable to any person who did not already accept the conclusions. In this case, the argument begs the question or is circular. Chapter 6 Understanding Relevance: The second condition for cogency for an argument is the (R) condition and we are going to look at the three basic ideas of relevance. (i) Positive relevance (ii) Negative relevance (iii) Irrelevance Chapter 6 Positive Relevance: A statement A is positively relevant to another statement B if and only if the truth of A counts in favour of the truth of B. This means that A counts as evidence for B. See page 148 for examples: Chapter 6 Negative Relevance: A statement A is negatively relevant to another statement B if and only if the truth of A counts against the truth of B. This means that if A is true, it counts as evidence or reason to think that B is not true. See page 149 for examples. Chapter 6 Irrelevance: A statement A is irrelevant to another statement B if and only if A is neither positively relevant nor negatively relevant to B. A doesn’t provide a reason to or a reason not be believe in the truth or falsity of B. See page 149 for examples. Chapter 7 We dealt with Categorical Logic in chapter 7. To start, we learned the four categorical forms. In categorical logic, the terms all, no, some, and not are the basic logical terms. The four categorical forms are: A: All S is P E: No S is P I: Some S is P O: Some S is not P Chapter 7 The A form categorical statement is: A: All S is P This is a universal affirmation statement. It says that all the members of the S category are members of the P category. For example: All sisters are female persons. All my sandwiches are peanut butter. Chapter 7 The E form categorical statement is: E: No S is P This is a universal negation statement. It says that none of the members of the S category are members of the P category (Ss are excluded from the P category). For example: No sisters are male persons. None of my sandwiches are pastrami. Chapter 7 The I form categorical statement is: I: Some S is P This is a particular affirmation statement. It says that at least one member of the S category is a member of the P category. For example: Some sisters are pilots. Some of my sandwiches are pre-made. Chapter 7 The O form categorical statement is: O: Some S is not P This is a particular negation statement. It says that at least one member of the S category is not a member of the P category (some Ss are excluded from the P category). For example: Some sisters are not pilots. Some of my sandwiches are not pre-made. Chapter 7 The Square of Opposition shows the logical relationship between the different categorical forms. A: All S are P E: No S are P I: Some S are P O: Some S are not P A and O are contradictories: they have to have opposite truth values. The same goes for I and E. Chapter 7 A and E statements are contraries because they cannot both be true, but they can both be false. I and O statements are referred to as subcontraries statements because they can both be false, but they cannot both be true. See page 181 for examples. Chapter 8 The logical connectives not, and, or, and if then will be represented by the following: –, •, ∨, and ⊃. We are going to define these symbols using truth-tables and thus they will have truth-table definitions. The point of a truth-table definition is to provide all the possible cases of truth or falsity for the values of the the sentence letters. Each connective will have its own definition. Chapter 8 Not Not functions to change the truth of a statement to its opposite. The truth-table definition for not is quite simple. If P is true, the not P is false. If P is false, then not P is true. This is our truth-table definition of not. Chapter 8 And And is a conjunction and connects two conjucts. The conjunction is true when both conjuncts are true and false ever where else. Here is our truth-table definition of and. The only time P • Q is true is when both P and Q are true. Chapter 8 Or Or is disjunction and it is true when either one or both of the disjuncts are true and false when both disjuncts are false. Here is the truth-table definition of or. Because we have defined or a being true when both disjuncts are true, this is called inclusive or Chapter 8 We are going to define the horseshoe as true whenever the consequent is true or whenever the antecedent is false. The only time a conditional statement is false is when the antecedent is true, and the consequent is false. So, if it is raining and my car isn’t wet, because it is in the garage, then the prior conditional is false. Here is the truth-table definition of the conditional. Chapter 9 Induction is the basis for our common sense beliefs about the world. In the most general sense, inductive reasoning, is that in which we extrapolate from experiences to what we have not yet experiences. In this chapter we are going to focus on: inductive generalizations, statistical syllogisms, and common errors or fallacies that are associated with inductive reasoning in general. Chapter 9 Inductive arguments have the following characteristics: 1.The premises and the conclusion are all empirical propositions. 2.The conclusion is not deductively entailed by the premises. 3.The reasoning used to infer the conclusion from the premises is based on the underlying assumption that the regularities described in the premises will persist. 4.The inference is either that unexamined cases will resemble examined ones or that evidence makes an explanatory hypothesis probable. See page 255 for a full explanation. Chapter 9 Inductive Generalizations (IG) In an IG, the premises describe a number of observed objects or events as having some particular feature. From this observed set of objects or events a conclusion asserts a claim about all (or most) of the objects and events of the same type have the feature in question. 1. 85% of polled students at Notre Dame think the football team is great. So, probably: 1. 85% of all Notre Dame students think the the football team is great. The word probably indicates that there is an extrapolation from the polled (observed) group the the entire group. Chapter 9 Phrases like: probably, in all likelihood, and most likely are often used in inductive arguments. Inductive arguments and inductive reasoning is used in contexts of prediction. Reasoning from the past to the future. Induction requires a belief in the regularities in the world. Chapter 9 Some important points about the many types of IGs. We need to take into account: (1)Sample size relative to the size of the target population. (2)Samples need to be random Random for samples is defined as: every member of the population having an equal chance of being chosen for the sample. If this is the case, then the sample is random. Chapter 9 Problems of Sampling: Size issues: more samples of a population does not necessarily make an IG stronger. What one needs for the sample is for it to be representative. Representativeness will work as a substitute condition for randomness. Sometimes it is more reliable than random depending on the point of the sample. What one needs for a sample size depends on the variability of the population. (260) Chapter 9 Guidelines for Evaluating Inductive Generalizations 1.Try to determine what the sample is and what the population is. If it is not stated what the population is, make an inference as to what population is intended, relying on the context for cues. 2.Note the size of the sample. If the sample is lower than 50, then, unless the population is extremely uniform or itself very small, the argument is weak. 3.Reflect on the variability of the population with regard to the trait or property, x, that the argument is about. If the population is not known to be reasonably uniform with regard to x, the sample should be large enough to reflect the variety in the population. 4.Reflect on how the sample has been selected. Is there any likely source of bias in the selection process? If so, the argument is inductively weak. 5.For most purposes, samples based on volunteers, college students, or persons of a single gender, race, or social class are not representative. 6.Taking the previous considerations into account, try to evaluate the representativeness of the sample. If you can give good reasons to believe that it is representative of the population, the argument is inductively strong. Otherwise, it is weak. Chapter 10 A causal inductive argument is an inductive argument in which the conclusion is a claim that one thing causes another. (286) For example: (i) Clogged arteries cause heart attacks (ii) A rough surface produces friction (iii) Exercise during heat causes sweating Causal inferences are often an attempt to explain or predict an outcome. Chapter 10 The meaning of cause can vary as well because of the different nature of causal relationships. Here are four possible meanings for cause: (i) As a necessary condition (ii) As a sufficient condition (iii) As both a necessary and sufficient condition (iv) As a contributory factor (neither necessary or sufficient) Each of these meanings of ‘cause’ are useful in analyzing arguments and premises in argument. We will see examples of each. Now you know what we did, so review, practice and do your best.