3. Evaluating Arguments: When Is an Argument a Good One? 1 Two Aspects of Evaluation 1. Evaluation of premises 2. Evaluation or reasoning from premises to conclusion 2 1
Cogency An argument that has both satisfactory premises (i.e., true or plausible premises) and a structure that provides rational support for its conclusion may termed a good, strong, convincing or sound argument. For arguments in natural languages Govier suggests that we use the word cogent as our basic evaluative term 3 ARG Conditions This is Govier s shorthand acronym for the basic elements of a cogent argument: Acceptable premises Relevant premises Adequate Grounds for the conclusion 4 2
Acceptable Premises As a first approximation, we can say that a premise is acceptable if it is reasonable for those to whom the argument is addressed to believe (i.e., to accept) that premise. A bit more precisely: A premise is acceptable if there is some reason to believe that that premise is true and no (known) good reason to believe that it is false. (More about acceptability later, in Ch. 5) 5 Relevance of Premises Premises are relevant to a conclusion if they state evidence or offers reasons that (actually) support the conclusion or can be arranged into a proof from which the conclusion can be derived. (This latter idea of arranging into proof will be considered more extensively in connection with the idea of validity in propositional logic, Ch. 8). 6 3
Adequate Grounds Premises provide adequate grounds for a conclusion when, considered together, the premises provide sufficient reason to accept that conclusion. Notice: Relevance is not the same as sufficiency. One person s personal experience may be relevant to some general claim, yet not be sufficient to support it 7 The Social Sciences and Humanities Research Council is obviously corrupt. Every time I apply for a grant, they give me the run-around about forms and paperwork, and they always seem to find some reason to reject my grant application. The fact that one person has had bad, frustrating experiences with SSHRC is certainly relevant to the claim that the organization is corrupt. But without some additional information about how others are treated, and perhaps some information about how the person offering the argument compares with other applicants, this is clearly not sufficient to establish the conclusion. 8 4
Cogency, Soundness, Validity In formal logic, a sound argument can be defined as an argument in which all the premises are true and which has a structure such that the premises deductively entail the conclusion. Deductive entailment is a very strong logical relation in which it is logically impossible for the premises to be true and the conclusion false. 9 An Example (Govier s) 1. Either interest rates will go down, or they will go up. 2. Interest rates will not go down. Therefore, 3. Interest rates will go up. Notice that the conclusion follows not because of anything you may happen to know about interest rates, but, given that the premises are true, simply by virtue of the form of the argument. 10 5
Another Example 1. If Saskatoon is the capital of Saskatchewan, then Saskatoon is in Saskatchewan 2. Saskatoon is the capital of Saskatchewan Therefore, 3. Saskatoon is in Saskatchewan This argument is deductively valid: The truth of its premises guarantees the truth of its conclusion. But is it sound? 11 Yet another 1. If Saskatoon is in Ontario, then Saskatoon is south of Whitehorse. 2. Saskatoon is south of Whitehorse Therefore, 3. Saskatoon is in Ontario Notice that both premises are true. Their truth does not deductively entail the truth of the conclusion, however, since this is an invalid argument form. 12 6
Cogency vs. Soundness Generally speaking any argument that is sound (all true premises + valid form) is also cogent (satisfies ARG conditions). But not all arguments that are cogent are sound: Premises may be rationally acceptable even if they are not known with certainty to be true. Not all arguments are deductive. Premises may support the conclusion in other ways besides deductive entailment. 13 Cogent Arguments Sound Arguments Arguments that are both Cogent and Sound 14 7
A Small Step Backwards: Relevance & Grounds So far we have been using these words in a rather vague sense. One way of getting at a clearer account of relevance and grounds (R and G conditions), is to consider the various ways in which the premises of an argument can be said to support its conclusion. This involves looking at various different types of arguments/reasoning 15 Four Types of Argument/Reasoning 1. Deductive entailment (deductive reasoning) 2. Inductive support (inductive reasoning) 3. Analogy (analogical reasoning) 4. Conductive support Each of these are ways in which premises may be properly connected to conclusions. What counts are relevance and adequacy of grounds is somewhat different for each type, however 16 8
Deductive Entailment In a deductive inference, the conclusion follows just by virtue of the truth of the premises, given a valid argument form. Famous example: All men are mortal. Socrates is a man. Therefore, Socrates is mortal 17 In the case of a deductive argument that is valid (i.e., of a known-to-be valid form), the R condition is always satisfied and, if the premises of that argument are all true, the G condition is also automatically satisfied. Evaluating such an argument (determining whether or not it is cogent), then, involves determining whether or not the A condition is satisfied i.e., whether its premises are true. 18 9
Govier s example: 1. A mathematical proof is an intellectual exercise. 2. Some computers can do mathematical proofs. Therefore, 3. Some computers can do an intellectual exercise. 19 Notice that deductive entailment is always an instance of linked support: 1 + 2 3 20 10
Inductive Support Inductive reasoning is a basic technique in science reasoning from particular cases to general conclusions. Generalized example: t1 sample of X glowed orange when Y present t2 sample of X glowed orange when Y present t3 sample of X glowed orange when Y present tn So, probably, X glows orange when Y is present 21 Obviously, in inductive reasoning, the number of observations contributes to the adequacy of the probable conclusion. (This is what statisticians and research scientists are ultimately referring to when they speak of sample size.) 22 11
Govier s Example 1. All the students I have met who graduated from school X got good grades in mathematics. So, probably, 2. All students who have graduated from school X got good grades in mathematics. The inference here is a generalization from a sample to a larger group. 23 Some Incidentals About Induction I Inductive inference assumes that unobserved cases will resemble observed ones. That is, it assumes that there are regularities in the world and our experience of it. (Some philosophers would note as well: inductive inference depends on these regularities, but these regularities are not themselves observable.) 24 12
Some Incidentals About Induction II When inductive reasoning is in question, it is common to speak of evidence rather than reasons. Also, as we have noted, an inductive argument can supply only probable (as opposed to certain) support for its conclusion (i.e., its inductive generalization) 25 For a valid deductive argument, it is logically impossible that the conclusion does not follow from the premises if those premises are true. But it is not logically impossible that, say, the next student to graduate from school X will turn out not to be good at mathematics. Inductive inference assumes that there are regularities in the world, but sometimes the world is irregular or surprising. 26 13
Inference to the Best Explanation 1. These eighty students who graduated from school X all have good marks in mathematics 2. The best and most natural explanation for that is that mathematics is well taught at school X Therefore, probably, 3. Mathematics is well taught at school x. Premise 2 offers an hypothesis that purports to explain the empirical observation in premise 1. 27 In assessing arguments that make use of hypotheses, we need to determine whether the hypothesis is actually acceptable (A condition), that is, whether it really is the best available explanation. If you create arguments that use inference to the best explanation, ideally you should be prepared to offer a sub-argument supporting the hypothesis. 28 14
Analogy Another basic form of reasoning commonly used in science (and in law, public administration, and ethics). E.g., in assessing the safety of some drug Y for humans, researchers may perform studies on rats, on the assumption that rat physiology is analogous to (i.e., relevantly similar to) human physiology. 29 Conductive Support Not really a separate type of inference, I d say, but Govier believes it is useful to assign it special name and special significance. In conductive arguments, the support offered by the premises is always convergent 30 15
Convergent Support 1 2 3 4 31 An Example As Govier notes, legal reasoning is often conductive (i.e., strictly convergent) in nature: The accused 1. Has no alibi 2. Has a motive 3. Had a an opportunity to commit the crime 4. Was seen at the scene of the crime Any one of these factors might be successfully disputed by a defense attorney, yet a Crown prosecutor need not withdraw charges unless and until all of them have been successfully disputed. Each, after all, independently supports a guilty verdict. 32 16
Counterarguments In evaluating conductive arguments is often useful to think up counterarguments factors or reasons that would count against the conclusion. E.g.: The accused was seen at the scene of the crime, but he was also seen somewhere else at the same time; The accused has a motive, but so do many other people 33 Using ARG Conditions to Evaluate Arguments If we know what conditions an argument needs to satisfy in order to be a cogent argument, then we can evaluate the cogency of any argument by inspecting it to see if it satisfies those conditions 34 17
Govier Suggests 1. Start with the (A) condition. Are the premises acceptable? If they are, why? If not, why not? 2. Then move on to the (R) condition. Are the premises relevant to the conclusion? Do the premises deductively entail the conclusion? Do they provide inductive support for it? Etc. If (R) is to be satisfied, it must be possible to interpret the premises such that they offer some support for the conclusion. Otherwise, they are irrelevant. 35 3. If (A) and (R) are satisfied, then move on to (G). That is, assess whether the premises provide sufficient or adequate grounds for the conclusion. An argument is cogent, you ll recall, if, but only if, all three conditions are satisfied. 36 18
Some Examples 1. Debbi is either in La Ronge or she is in Saskatoon. 2. Debbi is not in La Ronge. Therefore, 3. Debbi is in Saskatoon 37 Example 2 1. Animals are not human beings. 2. Animals do not speak language as human beings do. 3. Animals do not have the same advanced cultures and technologies as human beings Therefore, 4. Animals do not have any moral rights. (1, 2, p. 77) 38 19
Example 3 We both own IBM ThinkPad notebook computers. We ve both owned our computers for about three years. We both use our computers for about the same length of time each day. The hard drive on my computer just crashed. So, it s likely that your hard disk will crash too. 39 Example 4 My truck won t start. It could be that I m out of gas. It could be that the starter motor is pooched. But I think it s the battery, since that would also explain why the lights and the CD player don t work either. 40 20
Example 6 1. Students in my political studies class have not been working as hard as students in my political studies class last year. Therefore, 2. Students at the University of Saskatchewan in general are not working as hard this year as they have in the past. And, 3. I think this is caused by affluence and low standards in high schools which produce poor work habits in students. (based on 1, 8, p. 78) 41 The Challenge of Argument This is Govier s term for the, sometimes difficult, task of addressing an argument as an argument, rather than simply disagreeing with it conclusion. Recall the Principle of (Modest) Charity : When someone offers us an argument, we assume she has reasons that justify her conclusion. It would be a failure of charity (and a show of disrespect) to simply reject her conclusion without considering her reasons. 42 21