The second reason for discussing the Victorian H.S.C. at such length was to bring out what seem to me to be the general atti- tudes to reasoning in our society, and to try to indicate the ways in which this sort of syllabus presupposes and reinforces them. ~ [Editor's Note: This paper was presented at ~e 1978 ALTA Conference together with a second paper in which Dr. Richards suggested details of a school curriculum in reasoning. This second paper, entitled "The Fourth R", was published in the Australian LOtiC Teachers' Journal, Vol. IV, No.2 February 1980), pp. i-10.] ~ 1. V.U.S.E.B. H.S.C. Handbook, 1978. p. 191. 2. Richards, T.J. The Language of Reason (Sydney, Pergamon, 1978). 3. l!?J:g. 4. .QE.. • .£.U. P • 19 3 • 5. Committee on English in the Sixth Form, "English and English Literature in the Sixth Form", V.U.S.E.B. duplicated, June 1978. Quote is from statement of aims, p. 6. 6 • .2E,.£i!.. p. 9. 7.~. response Deduction. Induction and Conduction David Hitchcock McMaster University The last issue of 'this Newsletter featured four articles (2, 5, 7, 10) on the inductive- deductive distinction. Sherlock Holmes would deduce that practitioners of informal logic have a great deal of interest in this topic. Or should that be "induces"? Perhaps a few more words on the topic will be conducive, if not conductive, to more enlightenment. In what follows, I first try to situate the dispute about the deductive-inductive distinc- tion within the context of the appraisal of arguments. I respond briefly to Samuel Fohr's objections (2) to my position. I then explore 7 through a series of examples Perry Weddle's renewed claim (10) that all carefully drawn arguments are deductively valid. I concede that it is possible to fill out the premises of a traditionally inductive argument in such a way as to make it deductively valid, but argue that in general this requires the addi- tion of premises justifiable only by induc- tively weak arguments. It is therefore a better strategy in argument appraisal to omit such premises and take the argument to be in- ductively strong. Consideration of these ex- amples leads naturally to a discussion of Trudy Govier'S defense of a third "conductive" standard of appraisal of arguments. I con- clude by advancing amended criteria for de- termining the appropriate logical standard for appraisal of an argument. I What is at issue in this debate? As prac- titioners of informal logic, we are oriented towards the appraisal of arguments which people actually advance in an attempt to con- vince others (or themselves) to believe or to do something. The question at issue, then, is whether any version of the distinction be- tween deduction and induction is helpful in appraising arguments. If so, which one? Usually our purpose in appra~s~ng an argu- ment is to come to a decision about whether to accept its conclusion. I use the term "cogent" of an argument which deserves to convince us of its conclusion, i.e., which provides adequate grounds for believing or doing what the conclusion says. I take an argument to be cogent for somebody when and only when el) that person has justifications which are independent of the conclusion for accepting its premises and (2) the conclusion follows from the premises. Some arguments are potentially cogent. That is, they would be cogent if they were filled out with pre- mises which their author perhaps takes for granted as known background information, ac- cepted normative assumptions, and so forth. The cogency or potential cogency of an argu- ment is a relational property; arguments are cogent or potentially cogent to those people who are in possession of relevant evidence. Furthermore, the appraisal of an argument is both an epistemological and a logical matter. Roughly three positions on the deductive- inductive distinction have emerged. (1) Perry Weddle (9, 10) maintains that we should abandon the deductive-inductive dis- tinction ...... some traditionally inductive and some traditionally deductive arguments provide conclusive grounds for their con- clusions and some do not." (9, p. 4) The ones that do not are apparently not care- fully enough drawn. We should presumably fill out their premises and/or hedge their conclusions so that they become deductive in the sense that "it is absolutely impossible for the premises to be true unless the con- clusion is true also." Having made the strength of the conclusion proportional to the strength of the premises, we can evaluate the cogency of the argument by evaluating the acceptability of the premises. There are then two questions to ask about any argument: Does the conclusion follow deductively from the premises? What is the relation of the premises to the world? (9, pp. 4-5) (2) Samuel Fohr (1, 2) maintains that we should retain the deductive-inductive dis- tinction. Since arguments do not exist in vacuo, but are put forward by persons to-Con- vrnce persons, we should pay attention to the intentions of persons who put them forward. "If a person intends that his premises neces- sitate his conclusion he is giving a deductive argument. If he intends that his premises render his conclusion probable he is giving an inductive argument." ll, p. 7) Fohr could add: If he intends that h~s premises be non-conclusively relevant to his conclusion he is giving a conductive argument. And so on. If arguers give no evidence of their in- tentions, we should ask them whether they in- tend their premises to provide conclusive or probabilistic (or non-conclusively relevant or ... ) support for their conclusion. If we cannot discover an arguer's intentions in this respect, we must construe the argument as ambiguous and test it against both deduc- tive and inductive (and con4uctive and .•• ) standards. An arguer who has no intentions about the strength of the link between pre- misers) and conclusion has not put forward a definite argument. Fred Johnson (7) ap- pears to advocate a variant of this position when he urges that we regard "deductive" and "inductive" as characteristic of arguings (acts of putting forward an argument) rather than of arguments themselves. He wants to revise Fohr's ~ocabulary in order to avoid misleading our students into the mistake of taking arguments themselves to be deductive or inductive. Since two people can put for- ward the same argument with different inten- tions as to the strength of the relation be- tween premises and conclusion, it is the arguing and not the argument which is deduc- tive or inductive. Johnson does not say how seriously we should take arguers' intentions in our appraisal either of their arguings or of their arguments, nor does he commit him- self on whether there is a defensible di~­ tinction between arguments which are deduc- tively valid and those which are inductively strong. Both Fohr and Johnson, however, are likely to think that arguers' intentions about the strength of the link between pre- mises and conclusion can succeed or fail. If so, they presuppose a prior distinction be- tween two (9r more) ways in which the con- clusion of an argument can follow from its premise(s). That is, they presuppose a dis- tinction between deductive validity and in- ductive strength (and perhaps other kinds of link as well) . (3) I maintain that we should retain the deductive-inductive distinction, not as a distinction between types of argument, but as a distinction between types of validity--or, as Trudy Govier (5) puts it, standards of ap- praisal. An argument is deductively valid if and only if the truth of its premises guar- antees the truth of its conclusion; that is, it is impossible for the premises to be true and the conclusion false. The description of a possible state of affairs in which its pre- mises are true and its conclusion false is a refutation of the claim that an argument is deductively valid. .~ argument is inductively strong if and only if the truth of its pre- mises makes the conclusion probable. To re- fute a claim that an argument is inductively strong, we must deploy arguments which show 8 that the conclusion is improbable relative to the evidence contained in the premises. Trudy Govier (5) defends at least one more standard of appraisal, which we might call, after Carl Wellman elll, a conductive stan- dard. An argument is conductively valid if and only if the truth of its premises pro- vides non-conclusive relevant reasons for ac- cepting the truth of the conclusion. It is hard to know how to refute a claim that an argument is conductively valid. I shall sug- gest later that, if the premises of such ar- guments are properly filled out, it is not possible to refute a claim to validity for such arguments. The only valid objection to a properly filled out argument for which con- ductive validity is claimed is an attack on one of its premises. As several of my critics pointed out (2, 5, 7), in maintaining that there is more than one type of validity, I implicitly commit my- self to criteria for determining which stan- dard of validity is appropriate for a given argument. Thus, the distinction between de- ductive and inductive (and conductive?) argu- ments reappears as the distinction between arguments for whose appraisal standards of deductive validity are appropriate and those for which inductive standards are appropriate (and those for which conductive standards are appropriate?). I return to this objection at the end of the paper. II Samuel Fohr (2) contends that an arguer who has no intentions about the strength of the link between his premises and his conclusion has not expressed a unique or definite argu- ment. I find this an odd view, especially since we experts in the field have not yet reached a consensus as to how many possible types of link there are. Weddle says one, I say two, and Govier says three or more. What is the ordinary person to do who simply wishes to express a definite, unambiguous argument? Fohr further suggests that people who have no such intentions may be giving reasons rath- er than giving an argument. I do not under- stand this distinction. To me an argument is a set of statements one of which is advanced on the basis of the rest. If I give my wife's promise as a reason why she should help me paint the kitchen, I make two state- ments one of which ("you should help me paint the kitchen") is advanced on the basis of the other ("you promised you would"). We could even put these statements in standard argu- ment format: You promised to help me paint the kitchen. Therefore, you ought to help me paint the kitchen. It seems to me that any case of giving rea- sons for an action or a belief is an argument which could be put into such a format. If not, we should have some clarification of the distinction. Per;:y Weddle (10, p. 12) expresses very well a crucial objection to taking arguers' intentions about the strength of the link be- tween their premises and their conclusion as decisive for the appraisal of their argu- ments. Typically, he points out, we are not so much concerned to judge the arguer as to judge the argument. We want to come to a decision about how good a justification the argument gives us for accepting the conclu- sion. I continue to believe that for this purpose the arguers' intentions are at best of heuristic value in determining which stan- dard of appraisal is appropriate. III Perry Weddle (9, 10) maintains that some traditionally inductive arguments become de- ductive arguments when their conclusions are hedged. By calling them deductive he means that it is impossible for the premises to be true and the conclusion false. The conclu- sions in question are such probability or likelihood statements as the following: It is 95 per cent probable that a sample ran- domly selected from this population will have a frequency of members having a certain char- acteristic within 1.96 standard deviations of the mean sample frequency. It is 95 per cent probable that among Canadian voters with an opinion they are willin~ to express between 32 and 36 per cent supported the Conservative Party at the time the poll was taken. It is 95 per cent probable that this drug when taken as directed brings symptomatic relief within one week to at least 50 per cent of suffers from this disease. There is a 40 per cent chance of rain today in the Metropolitan Toronto area. Any child born to this couple has a 25 per cent chance of having sickle cell anemia. What does it mean to say that such proba- bility statements are true? Clearly the probability is not a property of the state of affairs which "it is probable that" intro- duces. A sample selected from a population either does or does not have a frequency of a certain characteristic within a defined range. The extent of support at a given time for the Conservative Party among eligible Canadian voteJ:s willing to express an opinion is a definite percentage, with no probabil- ities about it. It either will or will not rain in Metropolitan Toronto today. A child born to this couple either will or will not have sickle cell anemia. We can interpret the probabilities in ques- tion in at least two different ways. One is as properties of the situation prior to the occurrence or non-occurrence of the event described in "that" clause. In this sense a probability statement would have an objective truth-value, dependent only on the situation at the time, and an explicitly complete des- cription of the relevant features of the sit- uation would provide conclusive grounds for accepting the truth of the probability state- ment. The other is as epistemic probabil- ities, as the degree of confidence which the maker of the statement is entitled to have in the truth of the "that" clause on the basis of the evidence at her disposal. In this sense a probability statement has a sub- jective truth-value, which can change as new information becomes available. I contend that arguments whose conclusions are probabil- ity statements in the first sense have been traditionally recognized as deductively valid. Traditionally inductive arguments have con- clusions which, when hedged, become probabil- ity statements of the second type. In such cases it is possible for the premises to be true and the conclusion false. Therefore one cannot make such arguments deductively valid 9 just by hedging the conclusion. One can make them deductively valid by also adding a strong premise. Such a premise, however, may lack any justification at all. Furthermore, it can at best be justified by an inductively strong argument, so we are forced at some point to acknowledge weaker than deductive links in cogent arguments. It seems more straightforward to acknowledge such weaker links in the original argument. I shall develop the above position in terms of a series of examples. In examining these examples I shall respond to Weddle's defense of his pOSition (10) against my earlier objections (6). (1) Weddle considers my objection that un- cited counter evidence may make the hedged conclusion of a traditionally inductive ar- gument false even though the premises are true. He considers this objection in rela- tion to the following argument: Set S consists of 360-member subset A and 6-member subset B. SmIth will select once at random from S. Therefore, Smith is likely to select a member of subset A. Weddle supposes that the unci ted counter- evidence would be knowledge of which individ- ual Smith actually selects. If Smith actu- ally selects a member of subset A, the prob- ability is not 360/366 but 1 that he selects a member of subset A. If Smith actually se- lects a member of sUbset B, the probability is not 6/366 but 0 that he selects a member of subset B. In either case, the premises are true but the conclusion false. Weddle deals with this supposed counter evidence in the following way: To object to the original argument on grounds which apply to the amended argument would be an ignoratio elenchi. The uncited evidence counts only against the amended version. The original was deductively valid come what may. I do not understand this response. In the first place, I do not understand what Weddle means by the amended argument. In the second place, if this further piece of evidence is taken by Weddle to make the conclusion false even though the premises are still true, how can he maintain that the original argument was deductively valid? By calling an argu- ment deductively valid he means that "it is absolutely impossible for the premises to be true unless the conclusion is true also". How then can an argument be deductively valid when it is capable of having true premises and a false conclusion? Actually I am quite prepared to agree that the argument cited by Weddle is deductively valid. My reason for doing so is that I consider the conclusion as a purported state- ment of the property of the situation at the time of utterance. That is, it reports the present probability (which, to be precise, is 360/366) that Smith will 3elect a member of subset A. Information-contemporary with or subsequent to Smith's selection from set ~ is irrelevant to this probability. Given the truth of the premises of Weddle's argu- ment, this conclusion is true. Furthermore, no conceivable additional evidence can alter the truth-value of this statement. In other words, it is impossible for the premises of this argument to be true and the conclusion false. Weddle's example, therefore, is deductively valid. However, it is not an argument which would be traditionally regarded as inductive. In philosophically sophisticated statistics texts, where such arguments tend to appear, it is pOinted out that the conclusion about the characteristics of a sample follows de- ductively from the premises about the char- acteristics of a population and about the randomness of the method of selecting members of the sample. In real life, of course, no- body reasons from the characteristics of populations to the characteristics of samples. We reason from the characteristics of samples to the characteristics of populations. (2) Let us consider, then, some more typical traditionally inductive arguments with their conclusions hedged and thei~ premises filled out. On or about January IS, 1977 the Can- adian Institute of Public Opinion (i.e., the Gallup poll), at the request of The Canadian magazine, surveyed 1,043 "representative French- and English-speaking Canadians in interviews across the country." This survey took place two months after the election of a provincial government in Quebec committed to political independence for Quebec. Among the questions the interviewers asked the 1,043 respondents was the question: Should the government of Canada negotiate special polit- ical and economic agreements with Quebec to try to prevent separation? Of the 1,043 res- pondents, 47.4 per cent (494) said "yes", 43.6 per cent (455) ,said "no", and 8.7 per cent (9ll said "don't know". (We were not told what the remaining three persons said.) The report of this survey in The Canadian did not make clear from what population the sam- ple was drawn; let us assume it was drawn from eligible Canadian voters living in Canada. Nor did it make clear how the sample was selected; it was probably selected on the basis of stratification and geographical clustering, out to keep things simple let us assume that it was obtained by some method of selection which gave each member of the population an equal chance of being selected as one of the 1,043 persons interviewed. Then, looking up appropriate tables in a statistics text, we can construct the fol- lowing hedged argument: 1,043 respondents were obtained from the population of Canadian voters living in Canada by simple random selection without replacement. The population is large enough that this procedure has virtually no probability of giving results different from those obtained by random selection with replacement. On or about January 15, 1977 an interviewer asked each respondent, "Should the government of Canada negotiate special political and economic agreements with Quebec to try to prevent separation?" Each person interviewed gave his or her honest opinion at the time. The process of interviewing did not alter the opinion that any person interviewed had on this question 10 at the time the interview began. 47.4 per cent of those asked this question said "Yes". 1 Therefore, it is 95 per cent probable that on or about January 15, 1977 between 45.3 and 49.5 per cent of Canadian voters living in Canada thought the government of Canada should negotiate special political and economic agreements with Quebec to try to prevent separation. (Incidentally, I made up the numbers in the conclusion. The important point is that a carefully hedged conclusion of this sort would give a 95% or 99% confidence interval.) To assess whether this argument is deductively valid, we have to ask whether it is possible for all the premises to be true but the con- clusion false. I maintain that it is pOSSible, and therefore that the above argument is not deductively valid. Suppose a rival magazine commissioned an- other polling organization at exactly the same time to do a survey by the same method of public opinion sampling on exactly the same question. (Such coincidences occur quite commonly during election campaigns, so this is not an outlandish example.) Suppose that this polling organization found that 43.2 per cent of 1,043 randomly selected respondents said "yes" when asked by an in- terviewer, and that each person asked gave his or her honest opinion at the time, an opinion not affected by the process of in- terviewing. Then, looking up our tables, again, we could conclude by a similar argu- ment to the one set out above that it is 95 per cent probable that on or about January 15, 1977 between 41.2 and 45.2 per cent (say) of Canadian voters living in Canada thought the government of Canada should negotiate special political and economic agreements with Quebec to try to prevent separation. We do not need to go into the mathematics to realize that when we take account of the evidence embodied in the premises of both arguments the conclusion of the first argu- ment will no longer be true. The probability of the frequency of the indicated opinion being within the range mentioned will be much less than 95 per cent. In fact, if we com- bine the two poll results together to get a sample twice as large in which 45.3 per cent of the respondents thought Canada should negotiate special agreements with Quebec, we can conclude that it is 95 per cent probable that between 44.1 and 46.5 per cent (say) of the population of eligible Canadian voters living in Canada think Canada should nego- tiate such special agreements. The probability in this case is the prob- ability that the method of selecting the sample and of calculating the confidence interval will produce an interval which in- cludes the population frequency of the =har- acteristic being examined. This probab~lity is fixed relative to the premises; that ~s. given, that the premises are true, it is im- possible for the conclusion to be false. However, when we apply this probability to an estimation of the population frequency, as ; commonly done, the probability is not f~xed relative to the premises. New information alters the probabilities. So any conClusion about the frequency of the characteristic in , the population, no matter how ca:t'efully hedged, does not follow deductively from the premises. Of course, we can always add the premise, "There is no other information relevant to the distribution of opinion on this question among this population at this time." With this premise added, the argument becomes deductively valid, since the sort of infor- mation which would show the conclusion false even though the premises are true is explic- itly barred by this new premise. It is this sort of premise which I called "open-ended". Note that adding it does not change the fact that the probability hedging the conclusion is still probability given the "evidence" cited in the premises. It is just that one piece of evidence is of a peculiar sort which precludes any other evidence showing up which has a bearing on the conclusion. Why shouldn't we add this premise and trans- form the argument into a deductively valid one? Presumably we are filling out unstated premises as a preliminary towards making an assessment of the argument. We want to find out whether it is cogent. The next step will be to inquire of each premise whether it is justified independently of the conclusion. But any premise strong enough to make a de- ductively valid argument out of an argument from sample characteristics to population characteristics is incapable of being justi- fied. At least, it can't be justified by a deductively valid argument. All that can be said in support of such a premise is that no other information relevant to the conclusion is available to the person criticizing the argument and that certain (describable) ef- forts have been made to find such information. In principle, no such set of efforts can ex- haust the possibilities. It's better to cut the knot at the place where it most obviously demands to be cut, and to construe the orig- 'inal argument as inductively strong, thus recognizing that new information can make the conclusion false, even though the premises continue to be true. (3) Let us consider another type of argu- ment whose conclusion is a probability state- ment. First I give an example of an argument which is deductively valid. Sickle cell ane- mia, geneticists think, is a single-gene re- cessive characteristic transmitted according to Mendel's laws of segregation and dominance. That is, a human being has sickle cell anemia if and only if he or she has in each non-sex cell in his or her body the gene for sickle cell anemia (which we might call the sickle cell gene) at a given place in both members of a given pair of chromosomes. A person is a carrier of sickle cell trait if and only if he or she has in each non-sex cell at the appropriate places on the chains of chromo- somes one sickle cell gene and one normal gene. A carrier does not have sickle cell anemia. However, two carriers who mate can produce a child with sickle cell anemia. Assume two people, Jim and Mary, are carriers. Then we can construct the following argument: Jim and Mary are carriers of sickle cell anemia. In reproduction Jim's sperm which have the sickle cell gene have a chance of uniting with a fertile egg equal to that of his sperm with the normal gene. 11 Likewise, Mary's eggs which have the sickle cell gene have a chance of being fertilized equal to that of those which do not have the normal gene. Sickle cell anemia is a single-gene recessive trait. Therefore, if Jim and Mary have a child, that child has a 25% probability of having sickle cell anemia. This is an argument with a probabilistic conclusion which is deductively valid. That is, it is impossible for the premises to be true and the conclusion false. One can avoid apparent counter-examples based on knowledge after the fact just as we did in the case of the argument about the sample characteristics based on the population characteristics. Suppose, for example, someone does an amni- ocentesis on Mary's unborn child, conceived by Jim, and discovers that the child has sickle cell anemia. (I believe there is no such test. However, there might be one.) Then the probability that this child has sickle cell anemia is not 25% but 100% Cor slightly less, if there is a margin of error in the testl. But this objection is beside the point, because the conclusion ascribes a probability as the property of a situation prior to any conception of a child. "It is now 25% probable that, if Jim and Mary do conceive a child in the future, the child will have sickle cell anemia." What happens once Jim and Mary conceive a child is irrelevant to the truth of the statement thus construed. Such arguments are best construed as argu- ments from stochastic hypotheses to predic- tions derived from them. That is, the back- ground of such an argument is a stochastic (probaoilisticl theory--in this case, Mendel's theory of the inheritance of single- gene traits. Such a theory I take, in com- mon with a number of contemporary philosophers of science cited by Giere U), to be a defi- nition of a system. That is, the theory is a definition of a Mendelian inheritance sys- tem for a characteristic as one which obeys Mendel's laws of segregation and dominance. Given the state of such a system at any par- ticular time, one can predict for each male- female pair in the system the probability that one of their offspring will have a cer- tain characteristic. (~L Now let us consider a parallel tradi- tionally induc'tive argument. A screening program identifies Jim and Mary as sickle cell carriers. A genetic counsellor explains to them what this means and advises them that, iz they conceive a child, there is a' 25 per cent probability that the child will have sickle cell anemia. We can set out the counsellor's argument as follows: Jim and Mary are carriers of sickle cell anemia. Sickle cell anemia is a single-gene recessive trait. Therefore, if Jim and Mary have a child, there is a 25% probability that this child will have sickle cell anemia. Is this argument deductively valid? I think not. There are possible states of affairs in which the premises are true and the conclu- sion false. Suppose, for example, a tech- nique is developed to make the sperm with the sickle gene immobile while keeping the other sperm alive. Suppose that Mary is artifi- cially inseminated with Jim's sperm after they have been treated in this way, and this insemination produces a pregnancy. Then, if the technique is fully effective, there is no prooaoility that the child thus conceived will have sickle cell anemia. So we have a counter-example in which ~he premises are true and the conclusion false. The argument is not deductively valid. What we have done here is to suppose some external interference with the operation of the law of segregation in a Mendelian in- heritance system. We have supposed that the real system of inheritance of characteristics is open to external influences, not closed according to Mendel's laws. In order to block such counter-examples, we have to add a stipulation that the system of transmission of characteristics from Jim and Mary to their children is closed under Mendel's laws. Why not add such a premise? .presumably we are filling out unstated premises as a pre- liminary towards making an assessment of the argument. ~ve want to find out whether it is cogent. The next step will be to inquire of each premise whether it is justified inde- pendently of the conclusion. But any premise strong enough to make a deductively valid ar- gument out of an argument from a stochastic hypothesis to a probabilistic prediction is incapable of being justified. At least, it can't be justified by a deductively valid argument. All that can be said in support of such a premise is that we have no reason to believe that external influences will inter- fere with the operation of the stochastic system and that certain ldescribable) effOrts have been made to find such. reasons. In principle, no such set of efforts can exhuast the possibilities. It's better to cut the knot at the place where it most obviously de- mands to be cut, and to construe the original argument as inductively strong, thus recog- nizing that new information can make the con- clusion false, even though the premises con- tinue to be true. (5) Let example. sion that day is as us consider Weddle's meteorological The argument supporting the conclu- there is a 70% chance of rain to- follows: The data available to us are such- and-such La low-pressure ridge moving down from the Gulf of Alaska, etc.). When the data have been such-and- such in the past, it has rained seven out of every ten times on the day after the data have been such-and-such. Therefore, there is a 70 per cent probability that it will rain tOI1!.orrow. This is not very sophisticated science. No well-developed stochastic theory, analogous to Hendel's theory of the inheritance of single-gene recessive characteristics, under- lies the meteorologist's forecasts. Unless the "etc." here is an open-ended "etc." which would be impossible to justify lat least deductively), it is possible that the collection of additional data or the forma- tion of more sophisticated theories would 12 lead to a radical alteration of the probabil- ity in the conclusion. That is, it is pos- sible for the premises to be true and the conclusion false. If this is one of those low pressure ridges for which we could in principle now predict (if we had the right theories and the right data) that it was going to change direction, then the probabil- ity of rain tomorrow might be as low as 10 per cent, and desultory rain at that. So it would not be that good an idea to take our umbrella. This is an example of uncited counter- evidence making the conclusion false even though. the premises remain true. I would ob- ject as before to making the argument deduc- tively valid by adding a premise to the ef- fect that no such counter-evidence is obtain- able. IV (6) I now turn to an argument which not only illustrates my disagreement with Perry Weddle but also opens up discussion of Trudy Govier'S contention (4, 5) that there is at least one additional type of link between premises and conclusion. Consider the fol- lowing argument: I wish to buy a new car. The only considerations relevant to my choice of a model are cost, comfort, safety, handling and reliability. On each of these factors model X is superior to every other model. Therefore, all things considered, I should buy model X. This is a deductively valid argument. That is, it is impossible for the premises to be true and the conclusion false. However, since this is a traditionally deductive ar- gument, it does not count in favour of Weddle's claim that traditionally inductive arguments when carefully formulated are de- ductively valid. Nor is it an example of a conductively valid argument. It does, how- ever, suggest an analogous argument which Weddle WOuld claim is deductively valid when carefully formula ted and ~vellman and Govier would classify as conductively valid. (7) To get a close analogue we could con- struct an imaginary argument which someone about to bUy a new car might use in making up her mind. However, I have chosen a real argument which is a somewhat more distant analogue. It comes from the "News from the World of Medicine" section of the December 1977 Reader's Digest (Canadian edition): Don't drink if you're pregnant. According to Dr. Joseph R. Cruse of the University of Southern California, women drinking any alcohol at all may run a risk of irreparable damage to their un- born babies •..• This brief excerpt combines an appeal to au- thority with a good reason for an omission. We might put the argument into standard form and fill out its premises as follows: Dr. Cruse says that pregnant women drinking any alcohol at all may risk causing irreparable damage to their babies. Dr. Cruse has the expertise required to make reliable judgements on this question. Dr. Cruse is saying what he honestly believes. Other things being equal, pregnant women should not do anything which subjects their babies to a possible risk of irreparable damage. Therefore, all things considered, you should not drink if you're pregnant. I add the last premise in order to bring out what I take to be the logic of such arguments. Wellman (ll} maintains that the validity of each conductively valid argument is sui generis, that there is no general form-of argument in terms of which such arguments are valid. I think, however, that there are always assumptions in such arguments that the reasons advanced are relevant to the recom- mendation drawn from them, and such assump- tions are best expressed in terms of ceteris paribus statements. When "such tacit prem~ses are made explicit, arguments of this sort are always valid. One can only object to them by questioning the truth of a premise or by citing additional reasons. Incidentally, it would not be fair to this argument to supply a strong normative premise which makes it deductively valid. Such a strong premise would be open to obvious counter-examples. It is just not true that no pregnant woman should do anything which subjects her baby to a possible risk of ir- reparable damage, no matter what the circum- stances. A pregnant woman cannot avoid doing some things which carry a possible risk of such damage, and nobody is obligated to do the impossible. Now let us consider the strength of the link between premises and conclusion in the argument as I expanded it above. Is the argument deductively valid? Suppose the premises true, and consider how the conclu- sion could still be false. Unless "run a risk" is a reporter's pleonasm, it probably captures the professor's hesitation about extrapolating empirical data concerning the effects of high doses of alcohol on unborn babies to the effects of low doses. In this type of research, a linear hypothesis about the relationship of dose and response is usually assumed. That is, if consuming 20 ounces of alcohol per day carries a 70 per cent risk of irreparable damage to an unborn child, it is assumed that consuming one ounce of alcohol per week carries a 1/2 of 1 per cent (70 divided by 20 1 divided by 7) risk of irreparable damage to an unborn child. An alternative hypothesis is that there is a threshhold dose below which there is no re- sponse at all. The "may" probably reflects uncertainty about the truth of the linear hy- pothesis. The difficulty is that it is al- most impossible to do a crucial experiment to decide between the linear and the threshhold hypothesis. Suppose, however, that such an experiment is performed, and the threshhold hypothesis wins out. Then the reason for drinking no alcohol at all no longer obtains. Assuming no other reasons for not drinking alcohol, the conclusion is no longer true. Again, there may be good reasons for a preg- nant woman to drink alcohol which override 13 the possible risk of damage to her unborn child. CIt is hard to think of any, but her personal enjoyment might be enough to over- ride a merely possible very remote risk of minor damage.} So there are at least two ways in which the premises could be true and the conclusion false. Now we could add further premises to pre- vent such counter-examples from being con- structed. We might, for example, add the assumptions that no further evidence will a- rise which contradicts Dr. Cruse's assertion. And we might add the assumption that no com- peting considerations outweigh the possible risk of irreparable damage to an unborn child. But it is impossible to justify the first of these assumptions, and difficult to justify the second one. Any such justification would inVOlve arguments which are not deductively valid. So on Weddle's theory we would have to conclude that this is not a cogent argu- ment. This seems to be the wrong appraisal. If we could justify the premises of the ex- panded argument which I set out above, then we would have a cogent argument which, how- ever, was not deductively valid. We would have to recognize that, since the premises provide non-conclusive support for the con- clusion, further evidence might arise or further considerations be appealed to which would lead reasonable people to reject the conclusion, even though they still accepted all the premises of the original argument. Perry Weddle might suggest hedging the conclusion of the argument in order to make it deductively valid. That is, instead of concluding that, all things considered, you should not drink if you're pregnant, the reporter ought to have proportioned the strength of his conclusion to the strength of his premises and concluded that, other things being equal, you should not drink if you're pregnant. Rere the relativity of the conclusion to the premises is patent, because the "other" means "other than what is cited in the premises". Further reasons for or, against drinking while pregnant could change the trut.ll-value of this st~tement. Further- more, it is not in general possible to hedge conclusions which are recommendations for action. In reasoning about what to do, we are interested in coming to a decision about what to do. At some point, we have to make an "all things considered" judgement and act. "Other things being equal" conclusions are not enough. Thus, hedging the conclusion of such arguments does not make them deductively valid, nor ein general} is it possible. Trudy Govier wishes to distinguish argu- ments whose premises are nonrelevant to their conclusion from arguments whose premises make their conclusion probable. She seems to have two reasons for making this distinction. In the first place, following Wellman, she takes the concept of probability to have its natu- ral application to the confirmation of em- pirical hypotheses by supporting evidence. As such evidence accumulates, and no discon- firming evidence is found, the probability of the empirical hypothesis increases: This is too narrow a range of application, as some of the examples above indicate. The probability of an empirical hypothesis like the special theory of relativity is quite unlike the prob- ability that a certain percentage of eligible ;:li! ,1111, :111 Canadian voters living in Canada think Canada should negotiate special arrangements with Quebec to prevent it from separating. The probability that an individual randomly se- lected from a population will belong to a certain subset of that population is some- thing else again. And the probability that it will rain today in Metropolitan Toronto or that a couple's next child will have sickle cell anemia is a probability attaching to the consequence of an empirical stochastic hy- pothesis. In the second place, Govier argues that it is linguistically unnatural to speak of considerations for or against a certain action as making it probable that one should perform or omit that action. Suppose, for example, that legalizing euthanasia carries a great danger of abuse and that we never know for certain that a person is incurably ill. These two considerations are relevant considerations against legalizing euthanasia, but it is unnatural to say that their truth makes it improbable that we should legalize euthanasia. Likewise, wheft Quebec Liberal party leader Claude Ryan uses an analogy with the time it takes to raise a family of five to support his claim that Canada has not reached political maturity, it is unnatural to say that this analogy, if it has some force, makes it probable that Canada has not reached political maturity. Appeals to natural linguistic usage are not very compelling unless they are supported by some rationale. In any living language, the range of application of words is constantly changing. If there is an obvious extension of the range of application of an existing word, why not extend it? What is crucial, therefore, is the reasons why we find it un- natural to extend the meaning of a word, in this case the meaning of "probable". The reasons why the word "probability" seems un- natural in cases where the premises are non- conclusively relevant to the conclusion seems to be that the concept of probability includes a cardinal measure. That is, if we say that something is probable, we can always be asked "How probable?" and be expected to give an answer which is either a percentage figure or a fraction between 0 and 1. tIn my examples above, I deliberately included such percent- ages.) But such responses are impossible in cases where.relevant reasons are being given for doing something or relevant criteria are being cited, either directly or through an analogy, in favour of a certain classifica- tion of a phenomenon. We should not exaggerate this difference between cases where the premises would nat- urally be said to make the conclusion prob- able and cases where the premises would nat- urally be said to provide relevant but non- conclusive reasons for accepting the conclu- sion. If the hypothesis that sickle cell anemia is a single-gene recessive character- istic is confirmed by examination of thou- sands of family histories, such evidence makes it very probable that the hypothesis is true. But we cannot cardinally measure this probability. We can recognize that an examination of thousands more cases which likewise showed the same pattern of inheri- tance consistent with the hypothesis would increase the probability. And we can recog- nize that the discovery of some patterns of inheritance which were highly unlikely on 14 that hypothesis would reduce the probability. , So we can make some ordinal comparisons be- tween the statuses of the hypothesis relative to different bodies of evidence. We cannot make ordinal comparisons very well between the probability that this hypothesis is true and the probability that another well-con~ firmed hypothesis (e.g., that Tay-Sachs dis- ease is a single-gene recessive character- istic) is true. This is precisely our situation with respect to the sorts of arguments which Govier cites. If we believe that failure to legalize eutha- nasia would condemn thousands of dying per- sons to long periods of extreme pain, that would be a competing consideration which would reduce our confidence that we should not legalize euthanasia. If we reflect on the pressures which legalized euthanasia would put on elderly people to consent to being killed in a country where there will be increasing resentment at the burden on its resources represented by an increasingly large proportion of elderly people, that would be an additional consideration increasing our confidence that we should not legalize eu- thanasia. Of course, we cannot make ordinal comparisons very easily (if at all) between the extent to which the two considerations cited by Govier militate against legalizing euthanasia and the extent to which the pos- sible risk of irreparable damage to unborn children militates against a woman drinking alcohol while sh,e is pregnant. Likewise, if further relevant similarities between raising a family of five and bringing the provinces of a disparate country to political maturity emerge, they would increase our confidence that Canada has not yet reached political maturity. If relevant dissimilarities emerge, such as the fact that some provinces had a history of partial self-government prior to Confederation, they would decrease our con- fidence that Canada has not yet reached po- litical maturity. Of course, we cannot make ordinal comparisons very easily Cif at all) between the extent to which (ll Claude Ryan's analogy between children reaching maturity and a country reaching maturity supports the claim that Canada has not reached political maturity and the extent to which (2) the popular analogy between the possible separa- tion of Quebec from Canada and the possible separation of a woman from her husband sup- ports the claim that there should be a na- tional referendum in which the rest of Canada has the opportunity to reassure Quebec that Canada wishes Quebec to remain within Con- federation. In all these respects there seem to be close parallels between the extent to which evidence confirms an empirical hypoth- esis and the extent to which relevant consid- erations or similarities support a decision or a classification. It seems difficult to justify making a fundamental distinction be- tween these two types of links between pre- mises and conclusion. In my view, the important distinction among cogen~ arguments with regard to the link be- tween their premises and their conclusion is that between those arguments where the truth of the premises guarantees the truth of the conclusion <-there is no possible state of affairs in which the premises are true and the conclusion false) and those arguments where the truth of th,e premises provides non- r I oonolu.ive 9r Ounds for accepting the conclu- sion (there is a possible state of affairs in I which the premises are true and the conclusion I ! false, but the premises make the conclusion probable or provide relevant reasons in its favourl. In some of the latter sorts of oases, we can quantify the strength of the link between premises and conclusion; in others, we cannot. In either case, we must recognize that we are dealing with an argu- ment where not only new information about the truth-value of the premises but also new in- formation independent of the truth-value of the premises but relevant to the conclusion should lead us to re-examine our acceptance of the conclusion. Certainly there is a wide variety of types of argument within the second broad classification of non-deduc- tively valid arguments. And the types of logic appropriate to the assessment of their validity go far beyond those traditionally encompassed by texts on inductive logic. If a difference is to be made among this second broad class of arguments, it might be on the basis of the sort of tacit premises which one no~lly adds in filling out the ellip- tical arguments which people present. In the case of apparently conductive arguments, these are typically of the form, "Other things being equal, anything with property ~ also has property a." Cl?roperty A could be a criterion for classification or-a reason for doing something or a relevant similarity between analogous cases.) In the case of apparently inductive arguments, it is not appropriate to fill out the premises with such statements. V Let me turn finally to the implications of a distinction among types of argument valid- ity for the classification of arguments. ~f one maintains that cogent arguments can be deductively valid or inductively strong (or conductively valid), then one has to decide which standard to use in appraising an argu- ment. This means that one must at least tentatively classify the argument as deduc- tive or inductive (pr conductive), in the sense that it is appropriately appraised by deductive or inductive (or conductive) stan- dards of validity. In my earlier article I suggested that this classification should be done on the basis of the apparent logical form of the argument. Fred Johnson's com- ments (7) have convinced me that such an ap- proach to the classification of arguments is too rigid and narrow. I suggest instead that we use a version of the principle of charity in settling on the standards by which to assess an argument. That is, we should assess it by those stan- dards which give it the best chance of being a cogent argument. In practice, this means that we should fill out elliptical arguments with premises which stand a chance of being justified and which make the argument deduc- tively valid or inductively strong (or con- ductively valid). Now it may be that an ar- gument will have a roughly equal chance of being cogent if we fill it out with premises which enable us to test for deductive valid- ity and if we fill it out with premises which enable us to test it for inductive strength. For example, it might lack cogen- cy on either interpretation. Or it might be 15 very cogent on either interpretation. How are we to classify such an argument? We can say that it is both deductive and inductive, or that it is neither. Nothing much hinges on our decision between these alternatives. In this sense, I would argue, classifying arguments as deductive or inductive (or con- ductivel is at best a tentative matter, one which does not produce a neat division of arguments into mutually exclusive and jointly exhaustive kinds. We do, however, have a mutually exclusive and jointly exhaustive division into kinds of standards for ap- praiSing the link in an argument between premises and conclusion. It is this divi- sion which justifies reference to deduction, induction and perhaps conduction as distinct types of reasoning. :# WORKS CITED (1) Fobr, Samuel D. "The Deductive-Inductive Distinction." Informal rOg~C News- letter, ii.2 (April 1980, -8-.--- (2) Fohr, Samuel D. "Deductive-Inductive: Reply to Criticisms." Informal Logic Newsletter, iii.l (October 1980), 5-10. (3) Giere, Ronald N. Understanding Scientific Reasoning. Holt, Rinehart and winston, 1979. (4) Govier, Trudy. "More on Deductive and Inductive Arguments." Informal Logic Newsletter, ii. 3 (June 1980), 7-8. . (5) Govier, Trudy. "Assessing Arguments: What Range of Standards?" Informal rO§'af Newsletter, iii.l (October 9 , 2-4. (61 Hitchcock, David. "Deductive and Induc- tive: Types of Validity, Not Types of Argument." Informal LO§iC News- letter, ii.3 (June 1980), -10. C71 Johnson, Fred. "Deductively--Induc- tively." Informal Logic Newsletter, iii.l (October 1980), 4-5. (8) Skyrms, arian. Choice and Chance: An Introduction to InductIve ~7~ic. -- 2nd eait~on. -oickenson, 1 • (9) Weddle, Perry. "Inductive, Deductive." Informal Lii99 Newsletter, ii.l (November ), 1-5. <'10) Weddle, Perry. "Good Grief! More on Deduction/Induction." Informal Logic Newsletter, iii.l (October 1980), 10-13. Cll) Wellman, Carl. Challen~e and Response. Southern Illinois Ulll.verslty Press, 1971.