~ 1 ", i(' J coming up in Milwaukee on April 23-25, 1981. We heartily congratulate the Western Confer- ence on the Teaching of Philosophy for or- ganizing this program, and hope that many of our readers will attend. We also applaud the initiative that Teaching Philosophf and its editor Arnold Wilson ave taken ~n offering a $200 prize and publication in that journal as incentives for writing papers on teaching informal logic and practical reasoning for the APA "The New Logic Course" program. Contributors to the Informal Ll~ic Newsletter who have sent us course out ~nes may well want to write their teaching ideas up and submit them. Remember the December 15 deadline. A new feature, "Chestnuts and Paradigms" is launched with this issue. We hope scholars among our readers will send us more goodies for this larder in the future. As the ILN moves toward a newsletter-c~ journal, we hope that re~ders will remember that our initial objective of serving as a clearing house for ideas, notices, news, announcements of interest to people teaching informal logic courses remains central. This is your mouthpiece, your notice-board. Please cont~nue to feel free to send us any and all material you would like to share with others. The sense of isolation, of working alone in the dark, which so many of us felt while we were teaching informal logic/criti- cal reasoning courses a few years ago, has to some extent lifted. The devotion of part of an APA program to informal logic indicates that things have begun to change; our subject is becoming respectable. May this augur a more self-confident and vigorous exchange of ideas in these columns. . . Ralph H. Johnson continues to serve as co- editor while on sabbatical this year (1980- 81). West coast (North American) readers may be interested to know that he is located in Los Angeles, and can contact him directly at 2553 Tanoble Drive, Altadena, California 91001 (213-791-3519). ~ ~~~::: .• =. .~: ... ~:' ~" ..... __ ... ;-,' .'1. ": !', .. :.: : ;:: ... I!' ... ' .. li; .~:' .. ', '.~:;.. .~':;:; :' .t ~.~.. '~ •• " . ..,'.' • i-:. . ' .. ~~. . ' ... •... ' .,,:;~II!I' ... : .•.. ;~fS'..- 5~ecial thanks for assistance in the produc- t~on and distribution of this issue of ILN to: Violet Smith, our stellar typist; --- Jerome V. Brown and June Blair for production assistance; Irene Antaya and Peter F. Wilkinson for doing the mailing. 2 responses The "inductive-deductive" debate continues unabated in this issue. David Hitchcock IS article in ILN, ii.3 sparked a response from Trudy Govier;-in which she argues further that deductive standards and inductive stan- dards do not exhaust the standards of argu- ment. Fred Johnson reacts also to Hitchcock, but mainly to Sam Fohr's article in ILN, ii.2; Johnson suggests we should tal~out inductive and deductive arguings, not argu- ments. Fohr himself has a response to the criticisms by Hitch.cock and Govier of his original piece in ILN, ii.2, as well as some comments on Fred Jonnson's suggestions; Fohr remains convinced that the inductive argument vs. deductive argument distinction is sound and exhaustive, and that his way of characterizing it is correct. Finally--so far as this issue goes, at any rate--Perry Weddle, who began the exchange with his article in ILN, ii.l, responds to Hitchcock (ILN, ii. 3) :--Fohr (ILN, i1. 2), and Govier (ILN, ii.3); and WedOTe hasn't much changed hrs-mind, either. Is that clear? Assess~rgu. nnents: Range af Standards? Trud y Govier Trent University David Hitchcock, following Brian Skyrrns, defends the inductive-deductive dichotomy by taking it to be a dichotomy' of standards, rather than an exhaustive division of argu- ments into two basic types. l He says that in deductive logic, we have a theory of the circumstances in which premises do or do not make it logically impossible for a conclusion to be false. And in inductive logic, we have a theory of the circumstances "in which an argument is inductively strong or inductively weak--that is, in which it is more or less probable that its conclusion is true, given that its premise(s) are true." Within each theory there are various types of logic: in deductive logic we have the logic of truth- functional sentence connectives, first-order quantifiers, the logic of identity ..• ; and within inductive logic we have "the logic of r the confirmation and disconfirmation of hy- potheses, the logic of analogical arguments the logic of inferences from sample charac-' teristics to population characteristics the logic of controlled experiments to prov~ causal claims, the logic of conductive or balance-of-considerations or good reasons arguments, and so forth" C~, i1. 3, p. 10l. On this account the exhaustive dichotomy between inductive and deductive arguments is to be replaced by a dichotomy of standards of good argument or, as Hitchcock puts ~t, "types of validity". Hitchcock admits-- indeed he argues--that for many cases it will not be easy to decide just which standard is the appropriate one to apply, and this is why it is inappropriate to regard the inductive/ deductive distinction as a distinction be- tween types of argument. Perhaps it is easier to distinguish standards than to sort out arguments. However, there will presum- ably be some fundamental connection between the variety of arguments tHere are and the number of different standards which theore- ticians see fit to articulate; a primary reason, I take it, for developing an area of logic around a "type of validity" would be that there are a number of arguments which are appropriately assessed by the standard thereby developed. This caveat aside, I am inclined to agree wit~ Hitchcock that it is more profitable to dHferenti.ate types of standard than types of argument. However, I disagree wi~ his view that 'inductive/deductive' will exhaust the range of standards. On Hitc~cock's view, premises can provide grounds for conclusions, and the strength. of these grounds can be assessed in two and only two ways. We can ask whether the tru~ of the premises would make the falsity of the conclusion logically impossible, thus assessing the argument by the standards of deductive logic. Or we can ask whether the trut~ of the premises would make the falsity of the conclusion improba- ble, thereby assessing the argument by the standards of inductive logiC. The word 'probable' is a difficult one, used in many different contexts. Even within the theory of probability we have very dif- ferent interpretations of what "probabilities" are about-~fogical probability, subjective probability,and the relative frequency theory. The indeterminat~ meaning of 'prob- able' and 'improbable' may make it seem reasonable to say that if premises provide grounds for a conclusion they either do so by making its falsehood impossible, or by making its falsehood improbable; and there is no third alternative. I think, however, that this is a falsely simple view of the matter. probabilities are attached to empirical hy- potheses which are less than certa~n. There are conclusions which are not exactly empir- ical--being, for instance, evaluative or conceptual--and which are yet defended by premises nonconclusively relevant to them. Arguments in which this sort of structure is found are quite different from those argu- ments typically dealt with in inductive logics, and "probable/improbable", despite their vagueness and flexibility, seem out of place in dealing with them. Some such argu- ments are conductive (the "good reasons" type); others analogical. Hitchcock wanted 3 to assess both by a "making probable" induc- tive standard. I think that this is inap- propriate. Consider: ~. Assisted euthanasia should not be legalized, because (ll the danger of abuse is too great, and (21 medical advances being possible, we never know for certain that a particular patient is incurably ill. Argument ~ is a ".good reasons" argument; ell and C2l. are put forward as reasons in support of the conclusion. Hitchcock said that suc~ arguments would typically be assessed by in- ductive standards. Thus we are to ask whether Cll. and (21 "make it probable" that assisted euthanasia should not be legalized. But the concept of probability seems most out of place here. Does the danger of abuse make it imerobable that euthanasia should be legal~zed? It is a reason against the legal- ization--not a conclusive one, but a reason; however, whether euthanasia should oe legal- ized is a question of policy to which "prob- ability", much more at home in empirical contexts, is only applied by linguistic st~etching. That there is a danger of abuse is not a bit of empirical evidence counting against a Claim which we have not veri-fied yet, but could verify later; rather, it is a factor which counts, or weighs, against our deciding to legalize assisted euthanasia. T? speak of the conclusion as rendered prob- able by (1) and C2l is linguistically unnat- ural; one might stretch "probable" and "im- probahle" for this context and others like it, but by so doing, one would hide 4 real difference. ' Look at another case: B. It takes 30 years to raise a family of five, se: how long does it ;take for a whole country to reach polit- ical maturity? (Claude Ryan on Quebec nationalism, quoted in the Calgary Herald, August 20, 1979.l In this rhetorical question, we have the material for the follOWing analogical argu- ment: (1) It takes 30 years to raise a family of five. (2) Just as children must mature, a whole country must reach political maturity. C(l) It takes a long time for a whole country to reach political maturity. (Implied) C(2) Quebec has not yet reached political maturity. I shall not venture to comment here on the merits of ~s argument; rather I shall ad- dress myself to the question as to whether the concept of probability will serve us well when we come to assess it. Ryan is asking us to assimilate the development of a nation to the development of child=en: to assess his argument we must ask ourselves how alike these are, and how unalike. 2 The c~t "maturity" is normative in either applica- tion. Ryan I s argument is not like the kind of analogical argument where we infer, on the basis of a closely developed analogy, the presence of some empirically discerniDle characteristic Ce. g., hydrogen in the atmo- sphere of Mars) from other shared features. There the notion of enhancing the probability of a conclusion would have its normal and proper location. Ryan asks us to think of nations as we would think of children and to use the concept "political .maturity". Clear- ly his argument is not deductively conclusive, nor does it seem intended as such. And yet to think that there may be something in the comparison is not to think that the proba- bility of the statement, "Quebec has not yet reached political maturity," is increased by the comparison. It is hard to give any sense at all to the notion of such a statement" s having a probability, measureable or other- wise. My own argument here, and indeed--I sus- pect--many philosophical arguments are of the type I have been trying to describe. When assessed by standards of deductive validity, they fail tests imposed, for the reasons of- fered do not logically entail the conclusions. They offer-support for a conclusion, and less than logically conclusive support. But yet it seems inappropriate to see these premises as enhancing probability. For the issues are issues of value, or of appropriateness of classification--issues in quite other ter- ritory from the realm of empirical hypothesis where the concept of probability has its natural place. I suggest that "inductive" and "deductive" are indeed two types of standard for ap- praising arguments, but that there is no particular reason for thinking that these exhaust the range of standards. In fact, there is quite good reason in the study of actual cases for thinking that they do not. NOTES l"Deductive and Inductive: Types of Valid- ity, Not Types of Argument", by David Hitch- cock, Informal Logic Newsletter, ii.3, June, 1980. 2I have been influenced here by John Wis- dom's Virginia Lectures, entitled "Explana- tion and Proof". These lectures are, unfortunately, available only in manuscript; however a useful resume of the material may be found in D. Yalden-Thomas, "The Virginia Lectures", in Renford Bambrough.., Wisdom: TWel ve Essays. (f . 4 Deductively· Inductively Fred Johnson Colorado State University Fohr (ILN, ii.2) gives an account of deduc- tive arguments that is deSigned to be com- patible with the following claims: a) There are invalid deductive arguments, and bl No arguments are both deductive and inductive. He succeeds in his objective but I think there are compelling reasons for rejecting his account. He can find a place for the deductive-inductive distinction but the terms involved apply to arguings not ~- ~. Fohr states that: 1. "Real arguments ••• are given by people to convince someone of something." 2. " ••• arguments do not exist in vacuo but are person-related.v- 3. r;-:-.an example on a page of a logic textbook is not strictly speaking an argument. • • • We should call this example a 'possible argument' . " 4. "If a person intends that his premises necessitate his conclusion he is giving a deductive argument." As they stand 1-4 are confusing. For example, 1 and 2 taken together suggest that you can give something that does not exist. The use of "~ssible" in 3 is confusing. Presumably, possible arguments are actual somethings, just as possible statements are actual some- things, viz., actual sentences. But what are the actual things that possible argument are? To avoid such puzzles let us rewrite 1-4 as follows: 1'. An argument is a try by an A to con- vince a a that £ by offerinq as evidence -E. 2'. Ttle A and-the B are crucial to the definition in r'. 3'. The ordered pair ErC with constituents mentioned in l' is not an argument. 4'. A deductive argument is a try by an ~ to convince a ~ that £ by using evidence E given that A construes ;. as necessitating £. -. l' -4 t are compatible with a1 and bl.. An invalid deductive argument is a deductive argument in which the E does not necessitate the C. An argument cannot De both deductive and Inductive since it is impossible for someone simultaneously to construe E as necessitating and not necessitating-£. The prob~em with 1'-4' is that this notion of an arg~ent does not accommodate what "politicians, lawyers, housewives, histori- ans, economists, psychologists, and others" (Govier, ILN, ii. 3 ) know: someone' s argu- ment can Di""'"the same as someone else' 5; someone's argument at one time can be the same as this person's argument at another time. A try by A to convince is not the same as a try by-B to convince any mor~ than a try by A to lev1tate is the same as a try by B to levitate. (And A's earlier try is not-the same as his later try.) Of course, people can try to do the same thing but the tries are not the same. So let us modi£y 1'-4' in order to be able to say with justi£ication that A's argument is the same as B's and also preserve a form of the deductive-inductive distinction. 1". A is arguing iff A is trying to convince B that C-by offering as ~vidence C. - 2". "Arguings" do not exist'in vacuo but are person-related. -- ----- 3". The ordered pair E;C with constituents mentioned in I" is an argument (but it is not an "arguing"). 4". A is arguing deductively iff A is trying to convince B that C by offering as evidence E and-A construes ; as necessitating £.- - Since the same ordered pair E;C may be in- volved when A is arguing as when B is argu- ing .. A's argumePts may be the same as B's. Couple 4" with the claim that A is arguing inductively iff A is arguing and is con- struing E as providing only partial evidence for C ana we have a form of the deductive- inductive distinction. Our "approved terminology" includes: "argu- ings," "arguments," "arguing deductively" (or "deductive arguings") , but not "deductive arguments." It is tempting to instate the latter familiar term by agreeing that A's argument is dequctive iff ~ is arguing- deductively. This would be a pedagogical mistake. Talking about deductive arguments to our students would have the same effect as talking about happy houses and emphatic be- liefs to people who are in the first stages of learning our language. My hunch is that people in the latter category would think w·e are talking about features ~f houses and ae- liels rath~r than features of persons, and our students would think we are talking about features of arguments rather than features of persons. It does not follow that there are not other methods of instating the "deductive argument" terminology. I will mention only one more, which is discussed by Hitchcock (ILN, ii.3). He takes seriously (to my surpriser-a remark by Weddle (lIoN, iLl) that "what distin- guishes deductive arguments from inductive arguments is the sf",ctions of logic books in which they happen to be found." We can ex- tract the following definitions from Hitch- cock's remarks: E;C is a deductive argument iff the reIation between the premises and the conclusion of E;C is best ex- plored by USing a truth-functional calculus, or a first order predicate calculus, or 55, or ...• 5 E;C is an inductive argument iff the . reIation between the premises and the conclusion of E;C is best ex- plored by considerIng the structures of analogical arguments, or the structl:,res of arguments with causal conclusions and premises justified by controlled experiments, or ••.• The definitions refer to a bundle of calculi and n bundle of structures? But what makes the two bundles two? In which bundle do fuz- zy logics occur? Isn't it possible that there is a valid argument whose propositional calculus mate is invalid-in-the-propositional calculus, whose 55 mate is invalid-in-55 and, in general, whose X mate is invalid-in-X, where X is any calculus found in the first bundle? Would such an argument be inductive? Would we ever be in a position to assert tnat the relation between the premises and the conclusion of an invalid argument would not be best explored by looking at the structures referred to in the definiens of the defini- tion of "inductive argument"? (That is, would we ever be in a position to say that an invalid argument is deductive?) We do not even need to begin to try to answer these questions without recognizL~g that students in our informal logic courses should not labor over this definition of a deductive- inductive distinction. ~ Deductive-Inductive: Reply to Criticisms Samuel D. Fohr U. of Pittsburgh at Bradford I In my initial article on this subject LILN, ii.. 2) I argued for the view that the tradr::- tional distinction hetween deductive and in- ductive arguments was both viable and impor- tant. I distinguished between the two types of arguments by saying that deductive argu- ments: were ones put forward with the inten- tion that the premisses necessitated the con- clusion whereas inductive arguments were ones put forward with the intention that the pre- misses rendered the conclusion probable. Dilferent sorts of objections have been ra5.sed regarding these ideas, but I still feel that my views are correct and in what follows I will explain why. " I II David Hitchcock (ILN, ii.3) argued that we should follow Brian-skyrm's advice (Choice and Chance, 2nd ed., Dickenson, 1975) and scrap the traditional deductive-inductive argument distinction in favor of a distinc- tion between deductive validity and inductive strength. "The main question to be asked in this connection about any argument is how strong the link is between the arguer's ~re­ misses and his conclusion, not whether the arguer's claim about their link is correct." (p. 10) According to this view we should ask about any argument: is it deductively valid, or at least inductively strong, or neither? The person's intentions are not important. Hitchcock's principal criticism of my view is that my analysis of deductive and induc- tive arguments in terms of people's inten- tions is not exhaustive. For people often give arguments with no inte~tion about how their premisses support their conclusion. Suppose, for example, I say to my wife: 'You should help me paint the kitchen this evening. You promised you would.' My intention is to convince her to help me paint the kitchen, on the ground that she promised she would. But I make no claim, nor (let us suppose) do I have any intention, about the strength of the link between my premise and my conclusion. Cpo 10) He adds that he thinks many people have no intenti.ons. about the strength of their argu- ments when they put them forward. W~le r think t~s sort of an oojection can oe pushed too far, I would oe the last one to claim that in all cases people have such intentions--even if they are completely unaware of them. I say that t~s sort of an objection can be pushed~too far because a person doesn't have to state an intention explicitly, or even be thinking of something, in order to have an intention. We do many things in an automatic fashion. But if ques- tioned a person migh.t say, "Of course I in- tended the premisses to necessitate the con- clusion." On the other hand, there is little doubt that there have been many cases where people:, perhaps because they attempted to give arguments on the spur of the moment, had no intentions one way or the other. While Hi.tchcock seems to think that this proves ·that my analysis of arguments in terms of intentions is not exhaustive, I think there are other ways to view the matter. I must remind the reader of a point I made in my first article: arguments are made by people to convince someone of something. Arguments do not exist in vacuo. The exam- ples in logic textbooksiare really possible arguments (unless they are real-life exam- ples). When a person utters something which could be construed as an argument but has no intention about the relationship of the pre- misses to the conclusion then that person has not really expressed a unique argument. Without the intention we cannot say that per- son has expressed a particular argument. ,vhen a person utters what could be con- strued as an argument but has not expressed 6 any intention about its strength, it is all the same whether that person has no intention or merely hasn't made the intention clear. In such cases we have a real problem in knowing how to judge the person's statement, for the statement is ambiguous. If we are not in a position to ask the person any ques- tions we can either decide to judge the statement as one kind of argument, e.g., as deductive, or judge it first as a deductive argument and then as an inductive argument. If we are in a position to ask questions we should avail ourselves of the opportunity. I am thinking of questions like, "Are you saying that the conclusion of your argument must be the case if your premisses are cor- rect?" In the example Hitchcock used his wile .might have replied, "What are you saying? That since I promised I'd help you paint ~s evening it follows that no matter what r am obligated to help you paint? Or if you're not saying ~s, then what are you saying?" She might have said ~s while in the midst of doing some important household task. There is one other way of viewing Hitch- cock's example which mayor may not be apro- pos. It is that ~s example doesn't involve any argument at all. For we need not take the giving of a reason to be equivalent to the giving of an argument. CThis was sug- gested to me by Prof. George Mavrodes of the University of Michigan.) It may be that in saying what he said to his wife Hitchcock had no intention about the relationship of his premisses to his conclusion because he was not really giving an argument. Whether or not this nort of approach applies to Hitch- cock's example, it is probably the correct approach in many instances of reason giving. To sum up this section of my reply, I be- lieve that my analysis of arguments in terms of the arguer's intentions is exhaustive. Where there are absolutely no intentions th.ere is no definite argument expressed. And in many such cases we may be correct in saying that even though the person gave a reason there was really no attempt to give an argu- ment. III In wishing to discard the deductive-induc·· tive distinction Hitchcock is running up against the actual practice of philosophers doing logic. When faced with judging the worth of an argument philosophers will com- monly decide how it is to be analyzed and only then examine it. In other words, ante- cedently to judging it they will decide how it is to be judged. If they decide it is an inductive argument they do not look to see if the premisses necessitate the conclusion. On the other hand, if they decide it is a deductive argument they do not examine whether or not the premisses render the conclusion probable. Are philosophers de- luded in thinking that arguments fall into two categories? Have they been going about things in the wrong way for these many years? I don't believe so and I don't tbink Hitch- cock does either. He seems to realize that philosophers practicing logic decide how an argument is to be judged before judging it. For after listing certain types of log~c he says: r j t ~ t '1 9 b 101 S i j n i j s a 1 e t d w; d. n. il 14 sl We ought to assess an argumen·t on the oasis of which. of these special- ized types of logic seems to provide the most appropriate framework--in other words, on the apparent logical form of the argument. In doing so, we may be guided b.y the claim or intention of the arguer ab.out the strength of the link oetween pre- misses and conclusion. But such a claim or intention is at best of heuristic value, and may have to be discounted. Cpo 10) In saying this he is implicitly admitting a distinction between types of arguments--a distinction which is antecedent to any judg- meni: of arguments. Naturally, I disagree with the last part of his statement. When people's intentions are indicated we should honor them, even when we can see that they sold themselves short or oversold themselves. If we do not honor a person' s intentions~hen we are not truly dealing with that person's argument. Instead of judging that person's argument we will end up judging a different argument. Rather than ignoring a person's expressed intentions when we feel that person is misguided, we should say such things as, ·You seem to think that your premisses are conclusive, but they really aren't." We might go on to say, if the example allowed, "If you would change yOlu conclusion to a weaker statement, if you said 'It was likely that such and such,' you would have a strong argument. " When faced with a statement (in the absence of the person who made it) which could be construed as an argument but which carries no indication of intention, a philosopher prac- ticing logic will usually try to peg it as having a certain form. Once this is done the statement will be judged accordingly. Thus a statement which seems to involve a generalization from individual instances will be judged as an inductive argument. And one which seems to have the form of a categorical syllogism Cor of transposition, or modus . ponens, or disjunctive syllogism, or the fal- lacy of denying the antecedent) will be judged as a deductive argument. There is nothing wrong with this practice as long as it is understood that el) We may not be doinq justice to the arguer, and (2) We may our- selves be turning an ambiguous statement into a definite argument. IV Trudy Govier (ILN, ii.3) finds many prob- lems with the inductive-deductive distinction, especially with my way of drawing the distinc- tion, but shares my "reluctance to scrap the distinction." There are basically two things which disturb her about my views and I will discuss them one at a time. First of all, Govier feels that any expla- nation of the deductive-inductive distinction in terms of the arguer's intentions is prob- lematic. In response to my original article she writes: If we really take Fohr seriously on the overriding importance of intention, then we will have to accept the peculiar consequence that there are inductive 7 arquments which are deductively valid and deductive arguments which are inductively strong. For instance, suppose someone argues: 1. Either Levesque will be defeated at the next election, or he will win and call another referendum. 2. Since Quebeckers are fond of Levesque, he will not be defeated at the next election. 3. Thus, there will in all likelihood be another referendum. This argument is deductively valid, but the conclusion contains the tentative expression 'in all like- lihood'. (p. 7) Govier goes on to say that the person might have expressed the conclusion hesitantly be- cause of an uncertainty about the first pre- mise. I take it that the uncertainty was over whether Levesque would call for another referendum. There is an old saying to the effect that an example is not an argument. It is one thing to illustrate a general comment with an example, but quite another to prove a general point with an example. This particular exam- ple is capable of many different elucida- tions. First of all, we may add to Govier's analysis that the person putting forward the argument might be unsure of the second pre- mise as well as the first. That is, the per- son may believe that since Quebeckers are fond of Levesque in all likelihood he will not be defeated in the-next election. Most people are aware of the fact that a politician's favor with the voters can change drastically in a short period of time, so it would be probable that the person putting forward the argument really' had a weaker version of the second premise in mind. In fact, if we could find a person who actually put forward this argument we could probably get that person to admit to overstatement. Why bother aSking people about their argu- ments? Because we should be interested in their intentions. It is important to find out if they really said what they meant. They may have been thinking one thing and saying another. In this particular case the upshot was a hesitant conclusion following s.ome forthright premisses. Once we get clear as to wl~at was really going on in the arguer's mind we can see that the arguer was really thinking of an argument whose form is deduc- tively valid, although one with the phrase "in all likelihood" in the conclusion. The form is: p, or q and r probably not p therefore probably r Before I would as~ec.s an argument such as the one in Govier's example I would question the arguer. I might ask, "Why do you say 'In all likelihood' instead of just stating straight out that •.• ?" If I was not in a position to question the arguer then I would have to honor the arguer's intentions as indicated in judging the argument. I am willing to live with the consequence that according to my views I am forced to call this argument in- ductive even though it has a deductively valid form. ·", r " '1 (;1 \1 ,it I , . ' ." It may be said that if an argument I would call inductive could be analyzed as having a deductively valid form, or an argument I would call deductive could be analyzed as being of a strong inductive type, then my distinction between deduct.ive and inductive arguments is not very important or signifi- cant. I have no control over the valuation another person may put c.n the deductive- inductive distinction as I have drawn it. However, it would seem to me that one thing which might lead a person to downgrade it is a preoccupation with neat textbook examp~es which nobody in their righ.t mind would ever actually use in trying to convince someone of something. I am more concerned with the real arguments of real people. For this reason I am concerned with what people intend when they give arguments. The analysis of such ar0uments is a much more complex affair than is evLdent from most logic textbooks. Govier's other objection to my view is that the two-fold deductive-inducti.ve dis- tinction doesn't really do justice to the wide ,~ariety of types of arguments. To put it another way, this two-fold classification is not very helpful in describing the nature of an argument. Furth.ermore, since "induc- tive logic deals exclusively with confirma- tion/disconfirmation of empirical hypotheses by empirical data on particulars" people may get the idea that "all arguments are either deductive or scientific-empirical-inductive. Such a belief we inherit from positivism, and it is this legacy which makes people think that there cannot be arguments L~ support of moral judgments" (p. 8). In order to under- stand Govier'S concern one must keep in mind that she views ethical arguments as non-con- clusive. According to her views they would therefore fall into the inductive category along with legal and other types of argu- ments, and possibly get lost in the .shuffle. r wish to say first of all that I share Govier's concern th.at ethical arguments not be overlooked. In my logic courses I have found that most students don't think there can be arguments in support of moral judg- ments. Thus when they spot a passage with the word "should" in it, they automatically assume that no argument is being presented. No doubt this is due to the blight of ethical relativism in our progressive age. The re- sult is that many people think that ethical judgments are a matter of individual taste. Be this as it may, it does not seem to me that we should on this account reject the deductive-inductive distinction. Rather, ,what is necessary is to impress on students and others that there can be reasons for moral judgments, and that indeed there are perfectly good arguments with conclusions which begin with the words "You should" and "You shouldn't". I find myself in disagreement with Govier's classification of all ethical arguments as non-conclusive and hence inductive. It seems to me that most ethical arguments are en thy- memes, and, leaving aside for the moment the matter of the arguer's intentions, if these enthymemes are fleshed out using the prin- ciple of charity the result will be an argu- ment with a deductively valid form. If some- one said to his wife, "Yo.U should help me paint the kitchen this evening. You promised you would," and we took this to be an argu- 8 ment, then we should reconstruct it in the following way: When you have promised to do something then you should do it. You promised to help me paint the kitchen this evening and there are no extenuating circumstances. Therefore you should help me paint the kitchen this evening. I would not want to claim that all ethical arguments will be found to have a deductively valid form, but only tnat many of the most commonplace types will be found to have such a form. V I have already remarked on the complexity of many real life arguments. Nowhere is this more evident than in the case of arguments which Carl Wellman has chosen to call conduc- tive (Challenge and Response, Southern Illinois U., 1971). In her critical review of Challenge and Response (ILN, ii.2), Trudy Govier discusses Wellman's conception of the conductive argument. She quotes the fol- lowing pa~sage from the book. The conductive argument: derives its conclusion from a variety of premises each of which has some independent relevance. Typically, although by no means always, several reasons are given in such arguments; and in those cases where a single reason is advanced, there are others which might have been given as well. Since what is characteristic of this sort of reasoning is the leading together of various considerations, it seems appropriate to label it 'conduction'. (p. 52) Govier goes on to say: The conductive argument is one in which the premise, or premises, are each separately relevant to the conclusion, though none is sufficient to show its truth. (p. 121 I do not see any need for adding a new cate- gory to the deductive-inductive classifica- tion, and I do not believe that the sort of argument Wellman calls conductive (and which is commonplace enough) has been analyzed cor- rectly. In showing how such arguments should be analyzed I would lLke to work with a real life example. It comes from a collection of articles and editorials assembled by Alan Harris and Gerald Gurney (Argument, Cam- bridge, li68, p. 5). The example I have in mind is an editorial which appeared in the Daily Telegrap~ on January 28, 1964. The wI1ter argues that England should not raise the minimum school leaving age from 14 to 16. He gives three reasons. (11 There is already a projected teacher shortage of 35,000 and raising the school leaving age would cause even a greater shortage. (2) "Already there are m~y l4-year olds ••• who derive no obvi- ous pleasure or profit from remaining at school. These children jeopardize the educa- tion of those who would benefit by it." (3) It WOUld. further prolong the task of instruc- ting the uninstructable which has broken the hearts of ~any teachers. From the tone of the editorial (which is all there is to go on) I would judge that the writer thinks each of the three reasons is conclusive. What he is doing is presenting three independent deductive arguments, all of which are enthymemes. Using the principle of charity I would reconstruct them in the fol- lowing way: (1) If raising the minimum school lea,ring age would cause a severe shortage of teachers, then the minimum should not be raised. Raising the minimum school leaving age 'tlould cause a severe shortage of teachers. Therefore the mini- mum age should not be raised. (Perhaps an extenuation clause should be put in the consequent of the first premiss in this and the next two arguments.) (2) If raising the minimum age would result in t~e presence in school for two more years of,students who would jeopardize the education of those students who could benefit by these years of schooling then the minimum age nhould not be raised, etc. (3) If raising the minimum age would result in the prolongat.ion of the heartbreaking task of instructing the uninstructable th$n the mini- mum age should not be raised, etc. All three of these arguments have the .modus. ponens form and are t.h.us deductively valid.· The ques.tion will come; if the editorial writer though± that i.n each. of the cases the premisses entailed the conclusion, why did rue present three arguments? r will answer that question with another: Why did St. Thomas. Aquinas give five separate arguments for the existence of God? Not because he though± any of tnem were weak, but probably because he felt that thei.r combined weight would be more convincing. The same could be true of the editorial \oj·riter. There is one other possibility in the case of the edito- rial writer. He may have felt th.at various people would question the premisses ne used in one or another of his arguments. So ne played it safe by giving more tnan one argu- ment. I cannot leave the subject of conductive arguments witnout a reminder about a point I made at the end of Section II: The mere .9iving of a reason is not equivalent to 9iving an argument. Indeed, I have the feeling that many of the statements Wellman would call examples of conductive arguments are probably not arguments at all. VI In conclusion I would like to make the fol- lowing points: (1) 'l'he deductive-inductive distinction is viable and important. (I dis- cussed this in detail in my initial article.) (2) :-ly way of drawing the distinction is exhaustive. (3) While calling an argument deductive or inductive may not tell everything of importance about that argument, 9 it at least gives some useful infor- mation. (4) There is no need to add any other catE:gory to the two I have been explai~ing and defending. (51 Analyzing real-life arguments rath.er than textbook examples is a very complex matter, much more complex tnan one would think from reading most books on logic. To expand on point (51, most real life arguments are enthymemes. The reason is that people seldom bother stating all thei~ pre- misses. Typically, these arguments will be of th.e generalization-specific instance type. And themiasing premise will us.ually he the generalization, which. can be expressed in the form "All S are p" or the fODll "If some- thing is; an 5 tnen it is a P." Or if tne argument is not of th.is type tnen it will probably he of the mOdusI1onens or modus tolle,ns fODll, witiL ~ p then q" premise missing. The danger of reconstructing enthy- memes Cas 1: attempted to do in the last sec- tiont is that one may come up witn an argu- ment wnich is different from wnat the arguer nad in mind. Indeed, the arguer mignt be surprised to find out what sort of premiss would De needed to make the argument com- plete. Tne truth. is th.at many people are unaware of their assumptions. Besides the problem of reconstruction there is the problem of the arguer's intentions about the strength of the relationship be- tween the premisses and conclusion. When those intentions are made obvious, we cannot ignore them, however much we might like to. For to ignore them is to ignore that person's particular argument. In those cases where the arguer has intentions but doesn't indi- cat.e them we are placed in the difficult position of guessing them in order to proper- ly and fairly judge the argument. We may very easily make a mistake. When the arguer has no intentions then no definite argument has been made. In such cases the arguer will not have indicated any intentions and we are placr:d in the same position as in the previous type of case. Only here, any guessing we do will really be making a particular argument out of a statement which was not one origi- nally. As a parting thought I would say that aftE.r examining various editorials and let- ters to the editor I have reached the conclu- sion that in many instances people would be hard pressed to explain "just what their argument is." Appendix ~ Terminology In t~e current issue of the Informal ~oiic NewslettE;r Fred Johnson takes me to tas or using language in a confusing way and thereby vitiating my account of the deductive-induc- tive distinction. He quotes the following from my original article: •.. an example on a page of a logic textbook is not strictly speaking an argument.... ~"e shou.:'.d call this example a 'possible argument'. He goes. on to say, "Pres.umably, possible arguments. are actual somethings, just as poss.iDle statements are actual somethings, v~z., actual sentences.. But what are tne actual things th.at possilile arguments are?" The answer to this question is very simple: ," ,: ", '1 ~, 'Ii .11 :!1 ·1 j~ ,~ 1 f , possible arg'l.Ul\ents. By '·possible argument" I meant a group propositions which could Qe used by someone to convince someone-o?:Some- thing. Presumably not just any group of propositions could Qe so used. Johnson also claims that on my account of things, properly clarified, two people could not make the same argument. I would cer- tainly admit that any number of people could make the same argument, but I do not believe anything I wrote in my original article would preclude this. I did say that arguments· are person-related. By this I meant only that what makes a real argument out of a possible argument is that someone sometime actually used it to convince someone of something. This doesn't preclude two people from giving the same argument. All that is necessary is that they express the same propositions with the same intention as to the strength of the connection between the pr~~isses and conclu- sion. There is one seemingly odd result of this way of looking at t~~ngs. If two people expressed the same set of propositions with different intentions then they would be giving different arguments. However, I think it would be admitted that if they had differ- ent intentions then we would judge their arguments by different criteria. And this certainly accords with conunon sense. Host philosophers who teach logic are ac- customed to referring to specially made up examples in logic books as arguments, so I can understand why they might be somewhat repulsed by my suggestion that we call them possible arguments. Yet it 5.eems quite proper to say of certain textbook examples, "They are: not real arguments," the sense being that riO one would ever think of using them in real life,i.e., they are merely instructional examples. So I am not departing from established usage to any great. extent. Furthe~ore, if we do not adopt my suggestion about textbook examples we might as well for- get about trying to distinguish between de- . ductive and inductive arguments. Some may say thilt it would be better i.f we did just that. But r. believe we would be the poorer for it. :tit Goad Grief! Marean Deduction/Induction Perry Weddle CalifOrnia State u., Sacramento While at moments sharing the reluctance of ILN contributors to scrap the modern distinc- tion (~ la Copi) between inductive and deduc- tive arguments, I still find myself overcome by my expressed misgivings, and others. l 10 I David Hitchcock (ILN, ii.3, p. 9) thinks me mistaken to maintain-that with the premises filled out and/or the conclusion appropriately hedged, a good traditionally inductive argu- ment becomes deductively tight--always in such cases counter evidence may lurk unci ted, which could render the conclusion false. Such an argument would become deductively valid only if we were fo stipulate that its premises describe a closed system, or to add an open-ended premise excluding counter evidence. "Closed system." If Hitchcock intends his conunent to be an objection then he needs to argue ~y one cannot stipulate that the pre- mises 0 a traditionally inductive argument describe a closed system. He needs also, I think, to argue that one would have to stip- ula.te such, and to argue that premises de- scribe systems at all. In my article (ILN, ii.l, pp. 3-4) I observe that the most familiar reaches of technology, where sufficient conditions are completely understood, do constitute what amount to closed syster,s. At least there, the relation- ship betw~en a conclusion and the premises which predicted it is deductively tight. Being (usually unknowing) participants in the very Humean attitude that observer error is infinitely more likely than suspension of the laws of nature, astute, very reasonable people there never even dream of true premises yielding a false conclusion. Suspension of the laws of nature ~s not an option. The likes of, e. g., "We must. 've goofed, only we car.'t see where," invariably supercede the likes of, e.g., "Well, God must've inter- vened," or, "Well, Snell's Law always worked here Qefore, but it didn't work last Tuesday." The argument structure, that is, invariably remains unquestionedly valid, while the premise set is assumed false. NOW if we are to be observers of argument as actually found, then here we have countless examples which fit both the inductive and deductive traditional categories. It is hard there to see how one could stipulate that the premises of such arguments describe closed . systems, since their premises seem already in fact to describe such systems. If they can be said to describe at all. What allows systems sometimes to be open and sometimes closed, I would venture, is the practices and purposes of this or that activ- ity. And if it is the participants who clos~ or don't close the system, then the premises will be within the system, but will not de- scribe it. Decimal arithmetic is closed when it's a matter of doing decimal arithmetic-- keeping accounts, reCiting the times tables or measuring jumps. Amidst any such activ- ity it would be inappropriate, told that 5 modules added to 8 always yields 13 modules, to object that in other systems or possible systems--ordinary horology, for instance--S modules added to 8 yields other than 13 mod- ules. Similarly, in logic class it makes senSf: to tre .. t the premises of a valid form-- complete enumeration, for example--as ex- hausting all possibilities. There the form's the thing; there we want to emphasize that exhaustion. To mention practical difficul- ties in clOSing the system would be inap- propriate. Were a student to object, "Yeah, but you can't know you've counted 'em all," we would have to reply, "That's not the point: what I'm saying is: if all this stuff over here is true--never mina-how you know it --then the conclusion has to be true." By thE. very useful emphasis on form, and because e:f the importance of the notion of validity, the system has been closed. In o.ther circumstances the premises of valid arguments, including complete enumera- tions, are anything but closed. There, not just validity matters, but soundness. with complete enumerations, for instance, prac- tical difficulties in counting will make or break the argument. The "system" the pre- mises try to exhaust may be very open indeed --as when a junta chief concludes that every officer is. loyal, or as when a surgeon an- nounces, "Therefo.re, we believe that we have removed the whole cancer." In form many traditionally inductive argunents are as closed as thei.r deductive count:erparts. And the practical difficulties attending ,claims about soundness remain as great for t.radi- tionally deductive arguments as for their inductive counterparts. In making an induc- tive-deductive distinction, therefore, one will find the notion of open and closed systems of doubtful help. "Open-ended premises. II Hitchcock objects to open-ended prer:'.ises as follows: "But adding such premises changes a traditionally inductive argument into a traditionally de- ductive one." fiow this counters my point may be hard to see, for it precisely is my point. We need a reason why open-ended premises can- not legitimately be added to traditionally inductive arguments, but none is forth- coming. One possible reason, hinted at in Hitchcock's next paragraph, would be that no arguer can take into account every bit of potential counter evidence. Such a reason would be epistemological, about the warrant backing any open-ended premise. But my point, the or.iginal issue, was not epistemo- logical, not about warrants backing premises, but logical, about the relation of premises to conclusion, and against that point such a reason would not tell. Responsible general- izers and forecasters almost invariably incorporate what amount to such open-ended premises. eSee the "subarguments" para- graph's, my article, p. 4). And if we are to evaluate actual arguments, then we will find ourselves evaluating plenty containing open- ended premises. This is not the place to discuss whether open-ended premises in so-called inductive arguments commit epistemological excess. (For all I know, Hume's sceptical rumina- tions on cause are spotless.) But if open- ended premises were to commit such excess, and if that excess were to exclude them from good so-called inductive arguments, then it would certainly exclude them from their de- ductive counterparts too. Premises such as, "All shiny new high-performance automobiles are major sources of pollution" (p. 173), "All pornographic films are menaces to civil- ization and decency" (p. 197), and, "Ambas- sadors are always dignified" (p. 352), (all from Irving Copi's section on deduction) rest on epistemological footings no different than those of the universal or "s.uba.rgument" pre- meses in careful forecasts and generaliza- 11 tions. That we would accept open-ended generalizations in one place while excluding them from another is unreasonable. More- over, any so-called inductive argunent can as easily be constructed hypothetically as can its deductive counterpart. AIguers incor- porating open-ended premis:es in hypothe- tically phrased forecasts, generalizations, and the like can scarcel:t be accused of epistemological excess. Given that our subject-matter is the rea- soning by which one attempts to regulate the ,.ffairs of life, then what counts will be the, reliability of conclusions. Ivhether arguers stray logically or whether epistemologically, the damage ,,;ill have been equal. In cor- recting arguments it may sometimes be better to interpret the error as logical, and some- times bettElr to interpret it as epistemo- logical (and sometimes better to do both) . Suppose a person to have reasoned that such- and-such z is no good because the z's he's experiencfid are no good. To spotlTght the error one might reconstruct the argument as invalid--e.g., "You argue like this: 'Some z's are no good, the few you know, and such- and-~uch here is a z, and so it's no good. ' Now that's ••.. ,,- Another way to spotlight the error would be to assume the logic impec- cable, to unearth filling-out premises, which will fail epistemologically--e.g., "Your reasoning would be OK if you knew from your experience that an¥ z was no good, but here you are, one tiny ~naividual in Sacramento, surrounded by z's of probably a special kind, which you can't really observe carefully, and yet from that you want .... " Whether treating ~error as logical or as epistemo- logical makes the more sense would be a mat- ter of forensic or pedagcgical judgment. But in any case, one is free to proceed either way. "Uncited counter evidence." Hitchcock also objects (ILN, ii.3, p. 9) that traditionally inductive arguments cannot become deductive simply by hedging their conclusions: "Since there may be uncited counter evidence, the predicted occurrence may in reality be highly improbable, even though the premises provide grounds for thinking it will occur." This is a challenging objection. Consider the following, which should qual- ify with most traditionalists (I'd best not say all) as deductively valid: Set S consists of 36Q-me.mb.E\r subset ~, ana 6-me.ruber subset B. Smith will select once-at random from S. Therefor.e., Smith is likely to select a member of subset A. If we want to evaluate this argument logical- ly, then the issue will be the relationship between those premises and that conclusion. Suppose, now, that we learn further that Jones has peeked at the member to be selected, which is of subset B. To object to the orig- inal argument on grounds which apply to the amended argument would be an ignoratio elench~. The uncited cour.i:er ev~dence counts only against the amended version. The orig- inal was deductively valid come what may. Now the same may be said of properly hedged arguments in terms of likelihood or prob- ability, and of similar data-based assess- ments of the present or future. After all, if my "Smith" argument were a draft lottery "Ii 1",11 :;:iII M ::111 ~1I+'y ::1 iI'1 1 ,It , : • ! its validity would be unaffected lthough it would assume a rich potential for premise falsity), and it would also qualify according to tradition as inductive. The argument in my article CILN, iLl, p. 3) stating the likelihood or-rain is classically inductive, yet instantiates the deductive form, "When x, l. is likely; and x; so l. is likely." Un- cited counter evidence may plague fore- casters and generalizers, but it does not render their properly hedged arguments deductively invalid. Hitchcock admits that in such arguments "the premises provide probable grounds for thinking (the predicted occurrence] will oc- cur" (ILN, ii.3, p. 9), and yet such argu- ments OO-conclude precisely that the occur- rence is probable. How then could they be invalid? Something is fishy. I suspect that Hitchcock imagines unci ted counter evidence to falsify the conclusion because he thinks that the conclusion of such a forecast is, as he puts it, a "predicted state of affairs," a "predicted occurrence" (p. 9}. Most hedged forecasts .are no more than general prob- ability statements applied to an impending case. Such applications do not exactly pre- dict occurrences Calthough ~,e may speak that way if we wish) but merely unfold the prob- abilities implicit in the data. So when an alleged "predicted occurrence" fails to hap- pen because of uncited counter evidence, the argument's conclusion can seem false, even though i.ts premises be true. Let us imagine meteorology to be a very "open" aystem Cas is, aay, oncologyl. .From data, plus an assessment of conditions today, meteorologists forecast "about a 70.% chance of rain tomorrow." That 70% f:i:.gure incorpo- rates already the potent:i:.al for uncited counter ev~dence, such as competing high- pressure ridges. The data is only true in th.e aggregate; averall, 7 of 10 cases with conditions like today's have yielded rain next day. .For all these meteorologists know, in many of the cases reflected in the data rain may in reality have been highly unlikely. So when they apply the data as a probability to tomorrow's case, they do not exclude that other things may happen. The conclusion is not falsified by whatever happens tomorrow. Neither is the "likely" conclusion in my argument. Looking back on a record in which, at the 70.% forecast level, it had rained on 140 of 200 occasions, these meteorologists could congratulate themselves on a perfect . record. This point may be psycho10g~cally more convincing with quantity quite removed. Suppose that the forecasters had concluded neither "likely" nor "about 70.%" but instead, "and so it would be a good idea tomorrow to take an umbrella." Regardless of what hap- pened that day it was still a good idea to have taken an umbrel1a-.---- II Intentions. Samuel Fohr LILN, iL2, p. 9) suggests that looking to arguer intentions separates· inductive and deductive arguments: 12 If a person intends that his premises necessitate his conclusion he is giving a deductive argument. If he intends only that his premises render his conclusion probable he is giving an inductive argument. To Trudy Govier's and Hitchcock's comments (ILN, ii.3) on Fohr's suggestion I would add only a little. Fohr is correct, surely, that real arguments must be judged as wholes, including the backdrop detail which formal treatments assume or omit. But only some- times will this judging include the arguer's intentions about conclusion strength. It will when the subject is the ar~er's argument-- the arguer, actually--as w n we puzzle over just how Copernicus meant his conclusion CFohr,ILN, ii.2, p. 7} about the earth's configur-ation. More usually, however, the topic is not the arguer's argument but the argument, period. Much reasoning is colle- gial, hypothetical, experimental, taking place in conference, bar-, board-, war, locker, and operating rooms. The truth of the conclusion may De vitally important. ~ve want to know not, "Does So-and-so think these premises clinch that conclusion?" S'Ut';'""""no those premises clinch it?" Until the latter quest:i:.on has oeen answered, conferees may have no opinion about the firmness of the conclusion, no intentions whatsoever. The presenter of the argument (~ho may have been free associating, experimenting, or playing the deyil's advocate> drops out as incidental. This is particularly true of evaluating one's own thinking. My present intentions, if any, regarding the argument I now confront scarcely matter, since r will be trying to let the argument form my intentions. Again here, the strengt~ the conclusion is prior to, independent of, whatever the arguer may think of it. III Inductive and deductive standar.ds. Al- though Fohr is correct (ILN, i~.2, p. 8) "that it is ver.y importa~that a person put- ting forward an argument know what he is trying to do," the "what" doesn't include knowing whether the argument is inductive or deductive. We must teach our students always, as Hume would maintain, to proportion the strength of the conclusion to the strength of the evidence. One has no more business hedging the result of a mathematical demonstration than of not qualifying the re- sult of a preliminary investigation. And whether a well-drawn "absolutely," or a "probably," or a "good idea to take your um- brella," follows from the premises, it fol- lows from the premises. The relationship be- tween premises and conclusion is the same. Inductive and deductive standards (Govier, p. 8; Hitc:hcock, p. lO-ILN, ii.3) are the same standard. Whether ip.[stemo10gica1 ques- tions are appropriate depends not on what kind of argument it is-whether syllogism, generalization, or what--but on what those giving it and attending to it are trying to do. I 1 o o. T 1, E: fe a: se tl d: 9' tl iJ ql :ld lat 's iill er l1e ese er en g tal. , ::mt n ior 'I Lon :al !s- lwoRKS CITED Copi, Irving M. Introduction to t9;~c. 5th edn., Macmillan, New York, : Fohr, Samuel D. "The Deductive-Inductive Distinction." ILN, ii.2 (April 1980), 5-8. - Govier, Trudy. "More on Deductive and Induc- tive Arguments." ILN, ii.3 (.June 198Q1, 7-8. - Hitchcock, David. "Deductive and Inductive: Types of Validity, Not Types of Argu- ment."~, i1.3 [June 19801,9-10. Weddle, Perry. "Inductive, Deductive." ~, ii.l (November 19791, 1-5. ~ discussion nate Proofs and Begging the Ciuestion Milton H. Snoeyenbos Georgia State University Logicians utilize two distinct conceptions of proof. On the one hand, there is a formal or syntactic concept: given a formal theory T consisting of formulas, well-formed formu- las (wfs), axioms and inference rules, a proof, in T is a sequence of wfs such that for each wf in the sequence either it is an uiom of T or it is a direct consequence of some of the preceding wfs by virtue of one of ~e inference rules. On the other hand, a distinct concept, often used in natural lan- ~age contexts, is that an argument consti- tutes a proif2 of the truth of its conclusion if it is va ~d, has true premises, and is not question-begging. 13 While the fo~er concept is not controver- sial, "proof2" is sometimes thought to be problematic. James Tomberlin considers the following substitution instances of disjunc- tive syllogiSll1: (Jl.ll: NQvP, Q/P and CA21: *PvR, NR/*P, where Q=New York is in the U.S.A., P=tne mind-body identity theory is correct, R=Moscow is in the U.S.A.l Tomberlin asserts that neither argument begs a question since both are instances of disjunctive syllogism. The second premise of each argument is true. Furthermore, either the, first premise of Al or the first premise of A2 is true, since « -QvP) v( """PvR» is a theorem of proposi- tional logic. It follows that either Al or A2 constitutes a proof2 of its conclusion. Yet Tomberlin rightly notes that since the truth or falsity of the identity theory could not be decided by appeal to either argument, neither can be said to prove? its conclusion. He concludes that the analys~s of "proof2" in terms of validity, true premises and the absence of question-begging must be incorrect. Tomberlinla rejection of the standard anal- ys.i-s of l·proo f2" follows only if we accept the claim that neither Al nor A2 begs the iss:ue. He appears to have a formalist con- ception of begging the question, for his claim that Al and A2 do not beg any questions rests on his claim that both are instances of disjunctive syllogiSll1. But this overlooks the often voiced claim that question-begging is a non-formal fallacy. From the formal point of view an argument such as (/,/(1, is a perfectly acceptable proofl of its conclusion. However, even if "is true, from a non-formal, say, an epistemic, point of view, the premise could not be said to constitute a proof2 of the conclusion, for to know the premise is true we. must know that the conclusion is true, i.e., the argument begs the issue. Let us say, then, that an argument begs the question if and only if in order to know that some member of its premise set is true we must know that its conclusion is true. On this conception of question-begging do Al and A2 beg any questions? In either case we can know the second premise is true without knowing the conclusion is true. But, in con- sidering the first premise, "knowing that «(J, or B) is true" is ambiguous. In some cases I may know that (/X,or/S) is true and know which disjunct is true; in other cases I may know that (c:t or f3) is true yet not know which disjunct is true, as with (5 or ~S) where S is any controversial proposition. If we consider Al in its actual epistemic context, we know that~Q is false. Hence, to know that (NQ or P) is true we must know that P is true. Since P is the conclusion to be established, Al begs the issue. If we con- sider A2 in its actual epistemic context, then, since we know R is false, to know that ( ""P or R) is true we must know that NP is true. Since""p is the conclusion to be established, A2 begs the issue. It follows that neither Al nor A2 constitutes a "proof2" of its conclusion, for both beg the question. As a result, Tomberlin's counterexample does not demonstrate the unacceptability of the st'andard analysis of "proof2." NOTE lJames. E. Tomberlin, "On Proofs," Inter- national LOi~c Review, vol. VII, no.~ (December, 76\., pp. 233-35. '*