5 The Problem of Missing Premises

Missing premises – or the allegation that they are needed – often play a kind of deus ex machina role in deliberations about argument type and structure. That is to say, premises said to be missing can too easily be imported into an account to serve or save a favoured account. The strategy enables ad hoc defenses of one or another interpretation, and should be avoided.

With few exceptions (David Hitchcock is clearly one), scholars have been hesitant to seriously address the rather messy set of issues that constitute the problem of missing premises. Which arguments have missing premises? How do we know, or how should we judge, what those missing premises are? And how do our responses to these questions depend on broader theories about argument typology? Argument interpretation? Argument criticism? Not all assumptions amount to missing premises, but how is the distinction between assumptions and missing premises to be drawn? I think I can safely say that none of these questions have been answered and few, if any, have been given sustained consideration.

As mentioned in this essay, various terms are used as roughly equivalent to “missing premises”. These include “implicit premises”, “unstated premises”, “hidden premises”, and “assumptions.” I argue, and would still maintain, that the term “assumptions” is too general and hence unsuitable as a substitute. But what about the others? It has been maintained (in a 1985 article by Jim Gough and Christopher Tindale) that the term “hidden premises” should be preferred, because that term suggests that the material to be added is present in a discourse in a slightly disguised form; it is there to be found; it is not simply added. I agree that one should carefully consider what is there before supplementing with something that is not there. But there are challenges hidden in the notion of ‘hiding’. We can dispute as to whether the associated conditional or a universalization of it is hidden in a succession of two particular claims, just as we can dispute whether such claims are missing.

More radical is a suggestion urged by Dan Levi in 1995: he argued that the problem of missing premises emerges only because analysts insist on setting out arguments in a premise-conclusion (PC) structure. Then, looking to their structure and finding it to be less than complete and clear, they sense that something is ‘missing’. If people following this strategy – including of course myself – would employ a different method, shifting away from PC models, the problem of missing premises would disappear. Avoiding the strategy of standardization, one would preserve relevant rhetorical aspects of context and voice, and these aspects would assist in interpreting the argument. If one did not seek a PC structure, one would not have to worry whether this or that version of it was correct. This radical suggestion would challenge much work in informal logic and does not seem to have been seriously pursued. It is similar in some respects to suggestions made later by Harald Wohlrapp in The Concept of Argument.

In this chapter I challenge deductivism both as a theory and as providing a response to the problem of missing premises. I also consider how the role of charity — the ways in which a commendable desire to be polite and fair to an arguer — may lead us to rework that person’s argument so as to make it fit with our own views. As I argue here, charity can be taken too far. It needs to be qualified, and when it is, its implications for missing premises are altered. Whether it is a deductivist lens or the generosity of charity, we tend to reconstruct arguments to be clear and cogent in the ways we would like. The risk we face is that this tendency will produce distortions; the fact that a reconstructed argument strikes us as clear and cogent does not show that the improvement constitutes an accurate version of the original. What I call in this chapter ‘strong charity’ has been more recently discussed as ‘steelmanning.’ Steelmanning is the opposite of strawmanning: instead of addressing a weak version of an opposed position as in the straw man, one addresses what one takes to be a strong version of an opposed position. Among those who discuss steelmanning, many seem to favour it, but some object on the grounds that a person who purports to strengthen a position may distort it and, in any event, displays arrogance in presuming the ability to know best what the best opposed argument is.

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One thing which makes people differ as to theory of argument and as to the analysis of particular arguments is different approaches to the matter of missing premises. For instance, some people insist that analogies all have a missing premise and that when this is filled in, they can be seen to be deductive arguments. Others find no need for such supplementation and would regard analogies as a distinct type.

In fact, the ‘problem’ of missing premises is too complex to be just one problem. There are a number of distinct problems. To begin with, we must distinguish the question of which arguments have missing premises from the question of how to decide just which missing premises they have. In addition, there are several different purposes for which people may examine arguments, and for different purposes, quite different approaches to reconstruction through the addition of premises are appropriate.

Of course, premises are not the only thing that can be missing from arguments. Arguments may have unstated or missing conclusions as well. This is less often discussed than the problem of missing premises, for it makes less difference to the overall structure of the argument. It does, however, make an immense difference to the classification of discourse as being argumentative or not. Often people write in an argumentative tone, in a context of controversy, indicating they are ‘opposed’ to something, but do not state explicitly that the thing is wrong or incorrect. Rather, they strongly imply it. Here, it seems interpretively appropriate to regard what is said as an argument, though the conclusion is not stated explicitly.^l Those who are generous in adding premises and ungenerous in supplementing conclusions will find few fallacies in natural argumentation. Those who are ungenerous in adding premises and generous in adding conclusions will find many. We can see, then, how the matter of missing conclusions has a significant effect on one’s overall view of argument.

There are a number of different terms used as virtual synonyms of ‘missing premise’. These include ‘tacit premise’, ‘unstated premise’, ‘hidden premise’, ‘suppressed premise’, ‘implicit assumption’, ‘assumption’, ‘underlying assumption’, ‘suppressed assumption’, and others. It is a serious mistake, I think, to identify unstated premises with unstated assumptions. Many assumptions that are required for arguments to work are not required to fill inference gaps-the standard role for missing premises.² For this reason it is better to speak of missing or unstated premises rather than missing or unstated assumptions. As to other variations in terminology, these do, to be sure, have nuances that could be exploited to good purpose and would become significant. For instance, to speak of premises as ‘hidden’ suggests that the stated material contains good cues that these premises are endorsed by the arguer and contained in the text, though not in the form of explicit statements.³ To say that they are ‘missing’ does not suggest those cues in the text, but does suggest a strongly realist notion of interpretation. Here, these nuances are not exploited: the standard philosophical usage, according to which ‘unstated premise’, ‘missing premise’, ‘implicit premise’, ‘tacit premise’, and ‘hidden premise’ are used as virtual synonyms, is followed.

1. Deductivism and Missing Premises

Deductivism is the view that all good arguments are deductively valid. Applied to the problem of missing premises, deductivism yields the suggestion that an argument should be supplemented with additional premises to the point where (as reconstructed) it becomes deductively valid. When thus reconstructed, it is a fully ‘filled out’ argument that can then be subjected to critical scrutiny. Sometimes the added premises make the argument a sound one, for they are true, and thus the reconstructed argument is valid and has true premises. Sometimes they show the argument to depend on unverifiable premises. And sometimes these added premises are false, or implausible, and show the argument to be a poor one. On a strong deductivist view, all arguments have, implicitly, all the premises needed to make the stated premises and the added ones entail the conclusion. Criticism of an argument is not appropriate until these unstated premises have been filled in. This is often an extensive task, to say the least.

Understood in this way, deductivism has the curious consequence that logic is relevant solely to the reconstruction of arguments and not to their appraisal, once reconstructed. When appropriately reconstructed, all arguments are logically equal inferentially, and all are logically good. The difference between cogent arguments and poor ones can only be found in the truth or plausibility of their premises.

The deductivist account will be natural and familiar to many readers, and is often appealed to by philosophers — in both theoretical and practical contexts. It is at work in many texts on natural reasoning. Here we will look briefly at one such text, that of Stephen Thomas. Thomas is interesting in this regard because his deductivist policy on missing premises is, in fact, incompatible with his broader theory of argument. That is a Spectrum Theory. The fact that Thomas lapses into this policy when trying to handle the problem is evidence of the naturalness and very great intuitive appeal of the deductivist approach.

In Practical Reasoning in Natural Language, Thomas goes into considerable detail telling students how to add premises to arguments in order to render them deductively valid. He says that when all these premises have been added, then:

Any uncertainties about the truth of the final conclusion which were due to inconclusive inferences in the original argument have now been driven back onto the total set of basic reasons in the new constructed revision. That is, all uncertainty about the inferences has been eliminated (since all are now ironclad) and it remains only to determine whether every member of the new set of basic reasons is true.⁴

(The ‘basic reasons’ are the premises.) Once the missing premises, or premises deemed to have been missing, have been added, the argument is valid. It is valid because it has been made valid. We should note, as Thomas does, that it is always possible to make an argument deductively valid. One can sometimes do this with significant and genuinely illuminating additions, as Thomas points out. Failing this, we can do it with trivial and unilluminating additions, as he and a number of other analysts have pointed out.

The simplest method for achieving deductive validity is to link up all the stated premises to form a conjunction. Call this conjunction CON. Then, calling the conclusion C, supplementing the original with the claim ‘If CON, then C’ will render the argument deductively valid. The statement ‘If CON then C’ may be called the associated conditional.⁵ Of course, the associated conditional is not the only possibility here. Any statement that entails the associated conditional will do equally well. Another vacuous, but always available possibility is to the add conclusion, or a generalization of it, as a missing premise. This strategy will also make the argument deductively valid — though question-begging. Again, there are an indefinite number of possible variations on this move, for we could add any statement which entailed the conclusion, in order to make the argument deductively valid.

Naturally enough, Thomas now recommends premise assessment as the next (and only possible) stage of argument criticism.

Only if one or more of them is false can the argument’s final conclusion be false. If all the basic reasons in the revised argument (i.e., original plus new reasons) are true, then so too is the argument’s final conclusion. So if you know that all the basic reasons are true, then you know that the conclusion is also true. But if a falsehood arises in every possible set of suppressed assumptions whose addition would create a deductively valid expansion of the original argument, then the original argument is unsound.⁶

The emphasis is added here to indicate the link, in Thomas’ analysis, between deductivism as a solution to the problem of missing premises and deductivism as a theory of argument. This is an unqualified deductivist view.

Thomas supposes that the premises needed to make the original argument deductively valid are somehow part of the original argument and that their evaluation is pertinent to the evaluation of the original argument.⁷ Nondeductivists would deny this. Consider, for instance, the case of analogy. If we add to an argument by analogy sufficient premises to make that argument deductively valid, those added premises may very well be seen by a critic going beyond the original premises. If the added premises turn out to be false or unacceptable, that will not (at least, not in the eyes of the non-deductivist critic) indicate that the original argument was at fault. On the critic’s view, the original argument was not deductive. The fact that a premise needed to make it deductively valid turns out to be a false premise shows nothing about the merits of the original argument.

Thomas is committed to disagreeing with such a position: he insists that when the added premises are false, the original argument is shown to be unsound. This indicates that he thinks of the original argument as having really depended on these claims; although they were not stated, they are necessary to make the argument work. But making it work means making it work as a deductively valid argument. Since the account is applied to all arguments, without qualification, we can only suppose that Thomas holds that for an argument to work, the premises have got to entail the conclusion. This stance is, of course, that of deductivism. The relevance of the supplemented premises to the critique of the original, unreconstructed argument presupposes that whatever sort of argument the original seemed to be, it was actually an aspiring deduction which, as stated, didn’t pass the (deductive) test. If this theoretical presumption were false, the falsity (or unverifiability, or implausibility) of the added premises would show nothing about the original argument.

Another significant feature of this account is Thomas’ claim that only if one or more premises in the argument is false can we regard the original argument as unsound. The original argument will be unsound only if ‘a falsehood arises in every possible set of suppressed assumptions whose addition would create a deductively valid expansion of the original argument’. The problem is that there is an indefinitely large number of ways of expanding a stated argument so as to produce a deductively valid argument. (This result is obvious even from the possibilities generated by the trivial associated conditional and ‘add the conclusion’ strategies described earlier. Of course there are many other devices which can be employed.) Given this fact, it is hard to see how we could ever be in a position to assert with confidence that a falsehood will arise in every possible set of supplementary premises. Thomas seems to be aware of the difficulty, because he says:

For practical purposes, you can take this to mean that if every reasonable attempt to supply the argument’s suppressed assumptions requires the addition of some falsehood, then for all intents and purposes, you may regard the original argument as unsound.⁸

This position is neither practically satisfactory nor theoretically adequate.

An unqualified deductivist policy on missing premises licenses overabundant expansion of arguments. One way in which it is overabundant is that it raises the prospect of all arguments which are not, as stated, deductively valid, being enthymemes — a counterintuitive prospect, to put it mildly. On this view, there are no fallacies (formal or informal), no enumerative inductions (hasty or otherwise), no analogies, no inferences to the best explanation, and so on. This is a counterintuitive result which runs contrary to established traditions in logic and to recent work in the philosophy of science. ⁹ Another way in which unqualified deductivism is overabundant is that it licenses an indefinitely large number of expansions for each argument. Finding a flaw in any one of these will not constitute a definitive criticism of the original argument, for there are always many alternative reconstructions remaining to be considered; on purely deductivist grounds, these reconstructions are all of equal merit. Thus deductivism by itself cannot provide a complete and adequate policy on missing premises. It must be qualified so as to apply only to some arguments and supplemented so that not all deductivist reconstructions are of equal critical relevance. Later we will consider what some of the appropriate qualifications might be.

The problems with a deductivist approach to missing premises appear in a more concrete guise when we consider specific examples. First, let us look at an example of a poor argument, and see how a deductivist policy on missing premises will advise us to reconstruct it. As an example, here is a short argument of Garret Hardin’s on sterilization.¹⁰

It should be easy to limit a woman’s reproduction by sterilizing her at the birth of her nth child. Is this a shocking idea? If so, try this ‘thought experiment’: let n equal 20. Since this is not shocking, let n diminish until population control is achievable.

Here Hardin argues from the premise that it would be tolerable to sterilize a woman after her twentieth child to the conclusion that it would be tolerable to sterilize a woman at whatever point was necessary in order to achieve population control. The argument appears to be an outright fallacy of a rather original kind.¹¹ (Is it some kind of reverse slippery slope?) And yet the inference from permissibility in the one context to permissibility in the other seems simply mistaken: there is an enormous, and morally significant, difference between them. We can add premises which will fill the gap in various ways. Three possibilities are:

3. If it is permissible to sterilize a woman after her twentieth child, then it is permissible to sterilize her at whatever point is necessary in order to achieve population control.
   or

4. If it is permissible to perform an operation on a woman in an extreme case, then it is permissible to perform that operation on a woman in a less extreme, but socially significant, case.
   or

5. Whenever it is permissible to do anything in an extreme case, then it is permissible to do that same thing in a less extreme, but socially significant, case.

(3) will suffice to make the argument deductively valid. However, this is a redundant and useless addition, because (3) is the associated conditional, which simply reiterates the original argument. If we can assess (3), we can assess the original argument directly and have no need of (3).

The other additions are not purely reiterative. However, unlike (3) they may not by themselves suffice to make the argument deductively valid. They are generalizations on the associated conditional, and we have to grant that the generalization is done appropriately. This, for (4), means granting that sterilization is an operation; that sterilizing a woman after she has had 20 children is sterilizing her in an extreme case; and that sterilizing a woman at whatever point is necessary to achieve population control is sterilizing her at a socially significant, but non-extreme, point. Similar points arise for (5). More importantly, (4) and (5) go considerably beyond the original argument in scope. It is perhaps not fair to commit the unhappy author to these sweeping premises, which are so much more easily attacked even than his original inference. The generalizations on the associated conditional have the critical virtue of non-redundancy. But they can be critically useful only insofar as they open the door to considerations which are not exactly what would be called for by the original inference. There is, then, some critical benefit from adding these more general premises. But exactly the feature which makes them appear critically useful makes them interpretively questionable.¹²

Another example reveals further peculiar problems. Consider the following brief passage from Stephen Toulmin and June Goodfield’s The Architecture of Matter. Toulmin and Goodfield report describing to a colleague who commented on Voltaire’s efforts to weigh fire. They asked their colleague how he would have persuaded Voltaire that experiments directed toward the weighing of fire were useless. The man replied lightly that he should have told Voltaire to use his common sense. Of this response, Toulmin and Goodfield comment:

The common sense of Voltaire’s time was not, and could not have been, identical with the common sense of our own period. For Lavoisier helped to create our contemporary common-sense ideas about matter, just as Newton, earlier, had helped to establish our common-sense picture of the planetary system. If, in retrospect, it seems too obvious that fire is not a substance, we should regard this ‘obviousness’ with grave suspicion.¹³

Here, we have a subargument and then an argument, both with a single stated premise and conclusion:

1. Lavoisier helped to create our contemporary common-sense ideas about matter.

2. The common-sense of Voltaire’s time was not identical with the common-sense of our own time.

3. The ‘obviousness’ of the idea that fire is not a substance should be regarded with suspicion.

Neither the subargument from (1) to (2), nor the main argument from (2) to (3) is deductively valid as it stands. We have seen, above, that there are certain problems which arise when the associated conditional or generalizations of it are used as supplementary premises. We shall approach the Toulmin and Goodfield example in another way, then, by trying to add premises which will make the argument deductively valid and which are neither the associated conditional nor generalizations of it. Some natural and plausible additions, which would appear necessary whether one was a deductivist or not, are:

4. Lavoisier had not yet created our contemporary common-sense in Voltaire’s time.

5. What seems obvious depends upon our common-sense.

6. Common-sense that can fluctuate from one time to another should be regarded with suspicion.

   But still, (1) and (4) do not entail (2); (2) and (5) and (6) do not entail (3). We need more additions yet. For the subargument, for instance, we need:

7. No two sets of common-sense beliefs are identical unless they are created at the same time.

8. The common-sense of Voltaire’s time had been created at his time.

Even this may not be sufficient.

When we do not revert to the associated conditional or a generalization of it, the necessary additions start to seem indefinitely many and excruciatingly pedantic. A ‘reconstruction’ of two very simple arguments which has seven or more supplementary premises is a critical and pedagogic monster. Are these premises really ‘there’, unstated, because they are ‘needed’ in order to make the original inferences work in a deductive sense of ‘work’?

These examples indicate that deductivism does not always make for easy and elegant criticism. It is not always interpretively plausible, and it can be cumbersome in practice. Reiterative addition of the associated conditional is simple and always applicable; however it is a critically redundant manoeuvre. Generalizations of the associated conditional are not by themselves sufficient without further premises spelling out the ‘assumption’ that the generalization is an appropriate one. It may be interpretively incorrect to attribute the generalization to the arguer. If the arguer is not committed by the original argument to that generalization, then any analysis of that argument via a reconstruction with the generalization as a missing premise will be misdirected. In addition, attempts to make some arguments deductively valid will be cumbersome when they avoid the associated generalization and its conditional – as some deductivists have, themselves, admitted.

But in so many contexts, and to so many people, deductivist instincts on missing premises seem correct. The above account will doubtless not dissuade convinced deductivists. Why is this approach to missing premises so appealing to so many people, despite its running counter to strong theoretical traditions in logic and to economy in criticism and analysis? There seem to be at least two plausible explanations.

First of all, the deductivist reconstruction of an argument will often be straightforward and elegant. It will make sense. It will provide a model in which the stated premises, together with other claims, lead in a direct logical way to the stated conclusion. The model will be a logically clear and coherent argument, even though some of the premises of that argument may be disputable. Such an argument has definite logical appeal; its appealing character may make it seem an excellent substitute for the original argument, which lacked such logical coherence and structure. Given all this, it is easy to confuse two issues: the real issue of whether the model is an accurate rendition of the original argument and the quite distinct issue of whether the reconstructed model is a logically ‘virtuous’ argument. The second matter is guaranteed in the nature of the case. The first is something else entirely. It is one thing for a reconstructed argument to be clear and another for it to be the correct (or even a correct) model of a stated argument.

We should not let the logical appeal of a reconstruction lead us, by itself, to the belief that the reconstruction accurately reflects an original. The beauty of a portrait does not show that it accurately represents its subject. There is perhaps a tendency to confuse the clarity of the reconstruction considered on its own terms with its interpretive accuracy as a plausible version of the original argument.

Secondly, the following line of reasoning is tempting: If a person argues for a conclusion, C, then provided that he or she is arguing sincerely, he or she believes C to be true. If that person believes C to be true, then he or she must believe a set of claims which entails C. Thus, if the arguer’s stated premises do not entail C, it is appropriate to supplement them to the point where they do entail C.

The problem with this account comes in the second statement. First of all, the ‘must’ is ambiguous as between a psychological and a logical must. Interpreting ‘must’ as psychological, the statement is false, because people often believe claims with no support or with some partial support, or on fallacious grounds, as a matter of psychological fact. Also, psychologically interpreted the claim could require a vicious infinite regress of beliefs. The logical interpretation of the ‘must’ makes the statement somewhat more plausible. The claim would then amount to the insistence that anyone who believes a conclusion C is logically committed to some set or other of claims which entails C. On this view, if we take an argument which that person puts forward for C and we read into it enough premises to make the stated premises, together with the new ones, entail C, we will not go beyond anything to which that arguer is not already committed.

On this interpretation, the claim amounts to an especially strong version of foundationalism. It is open to all the criticisms which can be made of traditional foundationalism, and more besides.¹⁴ Furthermore, even if it were true that anyone who believes C is committed to some set of claims that entails C, given that the number of such sets is indefinitely large, the connection between this set and the one generated by a logician reconstructing the original argument is likely to be remote.

Thus, deductivism cannot offer a complete and satisfactory policy on missing premises. The intuitive appeal of the policy disappears when we look more closely at theory and practice and when we examine some of the accounts which may underlie those intuitions. To add to arguments all premises necessary to make those arguments deductively valid and regard these additions as premises which were missing in the unreconstructed version of the argument is not, in general, a reasonable thing to do.

It may be suggested that a deductivist approach to missing premises can be endorsed, in the interests of clarity and elegance, without any commitment to a deductivist theory of argument. David Hitchcock has taken this approach, which he regards as a kind of heuristic deductivism. But there are two problems with this approach. First of all, it is hard to give a good reason for seeking to reconstruct an argument so as to render it deductively valid, if one does not endorse a deductivist theory of argument. We can find a missing premise, or gap-filler, such that, if it is added, the resulting argument becomes deductively valid. But if someone asks, why should we want to render this argument deductively valid, no answer will be forthcoming. Secondly, as indicated here, deductivism does not in fact generate an elegant solution to the problem of missing premises.¹⁵

The story is different so far as missing conclusions are concerned. If an arguer has stated several claims and there is good reason to interpret these claims as premises in an argument, then there is never any problem about ‘reading in’ a statement which is, in fact, entailed by those claims. Anyone who does so will attribute to an arguer no more than he or she is already logically committed to. We are not committed to all claims which entail beliefs we hold, but we are committed to all claims which are entailed by beliefs we hold.

Suppose that an advertisement reads as follows:

The bigger the burger, the better the burger. The burgers are bigger at Burger King

We can justify adding the unstated conclusion that the burgers are better at Burger King. The entailed claim can appropriately be regarded as a conclusion that is supported by the stated material. There is good reason for taking advertisements of this type as arguments. Sometimes there are problems about interpreting passages as arguments, and the issue of whether to add a conclusion which is not stated but is entailed or suggested is linked to this interpretive issue. Whether a person is trying to prove a point or is rather merely giving a description, explanation, illustration, or comment is often a moot point. This interpretive problem can make the addition of conclusions questionable in some contexts. But in general, it seems a more manageable problem than the problem of missing premises, and a deductivist approach to it will always give results within reasonable interpretive bounds.¹⁶

2. Missing Premises and Assumptions

Often the problem of missing premises is thought to be a problem about assumptions. The idea is something like this: when people present arguments, they do not always mention all of the beliefs which they hold which are pertinent unstated claims, the truth of which is a necessary condition of the argument’s working the way it should. People could not state everything pertinent to the argument in this way. They necessarily leave much unstated. Often unstated assumptions would be accepted by virtually everyone, and it would be a great bore for the arguer and the audience to spell them out. Sometimes arguers are not aware of their unstated assumptions; sometimes these assumptions are highly questionable, and neglecting to spell them out lulls the unwary audience into accepting things it would not have granted on critical scrutiny.¹⁷ It is often said that such unstated assumptions are the missing premises of the stated argument.

A statement of this view appears in Irving Copi’s Symbolic Logic, in a discussion of the logic of relations:

Relational arguments are often used, and many of them depend essentially on the transitivity, or symmetry, or one of the other properties of the relations involved. But that the relation in question has the relevant property is seldom – if ever – stated explicitly as a premise. The reason is easy to see. In most discussions a large body of propositions can be presumed to be common knowledge. The majority of speakers and writers save themselves trouble by not repeating well-known and perhaps trivially true propositions that their hearers or readers can perfectly well be expected to supply for themselves. An argument which is incompletely expressed, part of it being ‘understood’, is an enthymeme.¹⁸

It is clearly true, as Copi says, that in most discussions many propositions are presumed true, as common knowledge. Discussion would be completely impossible without such presumptions. But whether all such presumptions should be counted as assumptions that amount to missing premises and all arguments depending on them should be regarded as enthymemes, are further questions.

In On Certainty, Wittgenstein argued that in order for some problems to be discussed and considered, many other aspects of life and language must be accepted as givens. In a specific context, someone might wonder whether his hand is made of real human flesh. (Perhaps someone had a hand transplant and cannot remember whether it was the left or the right — my example.) But to contemplate even such a radical question, a person must nevertheless take for granted other aspects of mundane life-such as knowing what ‘hand’, ‘flesh’, and ‘human’ mean. On Certainty gives us a sustained elaboration of the fact that we cannot question everything at once. Questions and problems require a background.

That is to say, the questions that we raise and our doubts depend on the fact that some propositions are exempt from doubt, are, as it were, like hinges on which those turn

. . it belongs to the logic of our scientific investigations that certain things are indeed not doubted.

But it isn’t that the situation is like this: We just can’t investigate everything, and for that reason we are forced to rest content with assumptions. If I want the door to turn, the hinges must stay put.¹⁹

This view of the background of questions can be applied directly to the case of arguments. A person who presents an argument puts forward reasons to support his conclusion, trying to raise the credibility of that conclusion to an audience he is addressing. The argument can be seen as aimed towards its conclusion, and as attempting to resolve a particular question-whether that conclusion is true. In the context, the question is open.²⁰ This question, like others, will make sense only against an assumed background of beliefs and practices.

What is wrong with Copi’s account is not his claim that discussion requires assumptions, but the conflation of such assumptions with missing premises. Copi is following logical tradition when he says that if part of an argument is missing, that argument is an enthymeme. But the parts of an argument, according to logical tradition, are its premises and conclusion. Thus an enthymematic argument is one in which one or more premises, or the conclusion, is not stated. So far, so good. But logical tradition also has it that there exist non-enthymematic arguments. This is an element of the tradition worth preserving, if ‘enthymeme’ is to play a useful role in the classification, understanding, and criticism of arguments. If unstated assumptions and missing premises are identified, then every argument will be an enthymeme, because it is clearly true, as Copi says, that in every argumentative discussion there are unmentioned presumptions on which the arguer and his or her audience agree.

Missing premises constitute a subset of these unstated assumptions, not the whole set. One important first step in resolving the problem of missing premises is to distinguish between those assumptions that are required by the argument but are not missing premises, and those assumptions that do amount to missing premises. There are many ways in which an argument may be based on an assumption, A. These include at least the following:

1. The truth of A may be a necessary condition for the terms used in the argument to have a referent.

2. The truth of A may be a necessary condition for the subject of the argument to be of interest to anyone.

3. The truth of A may be a necessary condition for the meaningfulness of any language.

4. The truth of A may be a necessary condition for properly inferring the conclusion from the stated premises.

5. The truth of A may be a necessary condition for the appropriacy of the methodology used by the arguer when he or she cites the premises as support for the conclusion.

6. The truth of A may be a necessary condition for the truth of one of the stated premises.

7. The truth of A may be a necessary condition for words used in stating the premises and conclusion to have the meaning which they do have, and on which proper understanding of the argument depends.

To make matters worse, these do not exhaust the possibilities. If we think of missing premises as premises that should be added in order to make the inferences of the stated argument work, then at most assumptions of the type in (4) and (5) would qualify as missing premises. (As we shall see later when discussing Lewis Carroll’s argument, level (5) assumptions should not be regarded as premises.) Copi’s account seems to require that all assumptions pertinent to the workings of an argument be incorporated within that argument as premises. This would make even short arguments indefinitely long when they were completely ‘filled out’.

That this is really what Copi means is confirmed by his discussion of an example from the logic of relations. After the passage quoted earlier, he goes on to say:

In most cases there is no difficulty in supplying the tacit premises that the speaker intended but did not express. Thus, the first specimen argument stated at the beginning of this chapter:
Al is older than Bill.
Bill is older than Charlie.
Therefore, Al is older than Charlie.
ought to be counted as valid, since it becomes so when the trivially true proposition that ‘being older than’ is a transitive relation is added as an auxiliary premise. When the indicated missing premise is supplied, a formal proof of the argument’s validity is very easily set down.²¹

But this must be wrong. The argument which, according to Copi, has the missing premise ‘Being older than’ is a transitive relation’ is in fact, deductively valid as stated. Copi’s account goes beyond deductivism in that he seeks to make the argument not just deductively valid, but deductively valid in virtue of its form as identified within a specific system of logic. The stated premises do entail the stated conclusion. It is just not formally provable that this is the case. One can formally derive the conclusion from the premises, given the apparatus developed to that point in Copi’s book, if one adds the auxiliary premise.

The proposed auxiliary premise is meta-linguistic. But other metalinguistic premises are also ‘assumed’ in the argument Copi discusses. For instance, the argument ‘assumes’ that ‘Al’ can be used to name something that has an age, and that ‘Al’ names the same entity in the conclusion as in the first premise. These meta-linguistic assumptions are essential to the workings of the argument. If the first did not hold, the first premise and the conclusion would be meaningless. If the second did not hold, the premises would not be relevant to the conclusion. If we follow Copi in adding one meta-linguistic premise and insisting it was ‘missing’ from the original argument, why should we stop at one?

That language and concepts work is ‘assumed’ by every argument. If all the pertinent workings need to be spelled out in auxiliary premises, even the smallest, clearest arguments will be enthymemes that have to be filled out in an highly cumbersome way. Following through on the demand that meta-linguistic assumptions be incorporated as premises will lead us to a vicious infinite regress. The supplemented arguments will use new terms and premises spelling out assumptions requisite to these will also need to be added, and so on.

Copi is quite entitled to add a premise for some specific purpose, but he is not entitled to regard the original argument as an enthymeme solely because this can be done. The policy of adding meta-linguistic premises because what they say is ‘assumed’ is not a constructive one. Missing premises are a subset of the unstated assumptions behind an argument. The problem is to specify what that subset is.

There is an unfortunate tendency to use ‘missing premise’ and ‘missing assumption’ virtually as synonyms. This can be seen in Michael Scriven’s early work at one point. Scriven advises that ‘in assumption hunting you’re trying to reconstruct the premises that someone would have put forward if stating the argument in full. He continues as follows:

The requirement that the extra or ‘missing’ premise (which is what an assumption is) be new immediately precludes a mere repetition of the supposed connection between the given premises and the required conclusion. There’s nothing new about the statement that what is already being provided is supposed to give support to what is alleged to be the conclusion of the argument. So, typically, an assumption should be referring to something else that hasn’t been mentioned in the given premises.²²

The same sort of thing occurs in the first edition of Johnson and Blair’s Logical Self-Defense. The authors begin their discussion of missing premises by saying that a missing premise is a proposition which, though unstated in an argument, is needed in order to link the stated premises with the stated conclusion. Later they say that a missing premise is necessary for the intelligibility of the argument, and may be called an assumption.²³ They seem to have decided that this equivalence was a mistake, because the second edition of the work says instead that missing premises are one type of assumption.²⁴

Not all assumptions underlying an argument are its missing premises. There are assumptions that must hold if one argues about anything (general pragmatic assumptions), assumptions that must hold if anyone is to argue about this particular thing (specific pragmatic assumptions), meta-linguistic propositions about the meaning and appropriate use of words used to state the argument, evidence which would support stated premises, and much else. None of these assumptions are properly regarded as missing premises.

Missing premises are to fill a quite specific role, one not filled by these kinds of assumptions. As Robert Ennis argued in an important paper, they are to fill a ‘gap’ identified in the stated argument.²⁵ The gap is an inference gap, and is deemed by the critic to arise because the stated premises do not, by themselves, lead to the stated conclusion in the appropriate way. If we have interpreted a passage as containing an argument, and we are sure that that argument is supposed to work as a syllogism, we will easily be able to supply the appropriate missing premise.²⁶ If we have interpreted it as a passage containing an argument and we are sure that the argument is supposed to work as a formally valid propositional argument, again we can supply the appropriate missing premise.²⁷ In both cases, inserting the missing premise presupposes the interpretive judgments, and once these are made, we apply a familiar model to generate a missing premise. We have a theory of argument that tells us that the model is of a type of argument which exists and is legitimate, and we have interpreted the passage in question as containing an argument of this sort. The theory of argument, and considerable interpretation are presupposed to give a solution to the problem of missing premises.

One difficulty with deductivism is that the theory of argument and the policy on missing premises are too intimately related. In order to maintain deductivism, we need to apply a deductivist policy on missing premises practically everywhere. Yet there seems no rationale for such a policy save in deductivism itself. The deductivist approach to interpretation thus seems question-begging and self-serving or, to put it another way, too ad hoc.

I would say, with Ennis, that arguments have missing premises when they have inference ‘gaps’. These gaps are identified when we apply our theory of argument and canons of interpretation to the discourse in which the argument appears. If we see the argument as an inference to the best explanation, and we understand that kind of argument as one in which the inferential pattern must go in such-and-such way, then when the argument fails to exemplify the appropriate pattern, it will have a ‘gap’. Something will be missing, and we can make this something appear by adding a premise. Clearly, perceiving these gaps is tantamount to perceiving some inferences as inadequate.²⁸ This perception depends on our perception of how the inference is working in the stated argument, which is a matter of interpretation. It also depends on our view of how it should work, to yield an argument without ‘gaps’. This is a matter of logic. This issue explicitly reveals the need for a theory of argument, for our view will depend on our view as to how many types of good inference there are.

That missing premises fill gaps in arguments does not yet tell us which of several possible gap-fillers should be selected as ‘best’. One problem about missing premises is to apply a theory of argument and to interpret a discourse and generate the judgment that there is an argument there with a missing premise. Another is, given different candidate statements which would all fill the identified gap, to select one of them as the most appropriate gap filler. Even when we limit the role of missing premises to that of filling inference gaps, there is considerable room for disagreement about them. Some people see gaps where others don’t, due to disagreements about the theory of argument. And some people see gaps where others do not because of disagreements about the explicitness or implicitness of inference rules. All this has only to do with the first question of whether a gap exists. Needless to say, there is also disagreement about the second problem, that of selection of candidate fillers from an array of possible ones once we have granted that there is a gap to be filled at all.

On the matter of premises and inference rules the locus classicus is, of course, Lewis Carroll’s famous dialogue about Achilles and the Tortoise. The stubborn Tortoise shows us the possibility of finding inference gaps in even the most straightforward modus ponens reasoning.²⁹ This meticulous character insists that in reasoning ‘A and B; If A and B, then Z; Therefore, Z.’, we ‘assume’ that if A and B, and if A and B, then Z, then Z. He insists that the ‘assumption’ be written into the argument, since the shorter version required the ‘assumption’. But then his lengthened argument requires a comparable, but longer assumption, in the form of a new associated conditional. The same problem arises at every stage; it repeats. The dialogue shows that inference is impossible unless the mind is willing to move from some claims to others according to a rule which is not ‘written in’. That is, principles of inference according to which inferences are made cannot, on pain of a vicious infinite regress, be written into the argument as unstated premises. They must be used and not said, at some point, or no inference is possible.

Every argument ‘assumes’ the associated conditional, ‘if CON then C’. There is no point in adding this conditional as an explicit premise in the interests of completeness, for the amended argument will again depend on just such a principle — namely its own associated conditional. There is no point in adding it for critical understanding, for it is no easier and no harder to assess than the original unreconstructed argument. Whatever else we say about the determination of which statements are the missing premises, we can agree to ban the associated conditional as one of them.

Carroll’s Tortoise seems especially meticulous and demanding because he will not reason according to modus ponens without having that rule stated as a premise in the argument. Logicians feel outraged because modus ponens is, paradigmatically, a logically sound principle, and because the unamended argument exemplifying the modus ponens pattern is paradigmatically not enthymematic. However, comparable moves seem more plausible when we move from deductive to nondeductive inference or from formal deductive inference to substantive deductive inference. (Substantive deductive inference depends on meaning rather than on form.)

A hot topic for discussion among philosophers of logic used to be whether the inference from ‘this is red’ to ‘this is colored’ required another premise, ‘whatever is red is colored’. Many people believed that it did, for the inference was ‘material’ and not ‘formal’. The example is like the relational argument Copi discussed, in that it is deductively valid in its original unamended form, in the perfectly straightforward sense that a state of affairs in which the premise is true and the conclusion false is an impossible one. It seemed to some logicians to be incomplete, because it did not exemplify a formal pattern of valid inference. Gaps will appear when one’s theoretical expectations are not satisfied. For a non-formalist deductivist, this argument is complete as it stands; for a formalist, it needs amendment.

Judith Jarvis Thomson discussed the problem, and took the following stand:

there is no such possibility as the possibility ‘if this is red, it is colored’ were not true, for ‘if this is red, it is colored’ is not merely true, but necessarily true. And therefore, ‘this is red’ does by itself imply ‘this is colored’. And therefore there is in this no reason for saying that a man who so argues suppresses a further premise. Even if we grant that such a man is not reasoning unless he believes that if the thing is red, it is colored, there is in this no reason for saying that what he must believe if he is to be reasoning must be called a suppressed premise of his reasoning.³⁰

The point emphasized here is a generalization of the point Carroll made with reference to the associated conditional. Anyone arguing from some premises (CON) to a conclusion (C), must is committed to the claim that if CON then C. This commitment is indicated by his reasoning in the way he does reason, and it is ‘assumed’ by his argument. However, to say this is not to say that it is a missing premise in the argument.

Thomson reiterates the point in general terms, saying:

to show that you must believe that p is a reason for q if you are to be reasoning in saying ‘p, so q‘ is not yet to show that ‘p is a reason for q‘ must be construed as a suppressed premise of the argument.³¹

It is important, then, to distinguish within those assumptions that are necessary in order for the inferences of an argument to work. Only some, bearing particularly and usefully on the argument at hand, are properly regarded as missing premises. The associated conditional should not be regarded as a missing premise. Nor should the conclusion. Nor should a necessary truth which relates the meanings of terms used in an argument already deductively valid without the addition of such a truth. Nor should methodological principles. In reasoning and arguing, we work according to some explicit or implicit rules, and these work as rules, not as premises of our arguments. The mind needs some such rules in order to reason and argue at all. Writing them in as missing premises will not avoid this need. It is a primary task of logic and the theory of argument to articulate and rationalize these principles of inference. However, that is not to say that they are to appear as premises in every argument in which we reason according to them. Carroll showed why this is so for simple deductive logic. The point can be extended.

It is easy to ignore this point, as we can see in a recent paper discussing hidden premises. In ”Hidden’ or ‘Missing’ Premises’, James Gough and Christopher Tindale incorporate a methodological principle as a missing premise in their analysis of an analogy. They discuss the following argument:

A man who drives his car into the rear of another car is not guilty of careless driving if his brakes failed. Similarly, if a man kills another man he is not found guilty of murder if his mind failed to perceive reality due to mental illness. Mental instability is not sufficient to establish insanity, as Mr. C. contends. Our judicial system justly requires that a person must have rationally formed the intention to kill another person to be considered a murderer. Insanity is, therefore, an appropriate defense for murder. ³²

As Gough and Tindale point out, in this argument the analogy between failing brakes in a car accident and a failing mind in a murder is used to support the conclusion that insanity is an appropriate defense for murder. But it is not the sole basis for that conclusion. The analogy is used to support what our judicial system requires – namely that one intend to kill in order to be considered a murderer. However, what is at issue in the present context is not the structure of the larger argument, but the way in which the analogy works. Gough and Tindale say:

Here the conclusion: ‘Insanity is, therefore, an appropriate defense for murder’ is supported by a number of premises including the following hidden assertion of a comparison:
HP – The two situations are comparable, so if you accept the principle in the case of the driver/brakes, you should also accept it in the case of the murder/mental illness.

The authors are arguing, throughout their paper, that it is better to think of the problem of hidden premises than of the problem of missing premises, because this rendering of the problem makes us more likely to stick closely to the exact text or discourse and less likely to ‘read in’ whatever suits our logical fancy as part of someone else’s argument. They believe that the statement which they would add to the analogy is in this sense ‘hidden’ in the original argument.

This assertion is not missing, but can actually be found in the argument. One of the considerations in assessing the strength of this argument will be the adequacy/legitimacy of this analogy.³³

At this point we have a slide into incorporating methodology as premises. Any argument from analogy does assume that from some similarities, others follow or are made likely. We have to assess this part of the argument. Of course this involves determining how closely similar the things are in the relevant

respects; that is what is involved in the evaluation of an analogy. But that does not mean that some assertion to the effect that the things are ‘comparable’ and inferences can be made from their comparability needs to be contained. If a person did not believe that this was the case, or that the two cases he compares ‘are comparable’, he would not reason by analogy, just as a person would not reason ‘p, so q’ unless he believed that p is a reason for q. In the latter case, as we have seen, we should not regard the inferential assumption as a missing premise.

We do not put into every deductively valid argument the supplementary premise ‘when the truth of the premises makes the falsehood of the conclusion a logical impossibility you can infer the conclusion from the premises’ or ‘no contradictory state of affairs is possible’. We do not put into classically inductive arguments the supplementary premise ‘unexamined cases are more likely than not to resemble examined cases’. We do not put into arguments by explanation a supplementary premise that ‘the best explanation of observed phenomena is likely to be correct’. To do so would be to emulate the Tortoise, in wanting our rule of procedure to be spelled out as a premise. Missing premises are those gap-fillers that will make inferences from stated premises to conclusions work as they ‘should’ and that meets further conditions – to be specified. The gaps they fill are identified by interpreting discourse in the light of a theory of argument. No theory of argument should identify gaps on the grounds that inference rules are unstated, as Carroll’s arguments show.

It is seriously misleading to use ‘missing premise’ and ‘unstated assumption’ as though they were synonyms. Only some unstated assumptions are in the proper sense missing premises. Other unstated assumptions are worth noting, sometimes, and criticizing them often provide important insights. Nevertheless, pragmatic, meta-linguistic, necessary, or methodological propositions which must hold in order for the argument to work are not, as such, propositions which fill in a specific inference gap in an argument. They do not play the role missing premises are supposed to play.

3. Pragmatism, Scepticism and Missing Premises

When we perceive an inadequacy in the inferential basis for an argument, we may decide that that argument has one or more missing premises. Then we have to select from among an indefinitely large number of candidate premises that could fill this logical gap. There are various considerations that enter in here. There is the desire to be charitable and fair to the arguer, often taken to entail attributing to him or her tacit premises which will be true or plausible and will strengthen the argument from an epistemic point of view. There is the desire for interpretive accuracy, leading to a perceived need to justify supplementation with reference either to other stated material or to the known background beliefs and assumptions of the arguer. And there is the desire for efficiency and simplicity in argument analysis. Obviously, these can pull us in different directions.

At this point we encounter a broader issue. That is the purpose of argument interpretation and criticism. There are two directions we may go, one emphasizing the issue which the argument is about, so that we try to fill out the best argument possible for the conclusion; and the other, a more closely interpretive approach, emphasizing what the arguer said and whether the stated reasons should be amended, in accordance with his or her implied beliefs and intentions.

The idea that argument evaluation should be closely linked with very charitable reconstruction is rather popular among philosophers and logicians. However, it is open to more objections than many people realize. Reconstructing an argument is not the same thing as appraising it, and argument analysis should not be construed as a task which involves the ambitious accumulation of all evidence bearing on the conclusion. The reconstructive view, in its most strongly charitable sense, leaves it a mystery why we should pay any attention to the stated premises at all. If our purpose is to determine whether the conclusion is true or not, then we can think about the conclusion directly, and the appraisal of anybody’s argument for it is a subsidiary project. Pedagogically, the matter is of some importance. A course on argument analysis deals primarily with the structure of argument and the appraisal of inference. Arguments on such issues as abortion or evolution are examples. If the primary purpose of examining such examples were to determine the truth of the conclusion, then the course on argument analysis would have to be a course on abortion and everything else. No one is qualified to teach such a course.

How charitable we should be is an issue that will arise when other principles have already been applied. First we use interpretation and our theory of argument to show that a stated argument has inference gaps. Then we have an array of candidate gap-fillers, all of which will do the logical work of filling the gap or gaps. From these, we can select those that cohere with the beliefs, intentions, and commitments of the arguer, so far as we are able to determine these. We have to decide how much it matters whether we have evidence that arguers did accept these candidate premises, and whether our own standards of truth and plausibility are going to be used in reaching our beliefs about what these arguers would have been likely to believe. We have to balance charity and interpretive accuracy, and how we do this is likely to depend in part on our purpose in appraising the argument in the first place. Overly strong charity ignores the possibility that other people may actually think and reason in ways which would strike us as implausible, odd, or downright wrong. Overly literal interpretation may produce accusations of pedantic, non-substantive, and uninteresting analysis.

When we look at other people’s arguments, we should try to understand what they have said and determine whether they have good reasons for their conclusions. Everyone would agree on this, but people have different standards of what real understanding is, some linking it with charity in that understanding must mean making sense of from our own point of view. If we apply the principle of charity to see how well we, or someone, could defend that conclusion, we move argument analysis in the direction of reconstructive discovery and substantive investigation. If we stick closely to the text and immediately implied beliefs of the arguer, argument analysis looks more like an interpretive project.

Thus, it appears that what missing premises an argument has will depend not only on how it is classified and how ‘gappy’ it is found to be from a theoretical point of view, but also on the purposes we have in analyzing it. If our purpose is to discover whether the conclusion advanced is true, we will find one tacit premise, perhaps, whereas if our purpose is to see how the arguer in fact reasoned from the stated premises to the stated conclusion, we may find another. Thus, pragmatic considerations enter into the identification of the very structure of an argument. To the classically trained mind, this conclusion will doubtless appear bizarre and unacceptable. We might think that if missing premises have to be identified with reference to the purposes of the critic, the game is given away altogether. The missing premise is altogether a product of the critic’s imagination, rather than being a feature of the argument itself.

In an earlier paper, I made the sceptical suggestion that missing premises are nowhere except in the mind of the critic. In that paper, I linked the discovery of missing premises to a concept of ‘complete argument’ which could be universally applied. I said that we have no obviously applicable notion of exactly what would have to be there in order for the argument to be complete. I asked whether it is as though we judged a young family of man, wife, and two small children to be complete, but had no basis for a view as to how large their complete family should be. I then suggested that in this situation, when a person judges that an argument has a missing premise, he is virtually reduced to saying he would expect as part of the argument, something which is not there. He would expect one or more additional premises. But why? The argument as it stands is not complete. But why? What are complete arguments like, and why does this argument fail to be one? In the absence of a universally applicable notion of complete argument, it appears that the missing premise is a product of the reflective mind. Like Humean causes, it is thrust upon the external text by the active intellect-of the critic.³⁴

What now strikes me about these earlier reflections is the presumption that we need one single general account of what a complete argument is in order to say that a particular argument has a missing premise. I now believe that this is not required. What we need is something less ambitious though perhaps still hard to obtain in some cases. We need a concept of complete argument which we can properly apply to the case at hand. That account need not be applicable to all arguments. Seeing an argument as having a missing premises means seeing its explicit inference structure as inadequate. There is a ‘gap’ to be filled, not because there are some unstated assumptions that bear on the argument, not because the argument fails to be deductively valid, and not because some stated premises need defense. The gap exists because the premises, as stated, cannot give the appropriate support to the conclusion. We can either see the argument as inferentially flawed or see it as having missing premises. But many judgments have gone into the identification of this gap and many more are needed in order to determine which of the various candidate fillers is most appropriate.

Are gaps there in the argument? Or are they projected by the critic? They are really there, presuming that correctness of all the critic’s interpretive and theoretical judgments. They are not ‘just there’ in a theory-neutral sense. Dogmatic pronouncements to the effect that arguments surely have this or that missing premise should always be regarded with suspicion.

All of these considerations suggest that the problem of missing premises is much more complicated that it might seem at first. It involves all the following factors:

1. Interpretation of the discourse as containing an argument in which particular statements are the stated premises and a further statement is the stated conclusion.

2. Classification of the stated argument as being of some particular type. (Application of one’s theory of argument.)

3. Logical judgment that the stated argument is not inferentially sound as an example of that type.

4. Logical judgment that the stated argument would be inferentially sound if one of a candidate set of supplementary premises were added.

5. Logical/epistemic interpretive judgment that the argument is some kind of enthymeme rather than a fallacy or non sequitur and that the gap identified should be filled

6. Selection of one candidate from others, based both on epistemic (modest charity) considerations and on interpretive considerations – respect for the actual discourse and beliefs which the arguer held or would have been likely to hold.

Confident statements to the effect that such and such argument clearly has some statement as its missing premise are inappropriate. Whether a statement is a missing premise in some argument depends on our theory of argument, our purpose in analyzing the argument, and much else.

Notes

1. This matter is thoroughly discussed in Chapter One of the second edition of R.H. Johnson and .1.A. Blair’s Logical Self-Defense. (Toronto: McGraw-Hill-Ryerson. 1983).

2. The view that missing premises are gap-fillers has been defended and explained by Robert H. Ennis in ‘Identifying Implicit Assumptions’ (Synthese, 51: pp. 61-86) and endorsed in David Hitchcock in ‘Filling Premise-Gaps in Arguments’ (unpublished paper presented at the Second International Symposium on Informal Logic, University of Windsor, Windsor, Ontario, June, 1983).

3. James Gough and Christopher Tindale emphasized the semantic contrast between ‘hidden’ and ‘missing’ in their paper, ‘ ‘Hidden’ or ‘Missing’ Premises’. (Unpublished paper presented at the Second International Symposium on Informal Logic; University of Windsor, Windsor, Ontario. June, 1983.)

4. Stephen Thomas, Practical Reasoning; in Natural Language, (Englewood Cliffs, New Jersey: Prentice Hall, 1981: Second Edition), p. 174.

5. A term coined, I believe, by David Hitchcock.

6. Thomas, p. 175.

7. In ‘Filling Premise-Gaps in Arguments’, David Hitchcock argues that it is possible to endorse a deductivist approach to missing premises without subscribing to a deductivist theory of argument. The same point is developed in ‘Enthymemes’, a paper he presented to the American Philosophical Association meetings in December, 1983. One might apply a deductivist policy to only some arguments, or to all arguments for purely heuristic reasons, or to all arguments for some specific purposes. Thus one might use deductivism as a policy on missing premises without subscribing to it as an overall theory of argument. However, these more qualified views leave open the broader question of the rationale for deductivist supplementation. If one does not believe that the stated argument was in some sense deductive, it is hard to see why the merits of the supplemented argument have any bearing on the original argument.

8. Thomas, p. 175.

9. Established tradition in logic has it that there are numerous fallacies, formal and informal, and that there is at least one type of nondeductive argument, namely inductive arguments. Philosophy of science is sceptical even about the prospects of formal models for inductive reasoning in science, not to mention pessimism about reducing scientific reasoning to deductive models.

10. Taken from Garret Hardin’s ‘Parent: Right or Privilege’?’, in Science, 1970.

11. Compare the discussion of the example by David Pomerantz in Informal Logic Newsletter, Vol. iii, No. 1.

12. Despite the tendency of some logicians to read in the associated conditional routinely when the argument fails to be deductively valid, a number of writers on the topic have pointed out the uselessness of this manoeuvre from a critical point of view. See Ralph H. Johnson, ‘Toulmin’s Bold Experiment (Informal Logic Newsletter, Vol. iii, nos. 2 and 3); David Hitchcock, Critical Thinking A Guide to Evaluating Information (Toronto: Methuen Publications, 1983), ‘Filling Premise-Gaps in Arguments’, and ‘Enthymemes’. Generalizations of the conditional do not share this feature of sheer redundancy, but they lack it at an interpretive cost. Since the generalization necessarily goes beyond what is said in the original, there is always the question of whether the author is really committed to it. This seems to me to constitute a real objection to Hitchcock’s approach.

13. Stephen Toulmin and June Goodfield, The Architecture of Matter, (Middlesex, England: Penguin Books, 1962), p. 21.

14. This would be a particularly strong version of foundationalism because it would conjoin to the usual foundationalist demand for basic statements a further demand that these basic statements deductively entail the statements they support. As the difficulties of foundationalism have been thoroughly discussed in writings on epistemology, I shall not revisit them here.

15. Some deductivists admit that there are many examples in which anything other than the associated conditional or a generalization of it will be very cumbersome. Compare the discussion in S.N. Thomas Practical Reasoning in Natural Language (pp. 171-182) and Samuel D. Fohr, ‘Deductive-Inductive: Reply to Criticisms’ (Informal Logic Newsletter, Vol. iii, no. I, pp. 5-10).

16. 1 don’t claim to resolve this issue here, of course. It is discussed in an introductory way in my text, A Practical Study of Argument, (Belmont, Calif: Wadsworth, 1985 and 1987), Chapter 2.

17. Often missing premises are deemed to be premises that, if stated, would immediately reveal themselves as controversial. Sometimes the contrary view is taken: these premises are unstated because they are so obvious and uncontroversial that nobody would bother mentioning them.

18. Irving Copi, Symbolic Logic, (New York: Macmillan, 1972; Third Edition), p. 154

19.On Certainty, (Oxford: Basil Blackwell, 1969), sections 341, 342, and 343.

20. Typically, that is.

21. Copi, Symbolic Logic, Third Edition, p. 155.

22. Michael Scriven, Reasoning (New York: McGraw Hill, 1976), p. 173.

23. R.H. Johnson and J.A. Blair, Logical Self-Defense, (Toronto: McGraw-Hill-Ryerson, 1977; First Edition) pp. 43 and 186.

24.Logical Self-Defense, Second Edition (Toronto: McGraw Hill-Ryerson, 1983), pp. 180-84.

25. Ennis, Op. cit.

26. See David Hitchcock, ‘Enthymemes’; Rolf George, ‘Enthymematic Consequence’, (American Philosophical Quarterly, Vol. 9, pp. 113-116); Rolf George, ‘Bolzano’s Consequence, Relevance, and Enthymemes’ (Journal of Philosophical Logic, VI. 12, pp. 299-318).

27.We have a pattern, and so can determine what is missing from it.

28. One tough issue is to determine when the inferences are just plain incorrect (fallacy) and when they are insufficiently explicit (enthymeme).

29. Douglas Hofstadter’s treatment of Lewis Carroll’s paradox in Gödel. Escher. Bach (New York: Basic Books, 1979) revived my interest in Carroll’s dialogue, which first appeared in Mind for 1896.

30. Judith Jarvis Thomson, ‘Reasons and Reasoning’, in Max Black, Editor, Philosophy in America (Ithaca, New York: Cornell University Press, 1965), p. 287.