1 Introduction

My question is, how may presumptions, assumptions, and presuppositions of ordinary arguments be distinguished? It might be wondered whether this paper really has a topic. Often in ordinary (hence, non-legal) contexts, the notions of an argument’s presumption, assumption, and presupposition do not appear to be distinguishable. For example, consider this argument (adapted from Nosich 1982, p. 211):

Example (1)

Since serious crimes should be punished with the most severe punishment possible, capital punishment should be the punishment for serious crimes.

It seems that it would be perfectly and equally natural to say that this argument presumes, assumes, or presupposes that capital punishment is the most severe punishment possible, or that this proposition is a presumption, assumption, or presupposition of the argument. If there were nothing that distinguishes these notions—if they were all simply the notion of an implicit premise—then this paper would not have much more to say.

Yet as we will see, often in ordinary contexts and perspectives, differences do emerge between these aligned notions that bring them into sharper focus. I will argue, moreover, that assumption and presupposition, but not presumption, belong to the fundamentals of logic as basic—and distinct—logical notions. Presumptions of ordinary arguments are inherently conventional in ways that their assumptions and presuppositions are not. This account avoids rendering the notion of presumption vacuous and collapsing any substantial distinction between assumption and presumption, which is a vulnerability of alternative views such as Hansen’s and Bermejo-Luque’s, as will be shown. The issues addressed tend to lie at the heart of logic. The most elementary analysis of an argument is that it is composed of a premise(s) and a conclusion. But what is it that makes a proposition (logically) a premise, that is, an assumption, of an argument?

It is important to note that my approach is mostly from the point of view of traditional logic and argument analysis, or if you prefer, is monological as opposed to dialogical or dialectical. To be sure, discourse and argumentative exchanges are fundamental in such diverse fields as the study of legal reasoning, pragmatics, and the evolution of thought and language. Yet in logic, dialectics may get the cart before the horse insofar as its concepts are extensions from the core. Certainly, as involving not only reasoning but also the communicative situation, the dialogical is an order of magnitude more complicated than the monological. For instance, although Freeman’s Acceptable Premises (2005) is a first-class work of logic and philosophy, it attempts to explain premise acceptability in terms of presumption, and presumption in terms of dialectics (esp. p. 32). One cannot help but wonder whether this endeavors to explain the obscure by the increasingly obscure.

Section 2 will attempt to distinguish the basic logical notion of a presupposition of an argument. Section 4 will do this for assumption, after Sect. 3 briefly compares and contrasts presumptions and assumptions of (ordinary) arguments. Much will come together in Sect. 5, where presumptions of arguments are more thoroughly distinguished from the other two aligned notions.

2 Presuppositions

It would be of little interest to point out that the Example (1) argument assumes or presumes the proposition expressed by the ‘since’ clause. That the argument does this is on the face of it obvious because the premise is overtly stated and is explicitly signaled as a premise by the appearance of the argument-indicator word ‘since’. In the study of argument, identifying premises typically presents a theoretical challenge only where an assumption or presumption is enthymematically implicit, unstated, ‘unexpressed’, ‘suppressed’, ‘hidden’, or ‘missing’ with respect to the overtly stated argument. In contrast to an assumption or presumption, and this is the first difference we note between the three notions, the idea of an overt or explicit presupposition seems to be a contradiction in terms. The concept of presupposition connotes implicitness; if the proposition were explicit, it would be a supposition rather than a presupposition. It would be a misuse of language to say that the Example (1) argument presupposes the proposition expressed by the ‘since’ clause.

Continuing in the vein that puts assumptions and presumptions in one class, and presuppositions in another, Llewelyn points out that a distinguishing fact about ‘presuppose’ is that it has “no imperative nor any other postular use” (1962, p. 162). We can say ‘Assume’ or ‘Presume’ that p, or ‘Let us presume (assume)’ that p, perhaps adding ‘for the sake of argument’. But we cannot tell or ask our audience to ‘Presuppose’ that p or ‘Let us presuppose that p (for the sake of argument)’. One cannot do this because there is no choice in the matter. One does not construct arguments by making presuppositions, which one may more or less freely do with assumptions and presumptions. Presuppositions are given in the content of discourse; they are not for the making. I think the reason for this is that, as far as logic is concerned, presupposition is primarily a logical relation between propositions or statements, not a distinctively argumentative function or role. In Llewelyn’s terminology, it is “referential presupposition” that is primary, not “premissory presupposition” (p. 166). Govier (1972) argues that as logical relations the concepts of presupposition and that of necessary condition are essentially the same, such that p presupposes q if and only if q is a necessary condition of p. She also recognizes the premissory function. She says (p. 452) that in certain “contexts ‘presuppose’ functions almost as ‘assumes’ does; here, of course, it differs from the relation of necessary condition. This difference is not one which holds generally, however.” Only by extension is presupposition a distinctively argumentative or premissory function equivalent to assumption or presumption.

During the past half century, the study of presupposition, particularly from a technical linguistic perspective, has intensified. Much work is based on the foundational distinction, as Shanon (1976, p. 247) puts it, between “two notions of presuppositions in natural language: the logical (or semantic) and the pragmatic. A sentence S logically presupposes a sentence P just in case S logically implies P, and the negation of S also logically implies P.” Beaver and Geurts later (2011, sec. 4.2) explain pragmatic presupposition as

not what words or sentences presuppose, but what people presuppose when they are speaking. A pragmatic presupposition associated with a sentence is a condition that a speaker would normally expect to hold in the common ground between discourse participants when that sentence is uttered.

The current research landscape is described by Beaver and Geurts as involving three main theories of presupposition: the logical/semantic, the pragmatic, and that of “local contexts and the dynamic turn.”

Further details of these developments need not concern us here. We are interested in how best logically to distinguish presuppositions of ordinary arguments from their assumptions and presumptions, and it seems we have enough for that. On the whole, I think it suffices to explicate the notion of a presupposition of an argument as follows:

A presupposition of an argument

pertains to a propositional element (a premise or the conclusion) e of the argument, such that the presupposition is a necessary condition for the truth of e or for a term in e to have a referent.

For instance, three presuppositions of the Example (1) argument are:

Serious crimes can be punished with the most severe punishment possible.

Capital punishment can be the punishment for serious crimes.

There are serious crimes.

Notice that I am not proposing that the putative conceptual truth that ought implies can is a presupposition of the argument, even though it is required to derive the first and second presuppositions on this list. That ought implies can is a presupposition in some sense of something that is in effect larger than any particular argument, namely, rationality itself. Similarly, neither should we hold that a perfectly general rule of inference such as Hypothetical Syllogism is a presupposition, or for that matter, an assumption or presumption, of an argument that instantiates Hypothetical Syllogism [as is reasonable to understand Example (1)].Footnote 1 If we do, we embark on an infinite regress akin to the one identified by Carroll (1895).

3 Presumptions Versus Assumptions

Why is there the notion of being presumptuous, but not a parallel notion of being assumptuous? Both Llewelyn (1962, p. 163) and Kauffeld (1995, p. 510) note this difference, but their explanations of it and of the difference in general between ordinary presumptions and assumptions are not entirely adequate, I believe. As will be more fully argued in Sect. 5, the fundamental difference between presumptions and assumptions of ordinary arguments is that presumptions are inherently conventional in ways that assumptions are not. Presumptions are determined by rules or social inventions that can be flouted or abused, which allows presumptuousness. Kauffeld explains what he sees as the main difference between ordinary presumptions and assumptions as follows (2013, pp. 3–4; cf. his 1995, pp. 509–510):

I presume that A will be home by seven on the grounds that A promised me to be home by that time; whereas, I might assume that A will return at that time because she normally does and no one, myself included has (so far as I can see) reason to suppose otherwise… One may be justified or warranted in assuming that p, but an assumption is something one takes upon oneself in that typically one bears a singular responsibility for the adequacy of what one assumes. When a person presumes something, he or she characteristically takes it as something to which he or she is entitled.

I think this is right insofar as it points out that presumptions are introduced through conventional rules (here, those that concern how to treat promises) and assumptions are comparatively independent, and it puts assumptions and presumptions in at least some argumentative role—that of conclusions of arguments or “the products of inferences.” But this is not exactly the right role for our purposes, since it derives from a kind of sociological or pragmatic approach according to which “assumptions and presumptions both rest directly on suppositions about social context” and “have primarily to do with supposition about interactions between people.” This excludes or renders secondary huge sets of cases, for instance, assumptions of arguments of math, theoretical physics, botany, zoology, electrical engineering, etc. The primary logical role of an assumption or presumption is that of a premise (premissory). Kauffeld does acknowledge this function, but apparently sees it as secondary; he allows that “both assumptions and presumptions” can “serve as the bases for further reasoning” (1995, p. 509).

Other treatments that compare and contrast presumptions and assumptions do so mostly en passant. For example, Bermejo-Luque defines a presumption as “the speech-act of putting forward a proposition as a reasonable assumption” (2013, p. 4; cf. 2016, p. 9). Even though in these papers she has much more to say about presumption, some of which we will consider in Sect. 5, she has little more to say about assumption other than that “assumptions are just acts of taking a proposition to be true” (2013, p. 6n; cf. 2016, p. 10). But of course in logic assumptions are not just this, as this does not fully capture their argumentative (premissory) function. Godden and Walton (2007) construe presumptions to be “inherently dialectical in nature” (p. 314). They similarly construe the notions of assumption and assertion. They maintain that if a participant makes an assertion in a dialogue, evidence must also be provided by that proponent; assertion carries its own burden of proof. But for a presumption, the burden of proof lies not with its proponent, but with the dialogue’s other party, such that if the other party fails to argue against it, the presumption becomes a common commitment of the dialogue. In contrast “assuming bears no cost, but has no force: an opponent can reject the assumption whenever it begins to harm his position” (pp. 326–327, 328n15; cf. Walton 2014, e.g., p. 115). I have already expressed my reservations—having to do with getting the cart before the horse—about explaining basic logical notions dialectically. The next section will indicate how far this dialectical notion of assumption diverges from the basic logical notion.

4 Assumptions

Some of the ideas in this section appeared in earlier form in Plumer (1999).

The most elementary analysis of an argument is that it is composed of a conclusion and at least one premise or statement of evidence for the conclusion. In the fundamental logical sense of ‘assumption’, assumptions simply are premises. They are not just anything that happens to be stated before the conclusion. An assumption must be ‘presupposed’ by the argument as a whole; a proposition must be integral to the reasoning or inferential structure of an argument, not just to a claim made within the argument, in order for the proposition to be (logically) an assumption or premise of the argument. This suggests the following:

Principal criterion for determining an assumption of an argument

It could not be the case that both the argument aside from the putative assumption is fully cogent and the putative assumption is false.

This criterion can be applied recursively to any putative assumption of the argument, whether implicit or explicit. Yet as mentioned in Sect. 2, identifying premises typically presents a theoretical challenge in the study of argument only where the candidate is implicit with respect to the overtly stated argument. So we see the principal criterion accord, for instance, with Burke’s explication of “the sense in which an argument may be said to assume any unstated proposition on which its inference depends, meaning any proposition which needs to be true, if the inference is to be justified.” However, Burke himself rejects this as unhelpful on the grounds that there are “infinitely many” such propositions. “Examples: that there is at least one inference; that there is at least one justified inference; that there is at least one thing that is either an inference or a polar bear” (1985, p. 114; cf. Govier 1987, pp. 92–94; Grennan 1994, p. 190). What this fact indicates is not that the principal criterion is useless; instead, it indicates that the principal criterion needs to be supplemented by other criteria. Because all of Burke’s examples are presuppositions of rationality, or at least of the existence of rationality, none are implicit assumptions of any particular argument (unless, of course, such is the subject matter of the argument).

In the principal criterion, the central meaning of the clause that ‘the argument aside from the putative assumption is fully cogent’ is that given the truth of what I will call the received premises (i.e., all of the implicit and explicit premises, considered apart from the putative assumption), the conclusion can be inferred to be true. The standard of an allowable inference here is to be taken as varying in stringency according to whether the argument is deductive (in which case validity is the basic standard) or nondeductive. Of course a nondeductive argument may have a conclusion that is in fact false, yet it still be reasonable to infer that it is true from the truth of the premises. Cogency is perhaps a loose evaluative concept, but I take it to pertain only to an argument’s reasoning or logic, not also to the truth value of its propositional elements (unlike the technical concept of soundness). Depending on how the constituent notions are explicated, we can agree with Johnson and Blair’s (1977) “well-known and widely accepted RSA criteria for argument cogency: the premises are to be relevant, sufficient, and acceptable” (Paglieri 2015, p. 70), if acceptability is clearly distinguished from truth (as in Govier 2010, p. 108, in contrast to Adler 2006, p. 225). And in no case is cogency purely a matter of formal validity. For example, adding the stated conclusion or the contradictory of a stated premise to the stated premises would make any argument formally valid. But the argument would lack cogency insofar as it grossly begs the question or engages in self-contradiction. In order to be fully cogent, it seems an argument must not commit any informal fallacy (that pertains to its reasoning).

The rationale behind the principal criterion should be reasonably clear. Suppose the criterion is violated. That is, suppose that the putative assumption is false, and given the truth of the argument’s received premises—premises that might, but need not, include an alternative to the putative assumption—the conclusion can still be inferred to be true in a fully cogent way. Then surely, the putative assumption does not figure in the argument’s reasoning; for the putative assumption does not have to be taken to be true in order to so-infer that the argument’s conclusion is true. Hence, it is not in fact an assumption of the argument. Example (1) provides as good an illustration of this as any, where the putative assumption is (e.g.) capital punishment is the most controversial punishment possible.

Notice that the principal criterion does not deny the logical truth that it could be the case that both an argument as a whole is fully cogent and an assumption of it is false. Unlike the principal criterion, this logical truth involves the notion that if all of the argument’s premises, including the assumption, were true, the conclusion could be inferred to be true. Yet a key point of the principal criterion is that the most critical and heuristically useful idea for identifying implicit assumptions is the following test: take the argument with its received premises to be fully cogent—then must the putative assumption be true? If the answer is ‘yes’, then (barring the need to apply other criteria) the putative assumption is an actual implicit assumption of the argument. The criterion thereby treats the proposition as an ‘inference license’. The general idea is that the same proposition may be treated both as a fact that helps to justify the inference in an argument where the proposition is abstracted out of the argument and as an implicit premissory element of the argument. As Sloman concludes, “any analysis of a particular argument in terms of a suppressed premiss may be replaced by an equally general analysis in terms of a rule of inference and vice versa” (1964, p. 88; cf. Hitchcock 1985, pp. 94–95; Smiley 1995, pp. 730–732). However, because such a proposition must contain at least one content expression (given the criterion that an implicit assumption not be a general presupposition of rationality), insofar as it is a “rule of inference” at all, it is nonformal or specific. Contrast (e.g.) Hypothetical Syllogism, which as topic-neutral is a formal or general rule of inference. And as mentioned, treating such a rule of inference as an assumption of an argument that instantiates it embarks on an infinite regress akin to the one identified by Carroll (1895).

A virtue of the principal criterion for determining an assumption of an argument is that in general it rules out contingent (i.e., neither necessarily true nor necessarily false) implications or presuppositions of any propositional element of an argument. For instance, consider the presupposition serious crimes can be punished with the most severe punishment possible of the stated premise in Example (1). Since by definition such implications are already part of the content of the argument, the argument could quite well be fully cogent without re-introducing them into the argument individually as further members of its premise set. Such implications violate the principal criterion in the following way: Although if such a putative assumption is false the conjunction of the argument’s conclusion and received premises is also false, it still could be that if the received premises were true the conclusion could be inferred to be true in a fully cogent way. Just as it is a logical truth that it could be the case that both an argument as a whole is fully cogent and the conjunction of its propositional elements is false, it is a logical truth that it could be the case that both an argument, considered apart from such an implication, is fully cogent and the implication is false. (Of course an exception arises from the curiosity that every proposition logically implies itself. If it is already established of a proposition that it is an assumption of an argument, this curiosity does not mean that the proposition is not an assumption of the argument.)

However, the principal criterion is not so powerful as to preclude any arbitrarily selected necessary truth from being counted as an implicit assumption; the same applies, for example, to the proposition that there is at least one fully cogent argument. So we still need, respectively, the criteria that an implicit assumption be neither an implication/presupposition of a propositional element of the argument (Sect. 2), nor a general presupposition of rationality (assuming that not all general presuppositions of rationality are necessary truths). This points to a limitation of the account: it cannot be used to determine any necessarily true assumptions, as of an argument that has other necessarily true propositional elements, e.g., a mathematical argument. This is a consequence of a so-called ‘paradox’ of logical implication—a necessary truth is implied by any proposition whatsoever. As for arguments that have necessarily false propositional elements, insofar as they would lack cogency in virtue of having such elements, it is not clear that these arguments could even have implicit assumptions since a logically implicit assumption contributes to an argument’s cogency.Footnote 3

The main objection to any such account, as Malone succinctly puts it (2003, p. 248), is that “if more than one statement could do the job, then no particular one is necessary” or logically an implicit assumption of a given argument. In this vein, Ennis says (1982, p. 82; cf., e.g., Nolt 1986, p. 572; Govier 1992, p. 404):

The basic idea is that any incomplete argument can be completed in a number of different ways. Consider the simple argument, “Since Mike is a dog, Mike is an animal.” To suggest the range of possible gap-fillers, I shall note two, the one that first occurs to most people [note this admission] and another one:

  1. 1.

    All dogs are animals.

  2. 2.

    All dogs whose name begins with “M” are animals.

A person is not logically prohibited from offering the argument, denying 1, and using 2 as a gap-filler. This shows that 1 is not logically necessary for the offering of the argument.

If this were correct, 1 would violate the principle criterion in that 1 could be false, yet if the received premises—taken as including 2—were true, the conclusion could be inferred to be true in a fully cogent way.

However, the argument “Since Mike is a dog, Mike is an animal” with 2 as the ‘completion’ is in fact invalid. It would be valid if it had the more specific or narrower claim ‘Mike is a dog whose name begins with “M”’ as the explicit premise. Indeed, if this were the explicit premise, 2 would be the implicit assumption. The general principle operating here is that it is specificity and details of the context and explicit argument that determine the implicit assumption and the inferences licensed by it. Yet in the original argument (“Since Mike is a dog, Mike is an animal”) and context the only evidentiary claim made about Mike is that he is a dog. So what follows from this about Mike (that he is an animal) follows for any dog. There is nothing in the context to indicate that Mike is in any way special with respect to being a dog; qua dog, Mike is an arbitrarily selected individual. In logic, the principle of rationality that we are to treat similar cases similarly is the quantification rule of Universal Generalization (UG). 1 as the implicit assumption here is determined by the fact that UG applies to the stated argument’s inference. Therefore, it does not seem too strong to hold in this case that both “offering the argument” and “denying 1” would be self-contradictory. Similarly, as Copi (1978, p. 357) puts it, “in the geometer’s proof the only assumption made about ABC is that it is a triangle, hence what is proved true of ABC is proved true of any triangle.” This is just UG at work.Footnote 4

These considerations apply equally well to a case Walton et al. discuss (2008, pp. 211–212): “Jones is a politician, so he is not to be trusted.” But they indicate that the context could be such that it indicates that application of a nondeductive scheme of “circumstantial ad hominem” is appropriate, and accordingly, “usually, politicians cannot be trusted” is the implicit assumption. Fine, although this would be more compelling if the original explicit argument concluded with something on the order of ‘so probably [or even the simple intensive ‘surely’], he is not to be trusted’.Footnote 5

As was discussed earlier, necessary truths trivially satisfy the principal criterion for determining an assumption of an argument. The other half of the story is that any putative assumption of an argument that is wholly or irredeemably fallaciousFootnote 6 will trivially satisfy the principal criterion, simply because the argument could not be fully cogent and remain the same argument. The avoidance of this trivial satisfaction constitutes one reason it is important to see that in the very act of attributing a proposition to an argument as an implicit assumption, one takes the argument to be cogent to at least some extent. Cogency is what assuming the proposition is (appropriating Ennis’ terminology) “logically necessary for”; the proposition fills a “gap” in the explicit argument’s reasoning, thereby making the reasoning stronger than it otherwise would be. Yet it could still be weak or fallacious in other respects. This last point is critical if we are to maintain the distinction, as we must, between incomplete or enthymematic arguments that are fully cogent and those that are not; as Paglieri and Woods show, “their validity cannot be a necessary consequence of their incompleteness” (2011a, p. 467). They analyze an example where the alternatives are, first, interpreting the argument as a case of modus ponens with the major premise implicit. Given the example’s particulars, this would entirely trivialize the argument since it would take the argument’s associated or “corresponding conditional” as implicit,Footnote 7 not to mention the putative assumption “is not just false, but notoriously so.” Thus, they say that the “correct interpretation in this case demands acknowledging the invalidity of the argument” as an instance of Affirming the Consequent, with the “moral” being that “we are more than ready to consider our fellow arguers to be inferentially mistaken, if this helps justifying a presumption of sanity for their beliefs” (p. 487; see also their 2011b). Of course in other cases such as hypothesis confirmation, variations on the deductively invalid pattern of Affirming the Consequent can be cases of good reasoning. As Johnson and Blair say, “with few exceptions, the patterns of argument that are liable to be fallacious need not always be so” (2006, p. xv).

5 Presumptions

One cannot help but be more at sea with presumptions in ordinary arguments. This is because the most accepted, developed, and systematic manifestation of presumptions lies not in ordinary arguments, but in legal reasoning (with the presumption of innocence being the favorite example) and formal discourse (cf., e.g., Walton 2014). Is this the core from which all other uses of presumptions somehow extend? Indeed, some think that it is the “hard core” (Ullman-Margalit 1983, p. 144). Practically a defining feature of this apparent core is that it is mostly a conventional edifice, even given that there is such a thing as ‘natural’ law. It is conventional at least insofar as it consists of social inventions that arise from factors that range from the need to ensure protection from harm, to expediency and simply having a way to proceed and make decisions in an orderly fashion. In the construction of the edifice, there are alternatives, and choices are made among them that are to some degree arbitrary or biased (for discussion of such features, see, e.g., Ullman-Margalit 1983; Rescorla 2015). This again suggests a means (that was indicated in Sect. 3) of distinguishing presumptions of ordinary arguments from their assumptions and presuppositions: the former are inherently conventional in ways that the latter are not. Now, let us more thoroughly see how this suggestion fares.

Certainly, the notion of a presumption is not itself a basic logical notion (although it may be a basic dialogical notion). It is not constitutive of the ‘laws of thought’, whereas such things as quantification rules and rules of inference clearly are. In this category of the fundamentals of logic also appear to fall the notions of presuppositions and assumptions of arguments insofar as presupposition and assumption are a kind of logical connective and inference license, respectively. As we have seen, the primary logical notion of a presupposition of an argument is that of a necessary condition for the truth of a propositional element e of the argument or for a term in e to have a referent. A logical assumption of an argument is essentially a proposition that must be true in order for the argument aside from that proposition to be fully cogent. Not to mention, assumptions of arguments simply are premises of arguments, one of the two essential constituents of arguments (the other being having a conclusion). Nothing that is both comparable and distinguishing can be said about presumptions of arguments.

I think the big picture of the class relations among this cast of characters and propositions as they may appear in ordinary arguments is as follows: Any proposition could be a presupposition or assumption of some argument or other, but only some propositions can be presumptions of arguments (because presumptions are inherently conventional). Nevertheless, all presumptions of arguments are either assumptions or presuppositionsFootnote 8 of those arguments, although not all assumptions and not all presuppositions are presumptions. While the same proposition can be both an assumption and a presumption of an argument, it cannot also be a presupposition of that argument.

Perhaps the most compelling candidate that has been offered as being a natural or nonconventional presumption is the idea that proof must stop somewhere, at least temporarily, relative to the purposes and circumstances at hand. These stopping points are propositions excepted from the burden of proof that allow proof to begin. As Wittgenstein says in On Certainty (343), “we just can’t investigate everything, and for that reason we are forced to rest content with assumption. If I want the door to turn, the hinges must stay put.” The idea appears to be practically a truism; of course we can’t be obligated to do what is impossible—endlessly provide further reasons for our reasons. It seems we must have what are commonly called “basic premises.” In any case, we can agree that the idea that proof must stop somewhere is a principle of something that is, so to speak, larger than any particular argument, viz, rationality itself. But is this principle somehow manifested as (premissory) presumptions of individual, ordinary arguments? Hansen (2003, pp. 7–8) seems to think so. Following Rescher, he says “in rational dialectics”—I do not see that this setting is necessary—“the natural rule of inference which yields presumptive propositions is one that presupposes the concept of a plausible proposition,” and quotes Rescher’s (1977, p. 38) statement of the rule:

Presumption favours the most plausible of rival alternatives—when indeed there is one. This alternative will always stand until set aside (by the entry of another, yet more plausible, presumption).

Hansen adds that “the alternative route to presumptions must be within a conventional framework” of “law, disputation, debate.”

Yet if a principle of rationality says in effect to always select premises that are the most plausible ones possible for assertion in your arguments, and if you succeed, is that enough to make all of your premises presumptions? Suppose everyone always succeeded in doing this. Then all assumptions would be presumptions. The danger here is making the (monological) notion of presumption vacuous and losing any distinction between assumption and presumption. The solution to this problem seems to be to hold that, yes, rationality favors the most plausible premises possible (and, as an example of a corollary, favors nonparadoxical views), so there is a kind of natural presumption in their favor, but that itself does not make those premises presumptions. It does not do this anymore than an argument’s simply conforming to the presupposition of rationality that ought implies can itself introduces content into the argument. Moreover, the principle of rationality about premise plausibility may not exactly be a version of the one that says that proof must stop somewhere, even though the most plausible “will always stand until set aside (by the entry of another, yet more plausible, presumption),” insofar as a premise’s being plausible indicates there are reasons for believing it.

The idea of a “basic premise” is equally vexed. Allen (1998, p. 1) says “Every argument has at least one premise it does not defend. Such a premise I call a basic premise”; similarly, following Freeman (2005, p. ix), Godden and Walton (2007, p. 329) employ the concept of “a basic premise (one not supported by other reasons).” Strictly speaking, it must be that every premise of every argument is a basic premise, since if it were defended, that defense would be yet another argument. The same argument cannot both have a proposition as a premise and (argumentatively) defend it. To be sure, in a less formal and harder to define sense of ‘argument’, an argument may have subsidiary conclusions that it defends and that also function as premises supporting its overall conclusion. But I think we do not have to stretch logic to see that the principle that proof must stop somewhere—at least temporarily, relative to the purposes and circumstances at hand—actually lies at the level of inquiry and evidence gathering, not at the level of individual arguments and their presumptions.

In contrast, consider some clear examples of presumptions that would be available for use in individual, ordinary arguments. The presumptions are introduced through conventional rules. It may be that such presumptions are so pervasive that they almost go unnoticed. In the first example (adapted from a comment by Douglas Walton), the rule is that if a skier is missing for two days in Banff National Park, the skier is presumably in serious trouble. Applying this rule to a particular skier missing for two days, generates the presumption that the skier is in serious trouble. Hansen says about a parallel case, “it appears that all cases of presumptive propositions may be established in a similar way” through “presumptive rules” (2003, p. 3). And one might argue, with the presumption here appearing as the premise, ‘the skier is in serious trouble, so a search-and-rescue should be mounted’. Or consider again Kauffeld’s example (from Sect. 3) where “I presume that A will be home by seven on the grounds that A promised me to be home by that time.” I can then argue, e.g., that since A will be home by seven, I should be able to go out by seven and leave the pets to A’s care. Another instance we can adapt from Kaufffeld (2013, p. 2) is where I am invited to a reception, and relying on rules of etiquette and décor, I presume “that I will be welcome.” I can then use that presumption as a reason that helps in determining my plans for the evening. An interesting variation is Bermejo-Luque’s (2013, p. 5; cf. 2016, p. 12) case where a presumption is deliberately introduced, with substantial prejudgment and bias, “as a means of promoting certain attitudes in others (as when we presume the honesty of our kids—even against some evidence…!).” Ullman-Margalit (p. 147) says presumptions are “concerned not so much with ascertaining the facts as with proceeding on them.” This is a notable feature that all of these cases exhibit, which I see as a mark of conventionality. This feature is also related to the fact that in all of the cases, the premissory presumption is clearly defeasible, a characteristic which is commonly taken to be a hallmark of presumptions (e.g., Godden and Walton 2007).

Bermejo-Luque’s example raises the matter of “so-called ‘conversational’ presumptions, like the presumption of truthfulness, or sincerity, or Grice’s Cooperative Principle” (Ullman-Margalit, p. 159). Some argue that at least some of these are “default option” presumptions because “all other things being equal, sincerity is cheaper than deception for the speaker, as much as trust is cheaper than scepticism for the hearer.” This parsimoniousness allegedly makes “sincerity and trust…intrinsically valuable,” and apparently, natural presumptions (Paglieri and Woods 2011a, pp. 478, 495). Of course, however, such presumptions are at their core pragmatic, which we saw explained in Sect. 2 as conditions that a speaker would generally take as obtaining in the common ground between discourse participants, not propositional elements or content of individual arguments. They are bases for arguing. Yet just as anything may be a topic of an argument, when there is an issue of truthfulness or sincerity, as in Bermejo-Luque’s example, such a condition may rise to the level of a premissory presumption, e.g., ‘my kids are honest, and they tell me that such and such happened to them, so it did’.

Let us return to the persistent idea that individual, ordinary arguments manifest the principle that proof must stop somewhere as (premissory) presumptions. Bermejo-Luque (2013, p. 1) says that in “monological argumentation, presumptions somehow dispense arguers from providing further reasons for some of their claims, and this seems to be necessary if their arguments are to stop at some point.” Yet exactly how might presumptions do this? I believe she is answering this question in proposing “the following definition: a presumption is the speech-act of putting forward a proposition as a reasonable assumption” (p. 4; cf. 2016, p. 9). In his reply to her 2013 paper, one thing Kauffeld argues is that presumptions in general are not speech acts (pp. 2–3), but the details need not concern us here since for our purposes it seems her definition can be read with “the speech-act of” excised. However, I see two potential difficulties that warrant some discussion. The first is again the danger of rendering the (monological) notion of presumption vacuous and collapsing the distinction between assumption and presumption. If I am a sincere arguer, what premises would I not ‘put forward as (at least?) reasonable assumptions’? Given a sincerity condition, all assumptions appear to be presumptions. Second, Bermejo-Luque claims that “in presuming that p, we are saying that it is reasonable to assume that p” (2013, p. 5); we “contend-that-it-is reasonable—in some particular sense—to assume that p” (2016, p. 10). This raises the specter of an infinite regress. If in presuming that p we are saying (p′) that it is reasonable to assume that p, then are we also saying (p′′) that it is reasonable to assume that p′ (i.e., that it is reasonable to assume that it is reasonable to assume that p) and that (p′′′) that it is reasonable to assume that p′′…? To say of an assumption that it is reasonable seems to be saying that it is acceptable. Bermejo-Luque holds that “in most contexts” reasonability is epistemic (2016, pp. 11–12). But premise acceptability is itself a general criterion of argument evaluation, as in Johnson and Blair’s (1977) widely utilized RSA criteria for argument cogency: the premises are to be relevant, sufficient, and acceptable. Thus, on Bermejo-Luque’s view, it looks like in virtue of making a presumption, at least in “most contexts” an argument affirms its own quality on the premise-acceptability parameter, in effect ‘patting itself on the back’. As Carroll (1895) shows, it risks infinite regress to treat arguments as making meta- or second-order claims about themselves.

6 Conclusion

Although in some contexts the notions of an ordinary argument’s presumption, assumption, and presupposition appear to merge into the one concept of an implicit premise, there are important differences between these three notions. I have argued that assumption and presupposition, but not presumption, belong to the fundamentals of logic as basic—and distinct—logical notions. Presumptions of arguments are inherently conventional in ways that their assumptions and presuppositions are not. So not all assumptions and not all presuppositions of arguments are presumptions of those arguments, although all presumptions of arguments are either assumptions or presuppositions of those arguments. This account avoids making the (monological) notion of presumption vacuous and dissolving the distinction between assumption and presumption.Footnote 9