On the rational resolution of (deep) disagreements

Disagreements come in all shapes and sizes, but epistemologists and argumentation theorists have singled out a special category referred to as deep disagreements. These deep disagreements are thought to pose philosophical and practical difficulties pertaining to their rational resolution. In this paper, I start with a critique of the widespread claim that deep disagreements are qualitatively different from normal disagreements because they arise from a difference in ‘fundamental principles’ or ‘hinge commitments.’ I then defend the following two claims: (1) All disagreements are deep to the extent that they are actual disagreements. This first claim implies, I will argue, that disagreements typically regarded as normal (‘shallow’) can be explained away as misunderstandings or communicative mishaps. (2) The resolution of a disagreement can be rational either through a joint experience of mutually recognized facts or through an exchange of arguments that leads to a reformulation of the disagreement that, in this new form, lends itself to a resolution through a joint experience of mutually recognized facts. I conclude with a reflection on the consequences of these two theses for the idea of deep disagreement and that of rational resolution.

Scholars have provided slightly different conceptualizations of this unbridgeable difference-(for overviews, see Lavorerio, 2021a;Ranalli, 2021). Fogelin (2005) explained the unbridgeable difference as triggered by the clash between "underlying principles" (p. 5) or "framework propositions" (p. 14). Pritchard (2009Pritchard ( , 2011 describes the difference as being triggered by a Wittgensteinian 'hinge commitment' that cannot be put up for discussion because it is the kind of epistemic entity that supports argumentative discussions in the first place (see Pritchard, 2021;Ranalli, 2020). Lynch and others describe the difference as being triggered by something called "fundamental epistemic principles" (Lynch, 2010(Lynch, , 2012Matheson, 2021;Smith & Lynch, 2021). These are principles that cannot be called into question during an exchange of arguments because they themselves constitute the basis on which we assess the acceptability of arguments and perhaps even the basis on which we recognize something as being an argument in the first place. Shields (2021) put forward an alternative pragmatic account in which the source of a deep disagreement is a clash of "concepts" that play a constitutive role for the parties involved.
Such differences in conceptualization notwithstanding, scholars have generally maintained the original line of thought proposed by Fogelin: deep disagreements enjoy a special status because they are generated by conflict between some special epistemic entities-be it fundamental principles, hinge commitments, concepts or some other such entity. The special status of deep disagreements gives rise to many interesting philosophical questions, but primarily it gives rise to one rather thorny problem. Given their relationship with the special epistemic entities mentioned above, deep disagreements seem to eschew the application of our standard tools for rational resolution. This is as much a philosophical problem as it is a practical one, as Zarefsky rightly observes: public discussions of health care, economic stimulus, and financial regulation seem with increasing frequency to devolve very quickly to bedrock assumptions about the rights of the individual and the role of the state, assumptions on which agreement seems impossible. So advocates on either side of these issues talk increasingly to the like-minded, and the belief that argumentation can be used productively to resolve differences is hollowed out and withers (Zarefsky, 2012: 181) If important social matters tend to give rise to deep disagreements, then if our methods for rational discussion and resolution fail precisely in the case of these disagreements, we might be forced to conclude that reason and argumentation play a disappointingly small role when we need it the most. There is therefore a practical urgency to understanding what deep disagreements are, how they occur and whether they can be rationally resolved.
In this paper I want to put forward an account that challenges the assumption that there are disagreements whose 'depth' prevents them from being rationally resolved. I will not deny of course that for some disagreements it remains highly unlikely that they will ever be resolved. But this practical improbability has nothing to do with the alleged special status (or 'depth') of these disagreements. My account is built around two theses: (1) All disagreements are deep disagreements to the extent that they are actual disagreements; and (2) The resolution of a disagreement can be rational either through a joint experience of facts or through an exchange of arguments that leads to a reformulation of the disagreement that can be resolved through a joint experience of facts.
I want to defend these two theses as follows. In Sect. 2, I take as a case in point the claim that the special status of deep disagreements is given by their being about propositions that are fundamental in some way. I show that the distinction between 'normal' principles and fundamental principles cannot be made (except arbitrarily) and that it is not warranted by the examples observed or constructed by scholars in the past. In Sect. 3, I build upon the demise of the distinction between standard principles and fundamental ones: if there are no fundamental principles out there that can throw our rational resolution methods into disarray, then there are no deep disagreements either-or better yet, all disagreements are deep to the extent that they are indeed disagreements. In Sect. 4, I then propose an account of how disagreements are rationally resolved regardless of their depth, and I specify the role played by argumentation in this resolution process. I illustrate this account with a modified imaginary case similar to the one employed by Lynch (2010) and Matheson (2021). In Sect. 5, I conclude by discussing the consequences of this account for scholarship on deep disagreements and the role we ascribe to argumentation in the resolution of disagreement.

The special status of deep disagreements
Although the metaphor of depth suggests incremental differences between disagreements, some being deeper than others, scholars typically ascribe to deep disagreements a qualitatively different status. In the case of a deep disagreement, the discussants work within different frameworks, or different perspectives, or perhaps different Kuhnian paradigms; they base their worldview on different fundamental principles, commitments, or concepts (for overviews, see Lavorerio, 2021aLavorerio, , 2021bRanalli, 2021). Let us look more closely into this claim. I will take as a case in point the view developed by Lynch and later by Matheson. According to this view, what we find at the 'rock-bottom' of a deep disagreement is a difference in fundamental epistemic principles (Lynch, 2010(Lynch, , 2012. You have a deep disagreement when you and your discussion partner do not agree on fundamental epistemic principles which express "how we ought to support our view of the facts, about the sort of evidence that should be admitted, and whose methods more accurately track the truth" (Lynch, 2010, p. 263). However, the problem with this definition is that it cannot be taken at face value since it is clearly too permissive. It allows to pass as a fundamental epistemic principle a host of propositions that should not strike us as deserving any special attention. It all depends on how broadly or narrowly we construe the scope of the terms 'we', 'ought to support', and 'should be admitted'. There is no reason why 'we' cannot stand for the small group of people that believe 'Neapolitans are the most reliable when it comes to the traditional thin-crust pizza dough'. It is then easy to imagine how such a statement would function as a principle in a discussion, regulating 'what sort of evidence should be admitted' and 'what method more accurately tracks the truth' etc. Yet I suspect that our Neapolitan-pizza principle is not the sort of principle Lynch means to single out.
Other definitions proposed along the same line seem to face a similar problem. Consider: a set of principles that you endorse that gives an account of what is evidence for what and assigns evidential weights. An epistemic principle claims that some epistemic property (justification, knowledge, warrant, etc.) obtains whenever some descriptive property obtains (Matheson, 2021) Here again, there is no reason to jump immediately to very general or very fundamental principles since lower-level ones seem to satisfy the definition just fine. The principle that only Neapolitans know their thin-crust pizza dough satisfies all those criteria: it tells you what counts as evidence (Neapolitan claims are evidence for Neapolitan pizza matters) and assigns evidential weight (Neapolitans know more than, say, Romans) and it claims that some epistemic property (warrant) obtains whenever the person who evaluated a Neapolitan pizza dough as good or bad is herself from Naples. I suspect that Lynch and Matheson want us to think of something more fundamental, but the definitions provided do not help us to reach the intended height. We must therefore make sense of this concept by looking at their examples.
An example employed by the two is the following: Cain and Abel, let's imagine, are having coffee and arguing about the age of the Earth. Abel asserts with great confidence that the earth is a mere 7,000 years old. Cain, amazed, points out that Abel's claim is not justified by the evidence of the fossil record, the best explanation of which is that the Earth is far older. 'Inference to the best explanation from the fossil and historical record can work sometimes' Abel concedes, 'but the best method for knowing about the distant past is to consult the Holy Book; it overrides any other competing evidence'. Cain scoffs and rejects the book as an unreliable source for knowing about the distant past; the only reliable method, he insists, is to employ a combination of abduction and induction from the fossil and historical record. (Lynch, 2010: 264) These principles clearly have a more fundamental ring to them (surely compared to our Neapolitan-pizza principle!). But upon closer examination neither the example nor the explanation given by Lynch point to propositions that are indeed all that fundamental. Consider the quoted passage. The disagreement between Cain and Abel was not in some general sense about the merits of deduction, induction, abduction, and the like. Cain and Abel did not run into any special epistemological deadlock. Rather, they disagreed on how to establish the age of the Earth. In fact, the discussion is not even about establishing the age of the Earth in general-they just disagree on the relative merits of the the Bible and fossil record. But notice now that the principle has all but lost its fundamental status. The proposition "In determining the age of the Earth with such-and-such degree of precision, method X is better than method Y" is suspiciously close to our example of the non-fundamental principle "In case you need to establish whether a pizza dough is a Neapolitan-style pizza dough, you must consult someone from Napoli". True, the methodologies advocated by Cain and Abel are different; we might even concede that they are in some sense 'very' different, 'incommensurably' different. And we might even assume it unlikely that Cain and Abel could ever reach an agreement on the matter. But the improbability of such a resolution is an empirical question and should not be confused with the conceptual problem of establishing whether their disagreement was a deep disagreement. But perhaps we are not to take the example all too seriously. "I will not quibble here about examples", adds Lynch in the same paper (Lynch, 2010, p. 263) and later discussing a similar example he advises us not to "get hung up on the toy example" (Lynch, 2012). But with the definition being too permissive and the examples being too specific, where else can we find an instantiation of a deep disagreement? Matheson provides some examples of such principles in the following passage:

Perception:
If it visually appears to you as if p, then you are prima facie justified in believing p. Testimony: If you are justified in believing that S is reliable and S asserts that p, then you are prima facie justified in believing that p. Seeming: If it seems to you that p, then you are prima facie justified in believing that p. Deduction: If you are justified in believing that p and that p entails q, then you are justified in believing that q. Magic-8: If the Magic-8 Ball says that p, then you are prima facie justified in believing that p. (Matheson, 2021) These are likely candidates. But what exactly makes these principles fundamental ones? True, they are more general than the age-of-Earth principle and Neapolitan-pizza principle. Yet a very general principle need not pose any problem simply by virtue of its generality. General principles can be discussed (defended, attacked, conceded, reconsidered, granted, rejected etc.) in much the same way more specific principles can. Why should we be afraid to treat these propositions like our garden-variety principles based on which we argue for the acceptability of claims in everyday life?
There is a recurring answer to this question, and it is the following: a fundamental principle, we are told, cannot be justified without appealing to itself (Lynch, 2010, p. 267;2012, p. 52;Matheson, 2021).
What makes a principle fundamental is that you can't justify it without employing the method that it endorses as reliable. For this reason, explicit defenses of such principles will always be subject to a charge of circularity (Lynch, 2012: 52) The principles that cause deep disagreements are thus fundamental because they cannot be justified without employing them in the justification process. Yet we have good reasons to doubt the very existence of such principles. Notice, to start with, Matheson's principles are not mutually exclusive. Why can I not, either in general sense or about a given case, deduce the reliability of induction or perceive the reliability of abduction or abduce the reliability of perception-or any other similar combination? Maybe not all combinations would work but certainly some can. Can I not trust an expert testimony in, say, epistemology on matters of induction? Clearly these are not rockbottom principles because they can be employed to support one another. 1 In some places, Lynch suggests that this epistemic circularity only occurs if the testing of the principle (the discussion) goes on for some time and the one upholding the principle is continuously pressed to justify their warrants. So, Cain and Abel might get away with offering one argument that is not circular (although notice this already refutes the idea that epistemic principles cannot be defended), but the point seems to be that we end up in circularity only if pressed long enough about the reason for accepting a principle. As Lynch exemplifies, Abel might: […] try to give some independent argument, in addition to the one I've given above, in defence of his principle, one that does not rely on what the book says. He might appeal to the teaching of various prophets, or other sacred texts. Cain will question the reliability of these sources. So, Abel might appeal to still more basic, non-inferential methods of belief formation, such as divine revelation or mystical perception of God's actions and will. But here again the question can (and presumably will) be raised about the reliability of such methods. As in Cain's case, it is difficult to see how Abel will be able to demonstrate their reliability without an epistemically circular argument, for it is difficult to see how one could defend one's claims to reliably speak for, or perceive, God without appealing either to the book, or to mystic perception again. (Lynch, 2010: 266) The claim that circularity occurs not immediately but only somewhere down the road is surely more plausible. But still, I do not think the example justifies the conclusion. Lynch glosses all too easily over the details of the discussion. Cain and Abel seem to disagree now on whether one can "speak for, or perceive, God" even though that was not their original dispute. Also, their endpoint is not quite identical to their starting point: strictly speaking neither generally appealing to "the book" nor appealing to "mystic perception" was Abel's initial point. Abel appealed to a specific part of the book which gave testimony for a specific question dealt with by specific means. Yet we might charitably ascribe these small equivocations to textual mishaps, but we cannot ignore the most important part: it is not at all obvious that Cain and Abel can end up where they started, let alone that they necessarily must. Consider how such a discussion would unfold: The initial principle under discussion in this scenario was, remember, that "the best method for knowing about the distant past is to consult the Holy Book". Let this be principle A. The discussion of A cannot itself be a discussion about the distant past, but it must be a discussion about the acceptability of A. In this new discussion, one will appeal to a different principle, say B, which is not about the distant past but about the choice between different methods for knowing the distant past. Moving further, the discussion of B will also not be about the same topic as B but rather some higher-order (or 'deeper', to go with the preferred metaphor) principle, say C, which pertains to the decision about how to choose between different methods for choosing between B and its alternatives. With enough resources, the discussion continues endlessly-I am assuming no one is disputing that-but it is difficult to see how the parties can ever arrive back at A as they continue in their discussion. Epistemic circularity might be possible in theory (see Münchausen's trilemma), and it might be possible under loose reconstructions of what is being appealed to, but circularity does not seem to be a feature of real-life disagreements since, as the discussion progresses, the principles that are being appealed to keep changing by increasing in generality.
The different strands of critique advanced in this section can be drawn together as follows. The ambition to single out deep disagreements creates the following predicament: if the principles are formulated to resemble principles that arguers would actually use in everyday life, then they are not fundamental enough to scare us out of our customary approaches to resolution; if, however, the principles are given a fundamental-sounding formulation, then their actual occurrence in real-life disagreements becomes doubtful and even if we grant the possibility of such an occurrence, circularity (often advanced as the wrench in the works) does not seem to occur anyway. Considering this predicament, some scholars have resorted to simply stipulating deep disagreement into existence and defining it rather as abstract entities, regardless of whether they would actually occur in real-life. 2 Such thought-experimental exercises constitute, of course, a valid way out of the predicament-they always do. But the lessons learned from examining such abstract entities will have little bearing on our understanding of how actual disagreements unfold and how they are resolved.

First thesis: all disagreements are deep
In this section I want to explain why the special status of deep disagreements could not have been established. The reason is the following: all disagreements exhibit the problems that scholars wished to ascribe to deep disagreements. I want to argue here for the first thesis announced in the introduction, i.e. (1) that all disagreements are either deep or else not disagreements at all.
Let us start from a basic conception of disagreement as two parties holding different commitments regarding the acceptability (or truth) of a statement ( van Eemeren & Snoeck Henkemans, 2016;Walton, 2015). The propositional content of this statement can be as simple or as complex as we wish and the force with which the propositional content is asserted can also vary along known lines from weak suggestion to strong conviction. Some scholars might wish to interject that what lies at the heart of deep disagreements (hinge commitments or otherwise) are not propositional entities (see Ranalli, 2021 for an overview of this issue). But we can allow for two individuals to be separated by their difference in non-propositional worldviews without concluding that this 'non-propositionality' must carry over to their disagreement. A die-hard communist and a die-hard liberal might have irreconcilably different worldviews, but to the extent that they disagree on something, they must express this disagreement as commitments pertaining to a statement with propositional content.
Instead of asking what would make this disagreement a deep one and trying to search for some Aristotelian archai in real-life situations, I propose to start from the other end. Let us ask what it would mean for two discussants, Cain and Abel, to resolve their disagreement rationally. Let us assume that Cain is stating q while Abel rejects q. What would it take for Cain to rationally convince Abel of the acceptability of q? Cain must argue. That is, Cain must advance at least one line of defense in favor of q. The proposition q must therefore be put in a relationship with a new set of propositions that, taken together, will count as a defense for q. Let us refer to this defense as the set of propositions D. Cain therefore advances the defense D in favor of q. Once more, the content of D, the propositions and principles included in D, are not relevant. (This is the advantage of starting from the other end). We can imagine Cain employing deduction, induction, abduction, and everything else on the market of logic and informal logic, and he can employ them at any level of generality, that is, he can appeal to 'deduction' as a general principle or to a much lower-level principle such as 'deduction about the age of the earth given fossil records.' The reader is free to add as members of D any epistemic entity she wishes. But as complex as the defense D might be, it still must connect to q (otherwise it is not a defense for q but just a random set of propositions and principles). Because of this, we can formalize the content of D as follows: D contains two propositions, namely 'p' and 'p therefore q', where p can encompass any number of other propositions, i.e., p ≡ (s 1 ∧ s 2 ∧ s 3 … s n ).
Let us imagine, to start with, that their disagreement is not deep at all. It is a 'normal', garden-variety disagreement about banal things such as where to go for dinner or who deserves a promotion. Under what conditions is Abel rationally convinced by D? Theories of argumentation differ quite significantly in this regard (Dutilh Novaes, 2021; van Eemeren et al., 2014). However, these approaches have in common the fact that convincing, whether rational or irrational, is an effect that is brought about by the propositions in D. The acceptability (or truth) of these propositions in D is transferred, it is said, to the acceptability of q. But now we run into an age-old problem: if Abel does indeed accept D, then he cannot possibly have rejected q because, by definition, the conclusion that q is the case ('… therefore q') is included in D. If, on the other hand, Abel rejects D, which pragmatically speaking might always happen, then they now have not one but two disagreements on their hands-the original one on q and the newly discovered one on D. Upon discovering that Abel does indeed accept D, Cain has all the right to be surprised by Abel's rejection of q, e.g., 1 Cain: Seth should be given a promotion (q) 2 Abel: Don't think so! (non-q) 3 Cain: If one fulfills all the criteria, they should get a promotion and Seth fulfills all the criteria Therefore Seth should be given a promotion! (D) Do you not agree with that? 4 Abel: I agree with all that! (D) 5 Cain (annoyed): So how can you still disagree with p?
For a logician, the fact that the conclusion is already present in the premises is good news because it means that acceptability (or truth) is preserved throughout the logical derivation. But for two discussants trying to resolve their disagreement, it spells trouble. Abel either does not agree with D, in which case there is no convincing, or he does agree with D in which case there was no disagreement to start with. Notice that it would be missing the point here to say that Abel could have some exceptional situation in mind which explains his disagreeing with q, i.e., that Seth might not be eligible for promotion due to some unexpressed reason that undercuts Cain's decision. For in that case, we would be forced to say that Abel does not actually agree with D. Pragmatically, we would then have to say that Abel misspoke at line 4 or that he was using the term 'therefore' as shorthand for 'therefore, unless such-and-such occurs'. In short, if Abel disagreed with p because of counterargument, then D could not have been part of his commitment.
Since Plato's Meno (82a-86d) there is of course a famous solution to all this. Abel was in some sense forgetful of his true commitments, just as the slave in the Platonic dialogue who is taught to double the area of the square is not ignorant but forgetful. Socrates taught the slave to double the area of the square by having him un-forget (anamnesia). This is of course compatible with the situation at hand. Consider the naturalness of Abel's response in line 6 below: 1 Cain: Seth should be given a promotion (p) 2 Abel: Don't think so! (non-p) 3 Cain: If one fulfills all the criteria, they should get a promotion and Seth fulfills all the criteria Therefore Seth should be given a promotion! (D) Do you not agree with that? 4 Abel: I agree with all that! (D) 5 Cain: So how can you still disagree with p? 6 Abel: You're right (q). I had forgotten that Seth fulfilled all the criteria (D) Has Abel been convinced? It is much more natural to describe what has happened as Abel learning or being reminded. After all the slave was also not convinced regarding the mathematical problem. Thus, when Cain and Abel discover their agreement on D, the more appropriate description of the situation would be to say that what seemed to be a disagreement in the beginning turned out to be a simple memory slip. Abel's reply in line 6 shows that he was not convinced, but merely reminded of his commitment to D, a commitment which reveals that the two agreed all along.
We can apply this line of reasoning to any principle that is brought up in an argumentative discussion. Thus, if Abel disagrees with the defense D advanced by Cain, then Cain can produce a new defense D 2 that supports D. But then regarding D 2 we will have to ask again whether Abel accepts it or not. If Abel does accept D 2 , he could not have disagreed with D in the first place, so we chalk the situation up to a case of misunderstanding, miscommunication, forgetfulness; if Abel does not agree with D 2 , the initial disagreement is increased rather than resolved for it now includes not only D but also D 2 . And it simply does not matter what principles, fundamental or not, are embodied in, or invoked by, the derivation from premises to conclusion in each of these defenses (D, D 2 , D 3 …). The problem will always appear in the same form: for Cain and Abel to indeed have a disagreement on their hand and not just a communicational mishap, then their disagreement must be deep in that new defenses only 'make matters worse', adding to their disagreement rather than resolving it. In short: a disagreement is either deep or it is not a disagreement at all.
Which of the scenarios is more likely to explain the complex debates mentioned in the literature on deep disagreements, debates on abortion, creationism, vaccination, liberalism, euthanasia, the existence of God and the like (Lavorerio, 2021a)? Clearly, the scenario where the disagreement persists, going from D to D 2 , from D 2 to D 3 , from D 3 to D 4 and so forth without any end in sight. But this simply means that the two are separated by many disagreements, not so much by a disagreement of a special type. I am not trying to minimize the seriousness of their dispute-resolving such a dispute is by no means easy and perhaps practically impossible. But we should not hasten to jump to the conclusion that their disagreement must therefore be qualitatively different from other disagreements. All disagreements, regardless of their content, whether they concern crucial social and political issues or just pizza crusts, are deep if they are indeed disagreements. But now the burden of proof is on me to show how resolution can indeed take place if all disagreements are deep. To this I turn in the next section.

Second thesis: disagreements can be rationally resolved through joint experiences
I argued in the previous section that depth is not a special feature of some disagreements but in fact a prerequisite for disagreement. If this is accepted, then the problem of resolution seems to have become even more urgent. For one of the reasons deep disagreements deserved our attention, as mentioned in the introduction, was that they challenged existing models and tools of rational resolution (Lavorerio, 2021b;Lynch, 2010;Matheson, 2021;Pritchard, 2011). But now if all disagreements are deep in the way proposed above, then it is even more urgent to explain how, if at all, disagreements can be resolved. If we were surprised before to find out that rational resolution might not work for some 'special' disagreements, we must be even more surprised now to find out that all disagreements exhibit this kind of depth. I must therefore turn to the question: Can disagreements be rationally resolved? If so, how? From the previous section we can start by excluding one traditional candidate: argumentation cannot do the requisite pragmatic work. This can be done based on what was explained in the previous section, i.e., if the propositional content of the advanced argumentation is already accepted, then what seemed to be a disagreement was only an apparent one (and the consensus is re-established through a process of reminding or some other form of realignment) and if the propositional content is not already accepted then the disagreement is real, but it is not resolved. It seems to follow that resolution, if possible, must come from non-verbal means. This might sound strange, but if we succeed in bracketing our epistemological expectations for a moment, we might discover that such a conclusion has its merits. After all, non-verbal experiences are often the source of some of our most spectacular changes of mind.
Let me modify the Lynch scenario to illustrate what I mean. Consider the following situation.
Cain and Abel are enjoying a drink together at a house-warming party and at one point they get into a heated discussion on whether the living room has a fireplace or not. They start an argumentative discussion. Cain advances numerous arguments that support his claim that the house does indeed have a fireplace, e.g., that he knows the interior of the house from the previous owner, the house was built in a certain style that always has a fireplace, he saw the fireplace etc. Abel advances an equal number of arguments based on other criteria: Abel has seen the house being built, he just checked the living room, has asked the current owner about it etc. Cain and Abel might delve so deep in their discussion that they might discover some great differences in their epistemic principles for testing the acceptability of such propositions. They both put forward acceptable, rational arguments according to the latest advances in epistemology yet there seems to be no end to their disagreement and no end to the resources they can bring to bear on each of their principles. Cain accepts his own arguments and rejects Abel's and vice versa.
But finding endless depth in an argumentative discussion need not invalidate the possibility of resolving the disagreement in a rational way through other means. It is in fact rather silly (if not directly irrational) to resort to verbal means in the described situation. Talking the talk is for people who cannot walk the walk. A rational thing to do here is simply walk to the living room and jointly check whether the living room has a fireplace. Cain and Abel can instantiate something we can see as the prototypical case of rational persuasion, namely a shared experience of facts.
One might object that in this case Cain and Abel are just agreeing on a 'fundamental epistemic principle' not unlike Matheson's Seeming principle cited in the previous section. They both accept some version of the following principle: 'If we have the joint visual experience of a fireplace, then the house has a fireplace.' This could be accepted but notice that they do not need to accept the same version of that principle because neither party is arguing based on that principle-so the troubles from the previous section are in this way avoided. Cain and Abel have found a joint commitment which allows them to give up all that arguing which was leading nowhere and in fact do something about their disagreement, namely, subject their views to a test. Of course, argumentation is still very important for it is through argumentation that they have arrived here. Through their argumentative interaction, Cain and Abel have discovered that, while they do not share any epistemic principle that could be the basis of any one of them being convinced through reason-giving, they are both part of the same epistemic culture (Knorr-Cetina, 1999), which allows them to visually distinguish a fireplace from a window or an accidental hole in the wall. In fact, unbeknownst to them, they might even accept the experience of 'seeing a fireplace' for different reasons such that they do not even agree on what exactly makes a certain hole in the wall a fireplace. The statement is thus neither an epistemic principle in the original sense (it does not serve their argumentation) nor is it necessary for their joint experience (for no one variant of it is necessary for accepting the test). Of course, I am not claiming that the shared visual experience must resolve their disagreement. Having arrived at the other room, the two might disagree that what they are looking at is indeed a fireplace. And I am not claiming that there is always a rational way out through joint experiences of this kind, or, conversely, that joint experiences are always a rational way to approach a disagreement (the discussants might both fall victim to some optical illusion). But if there are recognizable facts of the matter and if the discussants can jointly check them, it is sometimes rational to do so, and verbal interaction will play no role in this joint experience which resolves the disagreement. Is the resolution in the above imaginary case rational? Well, it depends on what it is that they are assessing and how they are assessing it. If Cain and Abel are foolishly investigating the living room of another house or if they are doing so during nighttime without a proper light source-then we might not regard their resolution as a rational one. It all depends on the chosen conduct given the situation, not their reasoning or their logical derivations.
Let me try to place this point of view in the already-existing debate on deep disagreements and their rational resolution. It is customary to make a distinction between 'pessimists' and 'optimists' when it comes to deep disagreements (Aikin, 2019(Aikin, , 2020Godden, 2019;Godden & Brenner, 2010). 'Pessimists' claim that arguments do not have the power to resolve our deep disagreements while 'optimists' claim, by and large, that arguments can be effective. Optimists come in different flavors, depending on the effect that one is ready to ascribe to arguments and the assumed explanation for that effect (Aikin, 2019, p. 2). The present account is clearly an optimist one-I claim that the rational resolution of deep disagreements is possible. But it fits into none of the distinguished flavors. Mine is not an instance of the so-called supplemental optimism because it is not shared reasons that do the trick-if by 'shared reason' one simply means shared propositional content that can be given as a reason. Mine is also not an instance of the so-called arbitrational optimism because it is not an "impartial third party" that can bring about the resolution. When Cain and Abel check the living room for a fireplace, it is difficult to see who exactly the third party to that discussion is. To complicate matters, I do not believe that all disagreements are amenable to such joint experience of facts. It seems to me that there must be 'facts of the matter' to a certain dispute, otherwise there might be nothing Cain and Abel could jointly experience. I suspect that at least some disagreements typically branded as 'deep' (e.g., long-lasting disagreements on political, religious, and moral matters) are disagreements without such facts of the matter that one can check through joint experiences. Such fact-free disagreements might indeed be irresolvable. So if I am an optimist I must be a mild one since I find it perfectly natural to suppose that some disagreements are fact-free in this way (cf. Pritchard, 2021Pritchard, , p. 1124. So, there is good news and bad news. The bad news is that rational discourse does little more than uncover a disagreement or uncover the fact that there is no disagreement. The good news is that rational discourse is not always needed since rational conduct is, in some situations, more than enough.

Conclusion: the function of argumentation in disagreement
I have started by calling into question the assumption that deep disagreements should be afforded a special status because of their connection to some extraordinary propositions. This led to the conclusion that disagreements are deep by definition, that is, the disagreeing parties have yet to discover any rock-bottom on which to build discursively towards a resolution. But this does not mean that they are condemned to act irrationally. Disagreements, deep as they may be, can sometimes be solved through shared experiences of facts. The rationality in such a case is heavily dependent on what is conventionally acceptable as experiencing facts given a certain context or epistemic culture. Are there irresolvable disagreements out there? Surely. For some disagreements, there are no fact that the parties could jointly experience. Other disagreements are simply too complex, and the parties have little reason (and patience) to undergo a thorough analysis. I want to conclude by noting that the function of argumentation (or reason-giving) is changed in this account. Argumentation does play an essential role in the resolution of disagreements, and it is exactly the role we have seen it play in both the imaginary examples of Lynch and Matheson and in the modified examples provided in this paper. Argumentation is the speech act by means of which we scope the depth of our disagreements. Argumentation is an explorative act. As we go deeper, we might discover: (i) that what seemed to be a disagreement is not a disagreement after all (there is some forgotten common ground); (ii) that the disagreement is real, and it can be resolved through joint experiences; and (iii) that the disagreement is real, but it cannot be resolved through joint experiences. Argumentation in the present account is still important but it is only indirectly related to resolution through its function of revealing what, if anything, the discussants share in terms of starting points. We must agree therefore with Newman's conclusion that "when men understand what each other mean, they see, for the most part, that controversy is either superfluous or hopeless" (Newman, 1844, p. 193). But we must add this: that men come to understand what each other mean in part by exchanging arguments.
I suspect one might feel that argumentation is thereby demoted. Yet both functions of argumentation-that of resolving and that of mutual understanding-have their origin in the Socratic-Platonic models of disagreement. The traditional account of argumentation fits the image of Socrates as the critical faultfinder, Socrates who took up the Oracle's pronouncement seriously and set about to test either his views or those of others. This is the Socrates who battles the sophists and their pupils in dialogues such as Protagoras, Gorgias, and Hippias Minor. This critical tradition has subsequently morphed into the rule-based, Aristotelian, and later Cartesian form of rationalism that we nowadays associate most naturally with rational conduct in argumentative interaction (Hamblin, 1970;Popa, 2021;Tindale, 2007). But there is a different Socrates appearing in the Platonic dialogues. This is the Socrates who claims to know nothing and proceeds, at least discursively, with the aim of understanding what the other party is saying. This is the ever-confused Socrates who seeks to understand what the others are saying and what their positions entail. Glimpses of this second Socratic attitude can be seen in dialogues such as the Apology, Phaedo and in some early passages from the Republic. Consider: Thrasymachus: I say that justice is nothing other than the advantage of the stronger. Well, why don't you praise me? But then you'd do anything to avoid having to do that. Socrates: I must first understand you, for I don't yet know what you mean. The advantage of the stronger, you say, is just. What do you mean, Thrasymachus? (Plato,Republic,338c) Critias: But this is the same thing as the other, Socrates. Socrates: Perhaps, but I'm in danger of being as confused as ever, because I still don't understand how knowing what one knows and does not know is the same thing as knowledge of self. (Plato,Charmides,170a) This side of Socrates inspired the skeptical turn in Plato's academy that later gave rise to Pyrrhonian skepticism focused on achieving precisely the suspension of judgment (epoche) that Socrates briefly exhibits in some dialogues. This strand of thinking eventually came to dominate the academy to such an extent that, by Augustine's time, being an 'academician' simply meant being a skeptic (see Contra Academicos). The view advocated here is evidently more compatible with the 'explorative' Socrates, the one concerned with the avoidance of misunderstanding rather than the avoidance of sophistry. Argumentation helps us understand our disagreements by uncovering their origin or by helping us discover that what appeared to be a disagreement is not one after all. It is of little use in the case our disagreement turns out to be deep, given that argumentation requires shared propositional content which, by definition, a deep disagreement does not furnish. But no matter-rational conduct might still be possible in that case and it is perhaps our moral duty to seek these forms of rational conduct.
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