The discussion about deep disagreement has gained significant momentum in the last several years. This discussion often relies on the intuition that deep disagreement is, in some sense, rationally irresolvable. In this paper, I will provide a theory of rationally irresolvable disagreement. Such a theory is interesting in its own right, since it conflicts with the view that rational attitudes and procedures are paradigmatic tools for resolving disagreement. Moreover, I will suggest replacing discussions about deep disagreement with an analysis of rationally irresolvable disagreement, since this notion can be more clearly defined than deep disagreement and captures the basic intuitions underlying deep disagreement. I will first motivate this project by critically assessing the current debate about deep disagreement. I then detail the notions of rationality and resolvable disagreement which are crucial for a suitable theory of rationally irresolvable disagreement before sketching various instances of rationally irresolvable disagreement. Finally, I argue for replacing theories of deep disagreement with theories of rationally irresolvable disagreement, an approach that has significant advantages over existing theories of deep disagreement which focus on hinge propositions or fundamental epistemic principles. Debates over deep disagreement (DD) have always centered on its relationship to rationally irresolvable disagreement (RID). Fogelin  summarizdeep disagreement. Fogelin refers to a specific Wittgensteinian concept of preconditions of argumentative exchange, when he notes “that deep disagreements cannot be resolved through the use of argument, for they undercut the conditions essential to arguing.” . He continues to characterize DD as follows:What is a deep disagreement? First let me say what I don’t mean by this notion. A disagreement can be intense without being deep. A disagreement can also be unresolvable without being deep. I can argue myself blue in the face trying to convince you of something without succeeding. The explanation might be that one of us is dense or pig-headed. And this is a matter that could be established beyond doubt to, say, an impartial spectator. But we get a very different sort of disagreement when it proceeds from a clash in underlying principles. Under these circumstances, the parties may be unbiased, free of prejudice, consistent, coherent, precise and rigorous, yet still disagree. And disagree profoundly, not just marginally. Now when I speak about underlying principles, I am thinking about what others (Putnam) have called framework propositions or what Wittgenstein was inclined to call rules. We get a deep disagreement when the argument is generated by a clash of framework propositions. Fogelin, , 8Let me recall DD, as introduced by Fogelin .1 FogeliQ1: What is deep disagreement?Q2: Is deep disagreement resolvable or not?Fogelin’s description of DD fits into his Wittgensteinian picture on the preconditions of meaningful and successful argumentation. However, his overall picture on DD remains rather sketchy, and, consequently, a vivid discussion on DD emerged, which centers mainly on the following two questions:The first question concerns the metaphysics of DD. Fogelin answers it by noting that “when we inquire into the source of a DD, we do not simply find isolated propositions […], but instead a whole system of mutually supporting propositions  that constitute, if I may use the phrase, a form of life.” Fogelin, , 9 On FoConcerning both questions, in particular concerning Q1, different views have been defended: The two main alternatives are Wittgensteinian theories or hinge theories about the nature of DD and fundamental epistemic principle theories.Lynch , 2016 an5There is more agreement about Q2 than about Q1. Most philosophers working on DD share Fogelin’s  pessimis6Let me start with a methodological point concerning DD. DD is not a commonsense notion of natural language, such as “knowledge” or “belief”. In cases of knowledge or belief, we can develop a theory and test it against our intuitions by considering controversial cases, as Gettier paradigmatically did with the JTB theory of knowledge. However, DD is also not a purely technical term that can be arbitrarily defined. Rather, DD can best be described as a semi-technical term. For analyzing such semi-technical terms, we often proceed as follows. A phenomenon is introduced, often by presenting paradigmatic cases, and through these examples we then form an intuitive grasp of the target phenomenon. After that, we can then analyze that notion within a systematic theoretical framework. However, different philosophers might have different intuitions about the target phenomenon. Moreover, they might think that different explanatory desiderata should be prioritized in theorizing about it. Accordingly, we might not always be able to judge which theory about the target phenomenon is true or false, but only whether those theories meet the specific explanatory desiderata.7is the target phenomenon, and, based on this intuition, develop their hinge accounts of DD. The same might hold mutatis mutandis for adherents of fundamental-epistemic-principles views. However, both parties might be right in that there is disagreement based on hinge-propositions respectively on fundamental epistemic principles. Thus, none of these theories might be simply false, and they might also succeed given the specific explanatory desiderata.All of these points apply to the discussion about DD. Adherents of hinge theories might think that disagreement about hinge propositions Creationist accepts a geological method Suppose that C is a restricted creationist concerning the age of the Earth in the sense that there is one geological method which C accepts that can potentially override the biblical sources. Applying this method delivers that the Earth is several billion years old and the disagreement between C and S is resolved.Scientist accepts a theological source Suppose that there is one passage in the bible such that S accepts that it can override scientific evidence. C and S consult this passage that delivers that the Earth is 6000 years old. The disagreement is resolved.Creationist and scientist accept a ‘neutral’ source Both parties agree to trust a third person concerning information about the age of the Earth, someone who is a religious leader and a trained geologist. Both parties believe what the third person reports and the disagreement is resolved.In this paper, I will begin by developing a theory of RID, then using this theory to analyze and reframe the existing debate about DD. There are good prima facie reasons to assume a close connection between DD and RID. Intuitions about DD often center on a form of disagreement that is not resolvable in a rational way, making paradigmatic cases of DD paradigmatic instances of RID. The intuitive connection between DD and RID can be illustrated by considering a paradigmatic case of DD that is rationally irresolvable and small variations of the case, which make the disagreement rationally resolvable. By comparing the cases, the reader is expected to feel a pull towards judging that the resolvable cases are not instances of DD. Disagreement about the age of the Earth between a creationist C and a scientist S is often regarded as a paradigmatic instance of DD. Suppose that C believes that the Earth is 6000 years old because of her bible-based religious belief system whereas S believes that the Earth is several billion years old based on scientific evidence. This kind of disagreement, presented as a paradigmatic case of DD, is usually assumed to be irresolvable, because C and S trust different sources that deliver different verdicts about the age of the Earth.Here, we have three modifications of the initial case of DD which differ concerning their resolvability. Do we still think that the parties initially deeply disagreed about the age of the Earth in these three modified cases? Intuitively, I think, they did not deeply disagree in any of these three cases because the disagreement could easily be resolved. Accordingly, we tend to judge that disagreement is not deep if we figure out that it is resolvable or that it has been resolved.There is a strong tendency to judge that DD cannot be resolved in a rational way, which has to be further specified.rationally resolved disagreement. In Sect. able and irresolvable disagreement. In Sect. rationally resolvable and irresolvable disagreement. Section Overview: In Sect. p iff A and B have different doxastic attitudes towards p.p, believing that p, rejecting that p  and suspending judgment about p.p iff (1) A believes that p and B rejects that p or suspends judgment about p or (2) A suspends judgment about p and B accepts or rejects that p. If one opts for a more fine-grained picture of credences, then A and B disagree about p if they have different credences concerning p.Let me start by clarifying the notions of disagreement and resolving disagreement. Two parties, A and B, which can be persons, groups, or institutions, disagree about Resolving disagreement is a process where A and B initially disagree about p and, because of argumentative interactions, end up having the same doxastic attitude towards p.I understand argumentative interactions in a very broad sense, involving, for example, verbal argumentation, non-verbal demonstration, scientific proof, or consulting sources such as witnesses, encyclopedias, or the internet. Disagreement can disappear in various ways, but not all cases of disappearing disagreement might involve potentially rational persuasion. In this paper, I will develop an account of RID. Thus, I will focus on those processes of resolving disagreement that can be regarded as potentially rational.13On our way to a theory of RID, let me provide a more detailed picture about the concept of rationality underlying rational resolvability and irresolvability. Rationality is a rather heterogenous concept, and the views defended about rationality are astonishingly diverse.Objective rationalityS is objectively rational concerning p and evidence E iff:p on the basis of E iff E supports p (sufficiently) stronger than ¬p andS believes that p on the basis of E iff E supports ¬p (sufficiently) stronger than p andS rejects that  p on the basis of E iff E equally supports p and ¬p. 16S suspends judgment aboutSubjective rationalityp and evidence E iff:S is subjectively rational concerning p on the basis of E iff S believes that E supports p (sufficiently) stronger than ¬p andS believes that p on the basis of E iff S believes that E supports ¬p (sufficiently) stronger than p andS rejects that p on the basis of E iff S believes that E equally supports p and ¬p.S suspends judgment about p because of E would also suffice. Moreover, S might not even hold an explicit belief about p and E and might form beliefs on the basis of E habitually rather than reflectively.The notion of subjective rationality is not meant to require that the subject possesses a complex concept of rationality. Believing that it is good or right to believe that What does it mean to say that two parties resolve disagreement in a rational way? The following definition captures a natural understanding of rationally resolving disagreement:Rationally resolving disagreement (objective)p iff they resolve the disagreement by using a method (or set of methods) M that is proper for inquiring into whether p is true, and A and B form the same, objectively rational doxastic attitude on the basis of M.A and B rationally resolve disagreement about objective rationality. A disagreement is rationally resolved in an objective sense when both parties rationally rely on appropriate methods for resolving their disagreement. Disagreement between A and B is irrationally resolved in an objective sense of rationality (a) if it is resolved but A and B did not use a proper method, (b) if A or B do not believe what the proper method indicates, or (c) if A and/or B believe what the proper method indicates but not because of this indication.Note that the concept of rationality involved here is a concept of p, presenting an objection against p, defending p by refuting an objection, or any combination of these elements. Other appropriate methods for resolving disagreement include performing scientific experiments, or observation and demonstration. Furthermore, we can classify methods for rationally resolving disagreement by the sources consulted: these are for example our senses, other reliable persons, technical measurement devices, reasoning, or a combination of these sources. This list is not meant to be complete, but it should suffice to provide a picture of which methods can lead to an objectively rational resolution to a disagreement.Objectively proper methods can include arguing for We have distinguished a concept of objective rationality from a concept of subjective rationality. Rationally resolving disagreement in a subjective sense of rationality can be defined as follows:Rationally resolving disagreement (subjective)p iff they resolve disagreement by using a method or set of methods M of which A and B believe that it is proper for inquiring into whether p is true and A and B form the same doxastic attitude on the basis of M A and B rationally resolve disagreement about p by using a crystal ball if they both believe that this is a proper method. Disagreement is irrationally resolved in a subjective sense (a) if it is resolved by using a method which A or B believes that it is not appropriate for determining whether p is true, (b) A or B form a belief that they believe to be irrational on the basis of M’s indication, or (c) A or B does not believe that p because of the method that is believed to be proper.According to this subjective concept, A and B can rationally resolve disagreement via any method, as long as they both believe that it is appropriate. For example, they can both rationally resolve disagreement about This subjective formulation of rationally resolving disagreement is presumably rather wide according to our understanding of resolving disagreement in a rational way. A more natural understanding relies on objective rationality. However, the concept of rationally resolving disagreement in a subjective sense of rationality will become central later on when we investigate the modal aspect of RID, which can only be plausibly interpreted in a subjective sense.p is resolvable iff A and B disagree about p and there is a nearby possible world where A and B do not disagree about p. However, this definition is intuitively flawed. Suppose that A and B disagree about p and there is nothing that anybody can do to resolve this disagreement. Suppose further there is a nearby possible world where A originally formed a different doxastic attitude towards p such that A and B agree about p. In this case, we would still say that the disagreement is irresolvable although there is a nearby possible world where A and B agree. The problem of this possible-worlds approach is that it does not capture the procedural, diachronic aspect of resolving disagreement.Now that we have two varieties of rationality on the table, I will analyze the notions of resolvable and irresolvable disagreement. Resolvability and irresolvability are modal notions. One way to define resolvable disagreement is in terms of possible worlds: One could say that disagreement between A and B about p is resolvable iff A and B disagree about p and there is a nearby possible future world where A and B agree about p. However, this definition is also arguably too wide.p at t1 but there is a nearby possible world where A is struck by lightning at t2 and from this moment on agrees with B about p. In this case, we would still hesitate to call the disagreement resolvable as no one, neither A nor B nor someone else, has done something to resolve the disagreement. Resolving disagreement means that A and B disagree at t1 about p but, because of argumentative interactions, agree at a later time t2 about p. Hence, for disagreement to be resolvable requires that one party is (or both parties jointly are) capable of doing something to resolve it.Accordingly, one might propose the following definition of resolvable disagreement in terms of possible worlds: Disagreement between A and B about Taking these issues into account, resolvable disagreement can be properly specified as follows:Resolvable disagreementp iff A and B disagree about p and there is a method M available to A and B such that consulting M leads to agreement between A and B about p.There is resolvable disagreement between A and B about irresolvable disagreement. A and B irresolvably disagree about p iff A and B disagree and this disagreement is not resolvable. This is a very general characterization of irresolvable disagreement, which also contains an element of vagueness concerning the required availability of methods. Accordingly, we can distinguish different forms of resolvability and irresolvability.With this understanding of resolvable disagreement, we can now give an account of Practical irresolvabilityp and for purely practical reasons there is no method available which can be consulted to resolve the disagreement. Example: A and B disagree about p and there is a third person that they both recognize as an authority on p, but A and B ran out of gas and cannot visit the third party to ask whether p is true.A and B disagree about Temporal irresolvabilityp and there is no method currently available which can be consulted to resolve the disagreement. Example: There is a scientific experimentum crucis that cannot be performed yet but that would resolve the dispute about p.A and B disagree about Fundamental irresolvabilityp and there is no potential method available at all (neither now nor at any other time) that can be consulted to resolve the disagreement.A and B disagree about the correct definition of irresolvable disagreement. However, it seems intuitively incorrect to say that disagreement is irresolvable just because A and B ran out of gas. Moreover, fundamental irresolvability seems to be a too restrictive form of irresolvable disagreement. Thus, the version of resolvability relevant here lies plausibly somewhere in between. I will provide further specifications whenever it is necessary.Fundamental irresolvability is irresolvable disagreement in its strongest form. For the purposes of the paper, it is not necessary to select So far, I have clarified the notions of rationally resolving disagreement and of resolvable disagreement. In this section, I will put these pieces together to provide an account of RID. I defined two notions of rational disagreement resolution, one that is based on an objective concept of rationality and one that relies on subjective rationality. Accordingly, we can distinguish an objective and a subjective concept of rationally resolvable and irresolvable disagreement.Rationally resolvable disagreement (objective)p in an objective sense if (1) there is a method (or a set of methods) M available to A and B that is proper for inquiring into whether p is true and, (2) if M were used to determine whether p is true, then A and B would form the same rational doxastic attitude concerning p on the basis of M.There is rationally resolvable disagreement between A and B about Rationally resolvable disagreement (subjective)p in a subjective sense, if (1) there is a method (or a set of methods) M available to A and B of which A and B both believe that it is proper for inquiring into whether p is true and, (2) if M were used to determine whether p is true, then A and B would form the same doxastic attitude concerning p of which A and B believe that it is rational on the basis of M.There is rationally resolvable disagreement between A and B about subjects to formulate versions of rationally resolvable disagreement. Disagreement about p is rationally resolvable in an objective sense if there is an objectively proper method M available for determining whether p is true and A and B are objectively rational concerning M and p, i.e., if M supports that p, then A and B believe that p because of M, if M supports ¬p, then A and B reject that p, and if M equally supports p and ¬p, then A and B suspend judgment about p. Rationally resolvable disagreement in an subjective sense can be defined analogously on the basis of subjective rationality and methods that are believed to be rational.One can also use the notions of objectively and subjectively rational irresolvable disagreement, RID, in an objective and a subjective sense. In the following, I will identify four possible interpretations of RID, two objective and two subjective. As I will argue, the only plausible understanding of RID is the first of the subjective interpretations. The two potential interpretations of RID in an objective sense are:p is true. In this case, there might be a method such that A and B resolve disagreement, but it is not objectively proper.There is no objectively proper method available to A and B for determining whether p is true but A and B do not agree on the basis of M. For example, even if A and B knew that M indicates that p, they nevertheless would not agree about p on the basis of M’s indication. In this case, A or B or both are not objectively rational concerning the proper method.There is an objectively proper method M available to A and B for determining whether Let us next come to the crucial notion of rationally (3)p is true.There is no method available for A and B such that A and B both believe that it is a proper method for inquiring into whether (4)There is a method available of which A and B believe that it is proper but A or B nevertheless do not form the belief that they believe to be rational on the basis of M’s indication.According to this classification, there are two candidate situations for determining objective RID, the lack of an existing proper method or improper doxastic attitudes towards an objectively proper method. Let’s now turn to RID in a subjective sense of rationality. Again, we can distinguish two interpretations:p but have different beliefs about whether M is proper, or (2.2) that they agree that M is proper but A proceeds to base her belief on M whereas B does not. In this case, B is subjectively irrational concerning M. Notably, (2.1) is an instance of (3) and (2.2) is an instance of (4).There is a connection between the potential reasons (1)-(4). In case (2), there is a proper method M available, but A and B cannot reach agreement via M. The reason can be (2.1) that A and B are subjectively rational concerning M and p is true. Suppose that A and B are perfectly rational. In particular, A and B are objectively rational and do not hold back any evidence. In this case, it is hard to see why lacking a proper method for determining whether p is true should lead to irresolvable disagreement because A and B would both just suspend judgment about p and agreement is reached.p if they reach agreement as to whether p is true or false. This is also a form of resolving disagreement. However, disagreement can also be resolved without settling a question, namely if A and B suspend judgment about whether p is true in the absence of clear evidence in favor of or against it.19I have identified four different candidates for understanding RID. What is the relevant form? Let us have a closer look at (1), where there is no proper method for determining whether p is true (3 and 2.1). Second, A and B have the same beliefs but at least one does not follow them (4 and 2.2). In this case, A or B (or both) fails to be subjectively rational. Not following one’s beliefs about rationality is an epistemic vice on the subjective level. It can be regarded as a form of stubbornness or, as Fogelin calls it, pig-headedness, which is not an instance of DD. These are also not interesting instances of irresolvable disagreement and in particular not of RID. Thus, (4) is not an appropriate analysis of RID. (1) is also inappropriate. (2), however, is either an instance of (3) or of the inappropriate interpretation (4). Consequently, case (3), i.e., RID involving subjectively rational parties, is the interesting form of RID, which I will investigate hereinafter.Concerning (2)-(4), we can basically distinguish two cases: First, A and B are subjectively rational but have different beliefs about proper methods for determining whether Let me next provide a more detailed picture about the kind of subjective rationality relevant for RID. Subjective rationality can be more or less explicit and reflective. On a basic level, subjects follow certain rules or principles of rationality without being able to explicitly articulate them. Take, for example, young children who know how to discuss or argue but are not able to express the underlying principles that they follow. On a more reflective level, subjectively rational subjects can explain their principles of rationality and defend them against objections. For the purposes of this paper, subjects who are subjectively rational on a more reflective level are more interesting, but the points made also apply to less reflective subjects who simply follow implicit rationality principles.p or because the party presents misleading evidence. If someone acts this way against her own beliefs about rationality then the party suffers from an epistemic vice that can be characterized as dishonesty. Accordingly, we can define subjective honesty as follows.Let me continue spelling out subjective rationality. In some cases, agreement cannot be achieved because one party holds back evidence that she could present in favor of or against Subjective honestyp and E iff: S presents E in order to settle the question whether p is true iff S believes that E is accurate and believes that E is relevant for p, i.e., if S believes that E either supports p or ¬p.20S is subjectively honest concerning subjectively virtuous in the following sense are interesting cases of RID about p:Moreover, we are interested only in subjects who do not aim to deceive the other in some other sense. Thus, only cases where A and B are Subjective virtuosityp and any evidence E,(1)  A and B are subjectively rational concerning (2)  A and B are subjectively honest, and(3)  A and B do not aim at deceiving or misleading each other in any other way.21resolved disagreement, we tend to be interested in cases relying on objective rationality. However, RID is the most interesting when it comes to a subjective sense of rationality.22  Note that there is a tension in the results acquired about interesting cases of rationally resolved and rationally resolvable disagreement. When we talk about rationally p. A and B cannot rationally resolve the disagreement at the moment, but if A entered B’s culture, then A would eventually come to adopt B’s beliefs and standards of rationality via education and thereby the disagreement would be resolved. In some sense, the disagreement is resolvable, nevertheless this is intuitively a case of RID. Hence, when we talk about RID, we tend to keep fixed the beliefs that A and B hold about rationality, i.e., given the beliefs that A and B hold, the disagreement is irresolvable.23Let me make a final adjustment. The more interesting cases of RID are those where we keep fixed the doxastic attitudes of A and B about rationality. Take the following case. A and B are members of different cultures and disagree about In this section, I will further develop the theory of RID. Above, I have characterized RID in terms of methods, which are not available to subjectively rational persons for resolving disagreement. Particularly interesting instances of RID are cases where A and B disagree about specific epistemic features in a systematic way. In this section, I will reflect on further forms of RID, relying on disagreements about evidence broadly conceived, on reliability of sources, and on rational argumentation. Finally, I will reflect on disagreement about supporting evidence and meta-evidence.Let me first characterize RID in general terms of evidence. In this paper, I will use a broad notion of evidence that includes consulted sources, argumentation, experiments, and so on.RID about evidencep iff A and B disagree about p, and there is no evidence E available to A and B such that A and B are subjectively virtuous concerning p and E and E leads to agreement between A and B about p.A and B rationally irresolvably disagree about p, then in the absence of any defeaters S believes that p because of E iff S believes that E is accurate and that E supports p.If S is subjectively rational concerning E and RID about the accuracy of evidencep and are subjectively rational concerning p and there is no evidence available to A and B such that A and B agree about its accuracy, then there is RID between A and B about p.If A and B disagree about RID about the support of evidencep and are subjectively rational concerning p and there is no evidence available to A and B such that A and B agree about whether it supports p, then there is RID between A and B about p.If A and B disagree about p. These claims hold regardless of whether one of the parties is also objectively rational concerning E and p.In the first case, there is systematic disagreement between A and B about the accuracy of evidence, in the second case about whether the evidences support p because of a source O and believes that O is unreliable.p for other reasons). This is a violation of rationality on a subjective level. S fails according to her own standards of forming beliefs on the basis of reliable sources and not on the basis of unreliable sources. Accordingly, we can define subjective rationality concerning sources as follows:So far, we have captured the idea of subjective rationality in very general terms of beliefs about evidence. Let me differentiate further the conception of subjective rationality, starting with beliefs about sources. Sources include perception, technical devises, testimony and so on. Let me first address subjective rational behavior concerning sources. There is something irrational about S if S believes Subjective rationality concerning sourcesp on the basis of O iff S believes that O is a reliable source in the domain of p and believes that O indicates that p.S is subjectively rational concerning source O iff: In the absence of defeaters, S believes that p on the basis of O although S does not believe that O is reliable or that O indicates that p or (2) if S does not believe that p on the basis of O although S believes that O is reliable and believes that O indicates that p. Based on this concept of subjective rationality concerning sources, we can identify two forms of RID, based on disagreement about the reliability of sources and on what sources indicate.Accordingly, S fails to be subjectively rational concerning O (1) if S believes that RID about the reliability of sourcesp, (2) are subjectively rational concerning p, and (3) there is no source available to A and B such that A and B are subjectively rational about it and agree about its reliability, then there is RID between A and B about p.If A and B (1) disagree about RID about the indication of sourcesp, (2) are subjectively rational concerning p, and (3) there is no source available to A and B such that A and B are subjectively rational about it and agree about its indication, then there is RID between A and B about p.If A and B (1) disagree about For the purposes of this paper, disagreement about the reliability of sources is more interesting. For example, the case of disagreement between a creationist and a scientist about the age of the Earth presented in Sect. p is true. These verbal exchanges include arguments for or against a proposition, presentations of defeaters, and replies against objections. For the sake of simplicity, I assume that these discursive maneuvers all share the structure of arguments, consisting of a set of premises and a conclusion, which are presented in support of the conclusion. In the context of argumentation, the attitude of subjective rationality can be characterized as follows:Various techniques can be used to resolve disagreement, including demonstration, consulting sources, argumentation, and often combinations of these techniques. In this subsection, I will sketch the possibilities and limits of rationally resolving disagreement via argumentation. I understand argumentation as a verbal exchange between two parties A and B with the goal of settling the question whether Subjectively rational arguerAs a speaker, S presents R only if S believes that the premises and the conclusion of R are true and believes that the premises properly support the conclusion andAs a hearer, S believes the conclusion of R because of R iff S believes sufficiently many premises and believes that the premises properly support the conclusion.S is a subjectively rational arguer iff, concerning any argument R,q and A presents an argument R to B. Since, A is a subjectively rational speaker, A believes the premises of the argument and its conclusion and believes that the premises properly support the conclusion. Given that B is a subjectively rational hearer, if B does not believe that the premises are true or does not believe that they properly support the conclusion, then B will not be persuaded. The disagreement remains unresolved. Suppose that A believes that q but that B suspends judgment about q or rejects it. Suppose further that A believes premises p1…pn and presents an argument based on these premises in support of q. If B does not believe the premises, then given that B is subjectively rational, B will not believe that q based on A’s argument. The same holds if B does not believe that the premises of A’s argument properly support the conclusion. In the case of evidence, we distinguished between disagreement about the accuracy of evidence and disagreement about the supporting relation between the evidence and the target proposition. Analogously, we can identify two forms of RID about arguments.Suppose now that A and B are subjectively rational arguers and disagree about RID about premisesp and there is no argument available to A and B such that A and B are subjectively rational arguers and agree about the truth of its premises, then there is RID between A and B about p.If A and B disagree about RID about the cogency of argumentsp and there is no argument available to A and B such that A and B are subjectively rational arguers and agree about whether the argument’s premises support p, then there is RID between A and B about p.If A and B disagree about Rational resolvability of disagreement between two arguers requires agreement about sufficiently many premises and agreement about the supporting relations between premises and conclusion.because of A’s presentation.trusts A in that B believes the content of A’s utterance because of A’s utterance. This trust might be a simple habit, as with small children who trust their parents, or reflective, if A explicitly and defensibly believes that B is a trustworthy person. Taking these two reasons for believing premises into account, we can say:Let me make one more refinement. B can believe the premises of an argument presented by A for two reasons. Firstly, B can already believe the premises prior to A’s presentation or, secondly, B can believe the premises p is true and there is no argument for or against p available such that A and B both believe the premises prior to engaging in argumentation and A and B do not trust each other concerning the premises, then there is RID between A and B.If A and B are subjectively rational arguers and disagree about whether p need not be the final step of a process aiming at resolving disagreement. A and B can collect supporting evidence about whether E is accurate or meta-evidence about whether E properly supports p, and supporting evidence and meta-evidence for the supporting evidence and the meta-evidence, and so on. However, the requirements for this supporting evidence and meta-evidence for resolving disagreement are always the same. Hence, at some point in a chain of proof, consisting of supporting evidences and/or meta-evidences, there has to be initial agreement about the accuracy of evidence and about the supporting relation. Hence, we can say:Resolving disagreement is a process that can proceed in various steps and on various levels. Disagreement between A and B about whether E is accurate or whether E properly supports RID about accuracy of evidence and of supporting evidencep, and there is no evidence for p and no supporting evidence available to A and B about whose accuracy A and B agree, then there is RID between A and B about p.If A and B are subjectively rational, disagree about RID about supporting relationp, and there is no evidence E and no meta-evidence at any level available to A and B such that A and B agree about its support, then there is RID between A and B about p.If A and B are subjectively rational, disagree about The first thesis states that A and B cannot rationally resolve their disagreement if they disagree about the accuracy of any evidence, including any supporting evidence. The second thesis makes an analogous claim about disagreement about meta-evidence concerning supporting relations. Moreover, combinations of these factors can also lead to RID.29To sum up: The potential evidence that can be used to resolve disagreement is manifold, including demonstrations, experiments, testimony, and argumentation. Often, disagreement is resolved by using a combination of these different methods. Accordingly, RID can appear due to combinations of factors, including missing agreement concerning the reliability of sources, the cogency of arguments, or the truth of premises.31RID-view of DD. In this final section, I will investigate the prospect of this view. DD is an intuitively introduced phenomenon motivated by intuitions about cases, and there are different views about DD that are defended. However, we have seen that one central tendency is to judge that DD is irresolvable via rational procedures.RID is an interesting phenomenon since it conflicts with the view that procedures that are rational or believed to be rational are paradigmatic tools for resolving disagreement. However, this paper also aims at investigating whether it is explanatorily fruitful to understand DD as an instance of RID. Call an affirmative answer to this question the The two central questions concerning DD are Q1, the metaphysical question about its nature, and Q2, the epistemic question about its resolvability. RID is a clearly defined notion, in contrast to the intuitively introduced notion of DD. As a result, the central metaphysical and epistemic questions are both clearly answered for RID. The metaphysical question is addressed by the account of RID provided in this paper and the different instances of RID. The question about the resolvability of RID is by definition answered in the negative. Moreover, it is clearly specified in which sense RID is rationally irresolvable.In order to get an RID-view of DD off the ground, we need to show that DD falls in the domain of the provided theory of RID. DD is introduced via paradigmatic cases, and there are different accounts of its nature. Consequently, I do not aim at providing a theory of RID that applies to all instances of DD or exactly matches the existing picture of DD, since there is no such unified picture. Nevertheless, in order to defend an RID-theory of DD, paradigmatic cases of DD should also be paradigmatic cases of RID. This is indeed the case. Paradigmatic cases of DD, such as the case of the creationist and the scientist, which are cases of disagreement about the reliability of sources, are also paradigmatic cases of RID.For evaluating whether the developed RID-view can be fruitfully used in explaining DD, we should gain a clearer understanding of what a theory of DD should achieve. Ranalli , 985 diaDisagreement It needs to be consistent with the conflict being a genuine disagreement.Reason-taking It needs to be consistent with the view that in cases of deep disagreement, the disagreeing parties at least take themselves to be giving reasons for their views.Systematicity It needs to explain why deep disagreements involve systematic disagreement.Persistence It needs to explain why deep disagreements tend to be persistent and thus irresolved.These are intuitively plausible criteria for a theory of DD, and I will use them hereinafter for evaluating different views about the relationship between RID and DD. As I see it, we can distinguish three main views about the relationship between RID and DD:33The replacement viewis RID. The provided theory of RID fully explains DD. Consequently, the notion of DD can be eliminated and theorizing about DD can be replaced by theorizing about RID.DD simply The combination viewRational irresolvability is a crucial necessary feature of DD, but it is not its only feature. DD is also deep in some significant sense beyond rational irresolvability. The provided theory of RID explains one crucial aspect of DD, but a full explanation of DD must also contain a theory explaining the systematicity and depth of DD.The separation viewRID and DD are two distinct phenomena, and rational irresolvability is not a necessary feature of DD. The provided theory of RID does not contribute to explaining DD, and a full explanation of DD does not contain a theory of RID.According to the replacement view, the concept of RID is prior to the concept of DD and the latter can be reduced to the former. The combination view and the separation view, in contrast, assume a conceptual independency (or even a priority) of DD from RID.propositions, hinge propositions or propositions about fundamental epistemic principles. RID, in contrast, is determined only by whether the beliefs of two subjectively rational parties sufficiently match, allowing RID to occur concerning any proposition. I regard this result as a methodological advantage of the replacement view over alternative theories. Regardless of which proposition type one spots as the potential subject of DD, either propositions about fundamental epistemic principles or hinge propositions, one has to provide a clear definition of this proposition type in order to define DD. However, both types of propositions are less than crystal clear. There is no wide agreement about what hinge propositions are and how they can be incorporated into a theory of DD,The replacement view has it that DD can be reduced to RID and that analyses of and claims about DD can be replaced by analyses of and claims about RID. There is a crucial difference between this replacement view of DD and alternative theories about DD, such as hinge theories and first principles theories. DD is often understood to be disagreement about a certain type of Moreover, RID also fulfills other desiderata for DD. (1) RID is clearly a case of genuine disagreement. (2) It is a paradigmatic case of reason-taking, since the two parties act according to their own standards of rationality. (3) Many cases of RID are systematic. In particular, many are concerned with the supporting quality of evidence, the reliability of sources, or the cogency of arguments. (4) RID is obviously persistent, since it is, by definition, rationally irresolvable.37supporting relation between the evidence and the target proposition, the premises and the conclusion of arguments, or on the reliability of sources; and, second, RID can involve disagreement about the accuracy of evidence, of the indications of sources, or the truth of the premises. Disagreement of the first kind is systematic, and paradigmatic instances of DD fall under this category. For example, DD between a creationist and a scientist about the age of the Earth is disagreement about the reliability of sources. Moreover, Lynch  crucial feature of DD. In response, adherents of the replacement view can defend a more nuanced version, according to which the provided theory of RID allows distinguishing between merely contingent and more systematic forms of RID. For example, RID can be based on merely contingent disagreements about the truth of all premises available, but it can also be based on systematic disagreement  about proper methods or reliable sources as in the case of the scientist and the creationist. A more nuanced form of the replacement view can then hold that RID can be more or less systematic and that DD is systematic RID. Call this the systematic replacement view.38One might object that the simple replacement view ignores that DD is deep and systematic in some relevant sense that RID is not, thereby missing a  are two distinct features of disagreement that can appear without each other. They are, in this sense independent of each other, and cannot be explained or understood in virtue of each other. DD is then just disagreement that jointly fulfills the two independent criteria. In contrast, the strong version of the combination view holds that DD is rationally irresolvable and systematic in some significant sense. However, the priority and order of explanation differs. For the strong combination view, depth and systematicity of disagreement are explanatorily prior to rational irresolvability, i.e., the latter can be explained in terms of the former. The weak combination view treats systematicity and rational irresolvability as independent of each other. The replacement view first develops a theory of RID. For the systematic replacement view, systematicity is just a further feature of rational irresolvability, as the simple replacement view ignores systematicity. Both replacement views do not provide a self-contained metaphysical theory about the depth of disagreement.40Both the systematic replacement view and the combination view assume that DD is rationally irresolvable explains the rational irresolvability of a particular disagreement in terms of systematicity or depth. Given this explanatory desideratum, the weak combination view that simply combines two independent features does not seem very attractive. Accordingly, I will focus on the strong combination view as the main rival of the systematic replacement view.How can we evaluate the combination view in comparison to the replacement view? There is wide agreement that DD is, in some sense, systematic and rationally irresolvable. This intuition is captured by both combination views, which meet all four of Ranalli’s criteria, including systematicity. However, adherents of DD might want to establish an explanatory connection between rational irresolvability and systematicity. This goal is only achieved by the strong combination view, which In comparison, I see three advantages for the systematic replacement view over the strong combination view. First, the theory of RID developed in this paper seems to me clearer than existing theories about hinge propositions or about first epistemic principles, which tend to involve rather vague and unclear notions.Admittedly, these methodological considerations do not provide conclusive reasons for favoring a systematic replacement view over a combination view. For instance, one might have an intuition about the explanatory priority of depth and systematicity over rational irresolvability so strong that it overrides all methodological considerations to the contrary. In this case, the provided theory of RID contributes to a combination view at least by clarifying in which sense disagreement can be rationally irresolvable and which kind of rational irresolvability has to be explained by theories of DD. Thus, a theory of RID still fulfills a significant desideratum.Finally, let me reflect on the third view on the relationship between RID and DD, the separation view. The replacement view and the combination view accept that rational irresolvability is a key feature of DD. Both accounts thereby exclude the possibility that DD is rationally resolvable. However, some authors, such as Feldman  and Mathsome instances of DD are rationally resolvable and a stronger view stating that all are. Any of these two views entails that all versions of the replacement view and the combination view are false, since they hold that rational irresolvability is a necessary condition on DD.The separation view holds that rational irresolvability and systematicity of disagreement are two distinct features that do not entail each other. Thus, there can be RID that is not an instance of DD and vice versa. We can distinguish a weaker separation view holding that Some might regard this as an advantage of the separation view, given the arguments presented in favor of the rational resolvability of DD. One advocate of the view that DD is rationally resolvable is Feldman. Feldman , 16 presRR2 There is a rational resolution of a disagreement available when there is some way of presenting arguments and evidence to which the rational response is a resolution of the disagreement .Based on this definition, Feldman argues that DD is resolvable in the sense that there is a rational reaction for both parties available such that the disagreement is resolved. Feldman admits that issues that are subject to DD are often fundamental and, therefore, hard to decide. However, he stresses the point that also suspension of judgment can be a rational resolution of disagreement and that, in many cases, a rational reaction for persons confronted with DD is to suspend judgment about the target proposition. If both parties suspend judgement, then they hold the same doxastic attitude concerning the target proposition and the disagreement is resolved. What Feldman seems to have in mind when talking about DD are cases of deep philosophical disputes, which are hard to resolve. However, also other rational resolutions to DD are possible, where one of the parties should rationally adopt the view of the other.42objective sense of rationality. Matheson  rational resolution to this disagreement in Feldman’s sense, namely accepting what the scientific evidence recommends. However, the DD is rationally irresolvable in a subjective sense since both parties, given that they are subjectively rational, will not reach agreement. There can be an objective rational resolution to DD available without there being a subjective rational resolution. Thus, Feldman’s and Matheson’s positive views about the rational resolvability of DD in an objective sense do not contradict the view that DD is rationally irresolvable in the subjective sense defended here.Feldman is right that DD is resolvable in this particular sense, but note that RR2 expresses a different sense of rational resolvability than the one developed here. According to Feldman, DD is resolvable in the sense that we can give a conceptual analysis of necessary and sufficient conditions of rationally resolving disagreement in an Matheson , 9 argueI do not know of any other plausible view about the rational resolvability of DD. For this reason, I currently do not see any motivation for accepting the separation view that rational irresolvability in a subjective sense and depth are two distinct features that should be strictly separated. Accordingly, I regard the separation view as the least plausible theory about the relationship between RID and DD. However, even if one opts for a separation view, then the provided theory about RID can contribute to clarifying this view.45This paper has offered a theory of RID. We can distinguish between objective and subjective forms of rationality. However, RID can only be formulated in terms of subjective rationality, i.e., two parties disagree in a way that is rationally irresolvable if they hold different views about rationality. Various forms of RID have been distinguished, based on different views about evidence, about the reliability of sources, and about cogent argumentation. One central motivation for developing a theory of RID is its potential application to DD, as existing theories of DD face certain shortcomings. In contrast, an RID-view of DD provides a clear definition of the relevant kind of disagreement and avoids these shortcomings. Moreover, this theory meets plausible explanatory desiderata for a theory of DD and also covers paradigmatic cases of DD. For these reasons, it is reasonable to replace the ongoing discussion about DD with (or at least accompany it with) a theory of RID.


The Current food environment has become increasingly obesogenic, with rates of obesity and related conditions continually rising. Advertisements for energy-dense foods are abundant and promote unhealthy eating behaviors by capitalizing on one’s attentional bias towards food cues, a cognitive process resulting from the sensitization of highly reinforcing food. A heightened awareness towards food cues may promote overconsumption of energy-dense foods. The current study employed novel eye-tracking methodology to capture sustained, or late-stage, attentional bias towards food cues. Late-stage attentional bias is the aspect of attentional bias under conscious control and likely more prone to modification compared to initial/ early-stage attentional bias, which reflects automatic processes. The present study hypothesized late-stage attentional bias towards food cues is greater among individuals classified as overweight/obese than those classified as normal weight. Thirty (30) participants classified as overweight/obese (BMI ≥25) and 47 classified as normal weight (BMI <25) were assessed for late-stage attentional bias towards food cues, conceptualized as the percentage of time fixated on food cues when both food and neutral images were presented during a food-specific visual probe procedure task. Percentage of time fixated on food cues was 51.25 ± 1.27 (mean + SE) among individuals classified as overweight to obese while those classified as normal weight had a percent fixation of 47.26 ± 0.87 (P=0.03). In conclusion, individuals classified as overweight to obese have greater late-stage attentional bias towards food cues. This establishes an important factor influencing energy intake that may be modified in future clinical trials. I.1. Today, over 70% of the American population is classified as overweight or obese3. Understanding contributing factors to this endemic could be essential for reversing these trends and improving the health of many.Obesity prevalence in the United States has steadily risen from 8% in the early 1980s to 22% by 20055. Inherent biases individuals have related to sensory or emotional feelings towards these foods is known to play a role in such overconsumption6. Food advertisements commonly found throughout popular media target these sensory and emotional feelings, promoting an environmental salience towards these foods, increasing their attractiveness7. Energy-dense, palatable foods are the most abundantly advertised foods, especially those targeting children and adolescents9. These advertisements have been linked to the overconsumption of energy dense, nutrient poor food and unhealthy BMI12. These correlations can be explained by the heightened responsiveness to environmental food cues individuals classified as overweight to obese can display, an area that has been under study as early as the 1970’s with Rodin and Slochower’s seminal work14. The term “attentional bias” has since been coined to convey this heightened responsiveness, specifically referring to a heightened attention toward a particular stimulus. Attentional bias towards addictive stimuli are well documented 15–18 supporting the incentive-sensitization hypothesis, which posits rewarding stimuli capture attention and induce cravings19. Following up on Rodin and Slochower’s initial work, attentional bias research has extended to eating behaviors, employing behavioral tasks such as a food-specific Stroop test or Dot-Probe tasks to measure reaction time and accuracy in identifying colors of food and neutral words. For these tasks, reaction time and accuracy become surrogate measures for attentional bias. Indeed, several trials have demonstrated a link between weight status and these measures of attentional bias, whereas individuals classified as overweight or obese have greater attentional bias towards food cues than normal weight controls23.Overconsumption of energy dense foods is a main contributing factor in the rising number of individuals classified as overweight to obese25. This data provides detailed information into how individuals respond to visual stimuli in real time. Unlike the aforementioned behavioral indices of attentional bias , eye tracking provides a direct measure of attentional processing and can differentiate between early and late stages of attentional processing. The direction of an initial fixation is thought to assess automatic processes related to the initial salience of the visual stimuli whereas total fixation time  is considered to assess late stages of attentional processing that are under coconscious control26. Many of these studies have utilized a visual dot-probe task in conjecture with eye tracking, where two images are presented on a computer screen  for a certain amount of time before a probe appears in place of one of the images. Participants are required to respond to the probe by selecting the corresponding computer key as quickly as they can indicating if the probe appears on the right or left side of the screen. In this way, both visual eye tracking data (assessed when looking at images before probe appears) and reaction time (time to react to probe) can be assessed as measures of attentional bias29. These studies all report differences in attentional bias between individuals classified as overweight to obese when compared to normal weight controls, although the parameters and exact indices seem to vary. Specifically, Werthmann et al. demonstrated only initial fixation direction and the time spent in that initial fixation differed between groups, indicating automatic processing is primarily different between weight status group25. Both Nijs et al. and Castellanos et al. additionally assessed the effects of fed and fasted states on attentional bias between weight status groups. Nijs et al. demonstrated no difference between groups or fed/fasted conditions in eye tracking data, whereas all participants demonstrated a greater attentional bias towards food. Interestingly, when looking at reaction time, this study demonstrated normal-weight individuals responded faster to the visual probe than the overweight/obese group29. Castellanos et al. demonstrated all participants had an elevated attentional bias while fasted, while only the overweight/obese group demonstrated greater attentional bias towards food cues in the fed condition. In contrast to Werthmann et al., these results applied to both initial fixation direction and total fixation time28. Graham et al. took a different twist, assessing the interaction between different types of food  and weight status. Interestingly, total fixation time did not differ between groups, while initial fixation direction was greater towards low-energy foods in the overweight/obese group compared to control27.More recently, eye-tracking technology has come to the forefront of attentional bias research, allowing for the noninvasive assessment of eye movements as individuals examine visual stimuli. Eye movements are directly observable and an ecologically valid measurement of the visual attention process, measuring the tendency to automatically devote attention to specific stimuli25.Employing these adjustments to the Dot-Probe task with eye tracking, the current study sought to demonstrate differences in attentional bias towards food cues  between individuals classified as overweight to obese (BMI≥25) and those who are classified as normal weight (BMI <25). We hypothesized individuals classified as overweight or obese would spend a greater percentage of time fixated on food cues than those classified as normal weight, indicating they have greater late-stage attentional processing, which is under coconscious control, as opposed to initial fixation direction that is automaticII.2.130. The inclusion/exclusion criteria remained the same for both studies, except for weight status, with only healthy individuals absent of any chronic condition  included.Participants classified as normal weight, BMI <25  and those classified as overweight to obese, BMI ≥25  were recruited using flyers and email advertisements. Recruitment occurred between April and November 2021 and was approved by the University of Kentucky IRB (protocol # 69120). Participants could not be tobacco users, pregnant, or nursing. Individuals were also required to be at least 18 years old. The sample of participants classified as overweight to obese were recruited from a separate study that included baseline assessments for attentional bias and body composition2.22.2.1Height was measured in triplicate to the nearest 0.1 cm using a stadiometer . Body weight was measured using a calibrated digital scale connected to the BodPod  to the nearest 0.01 kg. Measures were completed with participants wearing spandex shorts and sports bra  or no shirt  as required for the BodPod assessment (below). BMI was calculated during the screening and enrollment visit to ensure participants qualified for the study.2.2.231. The Siri or Schutte density model was used, depending on race, to convert body density to percent body fat33. Thoracic gas volume was measured according to manufacturer’s recommendations.Kg of body fat and fat-free mass were determined via air displacement plethysmography  and percent body fat calculated. Participants were assessed prior to completing the attentional bias task and were at least 3 hours post-prandial. The BodPod is a reliable and valid assessment tool for body composition in adults, offering a quick and noninvasive assessment of body composition2.2.318. The issue, we believe, in barrowing from addictive research in this scenario, is that food is much less reinforcing to most people compared to the reinforcing value of drugs of abuse among those with an addictive disorder35. Therefore, individuals with an addictive disorder will be much more sensitive towards drug-related stimuli than a healthy individual is towards food. Prior to our eye tracking studies, we piloted this task and observed great variability among 5 test subjects using the 1,000ms presentation time (within subject SD range 0–50.1) and for the 2,000ms presentation time (SD range 11.5 to 43.9). The 3,000ms presentation time yielded a within-subject SD range of 14.9 to 21.8 and therefore was chosen for this study. We believe this may be the reason some of these prior studies did not observe a difference between groups or conditions in total fixation time. We also improved upon prior studies by developing a novel metric to assess total fixation time, or late-stage attentional bias. This new metric, mean percentage of time fixated on food cues, or percent fixation time, is calculated by dividing the fixation time for the food cue by the fixation time for the food + neutral cue. This is done for each individual trial and then averaged across the entire test, providing an average % fixation time. This is an improvement over the traditional total fixation time as some trials may result in 0ms of fixation time for either image (in the event a participant blinks or looks away and their eyes were not recaptured quick enough). If a participant has even one of these trials, their total fixation time may look greatly reduced compared to a participant who did not have any such trials. By expressing fixation time as a percentage  we avoid this potential issue. Lastly, the current study assessed individuals who were neither satiated nor fasted, assessing every participant in the afternoon between lunch and dinner who reported to be only moderately hungry. This may represent a more typical, real-world scenario, where someone is not extremely hungry nor extremely full.The current study employed similar eye-tracking procedures as previous studies noted with a few important adjustments. First, we utilized a 3,000ms presentation time for the pictures of food cues . Of the prior studies mentioned, Castellanos et al.’s 2,000 ms presentation time was the longest, while others typically use 500 or 1,000ms, following prior eye-tracking addiction research that traditionally utilizes a 1,000ms presentation time38. Ten images of energy dense foods  were paired with ten images of non-food  stimuli that included nature images, furniture, and buildings. Other pairs included two neutral (non-food) images used as filler trials. All image pairs were matched for color and complexity, had dimensions of 680×491 pixels with a 96 dpi. Pairs were presented one at a time in random order. Image pairs were shown for a total of 3,000ms after which a yellow dot appeared in place of one of the images. Participants were instructed to right click the computer mouse if the yellow dot appeared on the right side of the screen and left click if the yellow circle appeared on the left of the screen. Participants were positioned so that their eyes were 65–75cm away from the screen. Calibrations were performed to ensure that the participants’ eyes were being tracked properly before each trial. Each pair of images (both those containing food images and those not) were shown twice. The orientation of the images were flipped so neither food nor neutral image was shown on the same side of the screen twice. There was a total of 80 trials (pairs) shown to each participant. Half (40) of the trials contained food cues and the other 40 pairs contained only non-food, filler, trials. The primary outcome was time in ms fixated on food and neutral images, which was used to calculate the percentage of time fixated on food cues as: ms fixated on food cues / .Attentional bias was assessed by the visual probe procedure adapted for food cues2.2.4Hunger and Satiety was assessed prior to the attentional bias assessment via visual analog scales (VAS) where participants dragged a slider on a computer to indicate how hungry they were on a scale of 0 “not hungry at all” to 100 “extremely hungry.” Participants were scheduled for their assessment visit between lunch and dinner and instructed to attend the experimental session 3–5 hours post prandial. This was designed so participants were neither hungry or satiated, thus assessing attentional bias under neutral conditions.2.3Repeated measures analysis of variance (ANOVA) was used to assess differences in attentional bias and demographic variables between groups . A linear regression model using attentional bias as the dependent variable was constructed using body fat percentage and age as predictor variables. In the planned repeated measures ANOVA a sample of 30 participants has 80% power to detect an interaction which is 0.37 times the standard deviation between participants provided the correlation within participants is 0.5 or larger (effect size 0.517). Thus, our sample size of 30 and 47 participants for each group was adequate.III.The group classified as obese/overweight was younger, had a greater BMI, and a greater body fat percentage when compared to the normal weight group . To testAs depicted in As expected, hunger was not correlated with attentional bias scores . This is likely due to participants were neither very hungry of very satiated when assessed, mean ± SE hunger score: 41.5 ± 5.6.IV.43 while others have linked greater attentional bias towards food cues to future weight gain44. This supports the notion obesity is not creating an attentional bias towards food cues, rather, obesity is the result of an attentional bias-mediated increase in energy intake42.In line with our hypothesis, the current study demonstrated individuals classified as overweight to obese have a greater late-stage attentional bias towards food cues than their normal-weight counterparts. Although a cause and effect relationship cannot be determined from the present cross-sectional study, others have linked greater energy intakes to greater attentional bias for food cues and food reinforcementUnlike prior studies addressing this question, attentional bias was conceptualized as the average percentage of time fixated on food cues after a 3,000ms presentation time, indicative of greater attentional processing that is under coconscious control. We chose not to focus on initial fixation direction as 1) this has been studied before and is not influenced by the novel aspects of the present study  and 2) this automatic process is likely not modifiable in future training interventions.45. Despite the inconsistency of assessment techniques, this review concluded that there is sufficient evidence demonstrating attentional bias towards food cues is increased among individuals classified as overweight to obese42.When considering the research on attentional bias towards food cues and its relationship with eating behaviors and weight status as a whole, it is difficult to arrive at a single conclusion due to the various methodology. A review of attentional bias literature by Hendrikse et al. recognized this wide-range of methodology in conceptualizing attentional bias, such as total fixation duration towards food cues, the order of fixation  or the reaction time to a dot probe46. Participant characteristics such as the physiological state assessed (fasted vs. satiated), age, sex, or other pre-existing conditions may have all contributed to variability between studies to cause difficulties in identifying differences. The 3,000ms presentation time of the current trial, conceptualizing attentional bias as mean percent fixation time, and assessing individuals who were neither extremely hungry or satiated are all potential reasons we were able to identify differences in attentional bias, specifically late-stage, in our groups of normal weight vs. those classified as overweight to obese.Conversely, a recent review concluded that individuals classified as overweight or obese did not differ when compared to normal weight controls in their fixation-direction or fixation-duration bias47. This is well documented in the drug abuse literature, where repeated exposure to the stimuli promotes a sense of wanting and an unavoidable craving48. Food cravings, much like drug abuse, increases the neural activity of the corticolimbic-striatal regions of the brain (motivation-reward regions) and is more pronounced among individuals classified as obese49. This is also supported in studies identifying a genetic component to food cue reactivity that share similarities with drug abuse53. As noted, this is likely a prime cause of over consumption and obesity, but also may pose as a barrier to weight loss as these individuals are more affected by food cues than their normal-weight counterparts. This scenario, where some individuals are more susceptible to food’s reinforcing effects due to certain genetic components of their dopamine reward system, is difficult to manage as exposure to the reinforcer (food in this case) is necessary for survival. This is an area where attentional bias training interventions could play a major role, aiding those individuals who are highly sensitive to food cues to either prevent weight gain or promote weight loss. Some attentional bias training trials are already underway and have demonstrated promising results for modifying late-stage attentional bias towards food cues54. The present trial, and its focus on late-stage attentional bias, is designed to provide foundational knowledge for such future attentional bias training studies- altering conscious attentional bias towards food cues to influence eating behaviors and promote obesity treatment. Future trials should focus on this aspect of attentional bias as these conscious processes governing eating behaviors is likely more relevant as we move forward towards these training studies.A possible underlying physiological response for the increased attentional bias with obesity lies in a modification of central neuronal pathways27. A better understanding as to why this was the case is needed, if it was a product of social desirability or if the presentation time was not long enough for participants to realize what they were looking at and focus on the high-energy dense foods. Future studies using percent fixation time to conceptualize attentional bias under conscious control is needed as this aspect of attentional bias is what future attentional bias training studies can target in attempting to promote changes in eating behaviors. A limited number of these training studies have been successful in altering attentional bias towards food cues55, although it would be interesting to see if using a 3,000 ms presentation time and the percent fixation time metric would uncover additional information regarding changes in sustained fixation.Future research may also focus on whether there is an attentional bias towards low energy dense foods, such as vegetables, as most literature only considers energy dense foods. As noted, Graham et al. demonstrated that initial fixation direction was greater towards low-energy foods in the overweight/obese group compared to control4.156. However, none of the participants had a BMI that would be expected with the most common eating disorder, anorexia nervosa, with the lowest BMI at 18.8 and considered normal weight. Besides body fat and BMI, the groups differed on age, although age did not predict attentional bias when included in the regression model. We also did not assess demographic factors that may be predictors of attentional bias for food cues such as food security, household income, and education.The current study did not screen for eating disorders that would influence attentional bias towards food cuesV.45. The present trial expands on these previous findings by 1: increasing the presentation time to 3,000ms and focusing on late-stage attentional bias, 2: utilizing a novel “percent fixation time” metric to better conceptualize attentional bias towards food cues, and 3: performing these tests between meals in a state where participants were neither hunger or fully satiated. Such methodological intricacies are important to consider when evaluating attentional bias for food cue research and making conclusions.The primary results of the present trial supported those of previous trials which have indicated a possible link between attentional bias and weight status


Owing to its high electrical conductivity, low density,and flexibility, graphene has great potential for use as a buildingblock in a wide range of applications from nanoelectronics to biosensingand high-frequency devices. For many device applications, it is requiredto deposit dielectric materials on graphene at high temperatures andin ambient oxygen. This has been proven to be highly challenging becausethese conditions cause significant degradation in graphene. In thiswork, we investigate the degradation of graphene at elevated temperaturesin an oxygen atmosphere and possible protection mechanisms to enablethe growth of oxide thin films on graphene at higher temperatures.We show that coating graphene with self-assembled monolayers of hexamethyldisilazane(HMDS) prior to a high-temperature deposition can significantly reducethe damage induced. Furthermore, a graphene sample treated with HMDSdisplayed a weaker doping effect due to weak interaction with oxygenspecies than bare graphene, and a much slower rate of electrical resistancedegradation was exhibited during annealing. Thus, it is a promisingapproach that could enable the deposition of metal oxide materialson graphene at high temperatures without significant degradation ingraphene quality, which is critical for a wide range of applications. Combined with its thicknessat the angstrom scale, high electrical conductivity means that graphenecan be an excellent electrode material for many different devicessuch as field-effect transistors,9 datastorage devices,10 photodetectors,11 and biosensors.13As a representative ofthe family of the wholly two-dimensional material, graphene has beenused in various field applications due to its unique physical propertiesand superior mechanical properties.14 the nontoxicity, uniformity, and low cost of both PLD andmagnetic sputtering still make them the most promising methods.In manydevice-manufacturing processes such as memory and radio frequencydevices, graphene is usually transferred onto the surface of a semiconducting,polymer or ceramic material, followed by the deposition or growthof the active materials on graphene. Pulsed laser deposition (PLD)and magnetron sputtering are the most used methods to grow ceramicfilms due to their capability to achieve high-quality films. Althoughlow-temperature growth methods such as atomic layer deposition havebeen introduced for oxide layer growth on graphene,15 Furthermore, otherstudies have shown that annealing graphene in oxygen can p-dope grapheneeven at low temperatures.16 As the temperatureincreases, it results in etch pits with nanoscale in a single graphenestructure. This causes more defects in graphene and reduces its electricalconductivity.19The growth of oxide films requires high-temperature annealing toactivate the adatoms and oxygen gas to compensate for the loss ofstoichiometry. However, it has been reported that the growth of anepitaxial oxide layer using PLD on top of graphene can damage graphene,which is attributed to the reactive gas atmosphere at high temperaturesduring deposition.In this study, a thorough exploration of graphene’s behaviorduring high-temperature annealing in an oxygen atmosphere is conducted.The aim is to preserve the graphene structure and maintain its properties.Two methods are chosen to protect the graphene layers: metal protectionand compound protection.20 Therefore, HMDS is chosen as the compound method during annealing.For metal protection, an ultrathingold film is used due to its chemical stability and volatility inthe oxygen atmosphere. Theoretically, gold should protect graphenefrom oxygen-related degradation. Previous studies have shown thatcoating graphene with a self-assembly monolayer of hexamethyldisilazane(HMDS) can also protect graphene during its exposure to plasma withoutdegrading its electrical performance.22O) for 12 h. The PMMA/graphenestack was then floated on two consecutive ultrapure deionized waterbaths to rinse the graphene surface for up to 1 h per bath. The freestandingPMMA/graphene layer was transferred to a SiO2/Si substrate,and PMMA/graphene on the substrate was baked on a hotplate for 2 hat 150 °C to improve the adhesion of the graphene to the substrate.PMMA was then removed using acetone for 5 h followed by isopropanol(IPA) for 5 min. The sample was then annealed at 250 °C for 5h to remove PMMA residues on graphene. All samples were classifiedas sample A, sample B, or sample C. Sample A represents the pure monolayergraphene only, sample B is the monolayer graphene covered with a 2nm gold layer using thermal evaporation, and sample C is the monolayergraphene treated with HMDS solution at room temperature for 12 h toform a uniform self-assembly monolayer on graphene surface (see the Supporting Information). To measure the electricalresistance, 16 Au electrodes with a diameter of 2 mm were formed usingthermal evaporation through a shadow mask.The chemical vapordeposition (CVD) graphene on copper foil was purchased from the Grolltexcompany. Cu foil was coated with poly (methyl methacrylate) (PMMA)to support the graphene transfer. Cu was then etched using ammoniumpersulfate  and atomic force microscopy (AFM) were also used to evaluatethe presence of HMDS and its influence on the graphene layer afterhigh-temperature annealing.After that, the sampleswere mounted in a vacuum chamber. The chamber was pumped down to 3× 10ℏwL = 2.33 eV) which used an optical fiber, an objective lens of 100×,and NA = 0.8, resulting in a laser spot of 0.4 μm. The laserpower was kept below 2 mW, and the spectral resolution was ∼3cm–1; the Raman peak position was calibrated basedon the Si peak position at 520.7 cm–1. The D, G,and 2D peaks were fitted with Lorentzian functions.Raman spectroscopy measurementswere performed using a Renishaw InVia Raman spectrometer with a laserwavelength of 532 nm (excitation energy EL = hν = 1486.6 eV) in an ultrahigh vacuumchamber for spectroscopic analysis with a base pressure of 5 ×10–8 bar.XPS experimentsand measurements were performed with Kα+ and an Al radiationsource  depth profiling was carried out using an IONTOF ToF-SIMS Vinstrument. A 25 keV Bi32 substrates wereused such as bare graphene, graphene coated with HMDS, and graphenecoated with a gold layer 2 nm thick using e-beam evaporation. Theproperties of graphene after HMDS coating are described in detailin the Supporting Information. The sampleswere annealed at temperatures of 300, 400, 500, 600, and 700 °C.Electrical resistance measurements were performed after each annealingprocess. An increase in electrical resistance was observed for allsamples after annealing above 500 °C. However, the HMDS-coatedgraphene exhibited the lowest degradation in electrical resistancecompared to gold-coated and bare graphene. Furthermore, a decreasein electrical resistance after annealing at 400 °C was observed.22 Also, in the case ofthe gold-coated graphene layer, one could anticipate the incorporationof gold in the graphene’s defect pits, which would effectivelyshorten the current percolation path.This could be attributed to the removal of PMMA residuals and improvedgraphene–metal contact.As the annealing temperatureincreased, all samples exhibited an increase in resistance which isrelated to the quality of graphene. The bare graphene sample showeda very high increase in resistance when the annealing temperatureexceeded 400 °C, while the resistance of all the other samplesshows a relatively lower increase or even a decrease at the same temperature.At higher temperatures, the resistance of the gold-coated graphenesamples increased 50-fold compared to that at room temperature. Incontrast, the resistance of HMDS-protected graphene only increasedfivefold. The resistance result is shown in –1 and 2D mode around 2682 cm–1 . The G mode and 2D originatefrom the doubly degenerate zone center phonon and second order ofzone-boundary phonons.23 D mode was alsofeatured around 1349 cm–1 which is produced by thedisorder inside graphene and can be used to evaluate the defect densityof graphene. After annealing, a shoulder appears in the G mode ataround 1620 cm–1 (I(D)/I(G)) and found no evidence of significant damage to thestructural properties of bare graphene and graphene coated with HMDSafter annealing. The ratio of the intensity of D mode over D′mode (I(D)/I(D′)) was also calculated according to Eckmann et al.24 We found that I(D)/I(D′) in bare graphene decreases significantlywith the increasing annealing temperature and the type of defectschanges from sp3 defects to vacancy defects. In contrast,there is only a small change in I(D)/I(D′) in graphene coated with HMDS asthe annealing temperature increases. Therefore, the change of I(D)/I(G) and I(D)/I(D′) cannot solely explain the large increase in graphene resistanceshown in Figure S3.)Raman spectroscopy was used to investigatethe properties of graphene after annealing. Changes that occur ongraphene with different protection during annealing can be expressedin terms of changes in the Raman spectrum of graphene. The Raman spectrumof as-transferred graphene shows the presence of G mode around 1594cm682 cm–1 S2. The G682 cm–1 S2. The G27 As the temperature increases,the G–2D frequency modes start to locate closer to the dopingline as an indication of the reduction of strain at a higher temperature.It is worth notingthat the 2D-peak mode of gold-coated graphene exhibited an asymmetricshape after 500 °C annealing. The asymmetry becomes less visiblewith the increase in annealing temperature. To identify the originof this shape, we plotted the G–2D frequency modes at eachannealing temperature to determine if there is any strain inducedin the Au-coated graphene after annealing. After 500 °C annealing,the G–2D frequency positions are located at the strained-grapheneline. Strain can reduce the symmetry in graphene and affect the orientationof graphene, resulting in the change of G and 2D modes.27 Therefore, the level of doping of the graphene sample canbe described as the distance between the intersection point and theprojection of the data point on the red dashed line. 2O and O2 introduce hole doping in graphene.28To further investigate the impact of annealingon the doping and strain of the bare graphene and graphene treatedwith HMDS, the G–2D frequency mode was plotted in 2 and graphene and henceincrease the level of p-doping.29 Therefore,the formation of O–C=O and C–O–C bondsand the increased coupling between the substrate and graphene at hightemperatures could contribute to the increase of scattering in grapheneafter annealing and possibly could play a role in the increase ofthe resistance.The low resistance of as-transferred graphenecoated with HMDS suggests that the formation of the HMDS layer byself-assembly possibly still exists even after high-temperature annealing.This layer acts as a barrier that may prevent oxygen diffusion tothe graphene film. To further explore this assumption, we performedXPS measurements to assess the elemental composition of graphene atroom temperature and after annealing at 700 °C. After annealingat 700 °C, the XPS C 1s spectrum reveals the presence of a C–O–Cpeak with increased density compared with graphene before annealing.Another O–C=O bond is observed in the C 1s spectrumof bare graphene after annealing 5a,b. Int2O andC–NH2  during the thin-film growth process.To investigate this hypothesis, a thin gold film was grown on HMDS-coveredgraphene using magnetron sputtering and SIMS was then employed toinvestigate the sample’s elemental depth profile. The resultsobtained are shown in 2 is enhanced across the thicknessof the sample which approaches the silicon substrate underneath thegraphene layer. The signal for Na+ which represents thepresence of graphene shows a slight increase at a depth of 45–50nm, which is consistent with the existence of a single layer of grapheneunderneath the gold film. Some organic compounds that contain Si werealso detected; however, these signals are likely to be related toPMMA with residues from the transfer process in the commercial CVDgraphene to silicon substrates. Thus, it is concluded that the characterizationusing SIMS detects hardly any signal that indicates the presence ofHMDS after the magnetron sputtering.The SIMS results show that the signal for gold remainsat a constant level throughout the entire film thickness of about50 nm. The signal for Si/SiO4This study demonstratesthat graphene’s electrical resistance and integrity can bepreserved during a treatment typical for oxide thin-film deposition,i.e., high temperatures in an oxygen atmosphere. A series of electricalresistance measurements and surface analyses using XPS and AFM showthat the SAMs of HMDS can provide better protection to graphene comparedwith a thin layer of gold. Furthermore, the SIMS results show strongevidence that HMDS disappears during a consecutive magnetron sputteringprocess. Thus, HMDS can provide adequate protection of graphene duringan oxide-thin-film deposition process without affecting the propertiesof the manufactured device.