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=== Based on rules of coherence === An influential rival to the reason-responsiveness account understands rationality as internal coherence.<ref name="Heinzelmann2022"/><ref name="Lord2018-1"/> On this view, a person is rational to the extent that their mental states and actions are coherent with each other.<ref name="Heinzelmann2022"/><ref name="Lord2018-1"/> Diverse versions of this approach exist that differ in how they understand coherence and what rules of coherence they propose.<ref name="Mele2004a"/><ref name="McClennen2004"/><ref name="Broome2021"/> A general distinction in this regard is between negative and positive coherence.<ref name="Harman2013"/><ref name="Thagard1998"/> Negative coherence is an uncontroversial aspect of most such theories: it requires the absence of [[contradiction]]s and [[Consistency|inconsistencies]]. This means that the agent's mental states do not clash with each other. In some cases, inconsistencies are rather obvious, as when a person believes that it will rain tomorrow and that it will not rain tomorrow. In complex cases, inconsistencies may be difficult to detect, for example, when a person believes in the axioms of [[Euclidean geometry]] and is nonetheless convinced that it is possible to [[Squaring the circle|square the circle]]. Positive coherence refers to the support that different mental states provide for each other. For example, there is positive coherence between the belief that there are eight planets in the [[Solar System]] and the belief that there are less than ten planets in the Solar System: the earlier belief implies the latter belief. Other types of support through positive coherence include explanatory and [[Causality|causal]] connections.<ref name="Harman2013"/><ref name="Thagard1998"/> Coherence-based accounts are also referred to as rule-based accounts since the different aspects of coherence are often expressed in precise rules. In this regard, to be rational means to follow the rules of rationality in thought and action. According to the enkratic rule, for example, rational agents are required to intend what they believe they ought to do. This requires coherence between beliefs and intentions. The norm of persistence states that agents should retain their intentions over time. This way, earlier mental states cohere with later ones.<ref name="Heinzelmann2022"/><ref name="Harman2013"/><ref name="Lord2018-1"/> It is also possible to distinguish different types of rationality, such as theoretical or practical rationality, based on the different sets of rules they require.<ref name="Mele2004a"/><ref name="McClennen2004"/> One problem with such coherence-based accounts of rationality is that the norms can enter into conflict with each other, so-called rational [[dilemmas]]. For example, if the agent has a pre-existing intention that turns out to conflict with their beliefs, then the enkratic norm requires them to change it, which is disallowed by the norm of persistence. This suggests that, in cases of rational dilemmas, it is impossible to be rational, no matter which norm is privileged.<ref name="Heinzelmann2022"/><ref name="Mintoff1997"/><ref name="Priest2002"/> Some defenders of coherence theories of rationality have argued that, when formulated correctly, the norms of rationality cannot enter into conflict with each other. That means that rational dilemmas are impossible. This is sometimes tied to additional non-trivial assumptions, such that [[ethical dilemmas]] also do not exist. A different response is to bite the bullet and allow that rational dilemmas exist. This has the consequence that, in such cases, rationality is not possible for the agent and theories of rationality cannot offer guidance to them.<ref name="Heinzelmann2022"/><ref name="Mintoff1997"/><ref name="Priest2002"/> These problems are avoided by reason-responsiveness accounts of rationality since they "allow for rationality despite conflicting reasons but [coherence-based accounts] do not allow for rationality despite conflicting requirements". Some theorists suggest a weaker criterion of coherence to avoid cases of necessary irrationality: rationality requires not to obey all norms of coherence but to obey as many norms as possible. So in rational dilemmas, agents can still be rational if they violate the minimal number of rational requirements.<ref name="Heinzelmann2022"/> Another criticism rests on the claim that coherence-based accounts are either redundant or false. On this view, either the rules recommend the same option as the balance of reasons or a different option. If they recommend the same option, they are redundant. If they recommend a different option, they are false since, according to its critics, there is no special value in sticking to rules against the balance of reasons.<ref name="Mele2004a"/><ref name="McClennen2004"/>
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