Although understanding is the object of a growing literature in epistemology and the philosophy of science, only few studies have concerned understanding in mathematics. This essay offers an account of a fundamental form of mathematical understanding: proof understanding. The account builds on a simple idea, namely that understanding a proof amounts to rationally reconstructing its underlying plan. This characterization is fleshed out by specifying the relevant notion of plan and the associated process of rational reconstruction, building in part on Bratman's theory of planning agency. It is argued that the proposed account can explain a significant range of distinctive phenomena commonly associated with proof understanding by mathematicians and philosophers. It is further argued, on the basis of a case study, that the account can yield precise diagnostics of understanding failures and can suggest ways to overcome them. Reflecting on the approach developed here, the essay concludes with some remarks on how to shape a general methodology common to the study of mathematical and scientific understanding and focused on human agency.
{"title":"Understanding in mathematics: The case of mathematical proofs","authors":"Yacin Hamami, Rebecca Lea Morris","doi":"10.1111/nous.12489","DOIUrl":"https://doi.org/10.1111/nous.12489","url":null,"abstract":"Although understanding is the object of a growing literature in epistemology and the philosophy of science, only few studies have concerned understanding in mathematics. This essay offers an account of a fundamental form of mathematical understanding: proof understanding. The account builds on a simple idea, namely that understanding a proof amounts to rationally reconstructing its underlying plan. This characterization is fleshed out by specifying the relevant notion of plan and the associated process of rational reconstruction, building in part on Bratman's theory of planning agency. It is argued that the proposed account can explain a significant range of distinctive phenomena commonly associated with proof understanding by mathematicians and philosophers. It is further argued, on the basis of a case study, that the account can yield precise diagnostics of understanding failures and can suggest ways to overcome them. Reflecting on the approach developed here, the essay concludes with some remarks on how to shape a general methodology common to the study of mathematical and scientific understanding and focused on human agency.","PeriodicalId":501006,"journal":{"name":"Noûs","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140534126","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
According to orthodoxy, the most fundamental kind of causation involves one event causing another event. I argue against this event‐causal view. Instead, the most fundamental kind of causation is thing causation, which involves a thing causing a thing to do something. Event causation is reducible to thing causation, but thing causation is not reducible to event causation, because event causation cannot accommodate cases of fine‐grained causation. I defend my view from objections, including C. D. Broad's influential “timing” argument, and I conclude with implications for agent‐causal theories of free will.
根据正统观点，最基本的因果关系是一个事件引起另一个事件。我反对这种事件因果观点。相反，最基本的因果关系是事物因果关系，即一个事物导致一个事物做某事。事件因果关系可以还原为事物因果关系，但事物因果关系却不能还原为事件因果关系，因为事件因果关系无法容纳细粒度的因果关系。我将从反对意见中为我的观点辩护，其中包括布罗德（C. D. Broad）颇具影响力的 "时间 "论证。
{"title":"Thing causation","authors":"Nathaniel Baron‐Schmitt","doi":"10.1111/nous.12494","DOIUrl":"https://doi.org/10.1111/nous.12494","url":null,"abstract":"According to orthodoxy, the most fundamental kind of causation involves one event causing another event. I argue against this event‐causal view. Instead, the most fundamental kind of causation is thing causation, which involves a thing causing a thing to do something. Event causation is reducible to thing causation, but thing causation is not reducible to event causation, because event causation cannot accommodate cases of fine‐grained causation. I defend my view from objections, including C. D. Broad's influential “timing” argument, and I conclude with implications for agent‐causal theories of free will.","PeriodicalId":501006,"journal":{"name":"Noûs","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140196178","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Sceptical arguments in epistemology typically employ sceptical hypotheses, which are rivals to our everyday beliefs so constructed that they fit exactly the evidence on which those beliefs are based. There are two ways of using a sceptical hypothesis to undermine an everyday belief, giving rise to two distinct sorts of sceptical argument: underdetermination-based and closure-based. However, both sorts of argument, as usually formulated in the literature, fall foul of evidential holism, for they ignore the crucial role of background beliefs. An analogy with the philosophy of science makes this point explicit. There is no simple way to “holism proof” the two sceptical arguments.
{"title":"Scepticism, evidential holism and the logic of demonic deception","authors":"Samir Okasha","doi":"10.1111/nous.12490","DOIUrl":"https://doi.org/10.1111/nous.12490","url":null,"abstract":"Sceptical arguments in epistemology typically employ <i>sceptical hypotheses</i>, which are rivals to our everyday beliefs so constructed that they fit exactly the evidence on which those beliefs are based. There are two ways of using a sceptical hypothesis to undermine an everyday belief, giving rise to two distinct sorts of sceptical argument: underdetermination-based and closure-based. However, both sorts of argument, as usually formulated in the literature, fall foul of evidential holism, for they ignore the crucial role of background beliefs. An analogy with the philosophy of science makes this point explicit. There is no simple way to “holism proof” the two sceptical arguments.","PeriodicalId":501006,"journal":{"name":"Noûs","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139739648","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
I like the view that the fundamental facts are logically simple, not complex. However, some universal generalizations and negations may appear fundamental, because they cannot be explained by logically simple facts about particulars. I explore a natural reply: those universal generalizations and negations are true because certain logically simple facts—call them φφ—are the fundamental facts. I argue that this solution is only available given some metaphysical frameworks, some conceptions of metaphysical explanation and fundamentality. It requires a ‘fitting’ framework, according to which metaphysical theories explain the aptness of representations in terms of how things are fundamentally. Fitting frameworks conceive of the fundamental facts as those that are metaphysically ‘real’; call them the ‘facts-in-reality’. Moreover, we must take as primary a plural notion of the facts-in-reality, not the singular notion of a fact-in-reality. By contrast, a metaphysics that grounds facts is incompatible with my strategy for keeping the fundamental facts logically simple.
{"title":"The fundamental facts can be logically simple","authors":"Alexander Jackson","doi":"10.1111/nous.12487","DOIUrl":"https://doi.org/10.1111/nous.12487","url":null,"abstract":"I like the view that the fundamental facts are logically simple, not complex. However, some universal generalizations and negations may appear fundamental, because they cannot be explained by logically simple facts about particulars. I explore a natural reply: those universal generalizations and negations are true because certain logically simple facts—call them φφ—<i>are the fundamental facts</i>. I argue that this solution is only available given some metaphysical frameworks, some conceptions of metaphysical explanation and fundamentality. It requires a ‘fitting’ framework, according to which metaphysical theories explain the aptness of representations in terms of how things are fundamentally. Fitting frameworks conceive of the fundamental facts as those that are metaphysically ‘real’; call them the ‘facts-in-reality’. Moreover, we must take as primary a plural notion of the facts-in-reality, not the singular notion of a fact-in-reality. By contrast, a metaphysics that grounds facts is incompatible with my strategy for keeping the fundamental facts logically simple.","PeriodicalId":501006,"journal":{"name":"Noûs","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139489824","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
When policymakers craft rules for use by the general public, they must take into account the ways in which their rules are likely to be misapplied. Should contractualists and rule consequentialists do the same when they search for rules whose general acceptance would be non-rejectable or ideal? I argue that these theorists face a dilemma. If they ignore the possibility of misapplication, they end up with an unrealistic view that rejects rules designed to protect us from others’ mistakes. On the other hand, if they take misapplication into account, they end up rejecting rules that appeal to what really matters morally in favor of easier-to-apply proxies for these rules. This leaves them unable to say why certain wrong acts are wrong, which in turn may lead them to mistaken verdicts about moral worth and wronging. I show how this misapplication dilemma applies to standard contractualist and rule consequentialist theories, but also suggest how it might generalize to other two-level theories, including those designed to avoid the ideal world objection.
{"title":"The misapplication dilemma","authors":"Daniel Webber","doi":"10.1111/nous.12485","DOIUrl":"https://doi.org/10.1111/nous.12485","url":null,"abstract":"When policymakers craft rules for use by the general public, they must take into account the ways in which their rules are likely to be misapplied. Should contractualists and rule consequentialists do the same when they search for rules whose general acceptance would be non-rejectable or ideal? I argue that these theorists face a dilemma. If they ignore the possibility of misapplication, they end up with an unrealistic view that rejects rules designed to protect us from others’ mistakes. On the other hand, if they take misapplication into account, they end up rejecting rules that appeal to what really matters morally in favor of easier-to-apply proxies for these rules. This leaves them unable to say <i>why</i> certain wrong acts are wrong, which in turn may lead them to mistaken verdicts about moral worth and wronging. I show how this <i>misapplication dilemma</i> applies to standard contractualist and rule consequentialist theories, but also suggest how it might generalize to other two-level theories, including those designed to avoid the ideal world objection.","PeriodicalId":501006,"journal":{"name":"Noûs","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139061250","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
I defend the thesis that legal standards of proof are reducible to thresholds of probability. Many reject this thesis because it appears to permit finding defendants liable solely on the basis of statistical evidence. To the contrary, I argue – by combining Thomson's (1986) causal analysis of legal evidence with formal methods of causal inference – that legal standards of proof can be reduced to probabilities, but that deriving these probabilities involves more than just statistics.
{"title":"Just probabilities","authors":"Chad Lee-Stronach","doi":"10.1111/nous.12486","DOIUrl":"https://doi.org/10.1111/nous.12486","url":null,"abstract":"I defend the thesis that legal standards of proof are reducible to thresholds of probability. Many reject this thesis because it appears to permit finding defendants liable solely on the basis of statistical evidence. To the contrary, I argue – by combining Thomson's (1986) causal analysis of legal evidence with formal methods of causal inference – that legal standards of proof can be reduced to probabilities, but that deriving these probabilities involves more than just statistics.","PeriodicalId":501006,"journal":{"name":"Noûs","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138823268","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In “Trusting Moral Intuitions” we argued that moral intuitions are trustworthy due to their being the outputs of a cognitive practice, with social elements, in good working order. Backes, Eklund, and Michelson present several criticisms of our defense of a socially conscious moral intuitionism. We respond to these criticisms, defending our claim that social factors enhance the epistemic credentials of moral intuitions, answering worries pertaining to the reliability of the moral intuition practice, and addressing concerns about both the individuation of this practice and the good conditions for its implementation.
{"title":"Socially conscious moral intuitionism","authors":"John Bengson, Terence Cuneo, Russ Shafer-Landau","doi":"10.1111/nous.12445","DOIUrl":"https://doi.org/10.1111/nous.12445","url":null,"abstract":"In “Trusting Moral Intuitions” we argued that moral intuitions are trustworthy due to their being the outputs of a cognitive practice, with social elements, in good working order. Backes, Eklund, and Michelson present several criticisms of our defense of a socially conscious moral intuitionism. We respond to these criticisms, defending our claim that social factors enhance the epistemic credentials of moral intuitions, answering worries pertaining to the reliability of the moral intuition practice, and addressing concerns about both the individuation of this practice and the good conditions for its implementation.","PeriodicalId":501006,"journal":{"name":"Noûs","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138559398","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Quasi-realists are expressivists who say much of what realists say. To avoid making their view indistinguishable from realism, however, they usually stop short of saying everything realists say. Many realists therefore think that something important is missing from quasi-realism. I argue that quasi-realists can undermine this thought by defending a version of quasi-realism that I call super-quasi-realism. This version seems indistinguishable from realism, but I argue that this is a mistaken impression that arises because we cannot believe super-quasi-realism.
{"title":"Superspreading the word","authors":"Bart Streumer","doi":"10.1111/nous.12484","DOIUrl":"https://doi.org/10.1111/nous.12484","url":null,"abstract":"Quasi-realists are expressivists who say much of what realists say. To avoid making their view indistinguishable from realism, however, they usually stop short of saying everything realists say. Many realists therefore think that something important is missing from quasi-realism. I argue that quasi-realists can undermine this thought by defending a version of quasi-realism that I call <i>super-quasi-realism</i>. This version seems indistinguishable from realism, but I argue that this is a mistaken impression that arises because we cannot believe super-quasi-realism.","PeriodicalId":501006,"journal":{"name":"Noûs","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138481443","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
What is praise? I argue that we can make progress by examining what praise does. Functionalist views of praise are emerging, but I here argue that by foregrounding cases in which expressions of praise are rejected by their direct target, we see that praise has a wider, and largely overlooked, social function. I introduce cases in which praise is rejected, and develop a functionalist account of praise that is well placed to make sense of the contours of these cases. My claim is that praise functions to affirm and entrench values, exerting pressure in praise's audiences to affirm the values expressed. I show how my account overcomes some of the limitations of recently developed accounts of praise.
{"title":"Proleptic praise: A social function analysis","authors":"Jules Holroyd","doi":"10.1111/nous.12482","DOIUrl":"https://doi.org/10.1111/nous.12482","url":null,"abstract":"What is praise? I argue that we can make progress by examining what praise does. Functionalist views of praise are emerging, but I here argue that by foregrounding cases in which expressions of praise are rejected by their direct target, we see that praise has a wider, and largely overlooked, social function. I introduce cases in which praise is rejected, and develop a functionalist account of praise that is well placed to make sense of the contours of these cases. My claim is that praise functions to affirm and entrench values, exerting pressure in praise's audiences to affirm the values expressed. I show how my account overcomes some of the limitations of recently developed accounts of praise.","PeriodicalId":501006,"journal":{"name":"Noûs","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138455935","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Relationalism maintains that mind-independent objects are essential constituents of veridical perceptual experiences. According to the argument from hallucination, relationalism is undermined by perfect hallucinations, experiences that are introspectively indistinguishable from veridical perceptual experiences but lack an object. Recently, a new wave of relationalists have responded by questioning whether perfect hallucinations are possible: what seem to be perfect hallucinations may really be something else, such as illusions, veridical experiences of non-obvious objects, or experiences that are not genuinely possible. This paper argues that however well new wave relationalism may handle brains in vats, drug users “seeing” pink elephants, and other extraordinary hallucinations, it struggles to accommodate mundane hallucinations, such as “hearing” your child cry out from the room down the hall when she is actually sound asleep or “feeling” vibrations on your thigh even when your phone isn't in your pocket. Mundane hallucinations are best explained as byproducts of noise in the perceptual system, and noise-induced hallucinations are resistant to the strategies that new wave relationalists deploy to explain away other hallucinations. Mundane hallucinations can thus underpin an especially powerful version of the argument from hallucination.
{"title":"Mundane hallucinations and new wave relationalism","authors":"Jacob Beck","doi":"10.1111/nous.12406","DOIUrl":"https://doi.org/10.1111/nous.12406","url":null,"abstract":"Relationalism maintains that mind-independent objects are essential constituents of veridical perceptual experiences. According to the argument from hallucination, relationalism is undermined by perfect hallucinations, experiences that are introspectively indistinguishable from veridical perceptual experiences but lack an object. Recently, a new wave of relationalists have responded by questioning whether perfect hallucinations are possible: what seem to be perfect hallucinations may really be something else, such as illusions, veridical experiences of non-obvious objects, or experiences that are not genuinely possible. This paper argues that however well new wave relationalism may handle brains in vats, drug users “seeing” pink elephants, and other extraordinary hallucinations, it struggles to accommodate mundane hallucinations, such as “hearing” your child cry out from the room down the hall when she is actually sound asleep or “feeling” vibrations on your thigh even when your phone isn't in your pocket. Mundane hallucinations are best explained as byproducts of noise in the perceptual system, and noise-induced hallucinations are resistant to the strategies that new wave relationalists deploy to explain away other hallucinations. Mundane hallucinations can thus underpin an especially powerful version of the argument from hallucination.","PeriodicalId":501006,"journal":{"name":"Noûs","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138554274","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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