Purity is the principle that fundamental facts only have fundamental constituents. In recent years, it has played a significant (if sometimes implicit) role in metaphysical theorizing. A philosopher will argue that a fact contains a derivative entity and cite Purity as a reason to deny that is fundamental. I argue that recent developments in higher order logic reveal a subtle ambiguity regarding the interpretation of Purity; there are stronger and weaker versions of that principle. Justifications for Purity support only the weaker interpretation, but arguments that rely upon it only succeed if the stronger interpretation holds. Consequently, nearly every metaphysician who has invoked Purity has made a mistake, in that their inferences are not justified by their arguments.
{"title":"Unstructured Purity","authors":"Samuel Z. Elgin","doi":"10.1111/nous.70029","DOIUrl":"https://doi.org/10.1111/nous.70029","url":null,"abstract":"Purity is the principle that fundamental facts only have fundamental constituents. In recent years, it has played a significant (if sometimes implicit) role in metaphysical theorizing. A philosopher will argue that a fact contains a derivative entity and cite Purity as a reason to deny that is fundamental. I argue that recent developments in higher order logic reveal a subtle ambiguity regarding the interpretation of Purity; there are stronger and weaker versions of that principle. Justifications for Purity support only the weaker interpretation, but arguments that rely upon it only succeed if the stronger interpretation holds. Consequently, nearly every metaphysician who has invoked Purity has made a mistake, in that their inferences are not justified by their arguments.","PeriodicalId":501006,"journal":{"name":"Noûs","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145920101","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}
Lukas Tank, Nils Wendler, Jan Peter Carstensen Mainka
In this paper, we introduce a new class of cases to the debate on rescue dilemmas and whether to save the greater number. We argue that situations involving both risk and overlap shine a new light on some of the most important issues within this discussion. First, they teach us that two of the most important lottery solutions to rescue dilemmas, Kamm's Proportional Lottery and Timmermann's Individualist Lottery, are not practically equivalent after all. Second, these cases show how Henning's recent Voting Solution does not consistently amount to saving the greater number, even if every person in need votes in their own self‐interest. Third, they illuminate the relation between Kamm's Proportional Lottery and a lottery based on voting. Finally, and most importantly, cases involving risk and overlap lay open that there are two different forms of aggregation at the heart of the debate: interpersonal aggregation in accordance with the will of the people and interpersonal aggregation against the will of the people. The latter seems much harder to defend than the former. To consistently save the greater number, or just give it a higher chance to be saved, one has to do the latter.
{"title":"Risk, Overlap, and Two Forms of Aggregation","authors":"Lukas Tank, Nils Wendler, Jan Peter Carstensen Mainka","doi":"10.1111/nous.70031","DOIUrl":"https://doi.org/10.1111/nous.70031","url":null,"abstract":"In this paper, we introduce a new class of cases to the debate on rescue dilemmas and whether to save the greater number. We argue that situations involving both risk and overlap shine a new light on some of the most important issues within this discussion. First, they teach us that two of the most important lottery solutions to rescue dilemmas, Kamm's Proportional Lottery and Timmermann's Individualist Lottery, are not practically equivalent after all. Second, these cases show how Henning's recent Voting Solution does not consistently amount to saving the greater number, even if every person in need votes in their own self‐interest. Third, they illuminate the relation between Kamm's Proportional Lottery and a lottery based on voting. Finally, and most importantly, cases involving risk and overlap lay open that there are two different forms of aggregation at the heart of the debate: interpersonal aggregation in accordance with the will of the people and interpersonal aggregation against the will of the people. The latter seems much harder to defend than the former. To consistently save the greater number, or just give it a higher chance to be saved, one has to do the latter.","PeriodicalId":501006,"journal":{"name":"Noûs","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2025-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145893637","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}
Transparency is the view that the deliberative question whether to believe P gives way to the question whether P. In this paper, I argue that transparency is false. I begin by teasing out two commitments of transparency: (i) the set of possible answers to the question whether to believe P is the same set of possible answers to the question whether P; (ii) the question whether to believe P can be settled on the basis of all and only those considerations on the basis of which the question whether P can be settled. Against (i), I argue that a distinct type of suspended judgment constitutes an answer to whether to believe P, but not whether P. Against (ii), I argue that the question whether to believe P, but not the question whether P, can be settled partly on the basis of considerations about which evidential standards to use.
{"title":"Believe It or Not: Transparency Is False","authors":"Conner Schultz","doi":"10.1111/nous.70025","DOIUrl":"https://doi.org/10.1111/nous.70025","url":null,"abstract":"Transparency is the view that the deliberative question whether to believe P gives way to the question whether P. In this paper, I argue that transparency is false. I begin by teasing out two commitments of transparency: (i) the set of possible answers to the question whether to believe P is the same set of possible answers to the question whether P; (ii) the question whether to believe P can be settled on the basis of all and only those considerations on the basis of which the question whether P can be settled. Against (i), I argue that a distinct type of suspended judgment constitutes an answer to whether to believe P, but not whether P. Against (ii), I argue that the question whether to believe P, but not the question whether P, can be settled partly on the basis of considerations about which evidential standards to use.","PeriodicalId":501006,"journal":{"name":"Noûs","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2025-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145829976","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 his Reply to Gaunilo , Anselm presented two additional arguments for the existence of God beyond those that appear in the Proslogion . In “The Logical Structure of Anselm's Argument,” Robert M. Adams isolates each. One, he develops into a modal ontological argument along the lines of other 20th century ontological arguments (e.g., those of Malcolm, Hartshorne, and Plantinga). The other he sets aside with the following remark: “[this argument] turns on the philosophy of time, not the philosophy of logic.” Now the argument's time has come. In this paper, I show the following: (i) this argument is valid in system K, and so requires fewer logical resources than other modal ontological arguments; (ii) its axiological premise is plausible, requiring only the judgment that a perfect being cannot begin to exist, and can be defended; (iii) its metaphysical premise follows from David Lewis's recombination approach to modal plenitude; (iv) unlike other modal ontological arguments, it requires as a premise only that a perfect being is possible, not that one is necessarily possible; and (v) while it avoids parodies and the charge of begging the question, it does face a symmetry counterargument, although one that is more complicated than standard symmetry objections.
{"title":"Anselm's Temporal‐Ontological Proof","authors":"Daniel Rubio","doi":"10.1111/nous.70028","DOIUrl":"https://doi.org/10.1111/nous.70028","url":null,"abstract":"In his <jats:italic>Reply to Gaunilo</jats:italic> , Anselm presented two additional arguments for the existence of God beyond those that appear in the <jats:italic>Proslogion</jats:italic> . In “The Logical Structure of Anselm's Argument,” Robert M. Adams isolates each. One, he develops into a modal ontological argument along the lines of other 20th century ontological arguments (e.g., those of Malcolm, Hartshorne, and Plantinga). The other he sets aside with the following remark: “[this argument] turns on the philosophy of time, not the philosophy of logic.” Now the argument's time has come. In this paper, I show the following: (i) this argument is valid in system K, and so requires fewer logical resources than other modal ontological arguments; (ii) its axiological premise is plausible, requiring only the judgment that a perfect being cannot begin to exist, and can be defended; (iii) its metaphysical premise follows from David Lewis's recombination approach to modal plenitude; (iv) unlike other modal ontological arguments, it requires as a premise only that a perfect being is possible, not that one is necessarily possible; and (v) while it avoids parodies and the charge of begging the question, it does face a symmetry counterargument, although one that is more complicated than standard symmetry objections.","PeriodicalId":501006,"journal":{"name":"Noûs","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2025-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145801034","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}
Roughly, the view I call “Additivism” sums up value across time and people. Given some standard assumptions, I show that Additivism follows from two principles. The first says that how lives align in time cannot, in itself, matter. The second says, roughly, that a world cannot be better unless it is better within some period or another. These principles, while plausible, presuppose a rich underlying structure of value—presuppositions that are implicit in the standard numerical framework of population ethics but that are often overlooked. A careful exploration of Additivism and the case for it reveals intricate connections between substantive questions about what value fundamentally consists in and structural questions about how to aggregate value.
{"title":"Aggregation and the Structure of Value","authors":"Weng Kin San","doi":"10.1111/nous.70026","DOIUrl":"https://doi.org/10.1111/nous.70026","url":null,"abstract":"Roughly, the view I call “Additivism” sums up value across time and people. Given some standard assumptions, I show that Additivism follows from two principles. The first says that how lives align in time cannot, in itself, matter. The second says, roughly, that a world cannot be better unless it is better within some period or another. These principles, while plausible, presuppose a rich underlying structure of value—presuppositions that are implicit in the standard numerical framework of population ethics but that are often overlooked. A careful exploration of Additivism and the case for it reveals intricate connections between substantive questions about what value fundamentally consists in and structural questions about how to aggregate value.","PeriodicalId":501006,"journal":{"name":"Noûs","volume":"34 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2025-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145704018","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}
It is a truism of mathematics that differences between isomorphic number systems are irrelevant to arithmetic. This truism is deeply rooted in the modern axiomatic method and underlies most strands of arithmetical structuralism, the view that arithmetic is about some abstract number structure. In this paper, I challenge this truism by showing that isomorphic systems can differ with regard to important computational features of numbers. This confronts arithmetical structuralists with a dilemma. On the one hand, many computability‐theoretic properties are only satisfied by particular number systems, and are hence disqualified as irrelevant by structuralist accounts. On the other hand, these properties turn out to be highly relevant to arithmetical practice. Hence, as I argue, arithmetical structuralism is not a tenable view about arithmetic.
{"title":"Structure and Computation","authors":"Balthasar Grabmayr","doi":"10.1111/nous.70023","DOIUrl":"https://doi.org/10.1111/nous.70023","url":null,"abstract":"It is a truism of mathematics that differences between isomorphic number systems are irrelevant to arithmetic. This truism is deeply rooted in the modern axiomatic method and underlies most strands of arithmetical structuralism, the view that arithmetic is about some abstract number structure. In this paper, I challenge this truism by showing that isomorphic systems can differ with regard to important computational features of numbers. This confronts arithmetical structuralists with a dilemma. On the one hand, many computability‐theoretic properties are only satisfied by particular number systems, and are hence disqualified as irrelevant by structuralist accounts. On the other hand, these properties turn out to be highly relevant to arithmetical practice. Hence, as I argue, arithmetical structuralism is not a tenable view about arithmetic.","PeriodicalId":501006,"journal":{"name":"Noûs","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2025-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145680250","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}
It is often taken for granted that right‐makers, that is, the things that make something—say, an action—right, do so by explaining why it is right. This view can be spelled out in terms of metaphysical ground: right‐making just is grounding of rightness facts. In this paper, I present three challenges to this view and argue that no purely ground‐based account of right‐making is fully satisfactory. Instead, I defend a novel version of a reasons‐based account, according to which right‐makers are grounds that ground in virtue of being a normative reason. This reasons‐based account, I shall argue, provides a unified solution to the challenges outlined and entails nuanced distinctions that alternative accounts brush aside. I show that my account is applicable to value‐making relations on the assumption that value is not prior to normative reasons. The discussion thus reveals a novel argument for buck‐passing accounts of value, that is, the view that value can be explained in terms of normative reasons.
{"title":"No Guide to Ground: Right‐Making and Right‐Makers","authors":"Singa Behrens","doi":"10.1111/nous.70027","DOIUrl":"https://doi.org/10.1111/nous.70027","url":null,"abstract":"It is often taken for granted that right‐makers, that is, the things that make something—say, an action—right, do so by explaining why it is right. This view can be spelled out in terms of metaphysical ground: right‐making just is grounding of rightness facts. In this paper, I present three challenges to this view and argue that no purely ground‐based account of right‐making is fully satisfactory. Instead, I defend a novel version of a reasons‐based account, according to which right‐makers are grounds that ground in virtue of being a normative reason. This reasons‐based account, I shall argue, provides a unified solution to the challenges outlined and entails nuanced distinctions that alternative accounts brush aside. I show that my account is applicable to value‐making relations on the assumption that value is not prior to normative reasons. The discussion thus reveals a novel argument for buck‐passing accounts of value, that is, the view that value can be explained in terms of normative reasons.","PeriodicalId":501006,"journal":{"name":"Noûs","volume":"36 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2025-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145680211","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}
Some hold that expected utility is too restrictive in the way it handles risk. Risk‐weighted expected utility is an alternative that allows decision‐makers to have a range of attitudes toward probabilistic risk. It holds that any attitude within this range is instrumentally rational, since these attitudes represent different, equally good, strategies for taking the means to one's ends. A different challenge to expected utility is that it is too restrictive in the way it handles ambiguity—it requires decision‐makers to have sharp probabilities—and risk‐weighted expected utility shares this restrictive feature. This paper presents a generalization of risk‐weighted expected utility which allows for ambiguity. It defends this theory as a theory of instrumental rationality, and argues that attitudes toward risk and attitudes toward ambiguity each represent different but important features of instrumental rationality.
{"title":"Taking Risks, With and Without Probabilities","authors":"Lara Buchak","doi":"10.1111/nous.70018","DOIUrl":"https://doi.org/10.1111/nous.70018","url":null,"abstract":"Some hold that expected utility is too restrictive in the way it handles risk. Risk‐weighted expected utility is an alternative that allows decision‐makers to have a range of attitudes toward probabilistic risk. It holds that any attitude within this range is instrumentally rational, since these attitudes represent different, equally good, strategies for taking the means to one's ends. A different challenge to expected utility is that it is too restrictive in the way it handles ambiguity—it requires decision‐makers to have sharp probabilities—and risk‐weighted expected utility shares this restrictive feature. This paper presents a generalization of risk‐weighted expected utility which allows for ambiguity. It defends this theory as a theory of instrumental rationality, and argues that attitudes toward risk and attitudes toward ambiguity each represent different but important features of instrumental rationality.","PeriodicalId":501006,"journal":{"name":"Noûs","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2025-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145553552","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}
How should we understand the duration of a pleasant or unpleasant sensation, insofar as its duration modulates how good or bad the experience is overall? Given that we seem able to distinguish between subjective and objective duration and that how well or badly someone's life goes is naturally thought of as something to be assessed from her own perspective, it seems intuitive that it is subjective duration that modulates how good or bad an experience is from the perspective of an individual's welfare. However, I argue that we know of no way to make sense of what subjective duration consists in on which this claim turns out to be plausible. Moreover, some plausible theories of what subjective duration consists in strongly suggest that subjective duration is irrelevant in itself.
{"title":"Welfare and Felt Duration","authors":"Andreas L. Mogensen","doi":"10.1111/nous.70022","DOIUrl":"https://doi.org/10.1111/nous.70022","url":null,"abstract":"How should we understand the duration of a pleasant or unpleasant sensation, insofar as its duration modulates how good or bad the experience is overall? Given that we seem able to distinguish between subjective and objective duration and that how well or badly someone's life goes is naturally thought of as something to be assessed from her own perspective, it seems intuitive that it is subjective duration that modulates how good or bad an experience is from the perspective of an individual's welfare. However, I argue that we know of no way to make sense of what subjective duration consists in on which this claim turns out to be plausible. Moreover, some plausible theories of what subjective duration consists in strongly suggest that subjective duration is irrelevant in itself.","PeriodicalId":501006,"journal":{"name":"Noûs","volume":"39 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2025-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145492491","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}
“Almost everyone,” Ronald Dworkin wrote in Sovereign Virtue , “assumes that democracy means equal voting power.” What, then, is voting power? The standard view defines it as the probability that a vote changes the outcome assuming that each possible combination of votes is equiprobable. This has significant implications: institutions like the US Electoral College give disproportionate voting power to voters in large states. But the standard view cannot be true. As an a priori account, it rests on the principle of indifference, and thus faces the problem of multiple partitions: we could assign an equal probability to each possible combination of votes or to each possible vote share. The choice to partition in terms of combinations of votes is arbitrary, and makes the standard view objectionably overconfident. These problems of arbitrariness and overconfidence undermine the standard view's main implications. And they call into question whether equal voting power should play a central role in democratic theory.
{"title":"What Voting Power Cannot Be","authors":"Daniel Wodak","doi":"10.1111/nous.70019","DOIUrl":"https://doi.org/10.1111/nous.70019","url":null,"abstract":"“Almost everyone,” Ronald Dworkin wrote in <jats:italic>Sovereign Virtue</jats:italic> , “assumes that democracy means equal voting power.” What, then, is voting power? The standard view defines it as the probability that a vote changes the outcome assuming that each possible combination of votes is equiprobable. This has significant implications: institutions like the US Electoral College give disproportionate voting power to voters in large states. But the standard view cannot be true. As an a priori account, it rests on the principle of indifference, and thus faces the problem of multiple partitions: we could assign an equal probability to each possible combination of votes <jats:italic>or</jats:italic> to each possible vote share. The choice to partition in terms of combinations of votes is arbitrary, and makes the standard view objectionably overconfident. These problems of arbitrariness and overconfidence undermine the standard view's main implications. And they call into question whether equal voting power should play a central role in democratic theory.","PeriodicalId":501006,"journal":{"name":"Noûs","volume":"78 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2025-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145441132","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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