Every year, the Vietnamese people reportedly burned about 50,000 tons of joss papers, which took the form of not only bank notes, but iPhones, cars, clothes, even housekeepers, in hope of pleasing the dead. The practice was mistakenly attributed to traditional Buddhist teachings but originated in fact from China, which most Vietnamese were not aware of. In other aspects of life, there were many similar examples of Vietnamese so ready and comfortable with adding new norms, values, and beliefs, even contradictory (...) ones, to their culture. This phenomenon, dubbed “cultural additivity”, prompted us to study the co-existence, interaction, and influences among core values and norms of the Three Teachings –Confucianism, Buddhism, and Taoism–as shown through Vietnamese folktales. By applying Bayesian logistic regression, we evaluated the possibility of whether the key message of a story was dominated by a religion (dependent variables), as affected by the appearance of values and anti-values pertaining to the Three Teachings in the story (independent variables). Our main findings included the existence of the cultural additivity of Confucian and Taoist values. More specifically, empirical results showed that the interaction or addition of the values of Taoism and Confucianism in folktales together helped predict whether the key message of a story was about Confucianism, β{VT ⋅ VC} = 0.86. Meanwhile, there was no such statistical tendency for Buddhism. The results lead to a number of important implications. First, this showed the dominance of Confucianism because the fact that Confucian and Taoist values appeared together in a story led to the story’s key message dominated by Confucianism. Thus, it presented the evidence of Confucian dominance and against liberal interpretations of the concept of the Common Roots of Three Religions (“tam giáo đồng nguyên”) as religious unification or unicity. Second, the concept of “cultural additivity” could help explain many interesting socio-cultural phenomena, namely the absence of religious intolerance and extremism in the Vietnamese society, outrageous cases of sophistry in education, the low productivity in creative endeavors like science and technology, the misleading branding strategy in business. We are aware that our results are only preliminary and more studies, both theoretical and empirical, must be carried out to give a full account of the explanatory reach of “cultural additivity”. (shrink)

This paper addresses the issue of finite versus countable additivity in Bayesian probability and decision theory -- in particular, Savage's theory of subjective expected utility and personal probability. I show that Savage's reason for not requiring countable additivity in his theory is inconclusive. The assessment leads to an analysis of various highly idealised assumptions commonly adopted in Bayesian theory, where I argue that a healthy dose of, what I call, conceptual realism is often helpful in understanding the interpretational value of (...) sophisticated mathematical structures employed in applied sciences like decision theory. In the last part, I introduce countable additivity into Savage's theory and explore some technical properties in relation to other axioms of the system. (shrink)

De Finetti would claim that we can make sense of a draw in which each positive integer has equal probability of winning. This requires a uniform probability distribution over the natural numbers, violating countable additivity. Countable additivity thus appears not to be a fundamental constraint on subjective probability. It does, however, seem mandated by Dutch Book arguments similar to those that support the other axioms of the probability calculus as compulsory for subjective interpretations. These two lines of reasoning can be (...) reconciled through a slight generalization of the Dutch Book framework. Countable additivity may indeed be abandoned for de Finetti's lottery, but this poses no serious threat to its adoption in most applications of subjective probability. Introduction The de Finetti lottery Two objections to equiprobability 3.1 The ‘No random mechanism’ argument 3.2 The Dutch Book argument Equiprobability and relative betting quotients The re-labelling paradox 5.1 The paradox 5.2 Resolution: from symmetry to relative probability Beyond the de Finetti lottery. (shrink)

Through the lens of the informational entropy-based notion of value, I attempt to provide explanations for the aspects of cultural additivity that I could not explain previously: the additivity limit and the drawbacks of cultural additivity.

The additive presupposition of particles like "too"/"even" is uncontested, but usually stipulated. This paper proposes to derive it based on two properties. (i) "too"/"even" is cross-linguistically focus-sensitive, and (ii) in many languages, "too"/"even" builds negative polarity items and free-choice items as well, often in concert with other particles. (i) is the source of its existential presupposition, and (ii) offers clues regarding how additivity comes about. (i)-(ii) together demand a sparse semantics for "too/even," one that can work with different kinds (...) of alternatives (focus, subdomain, scalar) and invoke suitably different further operators. (shrink)

How can we resist the repugnant conclusion? James Griffin has plausibly suggested that part way through the sequence we may reach a world—let us call it “J”—in which the lives are lexically superior to those that follow. If it would be preferable to live a single life in J than through any number of lives in the next one, then it would be strange to judge K the better world. Instead, we may reasonably “suspend addition” and judge J superior, as (...) if aggregating the lives in the larger world intrapersonally. I argue that the addition of new people with separate preferences renders this inference illicit when comparing J+ and K. When one pairwise comparison suspends addition and the other does not, the result is an intransitive value judgement: J < J+ < K < J, producing the mere addition paradox. (shrink)

“Cultural Additivity” is the concept proposed by Vuong et al. to demonstrate the interactions of various cultural values in a society. However, there have been multiple concepts discussing the interaction between different cultural values, such as Hybridization/Hybridity, Creolization, Syncretism, etc. So, how can we distinguish cultural additivity from other concepts, which may sound similar? In this essay, we propose a diagram for doing such a task .

This article develops an axiom system to justify an additive representation for a preference relation ${\succsim}$ on the product ${\prod_{i=1}^{n}A_{i}}$ of extensive structures. The axiom system is basically similar to the n-component (n ≥ 3) additive conjoint structure, but the independence axiom is weakened in the system. That is, the axiom exclusively requires the independence of the order for each of single factors from fixed levels of the other factors. The introduction of a concatenation operation on each factor (...) A i makes it possible to yield a special type of restricted solvability, i.e., additive solvability and the usual cancellation on ${\prod_{i=1}^{n}A_{i}}$ . In addition, the assumption of continuity and completeness for A i implies a stronger type of solvability on A i . The additive solvability, cancellation, and stronger solvability axioms allow the weakened independence to be effective enough in constructing the additive representation. (shrink)

I present a new argument for the repugnant conclusion. The core of the argument is a risky, intrapersonal analogue of the mere addition paradox. The argument is important for three reasons. First, some solutions to Parfit’s original puzzle do not obviously generalize to the intrapersonal puzzle in a plausible way. Second, it raises independently important questions about how to make decisions under uncertainty for the sake of people whose existence might depend on what we do. And, third, it suggests various (...) difficulties for leading views about the value of a person’s life compared to her nonexistence. (shrink)

In this essay, I argue the manifestations of social harmony in Confucian societies can be studied quantitatively using the "cultural additivity" framework and phenomenologically using the "mindsponge" model.

Accuracy arguments for the core tenets of Bayesian epistemology differ mainly in the conditions they place on the legitimate ways of measuring the inaccuracy of our credences. The best existing arguments rely on three conditions: Continuity, Additivity, and Strict Propriety. In this paper, I show how to strengthen the arguments based on these conditions by showing that the central mathematical theorem on which each depends goes through without assuming Additivity.

The shape of a life hypothesis holds that the temporal sequence of good or bad times in a life can itself be a valuable feature of that life. This is generally thought to be incompatible with additivism about lifetime well-being, which holds that lifetime well-being is fully determined by momentary well-being. This paper examines Dale Dorsey’s recent argument that these views are in fact compatible. I argue that accepting the conjunction of these views requires stronger commitments than Dorsey recognizes. After (...) arguing that these commitments are problematic, I conclude that we should reject the compatibility claim. (shrink)

In this essay, I discuss the assumption that the environmental resource abundance can determine the level of cultural additivity.

This paper presents a dilemma for the additive model of reasons. Either the model accommodates disjunctive cases in which one ought to perform some act $$\phi $$ just in case at least one of two factors obtains, or it accommodates conjunctive cases in which one ought to $$\phi $$ just in case both of two factors obtains. The dilemma also arises in a revised additive model that accommodates imprecisely weighted reasons. There exist disjunctive and conjunctive cases. Hence the (...) additive model is extensionally inadequate. The upshot of the dilemma is that one of the most influential accounts of how reasons accrue to determine what we ought to do is flawed. (shrink)

The quantitative argument against the notion of a best possible world claims that, no matter how many worthwhile lives a world contains, another world contains more and is, other things being equal, better. Parfit’s ‘ Mere Addition Paradox ’ suggests that defenders of this argument must accept his ‘ Repugnant Conclusion ’ : that outcomes containing billions upon billions of lives barely worth living are better than outcomes containing fewer lives of higher quality. Several responses to the Paradox are discussed (...) and rejected as either inadequate or unavailable in a theistic context. The quantitative argument fails if some world is such that addition to it is not possible, i.e., if it is intensively infinite, as Liebniz claimed. If the notion of such a world is incoherent, then no world is quantitatively best and the quantitative argument succeeds, but only at the cost of embracing the Repugnant Conclusion. (shrink)

In situations where we ignore everything but the space of possibilities, we ought to suspend judgment—that is, remain agnostic—about which of these possibilities is the case. This means that we cannot sum our degrees of belief in different possibilities, something that has been formalized as an axiom of non-additivity. Consistent with this way of representing our ignorance, I defend a doxastic norm that recommends that we should nevertheless follow a certain additivity of possibilities: even if we cannot sum degrees of (...) belief in different possibilities, we should be more confident in larger groups of possibilities. It is thus shown that, in the type of situation considered (in so-called ‘classical ignorance’, i.e. “behind a thin veil of ignorance”), it is epistemically rational for advocates of suspending judgment to endorse this comparative confidence; while on the other hand it is shown that, even in classical ignorance, no stronger belief—such as a precise uniform probability distribution—is warranted. (shrink)

One method for uncovering the subprocesses of mental processes is the “Additive Factors Method” (AFM). The AFM uses reaction time data from factorial experiments to infer the presence of separate processing stages. This paper investigates the conceptual status of the AFM. It argues that one of the AFM’s underlying assumptions is problematic in light of recent developments in cognitive neuroscience. Discussion begins by laying out the basic logic of the AFM, followed by an analysis of the challenge presented by (...) neural reuse. Following this, implications are analysed and avenues of response considered. (shrink)

This week, the Royal Swedish Academy of Sciences announced the names of Nobel laureates in different fields. This year, the Nobel Prize in Biomedical Sciences was awarded to Swedish geneticist Svante Paabo for his discoveries concerning the DNA sequence of apes and human evolution. His work is especially meaningful as the question of human origin has long been a major concern to mankind. Modern-day wise humans belong to the genus Homo sapiens, along with seven ancient human races that existed millions (...) of years ago. Over time, many species became extinct and Professor Paabo discovered the gene transfer of these extinct species to Homo sapiens. With this discovery, he laid the foundation for other scientists to continue to search for the origin of modern humans. (shrink)

Economic policy evaluations require social welfare functions for variable-size populations. Two important candidates are critical-level generalized utilitarianism (CLGU) and rank-discounted critical-level generalized utilitarianism, which was recently characterized by Asheim and Zuber (2014) (AZ). AZ introduce a novel axiom, existence of egalitarian equivalence (EEE). First, we show that, under some uncontroversial criteria for a plausible social welfare relation, EEE suffices to rule out the Repugnant Conclusion of population ethics (without AZ’s other novel axioms). Second, we provide a new characterization of CLGU: (...) AZ’s set of axioms is equivalent to CLGU when EEE is replaced by the axiom same-number independence. (shrink)

Fibers have the characteristics to enhance the endurance of concrete. One of them is carbon fiber. These carbon fibers have superb mechanical properties and maybe utilized more effectively. This study is focused towards analyzing the variation in strength of carbon fiber concrete at variable fiber contents and to establish it with that of conventional concrete. The mechanical properties analyzed are compressive strength, split tensile strength, flexural strength of carbon fiber concrete at (0%, 0.25%, 0.5%, 0.75%, 1%, 1.25%) percentages by volume (...) of concrete. Result data clearly shows percentage increase in compressive strength, split tensile strength and flexural strength for M25 grade of concrete in 7 days and 28 days with respect to the variation in % addition of carbon fibers. Maximum increase in strength was achieved at 1% addition of fiber content and it can be considered as optimum dosage. (shrink)

This chapter will amount to a detailed exposition and exploration of one of the most prominent arguments against the existence of an unsurpassable world: the argument from addition. Endorsed by a variety of thinkers such as St. Thomas Aquinas, Alvin Plantinga, and William Rowe, the argument from addition uses the possibility of adding good things to a candidate unsurpassable world to argue that every world is surpassable. While widely endorsed, the argument has come under recent criticism. By carefully working through (...) a targeted version of the argument, I set out to establish the following: (i) that a world can always contain more good things; (ii) that a suitably restricted additive aggregation principle allows us to say that adding more good things in a certain way is an improvement, and (iii) that objections to the argument from widespread value incomparability fail. (shrink)

From the point of view of a theorist in ethics, the interest in public policy usually centres on the policy outcomes. But this point of view does not take much account of the roles and practices through which public policies are enacted. What additional ethical focuses for the policy agent might these entail? I outline four features of policy making, centred on the agent's performance of their role in the process, that raise ethical issues. These features are: the nature of (...) the policy process; the definition of the public; the treatment of policy agents; and accounting for public policy decisions. Brief examples are used to illustrate the nature of the issues and support the conclusion that these present additional ethical focuses for agents in public policy roles. (shrink)

Craig (1981) presents and defends several different kalam cosmological arguments. The core of each of these arguments is the following ur argument.

Even-like particles have widely been analyzed as inducing scalar and additive presuppositions (cf. Horn 1969; Karttunen & Peters 1979; Rooth 1992; Gast & van der Auwera 2011). However, the additivity of even has been controversial since at least Horn 1992 and increasingly called into question (see Greenberg & Umbach 2021 for references); Greenberg specifically argues that scalar even-like particles can vary in additivity. This claim is surprising in light of the typological study in Gast & van der Auwera 2011, (...) which subsumes even and similar expressions under a larger class of additive particles. Against this background, we present an analysis of Italian addirittura, which with perfino has been described as scalar-additive (Visconti 2005) – but only optionally so – and is chosen preferentially over perfino precisely in those contexts that Greenberg takes to challenge the additivity of even. We argue, drawing on observations in Atayan 2017, that addirittura contrasts with perfino in deriving its scalar alternatives from rhetorical structure rather than focus structure. Once this is recognized we can view addirittura as additive, after all, in a rhetorical sense we describe below. (shrink)

One guide to an argument's significance is the number and variety of refutations it attracts. By this measure, the Dutch book argument has considerable importance.2 Of course this measure alone is not a sure guide to locating arguments deserving of our attention—if a decisive refutation has really been given, we are better off pursuing other topics. But the presence of many and varied counterarguments at least suggests that either the refutations are controversial, or that their target admits of more than (...) one interpretation, or both. The main point of this paper is to focus on a way of understanding the Dutch Book argument (DBA) that avoids many of the well-known criticisms, and to consider how it fares against an important criticism that still remains: the objection that the DBA presupposes value-independence of bets. (shrink)

The Levelling-Down Objection is a standard objection to monistic egalitarian theories where equality is the only thing that has intrinsic value. Most egalitarians, however, are value pluralists; they hold that, in addition to equality being intrinsically valuable, the egalitarian currency in which we are equal or unequal is also intrinsically valuable. In this paper, I shall argue that the Levelling-Down Objection still minimizes the weight that the intrinsic badness of inequality could have in the overall intrinsic evaluation of outcomes, given (...) a certain way of measuring the badness of inequality, namely, the Additive Individual-Complaints Measure. (shrink)

According to the Desire-Based Reasons Model reasons for action are provided by desires. Many, however, are critical about the Model holding an alternative view of practical reason, which is often called valued-based. In this paper I consider one particular attempt to refute the Model, which advocates of the valued-based view often appeal to: the idea of reason-based desires. The argument is built up from two premises. The first claims that desires are states that we have reason to have. The second (...) argues that desires do not add to the stock of reasons the agent has for having them. Together the two theses entail that desires are based on reasons, which they transmit but to which they cannot add. In the paper I deal with a counterexample to the second premise: tie-breaking desires. I first distinguish two interesting cases and argue that only the second challenges the premise. Then I move onto analyze this challenge by focusing on Ruth Chang’s recent employment of it. I show that contrary to its counterintuitive appearance, the challenge can be sustained. However, I also argue that Chang overlooks the full potential of one particular response to the challenge: the introduction of higher-order reasons determining the normative significance of these desires. At the same time, I show that this response has a problem that Chang does not consider. As a result, the response can only partially disarm the challenge of tie-breaking desires; or not at all, depending on what significance we attribute to the counterexamples. (shrink)

The Successive Addition Argument (SAA) is one of the key arguments espoused by William Lane Craig for the thesis that the universe began to exist. Recently, Malpass, Mind, 131(523), 786–804 (2021) has developed a challenge to the SAA by way of constructing a counterexample that originates in the work of Fred Dretske. In this paper, I show that the Malpass-Dretske counterexample is in fact no counterexample to the argument. Utilizing a distinction between properties of members and properties of collections, I (...) argue that Malpass’ counterexample has no bearing on the soundness of the SAA. I also develop a novel parity argument against Malpass’ argument that I demonstrate can only be resolved by way of the aforementioned analysis. (shrink)

The present article is the third part of a trilogy of papers, devoted to analysing the influence of semantic Platonism on contemporary philosophy of language. In Part I (Picazo 2021), the discussion was set out by examining a number of typical traces of Platonism in semantic theory since Frege. In Part II (Picazo 2021a), additional illustrations of such traces were provided, taken from a collection of recent commissioned essays on the philosophy of language (Schantz 2012). The present part is devoted (...) to providing yet additional illustrations of such traces, taken from a collection of classic essays on the subject: the book Modern Philosophy of Language, edited by Maria Baghramian in 1998. We shall, thus, describe a number of examples in which the influence of semantic Platonism on these essays can be felt. Prominent among these examples are the confusion between sentences and propositions (and related confusions), the avoidant attitude with respect to basic aspects of linguistic meaning, the overuse of analytic methodology for semantic research, the adoption of a background Platonic metaphysics of meanings and the overreaction against semantic Platonism and germane views, witnessing an inverse influence (‘by opposition’) from these views. (shrink)

The manufacturing industry is evolving rapidly, becoming more complex, more interconnected, and more geographically distributed. Competitive pressure and diversity of consumer demand are driving manufacturing companies to rely more and more on improved knowledge management practices. As a result, multiple software systems are being created to support the integration of data across the product life cycle. Unfortunately, these systems manifest a low degree of interoperability, and this creates problems, for instance when different enterprises or different branches of an enterprise interact. (...) Common ontologies (consensus-based controlled vocabularies) have proved themselves in various domains as a valuable tool for solving such problems. In this paper, we present a consensus-based Additive Manufacturing Ontology (AMO) and illustrate its application in promoting re-usability in the field of dentistry product manufacturing. (shrink)

In 2001 the Indonesian government agreed to the introduction in the Indonesian Papua of regional, consociational elements of power-sharing, despite the fact that the dominant model of this system in Indonesia is centripetalism. The so-called special autonomy for the Indonesian Papua has never been fully implemented, however. The article seeks to test the thesis that the Indonesian authorities' institution of consociational arrangements for Papua, and their subsequent failure to fully implement those arrangements, were, in fact, tactical moves serving to reduce (...) the threat arising from growing pro-independence aspirations among the Papuans and to firmly attach Papuan territory to Indonesia. This article has been published in "Hemispheres" 2016, Vol. 31, No. 4, pp. 5-20. (shrink)

In free speech theory ‘speech’ has to be defined as a special term of art. I argue that much free speech discourse comes with a tacit commitment to a ‘Subtractive Approach’ to defining speech. As an initial default, all communicative acts are assumed to qualify as speech, before exceptions are made to ‘subtract’ those acts that don’t warrant the special legal protections owed to ‘speech’. I examine how different versions of the Subtractive Approach operate, and criticise them in terms of (...) their ability to yield a substantive definition of speech which covers all and only those forms of communicative action that – so our arguments for free speech indicate – really do merit special legal protection. In exploring alternative definitional approaches, I argue that what ultimately compromises definitional adequacy in this arena is a theoretical commitment to the significance of a single unified class of privileged communicative acts. I then propose an approach to free speech theory that eschews this theoretical commitment. (shrink)

The present research investigated the relationship between meaning perceptions and the structure of counterfactual thoughts. In Study 1, participants reflected on how turning points in their lives could have turned out otherwise. Those who were instructed to engage in subtractive (e.g., If only I had not done X...”) counterfactual thinking (SCT) about those turning points subsequently reported higher meaning perceptions than did those who engaged in additive (e.g., ‘If only I had done X...’) counterfactual thinking (ACT). In Study 2, (...) participants who reflected upon life events from the perspective of understanding the past (versus preparing for the future) tended to engage in more SCT than ACT. Finally, in Study 3, participants engaged in more SCT than ACT about life events whose meaning was perceived as certain (as opposed to uncertain) – presumably to maintain their pre-existing sense of meaning. Implications for the study of counterfactual thinking and meaning are discussed. (shrink)

Some 14 months after the official publication of our joint study on ‘cultural additivity’ [1], a question has become larger, and left unanswered. The title of this short piece reflects that question, that is, “is it possible for us to investigate a hypothetical relationship between the working of mindsponge process and the cultural additivity phenomenon?”.

This is the English translation (with a brief introduction and relatively detailed commentary) of a long excerpt from Mikhail Bakhtin's notes titled "Additions and changes to Rabelais", written in the mid-1940s with reworking his then unpublished manuscript on François Rabelais in mind. This excerpt is most notable for being the only extant text in which Bakhtin discusses and analyses Shakespear's tragedies at relative length—a discussion interesting not only as a reading of Shakespeare, but also as an unusual and revealing example (...) of Bakhtin's thought. In addition to Shakespeare, the text deals briefly with Dostoevsky's novels and with Goethe's Faust, as well as with several themes Bakhtin develops in his better-known works, such as Menippean satire, seriousness, and laughter. (shrink)

based on organic materials can be mechanically exible to a large extent because of the loose intermolecular bonds in the nano-electrons created from them. Unlike these organic materials, minerals such as silicon, germanium, and gallium arsenide can be used in the structure of electronic devices only in crystalline states, and in this case, covalent bonds make exibility impossible in them. Makes. Properties such as strength, exibility, electrical conductivity, magnetic properties, color, reactivity, etc. Starting to change the properties of the material (...) by shrinking it depends more than anything on the type of material and the desired property. For example, by reducing the dimensions of a material, generally some mechanical properties of the material such as strength are improved. This increase in strength does not happen only in the range of a few nanometers, and the strength of materials of several tens and even hundreds of nanometers may be much higher than the large-scale mass material. On the other hand, the change of some properties such as color and magnetic properties may occur in dimensions of only a few nanometers. (shrink)

ABSTRACT Objective: In the bulk of literature on critical thinking, the influence of interest on cognitive and affective processes of individuals has always been a source of debate and disagreement; a reciprocal relationship to be detrimental or facilitative in the development and enhancement of critical thinking as a skill. The present paper aims at explaining and resolving the observed discrepancy, with the combination of a comparative (agreement method) and a (descriptive-analytical). Method: method, on the additive and regressive effect of (...) “interest” on critical thinking-product from the viewpoint of Islamic Traditions. Finding: The finding shows that although interest, as a human tendency, generally has a positive effect on critical thinking, in some cases, the same component prevents seeing the shortcomings and defects as well. Therefore, in critical thinking, which requires more judgment and evaluation in order to promote it, one must control the interest in the subject in order to form a critical view of the issue properly. Based on the results, it is suggested that more attention should be paid to the regressive role of interest in critical thinking, especially in the cognitive and metacognitive understanding of the mental structure of thinking. Accordingly, an updated and systematic rereading of religious doctrines is one of the necessities of the conscious life in the third millennium, especially when the effective and productive approach to psychological components is more and more needed for today's life. Conclusion: Also, it is strongly suggested that the insights driven by Islamic traditions especially those that tap upon the issues on psychology are diverse and rich, providing a cultivated and rich ground for an understanding of human cognition and mind. (shrink)

It is quite strange to see Eugenics’s vitality in China, where Confucianism is deep-rooted in the people’s beliefs, influencing their thinking and behaviors.

In this paper I argue for an association between impurity and explanatory power in contemporary mathematics. This proposal is defended against the ancient and influential idea that purity and explanation go hand-in-hand (Aristotle, Bolzano) and recent suggestions that purity/impurity ascriptions and explanatory power are more or less distinct (Section 1). This is done by analyzing a central and deep result of additive number theory, Szemerédi’s theorem, and various of its proofs (Section 2). In particular, I focus upon the radically (...) impure (ergodic) proof due to Furstenberg (Section 3). Furstenberg’s ergodic proof is striking because it utilizes intuitively foreign and infinitary resources to prove a finitary combinatorial result and does so in a perspicuous fashion. I claim that Furstenberg’s proof is explanatory in light of its clear expression of a crucial structural result, which provides the “reason why” Szemerédi’s theorem is true. This is, however, rather surprising: how can such intuitively different conceptual resources “get a grip on” the theorem to be proved? I account for this phenomenon by articulating a new construal of the content of a mathematical statement, which I call structural content (Section 4). I argue that the availability of structural content saves intuitive epistemic distinctions made in mathematical practice and simultaneously explicates the intervention of surprising and explanatorily rich conceptual resources. Structural content also disarms general arguments for thinking that impurity and explanatory power might come apart. Finally, I sketch a proposal that, once structural content is in hand, impure resources lead to explanatory proofs via suitably understood varieties of simplification and unification (Section 5). (shrink)

We present a new frame semantics for positive relevant and substructural propositional logics. This frame semantics is both a generalisation of Routley–Meyer ternary frames and a simplification of them. The key innovation of this semantics is the use of a single accessibility relation to relate collections of points to points. Different logics are modeled by varying the kinds of collections used: they can be sets, multisets, lists or trees. We show that collection frames on trees are sound and complete for (...) the basic positive distributive substructural logic $\mathsf {B}^+$, that collection frames on multisets are sound and complete for $\mathsf {RW}^+$ (the relevant logic $\mathsf {R}^+$, without contraction, or equivalently, positive multiplicative and additive linear logic with distribution for the additive connectives), and that collection frames on sets are sound for the positive relevant logic $\mathsf {R}^+$. The completeness of set frames for $\mathsf {R}^+$ is, currently, an open question. (shrink)

If the laws of nature are as the Humean believes, it is an unexplained cosmic coincidence that the actual Humean mosaic is as extremely regular as it is. This is a strong and well-known objection to the Humean account of laws. Yet, as reasonable as this objection may seem, it is nowadays sometimes dismissed. The reason: its unjustified implicit assignment of equiprobability to each possible Humean mosaic; that is, its assumption of the principle of indifference, which has been attacked on (...) many grounds ever since it was first proposed. In place of equiprobability, recent formal models represent the doxastic state of total ignorance as suspension of judgment. In this paper I revisit the cosmic coincidence objection to Humean laws by assessing which doxastic state we should endorse. By focusing on specific features of our scenario I conclude that suspending judgment results in an unnecessarily weak doxastic state. First, I point out that recent literature in epistemology has provided independent justifications of the principle of indifference. Second, given that the argument is framed within a Humean metaphysics, it turns out that we are warranted to appeal to these justifications and assign a uniform and additive credence distribution among Humean mosaics. This leads us to conclude that, contrary to widespread opinion, we should not dismiss the cosmic coincidence objection to the Humean account of laws. (shrink)

The topic of this thesis is how we should treat tiny probabilities of vast value. This thesis consists of six independent papers. Chapter 1 discusses the idea that utilities are bounded. It shows that bounded decision theories prescribe prospects that are better for no one and worse for some if combined with an additive axiology. Chapter 2, in turn, points out that standard axiomatizations of Expected Utility Theory violate dominance in cases that involve possible states of zero probability. Chapters (...) 3–6 discuss the idea that we should ignore tiny probabilities in practical decision-making. Chapter 3 argues that discounting small probabilities solves the ‘Intrapersonal Addition Paradox’ and thus helps avoid the Repugnant Conclusion. Chapter 4 explores what the most plausible version of this view might look like and what problems the different versions have. Chapter 5 focuses on one type of problem, namely, money pumps. The Independence Money Pump, in particular, presents a difficult challenge for those who wish to discount small probabilities. Finally, Chapter 6 discusses the implications of discounting small probabilities for the value of the far future. (shrink)

In his classic book “the Foundations of Statistics” Savage developed a formal system of rational decision making. The system is based on (i) a set of possible states of the world, (ii) a set of consequences, (iii) a set of acts, which are functions from states to consequences, and (iv) a preference relation over the acts, which represents the preferences of an idealized rational agent. The goal and the culmination of the enterprise is a representation theorem: Any preference relation that (...) satisfies certain arguably acceptable postulates determines a (finitely additive) probability distribution over the states and a utility assignment to the consequences, such that the preferences among acts are determined by their expected utilities. Additional problematic assumptions are however required in Savage's proofs. First, there is a Boolean algebra of events (sets of states) which determines the richness of the set of acts. The probabilities are assigned to members of this algebra. Savage's proof requires that this be a σ-algebra (i.e., closed under infinite countable unions and intersections), which makes for an extremely rich preference relation. On Savage's view we should not require subjective probabilities to be σ-additive. He therefore finds the insistence on a σ-algebra peculiar and is unhappy with it. But he sees no way of avoiding it. Second, the assignment of utilities requires the constant act assumption: for every consequence there is a constant act, which produces that consequence in every state. This assumption is known to be highly counterintuitive. The present work contains two mathematical results. The first, and the more difficult one, shows that the σ-algebra assumption can be dropped. The second states that, as long as utilities are assigned to finite gambles only, the constant act assumption can be replaced by the more plausible and much weaker assumption that there are at least two non-equivalent constant acts. The second result also employs a novel way of deriving utilities in Savage-style systems -- without appealing to von Neumann-Morgenstern lotteries. The paper discusses the notion of “idealized agent" that underlies Savage's approach, and argues that the simplified system, which is adequate for all the actual purposes for which the system is designed, involves a more realistic notion of an idealized agent. (shrink)

Despite several criticisms surrounding the DSM classification in psychiatry, a significant bulk of research on mental conditions still operates according to two core assumptions: a) homogeneity, that is the idea that mental conditions are sufficiently homogeneous to justify generalization; b) additive comorbidity, that is the idea that the coexistence of multiple conditions in the same individual can be interpreted as additive. In this paper we take autism research as a case study to show that, despite a plethora of (...) criticism, psychiatric research often continues to operate in accordance with this model. Then we argue that such a model runs into problems once facts about comorbidity are taken into account. Finally, we offer some suggestions on how to tackle the challenge raised by comorbidity and its impact on heterogeneity. To do so, we explore transdiagnostic stratification accounts and network models to show that combining these approaches can move us in the right direction. (shrink)

We investigate the conflict between the ex ante and ex post criteria of social welfare in a new framework of individual and social decisions, which distinguishes between two sources of uncertainty, here interpreted as an objective and a subjective source respectively. This framework makes it possible to endow the individuals and society not only with ex ante and ex post preferences, as is usually done, but also with interim preferences of two kinds, and correspondingly, to introduce interim forms of the (...) Pareto principle. After characterizing the ex ante and ex post criteria, we present a first solution to their conflict that extends the former as much possible in the direction of the latter. Then, we present a second solution, which goes in the opposite direction, and is also maximally assertive. Both solutions translate the assumed Pareto conditions into weighted additive utility representations, and both attribute to the individuals common probability values on the objective source of uncertainty, and different probability values on the subjective source. We discuss these solutions in terms of two conceptual arguments, i.e., the by now classic spurious unanimity argument and a novel informational argument labelled complementary ignorance. The paper complies with the standard economic methodology of basing probability and utility representations on preference axioms, but for the sake of completeness, also considers a construal of objective uncertainty based on the assumption of an exogeneously given probability measure. JEL classification: D70; D81. (shrink)

Some theorists have developed formal approaches to truth that depend on counterexamples to the structural rules of contraction. Here, we study such approaches, with an eye to helping them respond to a certain kind of objection. We define a contractive relative of each noncontractive relation, for use in responding to the objection in question, and we explore one example: the contractive relative of multiplicative-additive affine logic with transparent truth, or MAALT. -/- .

We introduce a ranking of multidimensional alternatives, including uncertain prospects as a particular case, when these objects can be given a matrix form. This ranking is separable in terms of rows and columns, and continuous and monotonic in the basic quantities. Owing to the theory of additive separability developed here, we derive very precise numerical representations over a large class of domains (i.e., typically notof the Cartesian product form). We apply these representationsto (1)streams of commodity baskets through time, (2)uncertain (...) social prospects, (3)uncertain individual prospects. Concerning(1), we propose a finite horizon variant of Koopmans’s (1960) axiomatization of infinite discounted utility sums. The main results concern(2). We push the classic comparison between the exanteand expostsocial welfare criteria one step further by avoiding any expected utility assumptions, and as a consequence obtain what appears to be the strongest existing form of Harsanyi’s (1955) Aggregation Theorem. Concerning(3), we derive a subjective probability for Anscombe and Aumann’s (1963) finite case by merely assuming that there are two epistemically independent sources of uncertainty. (shrink)

(Draft of Feb 2023, see upcoming issue for Chalmers' reply) In Reality+: Virtual Worlds and the Problems of Philosophy, David Chalmers argues, among other things, that: if we are living in a full-scale simulation, we would still enjoy broad swathes of knowledge about non-psychological entities, such as atoms and shrubs; and, our lives might still be deeply meaningful. Chalmers views these claims as at least weakly connected: The former claim helps forestall a concern that if objects in the simulation are (...) not genuine (and so not knowable), then life in the simulation is illusory and therefore, not as valuable as a non-simulated life. Taking up these questions, I argue that in general, the value of social knowledge for a meaningful life dramatically swamps the value of non-social knowledge for a meaningful life. Along the way, I propose a non-additive model of the meaningfulness of life, according to which the overall effect of some potential contributor of value to a life depends in part on what is already in a life. One upshot is that the vindication of non-social knowledge, absent a correlative vindication of social knowledge, contributes either not at all or scarcely at all to the claim that our lives in the simulation might be deeply meaningful. This is so even though the vindication of non-social knowledge does forestall the concern that in the simulation, our lives might be wholly meaningless. (shrink)

During the coronavirus pandemic, communities have faced shortages of important healthcare resources such as COVID-19 vaccines, medical staff, ICU beds and ventilators. Public health officials in the U.S. have had to make decisions about two major issues: which infected patients should be treated first, and which people who are at risk of infection should be inoculated first. Following Beauchamp and Childress’s principlism, adopted guidelines have tended to value both whole lives and life-years. This process of collective moral reasoning has revealed (...) our common commitment to both Kantian and utilitarian principles. For Kant, respecting people’s rights entails that we ought to value whole lives equally. Therefore we ought to allocate resources so as to maximise the number of patients who survive to discharge. By contrast, the principle of utility has us maximise life-years so that people can satisfy more of their considered preferences. Although people are treated impartially in the utilitarian calculus, it does not recognise their equal worth. Subjecting Kantian ethics and utilitarianism to the process of reflective equilibrium lends support to the idea that we need a pluralistic approach that would accommodate our moral intuitions regarding both the equal value of whole lives and the additive value of life-years. (shrink)