Standard Type Theory, STT, tells us that b^n(a^m) is well-formed iff n=m+1. However, Linnebo and Rayo have advocated the use of Cumulative Type Theory, CTT, has more relaxed type-restrictions: according to CTT, b^β(a^α) is well-formed iff β > α. In this paper, we set ourselves against CTT. We begin our case by arguing against Linnebo and Rayo’s claim that CTT sheds new philosophical light on set theory. We then argue that, while CTT ’s type-restrictions are unjustifiable, the type-restrictions imposed by (...) STT are justified by a Fregean semantics. What is more, this Fregean semantics provides us with a principled way to resist Linnebo and Rayo’s Semantic Argument for CTT. We end by examining an alternative approach to cumulative types due to Florio and Jones; we argue that their theory is best seen as a misleadingly formulated version of STT. (shrink)

Cumulative cultural evolution is often claimed to be distinctive of human culture. Such claims are typically supported with examples of complex and historically late-appearing technologies. Yet by taking these as paradigm cases, researchers unhelpfully lump together different ways that culture accumulates. This article has two aims: (a) to distinguish four types of cultural accumulation: adaptiveness, complexity, efficiency, and disparity and (b) to highlight the epistemic implications of taking complex hominin technologies as paradigmatic instances of cumulative culture. Addressing these issues both (...) clarifies the cumulative culture concept and demonstrates the importance of further cumulative culture research into non-human animals and ancestral hominins. (shrink)

I present a cumulative case for the thesis that we only know propositions that are certain for us. I argue that this thesis can easily explain the truth of eight plausible claims about knowledge: -/- (1) There is a qualitative difference between knowledge and non-knowledge. (2) Knowledge is valuable in a way that non-knowledge is not. (3) Subjects in Gettier cases do not have knowledge. (4) If S knows that P, P is part of S’s evidence. (5) If S knows (...) that P, ~P is epistemically impossible for S. (6) If S knows that P, S can rationally act as if P. (7) If S knows that P, S can rationally stop inquiring whether P. (8) If S knows each of {P1, P2, … Pn}, and competently deduces Q from these propositions, S knows that Q. -/- I then argue that the skeptical costs of this thesis are outweighed by its explanatory power. (shrink)

The systems Kα of transfinite cumulative types up to α are extended to systems K∞α that include a natural infinitary inference rule, the so-called limit rule. For countable α a semantic completeness theorem for K∞α is proved by the method of reduction trees, and it is shown that every model of K∞α is equivalent to a cumulative hierarchy of sets. This is used to show that several axiomatic first-order set theories can be interpreted in K∞α, for suitable α.

What explains the unique features of human culture? Culture is not uniquely human, but human culture is uniquely cumulative. Cumulative culture is a product of our collective intelligence and is supported by cognitive processes and learning strategies that enable people to acquire, transform, and transmit information and technologies within and across generations. Technological and social innovations are currently driving unprecedented changes in cultural complexity and diversity. Innovation is a cognitively and socially complex, multistep process that typically requires (cumulative) cultural learning (...) to achieve. I argue that the technological solutions that characterize twenty-first-century innovation can only be explained by understanding both the capacity to learn from and build upon the insights of others and the transmission systems that store the knowledge and technologies of previous generations. Human uniqueness is a product of cumulative cultural learning, transmission, and innovation. (shrink)

Three types of cumulative cases for theism are examined: incremental cases (like Richard Swinburne's), distributive cases (like William Lane Craig's), and emergent cases (like Basil Mitchell's).

In this article, I present a substantive proposal about the timing and nature of the final stage of the evolution of full human language, the transition from so-called “protolanguage” to language, and on the origins of a simple protolanguage with structure and displaced reference; a proposal that depends on the idea that the initial expansion of communicative powers in our lineage involved a much expanded role for gesture and mime. But though it defends a substantive proposal, the article also defends (...) and illustrates a methodological proposal too. I argue that language is a special case of a more general phenomenon—cumulative cultural evolution—and while we rarely have direct information about communication, we have more direct information about the cumulative cultural evolution of technical skill, ecological strategies, and social complexity. These same factors also enable us to make a reasonable estimate of the intergenerational social learning capacities of these communities and of the communicative demands these communities face. For example, we can, at least tentatively, identify forms of cooperation that are stable only if third party information is transmitted widely, cheaply, and accurately. So we can use these more direct markers of information accumulation to locate, in broad terms, the period in our evolutionary history during which we became lingual. (shrink)

Two strong arguments have been given in favor of the claim that no selection process can play a role in explaining adaptations. According to the first argument, selection is a negative force; it may explain why the eliminated individuals are eliminated, but it does not explain why the ones that survived (or their offspring) have the traits they have. The second argument points out that the explanandum and the explanans are phenomena at different levels: selection is a population-level phenomenon, whereas (...) adaptation occurs on the individual level. Thus, selection can explain why individuals in a certain population have a certain trait, but it cannot explain why a certain indi- vidual has this trait. After pointing out that both arguments ignore the significance of the limitation of environmental resources, I will construe a positive argument for the claim that cumulative selection processes can, indeed, play a role in explaining adaptations. (shrink)

This paper investigates how the credit incentive to engage in questionable research practices interacts with cumulative advantage, the process whereby high-status academics more easily increase their status than low-status academics. I use a mathematical model to highlight two dynamics that have not yet received much attention. First, due to cumulative advantage, questionable research practices may pay off over the course of an academic career even if they are not attractive at the level of individual publications. Second, because of the role (...) of bottleneck moments in academic careers, questionable research practices may be selected for even if they do not provide a benefit in expectation. I also observe that, within the model, the most successful academics are the most likely to have benefited from fraud. (shrink)

For nonmonotonic logics, Cumulativity is an important logical rule. We show here that Cumulativity fans out into an infinity of different conditions, if the domain is not closed under finite unions.

The von Neumann hierarchy of sets is heavily used as a basic tool in classical set theory, being an underlying ingredient in many proofs and concepts. In constructive set theories like without the powerset axiom however, it loses much of its potency by ceasing to be a hierarchy of sets as its single stages become only classes. This article proposes an alternative cumulative hierarchy which does not have this drawback and provides examples of how it can be used to prove (...) new theorems in. (shrink)

: This paper seeks to contribute to the development of a sociological understanding of scientific change. It first presents a conceptual framework for defining and understanding the conditions that give rise to episodes of cumulative change (both as the selective reconstruction of events and as the patterned structuring of innovations over time and across different settings). It argues that one of the most powerful structuring mechanisms is the existence of standardized research technologies. Then, the development of electroencephalography (EEG) is presented (...) as an illustrative case study. The EEG supported a dramatic episode of development in brain science, and did so primarily through technological standardization and reliability. The case shows how standard and manipulable technologies provide a framework for orderly change both in retrospective accounts and in specific historical periods of scientific practice. (shrink)

Crime is a serious social problem, but its causes are not exclusively social. There is growing consensus that explaining and preventing it requires interdisciplinary research efforts. Indeed, the landscape of contemporary criminology includes a variety of theoretical models that incorporate psychological, biological and sociological factors. These multi-disciplinary approaches, however, have yet to radically advance scientific understandings of crime and shed light on how to manage it. In this paper, using conceptual tools on offer in the philosophy of science in combination (...) with theoretical work represented in this special volume of Psychology, Crime and Law, I provide some perspective on why explanatory progress in criminology has remained elusive and evaluate some positive proposals for attaining it. -/- . (shrink)

Cognitive innovation has shaped and transformed our cognitive capacities throughout history. Until recently, cognitive innovation has not received much attention by empirical and conceptual research in the cognitive sciences. This paper is a first attempt to help close this gap. It will be argued that cognitive innovation is best understood in connection with cumulative cultural evolution and enculturation. Cumulative cultural evolution plays a vital role for the inter-generational transmission of the products of cognitive innovation. Furthermore, there are at least two (...) important functions of enculturation for cognitive innovation. First, enculturation is responsible for the ontogenetic acquisition of cognitive practices governing the interaction with innovative products. Second, successful processes of enculturation provide opportunities for subsequent innovative processes. The trans-generational trajectory of calculation from mathematical symbol systems to the first digital computers will serve as a paradigm example of the delicate interplay of cognitive innovation, cumulative cultural evolution, and enculturation. (shrink)

We conduct a standardized survey on risk preferences in 53 countries worldwide and estimate cumulative prospect theory parameters from the data. The parameter estimates show that significant differences on the cross-country level are to some extent robust and related to economic and cultural differences. In particular, a closer look on probability weighting underlines gender differences, economic effects, and cultural impact on probability weighting. The data set is a useful starting point for future research that investigates the impact of risk preferences (...) on the market level. (shrink)

In this paper I will argue that most objections to deductive analyses of a priori analogies are incorrect, often involve basic misinterpretations of what the deductive reconstruction of those arguments are saying, and sometimes also betray a confusion about what part of the reasoning corresponds to the analogical inference. In particular, I will be focusing on a raft of objections made by Juthe in [2015] and subject his alternative views to criticism. -/- I will then argue that Juthe does implicitly (...) have a good argument against deductivism: adding further analogues seems to have a cumulative force that they would not have on a deductivist analysis. This is so not only in ordinary analogical arguments but, perhaps surprisingly, with a priori analogical arguments. I will then argue that this does not favor a sui generis view of the analogical argument over inductivist views, and attempt to show that a confirmation-theoretic approach to analogical inference makes the best sense of our intuitions about the strength of analogical arguments. (shrink)

This last volume of Kierkegaard Research: Sources, Reception and Resources is a cumulative index to all the volumes of the series. The series was originally designed in a systematic fashion in order to make it as easily usable and accessible as possible. The individual parts of the series and the individual volumes have been organized to make it generally fairly simple to locate the main articles relevant for one's research interests. However, the placement of some individual articles might not always (...) be completely self-evident. Moreover, the sheer mass of material and information provided by the series makes a cumulative index a necessary accompanying resource. Further, given the scope of the series, it was inevitable that some names or topics are mentioned more than once in the series in different places beyond the main article ostensibly dedicated to them. The purpose of these indices is thus to help the readers to find an easy and direct way to the topics of their interest in the rich universe of Kierkegaard research. The material of the indices is divided into three tomes: Tome I is the Index of Names from A to K, Tome II covers the Index of Names from L to Z, while Tome III consists of the Index of Subjects and includes a complete overview of all the volumes, tomes and articles of the series. (shrink)

Capitalizing on a 15-year longitudinal dataset of 9–12 years old children in rural China, this study adopts a life course perspective and analyzes cumulative childhood adversity and its associations with mental health problems from childhood to adulthood. Four domains of childhood life are selected to construct cumulative childhood adversity: socioeconomic hardship, family disruption, physical issue, and academic setback. Overall, cumulative childhood adversity significantly associates with children’s internalizing and externalizing problems as well as adults’ depression and self-esteem. However, cumulative childhood adversity (...) has no significant relationship with internalizing and externalizing problems in adolescence. Furthermore, different domains of childhood adversity matter differently for mental health problems in different life stages. Physical issue and academic setback have the strongest association with internalizing and externalizing problems in childhood, while only socioeconomic hardship has a significant relationship with depression and self-esteem in adulthood. The relationship between cumulative childhood adversity and adult mental health problems is fully mediated by educational attainment. Finally, there is no gender difference in either the occurrence of cumulative childhood adversity or the association between cumulative childhood adversity and mental health problems. (shrink)

This is a critique of J. H. Sobel’s ’Logic and Theism’, defending the use of cumulative arguments, and the coherence of theistic metaphysics.

Microaggressions are a new moral category that refers to the subtle yet harmful forms of discriminatory behavior experienced by members of oppressed groups. Such behavior often results from implicit bias, leaving individual perpetrators unaware of the harm they have caused. Moreover, microaggressions are often dismissed on the grounds that they do not constitute a real or morally significant harm. My goal is therefore to explain why microaggressions are morally significant and argue that we are responsible for their harms. I offer (...) a conceptual framework for microaggressions, exploring the central mechanisms used for identification and the empirical research concerning their harm. The cumulative harm of microaggressions presents a unique case for understanding disaggregation models for contributed harms, blame allocation, and individual responsibility within structural oppression. Our standard moral model for addressing cumulative harm is to hold all individual contributors blameworthy for their particular contributions. However, if we aim to hold people responsible for their unconscious microaggressions and address cumulative harm holistically, this model is inadequate. Drawing on Iris Marion Young's social connection model, I argue that we, as individual perpetrators of microaggressions, have a responsibility to respond to the cumulative harm to which we have individually contributed. (shrink)

In this paper I examine the nature of Russell's ramified type theory resolution of paradoxes. In particular, I consider the effect of construing the types in Church's cumulative sense, that is, the range of a variable of a given type includes the range of every variable of directly lower type. Contrary to what seems to be generally assumed, I show that the decision to make the levels cumulative and allow this to be reflected in the semantics is not neutral with (...) respect to the solution of the paradoxes. I introduce a distinction between syntactical and semantical cumulativeness. It turns out that noncumulative type theories (in either sense) are equally capable of dealing with the paradoxes. Furthermore, whether cumulativeness is appropriate appears to be context dependent. (shrink)

This article proposes a new logical framework for NL quantification. The framework is based on Generalized Quantifiers, Skolem-like functional dependencies, and Maximality of the involved sets of entities. Among the readings available for NL sentences, those where two or more sets of entities are independent of one another are particularly challenging. In the literature, examples of those readings are known as Collective and Cumulative readings. This article briefly analyzes previous approaches to Cumulativity and Collectivity, and indicates (Schwarzschild in Pluralities. (...) Kluwer, Dordrecht, 1996) as the best proposal so far to deal with these readings. Then, it incorporates its insights in the logical framework defined in Robaldo (J Philos Log 39(1):23–58, 2009a), leading to a scalable logical account for NL quantification. (shrink)

Winter (2000) argues that so-called co-distributive or cumulative readings do not involve polyadic quantification (contra proposals by Krifka, Schwarzschild, Sternefeld, and others). Instead, he proposes that all such readings involve a hidden anaphoric dependency or a lexical mechanism. We show that Winter's proposal is insufficient for a number of cases of cumulative readings, and that Krifka's and Sternefeld's polyadic **-operator is needed in addition to dependent definites. Our arguments come from new observations concerning dependent plurals and clause-boundedness effects with cumulative (...) readings. (shrink)

Family income is associated with gray matter morphometry in children, but little is known about the relationship between family income and white matter structure. In this paper, using Tract-Based Spatial Statistics (TBSS), a whole brain, voxel-wise approach, we examined the relationship between family income (assessed by income-to-needs ratio) and white matter organization in middle childhood (N = 27, M = 8.66 years). Results from a nonparametric, voxel-wise, multiple regression (threshold-free cluster enhancement, p < 0.05, FWE corrected) indicated that lower family (...) income was associated with lower white matter organization (assessed by fractional anisotropy) for several clusters in white matter tracts involved in cognitive and emotional functions including fronto-limbic circuitry (uncinate fasciculus and cingulum bundle), association fibers (inferior longitudinal fasciculus, superior longitudinal fasciculus), and corticospinal tracts. Further, we examined the possibility that cumulative risk exposure might function as one of the potential pathways by which family income influences neural outcomes. Using multiple regressions, we found lower fractional anisotropy in portions of these tracts, including those found in the left cingulum bundle and left superior longitudinal fasciculus, was significantly related to greater exposure to cumulative risk (β = -0.47, p < 0.05 and β = -0.45, p < 0.05). (shrink)

Three indexes have been compiled: authors of main articles (including our special departments such as ‘Projects in progress’ and ‘Notes and discussions’); essay reviews; and book reviews. Co-author...

The final volume (XXVI) of Princeton's Kierkegaard's Writings series, the Cumulative Index provides wide-ranging navigation to the preceding twenty-five volumes in the series. Composed of over 90,000 entries, the Cumulative Index offers access to Kierkegaard's complex authorship and the extraordinary range of subjects he addressed in his writing. Covering the series' historical introductions, primary works, supplementary material (journal entries), and footnotes, the Cumulative Index provides a comprehensive entryway to the series' more than 11,000 pages of text. Readers are able to (...) survey via extended entries Kierkegaard's dual authorship(pseudonymous and signed), his frequent biblical references and allusions, his references to Christianity, God, and love, and his frequent use of analogies. A cumulative collation of the extensive supplementary material (over 4,000 journal entries) is also included, giving researchers and avid readers the opportunity to correlate and examine items from the current series, Søren Kierkegaard's Journals and Papers , and the original Danish Søren Kierkegaards Papirer. (shrink)

We present two results which shed some more light on the deep connection between ZFA and the standard ZF set theory: First of all we refine a result of Forti and Honsell in order to prove that the universe of ZFA can also be obtained as the least fixed point of a continuous operator and not only as the greatest fixed point of the powerset operator. Next we show that it is possible to define a new absolute Gödel operation in (...) addition to the standard ones in order to obtain the “constructible” model of ZFA as the least fixed point of the continuous operator of Gödel closure with respect to the standard and the new Gödel operations. (shrink)

This paper investigates different readings of plural and reciprocal sentences and how they can be derived from syntactic surface structures in a systematic way. The main thesis is that these readings result from different ways of inserting logical operators at the level of Logical Form. The basic operator considered here is a cumulative mapping from predicates that apply to singularities onto the corresponding predicates that apply to pluralities. Given a theory which allows for free insertion of such operators, it can (...) then be shown that the lexical semantics of the reciprocal expressions each other/one another consists of exactly two components, namely an anaphoric variable and a non-identity statement. This receives further support from the observation that it is exactly these two components that can be focused by only; all that remains to be done is to correctly manipulate these components at the level of LF. (shrink)

Much behavioral welfare economics assumes that expected utility theory does not accurately describe most human choice under risk. A substantial literature instead evaluates welfare consequences by taking cumulative prospect theory as the natural default alternative, at least where description is concerned. We present evidence, based on a review of previous literature and new experimental data, that the most empirically adequate hypothesis about human choice under risk is that it is heterogeneous, and that where EUT does not apply, more choice is (...) characterized by rank-dependent utility models than by CPT. Most of the apparently loss-averse choice behavior results from probability weighting rather than from direct disutility experienced when an outcome is framed as a loss against an idiosyncratic reference point. We then consider implications of this finding for methodological debates about how to model welfare effects of policies, and argue that abandonment of a dogmatic belief in CPT as the correct theory of risk human choice exposes a conceptual error that is widespread in behavioral welfare economics. We provide concluding reflections on second-order, philosophical issues around the grounding of normative commitments in policy-focused economics. (shrink)

Recent field studies have broadened our view on cultural performances in animals. This has consequences for the concept of cumulative culture. Here, we deconstruct the common individualist and differential approaches to culture. Individualistic approaches to the study of cultural evolution are shown to be problematic, because culture cannot be reduced to factors on the micro level of individual behavior but possesses a dynamic that only occurs on the group level and profoundly affects the individuals. Naive individuals, as a prerequisite of (...) an atomistic perspective, do not exist. We address the construction of a social approach to culture by introducing an inevitable social embedding of the individual development of social beings. The sociological notion of “habitus” as embodied cultural capital permits us to understand social transmission of behavioral components on a very basic level, resulting in a cumulative effect. Bits of information, movement, handling of material, attitudes, and preferences below distinct functional units are acquired through transfer mechanisms simpler than emulation and imitation such as peering, participation, co-performance, or engagement with a material environment altered by group members. The search for a zero point of cumulative culture becomes as useless as the search for a zero point of culture. Culture is cumulative. (shrink)

Although evidence of teaching behaviour has been identified in some nonhuman species, human teaching appears to be unique in terms of both the breadth of contexts within which it is observed, and in its responsiveness to needs of the learner. Similarly, cultural evolution is observable in other species, but human cultural evolution appears strikingly distinct. This has led to speculation that the evolutionary origins of these capacities may be causally linked. Here we provide an overview of contrasting perspectives on the (...) relationship between teaching and cultural evolution in humans, and briefly review previous research which suggests that cumulative culture can occur without teaching. We then report the results of a novel experimental study in which we investigated how the benefits of teaching may depend on the complexity of the skill to be acquired. Participants were asked to tie knots of varying complexity. In our Teaching condition, opportunities to interact with an experienced partner aided transmission of the most complex knots, but not simpler equivalents, relative to exposure to completed products alone, and also relative to information about the process of completion. We conclude by considering the plausibility of various accounts of the evolutionary relationship between teaching and cultural evolution in humans. (shrink)

Cover -- Half Title -- Title -- Copyright -- Contents -- Preface -- Acknowledgements -- Overview of Kierkegaard Research: Sources, Reception and Resources -- Index of Names, A-K.