The difference between carnap's and de finetti's conceptions of probability does not consist of a couple of requirements, As carnap asserted in a letter to de finetti. The paper is intended to give a theoretical justification for this denial. In order to do this, The author stresses the difference between (tolerant) objectivism and (radical) subjectivism. The difference is discussed in statistical terms. The discussion is faced with respect to predictive inferences, A type of statistical inference that both carnap and de (...) finetti advocate in many occasions. (shrink)

A collection of articles originally presented at two conferences, the first at Ventura Hall, Stanford, in April 1998; and the second at the University of Bologna in September 1999.

The long history of ergodic and quasi-ergodic hypotheses provides the best example of the attempt to supply non-probabilistic justifications for the use of statistical mechanics in describing mechanical systems. In this paper we reverse the terms of the problem. We aim to show that accepting a probabilistic foundation of elementary particle statistics dispenses with the need to resort to ambiguous non-probabilistic notions like that of (in)distinguishability. In the quantum case, starting from suitable probability conditions, it is possible to deduce elementary (...) particle statistics in a unified way. Following our approach Maxwell-Boltzmann statistics can also be deduced, and this deduction clarifies its status.Thus our primary aim in this paper is to give a mathematically rigorous deduction of the probability of a state with given energy for a perfect gas in statistical equilibrium; that is, a deduction of the equilibrium distribution for a perfect gas. A crucial step in this deduction is the statement of a unified statistical theory based on clearly formulated probability conditions from which the particle statistics follows. We believe that such a deduction represents an important improvement in elementary particle statistics, and a step towards a probabilistic foundation of statistical mechanics.In this Part I we first present some history: we recall some results of Boltzmann and Brillouin that go in the direction we will follow. Then we present a number of probability results we shall use in Part II. Finally, we state a notion of entropy referring to probability distributions, and give a natural solution to Gibbs' paradox. (shrink)

When subjects view stimulation of a rubber hand while feeling congruent stimulation of their own hand, they may come to feel that the rubber hand is part of their own body. This illusion of body ownership is termed ‘Rubber Hand Illusion’ . We investigated sensitivity of RHI to spatial mismatches between visual and somatic experience. We compared the effects of spatial mismatch between the stimulation of the two hands, and equivalent mismatches between the postures of the two hands. We created (...) the mismatch either by adjusting stimulation or posture of the subject’s hand, or, in a separate group of subjects, by adjusting stimulation or posture of the rubber hand. The matching processes underlying body ownership were asymmetrical. The illusion survived small changes in the subject’s hand posture, but disappeared when the same posture transformations were applied to the rubber hand. Mismatch between the stimulation delivered to the subject’s hand and the rubber hand abolished the illusion. The combination of these two situations is of particular interest. When the subject’s hand posture was slightly different from the rubber hand posture, the RHI remained as long as stimulation of the two hands was congruent in a hand-centred spatial reference frame, even though the altered posture of the subject’s hand meant that stimulation was incongruent in external space. Conversely, the RHI was reduced when the stimulation was incongruent in hand-centred space but congruent in external space. We conclude that the visual–tactile correlation that causes the RHI is computed within a hand-centred frame of reference, which is updated with changes in body posture. Current sensory evidence about what is ‘me’ is interpreted with respect to a prior mental body representation. (shrink)

We characterize the collapse of Buss' bounded arithmetic in terms of the provable collapse of the polynomial time hierarchy. We include also some general model-theoretical investigations on fragments of bounded arithmetic.

We show that every model of IΔ0 has an end extension to a model of a theory where log-space computable function are formalizable. We also show the existence of an isomorphism between models of IΔ0 and models of linear arithmetic LA.

Recently Shakurov pioneered the study of subalgebras of diagonalizable algebras of theories of arithmetic. We show that his results extend to weaker theories.

In this paper we argue that data science is a coherent and novel approach to empirical problems that, in its most general form, does not build understanding about phenomena. Within the new type of mathematization at work in data science, mathematical methods are not selected because of any relevance for a problem at hand; mathematical methods are applied to a specific problem only by `forcing’, i.e. on the basis of their ability to reorganize the data for further analysis and the (...) intrinsic richness of their mathematical structure. In particular, we argue that deep learning neural networks are best understood within the context of forcing optimization methods. We finally explore the broader question of the appropriateness of data science methods in solving problems. We argue that this question should not be interpreted as a search for a correspondence between phenomena and specific solutions found by data science methods; rather, it is the internal structure of data science methods that is open to precise forms of understanding. (shrink)

Despite the burgeoning literature on the governance and impact of cross-sector partnerships in the past two decades, the debate on how and when these collaborative arrangements address globally relevant problems and contribute to systemic change remains open. Building upon the notion of wicked problems and the literature on governing such wicked problems, this paper defines harnessing problems in multi-stakeholder partnerships as the approach of taking into account the nature of the problem and of organizing governance processes accordingly. The paper develops (...) an innovative analytical framework that conceptualizes MSPs in terms of three governance processes harnessing three key dimensions of wicked problems. The Roundtable on Sustainable Palm Oil provides an illustrative case study on how this analytical framework describes and explains organizational change in partnerships from a problem-based perspective. The framework can be used to better understand and predict the complex relationships between MSP governance processes, systemic change and societal problems, but also as a guiding tool in organizing governance processes to continuously re-assess the problems over time and address them accordingly. (shrink)

This chapter introduces readers to the empirical questions at issue in debates over gendered pronouns and assesses the plausibility of various possible answers to these questions. It has two parts. The first is a general introduction to the linguistics and psychology of grammatical gender. The second focuses on the meanings of gendered pronouns in English. It begins with a discussion of some methodological limitations of empirical approaches to the topic and the normative implications of those limitations. It then argues against (...) three simple theories of the semantics of gendered pronouns in English and proposes an alternative that fares better: the Gender-First View. Finally, it discusses the singular use of 'they' and its connection to nonbinary gender identities. (shrink)

Let be a saturated model of inaccessible cardinality, and let be arbitrary. Let denote the expansion of with a new predicate for. Write for the collection of subsets such that ≡. We prove that if the VC-dimension of is finite then is externally definable.

This paper explores the relationship between business experience in cross-sector partnerships and the co-creation of what we refer to as ‘dynamic capabilities for stakeholder orientation,’ consisting of the four dimensions of sensing, interacting with, learning from and changing based on stakeholders. We argue that the co-creation of dynamic capabilities for stakeholder orientation is crucial for CSPs to create societal impact, as stakeholder-oriented organizations are more suited to deal with “wicked problems,” i.e., problems that are large, messy, and complex. By means (...) of a grounded theory approach of inductive research, we collected and interpreted data on four global agri-food companies which have heterogeneous experience in participating in CSPs. The results of this paper highlight that only companies’ capability of interacting with stakeholders continually increases, while their capabilities of sensing, learning from, and changing based on stakeholders first increase and then decrease as companies gain more experience in CSP participation. To a large extent, this can be attributed to the development of corporate strategies on sustainability after a few years of CSP participation, which entails a shift from a reactive to a proactive attitude towards sustainability issues and which may decrease the need or motivation for stakeholder orientation. These findings open up important issues for discussion and for future research on the impact of CSPs in a context of wicked problems. (shrink)

We present a simple and completely model-theoretical proof of a strengthening of a theorem of Ajtai: The independence of the pigeonhole principle from IΔ0. With regard to strength, the theorem proved here corresponds to the complexity/proof-theoretical results of [10] and [14], but a different combinatorics is used. Techniques inspired by Razborov [11] replace those derived from Håstad [8]. This leads to a much shorter and very direct construction.

As a reply to the commentary (Humphreys in Found Sci, 2012), we explore the methodological implications of seeing artificial neural networks as generic classification tools, we show in which sense the use of descriptions and models in data analysis is not equivalent to the original empirical use of epicycles in describing planetary motion, and we argue that agnostic science is essentially related to the type of problems we ask about a phenomenon and to the processes used to find answers.

This paper deals with the metaphysics of the notion of quantity in the philosophy of Leibniz, and its aim is to defend the following bi-conditional: for any object x, x has a certain quantity if and only if x has a (metaphysical) limit or a bound. The direction from left to right is justified in §3, while in §4 I develop an argument to justify the direction from right to left. Since the bi-conditional links the metaphysical notion of limit to (...) the mathematical notion of quantity (and in this way it links Leibniz’s metaphysics with his conception of Mathesis Universalis), it allows the use of metaphysics to clarify the features of the mathematical notion of quantity. This task is accomplished in §5 and §6. Finally, §7 discusses a possible objection. (shrink)