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Abstract: Abstract In this paper I review the Neo-Davidsonian semantics of prepositional phrases and secondary predication. I argue that certain types of examples pose challenge to this semantics. I present an alternative to the Neo-Davidsonian analysis which successfully deals with the problematic examples. The core idea lies in representing theta-roles not as functions from events to their participants, but rather as argument-labels encoding the role of each argument in a given verb. As a result, natural-language predicates can now be treated in the manner in which relations are treated in the relational model of data, that is, as naming sets of tuples in which every object is given together with its role named by a corresponding attribute (a theta-role). Such a representation allows the employment of relational algebra operators to calculate the extensions of complex predicates (predicates built out of atomic predicates and/or atomic predicates and prepositions). I lay out the foundations of a relational FOL appropriate for the representation of natural-language predicates and present solutions to the problematic examples. From a practical perspective, the expressions of a relational FOL can be translated to a relational algebra or SQL, which makes it possible to operate with these three languages on the same relational model of data. From a philosophical perspective, a relational FOL permits a return to ‘property-based’ semantics, one in which properties named by predicates are those of individuals, and not of events. PubDate: 2022-12-03
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Abstract: Abstract This paper offers a review of Giuseppe Primero’s (2020) book “On the foundations of computing”. Mathematical, engineering, and experimental foundations of the science of computing are examined under the light of the notions of formal, physical, and experimental computational validity provided by the author. It is challenged the thesis that experimental computational validity can be defined only for the algorithmic method and not for the software development process. The notions of computational hypothesis and computational experiment provided by Primiero (2020) are extended to the case of software development. Finally, it is highlighted how the hypothetical-deductive method is involved in the practice of using models to corroborate computational hypotheses in software testing. As a concluding remark, it is underlined how defining experimental computational validity in the context of software development offers a sound experimental foundation to the science of computing. PubDate: 2022-11-21
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Abstract: Abstract There are many important connections between epistemic justification and moral justification. A recent example of such connections is offered by Sosa’s AAA model for the normative evaluation of epistemic performances. In order to count as knowledge, a belief has to be Accurate in attaining the truth, the subject has to be Adroit or competent for such task, and the belief has to be Apt in the sense that the accuracy of the belief has to manifest the adroitness of the subject. In addition, full knowledge would require full-aptness, which is obtained when the aim of aptness is achieved in an apt way. We have here a clear definition of the model. But the application of the model to particular performances is not so clear. Both the identification of a particular performance as a case of epistemic performance and the assessment of its aptness, or full-aptness, are strongly relative to intentional descriptions paying attention to contextual factors and personal aspects. Here is where we can find close proximity with ethics. An epistemic analog to the ethical problem of double effects appears. In our paper, we analyze that problem in detail, extracting some consequences. PubDate: 2022-11-14
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Abstract: Abstract Much of the work in moral philosophy and the political debate on abortion has focused on when in human development personhood begins. In this article, using a variant of Derek Parfit’s view on personal identity, I instead frame the question as one of victimhood. I argue for what I call the Victim Requirement for the wrongness of killing–killing is wrong only if there is an identifiable victim. An identifiable victim is, temporally speaking, in the midst of a chain of psychological connections in the sense of “Relation R.” I go on to argue for a version of psychological identity which makes consciousness a necessary condition of rational self-interest and numerical identity across time. The implications for the abortion debate, based upon the best neurological evidence, are that abortion cannot be wrong before at least 22 weeks of pregnancy and perhaps significantly later. I then respond to alternatives to my Victim Requirement and argue that they either fail on their own merits or are deeply problematic. Finally, I discuss the role of autonomy and consent in a world where fetal consciousness develops much earlier. PubDate: 2022-11-10
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Abstract: Abstract There are many ways in which biases can enter processes of scientific reasoning. One of these is what Ludwik Fleck has called a “harmony of illusions”. In this paper, Fleck’s ideas on the relevance of social mechanisms in epistemic processes and his detailed description of publication processes in science will be used as a starting point to investigate the connection between cognitive processes, social dynamics, and biases in this context. Despite its usefulness as a first step towards a more detailed analysis, Fleck’s account needs to be updated in order to take the developments of digital communication technologies of the 21st century into account. Taking a closer look at today’s practices of science communication shows that information and communication technologies (ICTs) play a major role here. By presenting a detailed case study concerning the database SCOPUS, the question will be investigated how such ICTs can influence the division of epistemic labour. The result will be that they potentially undermine the epistemic benefits of social dynamics in science communication due to their inherent tendency to reduce the diversity of scientific hypotheses and ideas. PubDate: 2022-11-07
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Abstract: Abstract One of the key concepts of Edmund Husserl’s transcendental phenomenology is the noema. Husserl uses the concept to denote the aspect of what is intended in experience as it remains within the transcendental domain of inquiry after the phenomenological reduction. Despite such seeming simplicity, Husserl’s discussion of the noema is ambiguous to the extent that it has sparked a wide-ranging debate in the secondary literature. The gist of the dispute concerns the question about the relation between the noema and the object: whether the noema is content, ontologically distinct from the object, or the object itself just considered differently in philosophical reflection. In this paper, I propose an interpretation that aims to reconcile two opposing positions of this debate (the so-called West and East Coast interpretations). The impetus for the reconciliation stems from the fact that both interpretations seem to be correct while they also suffer from their own shortcomings. I propose the reconciliation by applying a distinction Husserl makes between two areas of phenomenological investigation, neutralized pure phenomenology and non-neutralized phenomenology of reason. Having clarified the distinction between them, I suggest that both competing interpretations can be partially correct when reserved for the aspect of the noema in either of the two areas of phenomenological investigation. Finally, I show how this proposal could aid in resolving issues in the recent discussion concerning Husserl’s noema and the internalism–externalism debate in philosophy of mind. PubDate: 2022-11-07
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Abstract: Abstract With reference to an already existing and relatively widespread use of the expression in question, mathematical “thought experiments” (“TEs”) involve mathematical reasoning in which visualisation plays a relatively more important role. But to ensure an unambiguous and consistent use of the term, certain conditions have to be met: (1) Contrary to what has happened so far in the literature, the distinction between logical-formal thinking and experimental-operational thinking must not be ignored; (2) The separation between the context of discovery and the context of justification is to be rejected, at least in one of the main senses in which it was defended by the logical empiricists and Popper (this excludes any position which, ascribing to mathematical TEs only a heuristic role, regards them an intermediate step to attain more traditional forms of rigour); (3) The distinction between mathematical TEs and formal proofs must be regarded as one of degree, and not as a qualitative one, although this distinction may be used in a de facto way for particular or local purposes. PubDate: 2022-11-07
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Abstract: Abstract Is there anything like an experiment in mathematics' And if this is the case, what would distinguish a mathematical experiment from a mathematical thought experiment' In the present paper, a framework for the practice of mathematics will be put forward, which will consider mathematics as an experimenting activity and as a proving activity. The relationship between these two activities will be explored and more importantly a distinction between thought-experiments, real experiments, quasi experiments and proofs in pure mathematics will be provided. To do so, three examples of experimenting with triangles will be introduced and discussed. PubDate: 2022-11-06
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Abstract: Abstract This paper argues that the shared intersubjective accessibility of mathematical objects has its roots in a stratum of experience prior to language or any other form of concrete social interaction. On the basis of Husserl’s phenomenology, I demonstrate that intersubjectivity is an essential stratum of the objects of mathematical experience, i.e., an integral part of the peculiar sense of a mathematical object is its common accessibility to any consciousness whatsoever. For Husserl, any experience of an objective nature has as its correlate a “we,” which he terms the “community of monads”. Thus, even before mathematical objects gain expression, formalization, and axiomatization through natural and scientific language, from a phenomenological viewpoint their objectivity has its roots in raw pre-linguistic though intersubjective experience. Accordingly, I demonstrate the different senses in which the experience of mathematical objects is permeated by intersubjectivity, suggesting a picture of mathematical intersubjectivity as pre-linguistic common experience based on Husserl’s idea of a “community of monads”. PubDate: 2022-11-05
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Abstract: Abstract One of the main criticisms of the theory of collections of indiscernible objects is that once we quantify over one of them, we are quantifying over all of them since they cannot be discerned from one another. In this way, we would call the collapse of quantifiers: ‘There exists one x such as P’ would entail ‘All x are P’. In this paper we argue that there are situations (quantum theory is the sample case) where we do refer to a certain quantum entity, saying that it has a certain property, even without committing all other indistinguishable entities with the considered property. Mathematically, within the realm of the theory of quasi-sets \(\mathfrak {Q}\) , we can give sense to this claim. We show that the above-mentioned ‘collapse of quantifiers’ depends on the interpretation of the quantifiers and on the mathematical background where they are ranging. In this way, we hope to strengthen the idea that quantification over indiscernibles, in particular in the quantum domain, does not conform with quantification in the standard sense of classical logic. PubDate: 2022-10-23
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Abstract: Abstract In this paper we argue that there were several currents, ideas and problems in 19th-century logic that motivated John Venn to develop his famous logic diagrams. To this end, we first examine the problem of uncertainty or over-specification in syllogistic that became obvious in Euler diagrams. In the 19th century, numerous logicians tried to solve this problem. The most famous was the attempt to introduce dashed circles into Euler diagrams. The solution that John Venn developed for this problem, however, came from a completely different area of logic: instead of orienting to syllogistic like Euler diagrams, Venn applied Boolean algebra to improve visual reasoning. Venn’s contribution to solving the problem of elimination also played an important role. The result of this development is still known today as the ‘Venn Diagram’. PubDate: 2022-10-21
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Abstract: Abstract The goal of this paper is to answer the following question: Does it make sense to speak of thought experiments not only in physics, but also in mathematics, to refer to an authentic type of activity' One may hesitate because mathematics as such is the exercise of reasoning par excellence, an activity where experience does not seem to play an important role. After reviewing some results of the research on thought experiments in the natural sciences, we turn our attention to experiments and thought experiments in mathematics, especially in fundamental mathematics, and investigate what thought experiments can teach us there. If we accept the principle that mathematical practice can sometimes be best described by a pragmatist approach where the concept of experience in mathematics is considered from a new perspective, thought experiments can in some cases be a useful instrument different from both ‘mathematical experiments’ and ‘formal’ proofs: they are mathematical experiments using deviant methods. PubDate: 2022-10-13
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Abstract: Abstract We observe that Putnam’s model-theoretic argument against determinacy of the concept of second-order quantification or that of the set is harmless to the nominalist. It serves as a good motivation for the nominalist philosophy of mathematics. But in the end it can lead to a serious challenge to the nominalist account of mathematical objectivity if some minimal assumptions about the relation between mathematical objectivity and logical objectivity are made. We consider three strategies the nominalist might take to meet this challenge, and we argue that all these strategies are untenable. PubDate: 2022-10-13
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Abstract: Abstract We ask how to use machine learning to expand observability, which presently depends on human learning that informs conceivability. The issue is engaged by considering the question of correspondence between conceived observability counterfactuals and observable, yet so far unobserved or unconceived, states of affairs. A possible answer lies in importing out of reference frame content which could provide means for conceiving further observability counterfactuals. They allow us to define high-fidelity observability, increasing the level of correspondence in question. To achieve high-fidelity observability, we propose to use generative machine learning models as the providers of the out of reference frame content. From an applied point of view, such a role of generative machine learning models shows an emerging dimension of human-machine cooperation. PubDate: 2022-10-05
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Abstract: Abstract On the basis of previous studies in relational biology and the phenomenological calculus, in my contribution I outline the mathematical foundations of biological perception generally, and visual perception specifically. In this approach, the premise is that objects in nature are not directly accessible, and that real manifestations are projections of these invariant objects. The morphology of observables is mathematically entailed by the duality of projections and projectors in a bilinear algebra that is the phenomenological calculus. The relationships between what is not directly accessible (which can be defined as noumena) and phenomena may be explicated in terms of metabolism and repair, whence a geometric theory of the perceived, the visible in particular, may be formulated in the category-theoretic language of relational biology. PubDate: 2022-10-01 DOI: 10.1007/s10516-019-09416-3
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Abstract: Abstract Natural forms, often characterized by irregularity and roughness, have a unique complexity that exhibit self-similarity across different spatial scales or levels of magnification. Our visual system is remarkably efficient in the processing of natural scenes and tuned to the multi-scale, fractal-like properties they possess. The fractal-like scaling characteristics are ubiquitous in many physical and biological domains, with recent research also highlighting their importance in aesthetic perception, particularly in the visual and, to some extent, auditory modalities. Given the multitude of fractal-like scaling manifestations, we explore potential commonalities in the way they might affect aesthetic preference within and across different physical and sensory domains. We use a range of visual and tactile stimuli to explore the equivalence of fractal-scaling effects on aesthetic preferences within and across visual and tactile modalities. Our results suggest that, despite some superficial differences, the underlying dimensional structure mediating the preference across the two domains is remarkably similar. The qualitative nature of this dimensional structure as well as suggestions for future research are discussed. PubDate: 2022-10-01 DOI: 10.1007/s10516-019-09444-z
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Abstract: Abstract In this paper we first recall geometrical models of neurogeometical in Lie groups and we show that geometrical properties of horizontal cortical connectivity can be considered as a neural correlate of a geometry of the visual plane. Then we introduce a new model of non isotropic cortical connectivity modeled on statistics of images. In this way we are able to justify oblique phenomena comparable with experimental findings. PubDate: 2022-10-01 DOI: 10.1007/s10516-019-09426-1
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Abstract: Abstract We explain the general significance of integer-based descriptors for natural shapes and show that the evolution of two such descriptors, called mechanical descriptors (the number N(t) of static balance points and the Morse–Smale graph associated with the scalar distance function measured from the center of mass) appear to capture (unlike classical geophysical shape descriptors) one of our most fundamental intuitions about natural abrasion: shapes get monotonically simplified in this process. Thus mechanical descriptors help to establish a correlation between subjective and objective descriptors of perceived objects. PubDate: 2022-10-01 DOI: 10.1007/s10516-018-9411-5
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Abstract: Abstract Space—an essential dimension of our life—is analyzable from different viewpoints, which often gives rise to contrasting conceptualizations. Perceptual analyses shed light on the intrinsic anisotropy and deformations of perceived space, raising the issue of which geometry may be able to represent perceptual space. Pictorial drawings and painting have been relevant sources of information about the nature of living and perceived space. Although the geometry of perceptual space is still in its infancy, contributions are beginning to appear. This special issue contributes to the development of the geometry of perceptual space. PubDate: 2022-10-01 DOI: 10.1007/s10516-021-09559-2
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Abstract: Abstract Every linear perspective image has a center of the perspective construction. Only when observed from that location does a 2D image provide the same stimulus as the original 3D scene. Geometric analyses indicate that observing the image from other vantage points should affect the perceived spatial structure of the scene conveyed by the image, involving transformations such as shear, compression, and dilation. Based on previous research, this paper presents a detailed account of these transformations. The analyses are presented in a uniform manner, illustrated with special 3D diagrams, and embedded in a wider framework of related perspective paradigms. Such analyses provide the potential theoretical basis for empirical work on the effects of changes of observer vantage points on the perception of spatial structure in perspective images. PubDate: 2022-10-01 DOI: 10.1007/s10516-019-09421-6
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