Apart from the opposite semantic attitudes, the main difference between Late Medieval Realists and Nominalists lies in the antithetic evalutation of the nature and ontological status of essences. In the article a very interesting exemple of the medieval realist approach to the problem of essence, that of Walter Burley, is discussed. Because of Ockham's criticisms of the traditional realist conceptions, Burley's ontological convictions evolved over the years from a quite original version of the moderate realism inspired by Averroe's doctrine on (...) essence, to the radical (and somehow Platonic) form of realism proper to his final theories. (shrink)

The relationship between thought and reality was a focal point of Wyclif’s reflection. On the one hand, Wyclif believed that thought was linguistically constrained by its own nature; on the other hand, he considered thought to be related to reality in its elements and constitution. Hence he deemed language, thought, and external reality to be of the same logical coherence. Within this context, the theory of supposition was intended to explain the different roles that terms can have in relation to (...) language and the extra-mental world when they appear as extremes in propositions. Characteristically, his theory of supposition provides an account not only of the truth-values of a sentence, but also of its meaning; it is not therefore simply a theory of reference, but a sort of complex analysis of language viewed as a semiotic system whose unique interpretative model was reality itself. It gives clear evidence of Wyclif’s realist stance and of his conviction that any kind of linguistic and semantic features must be grounded on ontological structures. (shrink)

Recent advances on quantum foundations achieved the derivation of free quantum field theory from general principles, without referring to mechanical notions and relativistic invariance. From the aforementioned principles a quantum cellular automata theory follows, whose relativistic limit of small wave-vector provides the free dynamics of quantum field theory. The QCA theory can be regarded as an extended quantum field theory that describes in a unified way all scales ranging from an hypothetical discrete Planck scale up to the usual Fermi scale. (...) The present paper reviews the automaton theory for the Weyl field, and the composite automata for Dirac and Maxwell fields. We then give a simple analysis of the dynamics in the momentum space in terms of a dispersive differential equation for narrowband wave-packets. We then review the phenomenology of the free-field automaton and consider possible visible effects arising from the discreteness of the framework. We conclude introducing the consequences of the automaton dispersion relation, leading to a deformed Lorentz covariance and to possible effects on the thermodynamics of ideal gases. (shrink)

We prove that if G is a Δ 0 -definable function on the natural numbers and F = Π i = 0 n G , then F is also Δ 0 -definable. Moreover, the inductive properties of F can be proved inside the theory IΔ 0.

After leading to a new axiomatic derivation of quantum theory, the new informational paradigm is entering the domain of quantum field theory, suggesting a quantum automata framework that can be regarded as an extension of quantum field theory to including an hypothetical Planck scale, and with the usual quantum field theory recovered in the relativistic limit of small wave-vectors. Being derived from simple principles, the automata theory is quantum ab-initio, and does not assume Lorentz covariance and mechanical notions. Being discrete (...) it can describe localized states and measurements, solving all the issues plaguing field theory originated from the continuum. These features make the theory an ideal framework for quantum gravity, with relativistic covariance and space-time emergent solely from the interactions, and not assumed a priori. The paper presents a synthetic derivation of the automata theory, showing how the principles lead to a description in terms of a quantum automaton over a Cayley graph of a group. Restricting to Abelian groups we show how the automata recover the Weyl, Dirac and Maxwell dynamics in the relativistic limit. We conclude with some new routes about the more general scenario of non-Abelian Cayley graphs. The phenomenology arising from the automata theory in the ultra-relativistic domain and the analysis of corresponding distorted Lorentz covariance is reviewed in Bisio et al. (shrink)

The uncertainty on measurements, given by the Heisenberg principle, is a quantum concept usually not taken into account in General Relativity. From a cosmological point of view, several authors wonder how such a principle can be reconciled with the Big Bang singularity, but, generally, not whether it may affect the reliability of cosmological measurements. In this letter, we express the Compton mass as a function of the cosmological redshift. The cosmological application of the indetermination principle unveils the differences of the (...) Hubble-Lemaître constant value, $$H_0$$, as measured from the Cepheids estimates and from the Cosmic Microwave Background radiation constraints. In conclusion, the $$H_0$$ tension could be related to the effect of indetermination derived in comparing a kinematic with a dynamic measurement. (shrink)

Robots are versatile devices that are promising tools for supporting teaching and learning in the classroom or at home. In fact, robots can be engaging and motivating, especially for young children. This paper presents an experimental study with 81 kindergarten children on memorizations of two tales narrated by a humanoid robot. The variables of the study are the content of the tales (knowledge or emotional) and the different social behaviour of the narrators: static human, static robot, expressive human, and expressive (...) robot. Results suggest a positive effect of the expressive behaviour in robot storytelling, whose effectiveness is comparable to a human with the same behaviour and better when compared with a static inexpressive human. Higher efficacy is achieved by the robot in the tale with knowledge content, while the limited capability to express emotions made the robot less effective in the tale with emotional content. (shrink)

For an observation time equal to the universe age, the Heisenberg principle fixes the value of the smallest measurable mass at mH=1.35×10-69\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m_\mathrm{H}=1.35 \times 10^{-69}$$\end{document} kg and prevents to probe the masslessness for any particle using a balance. The corresponding reduced Compton length to mH\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m_\mathrm{H}$$\end{document} is, and represents the length limit beyond which masslessness cannot be proved using a metre ruler. In turns, is (...) equated to the luminosity distance dH\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d_\mathrm{H}$$\end{document} which corresponds to a red shift zH\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_\mathrm{H}$$\end{document}. When using the Concordance-Model parameters, we get dH=8.4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d_\mathrm{H} = 8.4$$\end{document} Gpc and zH=1.3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_\mathrm{H}=1.3$$\end{document}. Remarkably, dH\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d_\mathrm{H}$$\end{document} falls quite short to the radius of the observable universe. According to this result, tensions in cosmological parameters could be nothing else but due to comparing data inside and beyond zH\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_\mathrm{H}$$\end{document}. Finally, in terms of quantum quantities, the expansion constant H0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_0$$\end{document} reveals to be one order of magnitude above the smallest measurable energy, divided by the Planck constant. (shrink)

The German Johannes Sharpe is the most important and original author of the so called "Oxford Realists": his semantic and metaphysical theories are the end product of the two main medieval philosophical traditions, realism and nominalism, for he contributed to the new form of realism inaugurated by Wyclif, but was receptive to many nominalist criticisms. Starting from the main thesis of Wyclif's metaphysics, that the universal and individual are really identical but formally distinct, Oxford Realists introduced a new type of (...) predication, based on a partial identity between the entities for which the subject and predicate stood, called predication by essence, and then redefined the traditional post-Aristotelian categories of essential and accidental predication in terms of this partial identity. Sharpe substantially shares the metaphysical view and principles of the other Oxford Realists, but he elaborates a completely different semantics, since he accepts the nominalist principle of the autonomy of thought in relation to the world, and Ockham's explanation for the universality of concepts. Unfortunately, this semantic approach partially undermines his defence of realism, since it deprives Sharpe of any compelling semantic and epistemological reasons to posit universalia in re. Therefore, Sharpe's main ontological theses certainly are sensible and reasonable, but, paradoxically, within his philosophical system they cannot in any way be considered as absolutely consistent. (shrink)

Robots are versatile devices that are promising tools for supporting teaching and learning in the classroom or at home. In fact, robots can be engaging and motivating, especially for young children. This paper presents an experimental study with 81 kindergarten children on memorizations of two tales narrated by a humanoid robot. The variables of the study are the content of the tales (knowledge or emotional) and the different social behaviour of the narrators: static human, static robot, expressive human, and expressive (...) robot. Results suggest a positive effect of the expressive behaviour in robot storytelling, whose effectiveness is comparable to a human with the same behaviour and better when compared with a static inexpressive human. Higher efficacy is achieved by the robot in the tale with knowledge content, while the limited capability to express emotions made the robot less effective in the tale with emotional content. (shrink)

Philosophers have rightly condemned lookism—that is, discrimination in favor of attractive people or against unattractive people—in education, the justice system, the workplace and elsewhere. Surprisingly, however, the almost universal preference for attractive romantic and sexual partners has rarely received serious ethical scrutiny. On its face, it’s unclear whether this is a form of discrimination we should reject or tolerate. I consider arguments for both views. On the one hand, a strong case can be made that preferring attractive partners is bad. (...) The idea is that choosing partners based on looks seems essentially similar to other objectionable forms of discrimination. (In particular, the preference for attractive partners is arguably both unfair and harmful to a significant degree.) One can try to resist this conclusion in several ways. I consider three possible replies. The first has to do with the possibility of controlling our partner preferences. The second pertains to attractiveness and “good genes”. The last attempts to link certain aspects of attractiveness to a prospective partner’s personality and values. I argue that the first two replies fail conclusively, while the third only amounts to a limited defense of a particular kind of attractiveness preference. So the idea that we should often avoid preferring attractive partners is compelling. (shrink)

Walter Burley was one of the most prominent logicians and metaphysicians of the Middle Ages. This volume, which contain thirteen substantial articles on his philosophy, is aimed to reconstruct the internal evolution of his doctrines and the role they played in the development of Late Medieval philosophy.

Recent research showed the potential benefits of robot-assisted therapy in treating children with Autism Spectrum Disorder. These children often have some form of Intellectual Disability too, but this has mainly been neglected by previous robotics research. This article presents an empirical evaluation of robot-assisted imitation training, where the child imitated the robot, integrated into the Treatment and Education of Autistic and related Communication handicapped Children program. The sample included six hospitalized children with different levels of ID, from mild to profound. (...) We applied mixed methods to assess their progress, during treatment and three months later. Results show increased Gross Motor Imitation skills in the children, except for those with profound ID and the therapists’ positive attitude towards the humanoid robot. Furthermore, the therapists suggest how a robot could be used to autonomously collect and analyze the information obtained in the rehabilitation training for a continuous evaluation of the participants. (shrink)

According to a widespread view in metaphysics and philosophy of science, all explanations involve relations of ontic dependence between the items appearing in the explanandum and the items appearing in the explanans. I argue that a family of mathematical cases, which I call “viewing-as explanations”, are incompatible with the Dependence Thesis. These cases, I claim, feature genuine explanations that aren’t supported by ontic dependence relations. Hence the thesis isn’t true in general. The first part of the paper defends this claim (...) and discusses its significance. The second part of the paper considers whether viewing-as explanations occur in the empirical sciences, focusing on the case of so-called fictional models. It’s sometimes suggested that fictional models can be explanatory even though they fail to represent actual worldly dependence relations. Whether or not such models explain, I suggest, depends on whether we think scientific explanations necessarily give information relevant to intervention and control. Finally, I argue that counterfactual approaches to explanation also have trouble accommodating viewing-as cases. (shrink)

We discuss potential biorisks from large language models (LLMs). AI assistants based on LLMs such as ChatGPT have been shown to significantly reduce barriers to entry for actors wishing to synthesize dangerous, potentially novel pathogens and chemical weapons. The harms from deploying such bioagents could be further magnified by AI-assisted misinformation. We endorse several policy responses to these dangers, including prerelease evaluations of biomedical AIs by subject-matter experts, enhanced surveillance and lab screening procedures, restrictions on AI training data, and access (...) controls on biomedical AI. We conclude with a suggestion about future research directions in bioethics. (shrink)

The problem of truth in fiction concerns how to tell whether a given proposition is true in a given fiction. Thus far, the nearly universal consensus has been that some propositions are ‘implicitly true’ in some fictions: such propositions are not expressed by any explicit statements in the relevant work, but are nevertheless held to be true in those works on the basis of some other set of criteria. I call this family of views ‘implicitism’. I argue that implicitism faces (...) serious problems, whereas the opposite view is much more plausible than has previously been thought. After mounting a limited defence of explicitism, I explore a difficult problem for the view and discuss some possible responses. (shrink)

Much recent work on mathematical explanation has presupposed that the phenomenon involves explanatory proofs in an essential way. I argue that this view, ‘proof chauvinism’, is false. I then look in some detail at the explanation of the solvability of polynomial equations provided by Galois theory, which has often been thought to revolve around an explanatory proof. The article concludes with some general worries about the effects of chauvinism on the theory of mathematical explanation. 1Introduction 2Why I Am Not a (...) Proof Chauvinist 2.1Proof chauvinism and mathematical practice 2.2Proof chauvinism and philosophy 3An Example: Galois Theory and Explanatory Proof 4Conclusion. (shrink)

Gauss’s quadratic reciprocity theorem is among the most important results in the history of number theory. It’s also among the most mysterious: since its discovery in the late 18th century, mathematicians have regarded reciprocity as a deeply surprising fact in need of explanation. Intriguingly, though, there’s little agreement on how the theorem is best explained. Two quite different kinds of proof are most often praised as explanatory: an elementary argument that gives the theorem an intuitive geometric interpretation, due to Gauss (...) and Eisenstein, and a sophisticated proof using algebraic number theory, due to Hilbert. Philosophers have yet to look carefully at such explanatory disagreements in mathematics. I do so here. According to the view I defend, there are two important explanatory virtues—depth and transparency—which different proofs (and other potential explanations) possess to different degrees. Although not mutually exclusive in principle, the packages of features associated with the two stand in some tension with one another, so that very deep explanations are rarely transparent, and vice versa. After developing the theory of depth and transparency and applying it to the case of quadratic reciprocity, I draw some morals about the nature of mathematical explanation. (shrink)

Philosophers of science since Nagel have been interested in the links between intertheoretic reduction and explanation, understanding and other forms of epistemic progress. Although intertheoretic reduction is widely agreed to occur in pure mathematics as well as empirical science, the relationship between reduction and explanation in the mathematical setting has rarely been investigated in a similarly serious way. This paper examines an important particular case: the reduction of arithmetic to set theory. I claim that the reduction is unexplanatory. In defense (...) of this claim, I offer evidence from mathematical practice, and I respond to contrary suggestions due to Steinhart, Maddy, Kitcher and Quine. I then show how, even if set-theoretic reductions are generally not explanatory, set theory can nevertheless serve as a legitimate foundation for mathematics. Finally, some implications of my thesis for philosophy of mathematics and philosophy of science are discussed. In particular, I suggest that some reductions in mathematics are probably explanatory, and I propose that differing standards of theory acceptance might account for the apparent lack of unexplanatory reductions in the empirical sciences. (shrink)

Mathematicians distinguish between proofs that explain their results and those that merely prove. This paper explores the nature of explanatory proofs, their role in mathematical practice, and some of the reasons why philosophers should care about them. Among the questions addressed are the following: what kinds of proofs are generally explanatory (or not)? What makes a proof explanatory? Do all mathematical explanations involve proof in an essential way? Are there really such things as explanatory proofs, and if so, how do (...) they relate to the sorts of explanation encountered in philosophy of science and metaphysics? (shrink)

The field of AI safety aims to prevent increasingly capable artificially intelligent systems from causing humans harm. Research on moral alignment is widely thought to offer a promising safety strategy: if we can equip AI systems with appropriate ethical rules, according to this line of thought, they'll be unlikely to disempower, destroy or otherwise seriously harm us. Deontological morality looks like a particularly attractive candidate for an alignment target, given its popularity, relative technical tractability and commitment to harm-avoidance principles. I (...) argue that the connection between moral alignment and safe behavior is more tenuous than many have hoped. In general, AI systems can possess either of these properties in the absence of the other, and we should favor safety when the two conflict. In particular, advanced AI systems governed by standard versions of deontology need not be especially safe. (shrink)

This article argues that William James's thinking in The Varieties and elsewhere contains the view that social institutions, such as religious congregations and schools, are mediators between the private and public spheres of life, and are necessary for transforming personal feelings, ideals and beliefs into moral action. The Exercises of St Ignatius and the Just Community moral education approach serve as examples. Criticisms of the more commonly held view that James recognised only individual personal experiences as valid religious expressions are (...) marshalled. Furthermore, we argue that moral action or saintliness, the ultimate expression of religious faith according to James, is fundamentally social. The commonalities that the phenomenologies of moral action of St Ignatius and Lawrence Kohlberg have with William James's view are used to support the argument. (shrink)

In this paper we study the emergence of Minkowski space–time from a discrete causal network representing a classical information flow. Differently from previous approaches, we require the network to be topologically homogeneous, so that the metric is derived from pure event-counting. Emergence from events has an operational motivation in requiring that every physical quantity—including space–time—be defined through precise measurement procedures. Topological homogeneity is a requirement for having space–time metric emergent from the pure topology of causal connections, whereas physically homogeneity corresponds (...) to the universality of the physical law. We analyze in detail the case of 1+1 dimensions. If we consider the causal connections as an exchange of classical information, we can establish coordinate systems via an Einsteinian protocol, and this leads to a digital version of the Lorentz transformations. In a computational analogy, the foliation construction can be regarded as the synchronization with a global clock of the calls to independent subroutines in a parallel distributed computation. Thus the Lorentz time-dilation emerges as an increased density of leaves within a single tic-tac of a clock, whereas space-contraction results from the corresponding decrease of density of events per leaf. The operational procedure of building up the coordinate system introduces an in-principle indistinguishability between neighboring events, resulting in a network that is coarse-grained, the thickness of the event being a function of the observer's clock. The illustrated simple classical construction can be extended to space dimension greater than one, with the price of anisotropy of the maximal speed, due to the Weyl-tiling problem. This issue is cured if the causal network is quantum, as e.g. in a quantum cellular automaton, and isotropy is recovered by quantum coherence via superposition of causal paths. We thus argue that in a causal network description of space–time, the quantum nature of the network is crucial. (shrink)

In a recent letter, Dillion et. al (2023) make various suggestions regarding the idea of artificially intelligent systems, such as large language models, replacing human subjects in empirical moral psychology. We argue that human subjects are in various ways indispensable.

A proof P of a theorem T is transferable when a typical expert can become convinced of T solely on the basis of their prior knowledge and the information contained in P. Easwaran has argued that transferability is a constraint on acceptable proof. Meanwhile, a proof P is fixable when it’s possible for other experts to correct any mistakes P contains without having to develop significant new mathematics. Habgood-Coote and Tanswell have observed that some acceptable proofs are both fixable and (...) in need of fixing, in the sense that they contain nontrivial mistakes. The claim that acceptable proofs must be transferable seems quite plausible. The claim that some acceptable proofs need fixing seems plausible too. Unfortunately, these attractive suggestions stand in tension with one another. I argue that the transferability requirement is the problem. Acceptable proofs need only satisfy a weaker requirement I call “corrigibility”. I explain why, despite appearances, the corrigibility standard is preferable to stricter alternatives. (shrink)

This is a teaching and learning guide to accompany "Explanation in Mathematics: Proofs and Practice".

Models are indispensable tools of scientific inquiry, and one of their main uses is to improve our understanding of the phenomena they represent. How do models accomplish this? And what does this tell us about the nature of understanding? While much recent work has aimed at answering these questions, philosophers' focus has been squarely on models in empirical science. I aim to show that pure mathematics also deserves a seat at the table. I begin by presenting two cases: Cramér’s random (...) model of the prime numbers and the function field model of the integers. These cases show that mathematicians, like empirical scientists, rely on unrealistic models to gain understanding of complex phenomena. They also have important implications for some much-discussed theses about scientific understanding. First, modeling practices in mathematics confirm that one can gain understanding without obtaining an explanation. Second, these cases undermine the popular thesis that unrealistic models confer understanding by imparting counterfactual knowledge. (shrink)

In the past decades, an enormous amount of precious information has been collected about molecular and genetic characteristics of cancer. This knowledge is mainly based on a reductionistic approach, meanwhile cancer is widely recognized to be a ‘system biology disease’. The behavior of complex physiological processes cannot be understood simply by knowing how the parts work in isolation. There is not solely a matter how to integrate all available knowledge in such a way that we can still deal with complexity, (...) but we must be aware that a deeply transformation of the currently accepted oncologic paradigm is urgently needed. We have to think in terms of biological networks: understanding of complex functions may in fact be impossible without taking into consideration influences outside of the genome. Systems Biology involves connecting experimental unsupervised multivariate data to mathematical and computational approach than can simulate biologic systems for hypothesis testing or that can account for what it is not known from high-throughput data sets. Metabolomics could establish the requested link between genotype and phenotype, providing informations that ensure an integrated understanding of pathogenic mechanisms and metabolic phenotypes and provide a screening tool for new targeted drug. (shrink)

Recent progress in artificial intelligence (AI) has drawn attention to the technology’s transformative potential, including what some see as its prospects for causing large-scale harm. We review two influential arguments purporting to show how AI could pose catastrophic risks. The first argument — the Problem of Power-Seeking — claims that, under certain assumptions, advanced AI systems are likely to engage in dangerous power-seeking behavior in pursuit of their goals. We review reasons for thinking that AI systems might seek power, that (...) they might obtain it, that this could lead to catastrophe, and that we might build and deploy such systems anyway. The second argument claims that the development of human-level AI will unlock rapid further progress, culminating in AI systems far more capable than any human — this is the Singularity Hypothesis. Power-seeking behavior on the part of such systems might be particularly dangerous. We discuss a variety of objections to both arguments and conclude by assessing the state of the debate. (shrink)