The logical hexagon (or hexagon of opposition) is a strange, yet beautiful, highly symmetrical mathematical figure, mysteriously intertwining fundamental logical and geometrical features. It was discovered more or less at the same time (i.e. around 1950), independently, by a few scholars. It is the successor of an equally strange (but mathematically less impressive) structure, the “logical square” (or “square of opposition”), of which it is a much more general and powerful “relative”. The discovery of the former did not raise interest, (...) neither among logicians, nor among philosophers of logic, whereas the latter played a very important theoretical role (both for logic and philosophy) for nearly two thousand years, before falling in disgrace in the first half of the twentieth century: it was, so to say, “sentenced to death” by the so-called analytical philosophers and logicians. Contrary to this, since 2004 a new, unexpected promising branch of mathematics (dealing with “oppositions”) has appeared, “oppositional geometry” (also called “n-opposition theory”, “NOT”), inside which the logical hexagon (as well as its predecessor, the logical square) is only one term of an infinite series of “logical bi-simplexes of dimension m”, itself just one term of the more general infinite series (of series) of the “logical poly-simplexes of dimension m”. In this paper we recall the main historical and the main theoretical elements of these neglected recent discoveries. After proposing some new results, among which the notion of “hybrid logical hexagon”, we show which strong reasons, inside oppositional geometry, make understand that the logical hexagon is in fact a very important and profound mathematical structure, destined to many future fruitful developments and probably bearer of a major epistemological paradigm change. (shrink)

Whereas geometrical oppositions (logical squares and hexagons) have been so far investigated in many fields of modal logic (both abstract and applied), the oppositional geometrical side of “deontic logic” (the logic of “obligatory”, “forbidden”, “permitted”, . . .) has rather been neglected. Besides the classical “deontic square” (the deontic counterpart of Aristotle’s “logical square”), some interesting attempts have nevertheless been made to deepen the geometrical investigation of the deontic oppositions: Kalinowski (La logique des normes, PUF, Paris, 1972) has proposed a (...) “deontic hexagon” as being the geometrical representation of standard deontic logic, whereas Joerden (jointly with Hruschka, in Archiv für Rechtsund Sozialphilosophie 73:1, 1987), McNamara (Mind 105:419, 1996) and Wessels (Die gute Samariterin. Zur Struktur der Supererogation, Walter de Gruyter, Berlin, 2002) have proposed some new “deontic polygons” for dealing with conservative extensions of standard deontic logic internalising the concept of “supererogation”. Since 2004 a new formal science of the geometrical oppositions inside logic has appeared, that is “ n -opposition theory”, or “NOT”, which relies on the notion of “logical bi-simplex of dimension m ” ( m = n − 1). This theory has received a complete mathematical foundation in 2008, and since then several extensions. In this paper, by using it, we show that in standard deontic logic there are in fact many more oppositional deontic figures than Kalinowski’s unique “hexagon of norms” (more ones, and more complex ones, geometrically speaking: “deontic squares”, “deontic hexagons”, “deontic cubes”, . . ., “deontic tetraicosahedra”, . . .): the real geometry of the oppositions between deontic modalities is composed by the aforementioned structures (squares, hexagons, cubes, . . ., tetraicosahedra and hyper-tetraicosahedra), whose complete mathematical closure happens in fact to be a “deontic 5-dimensional hyper-tetraicosahedron” (an oppositional very regular solid). (shrink)

Some Carrollian posthumous manuscripts reveal, in addition to his famous ‘logical diagrams’, two mysterious ‘logical charts’. The first chart, a strange network making out of fourteen logical sentences a large 2D ‘triangle’ containing three smaller ones, has been shown equivalent—modulo the rediscovery of a fourth smaller triangle implicit in Carroll's global picture—to a 3D tetrahedron, the four triangular faces of which are the 3+1 Carrollian complex triangles. As it happens, such an until now very mysterious 3D logical shape—slightly deformed—has been (...) rediscovered, independently from Carroll and much later, by a logician , a mathematician and a linguist studying the geometry of the ‘opposition relations’, that is, the mathematical generalisations of the ‘logical square’. We show that inside what is called equivalently ‘n-opposition theory’, ‘oppositional geometry’ or ‘logical geometry’, Carroll's first chart corresponds exactly, duly reshap.. (shrink)

In 1995 Slater argued both against Priest’s paraconsistent system LP (1979) and against paraconsistency in general, invoking the fundamental opposition relations ruling the classical logical square. Around 2002 Béziau constructed a double defence of paraconsistency (logical and philosophical), relying, in its philosophical part, on Sesmat’s (1951) and Blanche’s (1953) “logical hexagon”, a geometrical, conservative extension of the logical square, and proposing a new (tridimensional) “solid of opposition”, meant to shed new light on the point raised by Slater. By using n-opposition (...) theory (NOT) we analyse Beziau’s anti-Slater move and show both its right intuitions and its technical limits. Moreover, we suggest that Slater’s criticism is much akin to a well-known one by Suszko (1975) against the conceivability of many-valued logics. This last criticism has been addressed by Malinowski (1990) and Shramko and Wansing (2005), who developed a family of tenable logical counter-examples to it: trans-Suszkian systems are radically many-valued. This family of new logics has some strange logical features, essentially: each system has more than one consequence operator. We show that a new, deeper part of the aforementioned geometry of logical oppositions (NOT), the “logical poly-simplexes of dimension m”, generates new logical-geometrical structures, essentially many-valued, which could be a very natural (and intuitive) geometrical counterpart to the “strange”, new, non-Suszkian logics of Malinowski, Shramko and Wansing. By a similar move, the geometry of opposition therefore sheds light both on the foundations of paraconsistent logics and on those of many-valued logics. (shrink)

Transmission of justification across inference is a valuable and indeed ubiquitous epistemic phenomenon in everyday life and science. It is thanks to the phenomenon of epistemic transmission that inferential reasoning is a means for substantiating predictions of future events and, more generally, for expanding the sphere of our justified beliefs or reinforcing the justification of beliefs that we already entertain. However, transmission of justification is not without exceptions. As a few epistemologists have come to realise, more or less trivial forms (...) of circularity can prevent justification from transmitting from p to q even if one has justification for p and one is aware of the inferential link from p to q. In interesting cases this happens because one can acquire justification for p only if one has independent justification for q. In this case the justification for q cannot depend on the justification for p and the inferential link from p to q, as genuine transmission would require. The phenomenon of transmission failure seems to shed light on philosophical puzzles, such as Moore's proof of a material world and McKinsey's paradox, and it plays a central role in various philosophical debates. For this reason it is being granted continued and increasing attention. (shrink)

In an effort to produce new and more sustainable technologies, designers have turned to nature in search of inspiration and innovation. Biomimetic design (from the Greek bios, life, mimesis, imitation) is the conscious imitation of biological models to solve today's technical and ecological challenges. Nowadays numerous different approaches exist that take inspiration from nature as a model for design, such as biomimicry, biomimetics, bionics, permaculture, ecological engineering, etc. This variety of practices comes in turn with a wide range of different (...) promises, including sustainability, increased resilience, multi-functionality, and a lower degree of risk. How are we to make sense of this heterogeneous amalgam of existing practices and technologies, and of the numerous promises attached to them? We suggest that a typology of biomimetic approaches would provide a useful hermeneutic framework to understand the different tensions that pull this variegated landscape in different directions. This is achieved through a critical analysis of the literature in different fields of biomimetic design and the philosophy of biomimicry, in order to derive conceptual and normative assumptions concerning the meaning and value of the imitation of nature. These two dimensions are then intersected to derive an analytical grid composed of six different biomimetic types, which enable the classification of existing and possible biomimetic approaches, practices, and technologies according to their specific conceptual assumptions and guiding norms. (shrink)

This book examines phenomenal conservatism, one of the most influential and promising internalist conceptions of non-inferential justification debated in current epistemology and philosophy of mind. It also explores the significance of the findings of this examination for the general debate on epistemic justification. According to phenomenal conservatism, non-inferential justification rests on seemings or appearances, conceived of as experiences provided with propositional content. Phenomenal conservatism states that if it appears to S that P, in the absence of defeaters, S thereby has (...) some justification for believing that P. This view provides the basis for foundationalism and many ordinary epistemic practices. This book sheds new light on phenomenal conservatism by assessing objections to it and examining epistemological merits and advantages attributed to it. In a nutshell, phenomenal conservatism is actually compatible with Bayesian reasoning, and it is unaffected by bootstrapping problems and challenges that appeal to the cognitive penetrability of perception. Nevertheless, appearance-based justification proves unstable or elusive and its antisceptical bite is more limited than expected. These difficulties could be surmounted if phenomenal conservatism were integrated with a theory of inferential justification. The book appeals to scholars and postgraduates in the field of epistemology and philosophy of mind who are interested in the rational roles of appearances. (shrink)

Technology clearly plays a central role in Black Panther. Black Panther tries to make us think about the benefits and risks of employing vibranium – and by extension any advanced technology – to different ends. Through the blend of traditional cultures and technology, the Black Panther movie works as a powerfully imaginative thought experiment that explores the technological and cultural ramifications of an enlightened technologically advanced Afrofuturistic civilization. Wakanda's depiction as an independent African technological utopia where people live in harmony (...) with nature and among themselves offers a celebration both of the fruits of technology and of traditional African cultures. By imagining what an African techno‐utopia might look like, the movie tries to reimagine the relations between technology and culture. Vibranium has a cultural and spiritual role that is more prominent than its strictly technological properties. (shrink)

This book discusses fundamental topics on contemporary Ockhamism. The collected essays show how contemporary Ockhamism can impact areas of research such as semantics, metaphysics and also the philosophy of science. In addition, the volume hosts one historian of Medieval philosophy who investigates the way in which William of Ockham “in flesh and bone” construed time and, more generally, future contingency. The essays explore the different meanings of this theory. They cover three main topics, in particular. The first examines the thesis (...) that sentences and propositions about the future have a definite truth value, without any ensuing commitment to determinism or fatalism. The second topic looks at the problem whether the branching-time model needs to countenance a privileged branch (the so-called Thin Red Line). Finally, the third topic considers the idea that there are so-called soft facts. These would be the subject matter of sentences and propositions verbally about the present or the past, but metaphysically about a later time, and which might change in the future. Overall, the book provides an updated and rigorous idea of the debate about Ockhamism. It gives readers a deeper understanding into this philosophical approach influenced by William of Ockham, characterized by the rejection of the Aristotelian idea that, in order to preserve the contingency of the future, future contingents must be deemed neither true nor false. (shrink)

Phenomenal Conservatism (the view that an appearance that p gives one prima facie justification for believing that p) is a promising, and popular, internalist theory of epistemic justification. Despite its popularity, it faces numerous objections and challenges. For instance, epistemologists have argued that Phenomenal Conservatism is incompatible with Bayesianism, is afflicted by bootstrapping and cognitive penetration problems, does not guarantee that epistemic justification is a stable property, does not provide an account of defeat, and is not a complete theory of (...) epistemic justification. This book shows that Phenomenal Conservatism is actually immune to some of these problems, though not all of them. Accordingly, it explores the prospects of integrating Phenomenal Conservatism with Explanationism (the view that epistemic justification is a matter of explanatory relations between one’s evidence and propositions supported by that evidence). The resulting theory, Phenomenal Explanationism, has advantages over Phenomenal Conservatism and Explanationism taken on their own. Phenomenal Explanationism is a highly unified, comprehensive internalist theory of epistemic justification that delivers on the promises of Phenomenal Conservatism while avoiding its pitfalls. (shrink)

Phenomenal conservatism (PC) is the internalist view that non-inferential justification rests on appearances. PC’s advocates have recently argued that seemings are also required to explain inferential justification. The most general and developed view to this effect is Huemer (2016)’s theory of inferential seemings (ToIS). Moretti (2018) has shown that PC is affected by the problem of reflective awareness, which makes PC open to sceptical challenges. In this paper I argue that ToIS is afflicted by a version of the same (...) problem and it is thus hostage to inferential scepticism. I also suggest a possible response on behalf of ToIS’s advocates. (shrink)

This is the introduction to Moretti, Luca and Nikolaj Pedersen (eds), Non-Evidentialist Epistemology. Brill. Contributors: N. Ashton, A. Coliva, J. Kim, K. McCain, A. Meylan, L. Moretti, S. Moruzzi, J. Ohlorst, N. Pedersen, T. Piazza, L. Zanetti.

L’epistemologia (detta anche filosofia della conoscenza o gnoseologia) è la disciplina filosofica che studia come gli esseri umani si rapportano da un punto di vista cognitivo alla realtà che li circonda. Le questioni fondamentali che la interessano sono principalmente di natura normativa. Riguardano il modo in cui dovremmo regolare le nostre credenze alla luce dell’informazione in nostro possesso, e la natura della conoscenza umana ed i suoi limiti. Questo capitolo è organizzato in modo corrispondente. La prima sezione tratta della nozione (...) di giustificazione epistemica, la seconda quella di conoscenza, e la terza introduce il problema filosofico dello scetticismo. (shrink)

Social research, from economics to demography and epidemiology, makes extensive use of statistical models in order to establish causal relations. The question arises as to what guarantees the causal interpretation of such models. In this paper we focus on econometrics and advance the view that causal models are ‘augmented’ statistical models that incorporate important causal information which contributes to their causal interpretation. The primary objective of this paper is to argue that causal claims are established on the basis of a (...) plurality of evidence. We discuss the consequences of ‘evidential pluralism’ in the context of econometric modelling. (shrink)

In this paper we focus on transmission and failure of transmission of warrant. We identify three individually necessary and jointly sufficient conditions for transmission of warrant, and we show that their satisfaction grounds a number of interesting epistemic phenomena that have not been sufficiently appreciated in the literature. We then scrutinise Wright’s analysis of transmission failure and improve on extant readings of it. Nonetheless, we present a Bayesian counterexample that shows that Wright’s analysis is partially incoherent with our analysis of (...) warrant transmission and prima facie defective. We conclude exploring three alternative lines of reply: developing a more satisfactory account of transmission failure, which we outline; dismissing the Bayesian counterexample by rejecting some of its assumptions; reinterpreting Wright’s analysis to make it immune to the counterexample. (shrink)

Sleep and dreaming are important daily phenomena that are receiving growing attention from both the scientific and the philosophical communities. The increasingly popular predictive brain framework within cognitive science aims to give a full account of all aspects of cognition. The aim of this paper is to critically assess the theoretical advantages of Predictive Processing (PP, as proposed by Clark 2013, Clark 2016; and Hohwy 2013) in defining sleep and dreaming. After a brief introduction, we overview the state of the (...) art at the intersection between dream research and PP (with particular reference to Hobson and Friston 2012; Hobson et al. 2014). In the following sections we focus on two theoretically promising aspects of the research program. First, we consider the explanations of phenomenal consciousness during sleep (i.e. dreaming) and how it arises from the neural work of the brain. PP provides a good picture of the peculiarity of dreaming but it can’t fully address the problem of how consciousness comes to be in the first place. We propose that Integrated Information Theory (IIT) (Oizumi et al. 2014; Tononi et al. 2016) is a good candidate for this role and we will show its advantages and points of contact with PP. After introducing IIT, we deal with the evolutionary function of sleeping and dreaming. We illustrate that PP fits with contemporary researches on the important adaptive function of sleep and we discuss why IIT can account for sleep mentation (i.e. dreaming) in evolutionary terms (Albantakis et al. 2014). In the final section, we discuss two future avenues for dream research that can fruitfully adopt the perspective offered by PP: (a) the role of bodily predictions in the constitution of the sleeping brain activity and the dreaming experience, and (b) the precise role of the difference stages of sleep (REM (Rapid eye movement), NREM (Non-rapid eye movement) in the constitution and refinement of the predictive machinery. (shrink)

This paper addresses a fundamental line of research in neuroscience: the identification of a putative neural processing core of the cerebral cortex, often claimed to be “canonical”. This “canonical” core would be shared by the entire cortex, and would explain why it is so powerful and diversified in tasks and functions, yet so uniform in architecture. The purpose of this paper is to analyze the search for canonical explanations over the past 40 years, discussing the theoretical frameworks informing this research. (...) It will highlight a bias that, in my opinion, has limited the success of this research project, that of overlooking the dimension of cortical development. The earliest explanation of the cerebral cortex as canonical was attempted by David Marr, deriving putative cortical circuits from general mathematical laws, loosely following a deductive-nomological account. Although Marr’s theory turned out to be incorrect, one of its merits was to have put the issue of cortical circuit development at the top of his agenda. This aspect has been largely neglected in much of the research on canonical models that has followed. Models proposed in the 1980s were conceived as mechanistic. They identified a small number of components that interacted as a basic circuit, with each component defined as a function. More recent models have been presented as idealized canonical computations, distinct from mechanistic explanations, due to the lack of identifiable cortical components. Currently, the entire enterprise of coming up with a single canonical explanation has been criticized as being misguided, and the premise of the uniformity of the cortex has been strongly challenged. This debate is analyzed here. The legacy of the canonical circuit concept is reflected in both positive and negative ways in recent large-scale brain projects, such as the Human Brain Project. One positive aspect is that these projects might achieve the aim of producing detailed simulations of cortical electrical activity, a negative one regards whether they will be able to find ways of simulating how circuits actually develop. (shrink)

This paper analyzes the rapid and unexpected rise of deep learning within Artificial Intelligence and its applications. It tackles the possible reasons for this remarkable success, providing candidate paths towards a satisfactory explanation of why it works so well, at least in some domains. A historical account is given for the ups and downs, which have characterized neural networks research and its evolution from “shallow” to “deep” learning architectures. A precise account of “success” is given, in order to sieve out (...) aspects pertaining to marketing or sociology of research, and the remaining aspects seem to certify a genuine value of deep learning, calling for explanation. The alleged two main propelling factors for deep learning, namely computing hardware performance and neuroscience findings, are scrutinized, and evaluated as relevant but insufficient for a comprehensive explanation. We review various attempts that have been made to provide mathematical foundations able to justify the efficiency of deep learning, and we deem this is the most promising road to follow, even if the current achievements are too scattered and relevant for very limited classes of deep neural models. The authors’ take is that most of what can explain the very nature of why deep learning works at all and even very well across so many domains of application is still to be understood and further research, which addresses the theoretical foundation of artificial learning, is still very much needed. (shrink)

In this paper we defend structural representations, more specifically neural structural representation. We are not alone in this, many are currently engaged in this endeavor. The direction we take, however, diverges from the main road, a road paved by the mathematical theory of measure that, in the 1970s, established homomorphism as the way to map empirical domains of things in the world to the codomain of numbers. By adopting the mind as codomain, this mapping became a boon for all those (...) convinced that a representation system should bear similarities with what was being represented, but struggled to find a precise account of what such similarities mean. The euforia was brief, however, and soon homomorphism revealed itself to be affected by serious weaknesses, the primary one being that it included systems embarrassingly alien to representations. We find that the defense attempts that have followed, adopt strategies that share a common format: valid structural representations come as “homomorphism plus X”, with various “X”, provided in descriptive format only. Our alternative direction stems from the observation of the overlooked departure from homomorphism as used in the theory of measure and its later use in mental representations. In the former case, the codomain or the realm of numbers, is the most suited for developing theorems detailing the existence and uniqueness of homomorphism for a wide range of empirical domains. In the latter case, the codomain is the realm of the mind, possibly more vague and more ill-defined than the empirical domain itself. The time is ripe for articulating the mapping between represented domains and the mind in formal terms, by exploiting what is currently known about coding mechanisms in the brain. We provide a sketch of a possible development in this direction, one that adopts the theory of neural population coding as codomain. We will show that our framework is not only not in disagreement with the “plus X” proposals, but can lead to natural derivation of several of the “X”. (shrink)

Nature is a key theme of philosophical concerns today. This book examines Merleau-Ponty’s investigations on nature and provides a timely guide to his remarkable approach to scientific advances and their implications for our understanding of nature.

We investigate an extension of the formalism of interpreted systems by Halpern and colleagues to model the correct behaviour of agents. The semantical model allows for the representation and reasoning about states of correct and incorrect functioning behaviour of the agents, and of the system as a whole. We axiomatise this semantic class by mapping it into a suitable class of Kripke models. The resulting logic, KD45n i-j, is a stronger version of KD, the system often referred to as Standard (...) Deontic Logic. We extend this formal framework to include the standard epistemic notions defined on interpreted systems, and introduce a new doubly-indexed operator representing the knowledge that an agent would have if it operates under the assumption that a group of agents is functioning correctly. We discuss these issues both theoretically and in terms of applications, and present further directions of work. (shrink)

In this chapter I introduce and analyse the tenets of phenomenal conservatism, and discuss the problem of the nature of appearances. After that, I review the asserted epistemic merits phenomenal conservatism and the principal arguments adduced in support of it. Finally, I survey objections to phenomenal conservatism and responses by its advocates. Some of these objections will be scrutinised and appraised in the next chapters.

We investigate an extension of the formalism of interpreted systems by Halpern and colleagues to model the correct behaviour of agents. The semantical model allows for the representation and reasoning about states of correct and incorrect functioning behaviour of the agents, and of the system as a whole. We axiomatise this semantic class by mapping it into a suitable class of Kripke models. The resulting logic, KD45ni-j, is a stronger version of KD, the system often referred to as Standard Deontic (...) Logic. We extend this formal framework to include the standard epistemic notions defined on interpreted systems, and introduce a new doubly-indexed operator representing the knowledge that an agent would have if it operates under the assumption that a group of agents is functioning correctly. We discuss these issues both theoretically and in terms of applications, and present further directions of work. (shrink)

Emancipating from prejudices, dogmatism, fears and mistrust through direct participation is the knot of education for democracy to be solved for a discipline such as education which, in contemporary times, cannot and must never be deaf to change. The essential assumption is that citizenship education needs a solid ethical and moral dimension, as well as a personal and social one, before political and administrative; only when the awareness of the inviolable rights of individuals, men and citizens, of their indifferent protection (...) and awareness of the choices to be made for their exercise emerges from below, then it is possible to organize the step to be taken in the direction of educational and training choices. (shrink)

SOCREAL 2013 : 3rd International Workshop on Philosophy and Ethics of Social Reality 2013. Hokkaido University, Sapporo, Japan, 25-27 October 2013. Session 2 : Imperatives and Norms.

Perceptual experience is one of our fundamental sources of epistemic justification—roughly, justification for believing that a proposition is true. The ability of perceptual experience to justify beliefs can nevertheless be questioned. This article focuses on an important challenge that arises from countenancing that perceptual experience is cognitively penetrable. -/- The thesis of cognitive penetrability of perception states that the content of perceptual experience can be influenced by prior or concurrent psychological factors, such as beliefs, fears and desires. Advocates of this (...) thesis could for instance claim that your desire of having a tall daughter might influence your perception, so that she appears to you to be taller than she is. Although cognitive penetrability of perception is a controversial empirical hypothesis, it does not appear implausible. The possibility of its veracity has been adduced to challenge positions that maintain that perceptual experience has inherent justifying power. -/- This article presents some of the most influential positions in contemporary literature about whether cognitive penetration would undermine perceptual justification and why it would or would not do so. -/- Some sections of this article focus on phenomenal conservatism, a popular conception of epistemic justification that more than any other has been targeted with objections that adduce the cognitive penetrability of experience. (shrink)

From epileptic seizures to depressive symptoms, predictive neurotechnologies are used for a large range of applications. In this article we focus on advisory devices; namely, predictive neurotechnology programmed to detect specific neural events (e.g., epileptic seizure) and advise users to take necessary steps to reduce or avoid the impact of the forecasted neuroevent. Receiving advise from a predictive device is not without ethical concerns. The problem with predictive neural devices, in particular advisory ones, is the risk of seeing one’s autonomous (...) choice supplanted by the predictions instead of being supplemented by it. For users, there is a potential shift from being assisted by the system to being over-dependent on the technology. In other terms, it introduces ethical issues associated with epistemic dependency. In this article, we examine the notion of epistemic authority in relation to predictive neurotechnologies. Section 1 of our article explores and defines the concept of epistemic authority. In section 2, we illustrate how predictive devices are best conceived of as epistemic authorities and we explore the subject-device epistemic relationship. In section 3, we spell out the risk of harms interconnected with epistemic deferral. We conclude by stressing a set of preliminary measures to prepare users for the authoritative nature of predictive devices. (shrink)