At M. Bernard's I saw several magnificent paintings on porcelain by Monsieur Constantin. In two hundred years, Raphael's frescoes will be known only through Monsieur Constantin.Stendhal, Voyage en France, 1837If we compare the forms that the act of copying has assumed in various civilizations, we cannot fail to notice that a certain number of phenomena are specific to European culture since the Renaissance. Perhaps one of the most singular of these phenomena is the will to create and to possess imperishable (...) reproductions of works that have been singled out, at a given moment, as the brightest jewels of Western art. The history of the fortune of Graeco-Roman sculptures has been masterfully related by Francis Haskell and Nicholas Penny in Taste and the Antique: The Lure of Classical Sculpture 1500-1900, even if it would no doubt be worthwhile to give further consideration to the critical fortune of materials used for reproduction, and particularly to the particular prestige attached to bronze—from the Mantuan works of Antico to the reconstitutions of Greek Urbilder in bronze, instead of the plaster used earlier, which were executed at the beginning of the twentieth century, such as the two Doryphoros that Georg Römer realized from various ancient marble copies of Polyclitus's athlete. But, in fact, it was not only in modern Europe that copies were made in bronze. The production of copies using this alloy was particularly prevalent in imperial China after the rediscovery, in the second half of the eleventh century of our era, of a collection of archaic bronzes from the Shang era. This is why I prefer to call attention to a practice that appears to me, in contrast, to be unique to the Western world: the copying of renowned paintings in materials that are supposed to defy time. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reflections on Raphael PAUL BAROLSKY The essence of all appreciation and analysis of art is the translation of visual perceptions into compelling verbal form. —Ralph Lieberman cultural unity Horace Walpole, Sir Joshua Reynolds, Johann Wolfgang Goethe, Eugène Delacroix, Honoré Balzac, Friedrich Hegel, Charles Baudelaire, Friedrich Nietzsche, Pierre Renoir, Nathaniel Hawthorne, August Wilhelm von Schlegel, Heinrich von Kleist, Franz Grillparzer, Fyodor Dostoyevsky, Ivan Turgenev, Wilhelm Heinrich Wackenroder, George Eliot, Jean-Auguste (...) Dominique Ingres, Roger Fry, Bernard Berenson, Theodor Hetzer, Roberto Longhi, Heinrich Wölfflin, and Stendhal are among the many essayists, critics, novelists, poets, painters and art historians who have responded to Raphael’s work as painter, architect or archeologist over the centuries. I can well imagine all of those listed above, among many others, united in an imaginary painting similar to the School of Athens—in other words, a vision that reconciles their various views of the world in a harmony analogous to the unity of philosophers in Raphael’s great fresco. Raphael is a towering figure in the history of European culture. The year 2020 was the 500th anniversary of the death of the great painter in Rome at the age of thirty-seven. In the wake of recent exhibitions that commemorated the artist’s achievement, I propose to touch briefly and lightly on a few aspects arion 28.2 fall 2020 100 reflections on raphael of Raphael’s life and works. Please think of these remarks as a series of suggestions, not attempts at definitive interpretation. I think of this essay as a rather experimental piece. THE SCHOOL OF ATHENS i should like to begin with a few brief remarks on what must be Raphael’s most famous work of art. I mean his School of Athens (fig. 1), which is, like Leonardo’s Mona Lisa and Last Supper or like Michelangelo’s David and Creation of Adam, an image widely known and admired. What more is there to say about The School Of Athens, one of the central images in the Stanza della Segnatura? You might spend the rest of your life reading about this great work and never understand it fully. Nevertheless, I want to focus for a moment on a central detail of the work and, on the basis of my description, point to a significant aspect of the fresco that has been universally overlooked. First the description, then the aperçu. Fig. 1. School of Athens. Ca. 1510–1512. Photo Credit : Erich Lessing / Art Resource, NY. Paul Barolsky 101 At the center of the School of Athens we behold the two great philosophers of classical antiquity: Plato and Aristotle. Plato holds a copy of his Timaeus, a dialogue that concerns the harmony of the heavens; Aristotle holds a copy of his Ethics, a work that pertains to human relations in this world. It was the goal of Renaissance thinkers to create a harmony or concord of the thought of these philosophers: a Concordia Platonis et Aristotelis. Raphael’s fresco, as is well known, presents the visual ideal of such harmony. Whereas Aristotle gestures downward, alluding to this world, in which his Ethics matter, Plato points heavenward, evoking the order of the cosmic realm described in Timaeus. Raphael makes visible the ideal of concordia when he movingly pictures the way in which the two philosophers gaze into each other’s eyes, as if to suggest this harmony. Borrowing from the language of Raphael ’s friend, Baldassare Castiglione, Raphael renders “the joining” of their souls. The monumental architecture of the scene, which echoes Bramante and has taproots in Piero della Francesca and Perugino, consists of three barrel-vaults beyond which we see patches of blue sky and puffs of cloud (fig. 2). The grandiose architecture of the image magnifies Raphael’s philosophers. Within this architectural framework, Plato’s gesture is deeply meaningful, since it prompts the viewer to look up and thus ascend toward the perfection of the celestial realm, beyond the imperfections of the physical world. Above the first barrel vault in the fresco we behold a section of the drum of a dome which is open to the sky. Within this section of drum there are two columns that are lined up directly... (shrink)

In recent philosophy of mathematics avariety of writers have presented ``structuralist''views and arguments. There are, however, a number ofsubstantive differences in what their proponents take``structuralism'' to be. In this paper we make explicitthese differences, as well as some underlyingsimilarities and common roots. We thus identifysystematically and in detail, several main variants ofstructuralism, including some not often recognized assuch. As a result the relations between thesevariants, and between the respective problems theyface, become manifest. Throughout our focus is onsemantic and metaphysical issues, (...) including what is orcould be meant by ``structure'' in this connection. (shrink)

Man : wolf or sheep? -- Different forms of violence -- Love of death and love of life -- Individual and social narcissism -- Incestuous ties -- Freedom, determinism, alternativism.

This edited volume explores the previously underacknowledged 'pre-history' of mathematical structuralism, showing that structuralism has deep roots in the history of modern mathematics. The contributors explore this history along two distinct but interconnected dimensions. First, they reconsider the methodological contributions of major figures in the history of mathematics. Second, they re-examine a range of philosophical reflections from mathematically-inclinded philosophers like Russell, Carnap, and Quine, whose work led to profound conclusions about logical, epistemological, and metaphysic.

Analytic philosophy--arguably one of the most important philosophical movements in the twentieth century--has gained a new historical self-consciousness, particularly about its own origins. Between 1880 and 1930, the most important work of its founding figures (Frege, Russell, Moore, Wittgenstein) not only gained attention but flourished. In this collection, fifteen previously unpublished essays explore different facets of this period, with an emphasis on the vital intellectual relationship between Frege and the early Wittgenstein.

This paper has a two-fold objective: to provide a balanced, multi-faceted account of the origins of logicism; to rehabilitate Richard Dedekind as a main logicist. Logicism should be seen as more deeply rooted in the development of modern mathematics than typically assumed, and this becomes evident by reconsidering Dedekind's writings in relation to Frege's. Especially in its Dedekindian and Fregean versions, logicism constitutes the culmination of the rise of ?pure mathematics? in the nineteenth century; and this rise brought with it (...) an inter-weaving of methodological and epistemological considerations. The latter aspect illustrates how philosophical concerns can grow out of mathematical practice, as opposed to being imposed on it from outside. It also sheds new light on the legacy and the lasting significance of logicism today. (shrink)

Gottlob Frege and Ludwig Wittgenstein (the later Wittgenstein) are often seen as polar opposites with respect to their fundamental philosophical outlooks: Frege as a paradigmatic "realist", Wittgenstein as a paradigmatic "anti-realist". This opposition is supposed to find its clearest expression with respect to mathematics: Frege is seen as the "arch-platonist", Wittgenstein as some sort of "radical anti-platonist". Furthermore, seeing them as such fits nicely with a widely shared view about their relation: the later Wittgenstein is supposed to have developed his (...) ideas in direct opposition to Frege. The purpose of this paper is to challenge these standard assumptions. I will argue that Frege's and Wittgenstein's basic outlooks have something crucial in common; and I will argue that this is the result of the positive influence Frege had on Wittgenstein. (shrink)

"This is a translation of Frauwallner's Abhidharmastudien.

For both Gottlob Frege and Bertrand Russell, providing a philosophical account of the concept of number was a central goal, pursued along similar logicist lines. In the present paper, I want to focus on a particular aspect of their accounts: their definitions, or re-constructions, of the natural numbers as equivalence classes of equinumerous classes. In other words, I want to examine what is often called the ‘Frege-Russell conception of the natural numbers’ or, more briefly, the Frege-Russell numbers. My main concern (...) will be to determine the precise sense in which this conception was, or could be, meant to constitute an analysis. I will be mostly concerned with Frege’s views on the matter; but Russell will come up along the way, for illustration and comparison, as will some recent neo-Fregean suggestions. (shrink)

For both Gottlob Frege and Bertrand Russell, providing a philosophical account of the concept of number was a central goal, pursued along similar logicist lines. In the present paper, I want to focus on a particular aspect of their accounts: their definitions, or reconstructions, of the natural numbers as equivalence classes of equinumerous classes. In other words, I want to examine what is often called the "Frege-Russell conception of the natural numbers" or, more briefly, the Frege-Russell numbers. My main concern (...) will be to determine the precise sense in which this conception was, or could be, meant to constitute an analysis.1 I will be mostly concerned with Frege’s views on the matter; but Russell will come up along the way, for illustration and comparison, as will some recent neo-Fregean proposals and results. The structure of the paper is as follows: In the first section, I sketch Frege's general approach. Next, I differentiate several kinds, or modes, of analysis, as further background. In the third section, I zero in on the equivalence class construction, raising the question of why it might, from a Fregean point of view, be seen as 'the right' construction, thus as an analysis in a strong sense. In the fourth section, I provide a contrasting, more conventionalist view of the matter, often associated with the Carnapian notion of explication, and expressed in some remarks by Russell. I then discuss the motivation for the Frege-Russell numbers in more depth. In the sixth section, I introduce a neo-Fregean alternative, to be examined along similar lines. Finally, I reflect further on the significance of the kinds of arguments available in this connection. (shrink)

© The Author [2017]. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: [email protected] Dedekind was a contemporary of Bernhard Riemann, Georg Cantor, and Gottlob Frege, among others. Together, they revolutionized mathematics and logic in the second half of the nineteenth century. Dedekind had an especially strong influence on David Hilbert, Ernst Zermelo, Emmy Noether, and Nicolas Bourbaki, who completed that revolution in the twentieth century. With respect to mainstream mathematics, he is best known for his contributions (...) to algebra and number theory. With respect to logic and the foundations of mathematics, many of his technical results — his conceptualization of the natural and real numbers, his analysis of proofs by mathematical induction and definitions by recursion (extended to the transfinite by Zermelo, John von... (shrink)

Is the mathematical function being computed by a given physical system determined by the system’s dynamics? This question is at the heart of the indeterminacy of computation phenomenon (Fresco et al. [unpublished]). A paradigmatic example is a conventional electrical AND-gate that is often said to compute conjunction, but it can just as well be used to compute disjunction. Despite the pervasiveness of this phenomenon in physical computational systems, it has been discussed in the philosophical literature only indirectly, mostly with (...) reference to the debate over realism about physical computation and computationalism. A welcome exception is Dewhurst’s ([2018]) recent analysis of computational individuation under the mechanistic framework. He rejects the idea of appealing to semantic properties for determining the computational identity of a physical system. But Dewhurst seems to be too quick to pay the price of giving up the notion of computational equivalence. We aim to show that the mechanist need not pay this price. The mechanistic framework can, in principle, preserve the idea of computational equivalence even between two different enough kinds of physical systems, say, electrical and hydraulic ones. (shrink)

Is the mathematical function being computed by a given physical system determined by the system’s dynamics? This question is at the heart of the indeterminacy of computation phenomenon (Fresco et al. [unpublished]). A paradigmatic example is a conventional electrical AND-gate that is often said to compute conjunction, but it can just as well be used to compute disjunction. Despite the pervasiveness of this phenomenon in physical computational systems, it has been discussed in the philosophical literature only indirectly, mostly with (...) reference to the debate over realism about physical computation and computationalism. A welcome exception is Dewhurst’s ([2018]) recent analysis of computational individuation under the mechanistic framework. He rejects the idea of appealing to semantic properties for determining the computational identity of a physical system. But Dewhurst seems to be too quick to pay the price of giving up the notion of computational equivalence. We aim to show that the mechanist need not pay this price. The mechanistic framework can, in principle, preserve the idea of computational equivalence even between two different enough kinds of physical systems, say, electrical and hydraulic ones. (shrink)

Do the dynamics of a physical system determine what function the system computes? Except in special cases, the answer is no: it is often indeterminate what function a given physical system computes. Accordingly, care should be taken when the question ‘What does a particular neuronal system do?’ is answered by hypothesising that the system computes a particular function. The phenomenon of the indeterminacy of computation has important implications for the development of computational explanations of biological systems. Additionally, the phenomenon lends (...) some support to the idea that a single neuronal structure may perform multiple cognitive functions, each subserved by a different computation. We provide an overarching conceptual framework in order to further the philosophical debate on the nature of computational indeterminacy and computational explanation. (shrink)

There are many different notions of information in logic, epistemology, psychology, biology and cognitive science, which are employed differently in each discipline, often with little overlap. Since our interest here is in biological processes and organisms, we develop a taxonomy of functional information that extends the standard cue/signal distinction (in animal communication theory). Three general, main claims are advanced here. (1) This new taxonomy can be useful in describing learning and communication. (2) It avoids some problems that the natural/non-natural information (...) distinction faces. (3) Functional information is​ ​produced through exploration and stabilisation processes. (shrink)

The phenomenon of digital computation is explained (often differently) in computer science, computer engineering and more broadly in cognitive science. Although the semantics and implications of malfunctions have received attention in the philosophy of biology and philosophy of technology, errors in computational systems remain of interest only to computer science. Miscomputation has not gotten the philosophical attention it deserves. Our paper fills this gap by offering a taxonomy of miscomputations. This taxonomy is underpinned by a conceptual analysis of the design (...) and implementation of conventional computational systems at various levels of abstraction. It shows that ‘malfunction’ as it is typically used in the philosophy of artefacts only represents one type of miscomputation. (shrink)

A single physical process may often be described equally well as computing several different mathematical functions—none of which is explanatorily privileged. How, then, should the computational identity of a physical system be determined? Some computational mechanists hold that computation is individuated only by either narrow physical or functional properties. Even if some individuative role is attributed to environmental factors, it is rather limited. The computational semanticist holds that computation is individuated, at least in part, by semantic properties. She claims that (...) the mechanistic account lacks the resources to individuate the computations performed by some systems, thereby leaving interesting cases of computational indeterminacy unaddressed. This article examines some of these views, and claims that more cases of computational indeterminacy can be addressed, if the system-environment interaction plays a greater role in individuating computations. A new, long-arm functional strategy for individuating computation is advanced. (shrink)

This paper deals with the question: how is computation best individuated? -/- 1. The semantic view of computation: computation is best individuated by its semantic properties. 2. The causal view of computation: computation is best individuated by its causal properties. 3. The functional view of computation: computation is best individuated by its functional properties. -/- Some scientific theories explain the capacities of brains by appealing to computations that they supposedly perform. The reason for that is usually that computation is individuated (...) semantically. I criticize the reasons in support of this view and its presupposition of representation and semantics. Furthermore, I argue that the only justified appeal to a representational individuation of computation might be that it is partly individuated by implicit intrinsic representations. (shrink)

The question ‘What is computation?’ might seem a trivial one to many, but this is far from being in consensus in philosophy of mind, cognitive science and even in physics. The lack of consensus leads to some interesting, yet contentious, claims, such as that cognition or even the universe is computational. Some have argued, though, that computation is a subjective phenomenon: whether or not a physical system is computational, and if so, which computation it performs, is entirely a matter of (...) an observer choosing to view it as such. According to one view, which we dub bold anti-realist pancomputationalism, every physical object (can be said to) computes every computer program. According to another, more modest view, some computational systems can be ascribed multiple computational descriptions. We argue that the first view is misguided, and that the second view need not entail observer-relativity of computation. At least to a large extent, computation is an objective phenomenon. Construed as a form of information processing, we argue that information-processing considerations determine what type of computation takes place in physical systems. (shrink)

Which notion of computation (if any) is essential for explaining cognition? Five answers to this question are discussed in the paper. (1) The classicist answer: symbolic (digital) computation is required for explaining cognition; (2) The broad digital computationalist answer: digital computation broadly construed is required for explaining cognition; (3) The connectionist answer: sub-symbolic computation is required for explaining cognition; (4) The computational neuroscientist answer: neural computation (that, strictly, is neither digital nor analogue) is required for explaining cognition; (5) The extreme (...) dynamicist answer: computation is not required for explaining cognition. The first four answers are only accurate to a first approximation. But the “devil” is in the details. The last answer cashes in on the parenthetical “if any” in the question above. The classicist argues that cognition is symbolic computation. But digital computationalism need not be equated with classicism. Indeed, computationalism can, in principle, range from digital (and analogue) computationalism through (the weaker thesis of) generic computationalism to (the even weaker thesis of) digital (or analogue) pancomputationalism. Connectionism, which has traditionally been criticised by classicists for being non-computational, can be plausibly construed as being either analogue or digital computationalism (depending on the type of connectionist networks used). Computational neuroscience invokes the notion of neural computation that may (possibly) be interpreted as a sui generis type of computation. The extreme dynamicist argues that the time has come for a post-computational cognitive science. This paper is an attempt to shed some light on this debate by examining various conceptions and misconceptions of (particularly digital) computation. (shrink)

There has been an ongoing conflict regarding whether reality is fundamentally digital or analogue. Recently, Floridi has argued that this dichotomy is misapplied. For any attempt to analyse noumenal reality independently of any level of abstraction at which the analysis is conducted is mistaken. In the pars destruens of this paper, we argue that Floridi does not establish that it is only levels of abstraction that are analogue or digital, rather than noumenal reality. In the pars construens of this paper, (...) we reject a classification of noumenal reality as a deterministic discrete computational system. We show, based on considerations from classical physics, why a deterministic computational view of the universe faces problems (e.g., a reversible computational universe cannot be strictly deterministic). (shrink)

What is nontrivial digital computation? It is the processing of discrete data through discrete state transitions in accordance with finite instructional information. The motivation for our account is that many previous attempts to answer this question are inadequate, and also that this account accords with the common intuition that digital computation is a type of information processing. We use the notion of reachability in a graph to defend this characterization in memory-based systems and underscore the importance of instructional information for (...) digital computation. We argue that our account evaluates positively against adequacy criteria for accounts of computation. (shrink)

The claims that “The brain processes information” or “Cognition is information processing” are accepted as truisms in cognitive science. However, it is unclear how to evaluate such claims absent a specification of “information” as it is used by neurocognitive theories. The aim of this article is, thus, to identify the key features of information that information-based neurocognitive theories posit. A systematic identification of these features can reveal the explanatory role that information plays in specific neurocognitive theories, and can, therefore, be (...) both theoretically and practically important. These features can be used, in turn, as desiderata against which candidate theories of information may be evaluated. After discussing some characteristics of explanation in cognitive science and their implications for “information”, three notions are briefly introduced: natural, sensory, and endogenous information. Subsequently, six desiderata are identified and defended based on cognitive scientific practices. The global workspace theory of consciousness is then used as a specific case study that arguably posits either five or six corresponding features of information. (shrink)

It is common in cognitive science to equate computation (and in particular digital computation) with information processing. Yet, it is hard to find a comprehensive explicit account of concrete digital computation in information processing terms. An information processing account seems like a natural candidate to explain digital computation. But when ‘information’ comes under scrutiny, this account becomes a less obvious candidate. Four interpretations of information are examined here as the basis for an information processing account of digital computation, namely Shannon (...) information, algorithmic information, factual information and instructional information. I argue that any plausible account of concrete computation has to be capable of explaining at least the three key algorithmic notions of input, output and procedures. Whist algorithmic information fares better than Shannon information, the most plausible candidate for an information processing account is instructional information. (shrink)

Floridi’s Theory of Strongly Semantic Information posits the Veridicality Thesis. One motivation is that it can serve as a foundation for information-based epistemology being an alternative to the tripartite theory of knowledge. However, the Veridicality thesis is false, if ‘information’ is to play an explanatory role in human cognition. Another motivation is avoiding the so-called Bar-Hillel/Carnap paradox. But this paradox only seems paradoxical, if ‘information’ and ‘informativeness’ are synonymous, logic is a theory of inference, or validity suffices for rational inference; (...) a, b, and c are false. (shrink)

The idea that the brain is an information processing system raises some challenging questions about whether information exists independently of brains. Answering these questions is relevant for clarifying the theoretical foundations of the sciences of mind and brain, but also for appropriately interpreting and evaluating the evidence about how brains—and other biological systems—work. This article claims that (1) informational descriptions in the sciences of mind and brain can be genuinely explanatory, despite assuming a mind-dependent notion of information; and (2) that (...) either Popperian objectivity or response-dependence in normal receivers is sufficient for grounding the explanatory role that information often plays in these sciences. Hierarchical predictive processing, which has become a central theoretical framework for neurocognitive research, is used as a case study for supporting these two claims. (shrink)

The distinction between knowledge-how and knowledge-that has long been debated in the epistemological literature. This distinction can, arguably, be better understood in terms of a more fundamental distinction between information-how and information-that. Information-how is prescriptive and informs a cognitive agent about which action can be performed to achieve a particular outcome. Information-that is descriptive and informs the agent about events, objects, and states of affairs in the world. Since the latter has received more attention in the epistemological literature, this article (...) focuses on the former. I offer a new account of information-how that answers the question, ‘When do data qualify as information-how?’. (shrink)

One type of computational indeterminacy arises from partitioning a system’s physical state space into state types that correspond to the abstract state types underlying the computation concerned. The mechanistic individuative strategy posits that computation can be uniquely identified through either narrow physical properties exclusively or wide, proximal properties. The semantic strategy posits that computation should be uniquely identified through semantic properties. We develop, and defend, an alternative functional individuative strategy that appeals—when needed—to wide, distal functions. We claim that there is (...) no actual computation outside of a functional context. Desiderata for the underlying notion of teleofunction are discussed. (shrink)

This paper deals with the question: What are the criteria that an adequate theory of computation has to meet? 1. Smith's answer: it has to meet the empirical criterion (i.e. doing justice to computational practice), the conceptual criterion (i.e. explaining all the underlying concepts) and the cognitive criterion (i.e. providing solid grounds for computationalism). 2. Piccinini's answer: it has to meet the objectivity criterion (i.e. identifying computation as a matter of fact), the explanation criterion (i.e. explaining the computer's behaviour), the (...) right things compute criterion, the miscomputation criterion (i.e. accounting for malfunctions), the taxonomy criterion (i.e. distinguishing between different classes of computers) and the empirical criterion. 3. Von Neumann's answer: it has to meet the precision and reliability of computers criterion, the single error criterion (i.e. addressing the impacts of errors) and the distinction between analogue and digital computers criterion. 4. “Everything” computes answer: it has to meet the implementation theory criterion by properly explaining the notion of implementation. -/- According to computationalists, minds are computational. Before we can judge the plausibility of any particular computationalist theory, we need to understand what notion of computation this theory employs. Although there are extant accounts of computation, any of which may, in principle, serve as a basis for computationalism, it isn’t clear that they’re all equivalent or even adequate as accounts of computation proper. By examining plausible alternatives to Smith’s adequacy criteria, our goal here is to resist his claim that no adequate account of computation proper is possible. (shrink)

How are new Bayesian hypotheses generated within the framework of predictive processing? This explanatory framework purports to provide a unified, systematic explanation of cognition by appealing to Bayes rule and hierarchical Bayesian machinery alone. Given that the generation of new hypotheses is fundamental to Bayesian inference, the predictive processing framework faces an important challenge in this regard. By examining several cognitive‐level and neurobiological architecture‐inspired models of hypothesis generation, we argue that there is an essential difference between the two types of (...) models. Cognitive‐level models do not specify how they can be implemented in brains and include structures and assumptions that are external to the predictive processing framework. By contrast, neurobiological architecture‐inspired models, which aim to better resemble brain processes, fail to explain important capacities of cognition, such as categorization and few‐shot learning. The “scaling‐up” challenge for proponents of predictive processing is to explain the relationship between these two types of models using only the theoretical and conceptual machinery of Bayesian inference. (shrink)