The First Hilbert problem is studied in this paper by applying two instruments: a new methodology distinguishing between mathematical objects and mathematical languages used to describe these objects; and a new numeral system allowing one to express different infinite numbers and to use these numbers for measuring infinite sets. Several counting systems are taken into consideration. It is emphasized in the paper that different mathematical languages can describe mathematical objects (in particular, sets and the number of their elements) (...) with different accuracies. The traditional and the new approaches are compared and discussed. (shrink)

The aim of this paper is to explore and understand the Albanian Party System. The analysis will cover the period from the collapse of the communist regime in 1991 until 2014. It will try to investigate what forces drive the battle of the parties, what cleavages 'divide' society and consequently the party system as well as which are the parties that count the most. in order to assess this, the paper will focus on the parliamentary parties and will relay on (...) various theoretical concepts of the contemporary literature on political parties. First it will draw on Sartori's concept of 'relevance' in order to understand whether all the parliamentary parties over the course of twenty four years of pluralism are important or not and what weight do they have. Then it will use the Laakso - Taagepera index of the Effective Number of Parties to understand how power is distributed within the parliament. (shrink)

Number systems differ cross-culturally in characteristics like how high counting extends and which number is used as a productive base. Some of this variability can be linked to the way the hand is used in counting. The linkage shows that devices like the hand used as external representations of number have the potential to influence numerical structure and organization, as well as aspects of numerical language. These matters suggest that cross-cultural variability may be, at least in part, (...) a matter of whether devices are used in counting, which ones are used, and how they are used. (shrink)

“Morphological computation” is an increasingly important concept in robotics, artificial intelligence, and philosophy of the mind. It is used to understand how the body contributes to cognition and control of behavior. Its understanding in terms of "offloading" computation from the brain to the body has been criticized as misleading, and it has been suggested that the use of the concept conflates three classes of distinct processes. In fact, these criticisms implicitly hang on accepting a semantic definition of what constitutes computation. (...) Here, I argue that an alternative, mechanistic view on computation offers a significantly different understanding of what morphological computation is. These theoretical considerations are then used to analyze the existing research program in developmental biology, which understands morphogenesis, the process of development of shape in biological systems, as a computational process. This important line of research shows that cognition and intelligence can be found across all scales of life, as the proponents of the basal cognition research program propose. Hence, clarifying the connection between morphological computation and morphogenesis allows for strengthening the role of the former concept in this emerging research field. (shrink)

The notion of a physiological individuals has been developed and applied in the philosophy of biology to understand symbiosis, an understanding of which is key to theorising about the major transition in evolution from multi-organismality to multi-cellularity. The paper begins by asking what such symbiotic individuals can help to reveal about a possible transition in the evolution of cognition. Such a transition marks the movement from cooperating individual biological cognizers to a functionally integrated cognizing unit. Somewhere along the way, did (...) such cognizing units simultaneously have cognizers as parts? Expanding upon the multiscale integration view of the Free Energy Principle, this paper develops an account of reciprocal integration, demonstrating how some coupled biological cognizing systems, when certain constraints are met, can result in a cognizing unit that is in ways greater than the sum of its cognizing parts. Symbiosis between V. Fischeri bacteria and the bobtail squid is used to provide an illustration this account. A novel manner of conceptualizing biological cognizers as gradient is then suggested. Lastly it is argued that the reason why the notion of ontologically nested cognizers may be unintuitive stems from the fact that our folk-psychology notion of what a cognizer is has been deeply influenced by our folk-biological manner of understanding biological individuals as units of reproduction. (shrink)

The idea the New Zealand Māori once counted by elevens has been viewed as a cultural misunderstanding originating with a mid-nineteenth-century dictionary of their language. Yet this “remarkable singularity” had an earlier, Continental origin, the details of which have been lost over a century of transmission in the literature. The affair is traced to a pair of scientific explorers, René-Primevère Lesson and Jules Poret de Blosseville, as reconstructed through their publications on the 1822–1825 circumnavigational voyage of the Coquille, a French (...) corvette. Possible explanations for the affair are briefly examined, including whether it might have been a prank by the Polynesians or a misunderstanding or hoax on the part of the Europeans. Reasons why the idea of counting by elevens remains topical are discussed. First, its very oddity has obscured the counting method actually used—setting aside every tenth item as a tally. This “ephemeral abacus” is examined for its physical and mental efficiencies and its potential to explain aspects of numerical structure and vocabulary (e.g., Mangarevan binary counting; the Hawaiian number word for twenty, iwakalua), matters suggesting material forms have a critical if underappreciated role in realising concepts like exponential value. Second, it provides insight into why it can be difficult to appreciate highly elaborated but unwritten numbers like those found throughout Polynesia. Finally, the affair illuminates the difficulty of categorising number systems that use multiple units as the basis of enumeration, like Polynesian pair-counting; potential solutions are offered. (shrink)

The initial argument presented herein is not significantly original—it is a simple reflection upon a notion of computation originally developed by Putnam and criticised by Chalmers et al. . In what follows, instead of seeking to justify Putnam’s conclusion that every open system implements every Finite State Automaton and hence that psychological states of the brain cannot be functional states of a computer, I will establish the weaker result that, over a finite time window every open system implements the trace (...) of FSA Q, as it executes program on input . If correct the resulting bold philosophical claim is that phenomenal states—such as feelings and visual experiences—can never be understood or explained functionally. (shrink)

The approximate number system (ANS) enables organisms to represent the approximate number of items in an observed collection, quickly and independently of natural language. Recently, it has been proposed that the ANS goes beyond representing natural numbers by extracting and representing rational numbers (Clarke & Beck, 2021a). Prior work demonstrates that adults and children discriminate ratios in an approximate and ratio-dependent manner, consistent with the hallmarks of the ANS. Here, we use a well-known “connectedness illusion” to provide evidence that these (...) ratio-dependent ratio discriminations are (a) based on the perceived number of items in seen displays (and not just non-numerical confounds), (b) are not dependent on verbal working memory, or explicit counting routines, and (c) involve representations with a part-whole (or subset-superset) format, like a fraction, rather than a part-part format, like a ratio. These results vindicate key predictions of the hypothesis that the ANS represents rational numbers. (shrink)

Nelson Goodman’s theory of symbol systems expounded in his Languages of Art has been frequently criticized on many counts (cf. list of secondary literature in the entry “Goodman’s Aesthetics” of Stanford Encyclopedia of Philosophy and Sect. 3 below). Yet it exerts a strong influence and is treated as one of the major twentieth-century theories on the subject. While many of Goodman’s controversial theses are criticized, the technical notions he used to formulate them seem to have been treated as neutral (...) tools. One such technical notion is that of the density of symbol systems. This serves to distinguish linguistic symbols from pictorial representations (after Goodman entirely rejected resemblance in that role) and is a crucial part of Goodman’s explanation of what constitutes aesthetic experience (and so indirectly what is art). Thus its significance for Goodman’s theory is fundamental. The aim of this paper is a detailed, logical analysis of this notion. It turns out that Goodman’s definition is highly problematic and cannot be applied to symbol systems in the way Goodman envisaged. To conclude, Goodman’s theory is problematic not just because of its controversial theses but also because of logical problems with the technical notions used at its very core. Hence the controversial claims are not simply contestable, but inaccurately expressed. (shrink)

In this article, some classical paradoxes of infinity such as Galileo’s paradox, Hilbert’s paradox of the Grand Hotel, Thomson’s lamp paradox, and the rectangle paradox of Torricelli are considered. In addition, three paradoxes regarding divergent series and a new paradox dealing with multiplication of elements of an infinite set are also described. It is shown that the surprising counting system of an Amazonian tribe, Pirah ̃a, working with only three numerals (one, two, many) can help us to change our (...) perception of these paradoxes. A recently introduced methodology allowing one to work with finite, infinite, and infinitesimal numbers in a unique computational framework not only theoretically but also numerically is briefly described. This methodology is actively used nowadays in numerous applications in pure and applied mathematics and computer science as well as in teaching. It is shown in the article that this methodology also allows one to consider the paradoxes listed above in a new constructive light. (shrink)

Berry, Daniels, and Ladin make a strong argument for discontinuing the use of, “lack of social support,” as an organ transplantation listing criterion. This argument, however, actually leads to conclusions much stronger than those that the authors’ propose: The argument works equally well against using, (1) any “psychosocial” factors at all as a listing criterion, and, (2) any criteria other than factors that directly relate to empirically established medical need, and/or empirically established survival rate. Moreover, while the authors rightly point (...) to a lack of empirical evidence connecting social support to survivability, they neglect mentioning that the empirical literature on social support provides grounds to favor listing persons who seem to, sadly, lack a social support system. (shrink)

In this paper, the role of the environment and physical embodiment of computational systems for explanatory purposes will be analyzed. In particular, the focus will be on cognitive computational systems, understood in terms of mechanisms that manipulate semantic information. It will be argued that the role of the environment has long been appreciated, in particular in the work of Herbert A. Simon, which has inspired the mechanistic view on explanation. From Simon’s perspective, the embodied view on cognition seems (...) natural but it is nowhere near as critical as its proponents suggest. The only point of difference between Simon and embodied cognition is the significance of body-based off-line cognition; however, it will be argued that it is notoriously over-appreciated in the current debate. The new mechanistic view on explanation suggests that even if it is critical to situate a mechanism in its environment and study its physical composition, or realization, it is also stressed that not all detail counts, and that some bodily features of cognitive systems should be left out from explanations. (shrink)

In this work we study dimensional theoretical properties of some a±ne dynamical systems. By dimensional theoretical properties we mean Hausdor® dimension and box- counting dimension of invariant sets and ergodic measures on theses sets. Especially we are interested in two problems. First we ask whether the Hausdor® and box- counting dimension of invariant sets coincide. Second we ask whether there exists an ergodic measure of full Hausdor® dimension on these invariant sets. If this is not the case (...) we ask the question, whether at least the variational principle for Haus- dor® dimension holds, which means that there is a sequence of ergodic measures such that their Hausdor® dimension approximates the Hausdor® dimension of the invariant set. It seems to be well accepted by experts that these questions are of great importance in developing a dimension theory of dynamical systems (see the book of Pesin about dimension theory of dynamical systems [PE2]). Dimensional theoretical properties of conformal dynamical systems are fairly well understood today. For example there are general theorems about conformal repellers and hyperbolic sets for conformal di®eomorphisms (see chapter 7 of [PE2]). On the other hand the existence of two di®erent rates of expansion or contraction forces problems that are not captured by a general theory this days. At this stage of de- velopment of the dimension theory of dynamical systems it seems natural to study non conformal examples. This is the ¯rst step to understand the mechanisms that determine dimensional theoretical properties of non conformal dynamical systems. A±ne dynamical systems represent simple examples of non conformal systems. They are easy to de¯ne, but studying their dimensional theoretical properties does never- theless provide challenging mathematical problems and exemplify interesting phe- nomena. We consider here a special class of self-a±ne repellers in dimension two, depending on four parameters (see 2.1.). Furthermore we study a class of attractors of piecewise a±ne maps in dimension three depending on four parameters as well. The last object of our work are projections of these maps that are known as gener- alized Baker's transformations (see 2.2.). The contents of our work is the following: In chapter two we give an overview about some main results in the area of di- mension theory of a±ne dynamical systems and de¯ne the systems we study in this work. We will explain, what is known about the dimensional theoretical properties of these systems and describe what our new results are. In chapter three we then apply symbolic dynamics to our systems. We will introduce explicit shift codings 4 and ¯nd representations of all ergodic measures for our systems using these codings. From chapter four to chapter eight we study dimensional theoretical properties, which our systems generally or generically have. In chapter four we will prove a formula for the box-counting dimension of the repellers and the attractors (see the- orem 4.1.). Then in chapter ¯ve we apply general dimensional theoretical results for ergodic measures found by Ledrappier and Young [LY] and Barreira, Schmeling and Pesin [BPS] to our systems. These results relate the dimension of ergodic measures to metric entropy and Lyapunov exponents. Using this approach we will be able to reduce questions about the dimension of ergodic measures in our context to ques- tions about certain overlapping and especially overlapping self-similar measures on the line. These overlapping self-similar measures are studied in chapter six. Our main theorem extends a result of Peres and Solomyak [PS2] concerning the absolute continuity resp. singularity of symmetric self-similar measures to asymmetric ones (see theorem 6.1.3.). In chapter seven we bring our results together. We prove that we generically (in the sense of Lebesgue measure on a part of the parameter space) have the iden- tity of box-counting and Hausdor® dimension for the repellers and the attractors. (see theorem 7.1.1. and corollary 7.1.2.). This result suggest that one can expect that the identity of box-counting dimension and Hausdor® dimension holds at least generically in some natural classes of non conformal dynamical systems. Furthermore we will see in chapter seven that there generically exists an ergodic measure of full Hausdor® dimension for the repellers. On the other hand the vari- ational principle for Hausdor® dimension is not generic for the attractors. It holds only if we assume a certain symmetry (see theorem 7.1.1.). For generalized Baker's transformations we will ¯nd a part of the parameter space where there generically is an ergodic measure of full dimension and a part where the variational principle for Hausdor® dimension does not hold (see theorem 7.1.3.). Roughly speaking the reason why the variational principle does not hold here is, that if there exists both a stable and an unstable direction one can not generically maximize the dimension in the stable and in the unstable direction at the same time. In an other setting this phenomenon was observed before by Manning and McCluskey [MM]. In chapter eight we extend some results of the last section to invariant sets that correspond to special Markov chains instead of full shifts (see theorem 8.1.1.). In the last two chapters of our work we are interested in number theoretical excep- tions to our generic results. The starting point of our considerations in section nine are results of ErdÄos [ER1] and Alexander and Yorke [AY] that establish singularity and a decrease of dimension for in¯nite convolved Bernoulli measures under special conditions. Using a generalized notion of the Garsia entropy ([GA1/2]) we are able 5 to understand the consequences of number theoretical peculiarities in broader class of overlapping measures (see theorem 9.1.1.). In chapter ten we then analyze number theoretical peculiarities in the context of our dynamical systems. We restrict our attention to a symmetric situation where we generically have the existence of a Bernoulli measure of full dimension and the identity of Hausdor® and box-counting dimension for all of our systems. In the ¯rst section of chapter ten we ¯nd parameter values such that the variational principle for Hausdor® dimension does not hold for the attractors and for the Fat Baker's transformations (see theorem 10.1.1.). These are the ¯rst known examples of dynamical systems for which the variational principle for Hausdor® dimension does not hold because of number theoretical peculiarities of parameter values. For the repellers we have been able to show that under certain number theoretical conditions there is at least no Bernoulli measure of full Hausdor® dimension; the question if the variational principle for Hausdor® dimension holds remains open in this situation. In the second section of chapter ten we will show that the identity for Hausdor® and box-counting dimension can drops because there are number theoretical pecu- liarities. In the context of Weierstrass-like functions this phenomenon was observed by Przytycki and Urbanski [PU]. Our theorem extends this result to a larger class of sets, invariant under dynamical systems (see theorem 10.2.1). At the end of this work the reader will ¯nd two appendices, a list of notations and the list of references. In appendix A we introduce the notions of dimension we use in this work and collect some general facts in dimension theory. In appendix B we state the facts about Pisot-Vijayarghavan number, we need in our analysis of number theoretical peculiarities. The list of notations contains general notations and a table with a summary of notations we use to describe the dynamical systems that we study. Acknowledgments I wish to thank my supervisor JÄorg Schmeling for a lot of valuable discussion and all his help. Also thanks to Luis Barreira for his great hospitality in Lisboa and many interesting comments. This work was done while I was supported by "Promotionstipendium gem. NaFÄoG der Freien UniversitÄat Berlin". (shrink)

In this study, the archaic counting systems of Mesopotamia as understood through the Neolithic tokens, numerical impressions, and proto-cuneiform notations were compared to the traditional number-words and counting methods of Polynesia as understood through contemporary and historical descriptions of vocabulary and behaviors. The comparison and associated analyses capitalized on the ability to understand well-known characteristics of Uruk-period numbers like object-specific counting, polyvalence, and context-dependence through historical observations of Polynesian counting methods and numerical language, evidence unavailable (...) for ancient numbers. Similarities between the two number systems were then used to argue that archaic Mesopotamian numbers, like those of Polynesia, were highly elaborated and would have served as cognitively efficient tools for mental calculation. Their differences also show the importance of material technologies like tokens, impressions, and notations to developing mathematics. This project has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No. 785793. (shrink)

Is calculation possible without language? Or is the human ability for arithmetic dependent on the language faculty? To clarify the relation between language and arithmetic, we studied numerical cognition in speakers of Mundurukú, an Amazonian language with a very small lexicon of number words. Although the Mundurukú lack words for numbers beyond 5, they are able to compare and add large approximate numbers that are far beyond their naming range. However, they fail in exact arithmetic with numbers larger than 4 (...) or 5. Our results imply a distinction between a nonverbal system of number approximation and a language-based counting system for exact number and arithmetic. (shrink)

Aristotle counts as the founder of formal logic. The logic he develops dominated until Frege and others introduced a new logic. This new logic is taken to be more powerful and better capable of capturing inference patterns. The new logic differs from Aristotelian logic in significant respects. It has been argued by Fred Sommers and Hanoch Ben-Yami that the new logic is not well equipped as a logic of natural language, and that a logic closer to Aristotle's is better suited (...) for this task. Each of them developed their own formalism - Sommers in form of term logic, Ben-Yami in form of his Quantified Argument Calculus (QUARC). I discuss Aristotle's logic - a term logic - and attempt a comparison between Aristotelian logic and (i) the new logic, (ii) Sommers' term logic, and (iii) Ben-Yami's QUARC. I consider differences between the systems, and show how they are related to and diverge from the new logic. (shrink)

Research in multi-agent systems typically assumes a regulative model of social practice. This model starts with agents who are already capable of acting autonomously to further their individual ends. A social practice, according to this view, is a way of achieving coordination between multiple agents by restricting the set of actions available. For example, in a world containing cars but no driving regulations, agents are free to drive on either side of the road. To prevent collisions, we introduce driving (...) regulations, insisting that everyone drives on the left hand side of the road. We accept this limitation on our freedom because it lowers the probability of a collision. -/- This paper describes AI systems that are based on the constitutive view of social practice. According to this alternative view, there are certain actions that are only available to the agent because he is participating in a practice of a certain sort. For example, you can swing a peculiarly shaped piece of wood without participating in any particular practice - but this action will only constitute a strike if you are participating in a game of baseball. I can raise my hand whenever I like, but this only counts as voting for the motion within the institution of voting. But not all the examples are from frivolous, optional or institutional activities. Sellars and Brandom argue that even the fundamental act of assertion is only possible within the context of a particular social practice: the Game of Giving and Asking for Reasons. -/- The constitutive view, which is familiar to philosophers, is relatively unknown within the AI community. -/- The central aim of this paper is to show how the constitutive view of practice can be put to use in AI applications. (shrink)

It is well known that the set of algebraic numbers (let us call it A) is countable. In this paper, instead of the usage of the classical terminology of cardinals proposed by Cantor, a recently introduced methodology using ①-based infinite numbers is applied to measure the set A (where the number ① is called grossone). Our interest to this methodology is explained by the fact that in certain cases where cardinals allow one to say only whether a set is countable (...) or it has the cardinality of the continuum, the ①-based methodology can provide a more accurate measurement of infinite sets. In this article, lower and upper estimates of the number of elements of A are obtained. Both estimates are expressed in ①-based numbers. (shrink)

It is shown that a complete axiomatization of classical non-tautologies can be obtained by taking F (falsehood) as the sole axiom along with the two inference rules: (i) if A is a substitution instance of B, then A |– B; and (ii) if A is obtained from B by replacement of equivalent sentences, then A |– B (counting as equivalent the pairs {T, ~F}, {F, F&F}, {F, F&T}, {F, T&F}, {T, T&T}). Since the set of tautologies is also specifiable (...) by purely syntactic means, the resulting picture gives an improved syntactic account of classical sentential logic. The picture can then be completed by considering related systems that prove adequate to specify the set of contradictions, the set of non-contradictions, and the set of contingencies respectively. (shrink)

Building on recent work, I present sequent systems for the non-classical logics LP, K3, and FDE with two main virtues. First, derivations closely resemble those in standard Gentzen-style systems. Second, the systems can be obtained by reformulating a classical system using nonstandard sequent structure and simply removing certain structural rules (relatives of exchange and contraction). I clarify two senses in which these logics count as “substructural.”.

_ Source: _Page Count 22 Analysis of the concept of habit has been relatively neglected in the contemporary analytic literature. This paper is an attempt to rectify this lack. The strategy begins with a description of some paradigm cases of habit which are used to derive five features as the basis for an explicative definition. It is argued that habits are social, acquired through repetition, enduring, environmentally activated, and automatic. The enduring nature of habits is captured by their being dispositions (...) of a certain sort. This is a realist account of habits insofar as the dispositions put forward must fit into some recognizable underlying system – in the case of humans a biological system – to fill the role as set out by the definition. This role is wide-ranging; in addition to the familiar cases of habitual behavior, habitual activities also include thinking, perceiving, feeling, and willing. (shrink)

What is the class of possible semiotic systems? What kinds of systems could count as such systems? The human mind is naturally considered the prototypical semiotic system. During years of research in semiotics the class has been broadened to include i.e. living systems like animals, or even plants. It is suggested in the literature on artificial intelligence that artificial agents are typical examples of symbol-processing entities. It also seems that semiotic processes are in fact cognitive processes. (...) In consequence, it is natural to ask the question about the relation between semiotic studies and research on artificial cognitive systems within cognitive science. Consequently, my main question concerns the problem of inclusion or exclusion from the semiotic spectrum at least some artificial systems. I would like to consider some arguments against the possibility of artificial semiotic systems and I will try to repeal them. Then I will present an existing natural-language using agent of the SNePS system and interpret it in terms of Peircean theory of signs. I would like also to show that some properties of semiotic systems in Peircean sense could be also found in a discussed artificial system. Finally, I will have some remarks on the status of semiotics in general. (shrink)

Human biological memory systems have adapted to use technological artifacts to overcome some of the limitations of these systems. For example, when performing a difficult calculation, we use pen and paper to create and store external number symbols; when remembering our appointments, we use a calendar; when remembering what to buy, we use a shopping list. This chapter looks at the history of memory artifacts, describing the evolution from cave paintings to virtual reality. It first characterizes memory artifacts, (...) memory systems, and the two main functions such artifacts have, which are to aid individual users in completing memory tasks and as a cultural inheritance channel (section 2). It then outlines some of our first symbolic practices such as making cave paintings and figurines, and then moves on to outline several key developments in external representational systems and the artifacts that support these such as written language, numeral systems and counting devices, diagrams and maps, measuring devices, libraries and archives, photographs, analogue and digital computational artifacts, the World Wide Web, virtual reality, and smartphones (section 3). After that, it makes some brief points about the cumulative nature of the cultural evolution of memory artifacts and speculates about the possible future of memory artifacts, arguing that it is very difficult to look beyond an epistemological horizon of more than five years (section 4). (shrink)

It is becoming more common that the decision-makers in private and public institutions are predictive algorithmic systems, not humans. This article argues that relying on algorithmic systems is procedurally unjust in contexts involving background conditions of structural injustice. Under such nonideal conditions, algorithmic systems, if left to their own devices, cannot meet a necessary condition of procedural justice, because they fail to provide a sufficiently nuanced model of which cases count as relevantly similar. Resolving this problem requires (...) deliberative capacities uniquely available to human agents. After exploring the limitations of existing formal algorithmic fairness strategies, the article argues that procedural justice requires that human agents relying wholly or in part on algorithmic systems proceed with caution: by avoiding doxastic negligence about algorithmic outputs, by exercising deliberative capacities when making similarity judgments, and by suspending belief and gathering additional information in light of higher-order uncertainty. (shrink)

Currently available systems of action deontic logic are not designed to model procedures to assess the conduct of an agent which take into account the intentions of the agent and the circumstances in which she is acting. Yet, procedures of this kind are essential to determine what counts as culpable not doing. In light of this, we design an action logic, AL, in which it is possible to distinguish actions that are objectively possible for an agent, viz. there are (...) no objective impediments for the agent to do them, and actions that, besides being objectively possible, are compatible with the setting or intentions of the agent. (shrink)

This article presents a novel challenge to epistemic internalism. The challenge rests on a set of cases which feature subjects forming beliefs under conditions of “bad ideology”—that is, conditions in which pervasively false beliefs have the function of sustaining, and are sustained by, systems of social oppression. In such cases, the article suggests, the externalistic view that justification is in part a matter of worldly relations, rather than the internalistic view that justification is solely a matter of how things (...) stand from the agent’s individual perspective, becomes the more intuitively attractive theory. But these “bad ideology” cases do not merely yield intuitive verdicts that favor externalism over internalism. These cases are, moreover, analogous to precisely those canonical cases widely taken to be counterexamples to externalism: cases featuring brains-in-vats, clairvoyants, and dogmatists. That is, such “bad ideology” cases are, in all relevant respects, just like cases that are thought to count against externalism—except that they intuitively favor externalism. This, the author argues, is a serious worry for internalism. What is more, it bears on the debate over whether externalism is a genuinely “normative” epistemology. (shrink)

SNePS, the Semantic Network Processing System 45, 54], has been designed to be a system for representing the beliefs of a natural-language-using intelligent system (a \cognitive agent"). It has always been the intention that a SNePS-based \knowledge base" would ultimatelybe built, not by a programmeror knowledge engineer entering representations of knowledge in some formallanguage or data entry system, but by a human informing it using a natural language (NL) (generally supposed to be English), or by the system reading books or (...) articles that had been prepared for human readers. Because of this motivation, the criteria for the development of SNePS have included: it should be able to represent anything and everything expressible in NL; it should be able to represent generic, as well as speci c information; it should be able to use the generic and the speci c information to reason and infer information implied by what it has been told; it cannot count on any particular order among the pieces of information it is given; it must continue to act reasonably even if the information it is given includes circular de nitions, recursive rules, and inconsistent information. (shrink)

The paper contains a novel realist account of causal production and the necessary connection between cause and effect. I argue that the asymmetric relation between causally connected events must be regarded as a product of a symmetric interaction between two or more entities. All the entities involved contribute to the producing, and so count as parts of the cause, and they all suffer a change, and so count as parts of the effect. Cause and effect, on this account, are two (...) different states of the very same compound substance, or system, one coming to exist out of the other. (shrink)

Bilateralists hold that the meanings of the connectives are determined by rules of inference for their use in deductive reasoning with asserted and denied formulas. This paper presents two bilateral connectives comparable to Prior's tonk, for which, unlike for tonk, there are reduction steps for the removal of maximal formulas arising from introducing and eliminating formulas with those connectives as main operators. Adding either of them to bilateral classical logic results in an incoherent system. One way around this problem is (...) to count formulas as maximal that are the conclusion of reductio and major premise of an elimination rule and to require their removability from deductions. The main part of the paper consists in a proof of a normalisation theorem for bilateral logic. The closing sections address philosophical concerns whether the proof provides a satisfactory solution to the problem at hand and confronts bilateralists with the dilemma that a bilateral notion of stability sits uneasily with the core bilateral thesis. (shrink)

An exact truthmaker for A is a state which, as well as guaranteeing A’s truth, is wholly relevant to it. States with parts irrelevant to whether A is true do not count as exact truthmakers for A. Giving semantics in this way produces a very unusual consequence relation, on which conjunctions do not entail their conjuncts. This feature makes the resulting logic highly unusual. In this paper, we set out formal semantics for exact truthmaking and characterise the resulting notion of (...) entailment, showing that it is compact and decidable. We then investigate the effect of various restrictions on the semantics. We also formulate a sequent-style proof system for exact entailment and give soundness and completeness results. (shrink)

Many philosophers and psychologists have attempted to elucidate the nature of mental representation by appealing to notions like isomorphism or abstract structural resemblance. The ‘structural representations’ that these theorists champion are said to count as representations by virtue of functioning as internal models of distal systems. In his 2007 book, Representation Reconsidered, William Ramsey endorses the structural conception of mental representation, but uses it to develop a novel argument against representationalism, the widespread view that cognition essentially involves the manipulation (...) of mental representations. Ramsey argues that although theories within the ‘classical’ tradition of cognitive science once posited structural representations, these theories are being superseded by newer theories, within the tradition of connectionism and cognitive neuroscience, which rarely if ever appeal to structural representations. Instead, these theories seem to be explaining cognition by invoking so-called ‘receptor representations’, which, Ramsey claims, aren’t genuine representations at all—despite being called representations, these mechanisms function more as triggers or causal relays than as genuine stand-ins for distal systems. I argue that when the notions of structural and receptor representation are properly explicated, there turns out to be no distinction between them. There only appears to be a distinction between receptor and structural representations because the latter are tacitly conflated with the ‘mental models’ ostensibly involved in offline cognitive processes such as episodic memory and mental imagery. While structural representations might count as genuine representations, they aren’t distinctively mental representations, for they can be found in all sorts of non-intentional systems such as plants. Thus to explain the kinds of offline cognitive capacities that have motivated talk of mental models, we must develop richer conceptions of mental representation than those provided by the notions of structural and receptor representation. (shrink)

A finer-grained delineation of a given explanandum reveals a nexus of closely related causal and non- causal explanations, complementing one another in ways that yield further explanatory traction on the phenomenon in question. By taking a narrower construal of what counts as a causal explanation, a new class of distinctively mathematical explanations pops into focus; Lange’s characterization of distinctively mathematical explanations can be extended to cover these. This new class of distinctively mathematical explanations is illustrated with the Lotka-Volterra equations. There (...) are at least two distinct ways those equations might hold of a system, one of which yields straightforwardly causal explanations, but the other of which yields explanations that are distinctively mathematical in terms of nomological strength. In the first, one first picks out a system or class of systems, finds that the equations hold in a causal -explanatory way; in the second, one starts with the equations and explanations that must apply to any system of which the equations hold, and only then turns to the world to see of what, if any, systems it does in fact hold. Using this new way in which a model might hold of a system, I highlight four specific avenues by which causal and non- causal explanations can complement one another. (shrink)

What is the value of intellectual playfulness? Traditional characterizations of the ideal thinker often leave out playfulness; the ideal inquirer is supposed to be sober, careful, and conscientiousness. But elsewhere we find another ideal: the laughing sage, the playful thinker. These are models of intellectual playfulness. Intellectual playfulness, I suggest, is the disposition to try out alternate belief systems for fun – to try on radically different perspectives for the sheer pleasure of it. But what would the cog-nitive value (...) be of such playfulness? I suggest that intellectual playfulness function as, at the very least, a kind of intellectual insurance policy against epistemic traps. An epistemic trap is a belief system that re-directs good-faith inquiry to bad results. Am epistemic trap manipulates background beliefs to fend off contrary evidence. For example, a conspiracy theory might include a set of beliefs about how the mainstream media has been taken over by some vicious cabal. Normal epistemic attempts will be captured by a well-wrought epistemic trap, because normal attempts at inquiry are guided by these background beliefs -- which set what counts as a plausible path to explore, and what is implausible or beyond the pale. And a clever epistemic trap will manipulate those background beliefs for ill effect. Intellectual playfulness, on the other hand, isn’t motivated by an epistemic interest in the truth, but in the sheer pleasure of intellectual exploration. Since intellectual playfulness isn’t oriented towards the truth, it won’t be constrained by an agent’s background beliefs – it won’t, for example, prefer to investigate apparently more plausible pathways. Intellectual playfulness offers an opportunity to escape from epistemic traps. But intellectual playfulness has its own limitations. It will only drive us to explore belief systems when that exploration is fun. What we need is an array of differently-motivated exploratory tendencies – empathy, curiosity, playfulness – each of which will each cover for the others’ limitations. (shrink)

The relationship between the One and the Multiple in mystic philosophy is a profound and central theme that explores the nature of existence, the cosmos, and the divine. This theme is present in various mystical traditions, including those of the East and West, and it addresses the paradoxical coexistence of the unity and multiplicity of all things. -/- In mystic philosophy, the **One** often represents the ultimate reality, the source from which all things emanate and to which all things return. (...) It is the absolute, the infinite, and the unchanging. The One is beyond all attributes and is often associated with the divine or the absolute truth. -/- The **Multiple**, on the other hand, represents the manifest world, the diversity of forms, and the realm of change and plurality. It is the world we experience through our senses, the domain of time and space, where differentiation and individuality are apparent. -/- The relationship between the One and the Multiple is not one of opposition but of emanation and unity. The Multiple is seen as a reflection, expression, or manifestation of the One. In this sense, the diversity of the world doesn’t contradict the unity of the One but rather demonstrates it in a myriad of forms. -/- Mystics seek to understand and experience this relationship through various practices and insights. They aim to transcend the illusion of separation and duality to experience the non-dual reality where the One and the Multiple are recognized as inseparable. -/- This concept can be illustrated by the metaphor of the ocean and its waves. The ocean represents the One—vast, deep, and all-encompassing—while the waves represent the Multiple—distinct, diverse, and ever-changing. Each wave is unique, yet it is not separate from the ocean. The wave’s existence is dependent on and made of the same substance as the ocean. In the same way, each individual entity in the Multiple is an expression of the One. -/- In summary, the relationship between the One and the Multiple in mystic philosophy is a dynamic interplay that challenges the conventional understanding of separation. It invites a deeper exploration of reality, where the apparent multiplicity of the world is a direct expression of the singular, underlying essence of all that is. -/- The relationship between the One and the Multiple in the context of mathematical philosophy is a profound topic that touches upon the very foundations of existence and knowledge. It’s a theme that has been explored by philosophers and mathematicians alike, often leading to the contemplation of unity and diversity within the structures of reality. -/- In mathematics, the concept of the One can be seen as the basis of unity from which all numbers derive. It’s the identity element in multiplication, the starting point in counting, and the foundation of dimension in geometry. The One is often associated with the concept of monism in philosophy, which posits that there is a single, underlying substance or principle that constitutes reality. -/- On the other hand, the Multiple represents the infinite variety and diversity of forms and numbers that arise from the One. It’s the embodiment of plurality and the complex interplay of different entities that mathematics seeks to understand and describe. This reflects the philosophical stance of pluralism, which acknowledges the existence of multiple realities or truths. -/- The interplay between the One and the Multiple can be seen in the mathematical concept of sets. A set can be thought of as a unity, a whole composed of distinct elements. Yet, each element within the set also retains its individuality, contributing to the diversity of the set’s composition. This duality is mirrored in the philosophical exploration of the universal and the particular, where the universal represents the One, and the particulars represent the Multiple. -/- In the realm of mathematical philosophy, this relationship often leads to questions about the nature of mathematical objects: Are they discovered as part of an objective reality (the One), or are they constructed by the human mind from a multitude of experiences (the Multiple)? This debate resonates with the philosophical inquiry into the nature of truth and reality. -/- Reflecting on the One and the Multiple can also lead to a deeper understanding of the self and the cosmos. Just as the number one is integral to the existence of all other numbers, the individual self can be seen as a unique expression of the universal whole. Similarly, the cosmos can be viewed as a grand unity composed of a multiplicity of forms and phenomena. -/- Gödel’s incompleteness theorems have a fascinating connection to the philosophical concepts of the One and the Multiple. These theorems, which are pivotal in mathematical logic and philosophy of mathematics, articulate the inherent limitations of formal axiomatic systems, particularly those sufficient to express the arithmetic of natural numbers. -/- Gödel’s incompleteness theorems have a fascinating connection to the philosophical concepts of the One and the Multiple. These theorems, which are pivotal in mathematical logic and philosophy of mathematics, articulate the inherent limitations of formal axiomatic systems, particularly those sufficient to express the arithmetic of natural numbers⁴. -/- The **first incompleteness theorem** reveals that within any such consistent system, there are propositions that are true but cannot be proven within the system itself. This reflects the idea of the Multiple in that there is an abundance of mathematical truths, a multiplicity that exceeds the unifying framework of any one system. It suggests that the realm of mathematical truth is more extensive than any single formal system can fully capture. -/- The **second incompleteness theorem** extends this by showing that a system cannot prove its own consistency. This relates to the concept of the One, as it implies that a system’s complete self-understanding, its unity and coherence, is unattainable from within. It must look beyond itself, to an external vantage point, to ascertain its consistency. -/- In the context of the One and the Multiple, Gödel’s theorems imply that the One (a consistent formal system) is inherently incomplete and cannot encompass the Multiple (the totality of mathematical truths). This resonates with philosophical discussions about the relationship between unity and plurality. Just as a single philosophical system cannot capture the entirety of truth, a single formal mathematical system cannot encapsulate all mathematical truths. -/- Moreover, Gödel’s work suggests that the pursuit of a single, unified theory of everything in mathematics—a One that encompasses all Multiples—is an inherently Sisyphean task. There will always be more truths (Multiples) than can be derived from any given set of axioms (the One). -/- In essence, Gödel’s incompleteness theorems provide a formal underpinning to the philosophical notion that the One cannot exist without the Multiple, and vice versa. They are interdependent, with the One giving rise to the Multiple, and the Multiple necessitating the One for its expression and comprehension. This interplay is a dance of limitations and possibilities, where the boundaries of logic, mathematics, and philosophy blur into one another. -/- The relationship between the One and the Multiple in the context of the mathematics of zero is a deeply philosophical inquiry that bridges the abstract world of numbers with the existential questions of being and non-being. -/- Zero, in mathematics, is a symbol of absence, a representation of nothingness, yet it holds a pivotal position as a number. It is the void from which all things emerge and to which they return. In the philosophy of mathematics, zero is the paradoxical junction where the One and the Multiple converge and diverge. -/- From the perspective of the One, zero can be seen as the origin—the singular point that precedes the existence of numbers. It is the empty set, the foundation upon which the edifice of mathematics is constructed. As the identity element in addition, zero maintains the integrity of numbers, for adding zero to any number leaves it unchanged, reflecting the immutable nature of the One. -/- Conversely, when we consider the Multiple, zero represents the infinite potentiality of creation. It is the canvas upon which the integers, both positive and negative, express their multitude. Zero is the balance point, the fulcrum around which the symphony of numbers dances. It embodies the plurality of possibilities, the beginning of the number line that stretches infinitely in both directions. -/- Philosophically, zero challenges our understanding of existence. It is both something and nothing—a number that quantifies the absence of quantity. This duality echoes the philosophical struggle to comprehend how the One gives rise to the Multiple. How does the unity of being manifest the diversity of the cosmos? Zero offers a mathematical metaphor for this mystery, as it encapsulates the transition from non-existence to existence, from the undifferentiated One to the differentiated Multiple. -/- In the realm of set theory, zero corresponds to the empty set—a set with no elements. This set is unique in that it is the only set that contains nothing, yet it is the foundation upon which all other sets are built. The empty set is the mathematical embodiment of the One, and all other sets, containing multiple elements, arise from it. -/- Reflecting on zero in the context of Gödel’s incompleteness theorems, we find a resonance with the idea that the One (a consistent formal system) cannot capture the entirety of the Multiple (the totality of mathematical truths). Zero, as the foundation of numbers, similarly suggests that from the nothingness of the One, the infinite complexity of the Multiple emerges—yet it can never be fully encompassed or expressed by any single system. -/- In conclusion, the mathematics of zero offers a profound reflection on the relationship between the One and the Multiple. It serves as a bridge between the abstract and the concrete, the known and the unknowable, challenging us to ponder the origins of existence and the nature of reality itself. -/- . (shrink)

Clark and Chalmers claim that an external resource satisfying the following criteria counts as a memory: the agent has constant access to the resource; the information in the resource is directly available; retrieved information is automatically endorsed; information is stored as a consequence of past endorsement. Research on forgetting and metamemory shows that most of these criteria are not satisfied by biological memory, so they are inadequate. More psychologically realistic criteria generate a similar classification of standard putative external memories, but (...) the criteria still do not capture the function of memory. An adequate account of memory function, compatible with its evolution and its roles in prospection and imagination, suggests that external memory performs a function not performed by biological memory systems. External memory is thus not memory. This has implications for: extended mind theorizing, ecological validity of memory research, the causal theory of memory. (shrink)

My objective is a better comprehension of two theoretically fundamental concepts. One, the concept of a substance in an ordinary (non-Aristotelian) sense, ranging over such things as salt, carbon, copper, iron, water, and methane – kinds of stuff that now count as (chemical) elements and compounds. The other I’ll call the object-concept in the abstract sense of Russell, Wittgenstein, and Frege in their logico-semantical enquiries. The material object-concept constitutes the heart of our received logico / ontic system, still massively influenced (...) by Aristotle after almost 2.5 millennia. On such an account, the fundamentality of material objects and their attributes are the metaphysical basis of the cosmos, as reflected in our received logic, Quine’s ‘canonical notation’ – derived via the empiricism of Russell from Frege’s function-based Begriffschrifft, and consisting of concrete singular terms and variables, quantifiers and predicate-expressions. The inadequacy of Frege’s approach to understanding concepts is reflected in his initial question. Frege enquires of ‘what it is that we are calling an object’, remarking that he regards a regular definition as impossible: “we have here something too simple to admit of logical analysis”. The imagined ultimacy or simplicity of the idea of a single object (arithmetically, just a unit – one as against two, three, four, etc.) as foundational to the calculus is just that – imagined. It is also guaranteed to block the comprehension of the substance-concept. (shrink)

The question “What is an organism?”, formerly considered as essential in biology, has now been increasingly replaced by a larger question, “What is a biological individual?”. On the grounds that i) individuation is theory-dependent, and ii) physiology does not offer a theory, biologists and philosophers of biology have claimed that it is the theory of evolution by natural selection which tells us what counts as a biological individual. Here I show that one physiological field, immunology, offers a theory, which makes (...) possible a biological individuation based on physiological grounds. I give a new answer to the question of the individuation of an organism by linking together the evolutionary and the immunological approaches to biological individuation. (shrink)

In recent years, there has been an increasing interest in thedevelopment of ontologically well-founded conceptual models for Information Systems in areas such as Service Management, Accounting Information Systems and Financial Reporting. Economic exchanges are central phenomena in these areas. For this reason, they occupy a prominent position in modelling frameworks such as the REA (Resource-EventAction) ISO Standard as well as the FIBO (Financial Industry BusinessOntology). In this paper, we begin a well-founded ontological analysisof economic exchanges inspired by a (...) recent ontological view on the nature of economic transactions. According to this view, what counts asan economic transaction is based on an agreement on the actions thatthe agents are committed to perform. The agreement is in turn based on convergent preferences about the course of action to bring about. This view enables a unified treatment of economic exchanges, regardless the object of the transaction, and complies with the view that all economictransactions are about services. In this paper, we start developing our analysis in the framework of the Unified Foundational Ontology (UFO). (shrink)

Derogatory terms (racist, sexist, ethnic, and homophobic epithets) are bully words with ontological force: they serve to establish and maintain a corrupt social system fuelled by distinctions designed to justify relations of dominance and subordination. No wonder they have occasioned public outcry and legal response. The inferential role analysis developed here helps move us away from thinking of the harms as being located in connotation (representing mere speaker bias) or denotation (holding that the terms fail to refer due to inaccurate (...) descriptive content). The issue is not bad attitudes or referential misfires. An inferential role semantic analysis of derogatory terms shows exactly what is at stake between those who argue that the terms should be eliminated (Absolutists) and those who claim they can be successfully rehabilitated (Reclaimers). The Reclaimer maintains, and the Absolutist denies, that certain contexts can detach the derogatory force from deeply derogatory terms. The article looks at these claims with respect to ‘nigger’ and ‘dyke,’ setting out the inferential role of each term and examining detachability potential. Explaining detachability in terms of linguistic commitments, this article also addresses the issue of whether such terms count as political discourse, and examines the implications of that issue. (shrink)

In this paper, I argue that what counts as the proper function of a trait is a matter of the de facto perspective that the biological system, itself, possesses on what counts as proper functioning for that trait. Unlike non-perspectival accounts, internal perspectivalism does not succumb to generality problems. But unlike external perspectivalism, internal perspectivalism can provide a fully naturalistic, mind-independent grounding of proper function and natural norms. The attribution of perspectives to biological systems is intended to be neither (...) metaphorical nor anthropomorphic: I do not mean to imply that such systems thereby must possess agency, cognition, intentions, concepts, or mental or psychological states. Instead, such systems provide the grounding for norms of performance when they internally enforce their own standard of (i.e., their own perspective on) what constitutes proper functioning or malfunctioning. By operating with a fixed, determinate level of generality, such systems provide the basis for an account of proper function that is immune to generality problems. (shrink)

Memory technologies are cultural artifacts that scaffold, transform, and are interwoven with human biological memory systems. The goal of this article is to provide a systematic and integrative survey of their philosophical dimensions, including their metaphysical, epistemological and ethical dimensions, drawing together debates across the humanities, cognitive sciences, and social sciences. Metaphysical dimensions of memory technologies include their function, the nature of their informational properties, ways of classifying them, and their ontological status. Epistemological dimensions include the truth-conduciveness of external (...) memory, the conditions under which external memory counts as knowledge, and the metacognitive monitoring of external memory processes. And lastly, ethical and normative dimensions include the desirability of the effects memory technologies have on biological memory, their effects on self and culture, and their moral status. Whilst the focus in the article is largely philosophical and conceptual, empirical issues such as the way we interact with memory technologies in various contexts are also discussed. We thus take a naturalistic approach in which philosophical and empirical concepts and approaches are seen as continuous. (shrink)

This chapter explores properties that bind individuals, knowledge, and communities, together. Section ‎‎1 introduces Hardwig’s argument from trust in others’ testimonies as entailing that trust is the glue ‎that binds individuals into communities. Section 2 asks “what grounds trust?” by exploring assessment ‎of collaborators’ explanatory responsiveness, formal indicators such as affiliation and credibility, ‎appreciation of peers’ tacit knowledge, game-theoretical considerations, and the role moral character ‎of peers, social biases, and social values play in grounding trust. Section 3 deals with establishing (...) ‎reliability standards for formation and breaching of trust. Different epistemic considerations and their ‎underpinning of inductive risks are examined through various communication routes within a ‎discipline, between disciplines, and to the public. Section 4 examines whether a collective entity can ‎be trusted over and above trust that is given to its individual members. Section 5 deals with the roles ‎technological artifacts play in distributed research and collective knowledge. It presents the common ‎view in which genuine trust cannot, in principle, be accorded to artifacts, so as an opposite view. We ‎show that what counts as a genuine object of trust is relevant to debates about the boundaries of ‎collective agency and as a criterion for extended cognitive systems.‎. (shrink)

While, prima facie, virtue/credit approaches in epistemology would appear to be in tension with distributed/extended approaches in cognitive science, Pritchard () has recently argued that the tension here is only apparent, at least given a weak version of distributed cognition, which claims merely that external resources often make critical contributions to the formation of true belief, and a weak virtue theory, which claims merely that, whenever a subject achieves knowledge, his cognitive agency makes a significant contribution to the formation of (...) a true belief. But the significance of the role played by the subject's cognitive agency in distributed cognitive systems is in fact highly variable: at one extreme, formation of a true belief seems clearly to be significantly creditable to the subject's agency; at the other extreme, however, the subject's agency plays such a peripheral role that it is at best unclear whether it should receive significant credit for formation of a true belief. The compatibility of distributed cognition and virtue epistemology thus turns on what it takes for a contribution to the formation of true belief to count as significant. This article argues that the inevitable vagueness of this notion suggests retreating from virtue epistemology to a form of process reliabilism and explores the prospects for a distributed reliabilist epistemology designed to fit smoothly with distributed cognition. In effect, distributed reliabilism radicalizes Goldberg's recent extended reliabilist view by allowing the process the reliability of which determines the epistemic status of a subject's belief to extend to include not only processing performed by other subjects but also processing performed by non-human technological resources. (shrink)

Modal logic is one of philosophy’s many children. As a mature adult it has moved out of the parental home and is nowadays straying far from its parent. But the ties are still there: philosophy is important to modal logic, modal logic is important for philosophy. Or, at least, this is a thesis we try to defend in this chapter. Limitations of space have ruled out any attempt at writing a survey of all the work going on in our field—a (...) book would be needed for that. Instead, we have tried to select material that is of interest in its own right or exemplifies noteworthy features in interesting ways. Here are some themes that have guided us throughout the writing: • The back-and-forth between philosophy and modal logic. There has been a good deal of give-and-take in the past. Carnap tried to use his modal logic to throw light on old philosophical questions, thereby inspiring others to continue his work and still others to criticise it. He certainly provoked Quine, who in his turn provided—and continues to provide—a healthy challenge to modal logicians. And Kripke’s and David Lewis’s philosophies are connected, in interesting ways, with their modal logic. Analytic philosophy would have been a lot different without modal logic! • The interpretation problem. The problem of providing a certain modal logic with an intuitive interpretation should not be conflated with the problem of providing a formal system with a model-theoretic semantics. An intuitively appealing model-theoretic semantics may be an important step towards solving the interpretation problem, but only a step. One may compare this situation with that in probability theory, where definitions of concepts like ‘outcome space’ and ‘random variable’ are orthogonal to questions about “interpretations” of the concept of probability. • The value of formalisation. Modal logic sets standards of precision, which are a challenge to—and sometimes a model for—philosophy. Classical philosophical questions can be sharpened and seen from a new perspective when formulated in a framework of modal logic. On the other hand, representing old questions in a formal garb has its dangers, such as simplification and distortion. • Why modal logic rather than classical (first or higher order) logic? The idioms of modal logic—today there are many!—seem better to correspond to human ways of thinking than ordinary extensional logic. (Cf. Chomsky’s conjecture that the NP + VP pattern is wired into the human brain.) In his An Essay in Modal Logic (1951) von Wright distinguished between four kinds of modalities: alethic (modes of truth: necessity, possibility and impossibility), epistemic (modes of being known: known to be true, known to be false, undecided), deontic (modes of obligation: obligatory, permitted, forbidden) and existential (modes of existence: universality, existence, emptiness). The existential modalities are not usually counted as modalities, but the other three categories are exemplified in three sections into which this chapter is divided. Section 1 is devoted to alethic modal logic and reviews some main themes at the heart of philosophical modal logic. Sections 2 and 3 deal with topics in epistemic logic and deontic logic, respectively, and are meant to illustrate two different uses that modal logic or indeed any logic can have: it may be applied to already existing (non-logical) theory, or it can be used to develop new theory. (shrink)

The belief norm of academic publishing states that researchers should believe certain claims they publish. The purpose of this paper is to defend the belief norm of academic publishing. In its defense, the advantages and disadvantages of the belief norm are evaluated for academic research and for the publication system. It is concluded that while the norm does not come without costs, academic research systemically benefits from the belief norm and that it should be counted among those that sustain the (...) practice of academic publishing. (shrink)

Relying on evidence from fifteen epigraphic collections and sixty-odd ancient sources as well as discussing a literature of over five hundred titles, the essay’s highly unorthodox conclusions are a case in point of the micrological ideal of achieving novelty on any given subject by way of transcribing and studying first-hand all relevant materials – edited and unedited alike. The paper’s ambition was to shed new light on one of the most intriguing analogies of the whole Aristotelian corpus, namely the comparison (...) between words and pebbles. A review of all material evidence and virtually all extant sources made short work of two related, albeit mutually exclusive, misconception about ancient reckoning boards and their workings: (1) the idea that – for all practical purposes – the abacus’ arrangement mirrored the decimal system, its columns and rows conveniently matching units, tens, hundreds, thousands, etc. (2) the idea that the inscriptions on several surviving counting boards were a nuisance to the extent that, being inconsistent to a fault with the decimal system itself, they made actual calculations harder than they already were (as opposed to making them easier, as one would expect). The paper demonstrated that the first assumption – the « decimal » bias – is simply mistaken and betrays little or no awareness of the epigraphic and archaeological evidence. The paper also demonstrated that the second assumption – the « abacus riddled with complications » bias – simply defeats the purpose of resorting to the abacus in the first place and betrays a poor understanding of its practical vocation which, most assuredly, was not to add to the very problem it was meant to solve. After bulldozing its way through both misunderstandings, the essay focused on the abacus most distinctive features, that is positionality (i.e. the abacus being a positional system through and through) and hybridity (i.e. the abacus’ place value system being monetary in nature and purpose, as opposed to it being abstract and homogeneous). The final result is an interpretation that moves away from the received views by showing that the prologue of the Sophistici elenchi offers no support to the notion that, when Aristotle referred to counters, he was leaning on a kinship of sorts – or any kinship, for that matter – between abstract calculation and speech. Once we turns the pebble’s simile on its head and set it back upon its feet (Aristotle’s pebble analogy is about pebbles, what else?), it becomes clear that it presupposed numeracy all right, but it was not about numeracy itself. Moreover its goal was not to explain why computational and linguistic symbolisms succeed, but to explain how they fail – failure being the whole point; in this particular instance, failure to detect and prevent abusive value shifts affecting words and counters alike. (shrink)

Basilio Sabazio was the first in Italy to argue for the unity and corruptibility of either sublunar or celestial matter. In this paper new insight of his intellectual activity between Napoli and Milano is provided, and in particular his relationship with Scipione Capece, from whose letter to Giovan Francesco di Capua, Count of Palena we learn that Sabazio was an expert in philology and astronomy. The surviving part of an essay by Sabazio to the astronomer Francesco Cigalini from Como is (...) here edited with some informations about Cigalini’s reply. A newly recovered Sabazio’s astronomical work is here edited – from which his endorsement of Eraclides Ponticus’ astronomical system is evident –, as well as his Consilium to Pope Paolo III about the urgency of convening a general council. (shrink)

Theories of number concepts often suppose that the natural numbers are acquired as children learn to count and as they draw an induction based on their interpretation of the first few count words. In a bold critique of this general approach, Rips, Asmuth, Bloomfield [Rips, L., Asmuth, J. & Bloomfield, A.. Giving the boot to the bootstrap: How not to learn the natural numbers. Cognition, 101, B51–B60.] argue that such an inductive inference is consistent with a representational system that clearly (...) does not express the natural numbers and that possession of the natural numbers requires further principles that make the inductive inference superfluous. We argue that their critique is unsuccessful. Provided that children have access to a suitable initial system of representation, the sort of inductive inference that Rips et al. call into question can in fact facilitate the acquisition of larger integer concepts without the addition of any further principles. (shrink)

Legal norms are an invention. This paper advances a proposal about what kind of invention they are. The proposal is that legal norms derive from rules which specify role functions in a legal system. Legal rules attach to agents in virtue of their status within the system in which the rules operate. The point of legal rules or a legal system is to solve to large scale coordination problems, specifically the problem of organizing social and economic life among a group (...) of people and their successors, though not every legal rule pertains to a coordination problem. The framework for thinking about legal norms that I describe is a framework for thinking about institutions and policies more generally. The idea is to show that legal norms are a species of institutional norm. There are two central ideas. The first is the idea of a role in an institution. The second is the idea of proxy agency. Proxy agency involves one agent or group acting under the authorization of another agent or group (perhaps subsuming it) in a way that makes the actions of the proxy count as actions (under a description) of the individual or group for which it is a proxy. We get the characteristic structure of a legal system by conceiving of an institutional group, itself conceived of as a set of interlocking roles realized in individuals, as having one or more roles for proxy agents who are authorized by the group to make policy for the group. The set of rules governing the basic constitution of the group and spelling out the powers of the policy proxies determine fundamental norms for the group with specific role responsibilities attaching to particular positions in institutional arrangements. The policies determine further norms whose force derives from the fundamental norms. We must then say some further things to distinguish institutions and policies which we wish to designate as legal. (shrink)

This paper addresses the question of what organisms are and therefore what kinds of biological entities qualify as organisms. For some time now, the concept of organismality has been eclipsed by the notion of individuality. Biological individuals are those systems that are units of selection. I develop a conception of organismality that does not rely on evolutionary considerations, but instead draws on development and ecology. On this account, organismality and individuality can come apart. Organisms, in my view, are as (...) Godfrey-Smith puts it “essentially persisters.” I argue that persistence is underpinned by differentiation, integration, development, and the constitutive embeddedness of organisms in their worlds. I examine two marginal cases, the Portuguese Man O’ War and the honey bee colony, and show that both count as organisms in light of my analysis. Next, I examine the case of holobionts, hosts plus their microsymbionts, and argue that they can be counted as organisms even though they may not be biological individuals. Finally, I consider the question of whether other, less tightly integrated biological systems might also be treated as organisms. (shrink)