We will explicate Cantor’s principle of set existence using the Gödelian intensional notion of absolute provability and John Burgess’ plural logical concept of set formation. From this Cantorian Comprehension principle we will derive a conditional result about the question whether there are any absolutely unprovable mathematical truths. Finally, we will discuss the philosophical significance of the conditional result.

The aim of this essay is to develop a formal reconstruction of Greek arithmetic. The reconstruction is based on textual evidence which comes mainly from Euclid, but also from passages in the texts of Plato and Aristotle. Following Paul Pritchard’s investigation into the meaning of the Greek term arithmos, the reconstruction will be mereological rather than set-theoretical. It is shown that the reconstructed system gives rise to an arithmetic comparable in logical strength to Robinson arithmetic. Our reconstructed Greek arithmetic is (...) then compared to modern developments in the foundations of arithmetic. Finally, it is shown that our reconstruction can help to clarify some issues in Plato’s philosophy of arithmetic, especially the question if Plato’s views can be compared to 19th – 20th century developments in the logical construction of arithmetic. (shrink)

This paper analyzes the coordination challenge a partial cartel faces when payoff asymmetries between potential cartel insiders and potential cartel outsiders are large. We introduce two experimental treatments: a standard treatment where a complete cartel can be supported in a Nash equilibrium and a modified treatment where a complete cartel and a partial cartel can both be supported in a Nash equilibrium. To assess the role of communication both treatments are additionally run with a “chat option,” yielding four treatments in (...) total. Our results show that subjects frequently reject the formation of partial cartels in the modified treatments. In all treatments with communication subjects are more likely to form complete cartels than partial cartels. The implications of these results are important for antitrust: payoff asymmetries between cartel members and outsiders may jeopardize the formation of partial cartels. Yet complete cartels may be formed instead, if institutional mechanisms with frequent communication are used to form cartels. (shrink)

Previous studies have shown that multiple reference frames are available and compete for selection during the use of spatial terms such as “above.” However, the mechanisms that underlie the selection process are poorly understood. In the current paper we present two experiments and a comparison of three computational models of selection to shed further light on the nature of reference frame selection. The three models are drawn from different areas of human cognition, and we assess whether they may be applied (...) to a reference frame selection by examining their ability to account for both existing and new empirical data comprising acceptance rates, response times, and response time distributions. These three models are the competitive shunting model, the leaky competing accumulator model, and a lexical selection model. Model simulations show that only the LCA model satisfactorily accounts for the empirical observations. The key properties of this model that seem to drive its success are its bounded linear activation function, its number and type of processing stages, and its use of decay. Uncovering these critical properties has important implications for our understanding not only of spatial term use, in particular, but also of conflict and selection in human cognition more generally. (shrink)

Platonic Patterns is a reprint collection of many of Holger Thesleff's studies in Plato—spanning from 1967 to 2003. It includes three books, four articles and a new introduction by the author, which sets the general outline of his interpretation of Plato. Whereas much of the scholarship on Plato has tended to operate within the frame of one language and/or a single school of thought, Thesleff constructively combines several discoveries and theories of various scholars with his own research, focusing on (...) how Plato can be understood in his own context. The work represents small but significant breakthroughs in research on Plato from an internationally inclusive standpoint. Having previously been published mainly in Finland by scholarly societies, availability outside the Nordic countries has, up until now, been minimal. Thesleff employs his singular expertise of Greek language and literature to make innovative contributions to the study and interpretation of Plato. He thematically stresses the significance of the less overt elements found in Plato's dialogues, such as Plato's use of humor and his linguistic expression, while taking into account the chronology and/or the intended audience. (shrink)

Both, bioconservatives and bioliberals, should seek a discussion about ideas of human perfection, making explicit their underlying assumptions about what makes for a good human life. This is relevant, because these basic, and often implicit ideas, inform and influence judgements and choices about human enhancement interventions. Both neglect, and polemical but inconsistent use of the complex ideas of perfection are leading to confusion within the ethical debate about human enhancement interventions, that can be avoided by tackling the notion of perfection (...) directly. In the recent debates, bioconservatives have prominently argued against the ‘pursuit of perfection’ by biotechnological means. In the first part of this paper, we show that—paradoxically—bioconservatives themselves explicitly embrace specific conceptions of human perfection and perfectionist assumptions about the good human life in order to argue against the use of enhancement technologies. Yet, we argue that the bioconservative position contains an untenable ambiguity between criticising and endorsing ideas of human perfection. Hence, they stand in need of clarifying their stance on human perfection. In the second part of the paper, we ask whether bioliberals in fact (implicitly) advocate a particular conception of perfection, or whether they are right in holding that they do not, and that discussing perfection is obsolete anyway. We show that bioliberals also rely on a specific idea of human perfection, based on the idea of autonomy. Hence, their denial of the relevance of perfection in the debate is unconvincing and has to be revised. (shrink)

Whatever ethical stance one takes in the debate regarding the ethics of human enhancement, one or more reference points are required to assess its morality. Some have suggested looking at the bioethical notions of safety, justice, and/or autonomy to find such reference points. Others, arguing that those notions are limited with respect to assessing the morality of human enhancement, have turned to human nature, human authenticity, or human dignity as reference points, thereby introducing some perfectionist assumptions into the debate. In (...) this article, we ask which perfectionist assumptions should be used in this debate. After a critique of views that are problematic, we take a positive approach, suggesting some perfectionist elements that can lend guidance to the practice of human enhancement, based on the work of Martha Nussbaum's Capability Approach. We suggest that the central capabilities can be used to define the human aspect of human enhancement and thereby allow a moral evaluation of enhancement interventions. These central capabilities can be maximized harmoniously to postulate what an ideal human would look like. Ultimately, the aim of this article is twofold. First, it seeks to make explicit the perfectionist assumptions found in the debate and eliminate those that are problematic. Second, the paper clarifies an element that is often neglected in the debate about human enhancement, the view of the ideal human towards which human enhancement should strive. Here, we suggest that some central capabilities that are essential for an ideal human being can be maximized harmoniously and can therefore serve as possible reference points to guide human enhancement. (shrink)

Is it necessary to have an ideal of perfection in mind to identify and evaluate true biotechnological human “enhancements”, or can one do without? To answer this question we suggest employing the distinction between ideal and non-ideal theory, found in the debate in political philosophy about theories of justice: the distinctive views about whether one needs an idea of a perfectly just society or not when it comes to assessing the current situation and recommending steps to increase justice. In this (...) paper we argue that evaluating human enhancements from a non-ideal perspective has some serious shortcomings, which can be avoided when endorsing an ideal approach. Our argument starts from a definition of human enhancement as improvement, which can be understood in two ways. The first approach is backward-looking and assesses improvements with regard to a status quo ante. The second, a forward-looking approach, evaluates improvements with regard to their proximity to a goal or according to an ideal. After outlining the limitations of an exclusively backward-looking view, we answer possible objections against a forward-looking view. Ultimately, we argue that the human enhancement debate would lack some important moral insights if a forward-looking view of improvement is not taken into consideration. (shrink)

Drawing on recent work in developmental and comparative psychology, this paper argues that demonstratives function to coordinate the interlocutors' joint focus of attention, which is one of the most basic functions of human communication. The communicative importance of demonstratives is reflected in a number of properties that together characterize them as a particular word class: In contrast to other closed-class expressions, demonstratives are universal, they are generally so old that their roots cannot be traced back to other linguistic items, they (...) are among the earliest words that children learn, and they are closely tied to a particular gesture. Moreover, demonstratives play an important role in the organization of discourse and the diachronic evolution of grammar, which arguably is also motivated by their communicative function to establish joint attention. (shrink)

In this paper, we propose a regularity theory of causation. The theory aims to be reductive and to align with our pre‐theoretic understanding of the causal relation. We show that our theory can account for a wide range of causal scenarios, including isomorphic scenarios, omissions, and scenarios which suggest that causation is not transitive.

Information management systems improve the retention of information in large collections. As such they act as memory prostheses, implying an ideal basis in human memory models. Since humans process information by association, and situate it in the context of space and time, systems should maximize their effectiveness by mimicking these functions. Since human attentional capacity is limited, systems should scaffold cognitive efforts in a comprehensible manner. We propose the Principles of Mnemonic Associative Knowledge (P-MAK), which describes a framework for semantically (...) identifying, organizing, and retrieving information, and for encoding episodic events by time and stimuli. Inspired by prominent human memory models, we propose associative networks as a preferred representation. Networks are ideal for their parsimony, flexibility, and ease of inspection. Networks also possess topological properties—such as clusters, hubs, and the small world—that aid analysis and navigation in an information space. Our cognitive perspective addresses fundamental problems faced by information management systems, in particular the retrieval of related items and the representation of context. We present evidence from neuroscience and memory research in support of this approach, and discuss the implications of systems design within the constraints of P-MAK’s principles, using text documents as an illustrative semantic domain. (shrink)

We aim to devise a Ramsey test analysis of actual causation. Our method is to define a strengthened Ramsey test for causal models. Unlike the accounts of Halpern and Pearl ([2005]) and Halpern ([2015]), the resulting analysis deals satisfactorily with both over- determination and conjunctive scenarios.

This book aims to lay bare the logical foundations of tractable reasoning. It draws on Marvin Minsky's seminal work on frames, which has been highly influential in computer science and, to a lesser extent, in cognitive science. Only very few people have explored ideas about frames in logic, which is why the investigation in this book breaks new ground. The apparent intractability of dynamic, inferential reasoning is an unsolved problem in both cognitive science and logic-oriented artificial intelligence. By means of (...) a logical investigation of frames and frame concepts, Andreas devises a novel logic of tractable reasoning, called frame logic. Moreover, he devises a novel belief revision scheme, which is tractable for frame logic. These tractability results shed new light on our logical and cognitive means to carry out dynamic, inferential reasoning. Modularity remains central for tractability, and so the author sets forth a logical variant of the massive modularity hypothesis in cognitive science. (shrink)

There is a growing consensus that the mental lexicon contains both abstract and word-specific acoustic information. To investigate their relative importance for word recognition, we tested to what extent perceptual learning is word specific or generalizable to other words. In an exposure phase, participants were divided into two groups; each group was semantically biased to interpret an ambiguous Mandarin tone contour as either tone1 or tone2. In a subsequent test phase, the perception of ambiguous contours was dependent on the exposure (...) phase: Participants who heard ambiguous contours as tone1 during exposure were more likely to perceive ambiguous contours as tone1 than participants who heard ambiguous contours as tone2 during exposure. This learning effect was only slightly larger for previously encountered than for not previously encountered words. The results speak for an architecture with prelexical analysis of phonological categories to achieve both lexical access and episodic storage of exemplars. (shrink)

Most recent accounts of personal autonomy acknowledge that the social environment a person lives in, and the personal relationships she entertains, have some impact on her autonomy. Two kinds of conceptualizing social conditions are traditionally distinguished in this regard: Causally relational accounts hold that certain relationships and social environments play a causal role for the development and on-going exercise of autonomy. Constitutively relational accounts, by contrast, claim that autonomy is at least partly constituted by a person’s social environment or standing. (...) The central aim of this paper is to raise the question how causally and constitutively relational approaches relate to the fact that we exercise our autonomy over time. I argue that once the temporal scope of autonomy is opened up, we need not only to think differently about the social dimension of autonomy. We also need to reconsider the very distinction between causally and constitutively relational accounts, because it is itself a synchronic (and not a diachronic) distinction. (shrink)

This paper offers a review of research on demonstratives from an interdisciplinary perspective. In particular, we consider the role of demonstratives in current research on language universals, language evolution, language acquisition, multimodal communication, signed language, language and perception, language in interaction, spatial imagery, and discourse processing. Traditionally, demonstratives are analyzed as a particular class of spatial deictics. Yet, a number of recent studies have argued that space is largely irrelevant to deixis and that demonstratives are primarily used for social and (...) interactive purposes. Synthesizing findings in the literature, we conclude that demonstratives are a very special class of linguistic items that are foundational to both spatial and social aspects of language and cognition. (shrink)

In this paper, we analyse actual causation in terms of production. The latter concept is made precise by a strengthened Ramsey Test semantics of conditionals: \ iff, after suspending judgement about A and C, C is believed in the course of assuming A. This test allows us to verify or falsify that an event brings about another event. Complementing the concept of production by a weak condition of difference-making gives rise to a full-fledged analysis of causation.

Modal logic has been applied in many different areas, as reasoning about time, knowledge and belief, necessity and possibility, to mention only some examples. In the present paper, an attempt is made to use modal logic to account for the semantics of theoretical sentences in scientific language. Theoretical sentences have been studied extensively since the work of Ramsey and Carnap. The present attempt at a modal analysis is motivated by there being several intended interpretations of the theoretical terms once these (...) terms are introduced through the axioms of a theory. (shrink)

Usage-based linguists and psychologists have produced a large body of empirical results suggesting that linguistic structure is derived from language use. However, while researchers agree that these results characterize grammar as an emergent phenomenon, there is no consensus among usage-based scholars as to how the various results can be explained and integrated into an explicit theory or model. Building on network theory, the current paper outlines a structured network approach to the study of grammar in which the core concepts of (...) syntax are analyzed by a set of relations that specify associations between different aspects of a speaker’s linguistic knowledge. These associations are shaped by domain-general processes that can give rise to new structures and meanings in language acquisition and language change. Combining research from linguistics and psychology, the paper proposes specific network analyses for the following phenomena: argument structure, word classes, constituent structure, constructions and construction families, and grammatical categories such as voice, case and number. The article builds on data and analyses presented inDiessel but approaches the topic from a different perspective. (shrink)

Democracy has come under pressure in many countries in recent years. Authoritarian tendencies, populism and the cult of leadership threaten pluralistic societies in Europe and other parts of the world. But democracy is more than just a method of finding a majority; it is inextricably linked to the fight against oppression and injustice in all contexts of life. Especially in times of democratic crisis, it is necessary to focus on its core aspects. The political thinking of French philosopher and writer (...) Albert Camus, who died in 1960, offers the basis for a redefinition of democracy that is linked to and dependent on rebellion. From his reflections, a radical theory of democracy can be derived that is based on the absurdity of the world, its incompleteness, revolt and resistance to authoritarianism, on doubt, dialogue and foreignness. (shrink)

In this international and interdisciplinary collection of critical essays, distinguished contributors examine a crucial premise of traditional readings of Plato's dialogues: that Plato's own doctrines and arguments can be read off the statements made in the dialogues by Socrates and other leading characters. The authors argue in general and with reference to specific dialogues, that no character should be taken to be Plato's mouthpiece. This is essential reading for students and scholars of Plato.

The present paper aims at a synthesis of belief revision theory with the Sneed formalism known as the structuralist theory of science. This synthesis is brought about by a dynamisation of classical structuralism, with an abductive inference rule and base generated revisions in the style of Rott (2001). The formalism of prioritised default logic (PDL) serves as the medium of the synthesis. Why seek to integrate the Sneed formalism into belief revision theory? With the hybrid system of the present investigation, (...) a substantial simplification of the ranking information that is necessary to define revisions and contractions uniquely is achieved. This system is, furthermore, expressive enough to capture complex and non-trivial scientific examples. It is thus closely related to a novel research area within belief revision theory which addresses the dynamics of scientific knowledge. (shrink)

In a series of 5 experiments, we investigated whether the processing of phonologically assimilated utterances is influenced by language learning. Previous experiments had shown that phonological assimilations, such as /lean#bacon/→ [leam bacon], are compensated for in perception. In this article, we investigated whether compensation for assimilation can occur without experience with an assimilation rule using automatic event-related potentials. Our first experiment indicated that Dutch listeners compensate for a Hungarian assimilation rule. Two subsequent experiments, however, failed to show compensation for assimilation (...) by both Dutch and Hungarian listeners. Two additional experiments showed that this was due to the acoustic properties of the assimilated utterance, confirming earlier reports that phonetic detail is important in compensation for assimilation. Our data indicate that compensation for assimilation can occur without experience with an assimilation rule, in line with phonetic-phonological theories that assume that speech production is influenced by speech-perception abilities. (shrink)

The paper provides a formal representation of goal systems. The focus is on three properties: consistency, conflict, and coherence. An aim is to attain conceptual clarity of these properties. It is argued that consistency is adequately regarded as a property relative to the decision situation or, more specifically, the set of alternatives that the agent faces. Moreover, as a condition of rationality, consistency is stronger than some writers have claimed. Conflict is adequately regarded as a relation over subsets of a (...) given goal system and should likewise be regarded as relative to the set of alternatives that the agent faces. Coherence is given a probabilistic interpretation, based on a support relation over subsets of goal systems. (shrink)

We put forth an analysis of causation. The analysis centers on the notion of a causal model that provides only partial information as to which events occur, but complete information about the dependences between the events. The basic idea is this: an event causes another just in case there is a causal model that is uninformative on both events and in which the first event makes a difference as to the occurrence of the other. We show that our analysis captures (...) more causal scenarios than the other counterfactual accounts to date. (shrink)

The well-known formal semantics of conditionals due to Stalnaker Studies in logical theory, Blackwell, Oxford, 1968), Lewis, and Gärdenfors The logic and 1140 epistemology of scientific change, North-Holland, Amsterdam, 1978, Knowledge in flux, MIT Press, Cambridge, 1988) all fail to distinguish between trivially and nontrivially true indicative conditionals. This problem has been addressed by Rott :345–370, 1986) in terms of a strengthened Ramsey Test. In this paper, we refine Rott’s strengthened Ramsey Test and the corresponding analysis of explanatory relations. We (...) show that our final analysis captures the presumed asymmetry between explanans and explanandum much better than Rott’s original analysis. (shrink)

The well-known formal semantics of conditionals due to Stalnaker Studies in logical theory, Blackwell, Oxford, 1968), Lewis, and Gärdenfors The logic and 1140 epistemology of scientific change, North-Holland, Amsterdam, 1978, Knowledge in flux, MIT Press, Cambridge, 1988) all fail to distinguish between trivially and nontrivially true indicative conditionals. This problem has been addressed by Rott :345–370, 1986) in terms of a strengthened Ramsey Test. In this paper, we refine Rott’s strengthened Ramsey Test and the corresponding analysis of explanatory relations. We (...) show that our final analysis captures the presumed asymmetry between explanans and explanandum much better than Rott’s original analysis. (shrink)

In this note we consider register-machines with symbol manipulation capabilities. They can form words over a given alphabet in their registers by appending symbols to the strings already stored. These machines are similar to Post's normal systems and the related machine-models discussed in the literature. But unlike the latter devices they are deterministic and are not allowed to read symbols from the front of the registers. Instead they can compare registers and erase them. At first glance it is surprising that (...) in general these devices are as powerful as the seemingly stronger models. Here we investigate the borderline of universality for these machines. (shrink)

We define a formal semantics of conditionals based on _normatively ideal worlds_. Such worlds are described informally by Armgardt (Gabbay D, Magnani L, Park W, Pietarinen A-V (eds) Natural arguments: a tribute to john woods, College Publications, London, pp 699–708, 2018) to address well-known problems of the counterfactual approach to causation. Drawing on Armgardt’s proposal, we use iterated conditionals in order to analyse causal relations in scenarios of multi-agent interaction. This results in a refined counterfactual approach to causal responsibility in (...) legal contexts, which solves overdetermination problems in an intuitively accessible manner. (shrink)

A simple explanation of theoreticity says that a term is theoretical if and only if it refers to nonobservational entities. Paradigmatic examples of such entities are electrons, neutrinos, gravitational forces, genes etc. There is yet another explanation of theoreticity: a theoretical term is one whose meaning becomes determined through the axioms of a scientific theory. The meaning of the term ‘force’, for example, is seen to be determined by Newton’s laws of motion and further laws about special forces, such as (...) the law of gravitation. Theoreticity is a property that is commonly applied to both expressions in the language of science, and referents and concepts of such expressions. Objects, relations and functions as well as concepts thereof may thus qualify as theoretical in a derived sense. (shrink)