This article offers an overview of inferential role semantics. We aim to provide a map of the terrain as well as challenging some of the inferentialist’s standard commitments. We begin by introducing inferentialism and placing it into the wider context of contemporary philosophy of language. §2 focuses on what is standardly considered both the most important test case for and the most natural application of inferential role semantics: the case of the logical constants. We discuss some of the (alleged) benefits (...) of logical inferentialism, chiefly with regards to the epistemology of logic, and consider a number of objections. §3 introduces and critically examines the most influential and most fully developed form of global inferentialism: Robert Brandom’s inferentialism about linguistic and conceptual content in general. Finally, in §4 we consider a number of general objections to IRS and consider possible responses on the inferentialist’s behalf. (shrink)

In this paper some classical representational ideas of Hertz and Duhem are used to show how the dichotomy between representation and intervention can be overcome. More precisely, scientific theories are reconstructed as complex networks of intervening representations (or representational interventions). The formal apparatus developed is applied to elucidate various theoretical and practical aspects of the in vivo/in vitro problem of biochemistry. Moreover, adjoint situations (Galois connections) are used to explain the relation berween empirical facts and theoretical laws in a new (...) way. (shrink)

In this paper, we argue that, barring a few important exceptions, the phenomenon we refer to using the expression “being moved” is a distinct type of emotion. In this paper’s first section, we motivate this hypothesis by reflecting on our linguistic use of this expression. In section two, pursuing a methodology that is both conceptual and empirical, we try to show that the phenomenon satisfies the five most commonly used criteria in philosophy and psychology for thinking that some affective episode (...) is a distinct emotion. Indeed, being moved, we claim, is the experience of a positive core value (particular object) perceived by the moved subject as standing out (formal object) in the circumstances triggering the emotion. Drawing on numerous examples, we describe the distinctively rich phenomenology characteristic of the experience as well as the far-reaching action-tendencies and functions associated with it. Having thus shown that the candidate emotion seem to satisfy the five criteria, we go on, in section three, to compare it with sadness and joy, arguing that it should not be confused with either. Finally, in section four, we illustrate the explanatory power of our account of “being moved” by showing how it can shed light on, and maybe even justify, the widespread distrust we feel towards the exhibition of ‘sentimentality’. On the whole and if we are right, we have uncovered an emotion which, though never or rarely talked about, is of great interest and no small importance. (shrink)

Epistemic utility theory is generally coupled with veritism. Veritism is the view that truth is the sole fundamental epistemic value. Veritism, when paired with EUT, entails a methodological commitment: norms of epistemic rationality are justified only if they can be derived from considerations of accuracy alone. According to EUT, then, believing truly has epistemic value, while believing falsely has epistemic disvalue. This raises the question as to how the rational believer should balance the prospect of true belief against the risk (...) of error. A strong intuitive case can be made for a kind of epistemic conservatism – that we should disvalue error more than we value true belief. I argue that none of the ways in which advocates of veritist EUT have sought to motivate conservatism can be squared with their methodological commitments. Short of any such justification, they must therefore either abandon their most central methodological principle or else adopt a permissive line with respect to epistemic risk. (shrink)

If feeling a genuine emotion requires believing that its object actually exists, and if this is a belief we are unlikely to have about fictional entities, then how could we feel genuine emotions towards these entities? This question lies at the core of the paradox of fiction. Since its original formulation, this paradox has generated a substantial literature. Until recently, the dominant strategy had consisted in trying to solve it. Yet, it is more and more frequent for scholars to try (...) to dismiss it using data and theories coming from psychology. In opposition to this trend, the present paper argues that the paradox of fiction cannot be dissolved in the ways recommended by the recent literature. We start by showing how contemporary attempts at dissolving the paradox assume that it emerges from theoretical commitments regarding the nature of emotions. Next, we argue that the paradox of fiction rather emerges from everyday observations, the validity of which is independent from any such commitment. This is why we then go on to claim that a mere appeal to psychology in order to discredit these theoretical commitments cannot dissolve the paradox. We bring our discussion to a close on a more positive note, by exploring how the paradox could in fact be solved by an adequate theory of the emotions. (shrink)

Abstract. In Dynamics of Reason Michael Friedman proposes a kind of synthesis between the neokantianism of Ernst Cassirer, the logical empiricism of Rudolf Carnap, and the historicism of Thomas Kuhn. Cassirer and Carnap are to take care of the Kantian legacy of modern philosophy of science, encapsulated in the concept of a relativized a priori and the globally rational or continuous evolution of scientific knowledge,while Kuhn´s role is to ensure that the historicist character of scientific knowledge is taken seriously. More (...) precisely, Carnapian linguistic frameworks, guarantee that the evolution of science procedes in a rational manner locally,while Cassirer’s concept of an internally defined conceptual convergence of empirical theories provides the means to maintain the global continuity of scientific reason. In this paper it is argued that Friedman’s neokantian account of scientific reason based on the concept of the relativized a priori underestimates the pragmatic aspects of the dynamics of scientific reason. To overcome this short-coming, I propose to reconsider C.I. Lewis’s account of a pragmatic the priori, recently modernized and elaborated by Hasok Chang. This may be<br><br><br><br><br><br><br><br><br><br&g t;<br><br><br><br><br><br>Keywords: Dynamics of reason, Paradigms, Logical Empiricism,Neokantianism, Pragmatism, Mathematics, Communicative Rationality. (shrink)

Quine’s classical classic interpretation succinctly characterized characterizes Carnap’s Aufbau as an attempt “to account for the external world as a logical construct of sense-data....” Consequently, “Russell” was characterized as the most important influence on the Aufbau. Those times have passed. Formulating a comprehensive and balanced interpretation of the Aufbau has turned out to be a difficult task and one that must take into account several disjointed sources. My thesis is that the core of the Aufbau rested on a problem that (...) had haunted German philosophy since the end of the 19th century. In terms fashionable at the time, this problem may be expressed as the polarity between Leben and Geist that characterized German philosophy during the years of the Weimar Republic. At that time, many philosophers, including Cassirer, Rickert and Vaihinger, were engaged in overcoming this polarity. As I will show, Carnap’s Aufbau joined the ranks of these projects. This suggests that Lebensphilosophie and Rickert’s System der Philosophie exerted a strong influence on Carnap’s projects, an influence that is particularly conspicuous in his unpublished manuscript Vom Chaos zur Wirklichkeit. Carnap himself asserted that this manuscript could be considered “the germ of the constitution theory” of the Aufbau. Reading Chaos also reveals another strong but neglected influence on the Aufbau, namely a specific version of neutral monism put forward by the philosopher and psychologist Theodor Ziehen before World War I. Ziehen’s work contributed much to the invention of the constitutional method of quasi-analysis. -/-. (shrink)

Why is it that most fictions present one and only one ending, rather than multiple ones? Fictions presenting multiple endings are possible, because a few exist; but they are very rare, and this calls for an explanation. We argue that such an explanation is likely to shed light on our engagement with fictions, for fictions having one and only one ending seem to be ubiquitous. After dismissing the most obvious explanations for this phenomenon, we compare the scarcity of multiple endings (...) in traditional kinds of fiction to their profusion in the case of interactive fictions. This contrast poses a challenge to accounts of our engagement with fictions in terms of games of make-believe. We conclude that solving this puzzle is likely to improve our philosophical understanding of fictions. (shrink)

This paper provides a comprehensive review of the experimental philosophy of action, focusing on the various different accounts of the Knobe Effect.

In this chapter, I present a comprehensive review of the literature on experimental philosophy of aesthetics.

The aim of this paper is to show that topology has a bearing on Leibniz’s Principle of the Identity of Indiscernibles (PII). According to (PII), if, for all properties F, an object a has property F iff object b has property F, then a and b are identical. If any property F whatsoever is permitted in PII, then Leibniz’s principle is trivial, as is shown by “identity properties”. The aim of this paper is to show that topology can make a (...) contribution to the problem of giving criteria of how to restrict the domain of properties to render (PII) non-trivial. In topology a wealth of different Leibnizian principles of identity can be defined - PII turns out to be just the weakest topological separation axiom T0 in disguise, stronger principles of can be defined with the aid of higher separation axioms Ti, i > 0. Topologically defined properties have a variety of nice features, in particular they are stable in a natural sense. Topologically defined properties do not have a monopoly on defining “good” properties. In the final section of the paper it is show that the topological approach is closely related to Gärdenfors’s approach of conceptual spaces based on the concept of convexity. (shrink)

In the past decade, experimental philosophy---the attempt at making progress on philosophical problems using empirical methods---has thrived in a wide range of domains. However, only in recent years has aesthetics succeeded in drawing the attention of experimental philosophers. The present paper constitutes the first survey of these works and of the nascent field of 'experimental philosophy of aesthetics'. We present both recent experimental works by philosophers on topics such as the ontology of aesthetics, aesthetic epistemology, aesthetic concepts, and imagination, as (...) well as research from other disciplines that not only are relevant to philosophy of aesthetics but also open new avenues of research for experimental philosophy of aesthetics. Overall, we conclude that the birth of an experimental philosophy of aesthetics is good news not only for aesthetics but also for experimental philosophy itself, as it contributes to broaden the scope of experimental philosophy. (shrink)

Einführung in die Philosophie Rudolf Carnaps.

We challenge an argument that aims to support Aesthetic Realism by claiming, first, that common sense is realist about aesthetic judgments because it considers that aesthetic judgments can be right or wrong, and, second, that becauseAesthetic Realism comes from and accounts for “folk aesthetics,” it is the best aesthetic theory available.We empirically evaluate this argument by probing whether ordinary people with no training whatsoever in the subtle debates of aesthetic philosophy consider their aesthetic judgments as right or wrong. Having shown (...) that the results do not support the main premise of the argument, we discuss the consequences for Aesthetic Realism and address possible objections to our study. (shrink)

Studying the folk concept of intentional action, Knobe (2003a) discovered a puzzling asymmetry: most people consider some bad side effects as intentional while they consider some good side effects as unintentional. In this study, we extend these findings with new experiments. The first experiment shows that the very same effect can be found in ascriptions of intentionality in the case of means for action. The second and third experiments show that means are nevertheless generally judged more intentional than side effects, (...) and that people do take into account the structure of the action when ascribing intentionality. We then discuss a number of hypotheses that can account for these data, using reactions times from our first experiment. (shrink)

In the philosophy of the analytical tradition, set theory and formal logic are familiar formal tools. I think there is no deep reason why the philosopher’s tool kit should be restricted to just these theories. It might well be the case—to generalize a dictum of Suppes concerning philosophy of science—that the appropriate formal device for doing philosophy is mathematics in general; it may be set theory, algebra, topology, or any other realm of mathematics. In this paper I want to employ (...) elementary topological considerations to shed new light on the intricate problem of the relation of qualities and similarity. Thereby I want to make plausible the general thesis that topology might be a useful device for matters epistemological. (shrink)

The debate over whether free will and determinism are compatible is controversial, and produces wide scholarly discussion. This paper argues that recent studies in experimental philosophy suggest that people are in fact “natural compatibilists”. To support this claim, it surveys the experimental literature bearing directly or indirectly upon this issue, before pointing to three possible limitations of this claim. However, notwithstanding these limitations, the investigation concludes that the existing empirical evidence seems to support the view that most people have compatibilist (...) intuitions. (shrink)

Do laypeople think that moral responsibility is compatible with determinism? Recently, philosophers and psychologists trying to answer this question have found contradictory results: while some experiments reveal people to have compatibilist intuitions, others suggest that people could in fact be incompatibilist. To account for this contradictory answers, Nichols and Knobe (2007) have advanced a ‘performance error model’ according to which people are genuine incompatibilist that are sometimes biased to give compatibilist answers by emotional reactions. To test for this hypothesis, we (...) investigated intuitions about determinism and moral responsibility in patients suffering from behavioural frontotemporal dementia. Patients suffering from bvFTD have impoverished emotional reaction. Thus, the ‘performance error model’ should predict that bvFTD patients will give less compatibilist answers. However, we found that bvFTD patients give answers quite similar to subjects in control group and were mostly compatibilist. Thus, we conclude that the ‘performance error model’ should be abandoned in favour of other available model that best fit our data. (shrink)

‘Frankfurt-style cases’ (FSCs) are widely considered as having refuted the Principle of Alternate Possibilities (PAP) by presenting cases in which an agent is morally responsible even if he could not have done otherwise. However, Neil Levy (J Philos 105:223–239, 2008) has recently argued that FSCs fail because we are not entitled to suppose that the agent is morally responsible, given that the mere presence of a counterfactual intervener is enough to make an agent lose responsibility-grounding abilities. Here, I distinguish two (...) kinds of Frankfurt counter-arguments against the PAP: the direct and the indirect counter-arguments. I then argue that Levy’s argument, if valid, can shed doubt on the indirect argument but leaves the direct argument untouched. I conclude that FSCs can still do their job, even if we grant that the mere presence of a counterfactual intervener can modify an agent’s abilities. (shrink)

The aim of this paper is make a contribution to the ongoing search for an adequate concept of the a priori element in scientific knowledge. The point of departure is C.I. Lewis’s account of a pragmatic a priori put forward in his "Mind and the World Order" (1929). Recently, Hasok Chang in "Contingent Transcendental Arguments for Metaphysical Principles" (2008) reconsidered Lewis’s pragmatic a priori and proposed to conceive it as the basic ingredient of the dynamics of an embodied scientific reason. (...) The present paper intends to further elaborate Chang’s account by relating it with some conceptual tools from cognitive semantics and certain ideas that first emerged in the context of the category-theoretical foundations of mathematics. (shrink)

The question of ontological foundation has undergone a noteworthy revival in recent years: metaphysicians today quarrel about how exactly to understand the asymmetrical and hyperintensional relationship of grounding. One of the reasons for this revival is that the old quantificationalist meta-ontology inherited from Quine has been effectively criticised by leading philosophers favourable to a meta-ontology, the aim of which is to come to know “which facts/items ground (constitute the base of) which other facts/items”, thus to examine the relation of ontological (...) dependence between beings (e.g. chemical properties depend on physical properties, the economic situation on the behaviour of individuals etc.), i.e. to explore the hierarchical structure of reality. I shall not discuss here the relationship of grounding in itself, but make some historical-formal remarks on the properties of the ultimate ontological foundational item itself and its aporetic nature. To do so I explore various more or less exotic philosophical ecosystems in the following order: Heidegger (Seyn), Plato (ἕν), Wáng Bi (道, dào). On the way I shall propose a new interpretation both of certain hypotheses in the Parmenides and of the nature of the opposition between Wáng Bì and Guō Xiàng in regard to the logical grammar of the expression “nothing (無, wú)” (transl. J. Dudley). (shrink)

Manipulation arguments that start from the intuition that manipulated agents are neither free nor morally responsible then conclude to that free will and moral responsibility are incompatible with determinism. The Zygote argument is a special case of Manipulation argument in which the manipulation intervenes at the very conception of the agent. In this paper, I argue that the Zygote argument fails because (i) very few people share the basic intuitions the argument rests on, and (ii) even those who share this (...) intuition do so for reasons that are unrelated to determinism. Rather, I argue that intuitions about the Zygote argument (and Manipulation arguments in general) are driven by people's intuitions about the deep self, as shown by the fact that intuitions about manipulated agents depend on the moral value of the agent's behavior. (shrink)

Rule-following is a normative doing and therefore needs to be reconsidered in a metaethical framework. Rule-following will be discussed in the light of cognitivism and non-cognitivism. It will be shown that neither cognitivism nor non-cognitivism are sufficiently good accounts for conceptualizing rule-following, because they are held captive by a quasi-mechanistical picture of rule-following. This idea stems from Stanley Cavell´s and John McDowell´s approach to rule-following. McDowell appeals to the idea that we participate in “shared forms of life” and therefore are (...) able to follow rules correctly. I believe that his quietist view can be amplified by conceptualizing different modes of following a rule. We can also follow a rule e.g. ironically and still grasp the conceptual content of the rule adequately. (shrink)

Sripada has recently advanced a new account for asymmetries that have been uncovered in folk judgments of intentionality: the ?Deep Self model,? according to which an action is more likely to be judged as intentional if it matches the agent's central and stable attitudes and values (i.e., the agent's Deep Self). In this paper, we present new experiments that challenge this model in two ways: first, we show that the Deep Self model makes predictions that are falsified, then we present (...) cases that it cannot account for. Finally, we discuss how the Deep Self model could be modified to accommodate these new data. (shrink)

The aim of this paper is to provide some acquaintance with the exegetical history of ἐξαίφνης inside the Platonic Tradition, from Plato to Marsilio Ficino, by way of Middle Platonism and Greek Neoplatonism. (Since this is only a draft, several modifications should be made later, notably in order to improve the English.) Some part has been presented in Los Angeles: “Damascius’ Theodicy: Psychic Input of Disorder and Evil into the World”, 16th Annual ISNS (International Society for Neoplatonic Studies) Conference, Loyola (...) Marymount University, 14th June 2018. (shrink)

In this paper it is shown that Heyting and Co-Heyting mereological systems provide a convenient conceptual framework for spatial reasoning, in which spatial concepts such as connectedness, interior parts, (exterior) contact, and boundary can be defined in a natural and intuitively appealing way. This fact refutes the wide-spread contention that mereology cannot deal with the more advanced aspects of spatial reasoning and therefore has to be enhanced by further non-mereological concepts to overcome its congenital limitations. The allegedly unmereological concept of (...) boundary is treated in detail and shown to be essentially affected by mereological considerations. More precisely, the concept of boundary turns out to be realizable in a variety of different mereologically grounded versions. In particular, every part K of a Heyting algebra H gives rise to a well-behaved K-relative boundary operator. (shrink)

This paper intends to further the understanding of the formal properties of (higher-order) vagueness by connecting theories of (higher-order) vagueness with more recent work in topology. First, we provide a “translation” of Bobzien's account of columnar higher-order vagueness into the logic of topological spaces. Since columnar vagueness is an essential ingredient of her solution to the Sorites paradox, a central problem of any theory of vagueness comes into contact with the modern mathematical theory of topology. Second, Rumfitt’s recent topological reconstruction (...) of Sainsbury’s theory of prototypically defined concepts is shown to lead to the same class of spaces that characterize Bobzien’s account of columnar vagueness, namely, weakly scattered spaces. Rumfitt calls these spaces polar spaces. They turn out to be closely related to Gärdenfors’ conceptual spaces, which have come to play an ever more important role in cognitive science and related disciplines. Finally, Williamson’s “logic of clarity” is explicated in terms of a generalized topology (“locology”) that can be considered an alternative to standard topology. Arguably, locology has some conceptual advantages over topology with respect to the conceptualization of a boundary and a borderline. Moreover, in Williamson’s logic of clarity, vague concepts with respect to a notion of a locologically inspired notion of a “slim boundary” are (stably) columnar. Thus, Williamson’s logic of clarity also exhibits a certain affinity for columnar vagueness. In sum, a topological perspective is useful for a conceptual elucidation and unification of central aspects of a variety of contemporary accounts of vagueness. (shrink)

Metaphysicians who are aware of modern physics usually follow Putnam (1967) in arguing that Special Theory of Relativity is incompatible with the view that what exists is only what exists now or presently. Partisans of presentism (the motto ‘only present things exist’) had very difficult times since, and no presentist theory of time seems to have been able to satisfactorily counter the objection raised from Special Relativity. One of the strategies offered to the presentist consists in relativizing existence to inertial (...) frames. This unfashionable strategy has been accused of counterfeiting, since the meaning of the concept of existence would be incompatible with its relativization. Therefore, existence could only be relativistically invariant. In this paper, I shall examine whether such an accusation hits its target, and I will do this by examining whether the different criteria of existence that have been suggested by the Philosophical Tradition from Plato onwards imply that existence cannot be relativized. (shrink)

Are nonhuman non-linguistic animals self-conscious? And how is it possible to find out whether they are or not? This question raises two interrelated problems: the conceptual problem and the methodological problem. In order to approach an answer, it is first and foremost necessary to establish criteria for self-consciousness by considering the phenomenon and the abilities connected with it. Subsequently, one can survey the experimental paradigms. Do the experiments really show that the identified ability has to be used to successfully master (...) the given task? Is the presence of self-consciousness the best explanation for the empirical data? This paper proposes that the underlying ability for self-consciousness is the capacity to have mental states, where the subject is thought of as the subject of the mental state. Furthermore, two important current experimental paradigms will be evaluated for their usefulness to identify the presence of self-consciousness. The verdict will be negative. Neither ‘mirror self-recognition’ nor ‘uncertainty monitoring’ need to employ the aforementioned ability in order to be executed. (shrink)

De se beliefs typically pose a problem for propositional theories of content. The Property Theory of content tries to overcome the problem of de se beliefs by taking properties to be the objects of our beliefs. I argue that the concept of self-ascription plays a crucial role in the Property Theory while being virtually unexplained. I then offer different possibilities of illuminating that concept and argue that the most common ones are either circular, question-begging, or epistemically problematic. Finally, I argue (...) that only a primitive understanding of self-ascription is viable. Self-ascription is the relation that subjects stand in with respect to the properties that they believe themselves to have. As such, self-ascription has to be primitive if it is supposed to do justice to the characteristic features of de se beliefs. (shrink)

Tullmann et Buckwalter (2014) ont récemment soutenu que le paradoxe de la fiction tenait plus de l’illusion que de la réalité. D’après eux, les théories contemporaines des émotions ne fourniraient aucune raison d’adopter une interprétation du terme « existence » qui rende les prémisses du paradoxe incompatibles entre elles. Notre discussion a pour but de contester cette manière de dissoudre le paradoxe de la fiction en montrant qu’il ne prend pas sa source dans les théories contemporaines des émotions. Bien plutôt, (...) son origine se situe dans ce que Radford (1975) décrit comme une incohérence dans nos réactions émotionnelles aux évènements fictionnels et non fictionnels. Malgré ce désaccord, nous concédons à Tullmann et Buckwalter qu’une solution satisfaisante au paradoxe de la fiction doit s’appuyer sur les théories des émotions. Ainsi, en guise de conclusion, nous expliquons comment il convient de comprendre l’incohérence en question et comment les théories des émotions pourraient contribuer à la résolution du paradoxe de la fiction. (shrink)

The first aim of this paper is to prove a topological completeness theorem for a weak version of Stalnaker’s logic KB of knowledge and belief. The weak version of KB is characterized by the assumption that the axioms and rules of KB have to be satisfied with the exception of the axiom (NI) of negative introspection. The proof of a topological completeness theorem for weak KB is based on the fact that nuclei (as defined in the framework of point-free topology) (...) give rise to a profusion of topological belief operators that are compatible with the familiar topological knowledge operator. Thereby a canonical topological model for weak KB can be constructed. For this canonical model a truth lemma for the K and B holds such that a completeness theorem for KB can be proved in the familiar way. The second aim of this paper is to show that the topological interpretation of knowledge K comes along with a complete Heyting algebra of belief operators B that all fit the knowledge operator K in the sense that the pairs (K, B) satisfy all axioms of weak KB. This amounts to a pluralistic relation between knowledge and belief: Knowledge does not fully determine belief, rather it designs a conceptual space for belief operators where different (competing) belief operators coexist. (shrink)

We use psychological concepts (e.g., intention and desire) when we ascribe psychological states to others for purposes of describing, explaining, and predicting their actions. Does the evidence reported by Knobe show, as he thinks, that moral evaluation shapes our mastery of psychological concepts? We argue that the evidence so far shows instead that moral evaluation shapes the way we report, not the way we think about, others' psychological states.

The first aim of this paper is to elucidate Russell’s construction of spatial points, which is to be <br>considered as a paradigmatic case of the "logical constructions" that played a central role in his epistemology and theory of science. Comparing it with parallel endeavours carried out by Carnap and Stone it is argued that Russell’s construction is best understood as a structural representation. It is shown that Russell’s and Carnap’s representational constructions may be considered as incomplete and sketchy harbingers of (...) Stone’s representation theorems. The representational program inaugurated by Stone’s theorems was one of the success stories of 20th century’s mathematics. This suggests that representational constructions à la Stone could also be important for epistemology and philosophy of science. More specifically it is argued that the issues proposed by Russellian definite descriptions, logical constructions, and structural representations still have a place on the agenda of contemporary epistemology and philosophy of science. Finally, the representational interpretation of Russell’s logical constructivism is used to shed some new light on the recently vigorously discussed topic of his structural realism. (shrink)

Abstract. The aim of this paper is to present a topological method for constructing discretizations (tessellations) of conceptual spaces. The method works for a class of topological spaces that the Russian mathematician Pavel Alexandroff defined more than 80 years ago. Alexandroff spaces, as they are called today, have many interesting properties that distinguish them from other topological spaces. In particular, they exhibit a 1-1 correspondence between their specialization orders and their topological structures. Recently, a special type of Alexandroff spaces was (...) used by Ian Rumfitt to elucidate the logic of vague concepts in a new way. According to his approach, conceptual spaces such as the color spectrum give rise to classical systems of concepts that have the structure of atomic Boolean algebras. More precisely, concepts are represented as regular open regions of an underlying conceptual space endowed with a topological structure. Something is subsumed under a concept iff it is represented by an element of the conceptual space that is maximally close to the prototypical element p that defines that concept. This topological representation of concepts comes along with a representation of the familiar logical connectives of Aristotelian syllogistics in terms of natural settheoretical operations that characterize regular open interpretations of classical Boolean propositional logic. In the last 20 years, conceptual spaces have become a popular tool of dealing with a variety of problems in the fields of cognitive psychology, artificial intelligence, linguistics and philosophy, mainly due to the work of Peter Gärdenfors and his collaborators. By using prototypes and metrics of similarity spaces, one obtains geometrical discretizations of conceptual spaces by so-called Voronoi tessellations. These tessellations are extensionally equivalent to topological tessellations that can be constructed for Alexandroff spaces. Thereby, Rumfitt’s and Gärdenfors’s constructions turn out to be special cases of an approach that works for a more general class of spaces, namely, for weakly scattered Alexandroff spaces. This class of spaces provides a convenient framework for conceptual spaces as used in epistemology and related disciplines in general. Alexandroff spaces are useful for elucidating problems related to the logic of vague concepts, in particular they offer a solution of the Sorites paradox (Rumfitt). Further, they provide a semantics for the logic of clearness (Bobzien) that overcomes certain problems of the concept of higher2 order vagueness. Moreover, these spaces help find a natural place for classical syllogistics in the framework of conceptual spaces. The crucial role of order theory for Alexandroff spaces can be used to refine the all-or-nothing distinction between prototypical and nonprototypical stimuli in favor of a more fine-grained gradual distinction between more-orless prototypical elements of conceptual spaces. The greater conceptual flexibility of the topological approach helps avoid some inherent inadequacies of the geometrical approach, for instance, the so-called “thickness problem” (Douven et al.) and problems of selecting a unique metric for similarity spaces. Finally, it is shown that only the Alexandroff account can deal with an issue that is gaining more and more importance for the theory of conceptual spaces, namely, the role that digital conceptual spaces play in the area of artificial intelligence, computer science and related disciplines. Keywords: Conceptual Spaces, Polar Spaces, Alexandroff Spaces, Prototypes, Topological Tessellations, Voronoi Tessellations, Digital Topology. (shrink)