According to the orthodox account of meaning and translation in the literature, meaning is a property of expressions of a language, and translation is a matching of synonymous expressions across languages. This linguistic account of translation gives rise to well-known skeptical conclusions about translation, objectivity, meaning and truth, but it does not conform to our best translational practices. In contrast, I argue for a textual account of meaning based on the concept of a TEXT-TYPE that does conform to our best (...) translational practices. With their semantic function in view, text-types are Archimedean points for their respective disciplines. The text-type of philosophy is no exception. Culture-transcendent conceptual analysis can proceed on firm footing without having to deny the reality of radical cultural and linguistic difference by treating components of text-types as the concepts to be analyzed. Analyses of central philosophical concepts are provided as a means of adjudicating philosophical controversy. (shrink)

Archimedes of Syracuse has long provided a touchstone for considering how we make and acquire knowledge. Since the early Roman chroniclers of Archimedes’ life, and especially intensively since Descartes, scholars have described, sought, or derided the Archimedean point, defining and redefining its epistemic role. “Knowledge,” at least within modernity, is rhetorically tied to the figure of the Archimedean point, a place somewhere outside a regular and constrained world of experience. If this figure still leads to useful ways of (...) thinking about knowing, we are left with the question of how different modes of making knowledge approach their “Archimedean” points. The question is especially important today as a renewed .. (shrink)

What effect has finding the Archimedean point in ourselves had on how we look at ethics? The modern era of philosophy began with Descartes finding within himself an unshakable point from which to pursue knowledge of the world and himself. This intellectual alienation from the world into the universal mathematical structures of the human mind has led to a reversal where, henceforth, production, rather than contemplation, of knowledge became epistemologically superior. Guided by Hannah Arendt’s discussion of the Archimedean (...) point and Earth alienation in the Human Condition, I will argue that this scientific form of thinking made its way into ethical investigation in the age of modern philosophy. Furthermore, I will provide an analysis of Kant’s categorical imperative and John Stuart Mill’s utilitarianism to show that despite modern science’s success in elucidating universal laws of nature, a scientific approach to ethics has not universalized our judgments of good and evil. (shrink)

In 1980 F. Wattenberg constructed the Dedekind completion

d of the Robinson non-archimedean field

and established basic algebraic properties of

d [6]. In 1985 H. Gonshor established further fundamental properties of

d [7].In [4] important construction of summation of countable sequence of Wattenberg numbers was proposed and corresponding basic properties of such summation were considered. In this paper the important applications of the Dedekind completion

d in transcendental number theory were considered. We dealing using set theory ZFC
(
-model of (...) ZFC).Given an class of analytic functions of one complex variable f  

z, we investigate the arithmetic nature of the values of fz at transcendental points en, n  .Main results are: (i) the both numbers e
 and e   are irrational, (ii) number ee is transcendental. Nontrivial generalization of the Lindemann- Weierstrass theorem is obtained. (shrink)

We study the representation of sets of desirable gambles by sets of probability mass functions. Sets of desirable gambles are a very general uncertainty model, that may be non-Archimedean, and therefore not representable by a set of probability mass functions. Recently, Cozman (2018) has shown that imposing the additional requirement of even convexity on sets of desirable gambles guarantees that they are representable by a set of probability mass functions. Already more that 20 years earlier, Seidenfeld et al. (1995) (...) gave an axiomatisation of binary preferences—on horse lotteries, rather than on gambles—that also leads to a unique representation in terms of sets of probability mass functions. To reach this goal, they use two devices, which we will call ‘SSK–Archimedeanity’ and ‘SSK–extension’. In this paper, we will make the arguments of Seidenfeld et al. (1995) explicit in the language of gambles, and show how their ideas imply even convexity and allow for conservative reasoning with evenly convex sets of desirable gambles, by deriving an equivalence between the SSK–Archimedean natural extension, the SSK–extension, and the evenly convex natural extension. (shrink)

Matti Eklund (2017) has argued that ardent realists face a serious dilemma. Ardent realists believe that there is a mind-independent fact as to which normative concepts we are to use. Eklund claims that the ardent realist cannot explain why this is so without plumping in favor of their own normative concepts or changing the topic. The paper first advances the discussion by clarifying two ways of understanding the question of which normative concepts to choose: a theoretical question about which concepts (...) have the abstract property of being normatively privileged and a further practical question of which concepts we are to choose even granting some concepts are thus privileged. I argue that the ardent realist’s best bet for answering the theoretical question while avoiding Eklund’s dilemma is to provide a real definition of this property. I point out the difficulties for providing such a definition. I then argue that even with an answer to the theoretical question, the ardent realist faces a further dilemma in answering the practical question. In sum, though I see no knock-down argument against ardent realism, it may nonetheless die a death by a thousand cuts. I close by considering a deeper reason for why ardent realism is so difficult to defend: every argument starts somewhere. It is unclear how there can be an Archimedean point that makes no reference to any normative concepts that can nonetheless be employed to convince everyone to adopt ours. I then briefly propose two options for someone still inclined towards realism: (i) accept that our normative concepts are normatively privileged without attempting to explain why this is so, or (ii) be less ardent and accept a perspective-dependent account of normativity. (shrink)

The nature of state governance in consolidated liberal democracies has important implications for the ideal theory debate. The states of these societies are polycentric. Decision-making power within them is disaggregated across multiple sites. This rules out one major justification for ideal theory. On this influential view, the ideal furnishes a blueprint of the morally perfect society that we should strive to realise. This justification is not viable in consolidated liberal democracies because their states lack an Archimedean point from which (...) the institutional structure as a whole can be designed to accord with the true ideal – whichever it might be. However, knowledge of the ideal can still aid agents in those societies to determine the worth of more modest political objectives other than the ideal itself. (shrink)

Information and communication technologies present new challenges for political theory and philosophy due to its large-scale and scope transformations. Their demands are reflected in institutional needs that cover a “cyber-political” space, i. e., a cluster of problems of the governance of the network of networks –Internet– that results in the formation of new institutions –e. g. ICANN. The question I try to answer here is: What characterizes cyberspace political discourses? The proposed hypothesis is that it is possible to interpret the (...) varied cyber-political positions from their relation with the actors that dispute cyberspace regulation. Taking this relationship as an Archimedean point, I distinguish between extreme positions –cyber-conservatism and cyber-libertarianism– and moderate positions –cyber-liberalism and cyber- socialism. Through the investigation of the works of the main proponents of each position (Goldsmith, Wu, Barlow, Assange, Lessig, Barbrook and Filby) I try to show the modifications in the traditional political positions after the incorporation of the prefix “cyber” and also, to highlight the benefits of the moderate positions over the extreme ones. (shrink)

I aim to show how the enigmatic phrase 'Unánime noche' in the famous first sentence of “The Circular Ruins” is inextricably linked to the story’s last words. Toward this purpose, I argue—against plausible foundational interpretations of the story—for a nonfoundational reading of the text and, moreover, that Borges’s use of ‘unánime’ (one soul) can be understood as one character or one form; namely, as an archetype of “Dreamanity” that leads to a vertiginous Third Man regress.

The philosophy of mathematics has been accused of paying insufficient attention to mathematical practice: one way to cope with the problem, the one we will follow in this paper on extensive magnitudes, is to combine the `history of ideas' and the `philosophy of models' in a logical and epistemological perspective. The history of ideas allows the reconstruction of the theory of extensive magnitudes as a theory of ordered algebraic structures; the philosophy of models allows an investigation into the way epistemology (...) might affect relevant mathematical notions. The article takes two historical examples as a starting point for the investigation of the role of numerical models in the construction of a system of non-Archimedean magnitudes. A brief exposition of the theories developed by Giuseppe Veronese and by Rodolfo Bettazzi at the end of the 19th century will throw new light on the role played by magnitudes and numbers in the development of the concept of a non-Archimedean order. Different ways of introducing non-Archimedean models will be compared and the influence of epistemological models will be evaluated. Particular attention will be devoted to the comparison between the models that oriented Veronese's and Bettazzi's works and the mathematical theories they developed, but also to the analysis of the way epistemological beliefs affected the concepts of continuity and measurement. (shrink)

This paper seeks to clarify and defend the proposition that moral realism is best elaborated as a moral doctrine. I begin by upholding Ronald Dworkin’s anti-Archimedean critique of the error theory against some strictures by Michael Smith, and I then briefly suggest how a proponent of moral realism as a moral doctrine would respond to Smith’s defense of the Archimedeanism of expressivism. Thereafter, this paper moves to its chief endeavor. By differentiating clearly between expressivism and quasi-realism, the paper highlights (...) both their distinctness and their compatibility. In so doing, it underscores the affinities between Blackburnian quasi-realism and moral realism as a moral doctrine. Finally, this paper contends—in line with my earlier work on these matters—that moral realism as a moral doctrine points to the need for some reorienting of meta-ethical enquiries rather than for the abandoning of them. (shrink)

Ronald Dworkin and Richard Rorty are sometimes thought to be diametrically opposed philosophers, particularly in their approach to foundational questions in moral thought. Dworkin is a champion of truth and objectivity in morality. Rorty, by contrast, is a great pragmatist who subscribed to a deflated vision of truth and unambiguously renounced objectivity, in favor of what he called “solidarity”. If their stated -isms and alliances were not evidence enough of discord, they also criticized one another in print, particularly on these (...) foundational, or metaethical, questions. The point of this chapter is to show that things are not what they seem: Rorty and Dworkin largely agree on metaethics. The difference between them is largely a difference in emphasis. (shrink)

After generalizing the Archimedean property of real numbers in such a way as to make it adaptable to non-numeric structures, we demonstrate that the real numbers cannot be used to accurately measure non-Archimedean structures. We argue that, since an agent with Artificial General Intelligence (AGI) should have no problem engaging in tasks that inherently involve non-Archimedean rewards, and since traditional reinforcement learning rewards are real numbers, therefore traditional reinforcement learning probably will not lead to AGI. We indicate (...) two possible ways traditional reinforcement learning could be altered to remove this roadblock. (shrink)

We prove a representation theorem for preference relations over countably infinite lotteries that satisfy a generalized form of the Independence axiom, without assuming Continuity. The representing space consists of lexicographically ordered transfinite sequences of bounded real numbers. This result is generalized to preference orders on abstract superconvex spaces.

Non-Archimedean population axiologies – also known as lexical views – claim (i) that a sufficient number of lives at a very high positive welfare level would be better than any number of lives at a very low positive welfare level and/or (ii) that a sufficient number of lives at a very low negative welfare level would be worse than any number of lives at a very high negative welfare level. Such axiologies are popular because they can avoid the (Negative) (...) Repugnant Conclusion and satisfy the adequacy conditions given in the central impossibility result in population axiology due to Gustaf Arrhenius. I provide a novel argument against them which appeals to the way that good and bad lives can intuitively outweigh one another. (shrink)

Metaethics is traditionally understood as a non-moral discipline that examines moral judgements from a standpoint outside of ethics. This orthodox understanding has recently come under pressure from anti-Archimedeans, such as Ronald Dworkin and Matthew Kramer, who proclaim that rather than assessing morality from an external perspective, metaethical theses are themselves substantive moral claims. In this paper, I scrutinise this anti-Archimedean challenge as applied to the metaethical position of expressivism. More precisely, I examine the claim that expressivists do not avoid (...) moral commitments when accounting for moral thought, but instead presuppose them; they do not look at ethics from the outside, but operate from within ethics. This paper defends the non-moral status of expressivism against anti-Archimedeanism by rejecting a new anti-Archimedean challenge which, on the basis of Hume’s Law, aims to exploit expressivist explanations of supervenience in order to show that expressivism is a substantive moral position. (shrink)

Functional analysis works with TVS (Topological Vector Spaces), classically over archimedean fields like
and .Canonical non-Archimedean functional analysis, where alternative but equally valid number systems such as p-adic numbers p etc. are fundamental, is a fast-growing discipline. This paper deals with TVS over non-classical non-Archimedean fields.

Lexical views in population axiology can avoid the Repugnant Conclusion without violating Transitivity or Separability. However, they imply a dilemma: either some good life is better than any number of slightly worse lives, or else the ‘at least as good as’ relation on populations is radically incomplete. In this paper, I argue that Archimedean views face an analogous dilemma. I thus conclude that the lexical dilemma gives us little reason to prefer Archimedean views. Even if we give up (...) on lexicality, problems of the same kind remain. (shrink)

We study whether it is possible to generalise Seidenfeld et al.’s representation result for coherent choice functions in terms of sets of probability/utility pairs when we let go of Archimedeanity. We show that the convexity property is necessary but not sufficient for a choice function to be an infimum of a class of lexicographic ones. For the special case of two-dimensional option spaces, we determine the necessary and sufficient conditions by weakening the Archimedean axiom.

Recent work in philosophy and cognitive science shows that knowledge is the norm of our social practice of assertion, in the sense that an assertion should express knowledge. But why should an assertion express knowledge? I hypothesize that an assertion should express knowledge because the point of assertion is to transmit knowledge. I present evidence supporting this hypothesis.

In the literature seeking to explain concepts in terms of their point, talk of ‘the point’ of concepts remains under-theorised. I propose a typology of points which distinguishes practical, evaluative, animating, and inferential points. This allows us to resolve tensions such as that between the ambition of explanations in terms of the points of concepts to be informative and the claim that mastering concepts requires grasping their point; and it allows us to exploit connections between types of (...) points to understand why they come apart, and whether they do so for problematic ideological reasons or for benignly functional reasons. (shrink)

Publication Zero Point shows the results of a four-years inquiry into the concept of 'measurability'. The book encompasses thirty-eight pictureworks and a philosophical thought experiment. It invites the reader to contemplate and compile their personal 'zero point' as a portrait of God. -/- Measurability appears to be a problematic concept. The boundaries between fixed and fluid; between sharp and vague; between coloured and non-coloured; between love and hate. When does one state of affairs turn into the other? When is something (...) still measurable? And: is it essential for something to be measurable at all? -/- A single drinking glass was the starting point for transformational processes of photographic images into multi-layered pictureworks. Pictorial spaces that are variable and subject to chance in an experimental, unconscious method of choice, chance, inspiration, and demolition. The results of split, remodel, and repeat invite you to explore and contemplate the notions of space and time as a dimension, in which meaning remains something definitely unfinished, but in which measurability is crucial. After all, when there is nothing to hold on to, you have to choose a point of departure from which you can reorganise your life. -/- There are several ways to leaf through the book and engage in its content. Each of the thirty-eight pictureworks is accompanied by a philosophical caption. These captions are part of a larger philosophical deliberation of three countenances which together make a portrait of God. Each caption can be read separately next to the picturework. Each picturework can be enjoyed next to a specific caption. Another way to work with the captions is to read them within their larger con text: unfold the last page of the book, reflect, and search for cross-references next to any particular picturework. (shrink)

I have two objectives in this article. The first is methodological: I elaborate a minimal phenomenological method and attempt to show its importance in studies of infant behavior. The second objective is substantive: Applying the minimal phenomenological approach, combined with Meltzoff’s “like-me” developmental framework, I propose the hypothesis that infants learn the pointing gesture at least in part through imitation. I explain how developments in sensorimotor ability (posture, arm and hand control and coordination, and locomotion) in the first year of (...) life prepare the infant for acquiring the pointing gesture. The former may directly enable the latter by allowing the infant to experience its own body as being “like those” of others, thus allowing it to imitatively appropriate a broader range of adult behavior. My proposal emphasizes the embodiment of mind in the development of cognition, contrary to latent dualistic tendencies in some developmental literature. (shrink)

I argue that knowing and having points of view are fundamentally different epistemic states if we assume that having justified true beliefs is necessary for knowledge. Knowers necessarily possess justified true beliefs, but persons holding points of view may, for example, lack justification, have false beliefs, or both. I examine these differences and expose other crucial differentiating patterns between the structure of knowledge and points of view that make the latter more likely to lead to disagreements. I (...) hypothesize that these patterns remain invariant in alternative views of knowledge like contextualism as long as we preserve the classical structure. Yet there is much research to be done on the multiple and contrasting properties that emerge if we consider non‐classical analyses of knowledge and points of view. (shrink)

The normative mechanics of promising seem complex. The strength and content of promissory obligations, and the residual duties they entail upon being violated, have various prima facie surprising features. We give an account to explain these features. Promises have a point. The point of a promise to φ is a promise-independent reason to φ for the promisee’s sake. A promise turns this reason into a duty. This explains the mechanics of promises. And it grounds a nuanced picture of immoral promises, (...) an argument against promissory bare wrongings, and a constraint on theories of why we have promissory obligations at all. (shrink)

I argue that it’s quite comprehensible to get upset about metaethical nihilism, to indulge what I call nihilistic despair. When we lose the objective moral or normative point of view, we lose the promise of luck-immune guidance and categorical importance, things many of us hope for. This is all quite Williams-friendly, but I reject his puzzling but suggestive remarks that nihilistic despair must be a self-pitying muddle. Finally, I argue that internalism about reasons is even more depressing than outright nihilism, (...) in one way at least. (shrink)

Cuneo and Shafer-Landau (2014) argued that there are moral conceptual truths that are substantive in content, what they called ‘moral fixed points’. I argue that insofar as we have some reason to postulate moral fixed points, we have equal reason to postulate epistemic fixed points (e.g. the factivity condition). To this effect, I show that the two basic reasons Cuneo and Shafer-Landau (2014) offer in support of moral fixed points naturally carry over to epistemic fixed (...) class='Hi'>points. In particular, epistemic fixed points exhibit the four ‘marks’ of conceptual truths that they identify and can be utilized to address important challenges to epistemic realism. I conclude that insofar as we have some reason to postulate moral fixed points, we have equal reason to postulate epistemic fixed points. -/- . (shrink)

I offer a novel two-stage reconstruction of Hume’s general-point-of-view account, modeled in part on his qualified-judges account in ‘Of the Standard of Taste.’ In particular, I argue that the general point of view needs to be jointly constructed by spectators who have sympathized with (at least some of) the agents in (at least some of) the actor’s circles of influence. The upshot of the account is two-fold. First, Hume’s later thought developed in such a way that it can rectify the (...) problems inherent in his Treatise account of the general point of view. Second, the proposed account provides the grounds for an adequate and well-motivated modest ideal observer theory of the standard of virtue. (shrink)

I examine what the point of self-ownership might best be thought to be.

An intuitive and widely accepted view is that (a) beliefs aim at truth, (b) many citizens have stable and meaningful political beliefs, and (c) citizens choose to support political candidates or parties on the basis of their political beliefs. We argue that all three claims are false. First, we argue that political beliefs often differ from ordinary world-modelling beliefs because they do not aim at truth. Second, we draw on empirical evidence from political science and psychology to argue that most (...) people lack stable and meaningful political beliefs. Third, we claim that the true psychological basis for voting behavior is not an individual’s political beliefs but rather group identity. Along the way, we reflect on what this means for normative democratic theory. (shrink)

The definition of a point in geometry is primordial in order to understand the different elements of this branch of mathematics ( line, surface, solids…). This paper aims at shedding fresh light on the concept to demonstrate that it is related to another one named, here, the Primary Geometric Object; both concepts concur to understand the multiplicity of geometries and to provide hints as concerns a new understanding of some concepts in physics such as time, energy, mass….

As Christian List (2021) has recently argued, the increasing arrival of powerful AI systems that operate autonomously in high-stakes contexts creates a need for “future-proofing” our regulatory frameworks, i.e., for reassessing them in the face of these developments. One core part of our regulatory frameworks that dominates our everyday moral interactions is blame. Therefore, “future-proofing” our extant regulatory frameworks in the face of the increasing arrival of powerful AI systems requires, among others things, that we ask whether it makes sense (...) to extend our blaming practices to these systems. In the paper, we argue for the admittedly surprising thesis that this question should be answered in the affirmative: contrary to what one might initially think, it can make a lot of sense to blame AI systems, since, as we furthermore argue, many of the important functions that are fulfilled by blaming humans can also be served by blaming AI systems. The paper concludes that this result gives us a good pro tanto reason to extend our blame practices to AI systems. (shrink)

This paper examines the conservative point of view about distributive justice. The first section explains the methodology used to develop this point of view. The second section describes one conservative point of view and briefly provides empirical evidence that it reflects the viewpoint of many ordinary conservatives. The third section explains how this conservative view can ground objections to social safety net programs, using as examples the recent health reform legislation and more extensive proposals for a true national health system. (...) The fourth section sketches ways that non-conservative philosophers might try to refute those objections. Examining a conservative point of view leads to several important conclusions. One is that the conservative point of view is not properly represented in contemporary philosophical discussions. Another is that the conservative point of view cannot be refuted by appealing to existing egalitarian writings. A third is that if progressive philosophers such as myself want to address the conservative point of view, we must expand the range of issues that we discuss in contemporary political philosophy. Doing so is a vital task, because otherwise we ignore the political views held by as much as half the American population. (shrink)

According to luck egalitarianism, it is unjust if some are worse off than others through no fault or choice of their own. The most common criticism of luck egalitarianism is the ‘harshness objection’, which states that luck egalitarianism allows for too harsh consequences, as it fails to provide justification for why those responsible for their bad fate can be entitled to society's assistance. It has largely gone unnoticed that the harshness objection is open to a number of very different interpretations. (...) We present four different interpretations of the harshness objection in which the problem pertains to counterintuitive implications, badness of outcome, disproportionality, or inconsistency, respectively. We analyse and discuss appropriate luck egalitarian replies. Disentangling these different versions clarifies what is at the heart of this dispute and reveals the point of the harshness objection. We conclude that only the inconsistency version involves a durable problem for luck egalitarianism. (shrink)

We show that any coherent complete partial order is obtainable as the fixed-point poset of the strong Kleene jump of a suitably chosen first-order ground model. This is a strengthening of Visser’s result that any finite ccpo is obtainable in this way. The same is true for the van Fraassen supervaluation jump, but not for the weak Kleene jump.

Why is it useful to talk and think about knowledge-how? Using Edward Craig’s discussion of the function of the concepts of knowledge and knowledge-how as a jumping off point, this paper argues that considering this question can offer us new angles on the debate about knowledge-how. We consider two candidate functions for the concept of knowledge-how: pooling capacities, and mutual reliance. Craig makes the case for pooling capacities, which connects knowledge-how to our need to pool practical capacities. I argue that (...) the evidence is much more equivocal. My suggested diagnosis is that the concept of knowledge-how plays both functions, meaning that the concept of knowledge-how is inconsistent, and that the debate about knowledge-how is at least partly a metalinguistic negotiation. In closing, I suggest a way to revise the philosophical concept of knowledge how. (shrink)

This essay provides a novel account of iterated epistemic states. The essay argues that states of epistemic determinacy might be secured by countenancing iterated epistemic states on the model of fixed points in the modal $\mu$-calculus. Despite the epistemic indeterminacy witnessed by the invalidation of modal axiom 4 in the sorites paradox -- i.e. the KK principle: $\square$$\phi$ $\rightarrow$ $\square$$\square$$\phi$ -- a hyperintensional epistemic $\mu$-automaton permits fixed points to entrain a principled means by which to iterate epistemic states (...) and account thereby for necessary conditions on self-knowledge. The hyperintensional epistemic $\mu$-calculus is applied to the iteration of the epistemic states of a single agent instead of the common knowledge of a group of agents, and is thus a novel contribution to the literature. (shrink)

Numerous evolutionary linguists have indicated that human pointing behaviour might be associated with the evolution of language. At an ontogenetic level, and in normal individuals, pointing develops spontaneously and the onset of human pointing precedes as well as facilitates phases in speech and language development. Phylogenetically, pointing behaviour might have preceded and facilitated the evolutionary origin of both gestural and vocal language. Contrary to wild non-human primates, captive and human-reared nonhuman primates also demonstrate pointing behaviour. In this article, we analyse (...) the debates on pointing and its role it might have played in language evolution from a meta-level. From within an Applied Evolutionary Epistemological approach, we examine how exactly we can determine whether pointing has been a unit, a level or a mechanism in language evolution. (shrink)

Political theorists study the attributes of desirable social-moral states of affairs. Schaefer (forthcoming) aims to show that "static political theory" of this kind rests on shaky foundations. His argument revolves around an application of an abstruse mathematical theorem -- Kakutani's fixed point theorem -- to the social-moral domain. We show that Schaefer has misunderstood the implications of this theorem for political theory. Theorists who wish to study the attributes of social-moral states of affairs should carry on, safe in the knowledge (...) that Kakutani's theorem poses no threat to this enterprise. (shrink)

The goal of this paper consists of developing a new (more physical and numerical in comparison with standard and non-standard analysis approaches) point of view on Calculus with functions assuming infinite and infinitesimal values. It uses recently introduced infinite and infinitesimal numbers being in accordance with the principle ‘The part is less than the whole’ observed in the physical world around us. These numbers have a strong practical advantage with respect to traditional approaches: they are representable at a new kind (...) of a computer – the Infinity Computer – able to work numerically with all of them. An introduction to the theory of physical and mathematical continuity and differentiation (including subdifferentials) for functions assuming finite, infinite, and infinitesimal values over finite, infinite, and infinitesimal domains is developed in the paper. This theory allows one to work with derivatives that can assume not only finite but infinite and infinitesimal values, as well. It is emphasized that the newly introduced notion of the physical continuity allows one to see the same mathematical object as a continuous or a discrete one, in dependence on the wish of the researcher, i.e., as it happens in the physical world where the same object can be viewed as a continuous or a discrete in dependence on the instrument of the observation used by the researcher. Connections between pure mathematical concepts and their computational realizations are continuously emphasized through the text. Numerous examples are given. (shrink)

Following a previous article (cf. Costa-Leite, A. (2018). Oppositions in a line segment, South American Journal of Logic, 4(1), pp.185-193) in which logical oppositions are defined in a line segment, this article goes one step further and proposes a method defining them using a zero-dimensional object: a point.

This paper investigates the prospects for a semantic theory that treats disjunction as a modal operator. Potential motivation for such a theory comes from the way in which modals embed within disjunctions. After reviewing some of the relevant data, I go on to distinguish a variety of modal theories of disjunction. I analyze these theories by considering pairs of conflicting desiderata, highlighting some of the tradeoffs they must face.

I defend a novel pragmatist account of truth that I call ‘truth from the agent point of view’ or ‘agential truth’, drawing on insights from Hilary Putnam. According to the agential view, as inquirers, when we take something to be truth-apt, we are taking ourselves and all other thinkers to be accountable to getting right a shared target that is independent of any individual's or community's view of that target. That we have this relationship to truth is what enables our (...) practices of disagreement and agreement, even when subject to the glare of self-conscious reflection, and represents a crucial ingredient in our capacity for rational thought. The resulting account shares elements with Huw Price's and Cheryl Misak's views, but also has important advantages over both. It also yields a surprising conclusion—that our best pragmatist account of truth may well be a version of the correspondence theory of truth. (shrink)

The semantic paradoxes are associated with self-reference or referential circularity. However, there are infinitary versions of the paradoxes, such as Yablo's paradox, that do not involve this form of circularity. It remains an open question what relations of reference between collections of sentences afford the structure necessary for paradoxicality -- these are the so-called "dangerous" directed graphs. Building on Rabern, et. al (2013) we reformulate this problem in terms of fixed points of certain functions, thereby boiling it down to (...) get a purely mathematical problem. (shrink)

I show that the Lottery Paradox is just a version of the Sorites, and argue that this should modify our way of looking at the Paradox itself. In particular, I focus on what I call “the Cut-off Point Problem” and contend that this problem, well known by Sorites scholars, ought to play a key role in the debate on Kyburg’s puzzle. Very briefly, I show that, in the Lottery Paradox, the premises “ticket n°1 will lose”, “ticket n°2 will lose”… “ticket (...) n°1000 will lose” are equivalent to soritical premises of the form “~(the winning ticket is in {…, (tn)}) ⊃ ~(the winning ticket is in {…, tn, (tn + 1)})” (where “⊃” is the material conditional, “~” is the negation symbol, “tn” and “tn + 1” are “ticket n°n” and “ticket n°n + 1” respectively, and “{}” identify the elements of the lottery tickets’ set. The brackets in “(tn)” and “(tn + 1)” are meant to point out that in the antecedent of the conditional we do not always have a “tn” (and, as a result, a “tn + 1” in the consequent): consider the conditional “~(the winning ticket is in {}) ⊃ ~(the winning ticket is in {t1})”). As a result, failing to believe, for some ticket, that it will lose comes down to introducing a cut-off point in a chain of soritical premises. In this paper I explore the consequences of the different ways of blocking the Lottery Paradox with respect to the Cut-off Point Problem. A heap variant of the Lottery Paradox is especially relevant for evaluating the different solutions. One important result is that the most popular way out of the puzzle, i.e., denying the Lockean Thesis, becomes less attractive. Moreover, I show that, along with the debate on whether rational belief is closed under classical logic, the debate on the validity of modus ponens should play an important role in discussions on the Lottery Paradox. -/- . (shrink)

Novels like Fight Club or American Psycho are said to be instances of unreliable narration: the first person narrator presents an evidently distorted picture of the fictional world. The film adaptations of these novels are likewise said to involve unreliable narration. I resist this extension of the term ‘unreliable narration’ to film. My argument for this rests on the observation that unreliable narration requires a personal narrator while film typically involves an impersonal narrator. The kind of ambiguous story-telling that we (...) find in literary fiction with unreliable narrators, where for certain descriptions it is unclear whether what we’re told is an accurate account of what’s happening in the story world or not, can instead be achieved by conventionalized filmmaking techniques for reporting the contents of mental states, like the point of view shot, but especially the more ambiguous blended perspective shot. (shrink)