Some hold that the lesson of Russell’s paradox and its relatives is that mathematical reality does not form a ‘definite totality’ but rather is ‘indefinitely extensible’. There can always be more sets than there ever are. I argue that certain contact puzzles are analogous to Russell’s paradox this way: they similarly motivate a vision of physical reality as iteratively generated. In this picture, the divisions of the continuum into smaller parts are ‘potential’ rather than ‘actual’. Besides the intrinsic interest of (...) this metaphysical picture, it has important consequences for the debate over absolute generality. It is often thought that ‘indefinite extensibility’ arguments at best make trouble for mathematical platonists; but the contact arguments show that nominalists face the same kind of difficulty, if they recognize even the metaphysical possibility of the picture I sketch. (shrink)

The principle of sufficient reason threatens modal collapse. Some have suggested that by appealing to the indefinite extensibility of contingent truth, the threat is neutralized. This paper argues that this is not so. If the indefinite extensibility of contingent truth is developed in an analogous fashion to the most promising models of the indefinite extensibility of the concept set, plausible principles permit the derivation of modal collapse.

I argue that we can and should extend Tarski's model-theoretic criterion of logicality to cover indefinite expressions like Hilbert's ɛ operator, Russell's indefinite description operator η, and abstraction operators like 'the number of'. I draw on this extension to discuss the logical status of both abstraction operators and abstraction principles.

The Monist’s call for papers for this issue ended: “if formalism is true, then it must be possible in principle to mechanize meaning in a conscious thinking and language-using machine; if intentionalism is true, no such project is intelligible”. We use the Grelling-Nelson paradox to show that natural language is indefinitely extensible, which has two important consequences: it cannot be formalized and model theoretic semantics, standard for formal languages, is not suitable for it. We also point out that object-object mapping (...) theories of semantics, the usual account for the possibility of non intentional semantics, doesn’t seem able to account for the indefinitely extensible productivity of natural language. (shrink)

In this paper I argue against grounding being necessarily well-founded, and provide some reasons to think it's actually not well-founded.

The chapter considers two semantic issues concerning will-sentences: Stalnaker’s Asymmetry and modal subordination in Karttunen-type discourses. The former points to a distinction between will and modal verbs, seeming to show that will does not license non-specific indefinites. The latter, conversely, suggests that will-sentences involve some kind of modality. To account for the data, the chapter proposes that will is semantically a tense, hence it doesn’t contribute a quantifier over modal alternatives; a modal feature, however, is introduced in the interpretation (...) of a will-sentence through a supervaluational strategy universally quantifying over possible futures. That this is not part of will’s lexical semantics is shown to have consequences that ultimately contribute to explain Stalnaker’s Asymmetry. Furthermore, that a modal quantification is present in the interpretation of a will-sentence is shown to imply the availability of modal subordination in Karttunen-type discourses. (shrink)

Descartes' philosophy contains an intriguing notion of the infinite, a concept labeled by the philosopher as indefinite. Even though Descartes clearly defined this term on several occasions in the correspondence with his contemporaries, as well as in his Principles of Philosophy, numerous problems about its meaning have arisen over the years. Most commentators reject the view that the indefinite could mean a real thing and, instead, identify it with an Aristotelian potential infinite. In the first part of this article, I (...) show why there is no numerical infinity in Cartesian mathematics, as such a concept would be inconsistent with the main fundamental attribute of numbers: to be comparable with each other. In the second part, I analyze the indefinite in the context of Descartes' mathematical physics. It is my contention that, even with no trace of infinite in his mathematics, Descartes does refer to an actual indefinite because of its application to the material world within the system of his physics. This fact underlines a discrepancy between his mathematics and physics of the infinite, but does not lead a difficulty in his mathematical physics. Thus, in Descartes' physics, the indefinite refers to an actual dimension of the world rather than to an Aristotelian mathematical potential infinity. In fact, Descartes establishes the reality and limitlessness of the extension of the cosmos and, by extension, the actual nature of his indefinite world. This indefinite has a physical dimension, even if it is not measurable. La filosofía de Descartes contiene una noción intrigante de lo infinito, un concepto nombrado por el filósofo como indefinido. Aunque en varias ocasiones Descartes definió claramente este término en su correspondencia con sus contemporáneos y en sus Principios de filosofía, han surgido muchos problemas acerca de su significado a lo largo de los años. La mayoría de comentaristas rechaza la idea de que indefinido podría significar una cosa real y, en cambio, la identifica con un infinito potencial aristotélico. En la primera parte de este artículo muestro por qué no hay infinito numérico en las matemáticas cartesianas, en la medida en que tal concepto sería inconsistente con el principal atributo fundamental de los números: ser comparables entre sí. En la segunda parte analizo lo indefinido en el contexto de la física matemática de Descartes. Mi argumento es que, aunque no hay rastro de infinito en sus matemáticas, Descartes se refiere a un indefinido real a causa de sus aplicaciones al mundo material dentro del sistema de su física. Este hecho subraya una discrepancia entre sus matemáticas y su física de lo infinito, pero no implica ninguna dificultad en su física matemática. Así pues, en la física de Descartes, lo indefinido se refiere a una dimensión real del mundo más que a una infinitud potencial matemática aristotélica. De hecho, Descartes establece la realidad e infinitud de la extensión del cosmos y, por extensión, la naturaleza real de su mundo indefinido. Esta indefinición tiene una dimensión física aunque no sea medible. (shrink)

Classical physics and quantum physics suggest two meta-physical types of reality: the classical notion of a objectively definite reality with properties "all the way down," and the quantum notion of an objectively indefinite type of reality. The problem of interpreting quantum mechanics (QM) is essentially the problem of making sense out of an objectively indefinite reality. These two types of reality can be respectively associated with the two mathematical concepts of subsets and quotient sets (or partitions) which are category-theoretically dual (...) to one another and which are developed in two mathematical logics, the usual Boolean logic of subsets and the more recent logic of partitions. Our sense-making strategy is "follow the math" by showing how the logic and mathematics of set partitions can be transported in a natural way to Hilbert spaces where it yields the mathematical machinery of QM--which shows that the mathematical framework of QM is a type of logical system over ℂ. And then we show how the machinery of QM can be transported the other way down to the set-like vector spaces over ℤ₂ showing how the classical logical finite probability calculus (in a "non-commutative" version) is a type of "quantum mechanics" over ℤ₂, i.e., over sets. In this way, we try to make sense out of objective indefiniteness and thus to interpret quantum mechanics. (shrink)

Contemporary discussions do not always clearly distinguish two different forms of vagueness. Sometimes focus is on the imprecision of predicates, and sometimes the indefiniteness of statements. The two are intimately related, of course. A predicate is imprecise if there are instances to which it neither definitely applies nor definitely does not apply, instances of which it is neither definitely true nor definitely false. However, indefinite statements will occur in everyday discourse only if speakers in fact apply imprecise predicates to such (...) indefinite instances. (What makes an instance indefinite is, it should be clear, predicate-relative.) The basic issue in the present inquiry is whether this indefiniteness ever really occurs; the basic question is, Why should it ever occur? (shrink)

According to Madhyamaka Buddhist philosophers, everything depends for its existence on something else. But what would a world devoid of fundamentalia look like? In this paper, I argue that the anti-foundationalist “neither-one-nor-many argument” of the Indian Mādhyamika Śrīgupta commits him to a position I call “metaphysical indefinitism.” I demonstrate how this view follows from Śrīgupta’s rejection of mereological simples and ontologically independent being, when understood in light of his account of conventional reality. Contra recent claims in the secondary literature, I (...) clarify how the Madhyamaka metaphysical dependence structure is not a straightforward infinitism since it does not honor strict asymmetry or transitivity. Instead, its dependence relations are irreflexive and extendable, admitting of dependence chains of indefinite (though not actually infinite) length and dependence loops of non-zero length. Yet, the flexible ontology of Śrīgupta's Madhyamaka can accommodate a contextualist account of asymmetry and support a revisable theory of conventional truth, delivering significant payoffs for the view, including the capacity to accommodate developments in scientific explanation. (shrink)

This essay endeavors to define the concept of indefinite extensibility in the setting of category theory. I argue that the generative property of indefinite extensibility for set-theoretic truths in category theory is identifiable with the Grothendieck Universe Axiom and the elementary embeddings in Vopenka's principle. The interaction between the interpretational and objective modalities of indefinite extensibility is defined via the epistemic interpretation of two-dimensional semantics. The semantics can be defined intensionally or hyperintensionally. By characterizing the modal profile of $\Omega$-logical validity, (...) and thus the generic invariance of mathematical truth, modal coalgebras are further capable of capturing the notion of definiteness for set-theoretic truths, in order to yield a non-circular definition of indefinite extensibility. (shrink)

It is argued that Gabriel Uzquiano's approach to set-theoretic indefinite extensibility is a version of in rebus structuralism, and therefore suffers from a vacuity problem.

In his Critique of Pure Reason, Kant famously includes immortality as one of the three “ideas” that give rise to “unavoidable problems of reason” (KrV, B7)1 and thereby constitute the basic subject-matter of metaphysics. Interpreters have paid a great deal of attention to the other two ideas, God and freedom; yet very few studies of Kantian immortality have ever been undertaken. This should come as no surprise, once we realize that Kant himself used the word “immortality” and its cognates only (...) 40 times in all three of his great Critiques. (By comparison, forms of the words “God” and “free(dom)” appear 119 and 509 times, respectively, in the three Critiques.) Kant’s theory of immortality – if he can be said to have one – is therefore exceedingly difficult to understand. For example, he says at one point (KrV, B395n): “Metaphysics has only three ideas as the proper purpose of its investigation: God, freedom, and immortality – and in such a way that the second concept, when combined with the first, is to lead to the third as a necessary conclusion.” How are we to understand this claim ? Does Kant really mean that combining the concept of freedom with the concept of God somehow gives rise to immortality as a necessary inference? In any case, why does Kant say so little about immortality, even though he portrays it as one of three ideas that constitute the “final aim” of all metaphysical speculation ? These and other puzzles raised by Kant’s occasional comments on immortality will be the focus of this paper. (shrink)

According to an influential idea in the philosophy of set theory, certain mathematical concepts, such as the notion of a well-order and set, are indefinitely extensible. Following Parsons (1983), this has often been cashed out in modal terms. This paper explores instead an extensional articulation of the idea, formulated in higher-order logic, that flat-footedly formalizes some remarks of Zermelo. The resulting picture is incompatible with the idea that the entire universe can be well-ordered, but entirely consistent with the idea that (...) the sets of any set-theoretic universe can be. (shrink)

I explain in what sense the structure of space and time is probably vague or indefinite, a notion I define. This leads to the mathematical representation of location in space and time by a vague interval. From this, a principle of complementary inaccuracy between spatial location and velocity is derived, and its relation to the Uncertainty Principle discussed. In addition, even if the laws of nature are deterministic, the behaviour of systems will be random to some degree. These and other (...) considerations draw classical physics closer to Quantum Mechanics. An arrow of entropy is also derived, given an arrow of time. Lastly, chaos is given an additional, objective meaning. (shrink)

The purpose of this paper is to show that the mathematics of quantum mechanics is the mathematics of set partitions linearized to vector spaces, particularly in Hilbert spaces. That is, the math of QM is the Hilbert space version of the math to describe objective indefiniteness that at the set level is the math of partitions. The key analytical concepts are definiteness versus indefiniteness, distinctions versus indistinctions, and distinguishability versus indistinguishability. The key machinery to go from indefinite to more definite (...) states is the partition join operation at the set level that prefigures at the quantum level projective measurement as well as the formation of maximally-definite state descriptions by Dirac’s Complete Sets of Commuting Operators. This development is measured quantitatively by logical entropy at the set level and by quantum logical entropy at the quantum level. This follow-the-math approach supports the Literal Interpretation of QM—as advocated by Abner Shimony among others which sees a reality of objective indefiniteness that is quite different from the common sense and classical view of reality as being “definite all the way down”. (shrink)

We argue that definite noun phrases give rise to uniqueness inferences characterized by a pattern we call definiteness projection. Definiteness projection says that the uniqueness inference of a definite projects out unless there is an indefinite antecedent in a position that filters presuppositions. We argue that definiteness projection poses a serious puzzle for e-type theories of (in)definites; on such theories, indefinites should filter existence presuppositions but not uniqueness presuppositions. We argue that definiteness projection also poses challenges for dynamic approaches, (...) which have trouble generating uniqueness inferences and predicting some filtering behavior, though unlike the challenge for e-type theories, these challenges have mostly been noted in the literature, albeit in a piecemeal way. Our central aim, however, is not to argue for or against a particular view, but rather to formulate and motivate a generalization about definiteness which any adequate theory must account for. (shrink)

The new logic of partitions is dual to the usual Boolean logic of subsets (usually presented only in the special case of the logic of propositions) in the sense that partitions and subsets are category-theoretic duals. The new information measure of logical entropy is the normalized quantitative version of partitions. The new approach to interpreting quantum mechanics (QM) is showing that the mathematics (not the physics) of QM is the linearized Hilbert space version of the mathematics of partitions. Or, putting (...) it the other way around, the math of partitions is a skeletal version of the math of QM. The key concepts throughout this progression from logic, to logical information, to quantum theory are distinctions versus indistinctions, definiteness versus indefiniteness, or distinguishability versus indistinguishability. The distinctions of a partition are the ordered pairs of elements from the underlying set that are in different blocks of the partition and logical entropy is defined (initially) as the normalized number of distinctions. The cognate notions of definiteness and distinguishability run throughout the math of QM, e.g., in the key non-classical notion of superposition (= ontic indefiniteness) and in the Feynman rules for adding amplitudes (indistinguishable alternatives) versus adding probabilities (distinguishable alternatives). (shrink)

There is a fundamental subsets–partitions duality that runs through the exact sciences. In more concrete terms, it is the duality between elements of a subset and the distinctions of a partition. In more abstract terms, it is the reverse-the-arrows of category theory that provides a major architectonic of mathematics. The paper first develops the duality between the Boolean logic of subsets and the logic of partitions. Then, probability theory and information theory (as based on logical entropy) are shown to start (...) with the quantitative versions of subsets and partitions. Some basic universal mapping properties in the category of Sets are developed that precede the abstract duality of category theory. But by far the main application is to the clarification and interpretation of quantum mechanics. Since classical mechanics illustrates the Boolean worldview of full distinctness, it is natural that quantum mechanics would be based on the indefiniteness of its characteristic superposition states, which is modeled at the set level by partitions (or equivalence relations). This approach to interpreting quantum mechanics is not a jury-rigged or ad hoc attempt at the interpretation of quantum mechanics but is a natural application of the fundamental duality running throughout the exact sciences. (shrink)

In this essay, we consider the formal and ontological implications of one specific and intensely contested dialectical context from which Deleuze’s thinking about structural ideal genesis visibly arises. This is the formal/ontological dualism between the principles, ἀρχαί, of the One (ἕν) and the Indefinite/Unlimited Dyad (ἀόριστος δυάς), which is arguably the culminating achievement of the later Plato’s development of a mathematical dialectic.3 Following commentators including Lautman, Oskar Becker, and Kenneth M. Sayre, we argue that the duality of the One and (...) the Indefinite Dyad provides, in the later Plato, a unitary theoretical formalism accounting, by means of an iterated mixing without synthesis, for the structural origin and genesis of both supersensible Ideas and the sensible particulars which participate in them. As these commentators also argue, this duality furthermore provides a maximally general answer to the problem of temporal becoming that runs through Plato’s corpus: that of the relationship of the flux of sensory experiences to the fixity and order of what is thinkable in itself. Additionally, it provides a basis for understanding some of the famously puzzling claims about forms, numbers, and the principled genesis of both attributed to Plato by Aristotle in the Metaphysics, and plausibly underlies the late Plato’s deep considerations of the structural paradoxes of temporal change and becoming in the Parmenides, the Sophist, and the Philebus. After extracting this structure of duality and developing some of its formal, ontological, and metalogical features, we consider some of its specific implications for a thinking of time and ideality that follows Deleuze in a formally unitary genetic understanding of structural difference. These implications of Plato’s duality include not only those of the constitution of specific theoretical domains and problematics, but also implicate the reflexive problematic of the ideal determinants of the form of a unitary theory as such. We argue that the consequences of the underlying duality on the level of content are ultimately such as to raise, on the level of form, the broader reflexive problem of the basis for its own formal or meta-theoretical employment. We conclude by arguing for the decisive and substantive presence of a proper “Platonism” of the Idea in Deleuze, and weighing the potential for a substantive recuperation of Plato’s duality in the context of a dialectical affirmation of what Deleuze recognizes as the “only” ontological proposition that has ever been uttered. This is the proposition of the univocity of Being, whereby “being is said in the same sense, everywhere and always,” but is said (both problematically and decisively) of difference itself. (shrink)

Beauvoir’s Ethics of Ambiguity appears to defend a distinctly existentialist, deontologically-constrained version of consequentialism. On that interpretation, her belief that freedom consists in the real possibilities provided by our concrete situation leads her to reject Kantian autonomy to allow for some consequentialist decisions, while her belief that our situation derives its meaning from freely-chosen projects leads her to limit such choices to their consequences for situated freedom rather than general happiness. However, I will argue that Beauvoir’s view is better understood (...) as a non-deontological, internal critique of consequentialism, rooted in Marx’s historical materialism rather than her existentialist commitments. Beauvoir challenges consequentialism’s tendency to evaluate decision-making over actions, and intended or predicted consequences over actual ones, considering consequences during a limited time-frame despite their variable, contingent future value. In other words, consequentialism is insufficiently consequentialist, a view rooted in historical materialism in two ways. First, her materialist understanding of freedom as situated possibility requires an ethics that prioritizes real rather than projected consequences. Materialist consequentialism acknowledges outcomes are never final and so refuses to assign unambiguous moral value. A decision’s ethical value is preserved only to the degree that the value of its real consequences for existing individuals’ projects is maintained into the indefinite future. Second, her view that value is historical, a human creation based in our actual situation’s contingent utility to our individually chosen projects, denies that any consequence has a fixed value independent of the historical development of humanity as realized through individual choices. Historical-materialist consequentialism demands moral agents retroactively reassess the moral status of every action in order to repair consequences that have, because of changing human purposes, become obstacles to freedom. Together, these historical materialist constraints ground Beauvoir’s demand for an ethics that is ambiguous in principle as well as practice: no decision, action, or consequence has a fixed moral value because consequences are always incomplete and, even when they do not change, the projects that give them value change. While compatible with existentialist conceptions of freedom, responsibility, and authenticity, her ethics does not require such commitments, making it more Marxist than existentialist in character. (shrink)

The meaning of definite descriptions (like ‘the King of France’, ‘the girl’, etc.) has been a central topic in philosophy and linguistics for the past century. Indefinites (‘Something is on the floor’, ‘A child sat down’, etc.) have been relatively neglected in philosophy, under the Russellian assumption that they can be unproblematically treated as existential quantifiers. However, an important tradition, drawing from Stoic logic, has pointed to patterns which suggest that indefinites cannot be treated simply as existential quantifiers. (...) The standard dynamic semantic treatment of those phenomena, however, has well-known problems with negation and disjunction. -/- In this paper I develop a new approach to (in)definites. On my theory, truth-conditions are classical. But in addition to truth-conditions, meanings comprise a second dimension of what I call bounds. It is at the level of bounds, not truth-conditions, that I locate the characteristically dynamic coordination between indefinites and definites. The resulting system thus has a classical logic. This approach avoids dynamic semantics’ logical problems, and, more generally, yields a new perspective on the relation between truth-conditional and dynamic effects in natural language. (shrink)

The question of whether Everettian quantum mechanics (EQM) justifies the existence of metaphysical indeterminacy has recently come to the fore. Metaphysical indeterminacy has been argued to emerge from three sources: coherent superpositions, the indefinite number of branches in the quantum multiverse and the nature of these branches. This paper reviews the evidence and concludes that those arguments don’t rely on EQM alone and rest on metaphysical auxiliary assumptions that transcend the physics of EQM. We show how EQM can be ontologically (...) interpreted without positing metaphysical indeterminacy by adopting a deflationary attitude towards branches. Two ways of developing the deflationary view are then proposed: one where branches are eliminated, and another where they are reduced to the universal quantum state. (shrink)

In this essay, I suggest that Spinoza acknowledges a distinction between formal reality that is infinite and timelessly eternal and formal reality that is non-infinite (i. e., finite or indefinite) and non-eternal (i. e., enduring). I also argue that if, in Spinoza’s system, only intelligible causation is genuine causation, then infinite, timelessly eternal formal reality cannot cause non-infinite, non-eternal formal reality. A denial of eternal-durational causation generates a puzzle, however: if no enduring thing – not even the sempiternal, indefinite individual (...) composed of all finite, enduring things – is caused by the infinite, eternal substance, then how can Spinoza consistently hold that the one infinite, eternal substance is the cause of all things and that all things are modes of that substance? At the end of this essay, I sketch how Spinoza could deny eternal-durational causation while still holding that an infinite, eternal God is the cause of all things and that all things are modes. I develop the interpretation more in the companion essay.1 1 In “Spinoza’s Monism II,” in the next issue of this journal. (shrink)

As automating technologies are increasingly integrated into workplaces, one concern is that many of the human workers who remain will be relegated to more dull and less positively impactful work. This paper considers two rival theories of meaningful work that might be used to evaluate particular implementations of automation. The first is achievementism, which says that work that culminates in achievements to workers’ credit is especially meaningful; the other is the practice view, which says that work that takes the form (...) of an open-ended practice is especially meaningful. Of the two, the practice view is the better tool for assessing the future of meaningful work, because achievementism is explanatorily inadequate in two ways. Moreover, the practice view can explain why the most meaningful forms of work cannot be automated. A procedure can only be automated as long as the steps are defined, whereas, in such work, which steps to take is indefinitely open to redefinition. This reveals the real threat to meaningful work to be a political-economic one. The relevant ethical questions there have to do with how much creative control workers retain in crafting their own jobs, when those jobs involve meaningful work in collaboration with machines; and how to liberate workers from jobs that do not involve meaningful work, which should be left to machines anyway. (shrink)

An old question in Spinoza scholarship is how finite, non-eternal things transitively caused by other finite, non-eternal things (i. e., the entities described in propositions like E1p28) are caused by the infinite, eternal substance, given that what follows either directly or indirectly from the divine nature is infinite and eternal (E1p21–23). In “Spinoza’s Monism I,” “Spinoza’s Monism I,” in the previous issue of this journal. I pointed out that most commentators answer this question by invoking entities that are indefinite and (...) sempiternal, but argued that perhaps we should not be so quick to assume that in Spinoza’s system, an infinite and eternal substance could cause such indefinite, sempiternal entities. But if such eternal-durational causation is denied, then it seems harder to see how Spinoza’s system could be coherent: if Spinoza holds that the infinite, eternal substance cannot cause anything that is not infinite and not eternal, then how can he also hold that all things are modes immanently caused by substance (E1p15, E1p18, E1p25)? In this essay, I explain how Spinoza’s system could be understood in light of a denial of eternal-durational causation. On the interpretation I offer, God is the cause of all things and all things are modes because the essences of all things follow from the divine nature and all essences enjoy infinite, eternal reality as modes immanently caused by the infinite, eternal substance. The same non-substantial essences can also be conceived as enjoying non-infinite, non-eternal reality, but so conceived, they are enduring, finite (or sempiternal, indefinite) entities that cannot be conceived as modes caused by and inhering in the one infinite, eternal substance. I conclude by pointing out that if we take this interpretive route, we do have to understand Spinoza as committed to acosmism, or a denial of the reality of the world – at least the world of enduring, finite things. (shrink)

The generality problem is widely considered to be a devastating objection to reliabilist theories of justification. My goal in this paper is to argue that a version of the generality problem applies to all plausible theories of justification. Assume that any plausible theory must allow for the possibility of reflective justification—S's belief, B, is justified on the basis of S's knowledge that she arrived at B as a result of a highly (but not perfectly) reliable way of reasoning, R. The (...) generality problem applies to all cases of reflective justification: Given that is the product of a process-token that is an instance of indefinitely many belief-forming process-types (or BFPTs), why is the reliability of R, rather than the reliability of one of the indefinitely many other BFPTs, relevant to B's justificatory status? This form of the generality problem is restricted because it applies only to cases of reflective justification. But unless it is solved, the generality problem haunts all plausible theories of justification, not just reliabilist ones. (shrink)

A number of philosophers of science and statisticians have attempted to justify conclusions drawn from a finite sequence of evidence by appealing to results about what happens if the length of that sequence tends to infinity. If their justifications are to be successful, they need to rely on the finite sequence being either indefinitely increasing or of a large size. These assumptions are often not met in practice. This paper analyzes a simple model of collecting evidence and finds that the (...) practice of collecting only very small sets of evidence before taking a question to be settled is rationally justified. This shows that the appeal to long run results can be used neither to explain the success of actual scientific practice nor to give a rational reconstruction of that practice. (shrink)

All reasoners described in the most widespread models of a rational reasoner exhibit logical omniscience, which is impossible for finite reasoners (real reasoners). The most common strategy for dealing with the problem of logical omniscience is to interpret the models using a notion of beliefs different from explicit beliefs. For example, the models could be interpreted as describing the beliefs that the reasoner would hold if the reasoner were able reason indefinitely (stable beliefs). Then the models would describe maximum rationality, (...) which a finite reasoner can only approach in the limit of a reasoning sequence. This strategy has important consequences for epistemology. If a finite reasoner can only approach maximum rationality in the limit of a reasoning sequence, then the efficiency of reasoning is epistemically (and not only pragmatically) relevant. In this paper, I present an argument to this conclusion and discuss its consequences, as, for example, the vindication of the principle 'no rationality through brute-force'. (shrink)

It would be unwise to dismiss the possibility of human brain organoids developing sentience. However, scepticism about this idea is appropriate when considering current organoids. It is a point of consensus that a brain-dead human is not sentient, and current organoids lack a functioning brainstem. There are nonetheless troubling early warning signs, suggesting organoid research may create forms of sentience in the near future. To err on the side of caution, researchers with very different views about the neural basis of (...) sentience should unite behind the “brainstem rule”: if a neural organoid develops or innervates a functioning brainstem that regulates arousal and leads to sleep-wake cycles, then it is a sentience candidate. If organoid research leads to the creation of sentience candidates, a moratorium or indefinite ban on the creation of the relevant type of organoid may be appropriate. A different way forward, more consistent with existing approaches to animal research, would be to require ethical review and harm-benefit analysis for all research on sentience candidates. (shrink)

Metaphysical underdetermination arises when we are not able to decide, through purely theoretical criteria, between competing interpretations of scientific theories with different metaphysical commitments. This is the case in which non-relativistic quantum mechanics (QM) finds itself in. Among several available interpretations, there is the one that states that the interaction with the conscious mind of a human observer causes a change in the dynamics of quantum objects undergoing from indefinite to definite states. In this paper, we argue that there seems (...) to be also a metaphysical underdetermination concerning London and Bauer’s theory of measurement between two methods of phenomenological reduction: the eidetic and the transcendental approaches. Recently, Steven French argued that both methods can be combined in order to interpret London and Bauer’s formalism. However, in this paper we argue that the eidetic one is the only viable phenomenological way to interpret this particular theory of measurement in QM based on the formalism presented by London and Bauer, hence breaking this phenomenological underdetermination. (shrink)

In “Descriptions as Predicates” (Fara 2001) I argued that definite and indefinite descriptions should be given a uniform semantic treatment as predicates rather than as quantifier phrases. The aim of the current paper is to clarify and elaborate one of the arguments for the descriptions-aspredicates view, one that concerns the interaction of descriptions with adverbs of quantification.

Classical logic is usually interpreted as the logic of propositions. But from Boole's original development up to modern categorical logic, there has always been the alternative interpretation of classical logic as the logic of subsets of any given (nonempty) universe set. Partitions on a universe set are dual to subsets of a universe set in the sense of the reverse-the-arrows category-theoretic duality--which is reflected in the duality between quotient objects and subobjects throughout algebra. Hence the idea arises of a dual (...) logic of partitions. That dual logic is described here. Partition logic is at the same mathematical level as subset logic since models for both are constructed from (partitions on or subsets of) arbitrary unstructured sets with no ordering relations, compatibility or accessibility relations, or topologies on the sets. Just as Boole developed logical finite probability theory as a quantitative treatment of subset logic, applying the analogous mathematical steps to partition logic yields a logical notion of entropy so that information theory can be refounded on partition logic. But the biggest application is that when partition logic and the accompanying logical information theory are "lifted" to complex vector spaces, then the mathematical framework of quantum mechanics is obtained. Partition logic models indefiniteness (i.e., numerical attributes on a set become more definite as the inverse-image partition becomes more refined) while subset logic models the definiteness of classical physics (an entity either definitely has a property or definitely does not). Hence partition logic provides the backstory so the old idea of "objective indefiniteness" in QM can be fleshed out to a full interpretation of quantum mechanics. (shrink)

Might it be that world itself, independently of what we know about it or how we represent it, is metaphysically indeterminate? This article tackles in turn a series of questions: In what sorts of cases might we posit metaphysical indeterminacy? What is it for a given case of indefiniteness to be 'metaphysical'? How does the phenomenon relate to 'ontic vagueness', the existence of 'vague objects', 'de re indeterminacy' and the like? How might the logic work? Are there reasons for postulating (...) this distinctive sort of indefiniteness? Conversely, are there reasons for denying that there is indefiniteness of this sort? (shrink)

In this paper I develop a philosophical account of actual mathematical infinity that does not demand ontologically or epistemologically problematic assumptions. The account is based on a simple metaphor in which we think of indefinitely continuing processes as defining objects. It is shown that such a metaphor is valid in terms of mathematical practice, as well as in line with empirical data on arithmetical cognition.

Abstract This paper offers an appraisal of Phillip Pettit's approach to the problem how a merely finite set of examples can serve to represent a determinate rule, given that indefinitely many rules can be extrapolated from any such set. I argue that Pettit's so-called ethnocentric theory of rule-following fails to deliver the solution to this problem he sets out to provide. More constructively, I consider what further provisions are needed in order to advance Pettit's general approach to the problem. I (...) conclude that what is needed is an account that, whilst it affirms the view that agents' responses are constitutively involved in the exemplification of rules, does not allow such responses the pride of place they have in Pettit's theory. (shrink)

Online shaming is a subject of import for social philosophy in the Internet age, and not simply because shaming seems generally bad. I argue that social philosophers are well-placed to address the imaginal relationships we entertain when we engage in social media; activity in cyberspace results in more relationships than one previously had, entailing new and more responsibilities, and our relational behaviors admit of ethical assessment. I consider the stresses of social media, including the indefinite expansion of our relationships and (...) responsibilities, and the gap between the experiences of those shamed and the shamers’ appreciation of the magnitude of what they do when they shame; I connect these to the literature suggesting that some intuitions fail to guide our ethics. I conclude that we each have more power than we believe we do or than we think carefully about exerting in our online imaginal relations. Whether we are the shamers or the shamed, we are unable to control the extent to which intangible words in cyberspace take the form of imaginal relationships that burden or brighten our self-perceptions. (shrink)

THE IMMORTAL FLY: ETERNAL WHISPERS. WHO IS SHE? Author: Rituparna Ray Chaudhuri. Hello, Recently my book named, ‘The Immortal Fly: Eternal Whispers : Based On True Events of a Family' been published from Partridge (USA) In Association with Penguin Random House (UK) and achieved a separate Google identity. -/- As being # the author of the book, I thought to define self in the book what is definition of 'Depression'. I wanted to explain self in many ways, but the best (...) quotation appeared to me : “My life will end someday, but it will end at my convenience.’’ -/- ***** I am missing "her". By now, years passed without 'her' . Even though, unlike before, everything is becoming to be more scattered, gloomy and desolate. She is no-where whom I share my feelings. Even now, when I do close my eyes, I can visualize the same that I had left years since on 7th February, 2019 at 8.20 A.M. in the hospital struggling a continuous period of fifty days : on the fifty one day, my father said, ”The End of our Fifty Years relationship has been completed with the Fifty Days”….’Whoever’ she was to others , but she is our legend…To me, she is ‘My Ma’. -/- The story could begin, 'I failed preciously on success of my life.' Simplicity, Innocence, Belief, Faith and Personality met unknowingly with filthy waves skillfully immersed in Betray, Sorcery, Jealousy, Greediness, Revenge, Lie... ‘’ ******* The Daughter writes, “I had asked Ma many times, but her ‘impenetrable personality’ and dynamic words to everyone with a tinge of smile as reflected on her face, she was reluctant to continue her conversation with me. I had thought, hence, I must not be indefinite on my spoken words. Who shall I blame!” Based on true story of a family came from South Calcutta (India) to a suburb, on staying at home of the Daughter’s maternal grandmother’s house, this book reveals in facts and true events how Destiny had unknowingly ‘further’ played an abominable role to Fate of The Daughter, when eventually one day on 7th February, 2019 everything was finished within 8.20A.M. The Daughter is, therefore, left alone on terrestrial with immortal words as written in her Diary, ‘Eternal Whispers’: “My words to self that I am to fulfill my Ma’s - wish. ’’ ‘’ -/- • Keywords: 1. Diary and True Events 2. The Chaotic Society 3. Fatality 4. Of A-Family 5. Science , Philosophy and Literature 6. Severe Depression 7. Medical Journey. -/- The Alternative Title of the Book: The Greatest Mistake or Fortune:: The book is mainly carrying with intense words of a journey of the relationship between a Mother with her Daughter has left readers in an abrupt situation where ,perhaps, I can define "Man is the innocent creature with 'his' personality under circumstances..." -/- . (shrink)

We investigate the morphosyntax of qualitative binominal constructions (QBCs) in a Southern Italo-Romance language from the Apulian town of San Marco in Lamis. QBCs are complex noun phrases like ‘a jewelN1 of a villageN2’, appearing here prepositionally (with the preposition də, ‘of’, allowing definites, indefinites, and demonstratives) and non-prepositionally (only allowing definites with definite articles and not proper names). We propose that in the latter, a categorial match in the determiner layer, which we call ‘match D’, relates N1 and (...) N2. N1 is embedded as a noun, allowing for: 1) the recursive DP strategy of non-prepositional genitives, and 2) the extension of this mechanism to QBCs. This leads to the impossibility of syntactic extraction, which we connect to the concept of phase. With non-denominal N1s, N1’s article is treated as a head-agreeing adjectival linker, forming a constituent with the modifier but agreeing with the head. A phrase is interpreted as a QBC if N1 and N2 share the same number features and if the features of N1 do not allow for it to be interpreted as the possessum of N2 . We also discuss external agreement with the construction, presenting data supporting the relevance of the [+HUMAN] feature for agreement relations. (forthcoming, Italian Journal of Linguistics). (shrink)

Addicts sometimes engage in such spectacularly self-destructive behavior that they seem to act under compulsion. I briefly review the claim that addiction is not compulsive at all. I then consider recent accounts of addiction by Holton and Schroeder, which characterize addiction in terms of abnormally strong motivations. However, this account can only explain the apparent compulsivity of addiction if we assume—contrary to what we know about addicts—that the desires are so strong as to be irresistible. I then consider accounts that (...) invoke the phenomenon of “ego depletion,” according to which a person can resist temptation for a while, but not indefinitely. Implicit in this account is the assumption that addiction-related desires persist long enough to deplete the addict’s willpower. The balance of the paper argues that the persistence of the desire to consume drugs is a significant form of dysfunction in its own right, and that it makes an important and independent contribution to the compulsivity of addiction. I argue that addiction involves dysfunction in a mechanism that normally prevents a person from being tempted to do something that would invite disaster. (shrink)

The study aims at determining the role and significance of such moral emotions as nobility, gratitude, admiration for the socially significant behavior of a person in society. That involves identifying a close relationship between those emotions and personality’s social behavior and that they can be one of the main incentives for socially significant behavior – theoretical basis. The importance of ethical emotions with positive valence when making decisions with their implementation in society determines the research’s theoretical and methodological basis. Those (...) are studied in the cognitive dimension of human social activity, considering their subjective experience and objectification. The authors determined that ethical emotions with positive valence, pleasant emotions stimulate a person to experience them again and behave socially desirable as such behavior allows reliving those emotions and self-actualizing. Emotions with a positive valence are most desirable for a person and are the essential behavior incentives in society. A person can act actively to achieve them, to experience them repeatedly, which is the basis of motivation for socially desirable and meaningful behavior. From exclusively subjective experiences, those emotions move into objectification, i.e., those motivated to act in conditions of a definite or indefinite social continuum. In due time, these socially crucial actions acquire normative content, sometimes even a form, since they serve as a model for others. Moral emotions with positive valence, empathy, rule-making, high culture, and responsibility to oneself and others form a good way of a person’s self-realization through positive social behavior. Furthermore, moral emotions with positive valence are the most important incentive for such behavior. (shrink)

In the future, human destiny may depend on our ethics. In particular, biotechnology and expansion in space can transform life, raising profound questions. Guidance may be found in Life-centered ethics, as biotic ethics that value the basic patterns of organic gene/protein life, and as panbiotic ethics that always seek to expand life. These life-centered principles can be based on scientific insights into the unique place of life in nature, and the biological unity of all life. Belonging to life then implies (...) a human purpose: to safeguard and propagate life. Expansion in space will advance this purpose but will also raise basic questions. Should we expand all life or only intelligent life? Should we aim to create populations of trillions? Should we seed other solar systems? How far can we change but still preserve the human species, and life itself? The future of all life may be in our hands, and it can depend on our guiding ethics whether life will fulfil its full potentials. Given such profound powers, life-centered ethics can best secure future generations. Our descendants may then understand nature more deeply, and seek to extend life indefinitely. In that future, our human existence can find a cosmic purpose. (shrink)

Questioning economic growth remains a heresy, but the mathematics of compound growth show its indefinite continuation to be impossible. This frames a problem best resolved while we are still able to do so.

In many different ontological debates, anti-arbitrariness considerations push one towards two opposing extremes. For example, in debates about mereology, one may be pushed towards a maximal ontology (mereological universalism) or a minimal ontology (mereological nihilism), because any intermediate view seems objectionably arbitrary. However, it is usually thought that anti-arbitrariness considerations on their own cannot decide between these maximal or minimal views. I will argue that this is a mistake. Anti-arbitrariness arguments may be used to motivate a certain popular thesis in (...) the philosophy of mathematics that rules out the maximalist view in many different ontological debates. (shrink)

This book surveys research in quantification starting with the foundational work in the 1970s. It paints a vivid picture of generalized quantifiers and Boolean semantics. It explains how the discovery of diverse scope behavior in the 1990s transformed the view of quantification, and how the study of the internal composition of quantifiers has become central in recent years. It presents different approaches to the same problems, and links modern logic and formal semantics to advances in generative syntax. A unique feature (...) of the book is that it systematically brings cross-linguistic data to bear on the theoretical issues, discussing French, German, Dutch, Hungarian, Russian, Japanese, Telugu (Dravidian), and Shupamem (Grassfield Bantu), and pointing to formal semantic literature involving quantification in around thirty languages. -- -/- 1. What this book is about and how to use it; 2. Generalized quantifiers and their elements: operators and their scopes; 3. Generalized quantifiers in non-nominal domains; 4. Some empirically significant properties of quantifiers and determiners; 5. Potential challenges for generalized quantifiers; 6. Scope is not uniform and not a primitive; 7. Existential scope versus distributive scope; 8. Distributivity and scope; 9. Bare numeral indefinites; 10. Modified numerals; 11. Clause-internal scopal diversity; 12. Towards a compositional semantics of quantifier words. (shrink)

Several philosophers argue that individuals have an interest-protecting right to parent; specifically, the interest is in rearing children whom one can parent adequately. If such a right exists it can provide a solution to scepticism about duties of justice concerning distant future generations and bypass the challenge provided by the non-identity problem. Current children - whose identity is independent from environment-affecting decisions of current adults - will have, in due course, a right to parent. Adequate parenting requires resources. We owe (...) duties of justice to current children, including the satisfaction of their interest-protecting rights; therefore we owe them the conditions for rearing children adequately in the future. But to engage in permissible parenting they, too, will need sufficient resources to ensure their own children's future ability to bring up children under adequate conditions. Because this reasoning goes on ad infinitum it entails that each generation of adults owes its contemporary generation of children at least those resources that are necessary for sustaining human life indefinitely at an adequate level of wellbeing. (shrink)

1) We will begin by offering a short introduction to Epistemic Logic and presenting Fitch’s paradox in an epistemic‑modal logic. (2) Then, we will proceed to presenting three Epistemic Temporal logical frameworks creat‑ ed by Hoshi (2009) : TPAL (Temporal Public Announcement Logic), TAPAL (Temporal Arbitrary Public Announcement Logic) and TPAL+P ! (Temporal Public Announcement Logic with Labeled Past Operators). We will show how Hoshi stated the Verificationist Thesis in the language of TAPAL and analyze his argument on why this (...) version of it is immune from paradox. (3) Edgington (1985) offered an interpretation of the Verificationist Thesis that blocks Fitch’s paradox and we will propose a way to formulate it in a TAPAL‑based lan‑ guage. The language we will use is a combination of TAPAL and TPAL+P ! with an Indefinite (Unlabeled) Past Operator (TAPAL+P !+P). Using indexed satisfi‑ ability relations (as introduced in (Wang 2010 ; 2011)) we will offer a prospec ‑ tive semantics for this language. We will investigate whether the tentative re‑ formulation of Edgington’s Verificationist Thesis in TAPAL+P !+P is free from paradox and adequate to Edgington’s ideas on how „all truths are knowable“ should be interpreted. (shrink)

In this article, I address a controversial aspect of Rawls’s treatment of the question of justice between generations: how the parties in the original position could be motivated to select Rawls’s preferred principle of intergenerational savings, which he dubs the just savings principle. I focus on the explanation found in his later work, where he proposes that the correct savings principle is the principle that any generation would have wanted preceding generations to have followed. By expanding upon this explanation, I (...) respond to the objection that this explanation disregards the perspective of the first generation. I demonstrate that this objection ceases to be a concern when a proper account of the parties’ reasoning is developed. What is notable about the explanation I defend is that it relies on the parties adopting maximax – not maximin – as a rule for rational decision making. Having established this intermediary conclusion, I depart with Rawls and consider what savings principle the parties would choose if given more options. Ultimately, I argue that the parties would select a principle that Rawls would have undoubtedly rejected if presented to him at face value. This is because the principle of savings I argue would be selected requires continual economic growth over generations to increase upwards indefinitely – a conclusion Rawls is explicitly trying to avoid in his theory of justice. (shrink)

We are able to participate in countless different sorts of social practice. This indefinite set of capacities must be explainable in terms of a finite stock of capacities. This paper compares and contrasts two different explanations. A standard decomposition of the capacity to participate in social practices goes something like this: the interpreter arrives on the scene with a stock of generic practice-types. He looks at the current scene to fill-in the current tokens of these types. He looks at the (...) current state of these practice tokens to see what actions are available to him. He uses his current desires to choose between these various possible actions. I argue that this standard explanation is defective, drawing on arguments by Searle and Wittgenstein and Garfinkel. I propose an alternative explanation, in which the participants must continually show each other the state of the scene in order to maintain the scene’s intelligibility. I provide a simple formal language in which to describe this alternative approach, in which we can state quite precisely what someone is doing when they participate in a practice. This language is related to both deontic and epistemic logics, but it is much simpler – it does not include the classic propositional connectives, and it is driven by a very different set of assumptions. The inspirations for this formal language are Searle’s analysis of directions of fit, Wittgenstein’s remarks on rule-following and Garfinkel’s ethnomethodology. (shrink)