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)

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 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.

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.

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)

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)

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)

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)

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.

Sentences with impersonal pronouns, like 'You do it like this', seem to make both statistical and prescriptive claims, that a certain way of behaving is common and that it is prescriptively good. We argue that these kinds of sentences are closely related to another kind of sentence, namely, indefinite singular generics, like 'A person does it like this'. We propose that there is a single underlying mechanism that allows both kinds of sentences to express mixed statistical/prescriptive readings. We then provide (...) a compositional semantic analysis of these sentences and explain how, together with this single underlying mechanism, it accounts for this phenomenon. (shrink)

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)

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)

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)

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)

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)

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)

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)

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)

This epistemic project examines an understudied existential risk emerging in the deepfake era: the fortunately up to this time (but not indefinitely so) reversible peril of humanity’s epistemic self-sabotage through an overestimation of algorithms linked to quantitative aspects and a paired underestimation of the own epistemic potential whose manifestations are in principle expressible via scientifically analyzable but currently often neglected qualitative facets. This scenario is metaphorically referred to as "π-Doom scenario". Instead of carefully crafting opaque hypotheses and formulating probabilistic predictions (...) of timelines that could easily evade scrutiny and/or could even themselves be initially generated by algorithms, scientifically and responsibly counteracting π-Doom requires new better riskier explanatory theories of intelligence, creativity and consciousness. A brief non-comprehensive literature review suggests that quite a few scientific instantiations (all of which have not yet been provisionally refuted) of that transformative requirement are already available at present. In short, π-Doom – the voluntarily or unintentionally effectuated cognitive resignation engendering an irrational algorithmically-motored process of running around in (epistemic) circles that could endanger the immediate future of a vulnerable civilization like present-day humanity – is wholly contingent on a choice of focus. (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)

Although he is best known as the founder of pragmatism, the name that Charles Sanders Peirce prefers to use for his comprehensive system of thought is "synechism" because the principle of continuity is its central thesis. This paper arranges and summarizes numerous quotations and citations from his voluminous writings to formalize and explicate his distinctive mathematical conceptions of hyperbolic and topical continuity, both of which are derived from the direct observation of time as their paradigmatic manifestation, and then apply them (...) in normative science and metaphysics, especially logic as semeiotic and cosmology. The resulting conclusion is that the intelligibility of the universe is plausibly explained by conceiving it as one immense sign, a vast inferential process: a semiosic continuum whose connected constituent signs are indefinite until deliberately marked off, with God the Creator as its overall dynamical object in the infinite past and God completely revealed as its overall final interpretant in the infinite future. (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)

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)

This paper explores the interaction of well-motivated (if controversial) principles governing the probability conditionals, with accounts of what it is for a sentence to be indefinite. The conclusion can be played in a variety of ways. It could be regarded as a new reason to be suspicious of the intuitive data about the probability of conditionals; or, holding fixed the data, it could be used to give traction on the philosophical analysis of a contentious notion—indefiniteness. The paper outlines the various (...) options, and shows that ‘rejectionist’ theories of indefiniteness are incompatible with the results. Rejectionist theories include popular accounts such as supervaluationism, non-classical truth-value gap theories, and accounts of indeterminacy that centre on rejecting the law of excluded middle. An appendix compares the results obtained here with the ‘impossibility’ results descending from Lewis ( 1976 ). (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)

Does the Big History of life on Earth disclose a trajectory that has been driven by selection? If so, will the trajectory continue to apply into the future? This paper argues that such a trajectory exists, and examines some of its key implications. The most important consequence is that humanity can use the trajectory to guide how it evolves and adapts into the future. This is because the trajectory identifies a sequence of adaptations that will be favoured by selection. If (...) humanity intentionally evolves its social systems and psychological capacities so that they follow the trajectory, humanity can avoid negative selection and instead survive and thrive indefinitely into the future. This would enable humanity to make a positive contribution to the future evolution of life in the universe. But it turns out that immediate selection will not drive the evolution of life on Earth further along this trajectory. Instead, intentional action by humanity is necessary. It is as if the evolution of life on any planet is a developmental process that has a very unusual characteristic: evolution will continue to develop successfully beyond a certain point only if it produces a sentient organism that: (i) awakens to the possibility it is embedded in a developing process; (ii) realizes that this developing process will continue successfully only if it chooses to intentionally drive the process forward; and (iii) commits to doing whatever is necessary to achieve this. On this planet, humanity is that sentient organism. The existence of such a key evolutionary role for humanity is capable of providing humanity with meaning and purpose in a larger scheme of things. For individuals who commit to driving the process forward, the nature of the trajectory has immediate consequences for what they should do with their lives, here and now. (shrink)

Pragmatism is a philosophical tradition that understands knowing the world as inseparable from agency within it. It thereby introduces some unique ideas and approaches to the analysis of concepts. Looking largely to pragmatism’s founder, Charles Peirce, this chapter presents an account of concepts as habits which associate specific kinds of environmental stimuli with schemata of action and ensuing experience, within linguistic communities. I explain how this account avoids Sellars’ ‘Myth of the Given’. I then explore how Peirce’s semiotic approach to (...) philosophy of language and mind theorized signifying habits as symbols which draw icons and indices together into propositional structures, thereby generating meanings that are specifically applicable and indefinitely generalizable. This original account of concept formation is further illuminated through an examination of Peirce’s philosophy of perception, which makes particularly manifest the process whereby primitive indices, or ‘percepts’, are enfolded in symbolic meanings through habitual ‘perceptual judgements’. (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)

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)

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.

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)

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)

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)

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)

Spinoza ’s letter of June 2, 1674 to his friend Jarig Jelles addresses several distinct and important issues in Spinoza ’s philosophy. It explains briefly the core of Spinoza ’s disagreement with Hobbes’ political theory, develops his innovative understanding of numbers, and elaborates on Spinoza ’s refusal to describe God as one or single. Then, toward the end of the letter, Spinoza writes: With regard to the statement that figure is a negation and not anything positive, it is obvious that (...) matter in its totality, considered without limitation [indefinitè consideratam], can have no figure, and that figure applies only to finite and determinate bodies. For he who says that he apprehends a figure, thereby means to indicate simply this, that he apprehends a determinate thing and the manner of its determination. This determination therefore does not pertain to the thing in regard to its being [esse]; on the contrary, it is its non-being [non-esse]. So since figure is nothing but determination, and determination is negation [Quia ergo figura non aliud, quam determinatio, et determinatio negatio est], figure can be nothing other than negation, as has been said. Arguably, what is most notable about this letter is the fate of a single subordinate clause which appears in the last sentence of this passage: et determinatio negatio est. That clause was to be adopted by Hegel and transformed into the slogan of his own dialectical method: Omnis determinatio est negatio. Of further significance is the fact that, while Hegel does credit Spinoza with the discovery of this most fundamental insight, he believes Spinoza failed to appreciate the importance of his discovery. The issue of negation and the possibility of self-negation stand at the very center of the philosophical dialogue between the systems of Spinoza and Hegel, and in this paper I will attempt to provide a preliminary explication of this foundational debate between the two systems. In the first part of the paper I will argue that the “determination is negation” formula has been understood in at least three distinct senses among the German Idealists, and as a result many of the participants in the discussion of this formula were actually talking past each other. The clarification of the three distinct senses of the formula will lead, in the second part of the paper, to a more precise evaluation of the fundamental debate between Spinoza and Hegel regarding the possibility of self-negation. In this part I will evaluate the validity of each interpretation of the determination formula, and motivate the positions of the various participants in the debate. (shrink)

It is more than a platitude to admit that we are always dying. It is a recognition of the fundamental finitude that marks our existence as human persons. It says something essential about the human condition. We are all born. We all die. And the very living of life is, leaving aside for the moment religious considerations, oriented toward death. Phenomenologists make much of this observation, perhaps none more so than Martin Heidegger who argues that our being-toward-death permits the ontological (...) grasping of Da-sein as a whole. Indeed for him, the“existential and ontological concept of death” is “the own most nonrelational, certain, and, as such, indefinite and not to be bypassed possibility of Da-sein.” However, if one spends much time around those who are very close to death it can begin to sound disingenuous to talk about death as one’s own most possibility. It is easy to think these patients are dying—not me. Still, the phenomenologist might claim that, vis-à-vis our being-toward-death, the difference between me and the terminally ill patient is a matter of degree and not kind. But, is this so? One may be excused for thinking not. There appears to be an important difference in the kinds of possible experiences open to us. I may experience healing if I become ill; on the other hand, the very condition of the patient with a terminal illness is defined by the impossibility of her experiencing healing. The primary aim of this paper is to argue that the terminally ill patient can, in fact, experience healing at the end of her life and in the face of impending death. I will not argue that the possibility of experiencing healing at the end of life means leaving room for divine intervention, though neither do I intend to preclude such a possibility. Rather, I will argue that healing is something that we experience quite apart from what happens to our biological make-up. While healing is often correlated with a change in the state of our bodies, it need not be. (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)

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)

Gareth Evans has argued that the existence of vague objects is logically precluded: The assumption that it is indeterminate whether some object a is identical to some object b leads to contradiction. I argue in reply that, although this is true—I thus defend Evans's argument, as he presents it—the existence of vague objects is not thereby precluded. An 'Indefinitist' need only hold that it is not logically required that every identity statement must have a determinate truth-value, not that some such (...) statements might actually fail to have a determinate truth-value. That makes Indefinitism a cousin of mathematical Intuitionism. (shrink)

There has been much discussion of so-called teleosemantic approaches to the naturalization of content. Such discussion, though, has been largely confined to simple, innate mental states with contents such as ?There is a fly here.? Even assuming we can solve the issues that crop up at this stage, an account of the content of human mental states will not get too far without an account of productivity: the ability to entertain indefinitely many thoughts. The best-known teleosemantic theory, Millikan's biosemantics, offers (...) an account of productivity in thought. This paper raises a basic worry about this account: that the use of mapping functions in the theory is unacceptable from a naturalistic point of view. (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)

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)

We take up the challenge of developing an international network with capacity to survey the world's scientists on an ongoing basis, providing rich datasets regarding the opinions of scientists and scientific sub-communities, both at a time and also over time. The novel methodology employed sees local coordinators, at each institution in the network, sending survey invitation emails internally to scientists at their home institution. The emails link to a ‘10 second survey’, where the participant is presented with a single statement (...) to consider, and a standard five point Likert scale. In June 2023, a group of 30 philosophers and social scientists invited 20,085 scientists across 30 institutions in 12 countries to participate, gathering 6,807 responses to the statement 'Science has put it beyond reasonable doubt that COVID-19 is caused by a virus'. The study demonstrates that it is possible to establish a global network to quickly ascertain scientific opinion on a large international scale, with high response rate, low opt-out rate, and in a way that allows for significant (perhaps indefinite) repeatability. Measuring scientific opinion in this new way would be a valuable complement to currently available approaches, potentially informing policy decisions and public understanding across diverse fields. (shrink)

Evolutionary psychiatry suggests that mental disorders can be explained in evolutionary terms (a) as failures of psychological mechanisms to produce the adaptive effects for which they were naturally selected, (b) as mismatches between naturally selected psychological mechanisms and contemporary environmental pressures, or (c) as naturally selected psychological mechanisms whose effects continue to be adaptive. In this paper, I present a philosophical critique of evolutionary psychiatry that draws on Subrena Smith’s matching problem for evolutionary psychology. For evolutionary psychiatry hypotheses to be (...) empirically supported, proponents of evolutionary psychiatry must demonstrate (1) that the contemporary psychological mechanisms involved in mental disorders resemble the psychological mechanisms of our evolutionary ancestors, (2) that the contemporary psychological mechanisms are phylogenetically descended from the ancestral psychological mechanisms, and (3) that the ancestral psychological mechanisms were naturally selected because their effects had adaptive benefits. However, for many mental disorders, evolutionary psychiatry lacks the methodological resources to demonstrate these conditions. Therefore, many evolutionary psychiatry hypotheses are empirically untestable and remain indefinitely underdetermined by data. (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)