Supervenience theses promise ontological economy without reducibility. The problem is that they face a dilemma: either the relation of supervenience entails reducibility or it is mysterious. Recently higher-order universals have been invoked to avoid the dilemma. This article develops a higher-order framework in which this claim can be assessed. It is shown that reducibility can be avoided, but only at the cost of a rather radical metaphysical proposal.

Higher-order realists about properties express their view that there are properties with the help of higher-order rather than first-order quantifiers. They claim two types of advantages for this way of formulating property realism. First, certain gridlocked debates about the nature of properties, such as the immanentism versus transcendentalism dispute, are taken to be dissolved. Second, a further such debate, the tropes versus universals dispute, is taken to be resolved. In this paper I first argue (...) that higher-order realism does not in fact resolve the tropes versus universals dispute. In a constructive spirit, I then develop higher-order realism in a way that leads to a dissolution, rather than a resolution, of this dispute too. (shrink)

We discuss the one–many problem as it appears in the Philebus and find that it is not restricted to the usually understood problem about the identity of universals across particulars that instantiate them (the Hylomorphic Dispersal Problem). In fact some of the most interesting aspects of the problem occur purely with respect to the relationship between Forms. We argue that contemporary metaphysicians may draw from the Philebus at least three different one–many relationships between universals themselves: instantiation, subkind and (...) part, and thereby construct three new ‘problems of the one and the many’ (an Eidetic Dispersal Problem, a Genus–Species Problem, and an Eidetic Combination Problem), which are as problematic as the version generally discussed. We then argue that this taxonomy sheds new and interesting light on certain discussions of higher-order universals in recent Australian analytic philosophy. (shrink)

This book articulates and defends Fregean realism, a theory of properties based on Frege's insight that properties are not objects, but rather the satisfaction conditions of predicates. Robert Trueman argues that this approach is the key not only to dissolving a host of longstanding metaphysical puzzles, such as Bradley's Regress and the Problem of Universals, but also to understanding the relationship between states of affairs, propositions, and the truth conditions of sentences. Fregean realism, Trueman suggests, ultimately leads to a (...) version of the identity theory of truth, the theory that true propositions are identical to obtaining states of affairs. In other words, the identity theory collapses the gap between mind and world. This book will be of interest to anyone working in logic, metaphysics, the philosophy of language or the philosophy of mind. (shrink)

The work presents the concept of a structural universal and the criticisms that have been leveled against it. A structural universal is a property had by an individual due to the nature of its proper parts and due to the relations obtaining between those parts. Mellor has argued that there is no reason to accept such universal in addition to the basic universals that compose them. David Lewis has argued –on the other hand– that it has not been satisfactorily (...) explained how universals are composed by other universals. The composition by which a structural universal is given cannot be a set-theoretical construction or a mereological sum. Several proposals to explain the nature of structural universals are discussed. Finally it is argued that a structural universal should be understood as a complexion of higher-order universals. (shrink)

The present article attempts at combining Big History potential with the potential of Evolutionary Studies in order to achieve the following goals: 1) to apply the historical narrative principle to the description of the star-galaxy era of the cosmic phase of Big History; 2) to analyze both the cosmic history and similarities and differences between evolutionary laws, principles, and mechanisms at various levels and phases of Big History. As far as I know, nobody has approached this task in a (...) systemic way yet. It appears especially important to demonstrate that many evolutionary principles, patterns, regularities, and rules, which we tend to find relevant only for higher levels and main lines of evolution, can be also applied to cosmic evolution. Moreover, almost everything that we know about evolution may be detected in the cosmic history, whereas many of the evolutionary characteristics are already manifested here in a rather clear and salient way. Of course, many of the characteristics are manifested in initial or nonsystematic forms but some features, on the contrary, appear to be more distinct just in the cosmic phase. And at the same time when many characteristics and features which are typical of biological and social evolution unexpectedly reveal their roots or protoforms at earlier phases, one becomes aware that the universal character of evolution is real and it can be detected in a number of manifestations. One should also bear in mind that the origin of galaxies, stars, and other celestial objects is the lengthiest evolutionary process among all evolutionary processes in the Universe. Such an approach opens new perspectives for our understanding of evolution and Big History, of their driving forces, vectors, and trends, it also creates a consolidated field for the multidisciplinary re-search. (shrink)

This essay in the "anthropology of science" is about how cognition constrains culture in producing science. The example is folk biology, whose cultural recurrence issues from the very same domain-specific cognitive universals that provide the historical backbone of systematic biology. Humans everywhere think about plants and animals in highly structured ways. People have similar folk-biological taxonomies composed of essence-based species-like groups and the ranking of species into lower- and higher-order groups. Such taxonomies are not as arbitrary in (...) structure and content, nor as variable across cultures, as the assembly of entities into cosmologies, materials or social groups. (shrink)

Universals are putative objects like wisdom, morality, redness, etc. Although we believe in properties (which, we argue, are not a kind of object), we do not believe in universals. However, a number of ordinary, natural language constructions seem to commit us to their existence. In this paper, we provide a fictionalist theory of universals, which allows us to speak as if universals existed, whilst denying that any really do.

The paper discusses some formal difficulties concerning the theory of universals of Trope-Only ontologies, from which the formal theory of predication advanced by Trope-Only theorists seems to be irremediably affected. It is impossible to lay out a successful defense of a Trope-Only theory without Russellian types, but such types are ontologically inconsistent with tropes’ nominalism. Historically, Tropists’ first way to avoid the problem is appealing to the supervenience claim, which however fails on its terms and, thus, fails as a (...) ground for a solution to the higher-order or ‘type’ problem. A later solution involves the invariance of primitive equivalence relations in order to make universals ontologically innocuous. However, I argue that this latter solution fails to meet the requirements imposed on an ontologically unbiased nominalist attitude. So, this paper discusses how Trope-Only theories alter standard formal moves in Nominalism, and also is interested in clarifying further the formal assumptions for these problems. (shrink)

1. Frege’s mistake Frege is justifiably considered the most important thinker in the development of our contemporary “modern” logic. One corollary to this historical role of Frege’s is that his mistakes are found in a magnified form in the subsequent development of logic. This paper examines one such mistake and its later history. Diagnosing this history also reveals ways of overcoming some of the limitations that Frege’s mistake has unwittingly imposed on current forms of modern logic. Frege’s mistake concerns the (...) semantics (meaning) of quantifiers. The mistake is to assume that this semantics is exhausted by the quantifiers’ (quantified variables’) ranging over a class of values. These values are the members of the domain (universe of discourse) of the language to which the quantifiers belong. The entire job description of the quantifiers is to indicate whither or not at least one member of the domain has a certain (possible complex) predicate (existential quantifier) and to indicate whether all of them have one (universal quantifier). In other words, quantifiers are higher order predicates indicating whether or not a given lower-order predicate is nonempty or exceptionless. This is in fact precisely how Frege proposes to treat quantifiers in his logical theory. (See Frege 1984, pp. 153-154, pp. 26-27 of the original.) This is obviously part of the semantical task of quantifiers. However, it is not the only one. Quantifiers have another function in language. There is a task that any language must be capable of fulfilling if it is to serve as a language of science and for that matter as a language suitable for innumerable purposes in everyday life. This task is to.. (shrink)

Carnap's philosophy is examined from new viewpoints, including three important distinctions: (i) language as calculus vs language as universal medium; (ii) different senses of completeness: (iii) standard vs nonstandard interpretations of (higher-order) logic. (i) Carnap favored in 1930-34 the "formal mode of speech," a corollary to the universality assumption. He later gave it up partially but retained some of its ingredients, e.g., the one-domain assumption. (ii) Carnap's project of creating a universal self-referential language is encouraged by (ii) and (...) by the author's recent work. (iii) Carnap was aware of (iii) and occasionally used the standard interpretation, but was not entirely clear of the nature of the contrast. (shrink)

The word ‘concept’ is sometimes used as a synonym for ‘property’, but many authors use it in a more specific sense, for example as standing for unsaturated entities whose extensions are sets and classes, for Fregean senses, or for abstract objects. Although there is no universal agreement on a definition of concepts, a viable theory of concepts has to address a number of formal issues: How to deal with counterfactual and possibly contradictory concepts, how to restrict comprehension schemes in (...) class='Hi'>higher-order logic to avoid semantic paradoxes like the Paradox of Predication, how to nominalize concepts, and how to express similarity and typicality of concepts. The article gives a brief survey of the most important problems in concept theory and their possible solutions. (shrink)

In this work I have tried to justify the principle theses of Meinong's Theory of Objects and to criticize some ontological theses that do not seem to derive from the Theory of Objects. This work has been divided into three parts according to the fundamental classification of objects given by Meinong: object of representation, object of thought, and objects of emotion. ;In the first part I have analysed the doctrine of intentionality in relation with intentional act and content, and their (...) sorts of presentation in discussion with Brentano. ;In following I have given an interpretation of "pure object" and its status of "Assersein" by which pure object is beyond being and non-being. This is developed in close connection to the doctrine of impossible objects and the Theory of Objects as the most universal science inasmuch as it harbors both real and unreal worlds . I have built an extensive critique of Russell's theory of Descriptions and Denoting, and other opposing views. The rest of this part is devoted to both incomplete objects and objects of higher order . The theory of incomplete object is connected to our way of knowing things, and it expresses the incompleteness of our intentional attitudes. The theory of objects of higher order tries to explain the problem of space-time continuum. ;The second part began with the demonstration of "existence" and nature of Objectives . The Objective is grasped by either a judgment or an assumption, whether its true/false value is included in it or not. I have developed an extensive analysis of modalities--factuality, necessity and possibility--, and quasi-modalities--probability and truth--in order to give a complete Theory of Knowledge integrated in an Ontology. ;The last part was an analysis the objects of emotional lived experiences: the "dignitative" and the "desiderative." The dignitative harbors ethical and esthetical values, while the desiderative contains moral and esthetical laws, and in general, the "duties." The main analysis of this part treats the question of justification of the ethical objects and their grounding in intellectual objects. (shrink)

This article seeks to show the importance of Cicero for Kant by pointing out the systematic relationship between their respective views on ethics and law. Cicero was important to Kant because Cicero had already elaborated an imperative, “quasi-jural” conception of duty or obligation. Cicero had also already prefigured the distinction between ethical duties and duties of justice. The article does not establish any direct historical influence, but points out interesting systematic overlaps. The most important in the realm of ethics are (...) a universal rationalism; a rule-based normative framework of duty; and skepticism about (Cicero), or rejection of (Kant), eudaimonism. In the realm of political theory, it is the centrality of law and of property that unites both thinkers; both reject voluntarism in thinking that consensus flows from the right external laws, not the other way around, and thus creates a juridical community; and lastly, both Cicero and Kant believe that transparence, or publicity, is a key ideal that might be presupposed by both the ethical and the juridical domain. The article thus shows that both Cicero and Kant separate ethics from law, but there are indications that neither has given up the aspiration to bridge the two realms on a higher plane. This reading of Kant yields both a more Ciceronian Kant and allows us to perceive Kantian aspects of Cicero. (shrink)

This compact booklet addresses informal logical aspects of infinite regress arguments. We know what infinite regress arguments are from such examples as Plato’s Third Man problem. It is presented here for tradition sake in its original formulation, where for convenience ‘man’ does duty for ‘human being’. Plato’s theory of abstract Ideas or Forms, in order to explain how it is that Phaedo and Meno are both men, posits their belonging to, participating in or falling under a higher ideal (...) abstract universal Man. The theory thereby takes the first irreversible step toward an infinite regress of ideal abstract universal men of increasingly higher order, beginning with the third MAN, for which there seems to be no legitimating explanatory rationale. A further example, to have several on hand, is the infinite regress that occurs on the assumption that every occurrent event has a temporally prior cause, or, simply, that every event has a cause that is also an event. The logical structure, class .. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 41.4 (2003) 564-565 [Access article in PDF] Samuel J. Kerstein. Kant's Search for the Supreme Principle of Morality. New York: Cambridge University Press, 2002. Pp. xiv + 226. Cloth, $60.00. Summed up in a sentence, this book is both a critical examination of Kant's claim to have derived a supreme moral principle and a limited defense of Kant's project that appears to depart (...) significantly from Kant's own approach. Methodologically, a large portion of this book is devoted to analyzing various key concepts and claims about the nature of the categorical imperative in the Groundwork of the Metaphysics of Morals and the Critique of Practical Reason and testing them against "everyday" moral intuitions via numerous examples and counterexamples.Kerstein begins by distinguishing between the tasks of deduction and derivation of a supreme moral principle, whereby a deduction is understood as an argument for the existence of a supreme moral principle, and a derivation simply assumes this conditionally and goes on to argue that a particular principle and no other can claim the title. Kerstein waives the discussion of whether Kant succeeds in giving a deduction and hence satisfactorily refutes moral skepticism. His focus in the book is on the derivation proposed primarily in Groundwork I and II that if there is a supreme moral principle, then it must be that law expressed in his formulations of the Categorical Imperative (hereafter "CI"). Kerstein addresses Bruce Aune's "traditional" reading of Kant's derivation, wherein the argument utterly fails because Kant allegedly infers a relatively substantive command ("Act only on that maxim which you can at the same time will to be universal law") from a purely formal, higher order, and hence relatively empty one ("Conform your actions to universal law"). He then devotes a chapter each to two recent, influential defenses of Kant's derivation that seek his argument outside the Groundwork. Kerstein addresses Henry Allison's attempt to rescue the derivation via an account of agency rooted in Kant's notion of transcendental freedom, elaborated in the second Critique. Kerstein rejects Allison's reconstruction on the grounds that it remains too abstract to generate the degree of specificity arrived at in Kant's Groundwork universalization formulation. Chapter Three examines Christine Korsgaard's alternative reconstruction of Kant's argument that focuses on the formulation of humanity ("Act so as to treat humanity, whether in your own person or that of any other, always as an end and never as a means only"). He rejects her interpretation because, again, the move from the abstract command to conform to universal law to the substantive formulation about humanity as a universally recognizable unconditional good fails. From the former, more abstract claim, he argues, it does not follow that there is a universally recognizable unconditional good, let alone that this good is humanity in itself (and not, say, utility [happiness], or even some intrinsic value unrelated to humanity, both of which Kant rejects as candidates for the unconditionally good).In his own reconstruction, Kerstein dissolves the criticism of the traditional reading of Kant's Groundwork derivation of the formula of universal law by simply denying that Kant [End Page 564] argues directly from the more generic principle to the specific versions of the CI (91ff). Instead he suggests that Kant's argument is less direct, made by way of laying out a set of criteria that any supreme principle must meet, and showing how the CI meets them while no other candidates can. In the second half of the book he takes a painstaking and critical look at a total of eight criteria, each of which Kant holds to be necessary and together are jointly sufficient for establishing the CI as "the supreme norm for the evaluation of the moral permissability and requiredness of an action, but not of its moral value" (165). This statement includes Kerstein's most controversial and interesting reconstructive claim, namely his denial that moral worth attaches only to actions done in accordance with duty as determined by the test... (shrink)

Necessitism, Contingentism, and Theory Equivalence is a dissertation on issues in higher-order modal metaphysics. Consider a modal higher-order language with identity in which the universal quantifier is interpreted as expressing universal quantification and the necessity operator is interpreted as expressing metaphysical necessity. The main question addressed in the dissertation concerns the correct theory formulated in this language. A different question that also takes centre stage in the dissertation is what it takes for theories to be equivalent.The (...) whole dissertation consists of an extended argument in defence of the truth of two seemingly inconsistent higher-order modal theories, specifically: 1.Plantingan Moderate Contingentism, a theory based on Plantinga’s [1] modal metaphysics that is committed to, among other things, the contingent being of some individuals and the necessary being of all possible higher-order entities;2.Williamsonian Thorough Necessitism, a theory advocated by Williamson [3] which is committed to, among other things, the necessary being of every possible individual as well as of every possible higher-order entity.Part of the case for these theories’ joint truth relies on defences of the following metaphysical theses: Thorough Serious Actualism, the thesis that no things could have been related while being nothing, and Higher-Order Necessitism, the thesis that necessarily, every higher-order entity is necessarily something. It is shown that Thorough Serious Actualism and Higher-Order Necessitism are both implicit commitments of very weak logical theories. The defence of Higher-Order Necessitism constitutes a powerful challenge to Stalnaker’s [2] Thorough Contingentism, a theory committed to, among other things, the view that there could have been some individuals as well as some entities of any higher-order that could have been nothing.In the dissertation it is argued that Plantingan Moderate Contingentism and Williamsonian Thorough Necessitism are in fact equivalent, even if they appear to be jointly inconsistent. The case for this claim relies on the Synonymy account, a novel account of theory equivalence developed and defended in the dissertation. According to this account, theories are equivalent just in case they have the same commitments and conception of logical space.By way of defending the Synonymy account’s adequacy, the account is applied to the debate between noneists, proponents of the view that some things do not exist, and Quineans, proponents of the view that to exist just is to be some thing. The Synonymy account is shown to afford a more nuanced and better understanding of that debate by revealing that what noneists and Quineans are really disagreeing about is what expressive resources are available to appropriately describe the world.By coupling a metatheoretical result with tools from the philosophy of language, it is argued that Plantingan Moderate Contingentism and Williamsonian Thorough Necessitism are synonymous theories, and so, by the lights of the Synonymy account, equivalent. Given the defence of their extant commitments made in the dissertation, it is concluded that Plantingan Moderate Contingentism and Williamsonian Thorough Necessitism are both correct. A corollary of this result is that the dispute between Plantingans and Williamsonians is, in an important sense, merely verbal. For if two theories are equivalent, then they “require the same of the world for their truth.”Thus, the results of the dissertation reveal that if one speaks as a Plantingan while advocating Plantingan Moderate Contingentism, or as a Williamsonian while advocating Williamsonian Thorough Necessitism, then one will not go wrong. Notwithstanding, one will still go wrong if one speaks as a Plantingan while advocating Williamsonian Thorough Necessitism, or as a Williamsonian while advocating Plantingan Moderate Contingentism.On the basis of a conception of the individual constants and predicates of second-order modal languages as strongly Millian, i.e., as having actually existing entities as their semantic values, in the appendix are presented second-order modal logics consistent with Stalnaker’s Thorough Contingentism. Furthermore, it is shown there that these logics are strong enough for applications of higher-order modal logic in mathematics, a result that constitutes a reply to an argument to the contrary by Williamson [3]. Finally, these logics are proven to be complete relative to particular “thoroughly contingentist” classes of models. (shrink)

A hypothesis of genome structural evolution is explored. Rapid and cohesive alterations in genome organization are viewed as resulting from the dynamic and constrained interactions of chromosomal subsystem components. A combination of macromolecular boundary conditions and DNA element involvement in far-from-equilibrium reactions is proposed to increase the complexity of genomic subsystems via the channelling of genome turnover; interactions between subsystems create higher-order subsystems expanding the phase space for further genetic evolution. The operation of generic constraints on structuration in (...) genome evolution is suggested by i) universal, homoplasic features of chromosome organization and ii) the metastable nature of genome structures where lower-level flux is constrained by higher-order structures. Phenomena such as genomic shock, bursts of transposable element activity, concerted evolution, etc., are hypothesized to result from constrained systemic responses to endogenous/exogenous, micro/macro perturbations. The constraints operating on genome turnover are expected to increase with chromosomal structural complexity, the number of interacting subsystems, and the degree to which interactions between genomic components are tightly ordered. (shrink)

In this article we discuss a version of the Robinson property studied recently by Gyenis in, and we present a solution to one of his open problems. We say that a first‐order structure satisfies the Robinson property whenever the union of two non‐trivial partial n‐types over different finite sets is realizable if and only if they are not explicitly contradictory. In his article, Gyenis showed that a universal, homogeneous structure over a language that consists of at most binary relation (...) symbols satisfies the Robinson property if and only if its age has a generalized amalgamation property (the so called prescribed amalgamation property, PAP). We go further and define a series of new kinds of amalgamation properties, APn for any natural number n. Using these properties we can characterize all universal and homogeneous structures that satisfy the Robinson property independently from the arities of relation symbols of the language. (shrink)

A universal reasoning approach based on shallow semantical embeddings of higher-order modal logics into classical higher-order logic is exemplarily employed to analyze several modern variants of the ontological argument on the computer. Several novel findings are reported which contribute to the clarification of a long-standing dispute between Anderson and Hájek. The technology employed in this work, which to some degree realizes Leibniz’s dream of a characteristica universalis and a calculus ratiocinator for solving philosophical controversies, is ready (...) to be fruitfully adopted in larger scale by philosophers. (shrink)

Plural expressions found in natural languages allow us to talk about many objects simultaneously. Plural logic — a logical system that takes plurals at face value — has seen a surge of interest in recent years. This book explores its broader significance for philosophy, logic, and linguistics. What can plural logic do for us? Are the bold claims made on its behalf correct? After introducing plural logic and its main applications, the book provides a systematic analysis of the relation between (...) this logic and other theoretical frameworks such as set theory, mereology, higher-order logic, and modal logic. The applications of plural logic rely on two assumptions, namely that this logic is ontologically innocent and has great expressive power. These assumptions are shown to be problematic. The result is a more nuanced picture of plural logic's applications than has been given thus far. Questions about the correct logic of plurals play a central role in the final chapters, where traditional plural logic is rejected in favor of a "critical" alternative. The most striking feature of this alternative is that there is no universal plurality. This leads to a novel approach to the relation between the many and the one. In particular, critical plural logic paves the way for an account of sets capable of solving the set-theoretic paradoxes. (shrink)

In the health care professions, the meaning of—and implications for—‘dignity’ and ‘value’ are progressively more important, as scholars and practitioners increasingly have to make value judgments when making care decisions. This paper looks at the various arguments for competing sources of human value that medical professionals can consider—human rights, autonomy, and a higher-order moral value—and settles upon a foundational model that is related to the Kantian model that is popular within the medical community: human value is foundational; human (...) dignity, autonomy, and rights derive from the relational quality of human dignity. Moral dignity is expressed though the relationships we cultivate, the communal ends we pursue, and the rights we enjoy. Correlatively, human dignity is inseparable from its ground, and the relationship between these two is best represented for Kant in the humanities formulation. The foundational model of dignity ensures that human value is non-circularly derived, but is ultimately tied to expressions of individual human dignity that comes from the dignity of morality. Linking Kant’s dignity of humanity to the dignity of morality affords a unique and efficacious response to the discussion of human value. In one sense, dignity is amplificatory, since its worth is inextricable with that of autonomy and the rights afforded to the autonomous. But that isn’t to say that the worth of dignity is merely amplificatory. Rather, human dignity indicates the absolute inner value found in each individual in virtue of being human. That inner worth engenders certain universal rights—derivable from the dignity and fundamental rational appeal of morality—just as it provides for the possibility for a community of beings to seek to live the moral life. (shrink)

This dissertation provides an account of individual autonomy. It begins by arguing that the dispute, in social and political philosophy, between negative and positive conceptions of liberty, can only be solved based on a theory of autonomy. The bulk of the dissertation then defends the view that individual autonomy consists in the capacity to regulate one's actions by values that are one's own in virtue of having been adopted through a process of critical reflection. ;This sort of view is regarded (...) with suspicion by those who doubt that rational judgment is central to a person's self, or identity. In particular, conative hierarchy views analyze autonomy as the capacity to act according to higher-order desires. But by doing so, they trivialize real worries about the possibility of achieving autonomy: Marxist social theory and Freudian psychoanalytic theory both seem to imply that autonomy is very difficult to achieve, and yet they do not pose any threat to the kind of "autonomy" described by conative hierarchy theories. Conative hierarchy theory fails to show that highest-order desires have special authority. ;Conative history theory recognizes that autonomy involves historical features in addition to structural ones. According to one version of that theory, a desire is autonomous if its subject would not have resisted its development, had she reflected on it with all relevant information about the processes involved, and with 'minimal rationality'. But the test fails when applied to hard cases, because it ignores the way in which the person's motives must depend causally upon her rational capacities. Furthermore, this view mistakenly follows conative hierarchy theory in denying the relevance of the distinction between a person's evaluative judgment and her mere desires. ;The conception of autonomy I defend derives support from the shortcomings of the two types of conative view. Their focus on desires masks the importance of values, principles, and ends. Most importantly, however, their shortcomings indicate that an autonomous person's values must be contingent upon critical reflection, which is free from certain irrational influences, even if its principles lack the universal validity of a categorical imperative. (shrink)

Chaos theory of the 1977 Nobel Prize laureate I. Prigogine allows to consider any religious system as a dissipative structure, the development of which corresponds to the leading characteristics of chaotic systems. It should be noted that dissipative structures are called systems whose activity creates chaos, which destroys the existing order and, at the same time, is the basis for the emergence of self-organization and higher-order order. Modern scientific studies have proved the universal nature of nonlinear (...) systems, have shown that isolated systems do not exist in the world at all - everything is interconnected. This fully applies to the development of religious systems. (shrink)

The conclusion of this chapter is that higher-order vagueness is universal: no sentence whatsoever is definitely true, definitely definitely true, definitely definitely definitely true, and so on ad infinitum. The argument, of which there are several versions, turns on the existence of Sorites sequences of possible worlds connecting the actual world to possible worlds where a given sentence is used in such a way that its meaning is very different. The chapter attempts to be neutral between competing accounts (...) of the nature of vagueness and definiteness. (shrink)

Can conjunctive propositions be identical without their conjuncts being identical? Can universally quantified propositions be identical without their instances being identical? On a common conception of propositions, on which they inherit the logical structure of the sentences which express them, the answer is negative both times. Here, it will be shown that such a negative answer to both questions is inconsistent, assuming a standard type-theoretic formalization of theorizing about propositions. The result is not specific to conjunction and universal quantification, but (...) applies to any binary operator and propositional quantifier. It is also shown that the result essentially arises out of giving a negative answer to both questions, as each negative answer is consistent by itself. (shrink)

A.1. Some philosophers, including Tarski and Russell, have concluded from a study of various versions of the Liar Paradox ‘that there must be a hierarchy of languages, and that the words “true” and “false”, as applied to statements in any given language, are themselves words belonging to a language of higher order’. In his famous essay on truth Tarski claimed that ‘colloquial’ language is inconsistent as a result of its property of ‘universality’: that is, whatever can be said (...) at all can in principle be said in it, with an extended vocabularly if necessary. Thus, in English we can talk about English expressions, what they denote, what they say, whether what they say is true or false, and so on: English contains its own metalanguage. This universality enables us to construct sentences which say of themselves that they are false, and by applying the law of excluded middle to them we easily derive a contradiction. Tarski concludes that ‘these antinomies seem to provide a proof that every language which is universal in the above sense, and for which the normal laws of logic hold, must be inconsistent’ . He then proposes to avoid such contradictions by the use of a hierarchy of languages such that statements about any one language can be made only in a different language at a higher level. (shrink)

This volume began as a remembrance of Alonzo Church while he was still with us and is now finally complete. It contains papers by many well-known scholars, most of whom have been directly influenced by Church's own work. Often the emphasis is on foundational issues in logic, mathematics, computation, and philosophy - as was the case with Church's contributions, now universally recognized as having been of profound fundamental significance in those areas. The volume will be of interest to logicians, computer (...) scientists, philosophers, and linguists. The contributions concern classical first-order logic, higher-order logic, non-classical theories of implication, set theories with universal sets, the logical and semantical paradoxes, the lambda-calculus, especially as it is used in computation, philosophical issues about meaning and ontology in the abstract sciences and in natural language, and much else. The material will be accessible to specialists in these areas and to advanced graduate students in the respective fields. (shrink)

This paper is a historical companion to a previous one, in which it was studied the so-called abstract Galois theory as formulated by the Portuguese mathematician José Sebastião e Silva ). Our purpose is to present some applications of abstract Galois theory to higher-order model theory, to discuss Silva's notion of expressibility and to outline a classical Galois theory that can be obtained inside the two versions of the abstract theory, those of Mark Krasner and of Silva. Some (...) comments are made on the universal theory of structures. (shrink)

The premises that a four foot man is short and that a man one tenth of an inch taller than a short man is also short entail by universal instantiation and "modus ponens" that a seven foot man is short. The negation of the second premise seems to entail there are virtually no borderline cases of short men, While to deny the second premise and its negation conflicts with the principle of bivalence, If not excluded middle. But the paradox can (...) be dissolved without resort to degrees of truth or any non-Classical system of logic. If some true predications can be semantically uncertain in a sense suitable for defining borderline cases, The second premise can be denied without denying the vagueness of "short" or reintroducing a sorites paradox along with higher order borderline cases. (shrink)

The unified theory of dose and effect, as indicated by the median-effect equation for single and multiple entities and for the first and higher order kinetic/dynamic, has been established by T.C. Chou and it is based on the physical/chemical principle of the massaction law (J. Theor. Biol. 59: 253-276, 1976 (質量作用中效定理) and Pharmacological Rev. 58: 621-681, 2006) (普世中效指數定理). The theory was developed by the principle of mathematical induction and deduction (數學演繹歸納法). Rearrangements of the median-effect equation lead to Michaelis-Menten, (...) Hill, Scatchard, and Henderson-Hasselbalch equations. The “median” serves as the universal reference point and the “common link” for the relationship of all entities and is also the “harmonic mean” of kinetic dissociation constants. Over 300 mechanism-specific equations have been derived and published using the mathematical induction-deduction process. These equations can be deduced into several general equations, including the median-mediated whole/part equation, combination index theorem, isobologram equation, and polygonogram. It is proven that “dose” and “effect” are interchangeable, thus, “substance” and “function” are interchangeable, which leads to “the unity theory” (劑效、心物、知行一元論) in quantitative mathematical philosophy (數學的定量哲學) in functional context. Therefore, a general theory centered on the “median” and based on equilibrium dynamics has evolved. In other words: [「中」的宇宙觀： 以「中」爲基凖的動力學生態平衡]. Based on the median-effect equation of the mass-action law, the fundamental claim is that we can draw “a specific cure” for only two data points, if they are determined accurately. This claim has far reaching consequences since it defies the general held belief that two points can dray only a straight line. Remarkably, the unity theory (一元論) providesscientific/mathematical interpretation in equations and in graphics of Chinese ancient philosophy, including Fu-Si Ba Gua (伏羲八卦), Dao’s Harmony (和諧), the Confucian doctrine of the mean (儒家中庸之道), Chou Dun-Yi’s (周敦頤, 1017-1073) From Wu-ji to Tai-ji and Taiji Tu Sho (無極而太極及太極圖說). The moderntopological analysis for trinity yields an exact correspondence to the Ba-Gua, which was introduced over 4,000 years ago. Furthermore, the median-centered algorithm, promotes modern ecological content (生態學) in the equilibral dynamic state of harmony. It is concluded that Western science and Eastern philosophy are directly linked and complementary to each other. Since the truth in mathematical quantitative philosophy (數學的定量哲學) has no boundaries, East and West philosophies can flourish together for the common goal and ideal in science and in humanity (世界大同). (shrink)

Principia Logico-Metaphysica contains a foundational logical theory for metaphysics, mathematics, and the sciences. It includes a canonical development of Abstract Object Theory [AOT], a metaphysical theory that distinguishes between ordinary and abstract objects. This article reports on recent work in which AOT has been successfully represented and partly automated in the proof assistant system Isabelle/HOL. Initial experiments within this framework reveal a crucial but overlooked fact: a deeply-rooted and known paradox is reintroduced in AOT when the logic of complex terms (...) is simply adjoined to AOT’s specially formulated comprehension principle for relations. This result constitutes a new and important paradox, given how much expressive and analytic power is contributed by having the two kinds of complex terms in the system. Its discovery is the highlight of our joint project and provides strong evidence for a new kind of scientific practice in philosophy, namely, computational metaphysics. Our results were made technically possible by a suitable adaptation of Benzmüller’s metalogical approach to universal reasoning by semantically embedding theories in classical higher-order logic. This approach enables one to reuse state-of-the-art higher-order proof assistants, such as Isabelle/HOL, for mechanizing and experimentally exploring challenging logics and theories such as AOT. Our results also provide a fresh perspective on the question of whether relational type theory or functional type theory better serves as a foundation for logic and metaphysics. (shrink)

Computational complexity is a discipline of computer science and mathematics which classifies computational problems depending on their inherent difficulty, i.e. categorizes algorithms according to their performance, and relates these classes to each other. P problems are a class of computational problems that can be solved in polynomial time using a deterministic Turing machine while solutions to NP problems can be verified in polynomial time, but we still do not know whether they can be solved in polynomial time as well. A (...) solution for the so-called NP-complete problems will also be a solution for any other such problems. Its artificial-intelligence analogue is the class of AI-complete problems, for which a complete mathematical formalization still does not exist. In this chapter we will focus on analysing computational classes to better understand possible formalizations of AI-complete problems, and to see whether a universal algorithm, such as a Turing test, could exist for all AI-complete problems. In order to better observe how modern computer science tries to deal with computational complexity issues, we present several different deep-learning strategies involving optimization methods to see that the inability to exactly solve a problem from a higher order computational class does not mean there is not a satisfactory solution using state-of-the-art machine-learning techniques. Such methods are compared to philosophical issues and psychological research regarding human abilities of solving analogous NP-complete problems, to fortify the claim that we do not need to have an exact and correct way of solving AI-complete problems to nevertheless possibly achieve the notion of strong AI. (shrink)

Principia Logico-Metaphysica contains a foundational logical theory for metaphysics, mathematics, and the sciences. It includes a canonical development of Abstract Object Theory [AOT], a metaphysical theory that distinguishes between ordinary and abstract objects.This article reports on recent work in which AOT has been successfully represented and partly automated in the proof assistant system Isabelle/HOL. Initial experiments within this framework reveal a crucial but overlooked fact: a deeply-rooted and known paradox is reintroduced in AOT when the logic of complex terms is (...) simply adjoined to AOT’s specially formulated comprehension principle for relations. This result constitutes a new and important paradox, given how much expressive and analytic power is contributed by having the two kinds of complex terms in the system. Its discovery is the highlight of our joint project and provides strong evidence for a new kind of scientific practice in philosophy, namely, computational metaphysics.Our results were made technically possible by a suitable adaptation of Benzmüller’s metalogical approach to universal reasoning by semantically embedding theories in classical higher-order logic. This approach enables one to reuse state-of-the-art higher-order proof assistants, such as Isabelle/HOL, for mechanizing and experimentally exploring challenging logics and theories such as AOT. Our results also provide a fresh perspective on the question of whether relational type theory or functional type theory better serves as a foundation for logic and metaphysics. (shrink)

Cartwright’s self-proclaimed philosophical heritage includes Aristotle and Otto Neurath. Her Aristotelianism includes the view that the aim of science is the identification of the capacities of things in nature. From Neurath she takes a “patchwork” view of theories according to which theories do not fit into an unified whole in which higher-order sciences reduce, in some way, to lower-order sciences. Instead, theories work for particular kinds of phenomena and there is no guarantee that any theory will work (...) outside of those situations for which it was constructed. Cartwright maintains that theories and laws may provide true descriptions of the world, but no one theory or set of laws is universal. She argues that, since laws and theories are not universal, all laws are ceteris paribus. The achievement of science does not rest on knowledge of laws, but knowledge of the capacities that the things in the world possess. (shrink)

The conclusion of this chapter is that higher-order vagueness is universal: no sentence whatsoever is definitely true, definitely definitely true, definitely definitely definitely true, and so on ad infinitum. The argument, of which there are several versions, turns on the existence of Sorites sequences of possible worlds connecting the actual world to possible worlds where a given sentence is used in such a way that its meaning is very different. The chapter attempts to be neutral between competing accounts (...) of the nature of vagueness and definiteness. (shrink)

Minimalism is the view that our concept of truth is constituted by our disposition to accept instances of the truth schema ‘The proposition that p is true if and only if p’. The generalisation problem is the challenge to account for universal generalisations concerning logical truths such as ‘Every proposition of the form 〈if p, then p〉 is true’. This paper argues that such generalisations can be deduced using a single example of the logical truth in question and a single (...) corresponding instance of the truth schema, employing the logical method of reasoning with arbitrary instances of universal and existential generalisations. Suggesting an inferentialist construal of Minimalism, the paper introduces conditional and general acceptance dispositions, distinguishes inferential meaning constitution from implicit definition, highlights the inferential nature of acceptance of instances of the truth schema, sketches a suitable account of structured propositions, compares higher-order with first-order means of quantification, and argues that the conception of truth Minimalism attributes to ordinary speakers is essentially inferential. It finally applies the deductive strategy to generalisations concerning logical validity as well as more complex logical truths. (shrink)

This paper refers to the connection between the metaphysical duality of ground and existence and inner dynamic of the particular will of man. We will analyse how the metaphysical monism, which Schelling attributes to Spinoza and later to Hegel, is responsible for the abolition of the freedom of the human individual, because it does not account for the existence of evil, and consequently reduces it to the existence of a higher order reference system that over and predetermines the (...) individual (1). We will first scrutinise the principles of separation and union, ground and understanding from the human point of view, namely as the will of ground and love, as particular and universal will (2). The will of man reveals itself as the culmination and model of the will that permeates nature, an essential aspect of the process of God’s revelation and becoming. The link between the principles of separation and union shows us the difference that Schellingian thought establishes between man and God, the real and the ideal. While God, or the purely ideal principle, precedes the separation in a logical-ontological sense, the will of man remains always in an indissoluble tension between the principles, since it is unable to overcome the opposition between good and evil that is characteristic of freedom. The good remains one of the results of human freedom and thus of the particular will of man. The good lies for Schelling not in the simple actualization of the general, but in the moment ineradicable particularity needed for the attainment of a real and effective principle (3). It is to this insurmountability of the particular will in the process of the constitution of man that our proposal of Schelling’s libertarian anarchism refers. The connection of this thesis with the critique of the State is also discussed (4). (shrink)

Even in psychological literature, which describes many determining variables related to the school domain, few studies have investigated the universal mechanism underlying parent–child relations, which is a prototype matrix for future student–teacher relations. The role of the imprinted schema of children’s obligations toward parents seems to be crucial for school functioning in classroom society. The Dual Filial Piety Model is comprised of two higher-order factors that correspond to the two focal filial piety attributes: reciprocal and authoritarian, which have (...) been shown to have distinct implications on social adaptation and individuals’ psychological functioning. In this study, we investigate the relationship between filial piety and student attitudes in a more individualistic and egalitarian culture and in a more collectivistic and hierarchical society. The measurement invariances of three scales, i.e., the Vietnamese adaptation of DFP Scale, the Utrecht Work Engagement Scale, and the Study Satisfaction Scale, were improved in the MLM analyses. Our results show that in more individualistic cultures, the RFP is a stronger predictor of study engagement and study satisfaction; however, the AFP is a better factor to predict study engagement in more collectivistic cultures. What is more, only RFP positively correlates with study satisfaction in individualistic culture. Our findings revealed that in different cultures, different aspects of filial piety should be emphasized by parents in the context of the future academic achievements of their children. The conclusion is that the prevention and intervention strategies or techniques intended for children with school problems should be culturally appropriate and addressed to the parents of kindergarten and later to very early-stage education teachers. The results of studies based on the DFPM may stimulate practical applications and policy development within the domain of success and failure in the academic environment. (shrink)

Despite universal agreement that corruption is norm-deviant, the criteria required to ascertain deviance remain elusive. The problem is even more pronounced for organizational corruption, not least because the construct remains somewhat ambiguous and is often conflated with proximate management constructs like antisocial or unethical organizational behavior. In this article, I identify the suitable criteria for the determination of deviance in organizational corruption and determine whether it is, indeed, antisocial or unethical. In order to minimize ambiguity, I first limit the (...) scope of organizational corruption to corruption within, rather than by, organizations, which is most conceptually challenging insofar as the aforementioned questions are concerned. I then conclude that organizational corruption should be specified solely with respect to the focal organization’s normative framework; it is anti-organizational rather than antisocial. Higher level normative prescriptions that arise from the organization’s embedding within its social context remain relevant, but only insofar as they are incorporated within the organization’s normative framework. Moreover, I argue that organizational corruption is not necessarily unethical, since the moral evaluation of an organizational act is, in principle, distinct from the determination of its deviance to organizational norms. (shrink)

There cannot be a reductive theory of modality constructed from the concepts of sparse particular and sparse universal. These concepts are suffused with modal notions. I seek to establish this conclusion by tracing out the pattern of modal entanglements in which these concepts are involved. In order to appreciate the structure of these entanglements a distinction must be drawn between the lower-order necessary connections in which particulars and universals apparently figure, and higher-order necesary connections. The (...) former type of connection relates specific entities. By contrast, the latter type of connection is unspecific: it relates entities to some others. I argue that whilst there may be techniques that succeed in providing reductive truth conditions for sentences that say particulars and universals figure in lower-order necessary connections, such techniques cannot succeed in providing reductive truth conditions for sentences that say these entities figure in higher-order necessary connections. I conclude that this situation leaves reductionists with a dilemma. If they wish to affirm that there are particulars and universals then the project of reducing modality by positing these entities must be abandoned. Alternatively, they may continue to deploy their usual reductive techniques but then they must abandon the doctrine that there is more than one fundamental category of entity. (shrink)

A novel conceptual framework is introduced for the Complexity Levels Theory in a Categorical Ontology of Space and Time. This conceptual and formal construction is intended for ontological studies of Emergent Biosystems, Super-complex Dynamics, Evolution and Human Consciousness. A claim is defended concerning the universal representation of an item’s essence in categorical terms. As an essential example, relational structures of living organisms are well represented by applying the important categorical concept of natural transformations to biomolecular reactions and relational structures that (...) emerge from the latter in living systems. Thus, several relational theories of living systems can be represented by natural transformations of organismic, relational structures. The ascent of man and other living organisms through adaptation, is viewed in novel categorical terms, such as variable biogroupoid representations of evolving species. Such precise but flexible evolutionary concepts will allow the further development of the unifying theme of local-to-global approaches to highly complex systems in order to represent novel patterns of relations that emerge in super- and ultra-complex systems in terms of compositions of local procedures. Solutions to such local-to-global problems in highly complex systems with ‘broken symmetry’ might be possible to be reached with the help of higher homotopy theorems in algebraic topology such as the generalized van Kampen theorems (HHvKT). Categories of many-valued, Łukasiewicz-Moisil (LM) logic algebras provide useful concepts for representing the intrinsic dynamic ‘asymmetry’ of genetic networks in organismic development and evolution, as well as to derive novel results for (non-commutative) Quantum Logics. Furthermore, as recently pointed out by Baianu and Poli (Theory and applications of ontology, vol 1. Springer, Berlin, in press), LM-logic algebras may also provide the appropriate framework for future developments of the ontological theory of levels with its complex/entangled/intertwined ramifications in psychology, sociology and ecology. As shown in the preceding two papers in this issue, a paradigm shift towards non-commutative, or non-Abelian, theories of highly complex dynamics—which is presently unfolding in physics, mathematics, life and cognitive sciences—may be implemented through realizations of higher dimensional algebras in neurosciences and psychology, as well as in human genomics, bioinformatics and interactomics. (shrink)

According to traditional universalism, properties are instantiated by objects, where instantiation is a ‘tie’ that binds objects and properties into facts. I offer two arguments against this view. I then develop an alternative higher-order account which holds that properties are primitively predicated of objects yet, unlike traditional nominalism, are nevertheless genuinely real. When it’s a fact that Fo, it’s not because object o instantiates F-ness, but just that Fo – where F still exists. Against orthodox higher-order (...) approaches, however, my arguments against instantiation also serve to support a sparse conception of properties. In developing the view, I introduce an extension of ontological and ideological commitment in the form of syntactic commitment. (shrink)

The paper considers recent proposals by Armstrong, Dretske, and Tooley that revive the view that statements of laws of nature are grounded by the existence of higher order facts relating universals. Several objections to such a view are raised and an alternative analysis, recognizing general facts, is considered. Such an alternative is shown to meet a number of the objections raised against the appeal to higher order facts and it is also related to views of (...) Hume and Wittgenstein. Further objections are then raised to all the non-Humean "realist" attempts to provide special facts to ground the laws of nature. (shrink)

In Bad Beliefs, Levy presents a picture of belief-forming processes according to which, on most matters of significance, we defer to reliable sources by relying extensively on cultural and social cues. Levy conceptualizes the kind of evidence provided by socio-cultural environments as higher-order evidence. But his notion of higher-order evidence seems to differ from those available in the epistemological literature on higher-order evidence, and this calls for a reflection on how exactly social and cultural (...) cues are/count as/provide higher-order evidence. In this paper, I draw on the three-tiered model of epistemic exchange that I have been developing recently, which highlights the centrality of relations of attention and trust in belief-forming processes, to explicate how social and cultural cues provide higher-order evidence. I also argue that Levy’s account fails to sufficiently address the issue of strategic actors who have incentives to pollute epistemic environments for their benefit, and more generally the power struggles, incentives, and competing interests that characterize human sociality. Levy’s attempted reduction of the political to the epistemic ultimately fails, but his account of social and cultural cues as higher-order evidence offers an insightful perspective on epistemic social structures. (shrink)

The subject matter of this thesis is analytic ontology. Chapters II and III deal with two versions of trope theory, or moderate nominalism; these are defined as ontologies which recognise properties and relations but no (real) universals. The key notion of both theories, trope, is characterised as an abstract particular. What the abstractness amounts to differs between the two. Yet another difference is that simplicity is an essential trait of a trope according to one theory, but not according to (...) the other. Though exact similarity is said to play an important role in both theories, as it turns out, this does not seem to be the case. The ontology dealt with in chapter IV is a mixture of moderate nominalism concerning qualities and realism concerning relations. In it, quality instances (moments) and universal relations are the ultimate constituents of the universe. While relations and moments are considered to be constituents of states of affairs, which are characterised as objects of higher orders, complexes that are objects of the first order are made up of moments on their own. Among these complexes one finds the ordinary objects. Paradoxically, although relations are necessary for the existence of complex first order objects, relations are not thought to be among the contents of these objects. The main subject of chapter V is a particular version of moderate realism; it is an ontology which is realistic in its recognition of universals and moderate in its recognition of instances of these universals. Instances combine to form complex networks. A theoretically motivated claim is that although each instance has a predicational aspect as well as a universal one, it is simple in the sense of lacking internal predicative structure; though, this claim can be called into question. Keywords: analytic ontology, moderate nominalism, moderate realism, particular, universal, abstract, concrete, abstract particular, abstract universal, concrete particular, concrete universal, trope, moment, complex unity, collection, instance, unit attribute, intensional aspect, predicational aspect, continuous composite, articulated composite. (shrink)

How well can we explain natural occurrences of cognitive behaviours given the theoretical frameworks available to us today? The thesis explores what has to be assumed in cognitive theory in order to provide such an explanation, in contrast to being able to predict behaviour under controlled circumstances. The behaviours considered are all of the type described as involving higher level cognition or being representation hungry. Examples are problem solving and certain types of decision-making. Three different theoretical frameworks are (...) examined: general theories such as Newell and Simon’s Universal Problem Solver, the stances sometimes referred to as “situated cognition,” particularly those that try to exclude cognitive components from their explanatory framework ; and domain-specific theories of cognition. The last category can broadly be separated into two different types of theories: those who claim that specialised cognitive processes are activated through situational features and those who claim that specialised cognitive processes are successful relative such features. The conclusion is that none of the stances are sufficient on their own. The proposed solution is instead to take both the hypothesised domain-specific process and the information it utilises into account. If we allow for “high-quality” information of a more domain-general nature, that indicates which parts of the current situation are important, or makes it possible for the individual to assume certain relations in advance, then this information can account for parts of the flexibility and stability required of the cognitive processes. Examples of such information are causal relations and epistemic information connected to social information. Since these point us to how the features of the situation at hand were produced, they help us identify relevant aspects of, and relations between different situations. By utilising high-quality information, domain-specific processes can be made broader, and less specialised, while keeping a close tie to the situations in which they are active. In this way we can begin to explain real life cognitive behaviours. (shrink)