Central figures in the phenomenological tradition, such as Aron Gurwitsch, Jean-Paul Sartre, and Maurice Merleau-Ponty, drew extensively on gestalt psychology in their writings. The dialogue between phenomenology and psychology they began continues today in the field of embodied cognitive science. We take up this conversation starting from Aron Gurwitsch’s rich phenomenological analysis of the perception of the cultural world. Gurwitsch’s phenomenological descriptions of the perception of the cultural world bear a striking resemblance to work in embodied cognitive science that takes (...) its inspiration from Gibson’s ecological psychology. Gibson coined the term “affordance” to refer to the possibilities for action that can be directly perceived by persons [Gibson 1979]. However, Gibson from his earliest writings made a distinction between a universal, strictly individual and nonsocial form of perception and a perception of the world that was subject to social and cultural influences. We use Gurwitsch to argue against Gibson’s individualist understanding of direct perception. Each affordance that can be selected as an object of perception refers to a wider sociocultural context, which Gurwitsch called an “order of existence”. We end our paper by taking up the question of the relation of phenomenological description of the perceptual world and explanations of perceptual experience provided by embodied cognitive science. (shrink)

The ontological argument fails because of an operator order switch between (1) “necessarily there is an perfect being” and (2) “there is a being which necessarily is perfect”. Here (1) is trivially true logically but (2) problematic. Since Kant's criticisms were directed at the notion of existence, not at the step from (1) to (2), they are misplaced. They are also wrong, because existence can be a predicate. Moreover, Kant did not anticipate Frege's claim that “is” is ambiguous (...) between existence, predication, identity, and class‐inclusion. To restore the ontological argument, an extra premise is needed to the effect that it is known who the existentially perfect being is. The question is raised whether Kant could have meant the failure of this extra premise by his thesis that existence is not a real predicate. (shrink)

We continue with the study of the Katětov order on MAD families. We prove that Katětov maximal MAD families exist under $\mathfrak {b=c}$ and that there are no Katětov-top MAD families assuming $\mathfrak {s\leq b}.$ This improves previously known results from the literature. We also answer a problem form Arciga, Hrušák, and Martínez regarding Katětov maximal MAD families.

The aim of the present paper is to provide a robust classification of valid sentences in set theory by means of existence and related notions and, in this way, to capture similarities and dissimilarities among the axioms of set theory. In order to achieve this, precise definitions for the notions of productive and nonproductive assertions, constructive and nonconstructive productive assertions, and conditional and unconditional productive assertions, among others, will be presented. These definitions constitute the result of a semantical analysis (...) of the notions involved. The conceptual clarification developed here results in a classification of valid sentences of set theory that goes against the standard view that extensionality is not an existence assertion. (shrink)

The Artin‐Schreier theorem says that every formally real field has orders. Friedman, Simpson and Smith showed in [6] that the Artin‐Schreier theorem is equivalent to over. We first prove that the generalization of the Artin‐Schreier theorem to noncommutative rings is equivalent to over. In the theory of orderings on rings, following an idea of Serre, we often show the existence of orders on formally real rings by extending pre‐orders to orders, where Zorn's lemma is used. We then prove that (...) “pre‐orders on rings not necessarily commutative extend to orders” is equivalent to. (shrink)

Linguistic category learning has been shown to be highly sensitive to linear order, and depending on the task, differentially sensitive to the information provided by preceding category markers (premarkers, e.g., gendered articles) or succeeding category markers (postmarkers, e.g., gendered suffixes). Given that numerous systems for marking grammatical categories exist in natural languages, it follows that a better understanding of these findings can shed light on the factors underlying this diversity. In two discriminative learning simulations and an artificial language learning experiment, (...) we identify two factors that modulate linear order effects in linguistic category learning: category structure and the level of abstraction in a category hierarchy. Regarding category structure, we find that postmarking brings an advantage for learning category diagnostic stimulus dimensions, an effect not present when categories are non‐confusable. Regarding levels of abstraction, we find that premarking of super‐ordinate categories (e.g., noun class) facilitates learning of subordinate categories (e.g., nouns). We present detailed simulations using a plausible candidate mechanism for the observed effects, along with a comprehensive analysis of linear order effects within an expectation‐based account of learning. Our findings indicate that linguistic category learning is differentially guided by pre‐ and postmarking, and that the influence of each is modulated by the specific characteristics of a given category system. (shrink)

Linguistic category learning has been shown to be highly sensitive to linear order, and depending on the task, differentially sensitive to the information provided by preceding category markers (premarkers, e.g., gendered articles) or succeeding category markers (postmarkers, e.g., gendered suffixes). Given that numerous systems for marking grammatical categories exist in natural languages, it follows that a better understanding of these findings can shed light on the factors underlying this diversity. In two discriminative learning simulations and an artificial language learning experiment, (...) we identify two factors that modulate linear order effects in linguistic category learning: category structure and the level of abstraction in a category hierarchy. Regarding category structure, we find that postmarking brings an advantage for learning category diagnostic stimulus dimensions, an effect not present when categories are non‐confusable. Regarding levels of abstraction, we find that premarking of super‐ordinate categories (e.g., noun class) facilitates learning of subordinate categories (e.g., nouns). We present detailed simulations using a plausible candidate mechanism for the observed effects, along with a comprehensive analysis of linear order effects within an expectation‐based account of learning. Our findings indicate that linguistic category learning is differentially guided by pre‐ and postmarking, and that the influence of each is modulated by the specific characteristics of a given category system. (shrink)

Central figures in the phenomenological tradition, such as Aron Gurwitsch, Jean-Paul Sartre, and Maurice Merleau-Ponty, drew extensively on gestalt psychology in their writings. The dialogue between phenomenology and psychology they began continues today in the field of embodied cognitive science. We take up this conversation starting from Aron Gurwitsch’s rich phenomenological analysis of the perception of the cultural world. Gurwitsch’s phenomenological descriptions of the perception of the cultural world bear a striking resemblance to work in embodied cognitive science that takes (...) its inspiration from Gibson’s ecological psychology. Gibson coined the term “affordance” to refer to the possibilities for action that can be directly perceived by persons [Gibson 1979]. However, Gibson from his earliest writings made a distinction between a universal, strictly individual and nonsocial form of perception and a perception of the world that was subject to social and cultural influences. We use Gurwitsch to argue against Gibson’s individualist understanding of direct perception. Each affordance that can be selected as an object of perception refers to a wider sociocultural context, which Gurwitsch called an “order of existence”. We end our paper by taking up the question of the relation of phenomenological description of the perceptual world and explanations of perceptual experience provided by embodied cognitive science. (shrink)

In (2001), (2003), and elsewhere, Ted Sider presents two arguments concerning the existential quantifier which are justly central to the recent discussion of metaontology. What we will call Sider's indeterminacy argument is an attempted reductio of the suggestion that the existential quantifier might be semantically indeterminate. What we will call Sider's naturalness argument is an argument for the claim that the semantic value of the existential quantifier is the most eligible existence-like meaning there is, à la David Lewis' eligibility (...) theory of meaning. We will argue that these arguments cannot be jointly maintained: Sider must give up at least one. Before arguing this, we will present Sider's two arguments in a bit more detail, and discuss their relationship. A few remarks on the broader significance of our conclusions are in order at the outset. One may think that since one successful argument for a given conclusion is sufficient the point that Sider's arguments cannot both work is purely academic. But we think that Sider's two arguments at bottom reflect different ways of thinking about metaphysics. Moreover, we think that it is only the naturalness argument that promises to deliver all that Sider wants when it comes to metaontology, and it is only the indeterminacy argument that promises to deliver all that Sider wants when it comes to ontology. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Some Reflections on Hume on Existence Stanley Tweyman In this paper, I focus on two claims which Hume makes with regard to existence. The first, which appears in a single paragraph inA Treatise ofHumanNature 1.2.6,1 is that existence cannotbe distinguishedfrom what we believe exists by a "distinction ofreason." The second appears in the Dialogues Concerning Natural Religion when Cleanthes criticizes Demea's a priori argument. Much of (...) Cleanthes' criticism of Demea's argument is developed from the Humean claim that, "Whatever we conceive as existent, we can also conceive as non-existent."2 My efforts are directed to showing that, although Hume takes very little space developing each of these points, certain difficulties attend each claim—difficulties which Hume either does not (in the case of the first) or cannot (in the case of the second) address when the claim itself is being made. Distinctions ofReason and the Thought ofExistence Among the distinctions which Hume introduces very early in the Treatise is that between simple and complex perceptions. Simple perceptions are those which admit of no distinction or separation, whereas those which are complex can be distinguished into the simple perceptions of which they are composed through the power that the imagination possesses ofproducing a separation wherever it perceives a difference. A simple perception, therefore, is a perceptual primitive that is not reducible into parts, that is, into the other more basic perceptions. Hume argues that although simple perceptions are not amenable to further distinctions in terms of parts, they are still susceptible to distinctions ofreason. As examples ofthis distinction,he speaks of "figure and the body figur'd; motion and the body movM" (T 24). The actual example employed in his discussion (T 25) is the distinction between the colour and figure in a globe of white marble. Hume points out that when presented with a globe ofwhite marble, the colour is inseparable and indistinguishable from the form or figure. However, ifwe also observe aglobe ofblack marble and a cube ofwhite marble, and compare them with the globe of white marble, we will be able to distinguish the colour and figure of the latter through the resemblances it has with the other two objects. That is, the colour of the globe resembles the colour of the cube, and the figure of the globe Volume XVIII Number 2 137 STANLEY TWEYMAN resembles the figure of the black marble. The awareness of these resemblances Hume refers to as "akind ofreflection" or "comparison," and that to which we are attending—in this case the colour of the figure—he refers to as an "aspect" (T 25). Thus, although simple perceptions lack parts, they do possess aspects—aspects which are discovered through finding resemblances between the perception in question and others: "we consider the figure and colour together, since they are in effect the same and undistinguishable; but still view them in different aspects, according to the resemblances, of which they are susceptible" (T 25). The factthatHume offers a separate name for the operation under discussion makes it appear as though it is a separate operation ofthe mind not yet covered in his discussion. However, this is not the case. Distinctions ofreason are made through comparing an idea with other ideas in order to determine certain resemblances between them. But all comparisons between ideas are regarded by Hume as attempts to establish philosophical relations between them: "The word Relation is... used... for that particular circumstance, in which, even upon the arbitrary union of two ideas in the fancy, we may think proper to compare them" (T 13). The text reveals that by the expression "that particularcircumstance"in the precedingquotation Hume isreferring to some resemblance or other which enables the two ideas to be compared: "resemblance:... is a relation, without which no philosophical relation can exist; since no objects will admit of comparison, but what have some degree ofresemblance" (T 14). What follows from this discussion is that distinctions of reason are nothing but the determination ofphilosophical relationsbetween a certain idea and others. Since philosophical relations exist between complex ideas, and since all distinctions ofreason are nothing but the establishment of philosophical relations, it follows that distinctions of reason can occur... (shrink)

Martin Heidegger devotes extensive discussion to medieval philosophers, particularly to their treatment of Truth and Being. On both these topics, Heidegger accuses them of forgetting the question of Being and of being responsible for subjugating truth to the modern crusade for certainty: ‘truth is denied its own mode of being’ and is subordinated ‘to an intellect that judges correctly’. Though there are some studies that discuss Heidegger’s debt to and criticism of medieval thought, particularly that of Thomas Aquinas, there is (...) no constructive reply to his assertions. As a result, Heidegger’s critique had an unprecedented effect on the credibility of medieval philosophy, whereby great portions of the philosophical community dismiss it altogether as an illegitimate Onto‐Theology. It is the aim of this study to offer a constructive reply that will fundamentally grapple with these allegations. By constructive reply we mean not only a reply that avoids the problems Heidegger raises regarding existence, essence and truth, but more importantly, one that uses Heidegger’s criticism in order to present a more insightful account of these notions. The present study is composed of two parts where the second serves as a sort of addendum. The first part, the core of this study, is an attempt to develop an understanding of the distinction between essence and existence that, on the one hand, accords with Heidegger’s criticism while on the other hand advances our understanding of how we think and understand reality. After presenting Heidegger’s depiction of Aquinas’s distinction between essence and existence (esse) as a real distinction, the study will present several views propounded by scholars of Aquinas regarding the status of this distinction. It will be argued that it is not clear whether the distinction is real, formal or conceptual, and that different types of distinction are applied in different places, particularly in regard to the phantasm that Aquinas considers essential to the human act of thinking. The second part diverges from the first part and focuses on Heidegger’s criticism of Aquinas’s conception of truth as adequation, i.e., what it is that grounds the possibility of truth as adequation. This divergence is necessary in order to present a full metaphysical response to Heidegger’s criticism. Since the aim of the present study is to argue that Aquinas’s philosophical system can contend with Heidegger’s criticism, a partial reply would greatly diminish its effectiveness. (shrink)

We examine second order intuitionistic propositional logic, IPC². Let $F_\exists $ be the set of formulas with no universal quantification. We prove Glivenko's theorem for formulas in $F_\exists $ that is, for φ € $F_\exists $ φ is a classical tautology if and only if ¬¬φ is a tautology of IPC². We show that for each sentence φ € $F_\exists $ (without free variables), φ is a classical tautology if and only if φ is an intuitionistic tautology. As a corollary (...) we obtain a semantic argument that the quantifier V is not definable in IPC² from ⊥, V, ^, →. (shrink)

We simultaneously generalize Silver’s perfect set theorem for co-analytic equivalence relations and Harrington-Marker-Shelah’s Dilworth-style perfect set theorem for Borel quasi-orders, establish the analogous theorem at the next definable cardinal, and give further generalizations under weaker definability conditions.

In 2004 Atserias, Kolaitis, and Vardi proposed $\text {OBDD}$ -based propositional proof systems that prove unsatisfiability of a CNF formula by deduction of an identically false $\text {OBDD}$ from $\text {OBDD}$ s representing clauses of the initial formula. All $\text {OBDD}$ s in such proofs have the same order of variables. We initiate the study of $\text {OBDD}$ based proof systems that additionally contain a rule that allows changing the order in $\text {OBDD}$ s. At first we consider a proof (...) system $\text {OBDD}$ that uses the conjunction rule and the rule that allows changing the order. We exponentially separate this proof system from $\text {OBDD}$ proof system that uses only the conjunction rule. We prove exponential lower bounds on the size of $\text {OBDD}$ refutations of Tseitin formulas and the pigeonhole principle. The first lower bound was previously unknown even for $\text {OBDD}$ proofs and the second one extends the result of Tveretina et al. from $\text {OBDD}$ to $\text {OBDD}$.In 2001 Aguirre and Vardi proposed an approach to the propositional satisfiability problem based on $\text {OBDD}$ s and symbolic quantifier elimination $ algorithms). We augment these algorithms with the operation of reordering of variables and call the new scheme $\text {OBDD}$ algorithms. We notice that there exists an $\text {OBDD}$ algorithm that solves satisfiable and unsatisfiable Tseitin formulas in polynomial time, but we show that there are formulas representing systems of linear equations over $\mathbb {F}_2$ that are hard for $\text {OBDD}$ algorithms. Our hard instances are satisfiable formulas representing systems of linear equations over $\mathbb {F}_2$ that correspond to checksum matrices of error correcting codes. (shrink)

We generalize Kada’s definable strengthening of Dilworth’s characterization of the class of quasi-orders admitting an antichain of a given finite cardinality.

The legitimacy of the dominant intensive meat production system with respect to the issue of animal welfare is increasingly being questioned by stakeholders across the meat supply chain. The current meat supply is highly undifferentiated, catering only for the extremes of morality concerns (i.e., conventional vs. organic meat products). However, a latent need for compromise products has been identified. That is, consumer differences exist regarding the trade-offs they make between different aspects associated with meat consumption. The heterogeneity in consumer demand (...) could function as a starting point for market segmentation, targeting and positioning regarding animal welfare concepts that are differentiated in terms of animal welfare and price levels. Despite this, stakeholders in the meat supply chain seem to be trapped in the dominant business model focused on low cost prices. This paper aims to identify conflicting interests that stakeholders in the meat supply chain experience in order to increase understanding of why heterogeneous consumer preferences are not met by a more differentiated supply of meat products produced at different levels of animal welfare standards. In addition, characteristics of the supply chain that contribute to the existence of high exit barriers and difficulty to shift to more animal-friendly production systems are identified. Following the analysis of conflicting interests among stakeholders and factors that contribute to difficulty to transform the existing dominant regime, different routes are discussed that may help and motivate stakeholders to overcome these barriers and stimulate the creation of new markets. (shrink)

The paper is inspired by and explicitly presupposes the readers’ knowledge of the Kürbis normalization procedure for the Milne tree-like natural deduction system _C_ for classical propositional logic. The novelty of _C_ is that for each conventional connective, it has only _general_ introduction and elimination rules, whose paradigm is the rule of proof by cases. The present paper deals with the Milne–Kürbis troublemaker—adding universal quantifier—caused by extending the normalization procedure to \(\mathbf {C^{\exists }_{\forall }} \), the first-order variant of _C_. (...) For both quantifiers, \( \mathbf {C^{\exists }_{\forall }}\) has only general quantifier rules, whose paradigm is the indirect rule of existential elimination. We propose the classical first-order tree-like natural deduction system \( \mathbf {NC^{\exists }_{\forall }}\) such that it contains all the propositional and half the quantifier rules of \(\mathbf {C^{\exists }_{\forall }}\) and differs from it with respect to the other half of the quantifier rules and the notion of a deduction. We show that in the case of \(\mathbf {NC^{\exists }_{\forall }} \), whose specifics is based on the Quine treatment of _flagged_ variables in the linear-style natural deduction system as well as on the Aguilera-Baaz treatment of _characteristic_ and _side_ variables for sequent-style calculi, the troublemaker doesn’t occur. In order to handle another specifics of \(\mathbf {NC^{\exists }_{\forall }}\) —an auxiliary notion of a _finished_ deduction that makes deductions _nonhereditary_—we show soundness and completeness of \( \mathbf {NC^{\exists }_{\forall }} \). While emphasizing the former with the help of the Smirnov technique, we additionally indicate a fixable gap in the Quine soundness argument. At last, the philosophical significance of the main result of this paper is developed in more detail. (shrink)

We prove that the existence of atomic models for countable atomic theories does not hold for Ln the first order logic restricted to n variables for finite n > 2. Our proof is algebraic, via polyadic algebras. We note that Lnhas been studied in recent times as a multi-modal logic with applications in computer science. 2000 MATHEMATICS SUBJECT CLASSIFICATION. 03C07, 03G15.

The existent ethical relationships are the result of the historical amalgamation of objective and subjective conditions. Ethical relationships are essential relationships in the real and rational order, which are maintained by a system of regulations on morals, laws and customs, and infused with a spirit of subjectivity. Rationality and legitimacy are the primary concerns of those relationships. A distinction between morals and ethos needs to be made when studying ethical order. Sound ethical order lies in effective regulation of morals and (...) effective control of law. In the process of social reform, ethical order promotes social development through the dialectical movement of freedom and necessity. A harmonious society is a society which is based on legitimate and just ethical order. (shrink)

In the article we study the existence predicate \(\varepsilon\) in the context of semantics for first-order modal logic. For a formula \(\varphi\) we define \(\varphi^{\varepsilon}\) - the so called existence relativization. We point to a gap in the work of Fitting and Mendelsohn concerning the relationship between the truth of \(\varphi\) and \(\varphi^{\varepsilon}\) in classes of varying- and constant-domain models. We introduce operations on models which allow us to fill the gap and provide a more general perspective on (...) the issue. As a result we obtain a series of theorems describing the logical connection between the notion of truth of a formula with the existence predicate in constant-domain models and the notion of truth of a formula without the existence predicate in varying-domain models. (shrink)

In order to make sense of Scotus’s claim that rationality is perfected only by the will, a Scotistic doctrine of truth is developed in a speculative way. It is claimed that synthetic a priori truths are truths of the will, which are existential truths. This insight holds profound theological implications and is used on the one hand to criticize Kant's conception of existence, and on the other hand, to offer another explanation of the sense according to which the (...) class='Hi'>existence of things is grasped. (shrink)

Essays on Existence and Essence presents a series of writings--including several previously unpublished--by Bob Hale on the topics of ontology and modality. The essays develop and consolidate a number of themes central to his work and to contemporary metaphysics, logic, and philosophy of language. They display Hale's innovative approach to some of the most fundamental issues in philosophy, in dialogue with other leading philosophers. The notion of a definition is examined as it applies both to words--verbal definitions-and to things--real (...) definitions--and the relations between these are brought out in order to address problems in the metaphysics of necessity and the semantics and epistemology of modality. Hale argues for an essentialist theory of the source of necessity and our knowledge of it, and provides rigorous and inventive responses to problems such a theory might face. This theoretical framework is applied to the recently influential truthmaking approach to semantics and logic, developing an exact truthmaker account of universal quantification and modal statements. Other topics covered include the Fregean theory of ontological categories, the status of second-order logic, the metaphysics of numbers, and the nature of analytic propositions. The volume opens with a substantial introduction by Kit Fine, providing a critical examination of Hale's philosophy, and closes with a complete bibliography of Hale's writings. (shrink)

Some internal and philosophical remarks are made regarding a system of a second order logic of existence axiomatized by the author. Attributes are distinguished in the system according as their possession entails existence or not, The former being called e-Attributes. Some discussion of the special principles assumed for e-Attributes is given as well as of the two notions of identity resulting from such a distinction among attributes. Non-Existing objects are of course indiscernible in terms of e-Attributes. In addition, (...) However, Existing objects indiscernible in terms of e-Attributes are indiscernible in terms of all attributes. (shrink)

Thinking is a festival and thus human beings experience, through cogitation, the sociable structure of their thinking. As they think, speak and listen they listen and speak and they are in the company of others. It was Plato, the sociable one, who thus spoke and was listened to: “And thinking, is it the same thing to you as to me?” This is the question that Plato puts in Socrates's mouth, when faced with Theaetetus in a dialogue named after him. Theaetetus (...) in turn asks a question: “How do you describe it?” And Socrates replies: “As a discourse that the mind carries on with itself about any subject it is considering. …, but I have a notion that, when the mind is thinking, it is simply talking to itself, asking questions and answering them, and saying yes or no.”. (shrink)

This study considers Newton's views on space and time with respect to some important ontologies of substance in his period. Specifically, it deals in a philosophico-historical manner with his conception of substance, attribute, existence, to actuality and necessity. I show how Newton links these “features” of things to his conception of God's existence with respect of infinite space and time. Moreover, I argue that his ontology of space and time cannot be understood without fully appreciating how it relates (...) to the nature of Divine existence. In order to establish this, the ontology embodied in Newton's theory of predication is analysed, and shown to be different from the presuppositions of the ontological argument. From the historical point of view Gassendi's influence is stressed, via the mediation of Walter Charleton. Furthermore, Newton's thought on these matters is contrasted with Descartes's and Spinoza's. In point of fact, in his earliest notebook Newton recorded observations on Descartes's version of the ontological argument. Soon, however, he was to oppose the Cartesian conception of the actuality of Divine existence by means of arguments similar to those of Gassendi. Lastly, I suggest that the nature and extent of Henry More's influence on Newton's conception of how God relates to absolute space and time bears further examination. (shrink)

The legitimacy of the dominant intensive meat production system with respect to the issue of animal welfare is increasingly being questioned by stakeholders across the meat supply chain. The current meat supply is highly undifferentiated, catering only for the extremes of morality concerns (i.e., conventional vs. organic meat products). However, a latent need for compromise products has been identified. That is, consumer differences exist regarding the trade-offs they make between different aspects associated with meat consumption. The heterogeneity in consumer demand (...) could function as a starting point for market segmentation, targeting and positioning regarding animal welfare concepts that are differentiated in terms of animal welfare and price levels. Despite this, stakeholders in the meat supply chain seem to be trapped in the dominant business model focused on low cost prices. This paper aims to identify conflicting interests that stakeholders in the meat supply chain experience in order to increase understanding of why heterogeneous consumer preferences are not met by a more differentiated supply of meat products produced at different levels of animal welfare standards. In addition, characteristics of the supply chain that contribute to the existence of high exit barriers and difficulty to shift to more animal-friendly production systems are identified. Following the analysis of conflicting interests among stakeholders and factors that contribute to difficulty to transform the existing dominant regime, different routes are discussed that may help and motivate stakeholders to overcome these barriers and stimulate the creation of new markets. (shrink)

In this paper, an argument of Alvin Plantinga's for the existence of abstract possible worlds is shown to be unsound. The argument is based on a principle Plantinga calls "Quasicompactness", due to its structural similarity to the notion of compactness in first-order logic. The principle is shown to be false.

This work identifies the influence of chaos theory on fractional calculus by providing a theorem for the existence and stability of solution in fractional-order gyrostat model with the help of a fixed-point theorem. We modified an integer order gyrostat model consisting of three rotors into fractional order by attaching rotatory fuel-filled tank and provided an iterative scheme for our proposed model as a working rule of obtained analytical results. Moreover, this iterative scheme is injected into algorithms for a system (...) of integer order dynamical systems to observe Lyapunov exponents and a bifurcation diagram for our proposed fractional-order dynamical model. Furthermore, we obtained five equilibrium points, including four unstable spirals and one saddle node, using local dynamical analysis which acted as self-exciting attractors and a separatrix in a global domain. (shrink)

I examine the debate between substantivalists and relationalists about the ontological character of spacetime and conclude it is not well posed. I argue that the hole argument does not bear on the debate, because it provides no clear criterion to distinguish the positions. I propose two such precise criteria and construct separate arguments based on each to yield contrary conclusions, one supportive of something like relationalism and the other of something like substantivalism. The lesson is that one must fix an (...) investigative context in order to make such criteria precise, but different investigative contexts yield inconsistent results. I examine questions of existence about spacetime structures other than the spacetime manifold itself to argue that it is more fruitful to focus on pragmatic issues of physicality, a notion that lends itself to several different explications, all of philosophical interest, none privileged a priori over any of the others. I conclude by suggesting an extension of the lessons of my arguments to the broader debate between realists and instrumentalists. 1 Introduction2 The Hole Argument3 Limits of Spacetimes4 Pointless Constructions5 The Debate between Substantivalists and Relationalists6 Existence and Physicality: An Embarassment of Spacetime Structures7 Valedictory Remarks on Realism and Instrumentalism, and the Structure of Our Knowledge of Physics. (shrink)

We prove the following surprising property of Heyting's intuitionistic propositional calculus, IpC. Consider the collection of formulas, φ, built up from propositional variables (p,q,r,...) and falsity $(\perp)$ using conjunction $(\wedge)$ , disjunction (∨) and implication (→). Write $\vdash\phi$ to indicate that such a formula is intuitionistically valid. We show that for each variable p and formula φ there exists a formula Apφ (effectively computable from φ), containing only variables not equal to p which occur in φ, and such that for (...) all formulas ψ not involving $p, \vdash \psi \rightarrow A_p\phi$ if and only if $\vdash \psi \rightarrow \phi$ . Consequently quantification over propositional variables can be modelled in IpC, and there is an interpretation of the second order propositional calculus, IpC2, in IpC which restricts to the identity on first order propositions. An immediate corollary is the strengthening of the usual interpolation theorem for IpC to the statement that there are least and greatest interpolant formulas for any given pair of formulas. The result also has a number of interesting consequences for the algebraic counterpart of IpC, the theory of Heyting algebras. In particular we show that a model of IpC2 can be constructed whose algebra of truth-values is equal to any given Heyting algebra. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:HUME ON CONTINUED EXISTENCE AND THE IDENTITY OF CHANGING THINGS Most discussions of Hume's rather cursory treatment of coherence as a factor in generating belief in what he calls the continu' d existence of objects in Of Scepticism with Regard to the Senses, have taken a common line in interpreting the nature of the problem Hume's treatment is designed to solve. For instance, perhaps the two most (...) ex2 3 tensive discussions, those of Price and Gomberg seem to agree that the problem is: how do we fill in the gaps among our perceptions, complete sequences or series that are incomplete, and come to believe in the existence of a world of unperceived objects. At the same time such discussions have focussed on the issue of whether the inference from the coherence of our perceptions to belief in the continued existence of objects (ICCE) is, as Hume claims, distinguishable from causal inference. Hume is read in such a way that ICCE if not causal is at least quasi-causal; that is, the only difference for Hume between the two sorts of inference has been taken to be one concerning the evidence on which each is based — causal inferences on past constant conjunctions or uniformities, ICCE on something less. I believe that these discussions have invariably omitted a key factor in understanding Hume's treatment of coherence, one that I want to point out and develop in this paper. Hume's discussion of coherence, like his discussion of constancy, is bound up with the concept of identity; for belief in the continued existence of an object, which coherence generates, is a belief about its identity. Hence a causal inference is distinguished from ICCE by Hume as only the latter necessarily involves belief in the identity of an object over time. Once this is recognized, we can view Hume's discussion^of coherence as requiring an answer to the question: "How do we come to believe in the identity of changing things?" I want to consider two interpretations of 106. the exact nature of ICCE for Hume — one suggested by examples offered in his discussion of coherence, the other suggested by remarks about the concept of identity in other sections of Part Four of Book One of the Treatise — and to argue that neither satisfactorily answers this question. This failure raises doubts not only about ICCE but about the tenability of Hume's characterization of the "vulgar" view of perception and his view of identity. When Hume first answers the question, "What qualities of our impressions or perceptions lead us to attribute to them a distinct and continued existence,?" by isolating the qualities of constancy and coherence, I think it is clear that the former is invoked to account for objects which are, at least in a relative sense, unchanging, which have always appear 'd to me in the same order and return upon me without the least alteration (T194), while the latter is invoked especially, if not solely, to account for objects that underto rather large changes over time, things which after a little absence or interruption may become hardly knowable. (T195) Hume's example concerns a fire in his chamber, which undergoes great change from the moment he leaves (or perhaps the moment it is lighted) to the time he returns (or perhaps the time it is a bunch of glowing embers), but which, nevertheless, compared to other fires undergoes a like alteration...in a like time. (T195) Whatever more coherence can do, it is required, at least initially, to account for just those cases which cannot be subsumed under constancy, in other words, cases in which changing objects are taken to possess distinct and continued existence. In the famous paragraph following his initial comments on coherence, Hume seemingly proceeds to explain how coherence gives rise to belief in continued existence. The account runs basically as follows. Hume hears a noise, as of a door turning; he sees a porter coming toward him. But, Hume says, I never have observ' d3 that this noise could proceed from anything but the motion of a 107. door; and therefore conclude, that the present phaenomenon is a contradiction to all past experience... (shrink)

There exist two known types of ultrafilter extensions of first-order models, both in a certain sense canonical. One of them comes from modal logic and universal algebra, and in fact goes back to Jónsson and Tarski :891–939, 1951; 74:127–162, 1952). Another one The infinity project proceeding, Barcelona, 2012) comes from model theory and algebra of ultrafilters, with ultrafilter extensions of semigroups as its main precursor. By a classical fact of general topology, the space of ultrafilters over a discrete space is (...) its largest compactification. The main result of Saveliev The infinity project proceeding, Barcelona, 2012), which confirms a canonicity of this extension, generalizes this fact to discrete spaces endowed with an arbitrary first-order structure. An analogous result for the former type of ultrafilter extensions was obtained in Saveliev. Results of such kind are referred to as extension theorems. After a brief introduction, we offer a uniform approach to both types of extensions based on the idea to extend the extension procedure itself. We propose a generalization of the standard concept of first-order interpretations in which functional and relational symbols are interpreted rather by ultrafilters over sets of functions and relations than by functions and relations themselves, and define ultrafilter models with an appropriate semantics for them. We provide two specific operations which turn ultrafilter models into ordinary models, establish necessary and sufficient conditions under which the latter are the two canonical ultrafilter extensions of some ordinary models, and obtain a topological characterization of ultrafilter models. We generalize a restricted version of the extension theorem to ultrafilter models. To formulate the full version, we propose a wider concept of ultrafilter models with their semantics based on limits of ultrafilters, and show that the former concept can be identified, in a certain way, with a particular case of the latter; moreover, the new concept absorbs the ordinary concept of models. We provide two more specific operations which turn ultrafilter models in the narrow sense into ones in the wide sense, and establish necessary and sufficient conditions under which ultrafilter models in the wide sense are the images of ones in the narrow sense under these operations, and also are two canonical ultrafilter extensions of some ordinary models. Finally, we establish three full versions of the extension theorem for ultrafilter models in the wide sense. The results of the first three sections of this paper were partially announced in Poliakov and Saveliev On two concepts of ultrafilter extensions of first-order models and their generalizations, Springer, Berlin, 2017). (shrink)

I examine the debate between substantivalists and relationalists about the ontological character of spacetime and conclude it is not well posed. I argue that the hole argument does not bear on the debate, because it provides no clear criterion to distinguish the positions. I propose two such precise criteria and construct separate arguments based on each to yield contrary conclusions, one supportive of something like relationalism and the other of something like substantivalism. The lesson is that one must fix an (...) investigative context in order to make such criteria precise, but different investigative contexts yield inconsistent results. I examine questions of existence about spacetime structures other than the spacetime manifold itself to argue that it is more fruitful to focus on pragmatic issues of physicality, a notion that lends itself to several different explications, all of philosophical interest, none privileged a priori over any of the others. I conclude by suggesting an extension of the lessons of my arguments to the broader debate between realists and instrumentalists. 1 Introduction2 The Hole Argument3 Limits of Spacetimes4 Pointless Constructions5 The Debate between Substantivalists and Relationalists6 Existence and Physicality: An Embarassment of Spacetime Structures7 Valedictory Remarks on Realism and Instrumentalism, and the Structure of Our Knowledge of Physics. (shrink)

Avicenna's proof for the existence of God (the Necessary Existent) in the Metaphysics of the Salvation relies on the claim that every possible existent shares a common cause. I argue that Avicenna has good reason to hold this claim given that he thinks that (1) every essentially ordered causal series originates in a first, common cause and that (2) every possible existent belongs to an essentially ordered series. Showing Avicenna's commitment to 1 and 2 allows me to respond to (...) Herbert Davidson's and Richard Swinburne's claim that Avicenna's proof for the Necessary Existent is incomplete and fallacious -/- . (shrink)

The most common philosophical view about the notion of existence is that it is a second-order property or existential quantification. A less common view is that existence is a (first-order) property of 'existent' as opposed to 'nonexistent' (past or merely intentional) objects. An even less common view is that existence divides into different 'modes of being' for different sorts of entities. In this paper I will take a closer look at the semantic behavior of existence predicates (...) in natural language, such as exist, occur, and obtain, arguing that existence predicates in natural language support the two less common philosophical views. I will develop explicit analyses of existence predicates in their time-relative and space-relative uses which will explain why they apply to some kinds of entities, but not others. (shrink)

Russell is often taken as a forerunner of the Quinean position that “to be is to be the value of a bound variable”, whereupon the ontological commitment of a theory is given by what it quantifies over. Among other reasons, Russell was among the first to suggest that all existence statements should be analyzed by means of existential quantification. That there was more to Russell’s metaphysics than what existential quantifications come out as true is obvious in the earlier period (...) where Russell still made a distinction between existence and being/subsistence. But even the later Russell, including that of the Logical Atomism lectures period, would not have understood ontological questions to be first and foremost questions of quantification. He would take fundamentality to be important too, which explains in part his assertions to the effect the the values of individual variables have a reality not attributable to values of higher-order variables, even ineliminable higher-order variables. (shrink)

We introduce several concepts concerning the indiscernibility of trees. A tree is by definition an ordered set such that, for any a∈O, the initial segment {b∈O:b (...) A of the form η∈O, where O is a tree, and aη labeled by η is an element in M. Such a set A is also called a tree in this paper. We study the indiscernibility of trees A in general settings and apply the obtained results to the study of unstable theories. (shrink)

The physical possibility of spacetimes containing closed timelike curves (CTCs) challenges the philosophy of time in the way that temporal ordering is, at best, remarkably non-standard: events on CTCs precede themselves. Apparently, such universes do not possess a consistent time order but only a consistent time direction. Thus, temporal directionality seems to be more fundamental than ordering in earlier-later or past-present-future. I will argue that this favors presentism as the adequate ontology of spacetimes: only presentism consistently copes with (...) the idea that temporal ordering depends on empirical constraints. The presentist Now is fundamentally undivided and productively directed towards existence. Time order arises by extending the Now, which can fail and in fact fails in universes containing CTCs. (shrink)

The essay collection "Kant on Proofs for God's Existence" provides a highly needed, comprehensive analysis of the radical turns of Kant's views on proofs for God's existence.— In the "Theory of Heavens" (1755), Kant intends to harmonize the Newtonian laws of motion with a physico-theological argument for the existence of God. But only a few years later, in the "Ground of Proof" essay (1763), Kant defends an ontological ('possibility' or 'modal') argument on the basis of its logical (...) exactitude while he praises the physico-theological argument for its beauty and appeal to the common sense. In the first "Critique" (1781/7), Kant replaces traditional constitutive ontological, cosmological, and physico-theological proofs with his own regulative theoretical and moral-practical religious arguments. He continues to defend a moral argument in the second "Critique" (1788). But in the third "Critique" (1790), Kant reintroduces a physico-theological besides an ethicotheological argument in order to unify the critical system of philosophy. Kant develops further moral arguments and arguments from evil in the "Theodicy" essay (1791) and the "Religion" (1793/4), and still searches for the right kind of proof for God's existence in the "Opus postumum" (1796–1804).—Part one of this volume is dedicated to an analysis of Kant's proofs for God's existence in their historical order that explains which proofs Kant favors or rejects in various periods of his thought. Part two contains a systematic classification of main kinds of proof for God's existence in Kant that outlines the argumentative structure of particular kinds of proof and discusses Kant's potential reasons for their variations and modifications. The essay collection speaks to Kant specialists, philosophers, and theologians, but introduces the topic to non-academic readers also. -/- Contributers: Uygar Abaci (Pennsylvania State University), Craig Bacon (University of South Carolina), Andrew Chignell (Princeton University), Eckart Förster (Humboldt University, Johns Hopkins University), Ina Goy (Beijing Normal University) Paul Guyer (Brown University), Graham Oppy (Monash University), Lara Ostaric (Temple University), Stephen Palmquist (Independent Scholar), Lawrence Pasternack (Oklahoma State University), Konstantin Pollok (University of Mainz), Oliver Sensen (University of Tulane), Allen Wood (Bloomington University, Stanford University). (shrink)

Let X be an infinite set and let and denote the propositions “every filter on X can be extended to an ultrafilter” and “X has a free ultrafilter”, respectively. We denote by the Stone space of the Boolean algebra of all subsets of X. We show: For every well‐ordered cardinal number ℵ, (ℵ) iff (2ℵ). iff “ is a continuous image of ” iff “ has a free open ultrafilter ” iff “every countably infinite subset of has a limit point”. (...) implies “every open filter on extends to an open ultrafilter” implies “has an open ultrafilter” implies It is relatively consistent with that (ω) holds, whereas (ω) fails. In particular, none of the statements given in (2) implies (ω). (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Hume on the Abstract Idea of Existence: Comments on Cummins' "Hume on the Idea of Existence"1 Fred Wilson Hume'sviews on theconceptofexistence: thisisone ofthemore obscure parts of Hume's philosophy. Professor Cummins has done a valuable service simply by trying to unravel some ofthe puzzles; it is still more valuable for shedding as much light as it does on the issues. There are nonetheless problems with the interpretation that (...) he develops, and I would like to bring out some ofthese. I will address three questions: (a)What, more precisely, is the (abstract) idea ofexistence? (b)What is the notion of"necessity" as Hume would use it in connection with the notion that something exists "necessarily," or, contrarily, "contingently"? (c)Does it follow from the fact that whatever thing we conceive we conceive as existent that every thing necessarily exists? In order toanswerthese questions somethingwillhave tobe said about Hume's doctrine ofabstractideas. Butonall theseissues, Humeis often not so much inadequate as incomplete; and I shall suggest that a numberofpoints canbeilluminatedbylookingatthe historical context that Hume himselfcould take for granted. The upshot will not be that Hume's views are unproblematic, but only that they are perhaps less problematic than Professor Cummins makes out. I. Abstract Ideas In many respects, Hume's doctrine of ideas is fairly traditional. We think in terms ofideas. In particular, our capacity to think generally, and to use general terms, is a matter ofhaving abstract ideas. In this, Hume follows the views ofhis predecessors such as Locke, Descartes and the Port Royal logicians. Hume also adopts the principle that what is conceivable is possible. Again, he follows the same tradition ofLocke, Volume XVII Number 2 167 FRED WILSON Descartes and the Port Royal logicians. Where Hume differs from his predecessors is in his account of what precisely an abstract is. For Hume's predecessors, one forms an abstract idea by separation. Thus, for Locke, forming ideas by abstraction consists in "separating them from all other Ideas that accompany them in their real existence."2 This sortofseparation is the mechanism bywhich "the Mind makes the particular Ideas, received from particular Objects, to become general" (Essay, 2.11.9). The Port Royal logicians make the same point: abstraction occurs with respect to "choses... composées" when one "les considérant par parties, et comme par les diverses faces qu'elles peuvent recevoir." In abstraction what is thus known is considered separately from the whole; either one considers "les parties séparément" in the case of"parties intégrantes," or one "peut séparer les choses en divers modes," or, finally, "quand une même chose ayant divers attributs, on pense à l'un sans penser à l'autre."3 The former occurs when, for example, we separate in thought the parts ofthe body. Thisis the simplestform ofabstraction. Berkeleyhas noproblems with this notion: "Iwill notdenyI can abstract, ifthatmay properlybe called abstraction, which extends only to the conceiving separately such objects, as is possible may really exist or be actually perceived asunder."4 Neither does Hume have problems with this notion; it is the basis of his—and Berkeley's—view that ideas are either simple or complex and that some of the complex ideas are a result of our combining simple parts in ways that are not found in reality, as, for example, in our idea ofthe New Jerusalem.5 It is the other two sorts ofabstraction that are more problematic. Consider the first of these two forms of abstraction. We begin with simple ideas ofsensation, for example, white (Essay, 2.3.1). One forms the abstract idea of white by separating the property white from the other qualities with which it is conjoined in the white particulars, for example, snow or milk (Essay, 2.21.73), that are given in sense experience. The resultingideais distinct from other ideas, for example, blue or heat (Essay, 2.12.1). The example given by Nicole and Arnauld is thatofthe geometers who explore the idea ofthree-dimensional space by considering first length alone, then area, and finally volumes or solids (which is the same, for these Cartesians as "corps," body) (Logique, 1.5). This is one form ofseparation. By this means one forms abstract... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:HUME ON CONTINUED EXISTENCE AND THE IDENTITY OF CHANGING THINGS Most discussions of Hume's rather cursory treatment of coherence as a factor in generating belief in what he calls the continu' d existence of objects in Of Scepticism with Regard to the Senses, have taken a common line in interpreting the nature of the problem Hume's treatment is designed to solve. For instance, perhaps the two most (...) ex2 3 tensive discussions, those of Price and Gomberg seem to agree that the problem is: how do we fill in the gaps among our perceptions, complete sequences or series that are incomplete, and come to believe in the existence of a world of unperceived objects. At the same time such discussions have focussed on the issue of whether the inference from the coherence of our perceptions to belief in the continued existence of objects (ICCE) is, as Hume claims, distinguishable from causal inference. Hume is read in such a way that ICCE if not causal is at least quasi-causal; that is, the only difference for Hume between the two sorts of inference has been taken to be one concerning the evidence on which each is based — causal inferences on past constant conjunctions or uniformities, ICCE on something less. I believe that these discussions have invariably omitted a key factor in understanding Hume's treatment of coherence, one that I want to point out and develop in this paper. Hume's discussion of coherence, like his discussion of constancy, is bound up with the concept of identity; for belief in the continued existence of an object, which coherence generates, is a belief about its identity. Hence a causal inference is distinguished from ICCE by Hume as only the latter necessarily involves belief in the identity of an object over time. Once this is recognized, we can view Hume's discussion^of coherence as requiring an answer to the question: "How do we come to believe in the identity of changing things?" I want to consider two interpretations of 106. the exact nature of ICCE for Hume — one suggested by examples offered in his discussion of coherence, the other suggested by remarks about the concept of identity in other sections of Part Four of Book One of the Treatise — and to argue that neither satisfactorily answers this question. This failure raises doubts not only about ICCE but about the tenability of Hume's characterization of the "vulgar" view of perception and his view of identity. When Hume first answers the question, "What qualities of our impressions or perceptions lead us to attribute to them a distinct and continued existence,?" by isolating the qualities of constancy and coherence, I think it is clear that the former is invoked to account for objects which are, at least in a relative sense, unchanging, which have always appear 'd to me in the same order and return upon me without the least alteration (T194), while the latter is invoked especially, if not solely, to account for objects that underto rather large changes over time, things which after a little absence or interruption may become hardly knowable. (T195) Hume's example concerns a fire in his chamber, which undergoes great change from the moment he leaves (or perhaps the moment it is lighted) to the time he returns (or perhaps the time it is a bunch of glowing embers), but which, nevertheless, compared to other fires undergoes a like alteration...in a like time. (T195) Whatever more coherence can do, it is required, at least initially, to account for just those cases which cannot be subsumed under constancy, in other words, cases in which changing objects are taken to possess distinct and continued existence. In the famous paragraph following his initial comments on coherence, Hume seemingly proceeds to explain how coherence gives rise to belief in continued existence. The account runs basically as follows. Hume hears a noise, as of a door turning; he sees a porter coming toward him. But, Hume says, I never have observ' d3 that this noise could proceed from anything but the motion of a 107. door; and therefore conclude, that the present phaenomenon is a contradiction to all past experience... (shrink)

Contemporary philosophers generally ignore the topic of duties to the self. I contend that they are mistaken to do so. The question of whether there are such duties, I argue, is of genuine significance when constructing theories of practical reasoning and moral psychology. In this essay, I show that much of the potential importance of duties to the self stems from what has been called the “second-personal” character of moral duties—the fact that the performance of a duty is “owed to” (...) someone. But this is problematic, as there is reason to doubt whether a person can genuinely owe to herself the performance of an action. Responding to this worry, I show that temporal divisions within an agent's life enable her to relate to herself second-personally, in the way required by morality. The upshots, I argue, are that we need an intra-personal theory of justice that specifies the extent of a person's authority over herself, and that we need to rethink our theories of moral emotions in order to specify how an individual ought to respond to attacks on her interests and autonomy that she herself perpetrates. (shrink)

This paper discusses the meaning of the concept of ‘second-order observation’ used by Niklas Luhmann. Luhmann identifies second-order observation as a defining characteristic of modern world society. According to Luhmann, all social systems construct a social reality on the basis of the observation of observations. Rating agencies in the economy or the peer-review process in the academic system are examples of social mechanisms manifesting second-order observation. Social media also represent organized second-order observation. The paper suggests that in a society based (...) on second-order observation, ‘genuine pretending’ is an adequate mode of existence. This notion is derived from the Daoist text Zhuangzi. It indicates a disassociation from social roles which allows their performers to exercise these roles with ease and, at the same time, maintain a state of sanity. (shrink)

The ultimate utility of science is widely agreed upon: the comprehension of reality. But there is much controversy about what scientific understanding actually means, and how we should proceed in order to gain new scientific understanding. Is there a method for acquiring new scientific knowledge? Is this method unique and universal? There has been no shortage of proposals, but neither has there been a shortage of skeptics about these proposals. This article proffers for discussion a potential scientific method that aspires (...) to be unique and universal and is rooted in the recent and ancient history of scientific thinking. Curiously, conclusions can be inferred from this scientific method that also concern education and the transmission of science to others. (shrink)

In this paper a proposal by Henkin of a nominalistic interpretation for second and higher-order logic is developed in detail and analysed. It was proposed as a response to Quine’s claim that second and higher-order logic not only are committed to the existence of sets, but also are committed to the existence of more sets than can ever be referred to in the language. Henkin’s interpretation is rarely cited in the debate on semantics and ontological commitments for these (...) logics, though it has many interesting ideas that are worth exploring. The detailed development will show that it employs an early strategy of using substitutional quantification in order to reduce ontological commitments. It will be argued that the perspective adopted for the predicate variables renders it a natural extension of Quine’s nominalistic interpretation for first-order logic. However, we will argue that, with respect to Quine’s nominalistic program and his notion of ontological commitment, still holds and thus Henkin’s interpretation is not nominalistic. Nevertheless, it will be seen that is addressed successfully and this provides further insights on the so-called “Skolem Paradox”. Moreover, the interpretation is ontologically parsimonious and, in this respect, it arguably fares better than a recent proposal by Bob Hale. (shrink)

There are two questions concerning Hume’s doctrine of existence which have not yet found any persuasive answer: What is his argument in favour of the thesis that there is no distinct idea of existence? What are the semantic and metaphysical consequences of this thesis within his philosophical framework? This paper mainly aims to answer question. In order to do that, I will first explain why some reconstructions suggested by interpreters such as Cummins and Bricke are problematic. One of (...) them relies on exegetically dubious presumptions; the other departs too much from Hume’s text. Then, I will offer my own reconstruction that makes maximal use of some principles which are very familiar to Hume’s readers, including the principle stating the similarity between perceptions and their images. After that, I will discuss a potential objection to my reconstruction and make a brief remark on question, arguing that, as opposed to numerous interpreters’ concerns, Hume’s thesis that there is no distinct idea of existence does not by itself prevent him from being able to conceive negative existential propositions. (shrink)

_A fresh, new translation of Augustine’s third work as a Christian convert__ "The 'Cassiciacum dialogues'... are of a high literary and intellectual quality, combining Ciceronian and neo-Platonic philosophy, Roman comedy and Vergilian poetry, and early Christian theology. They are also, arguably, Augustine’s most charming works, exhibiting his whimsical levity and ironic wryness."—_Credo__ The first four works written by St. Augustine of Hippo after his conversion to Christianity are dialogues that have influenced prominent thinkers from Boethius to Bernard Lonergan. Usually called (...) the “Cassiciacum dialogues,” these four works are of a high literary and intellectual quality, combining Ciceronian and neo-Platonic philosophy, Roman comedy and Vergilian poetry, and early Christian theology. They are also, arguably, Augustine’s most charming works, exhibiting his whimsical levity and ironic wryness. _On Order_ is the third work in this tetralogy, and it is Augustine’s only work explicitly devoted to theodicy, the reconciliation of Almighty God’s goodness with evil’s existence. In this dialogue, Augustine argues that a certain kind of self-knowledge is the key to unlocking the answers to theodicy’s vexing questions, and he devotes the latter half of the dialogue to an excursus on the liberal arts as disciplines that will help strengthen the mind to know itself and God. (shrink)

Quine takes philosophy to be continuous with science. Proper philosophical method is scientific method applied self-consciously to problems more general than those ordinarily considered within a particular science. Science is self-conscious common sense; and philosophy is self-conscious science. In order to understand and answer a basic philosophical question such as "What exists?" we must know something of the results of particular sciences like physics, chemistry, mathematics, biology, astronomy, and psychology. To learn what we can from these sciences is to do (...) philosophy of science; and for our purposes, "philosophy of science is philosophy enough.". (shrink)