We develop fundamental aspects of the theory of metric, Hilbert, and Banach spaces in the context of subsystems of second-order arithmetic. In particular, we explore issues having to do with distances, closed subsets and subspaces, closures, bases, norms, and projections. We pay close attention to variations that arise when formalizing definitions and theorems, and study the relationships between them.

We shall have to do a lot of thinking and a lot of educating before we can hope that our exchange processes will swing easily and gracefully from an expansion into a static phase instead of falling clumsily and painfully into a slump.

This book is designed for the sophomore/junior level Introduction to Advanced Mathematics course. Written in a modified R.L. Moore fashion, it offers a unique approach in which readers construct their own understanding. However, while readers are called upon to write their own proofs, they are also encouraged to work in groups. There are few finished proofs contained in the text, but the author offers “proof sketches” and helpful technique tips to help readers as they develop their proof writing skills. This (...) book is most successful in a small, seminar style class. Logic, Sets, Induction, Relations, Functions, Elementary Number Theory, Cardinality, The Real Numbers For all readers interested in abstract mathematics. (shrink)

Metaphysics is, historically as well as systematically, mostly taken to be the inquiry into reality, insofar it is considered to be: (1) the totality of everything there is; (2) of everything that exists; or (3) what is fundamental. This paper sets out to analyze the relation between all three metaphysical core notions and sketch the landscape of metaphysical theories that emerges from it. Taking The Fundamental, The Existent, and Totality to be the domains corresponding to each metaphysical (...) object of inquiry, it is argued that they stand in the settheoretical relations of: The Fundamental ⊆ The Existent ⊆ Totality. This general structure allows for a plurality of more detailed structures when we differentiate between the ones that treat at least two notions as extensionally equal and those that take them to be proper subsets. Furthermore, reductive and inflationary strategies between equating two of the notions will be differentiated, allowing for a detailed sketch of the landscape of metaphysical theories and their views on the nature of reality. In closing, it is argued that the metaphysical structure allowing for most differentiation in metaphysical status is to be preferred as it allows to adequately capture metaphysical disputes, constituting evidence for the importance of each metaphysical notion and a short plea against their conflation. (shrink)

The notion of fundamentality, as it is used in metaphysics, aims to capture the idea that there is something basic or primitive in the world. This metaphysical notion is related to the vernacular use of “fundamental”, but philosophers have also put forward various technical definitions of the notion. Among the most influential of these is the definition of absolute fundamentality in terms of ontological independence or ungroundedness. Accordingly, the notion of fundamentality is often associated with these two other technical (...) notions. (shrink)

Spinoza searched for a language that could help him to create a monistic system of ethics. Latin was in the 17th century a fairly malleable medium of communication. In its philosophical use it was largely a creation of Descartes. Spinoza wanted to use it in a way that would resemble Euclid's treatment of geometry. He needed a language that would clearly and precisely describe the process by which a man could liberate himself from the power of affection that hamper naturaly (...) propensity for social peace and mental equaenimity. He decided to begin by describing nature, which was responsible for man's proclivities and abilities. Consequently he needed a new conception of substance which on the one hand could be definied by some initial axioms, and on the other hand would sufficiently flexible to include various aspects of human thought. It is interesting that when Spinoza had to make a choice between flexibility and content, he resolved to adopt a strict method of reasoning at the cost of the received understanding of substance. It is possible that these linguistic considerations led him to adopt the view that substance is identical with God and as such encompasses all principles of operations of the human mind and premises for the deriving of all fundamental notions popular in his times. (shrink)

Fundamentality plays a pivotal role in discussions of ontology, supervenience, and possibility, and other key topics in metaphysics. However, there are two different ways of characterising the fundamental: as that which is not grounded, and as that which is the ground of everything else. I show that whether these two characterisations pick out the same property turns on a principle—which I call “Dichotomy”—that is of independent interest in the theory of ground: that everything is either fully grounded or not (...) even partially grounded. I then argue that Dichotomy fails: some facts have partial grounds that cannot be complemented to a full ground. Rejecting Dichotomy opens the door to recognising a bifurcation in our notion of fundamentality. I sketch some of the far-reaching metaphysical consequences this might have, with reference to big-picture views such as Humeanism. Since Dichotomy is entailed by the standard account of partial ground, according to which partial grounds are subpluralities of full grounds, a non-standard account is needed. In a technical “Appendix”, I show that truthmaker semantics furnishes such an account, and identify a semantic condition that corresponds to Dichotomy. (shrink)

The scientific successes of the last 400 years strongly suggest a view on which things are organized into layers, with phenomena in higher layers dependent on and determined by what goes on below. Philosophers have recently explored the idea that we can make sense of this idea by appeal to a relation called grounding. This book develops the rudiments of a theory of grounding, and applies that theory to questions of independent interest. The theorizing consists in saying in more detail (...) what grounding is and how it relates to explanations of the relevant sort, discussing objections to the deployment of a notion of grounding, and drawing points of contrast between a grounding-centered approach to relative fundamentality and other approaches in the literature. The book then turns to a demonstration of how this theorizing bears fruit in the investigation of other interesting questions. The applications are to central questions concerning (i) how to distinguish between truths that say how objective reality is in itself, quite independently of us, and truths that do not; (ii) the nature of truth; and (iii) the relation between fundamental physical facts and the rich panoply of other facts that depend on and are determined by them, including facts concerning our own doings. The aim is to advance our understanding of one of the deepest and thorniest questions which the stunning scientific achievements of the last 400 years pose: how higher-level phenomena, including ourselves, fit into an ultimately physical world. (shrink)

The notion of fundamentality is supposed to play an important role in philosophical inquiry and scientific theorising. Yet there is no consensus on how to formulate it in precise terms. According to a promising view, fundamentality is a form of ontological independence. This view has the merit of capturing a natural connection between fundamentality and ontological dependence. However, it has been recently argued that it is possible that there are fundamental and yet ontologically dependent entities; therefore, we should not (...) characterise the fundamental in terms of ontological independence. My aim is to show that such a possibility does not threaten a conception of fundamentality as a form of ontological independence. I illustrate this claim by providing a definition of equifundamentality and showing that fundamental and yet ontologically dependent entities can be treated as equifundamental. (shrink)

This is the first part of a two-tier overview article on fundamentality in metaphysics and the philosophy of physics. It provides an introduction to the notion of fundamentality in metaphysics, as well as to several related concepts. The key issues in the contemporary debate on the topic are summarised, making systematic reference to the most relevant literature. In particular, various ways in which the fundamental entities and the fundamental structure of reality may be conceived are illustrated and discussed. (...) A final brief section looks at the methodological issue of naturalism, paving the way for the survey of fundamentality in the philosophy of physics, which is carried out in the second part. (shrink)

I like the view that the fundamental facts are logically simple, not complex. However, some universal generalizations and negations may appear fundamental, because they cannot be explained by logically simple facts about particulars. I explore a natural reply: those universal generalizations and negations are true because certain logically simple facts—call them —are the fundamental facts. I argue that this solution is only available given some metaphysical frameworks, some conceptions of metaphysical explanation and fundamentality. It requires a ‘fitting’ (...) framework, according to which metaphysical theories explain the aptness of representations in terms of how things are fundamentally. Fitting frameworks conceive of the fundamental facts as those that are metaphysically ‘real’; call them the ‘facts-in-reality’. Moreover, we must take as primary a plural notion of the facts-in-reality, not the singular notion of a fact-in-reality. By contrast, a metaphysics that grounds facts is incompatible with my strategy for keeping the fundamental facts logically simple. (shrink)

This paper aims to examine the notion of τριάς in Proclus and in the Corpus Areopagiticum. As is well known, in Proclus’ metaphysical‑theological system the concept of «triad» plays a central role. In his philosophical perspective, triadic structures pervade the totality of reality in all its different levels and articulations, based on the fundamental triad consisting of remaining‑procession‑reversion. At the same time, the First Principle, also conceived as One‑Good and First God, due to its original simplicity, transcends all triadic (...) structures, while simultaneously constituting their original foundation. On its turn, Pseudo‑Dionysius’ theological thought shows several points of contact with Proclus’ metaphysical‑theological perspective, including the overall conception of the universe as ordered in triadic structures. However, while in Proclus the term τριάς can only refer to the triadic metaphysical structures permeating the totality of reality, in Pseudo‑Dionysius it most often designates the Trinity, that is, the three hypostases Father – Son – Holy Spirit. Moreover, whereas in Proclus the notion of «triad» cannot in any way be referred to the First Principle, which, due to its originality and absolutely transcendent simplicity, is released from all forms of relationality, in the Corpus Areopagiticum, especially in De divinis nominibus, the Trinity and God’s triune nature provide the foundation for the essential and inalienable relationship between God and the whole of creation. Nevertheless, for Pseudo‑Dionysius, just as in Proclus, God in his absolute transcendence with respect to all things appears, in a paradoxical way, placed above all forms of relatedness. Consequently, as the conclusion of this essay aims to show, an unsolvable tension emerges in the Corpus Areopagiticum between the nature of the Trinity and the absolute otherness of God. The mystical outcome of pseudo‑Dionysian theology, as shown especially in the final section of De mystica theologia, thus comes to represent the inescapable conclusion reached by theological reflection once it has realised the inability of thinking to admit the paradoxical coexistence in God of relation and absolute unrelatedness. (shrink)

ABSTRACT This essay has three goals. The first is to introduce the notion of fundamentality and to argue that physicalism can usefully be conceived of as a thesis about fundamentality. The second is to argue for the advantages of fundamentality physicalism over modal formulations and that fundamentality physicalism is what many who endorse modal formulations of physicalism had in mind all along. Third, I describe what I take to be the main obstacle for a fundamentality-oriented formulation of physicalism: ‘the problem (...) of abstracta’, which asks how physical can accommodate phenomena such as mathematics and universals, and which modal formulations do not face. I canvas three solutions: the inapt for ground solution, the concrete restriction, and the contingency restriction. (shrink)

It is widely assumed that the notion of doxastic justification should be explained in terms of the more fundamental notion of propositional justification, a notion which itself explains evidential support relations as a priori knowable. It is argued here, following Goldman, that this is a mistake. Doxastic justification is the more fundamental notion, and once one sees this, one must recognize that evidential support relations have an ineliminable psychological dimension which undermines the claim that they are knowable a (...) priori. (shrink)

The relation of being more fundamental than, as well as the Finean notion of partial grounding, are widely taken to be irreflexive, transitive, and asymmetric. However, certain time-travel cases that have been used to raise worries about the irreflexivity, transitivity, and asymmetry of proper part of can also be used to argue that more fundamental than and partially grounds do not have these formal properties. I present this worry and discuss several responses to it, with the aim of (...) showing that the problem is harder to address when applied to fundamentality and partial grounding than it was when merely applied to proper parthood. (shrink)

There is a long lineage of philosophers concerned with coming to understand what explains everything broadly construed, or within a certain, restricted domain. We call such explanations ultimate explanations. Contemporarily, philosophers of a certain stripe have devoted much attention to the notion of fundamentality - that there is something which is without explanation. This Element explores some of the connections between fundamentality and ultimate explanations both contemporarily and historically.

This article investigates the claim that some truths are fundamentally or really true — and that other truths are not. Such a distinction can help us reconcile radically minimal metaphysical views with the verities of common sense. I develop an understanding of the distinction whereby Fundamentality is not itself a metaphysical distinction, but rather a device that must be presupposed to express metaphysical distinctions. Drawing on recent work by Rayo on anti-Quinean theories of ontological commitments, I formulate a rigourous theory (...) of the notion. In the final sections, I show how this package dovetails with ' interpretationist' theories of meaning to give sober content to thought that some things — perhaps sets, or gerrymandered mereological sums — can be 'postulated into existence'. (shrink)

In this paper, I discuss the problem of scientific laws in general and laws of biology in particular. After reviewing the debate around the existence of laws in biology, I examine the subject in the light of the structuralist notion of a fundamental law and argue for the law of matching as the fundamental law of genetics.

In this paper, I propose a solution to an almost ignored problem in metaphysics and metametaphysics: what is categorial fundamentality and non-fundamentality? My proposal builds on E. J. Lowe’s view on the issue. By means of the newcomer notion of generic identity, I can give an account of something that Lowe did not explicate: the constitution of formal ontolog- ical relations. Formal ontological relations (e.g. instantiation) are internal relations that deter- mine ontological form and category-membership. I argue that categorial fundamentality (...) is hav- ing membership fully determined by a simple formal ontological relation or relations jointly in an order and categorial non-fundamentality is having membership at least partly determined by a derived formal ontological relation in an order. In contrast to Lowe, my proposal does not pre- suppose non-modal essentialism. (Please, ask for the penultimate draft.). (shrink)

In metaphysics, fundamentality is a central theme involving debates on the nature of existents, as wholes. These debates are largely object-oriented in their standpoint and engage with composites or wholes through the mereological notion of compositionality. The ontological significance of the parts overrides that of wholes since the existence and identity of the latter are dependent on that of the former. Broadly, the candidates for fundamental entities are considered to be elementary particles of modern physics (since they appear to (...) play the role of ultimate parts to all phenomena). The paper intends to show the inadequacy of the object-oriented notion of conditionality by pointing out that the parts and wholes possess varying conditions of existence. By alleging that only the parts are ontologically significant is to conflate such conditions and neglect the spectrum of conditions which exist in our world. A proposal for a revised notion of compositionality in terms of structural relatedness is also put forward. (shrink)

This article is aimed at highlighting some possible contributions of Hegel’s philosophy to the contemporary debate around process metaphysics. In the contemporary metaphysical debate, process metaphysics represent an attempt to highlight the limits of the traditional philosophical paradigm, which is based on the notion of substance, and to work within an alternative paradigm, which is based on the notion of process. What exists, then, are not substances, substrates, fixed and stable objects characterized by certain properties, but processes, events, occurrences. The (...) main idea of ​​process metaphysics is that being is dynamic and that this dynamic nature must be the main focus of any comprehensive philosophical explanation of reality. Looking at this revolution, it is necessary to define the very notion of process. In fact, this work of conceptual clarification of the fundamental notion of this new philosophical paradigm is still ongoing. My idea is that Hegelian philosophy can offer some relevant indications to do the job. In this sense, the article will be divided into two parts: on the basis of the analysis of some definitions of the notion of process in the contemporary debate around process metaphysics, I will show 1) the need to determine the minimal ontological structure of the notion of process; 2) the possibility of determining this structure through some conceptual tools provided by Hegel’s logic and in the Lectures on the History of Philosophy. (shrink)

Discussion of a metaphysical sense of 'inheritance' and cognate notions relevant to fundamentality.

Recent years have seen the appearance of many English-language hand books of logic and numerous monographs on topical discoveries in the foundations of mathematics. These publications on the foundations of mathematics as a whole are rather difficult for the beginners or refer the reader to other handbooks and various piecemeal contribu tions and also sometimes to largely conceived "mathematical fol klore" of unpublished results. As distinct from these, the present book is as easy as possible systematic exposition of the now (...) classical results in the foundations of mathematics. Hence the book may be useful especially for those readers who want to have all the proofs carried out in full and all the concepts explained in detail. In this sense the book is self-contained. The reader's ability to guess is not assumed, and the author's ambition was to reduce the use of such words as evident and obvious in proofs to a minimum. This is why the book, it is believed, may be helpful in teaching or learning the foundation of mathematics in those situations in which the student cannot refer to a parallel lecture on the subject. This is also the reason that I do not insert in the book the last results and the most modem and fashionable approaches to the subject, which does not enrich the essential knowledge in founda tions but can discourage the beginner by their abstract form. A. G. (shrink)

If we want to say what “fundamentality” means, we have to start by approaching what we generally see at the empty place of the predicate “____ is fundamental”. We generally talk about fundamental entities and fundamental theories. At this article, I tried to make a metaphysical approach of what is for something to be fundamental, and I also tried to talk a little bit of fundamental incomplete and complete theories. To do that, I start stating (...) the notion of “entity” and looking at the difference at perceived entities. The difference led us to talk about the entities’ structures and their powers, and about the supervenience between these last two. The supervenience talk made us to see the fight between emergentism and reductionism as the difference between the irreducibility of laws and the reducibility of powers and structures to lower-order domains. Then, we conclude that “fundamentality” is a mereological relation – a relation that a whole structure has to a certain combination of its structural parts or that a power has to a certain combination of its constituent powers – of to be identical and to exist in virtue of them. (shrink)

Recently, philosophers have tried to develop a version of truthmaker theory which ties the truthmaking relation closely to the notion of fundamentality. In fact, some of these truthmaker-fundamentalists, as I call them, assume that the notion of fundamentality is intelligible in part by citing, as central examples of fundamentals, truthmakers, which they understand necessarily as constituents of fundamental reality. The aim of this paper is first to bring some order and clarity to this discussion, sketching how far TF is (...) compatible with orthodox truthmaking, and then critically to evaluate the limits of TF. It will be argued that truthmaker theory cannot directly help with articulating the nature of fundamental reality and that T-REL does not necessarily relate truths with anything more fundamental, unless what is fundamental is what the truthbearers in question are about. I shall argue that TF faces a rather thorny dilemma and some general problems. I shall present two exhaustive types of fundamentalism on which a version of TF can be based: deflationary and inflationary. It will be argued that each version of TF runs into significant troubles accounting for all truth, specifically ordinary truths and metaphysical truths about the relations between ordinary facts and fundamental facts. I shall not attempt to solve these problems, but rather, at the end, diagnose the issues with TF as lying in the difficulties with reconciling the manifest image with the scientific and metaphysical images of reality. (shrink)

I see the question what it is that makes an inference valid and thereby gives a proof its epistemic power as the most fundamental problem of general proof theory. It has been surprisingly neglected in logic and philosophy of mathematics with two exceptions: Gentzen’s remarks about what justifies the rules of his system of natural deduction and proposals in the intuitionistic tradition about what a proof is. They are reviewed in the paper and I discuss to what extent they (...) succeed in answering what a proof is. Gentzen’s ideas are shown to give rise to a new notion of valid argument. At the end of the paper I summarize and briefly discuss an approach to the problem that I have proposed earlier. (shrink)

I argue that notions of relative fundamentality need to be invoked if there is to be something substantive at stake in the debate between proponents of Harvey Brown's dynamical approach to relativity and defenders of a more traditional interpretation of spacetime. I will review some problems that stand in the way of the advocate of the dynamical approach making good on their claim that dynamical symmetries are more fundamental than spacetime symmetries.

This is the second part of an overview article on fundamentality in metaphysics and the philosophy of physics. Here, the notion of fundamentality is looked at from the viewpoint of the philosophical analysis of physics and physical theories. The questions are considered (1) whether physics can be regarded as fundamental with respect to other sciences, and in what sense; (2) what the label ‘fundamental physics’ should exactly be taken to mean; (3) on what grounds a particular physical theory (...) should be considered fundamental; (4) what should be regarded as fundamental according to particular theories of physics; and (5) what indications come from contemporary physics concerning the fundamental structure of reality. (shrink)

In this paper, I propose a solution to an almost ignored problem in metaphysics and metametaphysics: what is categorial fundamentality and non-fundamentality? My proposal builds on E. J. Lowe’s view on the issue. By means of the newcomer notion of generic identity, I can give an account of something that Lowe did not explicate: the constitution of formal ontolog- ical relations. Formal ontological relations (e.g. instantiation) are internal relations that deter- mine ontological form and category-membership. I argue that categorial fundamentality (...) is hav- ing membership fully determined by a simple formal ontological relation or relations jointly in an order and categorial non-fundamentality is having membership at least partly determined by a derived formal ontological relation in an order. In contrast to Lowe, my proposal does not pre- suppose non-modal essentialism. (Please, ask for the penultimate draft.). (shrink)

The notion of a recognitional concept (RC) is stated precisely and shown to be unrelated to the proper notion of a perceptually based concept, defining of concept empiricism. More fundamentally, it is argued that the notion of an RC does not reflect a potentially sensible candidate theory of concepts at all and therefore ought to be abandoned from concept-theoretical discourse. In the later parts of the paper, it is shown independently of these points that Fodor's attacks on RCs are in (...) all central respects based on fallacies and confusions. Thus, even if the notion of an RC were one worth defending, it could not be threatened by Fodor's attacks on it. Throughout the paper, I aim at clarification regarding the logical relations between various concept-theoretical options. (shrink)

The Standard Model of elementary particle physics distinguishes between fundamental and accidental symmetries. The distinction is not based on empirical features of the symmetry, nor on a metaphysical notion of necessity. A symmetry is fundamental to the extent that other aspects of nature depend on it, and it is recognized as fundamental by its being theoretically well-connected. This paper clarifies the concept of what it is to be fundamental in this sense, and suggests broader implications for (...) the analysis of scientific knowledge. (shrink)

In this paper we describe a novel approach to defining an ontologically fundamental notion of co-presentness that does not go against the tenets of relativity theory. We survey the possible reactions to the problem of the present in relativity theory, introducing a terminological distinction between a static role of the present, which is served by the relation of simultaneity, and a dynamic role of the present, with the corresponding relation of co-presentness. We argue that both of these relations need (...) to be equivalence relations, but they need not coincide. Simultaneity, the sharing of a temporal coordinate, need not have fundamental ontological import, so that a relativizing strategy with respect to simultaneity seems promising. The notion of co-presentness, on the other hand, does have ontological import, and can therefore not be relativized to an observer or to an arbitrarily chosen frame. We argue that a formal representation of indeterminism can provide the structure needed to anchor the relation of co-presentness, and that this addition is in fact congenial to the notion of dynamic time as requiring real change. The resulting picture is one of an extended dynamic present, implying a formal distinction between static simultaneity and dynamic co-presentness. After working out the basics of our approach in the simpler framework of branching time, we provide our full analysis in the framework of branching space-times, which allows for a formal definition of modal correlations. The spatial extension of the dynamic present can reach as far as the modal correlations do. In the limit, the dynamic present could extend across a maximal space-like hypersurface. (shrink)

(Abstract - Inglês) Identity is traditionally taken to be a fundamental notion of our conceptual framework as well as a fundamental metaphysical component of entities. But as far as we make this claim we face ourselves with two problems: what is identity? And why would it be fundamental? These questions will guide us towards a discussion put forward by Bueno (2014), Krause and Arenhart (2015). Bueno holds that there are four aspects that make identity being fundamental: (...) (1) identity is assumed in every conceptual system; (2) it is required for a minimal characterisation of being an individual; (3) it cannot be defined; and (4) identity is required for quantification. On the other hand, Krause and Arenhart refuse the thesis that identity is fundamental replying to Bueno's arguments. In this dissertation we will deal with this debate. In the introduction we will deal with the first problem – what is identity? –, showing how this concept is traditionally understood, either for its metaphysical characteristics as for its formal account. After that we will deal with each of the four aspects defended by Bueno and challenged by Krause and Arenhart. After a critical presentation of each position we will also provide other arguments for the current debate. Finally we will outline an alternative view to those defended throughout this work. -/- (Resumo - Português) Tradicionalmente a identidade é adotada como uma noção fundamental de nosso arcabouço conceitual e como um componente metafísico fundamental das entidades. Mas logo ao fazermos essa afirmação nos deparamos com dois problemas: O que é a identidade? E por que ela seria fundamental? Estas perguntas irão nos guiar à discussão conduzida por Otávio Bueno (2014), Décio Krause e Jonas Arenhart (2015). Bueno defende que há quatro aspectos que fazem a identidade ser fundamental: (1) A identidade é pressuposta em todo sistema conceitual; (2) é requerida para uma caracterização mínima de indivíduo; (3) não pode ser definida; e (4) a identidade é requerida para a quantificação. Por outro lado, Krause e Arenhart recusam a tese de que a identidade seja fundamental, respondendo aos argumentos de Bueno. Neste trabalho iremos tratar desse debate. Na introdução iremos tratar do primeiro problema – O que é a identidade? –, mostrando como este conceito é tradicionalmente compreendido, tanto suas características metafísicas como também seu tratamento formal. Posteriormente iremos tratar de cada um dos quatro aspectos defendidos por Bueno e atacados por Krause e Arenhart. Além da exposição crítica de cada posição iremos também oferecer outros argumentos para o debate atual. Ao final iremos esboçar uma posição alternativa às defendidas ao longo do texto. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:ALBERTUS MAGNUS AND THE NOTION OF SYLLOGISTIC MIDDLE TERM J. M. HUBBARD College of St. Thomas St. Paul, Minnesota ABERT THE GREAT is recognized as one of the great scientific minds of the Middle A:ges, both for his commentaries on Aristotle's scientific works and for his own contributions to the study of nature. His contributions to the science of logic go largely unnoticed, however. This is probably due to (...) the ascendency of the Summulae tradition in medieval logic a.bout the time of Albert's death, for the Summulae traidition is quite different from the one represented in his commentaries on the logical writings of Aristotle. I should like to remedy this a bit by looking at how he understands the concept of middle term in Aristotle's Prior Analytics. There are two points with which we can begin this study. First, Albert insists that Ar.istotle's remark that second and third figure syllogisms are imperfect when compared to those of the first figure does not mean that they somehow lack the necessity cha.racteristic of syHogisms of the first figure. On the contra;ry, all syllogisms, in whatever figure, conclude necessa,rily. This is what it is to be a syllogism. First figure syllogisms are perfect with respect to us, for in them the necessity of consequence, which is the very na;bure of the syllogism, is manifest to us in a way that it is not in syllogisms of the second and third figures. Hence, the marks perfect and imperfeot refer not to the syllogisms in themselves but to the syUogisms in relation to us.1 1 Albertus Magnus, Oommentares CYn the Prior Analytics, Bk. I, Tr. 1, Ch. 8, pp. 469-71. See also Tr. 1, Ch. 6, p. 467, and Tr. 1, Chs. 5 and 6. Page 115 116 J. M. HUBBARD Seoond, the notion of syllogism is coextensive with the notion of middle term, for the middle term is the root and cause of the necessity that characterizes the syllogism. This is why some other kinds of argument, induction and example for instance, are not syllogisms strictly speaking, but only in a loose and improper sense; they lack a true middle term.2 What is it, then, to be a middle term of a syllogism on Albert's reading of Aristotle? Is the middle term middle in some quantitative sense, then? Although Albert uses the expressions scope, breadth, contain, etc., he is quite explicit that the notions of figure and term are transferred " metaphorically " from quantity to properly logical considerations.8 For logic deails not with quantity and its relations, but with relations that exist between things as conceived by the mind, the most fundamental of which is the relation of predica.bility. To be predicable is to be sayable of many things, and although a predicable can be considered a whole in relation to the things of which it is said (its parts then), such talk is metaphorical and not literal. A predicable (whole) is sayable of many things but is not constituted by them. Dog, for instance, is sayable of Fido and Rover, but being a dog is not being Fido and Rover. A whole in the ordinary sense, on the other hand, is not sayable of its parts and is composed of them. One could not say that a wall is a house, but a house is composed, among other things, of a wall. The notions of figure and term, and therefore of middle term, are taken from the quantitative aspects of things and trans£erred to properly logical things. This being so, the notion of middle term cannot be reduced to something quantatative, spatial organization for example. From these remarks one can anticipate how Albert would respond to the suggestion that the middle term is the one that is middle in universality with respect to the other two. This references will be to Oommentaria in Prioru.m A.nalytiooru.m in Opera Omnia, ed. A. Borgnet (Paris: Vives, 1890), Vol. 1. 2 Bk. II, Tr. 7, Ch. 4, p. 794. a Bk. I, Tr. I, Ch. 2, pp. 460-61. ALBERTUS MAGNUS AND THE MIDDLE TERM 117 would... (shrink)

The notion of order as a universal and fundamental conceptual category is discussed as being based on sets of similar differences and different similarities. A discussion of relationships between order and disorder is followed by a proposal for a mathematical theory based on non-ordinality which could also have relevance for indistinguishables in physics.

I present an argument for causal fundamentality, understood as the thesis that the causal history of every being, whose existence has a causal explanation, includes some uncaused beings. I argue that this thesis is a consequence of an actualist account of metaphysical modality whose novelty lies in its hybrid dispositional-essentialist foundation. I argue that my modal theory is extensionally correct and minimalistic. Its range of metaphysical necessities and possibilities is just as wide as needed to capture the pre-theoretical notion of (...) modality. Moreover, my theory is immune from the necessitism of standard essentialist accounts of modality and addresses the challenge of global possibilities facing dispositionalist modal theories thanks to its essentialist component. (shrink)

We offer an account of the nature and structure of the immorality of colonialism. We distinguish between the fundamental wrong of colonialism and the other wrongs that the fundamental wrong facilitated. On our view, the fundamental wrong was that colonizers regarded the colonized as incapable of managing their own affairs, in effect relegating them to the status of minors or mentally incompetent adults. We call this the nonautonomy assumption. It could also be called the inferior status assumption, (...) for reasons that will become clear as we proceed. We argue that, in addition to the nonautonomy assumption, the most serious wrongs of colonialism were severe economic injustices and practices of humiliation, and that these wrongs can reasonably be seen to be facilitated by or grounded in the fundamental wrong. We make the case that our analysis has two virtues: it provides a more comprehensive characterization of the wrongs of colonialism and the relationships between them than extant philosophical accounts and it helps make sense of the concepts of neocolonialism and internal colonialism, which extant accounts are unable to do. This has the added advantage of bringing discussions that have hitherto taken place in fields such as political theory, postcolonial studies, history, and critical theory into the ambit of analysis by political philosophers, using tools and concepts that philosophers have at their command, such as the notions of autonomy and inferior status. After developing our own view, we offer a critical appraisal of three prominent recent attempts to identify “the wrong” of colonialism, the views of Anna Stilz, Massimo Renzo, and Lea Ypi. We argue that by focusing on defects of the political structure of colonialism such as the deprivation of collective self‐determination, these accounts do not clearly identify the fundamental wrong of colonialism and either completely ignore or pay insufficient attention to severe economic injustices and practices of humiliation; and that they also render the notions of neocolonialism and internal colonialism unintelligible. While acknowledging that the nonautonomy assumption encouraged colonialists to deprive the colonized of collective self‐determination and recognizing that this was a serious wrong, we deny that the deprivation of collective self‐determination was the fundamental wrong of colonialism, as the denial of autonomy is more basic than the denial of political self‐management. The analysis we offer makes it clear that colonialism is not a topic of merely historical interest. The most serious wrongs suffered by colonized people did not end with decolonization, that is, the achievement of independent statehood. The fundamental wrong of colonialism was grounded in inequalities of power that persist today and that continue to contribute to economic injustices and to the failure to regard the weaker as equals, in a variety of contexts, including, but not limited to the case of formerly colonized peoples. (shrink)

In this paper, I argue for a new way of characterizing ontological emergence. I appeal to recent discussions in meta-ontology regarding fundamentality and dependence, and show how emergence can be simply and straightforwardly characterized using these notions. I then argue that many of the standard problems for emergence do not apply to this account: given a clearly specified meta-ontological background, emergence becomes much easier to explicate. If my arguments are successful, they show both a helpful way of thinking about (...) emergence and the potential utility of discussions in meta-ontology when applied to first-order metaphysics. (shrink)

I argue that dependence is neither necessary nor sufficient for relative fundamentality. I then introduce the notion of 'likeness in nature' and provide an account of relative fundamentality in terms of it and the notion of dependence. Finally, I discuss some puzzles that arise in Aristotle's Categories, to which the theory developed is applied.

In the article the issue of singling out some systemic criteria of differentiation between the fundamental and applied terminologies is considered. The authors point at the fact that each terminology has its own individual peculiarities, which mark it out against a general background of the terminological fund of a certain language. It is asserted that one of the most important and effective criteria that can be the basis of the approach to the study of sublanguages for special purposes is (...) a fundamental or applied character of the sphere of professional or scientific knowledge verbalized by a certain terminology. Such terms, as ‘fundamental terminology‘, ‘applied terminology‘ and ‘terminology of transition type‘, are introduced for scientific use. The fundamental terminology is understood as a sublanguage for special purposes that verbalizes the notions, forming the totality of fundamental knowledge, serving for the description of phenomena and processes in reality and in science, in the framework of which the fundamental research is carried out. The applied terminology is the name for the sublanguage for special purposes representing the notions, in which the results of human being’s practical scientific-industrial activity for changing the reality, forming the artificial habitat, are conceptualized. The terminology of transition type is the terminology that verbalizes the fragments of the field of scientific knowledge in which the research can have both a fundamental and applied character. The authors come to the conclusion that pure applied or fundamental terminologies are quite rare, that it is rational to speak about the degree of manifestation of the applied or fundamental character within the limits of this or that terminological system. (shrink)

Recent advances in the field of quantum cognition suggest a puzzling connection between fundamental physics and the mind. Many researchers see quantum ideas and formalisms merely as useful pragmatic tools, and do not look for deeper underlying explanations for why they work. However, others are tempted to seek for an intelligible explanation for why quantum ideas work to model cognition. This paper first draws attention to how the physicist David Bohm already in 1951 suggested that thought and quantum processes (...) are analogous, adding that this could be explained if some neural processes underlying thought involved non-negligible quantum effects. The paper next points out that the idea that there is a connection between fundamental physics and the mind is not unique to quantum theory, but was there already when Newtonian physics was assumed to be fundamental physics, advocated most notably by Kant. Kant emphasized the unique intelligibility of a Newtonian notion of experience, and this historical background prompts us to ask in the final part of the paper whether we can really make sense of any quantum-like experience. It is proposed that intelligibility is a relative notion and that, regardless of initial difficulties, quantum approaches to cognition and consciousness are likely to provide valuable new ways of understanding the mind. (shrink)

This paper examines the notion of cultural universals and then seeks to identify what the author wishes to idenlify as “cultural fundamentals” in philosophy and philosophical debate. The paper then asses the extent to which such fundamentals are obstacles to the “birth” of potential philosophers. Lastly I suggest a solution to this problem.

In the recent literature on all things metaontological, discussion of a notorious Meinongian doctrine—the thesis that some objects have no kind of being at all—has been conspicuous by its absence. And this is despite the fact that this thesis is the central element of the noneist metaphysics of Richard Routley (1980) and Graham Priest (2005). In this paper, we therefore examine the metaontological foundations of noneism, with a view to seeing exactly how the noneist's approach to ontological inquiry differs from (...) the orthodox Quinean one. We proceed by arguing that the core anti-Quinean element in noneism has routinely been misidentified: rather than concerning Quine's thesis that to be is to be the value of a variable, the real difference is that the noneist rejects what we identify as Quine's “translate-and-deflate” methodology. In rejecting this aspect of Quinean orthodoxy, the noneist is in good company: many of those who think that questions of fundamentality should be the proper focus of ontological inquiry can be read as rejecting it too. Accordingly, we then examine the differences between the noneist's conception of ontology and that offered by the fundamentalist. We argue that these two anti-Quinean approaches differ in terms of their respective conceptions of the theoretical role associated with the notion of being. And the contrast that emerges between them is, in the end, an explanatory one. (shrink)