This volume will be of particular interest to researchers working in the history, and in the philosophy, of logic and mathematics, and more generally, to ...

This monograph offers a fresh perspective on the applicability of mathematics in science. It explores what mathematics must be so that its applications to the empirical world do not constitute a mystery. In the process, readers are presented with a new version of mathematical structuralism. The author details a philosophy of mathematics in which the problem of its applicability, particularly in physics, in all its forms can be explained and justified. Chapters cover: mathematics as a formal science, mathematical ontology: what (...) does it mean to exist, mathematical structures: what are they and how do we know them, how different layers of mathematical structuring relate to each other and to perceptual structures, and how to use mathematics to find out how the world is. The book simultaneously develops along two lines, both inspired and enlightened by Edmund Husserl’s phenomenological philosophy. One line leads to the establishment of a particular version of mathematical structuralism, free of “naturalist” and empiricist bias. The other leads to a logical-epistemological explanation and justification of the applicability of mathematics carried out within a unique structuralist perspective. This second line points to the “unreasonable” effectiveness of mathematics in physics as a means of representation, a tool, and a source of not always logically justified but useful and effective heuristic strategies. (shrink)

This monograph offers a fresh perspective on the applicability of mathematics in science. It explores what mathematics must be so that its applications to the empirical world do not constitute a mystery. In the process, readers are presented with a new version of mathematical structuralism. The author details a philosophy of mathematics in which the problem of its applicability, particularly in physics, in all its forms can be explained and justified. Chapters cover: mathematics as a formal science, mathematical ontology: what (...) does it mean to exist, mathematical structures: what are they and how do we know them, how different layers of mathematical structuring relate to each other and to perceptual structures, and how to use mathematics to find out how the world is. The book simultaneously develops along two lines, both inspired and enlightened by Edmund Husserl’s phenomenological philosophy. One line leads to the establishment of a particular version of mathematical structuralism, free of “naturalist” and empiricist bias. The other leads to a logical-epistemological explanation and justification of the applicability of mathematics carried out within a unique structuralist perspective. This second line points to the “unreasonable” effectiveness of mathematics in physics as a means of representation, a tool, and a source of not always logically justified but useful and effective heuristic strategies. (shrink)

It is my aim in this paper to show that the contemporary assimilation of essence to modality is fundamentally misguided and that, as a consequence, the corresponding conception of metaphysics should be given up. It is not my view that the modal account fails to capture anything which might reasonably be called a concept of essence. My point, rather, is that the notion of essence which is of central importance to the metaphysics of identity is not to be understood in (...) modal terms or even to be regarded as extensionally equivalent to a modal notion. The one notion is, if I am right, a highly refined version of the other; it is like a sieve which performs a similar function but with a much finer mesh. (shrink)

In this book, which remained unfinished at his death, Husserl attempts to forge a union between phenomenology and existentialism.

This is the first English translation of Husserliana XXIII, the volume in the critical edition of Edmund Husserl's works that gathers together a rich array of posthumous texts on representational consciousness. The lectures and sketches comprising this work make available the most profound and comprehensive Husserlian account of image consciousness. They explore phantasy in depth, and furnish nuanced accounts of perception and memory.

Phenomenology has been defined by Husserl as “theory of the essences of pure phenomena,” yet the ontological status of essences in Husserlian phenomenology is far from a settled issue. The late Husserlian emphasis on genetic constitution and the historicity of the lifeworld is not immediately reconcilablewith the ‘unchangeable’ nature that is prima facie attributed to essences. However, the problem of the nature of ideality cannot be dropped from phenomenological accounts without jeopardizing the phenomenological enterprise as such. Through an immanent analysis (...) of Husserl’s meditation on essences a positive account of their ontological status is provided. Essences are interpreted as ontological thresholds, primordially rooted in our motivated confrontation with sensuous transcendence. Essences appear as emergent ontological features, which are not reducible to their particular realizations and which exhibit a fundamental continuity between consciousness and being. They manifest themselves as prospectively a priori (a precondition for further experiences), but retrospectively a posteriori (they are founded in experience). Finally, essences manifest the ‘co-essential’ nature of consciousness and sensuous transcendence: they are the way in which we are motivated and constitutively bound to articulate being, which in turn is apt to be thus articulated. (shrink)

Clarifying the nature of possibility is crucial for an evaluation of the phenomenological approach to ontology. From a phenomenological perspective, it is ontological possibility, and not spatiotemporal existence, that has pre-eminent ontological status. Since the sphere of phenomenological being and the sphere of experienceability turn out to be overlapping, this makes room for two perspectives. We can confer foundational priority to the acts of consciousness over possibilities, or to pre-set possibilities over the activity of consciousness. Husserl’s position on this issue (...) seems to change over time. Ultimately, the establishment of a phenomenological perspective must involve a rejection of any hypostatization of pre-set possibilities, but not all implications of this theoretical step seem to be drawn in Husserl’s texts. This paper is devoted to an illustration of how the phenomenological notion of possibility should change when we reject the hypostatization of possibility, that is, when we reject the idea that all acts of consciousness are to be conceived as realizations of pre-set “ideal forms”. We examine this question, first, by trying to clarify the conceptual constellation of “possibility” in Husserl’s texts. This leads to an overall classification of the features of constituted possibilities. Then we distinguish such constituted possibilities from their constituting conditions, which outlines a different sense of “possibility”. In the last instance two “possibilizing” dimensions are shown to lie at the root of all ontic possibilities. This leads to a final suggestion on the nature of the relation between experience and possibility. Actual experiences create the room for possibility: they are possibilizations. In this sense, experience is to be taken as a generative sphere which goes beyond the customary boundary between epistemic and ontological. From this point of view all experience is to be conceived as emergence. (shrink)

Recently, Kit Fine's (1994) view that modal truths aretrue in virtue of,grounded in, orexplained byessentialist truths has been under attack. In what follows we offer two responses to the wave of criticism against his view. While the first response is pretty straightforward, the second is based on the distinction between, what we call,Reductive Finean EssentialismandNon-Reductive Finean Essentialism. Engaging the work of Bob Hale onNon-Reductive Finean Essentialism, we aim to show that the arguments against Fine's view are unconvincing, while we acknowledge (...) the presence of a deep standoff between the two views. (shrink)

Husserl’s official account of essence is modal. It is also, I submit, incompatible with the role that essence is supposed to play, especially relative to necessity, in his overall philosophy. In the Husserlian framework, essence should rather be treated as a non-modal notion. The point, while not generally acknowledged, has been made before (by Kevin Mulligan for one); yet the arguments given for it, though perhaps sound, are not Husserlian. In this paper I present a thoroughly Husserlian argument for that (...) claim, as well as a Husserlian essentialist account of necessity. I also discuss the role of grounding within the account. (shrink)

In this paper, I provide a thorough discussion and reconstruction of Bernard Bolzano’s theory of grounding and a detailed investigation into the parallels between his concept of grounding and current notions of normal proofs. Grounding (Abfolge) is an objective ground-consequence relation among true propositions that is explanatory in nature. The grounding relation plays a crucial role in Bolzano’s proof-theory, and it is essential for his views on the ideal buildup of scientific theories. Occasionally, similarities have been pointed out between Bolzano’s (...) ideas on grounding and cut-free proofs in Gentzen’s sequent calculus. My thesis is, however, that they bear an even stronger resemblance to the normal natural deduction proofs employed in proof-theoretic semantics in the tradition of Dummett and Prawitz. (shrink)

This paper is devoted to Bolzano’s theory of grounding (Abfolge) in his Wissenschaftslehre. Bolzanian grounding is an explanatory consequence relation that is frequently considered an ancestor of the notion of metaphysical grounding. The paper focuses on two principles that concern grounding in the realm of conceptual sciences and relate to traditionally widespread ideas on explanations: the principles, namely, that grounding orders conceptual truths from simple to more complex ones (Simplicity), and that it comes along with a certain theoretical economy among (...) them (Economy). Being spelled out on the basis of Bolzano’s notion of deducibility (Ableitbarkeit), these principles are revealing for the question to what extent grounding can be considered a formal relation. (shrink)

There is currently intense interest in the question of the source of our presumed knowledge of truths concerning what is, or is not, metaphysically possible or necessary. Some philosophers locate this source in our capacities to conceive or imagine various actual or non-actual states of affairs, but this approach is open to certain familiar and seemingly powerful objections. A different and ostensibly more promising approach has been developed by Timothy Williamson, according to which our capacity for modal knowledge is just (...) an extension, or by-product, of our general capacity to acquire knowledge of true counterfactual conditionals — a capacity that we deploy ubiquitously in everyday life. Williamson’s account crucially involves a thesis to the effect that modal truths can be explained in terms of counterfactual truths. In this paper, I query Williamson’s account on a number of points, including this thesis. My positive proposal, which owes a debt to the work of Kit Fine on modality and essence, appeals instead to our capacity to grasp essences, understood in a neo-Aristotelian fashion, according to which essences are expressed by ‘real definitions’. (shrink)

In recent years, metaphysics has undergone what some describe as a revolution: it has become standard to understand a vast array of questions as questions about grounding, a metaphysical notion of determination. Why should we believe in grounding, though? Supporters of the revolution often gesture at what I call the Argument from Explanatoriness: the notion of grounding is somehow indispensable to a metaphysical type of explanation. I challenge this argument and along the way develop a “reactionary” view, according to which (...) there is no interesting sense in which the notion of grounding is explanatorily indispensable. I begin with a distinction between two conceptions of grounding, a distinction which extant critiques of the revolution have usually failed to take into consideration: grounding qua that which underlies metaphysical explanation and grounding qua metaphysical explanation itself. Accordingly, I distinguish between two versions of the Argument from Explanatoriness: the Unexplained Explanations Version for the first conception of grounding, and the Expressive Power Version for the second. The paper’s conclusion is that no version of the Argument from Explanatoriness is successful. (shrink)

Science in a new sense arises in the first instance from Plato's establishing of logic, as a place for exploring the essential requirements of "genuine" ...

Contents: Preface VII; Introduction 1; 1. The General Framework 5; 2. Some Standard Systems 61; 3. Systems in General 147; 4. Non-Standard Systems 177; Bibliography 210; General Index 215; Index of Symbols 219-220.

The main goal of this article is to examine Edmund Husserl’s method of “eidetic variation”—that is, to examine the way this method is supposed to work in connection with the notion of “similarity” (Ähnlichkeit). Unlike most interpretations, it will be suggested that similarity represents the leading methodologicalprinciple of eidetic variation. We will argue, therefore, that, on the one hand, this method is rooted in the sphere of association and passivity while, on the otherhand, it is constituted by the transposition of (...) a passive synthesis into an active operation. After having introduced and discussed a twofold notion of phantasy(as “localized phantasy” and as “pure phantasy”) as well as a twofold concept of eidos (as “hen epi pollon” and as “pure eidos”), the extent to which for Husserl there cannot be any eidetic variation without a monadology will be shown. (shrink)

The main goal of this article is to examine Edmund Husserl’s method of “eidetic variation”—that is, to examine the way this method is supposed to work in connection with the notion of “similarity” (Ähnlichkeit). Unlike most interpretations, it will be suggested that similarity represents the leading methodologicalprinciple of eidetic variation. We will argue, therefore, that, on the one hand, this method is rooted in the sphere of association and passivity while, on the otherhand, it is constituted by the transposition of (...) a passive synthesis into an active operation. After having introduced and discussed a twofold notion of phantasy(as “localized phantasy” and as “pure phantasy”) as well as a twofold concept of eidos (as “hen epi pollon” and as “pure eidos”), the extent to which for Husserl there cannot be any eidetic variation without a monadology will be shown. (shrink)

The Principle of Sufficient Reason states that everything has an explanation. But different notions of explanation yield different versions of this principle. Here a version is formulated in terms of the notion of a “grounding” explanation. Its consequences are then explored, with particular emphasis on the fact that it implies necessitarianism, the view that every truth is necessarily true. Finally, the principle is defended from a number of objections, including objections to necessitarianism. The result is a defense of a “rationalist” (...) metaphysics, one that constitutes an alternative to the contemporary dogmas that some aspects of the world are “metaphysically brute” and that the world could in so many ways have been different. (shrink)

The Crisis of European Sciences and Transcendental Phenomenology, Husserl's last great work, is important both for its content and for the influence it has had on other philosophers. In this book, which remained unfinished at his death, Husserl attempts to forge a union between phenomenology and existentialism. Husserl provides not only a history of philosophy but a philosophy of history. As he says in Part I, "The genuine spiritual struggles of European humanity as such take the form of struggles between (...) the philosophies, that is, between the skeptical philosophies--or nonphilosophies, which retain the word but not the task--and the actual and still vital philosophies. But the vitality of the latter consists in the fact that they are struggling for their true and genuine meaning and thus for the meaning of a genuine humanity.". (shrink)

Bob Hale presents a broadly Fregean approach to metaphysics, according to which ontology and modality are mutually dependent upon one another. He argues that facts about what kinds of things exist depend on facts about what is possible. Modal facts are fundamental, and have their basis in the essences of things--not in meanings or concepts.

Bob Hale presents a broadly Fregean approach to metaphysics, according to which ontology and modality are mutually dependent upon one another. He argues that facts about what kinds of things exist depend on facts about what is possible. Modal facts are fundamental, and have their basis in the essences of things--not in meanings or concepts.

Can the straight line be analysed mathematically such that it does not fall apart into a set of discrete points, as is usually done but through which its fundamental continuity is lost? And are there objects of pure mathematics that can change through time? Mathematician and philosopher L.E.J. Brouwer argued that the two questions are closely related and that the answer to both is "yes''. To this end he introduced a new kind of object into mathematics, the choice sequence. But (...) other mathematicians and philosophers have been voicing objections to choice sequences from the start. This book aims to provide a sound philosophical basis for Brouwer's choice sequences by subjecting them to a phenomenological critique in the style of the later Husserl. (shrink)

In this illuminating, highly engaging book, Jonathan Bennett acquaints us with the ideas of six great thinkers of the early modern period: Descartes, Spinoza, Leibniz, Locke, Berkeley, and Hume. For newcomers to the early modern scene, this lucidly written work is an excellent introduction. For those already familiar with the time period, this book offers insight into the great philosophers, treating them as colleagues, antagonists, students, and teachers.

There is a long tradition in philosophy of using a priori methods to draw conclusions about what is possible and what is necessary, and often in turn to draw conclusions about matters of substantive metaphysics. Arguments like this typically have three steps: first an epistemic claim , from there to a modal claim , and from there to a metaphysical claim.

It is argued that there are three main forms of necessity --the metaphysical, the natural and the normative--and that none of them is reducible to the others or to any other form of necessity. In arguing for a distinctive form of natural necessity, it is necessary to refute a version of the doctrine of scientific essentialism; and in arguing for a distinctive form of normative necessity, it is necessary to refute certain traditional and contemporary versions of ethical naturalism.

How does metaphysical grounding interact with the truth-functions? I argue that the answer varies according to whether one has a worldly conception or a conceptual conception of grounding. I then put forward a logic of worldly grounding and give it an adequate semantic characterisation.

Husserlian Essentialism is the view, maintained byEdmundHusserl throughout his career, that necessary truths obtain because essentialist truths obtain. In this thesis I have two goals. First, to reconstruct and flesh out Husserlian Essentialism and its connections with surrounding areas of Husserl's philosophy in full detail – something which has not been done yet. Second, to assess the theoretical solidity of the view. As regards the second point, after having presented Husserlian Essentialism in the first two chapters, I raise a serious (...) problem for it in Chapter 3. In the remainder of the thesis I endeavour to solve the problem. In order to do so, I propose to amend both Husserl's theory of essence and his theory of predication. The bulk of the emendation consists in working out an account of essence and an account of predication that do not presuppose, or in any way imply, the claims that: 1) for a universal to be in the essence of an object, either the object or one of its parts must instantiate the universal; 2) for a universal to be truly predicated of an object, either the object or one of its parts must instantiate the universal. These claims, notice, apart from being what gets Husserl in trouble, are well entrenched not only in Husserl's, but in most theories of essence and predication. It is thus interesting to see what an alternative option may be – even regardless of the Husserlian setting in which I work it out. (shrink)

Can one hold both that universals exist in the strongest sense (i.e., neither in language nor in thought, nor in their instances) and that they exist contingently—and still make sense? Edmund Husserl thought so. In this paper I present a version of his view regimented in terms of modal logic cum possible-world semantics. Crucial to the picture is the distinction between two accessibility relations with different structural properties. These relations are cashed out in terms of two Husserlian notions of imagination: (...) world-bound and free. After briefly presenting the Husserlian framework—his intentionalism, idealism and how universals figure in them—I set up my modal machinery, model the target view, and show that, depending on the chosen accessibility relation, the necessary or the contingent existence of universals can be derived. Importantly, since for Husserl both relations are bona fide, both derivations are legitimate. In Husserl’s philosophy, then, there is room for both necessary and contingent universals. (shrink)

Even the most cursory reader of Husserl’s writings must be struck by the frequent references to essences (“Wesen”, “Essenzen”), Ideas (“Idee”), kinds, natures, types and species and to necessities, possibilities, impossi- bilities, necessary possibilities, essential necessities and essential laws. What does Husserl have in mind in talking of essences and modalities? What did he take the relation between essentiality and modality to be? In the absence of answers to these questions it is not clear that a reader of Husserl can (...) be said to understand him. (shrink)

Simon Blackburn posed a dilemma for any realist attempt to identify the source of necessity. Either the facts appealed to to ground modal truth are themselves necessary, or they are contingent. If necessary, we begin the process towards regress; but if contingent, we undermine the necessity whose source we wanted to explain. Bob Hale attempts to blunt both horns of this dilemma. In this paper I examine their respective positions and attempt to clear up some confusions on either side. I (...) come to defend Hale’s conclusion that both horns of the dilemma can be resisted. I end by defending my own account of the source of necessity, and showing why it does not fall victim to Blackburn’s problem. (shrink)