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Kit Fine on Logic, Metaphysics and Ontology. Annotated Bibliography. Papers 1989-2006

Bibliography of Kit Fine

Books. Papers 1970-1988

Papers 2007-2016

Kit Fine. Annotated Bibliography of the Studies on His Philosophy

PAPERS FROM 1989 TO 2006

  1. Fine, Kit. 1989. "Incompleteness for Quantified Relevance Logics." In Directions in Relevant Logic, edited by Norman, Jean and Sylvan, Richard, 205-225. Dordrecht: Kluwer.

    Reprinted in: Alan Ross Anderson, Nuel D. Belnap, Jr., with contributions by J. Michael Dunn ... [et al.], Entailment: The Logic of Relevance and Necessity, Princeton: Princeton University Press, 1992 vol. II, pp. 235-261.

    "In the early seventies, several logicians developed a semantics for propositional systems of relevance logic.


    In the light of this work, it seemed reasonable to extend the completeness results to quantificational systems of relevance logic. But what systems should be chosen? One would like, in the first place, to deal with the systems that already exist in the literature, such as quantified R (RQ) or quantified E (EQ). This, at least, is a debt that we owe to the history of the subject. But one would also like to prove completeness for the quantificational analogues of propositional systems that have already been proved to be complete. These analogues might be obtained from the propositional system by adding a standard quantificational component, consisting of such and such axioms and rules. Such a component might be chosen in terms of its intrinsic plausibility as a quantificational basis. Less arbitrarily, it might be chosen so as to yield a complete system when combined with the minimal propositional system (the one complete under no special conditions on o, R or *). Not surprisingly, the pre-existing systems turn out to be equivalent to the systems obtained by the other approach.

    The construction of the quantificational analogue is not, in fact, as straightforward as this description might suggest; for the extension of the propositional semantics to the quantificational case is not unique. It must be decided whether the domain I of individuals is to be constant or not. If it is not constant, then there are various ways of dealing with nonexistent individuals, individuals that do not belong to the domain of the world or point under consideration. But once these decisions are made, the choice of the quantificational component can be fixed." (p. 205)

  2. ———. 1989. "The Problem of de re Modality." In Themes from Kaplan, edited by Almog, Joseph, Perry, John and Wettstein, Howard, 197-272. New York: Oxford University Press.

    Reprinted in: Modality and Tense. Philosophical Papers, as chapter 2, pp. 40-104.

    "I want now to evaluate Quine’s objections to quantified modal logic, dealing first with the metaphysical and then with the logical argument.

    I observed before that the metaphysical argument was operator-specific; for different operators it yields different problems. This observation applies as much to different notions of necessity as it does to notions other than necessity. There is not a single problem of essentialism, but a range of problems, that vary according to the notion of necessity in question.

    There are perhaps four principal notions of necessity for which the problem arises; these are, respectively, the logical, the analytic, the metaphysical, and the natural. Of these, the most important is undoubtedly the problem for the metaphysical notion. Indeed, not only is this problem of great importance in itself, but it is central, in my opinion, to any attempt to understand the nature of metaphysics.

    However, it is not my intention to discuss this problem here. I wish to follow Quine and concentrate my attention on the logical and semantic modalities." (p. 202)

  3. ———. 1989. "The Justification of Negation as Failure." In Logic, Methodology and Philosophy of Science VIII. Proceedings of the Eighth International Congress of Logic, Methodology and Philosophy of Science, Moscow, 1987, edited by Fenstad, Jens Erik, Frolov, Ivan and Hilpinen, Risto, 263-301. Amsterdam: North-Holland.

    "Prolog is a logic programming language; it is used to answer queries on the basis of information provided by the programmer. For the most part, the logic employed by Prolog is standard. But it uses a highly unorthodox rule for establishing negative facts. This rule, the so-called rule of negation as failure, allows us to deny a statement on the grounds that a certain attempt to prove it has failed.

    The rule is not classically valid; and therefore the question arises as to how it is to be justified. There are basically three different kinds of justification that have been proposed in the literature. The first is to re-interpret negation to mean something like unprovability. The second is to assume that the program is complete with respect to truths; all truths are derivable. The third is to suppose that the program is complete with respect to conditions; all sufficient conditions for the application of the predicates have been specified.

    My aim in this paper is to evaluate these various proposals and then to make a proposal of my own. I shall argue that the existing proposals all suffer from some defect or another: the first is unable to account for a classical reading of negation; the second delivers too much on programs which employ negation; and the third delivers too little on programs which make no use of negation.

    I shall then argue that my own proposal is able to avoid these difficulties. From one point of view, the proposal is not new; it is merely a form of the second proposal stated above, according to which all truths are derivable. However, the concept of derivability which is appealed to is quite novel; for the assumption that all truths are derivable, may itself be used in establishing that a given statement is derivable. The assumption has, in other words, a self-referential character.

    The proposal has various other features of interest. It provides a natural way of interpreting inductive definitions in which the positive instances of a predicate are allowed to depend upon its negative instances. It sanctions an extension of the rule of negation of failure, under which not only the finite, but also the transfinite, failure of a statement may constitute a ground for its denial. It is capable of variation in the choice of which other assumptions or rules are used in defining the concept of derivability.


    One feature of my exposition is worthy of special note. I have for the most part confined my attention to the sentential case, under which only truth-functional complexity is ever exposed. Such a case is usually regarded as trivial, since most of the interesting features of Prolog depend upon the use of variables. However, in this regard, the rule of negation as failure is an exception. Most of the problems in justifying the rule already arise at the sentential level; and to solve these problems at this level is to have gone a long way towards solving them altogether. There are, however, certain difficulties which are peculiar to the introduction of variables and terms; and these are considered at the end of the paper. It is argued, in particular, that the usual assumptions concerning an ontology of terms are needlessly strong and that an ordinary ontology of individuals can be countenanced in its place." (pp. 263-264)

  4. ———. 1990. "Quine on Quantifying In." In Propositional Attitudes: The Role of Content in Logic, Language and Mind, edited by Anderson, Anthony and Owens, Joseph, 1-26. Stanford: Center for the Study of Language and Information, Stanford University.

    Reprinted in: Modality and Tense. Philosophical Papers, as chapter 3, pp. 105-130.

    "It is my aim in this chapter to evaluate Quine’s argument against quantifying into modal contexts, dealing first with the peculiarly modal considerations and then with the more general logical considerations." (p. 2)

  5. ———. 1991. "The Study of Ontology." Noûs no. 25:263-294.

    "A constructional ontology is one which serves to construct complexes from simples. The present paper is concerned with the nature and with the study of such ontologies. It attempts to say, in the first place, how they are constituted and by what principles they are governed. But it also attempts to say how their study may lead one to adopt certain positions and to make certain definitions.

    The remarks on the study of ontology are meant to relate to the study of disciplines in general. I am interested in how the study of a discipline gets shaped by the positions which are adopted and the strategies which are pursued. These interact; for the pursuit of certain kinds of strategy will lead to the adoption of certain kinds of position, and the adoption of certain kinds of position will be required by the pursuit of certain kinds of strategy. One therefore needs to understand how they interact.

    Certain subsidiary themes run through the paper, all interrelated in one way or another. One concerns a dialectical conception of modality, one that is determined by what is left open at a given stage of enquiry. Another involves a particular way of expressing modal claims, in terms of certain objects requiring others. Yet a third is an interest in a relativist conception of ontology, according to which no ontology stands out as being correct.

    The paper concludes with a formal appendix, which attempts to make precise much of what can be made precise in the earlier informal part of the paper. Each part has been designed to be read independently of the other, although a proper understanding of either part depends upon reading them both." (p. 263)

  6. ———. 1991. "The Identity of Material Objects." In Topics in Philosophy and Artificial Intelligence, edited by Albertazzi, Liliana and Poli, Roberto, 33-37. Bozen: Istituto Mitteleuropeo di Cultura.

    Papers from the International Summer Schools in Bozen - 1989-1990.

    "1. The Problem of Identity

    What is a question of identity? Two responses to this meta-question of identity may be distinguished, which I call the comparative and the intrinsic. On the comparative conception, one answers a question of identity by saying when two objects of a given sort are the same. On the intrinsic conception, one answers a question of identity by saying what objects of a given sort are "in themselves".

    The comparative conception goes back to Locke's famous chapter on identity. It was extended by Frege. Very roughly, we may say that Frege extended the application of the comparative conception from the identity of concrete objects to the identity of abstract objects. This conception is the dominant one of today; it informs the work of Strawson, Quine, Wiggins and of others.

    The basic idea behind the comparative conception is to make the what of identity a when: to ask what an object of a given sort is is to ask when objects of that sort are the same. But to ask when two objects are the same invites the trivial answer: when they are the same. We need somehow to distinguish the intended answers to this question.

    This can often be done by means of the concept of a presentation. I mean to use this term in a suitably abstract sense. Thus a sentence might be regarded as a presentation of a proposition; there is no need for a presentation to be something mental or even for it to be that by which we grasp the object.

    An intended answer to an identity question then says when two presentations are presentations of the same object; and it says this in terms which do not presuppose the identity of the objects at issue.

    Different questions of identity - e.g. at a time, across time, across worlds - turn on different accounts of how the objects are to be presented.

    There is a fundamental criticism to be made of the comparative conception. For it says what kind of "career" the object has, not what kind of object it is that has the career. For example, a transtemporal criterion of identity for material things is compatible with a material thing being (a) a primitive substance, (b) a mereological sum of time-slices, (c) the embodiment of a form, (d) an event, and so on. Similarly, the extensional criterion of identity for sets is compatible with a set being (a) constructive, (b) "exclusive", i.e. determined by its non-members rather than by its members, (c) logical, i.e. determined by a property with the required extension rather than by its members.

    What is missing from the comparative conception? I would like to suggest that often what is missing is an account of how the objects of the given kind are generated or analysed. Thus primitive substances are not generated from anything else at all, mereological sums are generated by aggregation, embodiments are generated by a suitable embodiment operator, and so on. In each case, we need to say how (if at all) the object is to be analysed; we need to say what the object is in itself." pp. 33-34.

  7. ———. 1992. "Aristotle on Matter." Mind no. 101:35-57.

    "It is my belief that there is still a great deal to be learnt from Aristotle’s views on the nature of substance; and it is my aim in a series of papers, of which this is the first, to make clear what these views are and what it is in them that is of value. (1)

    A peculiarity of my approach, compared to current scholarly practice, is the attempt at rigour. I have tried to provide what is in effect a formalization of Aristotle’s views. I have, that is to say, attempted to make clear which of his concepts are undefined and which of his claims underived; and I have attempted to show how the remaining concepts are to be defined and the remaining claims to be derived.

    I can well understand a traditional scholar being suspicious of such an approach on the grounds that the various parts of Aristotle’s thought are either too unclear to be capable of formalization or else are clear enough not to require it.

    Since the matter is not one for a priori dispute, I can only ask the scholar to put his suspicions at bay until the details of the case are examined. I then think that it will be found that the attempt at rigour provides a most valuable guide for the study of the text.

    I have not tried to deal with all aspects of Aristotle’s thought on substance. I have concentrated on those which centre on the concepts of matter, form, part, and change; and I have neglected those which concern the related concepts of predication, function, priority and power. It is to be hoped that the investigation will be rounded out at some later time to include all of the central aspects of his work.

    It should also be mentioned that my treatment of the text has not been altogether scholarly. Partly this has been a matter of competence, and partly of inclination. I have been more concerned with the broad sweep of Aristotle’s views than with exegetical detail; and this has led me to conjecture that he held a certain opinion, not because of direct textual evidence but because it is what his view most naturally requires. Thus the Aristotle I have presented here is much more consistent, definite and complete than the Aristotle of the texts." (p. 35)

    (1) This paper is based upon the first two sections of my unpublished paper “Aristotle on Substance” . I should like to thank the members of a seminar I held at UCLA in the winter of 1991, and Frank Lewis in particular, for many helpful discussions on some of the topics of the paper. I am also grateful to Richard Sorabji for valuable remarks on an earlier version of the paper.

  8. ———. 1992. "Transparent Grammars." In Logic from Computer Science. Proceedings of a Workshop held November 13-17, 1989, edited by Moschovachis, Yiannis N., 129-151. New York: Springer.

    "1 . Introdution

    ‘Cat’ is a word which occurs in ‘cattle’, but it does not occur as a word; ‘1-1-2’ is a term which occurs in ‘1+ 2.3’, but it does not occur as a term. All such occurrences of expressions might be said to be accidental, since they are accidents of how the syntax of the language happens to be realized.

    The notion of accidental occurrence is significant in various areas of thought. In logic, it greatly aids the formulation and proof of meta-logical results if it can be assumed that the underlying language contains no accidental occurrences. For example, a subformula can then simply be defined as a formula which occurs within a given formula rather than as an expression which is thrown up by a parsing of that formula. In philosophy, the issue of whether one can quantify into modal contexts has been seen to turn on such questions as to whether the occurrence of ‘9’ in ‘necessarily, 9 > 7’ is accidental or not; and the absence of accidental occurrence has been regarded as a condition on any “ ideal language” . In computer science and in linguistics, the presence of accidental occurrences has an obvious relevance to parsing, since they lead to the danger that a parser might mistake an apparent constituent of the expression to be parsed for a genuine constituent.

    Let us say that a language or grammar is transparent if it permits no accidental occurrences. It is the main purpose of the present paper to investigate the conditions under which a context-free grammar is transparent.

    It is shown how any accidental occurrence reduces to a certain “ primitive” case; and it is shown how such primitive occurrences might be detected.

    On the basis of these results on reduction and detection, an effective test for transparency is then given.

    The concept of transparency represents a strengthening of the more familiar concept of nonambiguity. Any transparent grammar, at least of a well-behaved sort, is unambiguous, though not every unambiguous grammar is transparent. Moreover, what is required for many purposes is not merely an unambiguous but a transparent grammar. It is therefore significant in this regard that there is an effective test for the stronger property even though there is no effective test for the weaker one.

    The plan of the paper is as follows. The first two sections introduce the relevant notions from the theory of context-free grammars. The third section explains the connection between nonambiguity and transparency.

    The fourth section establishes the reduction of accidental occurrence to the primitive case. The next three sections deal with the question of detecting the primitive accidental occurrences: a more fully articulated or canonical version of the given grammar is introduced; it is shown how accidental occurrences in the given grammar correspond to certain kinds of expression in the canonical grammar; and a precedence analysis is given of those expressions in the canonical grammar which correspond to the primitive

    accidental occurrences in the given grammar. An effective test for transparency is then provided in the final section.

    The treatment of transparency in this paper has been very brief. Many of the results can be extended; and I have given a much fuller account in Fine [1]." (pp. 129-130)


    [1] Fine, K., Transparency I and II, submitted to Language and Control.

  9. ———. 1994. "Essence and Modality." Philosophical Perspectives no. 8:1-16.

    "The concept of essence has played an important role in the history and development of philosophy; and in no branch of the discipline is its importance more manifest than in metaphysics.

    Its significance for metaphysics is perhaps attributable to two main sources. In the first place, the concept may be used to characterize what the subject, or at least part of it, is about.

    For one of the central concerns of metaphysics is with the identity of things, with what they are.

    But the metaphysician is not interested in every property of the objects under consideration. In asking 'What is a person?', for example, he does not want to be told that every person has a deep desire to be loved, even if this is in fact the case.

    What then distinguishes the properties of interest to him? What is it about a property which makes it bear, in the metaphysically significant sense of the phrase, on what an object is?

    It is in answer to this question that appeal is naturally made to the concept of essence. For what appears to distinguish the intended properties is that they are essential to their bearers." (p. 1)


    "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.

    I shall also argue that the traditional assimilation of essence to definition is better suited to the task of explaining what essence is. It may not provide us with an analysis of the concept, but it does provide us with a good model of how the concept works. Thus my overall position is the reverse of the usual one. It sees real definition rather than de re modality as central to our understanding of the concept." (p. 3)

  10. ———. 1994. "Compounds and Aggregates." Noûs no. 28:137-158.

    "Some objects appear to be composed of parts: a quantity of sand of its grains, a throbbing pain of its throbs, a set of its members, and a proposition of its constituents.

    There seem to be two fundamentally different ways in which an object can be composed of parts. One is nonstructural in character; the parts just merge. The other is structural; the parts hang together within a structure. Thus of the examples above, the first two, the sand and the pain, are composed from their parts in a nonstructural fashion, while the last two, the set and the proposition, are composed in a structural manner.

    The notion of a nonstructural method of composition may be taken to be one which conforms to certain structure-obliterating identity conditions. These are as follows: order and repetition among the composing objects is irrelevant to the result; the composition of a single object is the object itself; and the composition of compositions of objects is the composition of those very objects'. Thus the first of these conditions excludes concatenation as a nonstructural method of composition; while each of the remaining conditions excludes the set-builder (the operation which composes a set from its members).

    Let us agree to call any nonstructural method of composition a method of fusion. There is a particular such method, I call it aggregation, which has been very prominent in the literature on part-whole. It may be characterized as a method of composition which conforms to the identity conditions above and which also conforms to the following existence conditions: the aggregate of objects which exist in time exists at exactly those times at which one of the objects exists; and an aggregate of objects which are located in space occupies, at any given time at which it exists, exactly those places which are occupied by one of the objects.

    It has often been supposed that aggregation is a legitimate method of composition, that objects may be composed from others in conformity with the conditions set forth above. What has made aggregation so attractive, apart from any intuitive appeal it may have, are two main factors (which will be discussed in more detail later in the paper). The first, and most important, is the identification of a thing with the content of its spatio-temporal extension. The second is the identification of a thing with the fusion of its time-slices. Both of these forms of identification require that the objects fuse in the manner of aggregation.

    It has also often been supposed that aggregation is the only legitimate method of fusion. Part of the appeal of this further position may arise from a general hostility to different methods of composition, whether they be methods of fusion or not. Under the form of nominalism championed by Goodman, for example, there can be no difference in objects without a difference in their parts; and this implies that the same parts cannot, through different methods of composition, yield different wholes.

    However, I suspect that many of those who would be open to structural methods of composition would still not be open to distinct nonstructural methods of composition. For it is hard to see, especially given the identification of a thing with its spatio-temporal content, what other methods of fusion there might be; and it is hard to see how there could be alternative conceptions of a fusion, of a whole at the same level as its elements and formed without regard to their order or repetition.

    Let us call the extreme position, that there is only one method of composition, mereological monism; let us call the less extreme position, that there is only one method of fusion, fusion monism; and let us call that particular version of fusion monism according to which aggregation is the sole method of fusion aggregation monism.

    The main purpose of this paper is to show that the last of these three positions is mistaken. I want to show that there is a method of fusion which is not aggregative, i.e. which does not conform to the characteristic existence conditions for aggregates. However, my attack on this position may be relevant to the two other positions as well. For granted that aggregation is itself a legitimate method of fusion, it follows that fusion monism should be dropped in favour of a pluralist position. And to the extent that the adoption of monism depended upon a general hostility to structural considerations, the way is then open to the admission of structural methods of composition.

    It is also my intention to attack two related forms of monistic doctrine. For just as we can single out the aggregative method of nonstructural composition, so we can single out the aggregative way of being a nonstructural part and the aggregative kind of nonstructural whole. One might then maintain that not only does aggregation constitute the only nonstructural method of composition, but that it also constitutes the only nonstructural way of being a part and the only nonstructural way of being a whole. We therefore have three forms of monism, one with respect to composition, another with respect to part, and a third with respect to whole. As will later become clear, the two further forms of monism aresuccessively weaker than the original; and so their denials might be taken, in mimicry of Quine, to comprise three grades of mereological involvement.

    From the discussion of monism will emerge objections to two other prominent doctrines: extensionalism and mereological atomism. According to the first of these, things are the same when their extensions (spatial, spatio-temporal, or modal-spatio-temporal) are the same; and according to the second, parts are prior to their wholes.

    For the purposes of attacking the aggregation monist, I have assumed that aggregation is a legitimate method of fusion. Towards the end of the paper, I suggest that there is no such method and propose a form of fusion monism in which some other method of fusion takes the place of aggregation. However, my tentative endorsement of fusion monism is not meant in any way to lend support to a general monist position." (pp. 137-139)

  11. ———. 1994. "A Puzzle Concerning Matter and Form." In Unity, Identity, and Explanation in Aristotle's Metaphysics, edited by Scaltsas, Theodore, Charles, David and Gill, Mary Louise, 13-40. Oxford: Clarendon Press.

    "Montgomery Furth has written (1), "given a suitable pair of individuals ... there is no reason of Aristotelian metaphysics why the very fire and earth that this noon composes Callias and distinguishes him from Socrates could not, by a set of utterly curious chances, twenty years from now compose Socrates ...". He does not specify what these "curious chances" might be. But we may suppose that Socrates eats Callias for his lunch and that, owing to the superiority of Callias' flesh and bone, it is the matter of this which remains in Socrates after the period of twenty years.

    That such an exchange of matter is possible is a point on which many Aristotelian scholars could agree. However, I wish to argue that such a case gives rise to a fundamental difficulty; for its possibility runs into conflict with certain basic metaphysical principles which are commonly attributed to him and which would also be commonly accepted.

    The problem consequently arises as to how this difficulty is to be resolved. This problem itself may be regarded in two somewhat different lights. On the one hand, it may be regarded as a difficulty for Aristotle. The question then is whether one can find a solution which would be acceptable to him, either in the sense that he would or that he could accept it. On the other hand, it may be regarded as a difficulty for a neo-Aristotelian, i.e. to someone who is sympathetic to the analysis of things into matter and form. The question then is to find a solution, regardless of whether or not it would be acceptable to Aristotle.

    For the most part, my concern has been with the exegetical question; and even here, my purposes have been somewhat limited. For I have not attempted to settle on one solution as opposed to another. My aim has been to map out the exegetical space rather than to locate the views of Aristotle within it.

    However, it should be mentioned that I count myself a neo-Aristotelian (and, indeed, it was my own commitment to hylomorphism which led me investigate Aristotle' views in the first place). It has therefore been of some importance for me to take the purely metaphysical question into account."(p. 13)

    (1) Furth, M. Transtemporal Stability in Aristotelian Substances, Journal of Philosophy, 75 (1978), 624-646; reprinted in Substance, Form, and Psyche: An Aristotelean Metaphysics, Cambridge University Press: Cambridge, 1988. (note abbreviated).

  12. ———. 1995. "The Logic of Essence." Journal of Philosophical Logic no. 24:241-273.

    "Central to this paper is a certain distinction. This is the distinction between objects simply having a property and their having that property essentially or by their very nature. Also central to the paper is a certain claim. This is the claim that the notion of essence, of objects essentially having a property, is not to be understood in terms of the notion of necessity.

    The claim is defended in my paper Essence and Modality. But the basic idea behind the defence can be given here. Consider Socrates and the singleton set containing him. Now although it is plausible to suppose that the singleton essentially contains the man, it is not plausible to suppose that the man essentially belongs to the singleton. There is nothing in the nature of Socrates which demands that there be any sets, let alone one that contains him. However, the standard accounts of essence in terms of necessity are unable to account for this asymmetry. For under such an account, the singleton essentially containing Socrates will consist in something like its being necessarily the case that the set contains Socrates if the set exists. But if this is true, then it will also be necessarily the case that Socrates belongs to the set if the man exists." (p. 241)

  13. ———. 1995. "Part-Whole." In The Cambridge Companion to Husserl, edited by Smith, Barry and Smith, David Woodruff, 463-485. Cambridge: Cambridge University Press.

    "Husserl's third Logical Investigation is perhaps the most significant treatise on the concept of part to be found in the philosophical literature. (1) In it Husserl attempts to analyze the notion of dependent part, to lay down the principles governing its use, and to relate it to more general considerations concerning the nature of necessity and unity.

    He begins his study with the consideration of objects in the psychological sphere. A typical example of the kind of object he has in mind is that of a visual datum, a red patch, let us say, and its various aspects or "moments"- its colour, say, or its extension. He takes each of these moments to be peculiar to the object in question; no other datum, no matter how great its resemblance to the original datum, will have the very same moments. He also takes the moments to be, in a suitably broad sense, part of the given object; they are thought to be actually present in it." (p. 463)


    "My aim in the present essay is to clarify certain formal aspects of Husserl's thought. I have here and there, inserted some critical comments; but my main concern has been to say what the views are, and not to say whether or not they are right. Husserl himself took the formalization of his ideas to be not only possible, but highly desirable. He writes (§24, 484):

    a proper working out of the pure theory we here have in mind would have to define all concepts with mathematical exactness and to deduce all theorems by argumenta in forma, i.e., mathematically. . . . That this end can be achieved has been shown by the small beginnings of a purely formal treatment in our present chapter. In any case, the progress from vaguely formed to mathematically exact concepts and theories is here, as everywhere, the precondition for full insight into a priori connections and an inescapable demand of science.

    Thus the present paper can be regarded as an attempt to carry though the project that he began." (p. 464)

  14. ———. 1995. "The Problem of Mixture." Pacific Philosophical Quarterly no. 76:266-369.

    Reprinted in: Frank A. Lewis and Robert Bolton (eds.), Form, Matter and Mixture in Aristotle, Oxford: Blackwell, 1996, pp. 82-182.

    "For Aristotle, the everyday world contains three main kinds of things: the elements, the homogeneous mixtures, and the heterogeneous substances. The topic of mixture was vigorously debated in medieval times (see Maier (1982): 142). But contemporary interest has focused on the objects at the extremes of his ontology -- the elements and the substances -- while the topic of mixture has been relatively neglected. This is unfortunate. For not only is the topic of great interest in its own right, it is also important for a wider understanding of Aristotle's scientific and metaphysical views.

    The intrinsic interest of the topic largely arises from the difficulty in seeing how a non-atomistic conception of matter is to be reconciled with a plausible view of mixture. The exegetical interest has perhaps two main sources. The first resides in the special position occupied by mixtures in Aristotle's ontology. For all substances are composed of mixtures; and all elements compose mixtures, in so far as they compose anything at all. Thus the mixtures provide the cushion, as it were, between the elements and the substances; and any account of the role of the elements or of the nature of the substances should deal with the relationship of each to the mixtures.

    The other source of exegetical interest lies in the relevance of the topic of mixture to other, more general, topics -- principally, potentiality and change. Just as mixtures occupy a kind of midpoint between the elements and the substances, so mixing occupies a kind of midpoint between accidental and substantial change; and the potentiality of the ingredients in a mixture is one of the more important and problematic forms of potentiality for Aristotle. Thus no exegesis of his views on either change or potentiality can be considered complete unless it takes into account his views on mixture.

    We now know that Aristotle's views on mixture are mistaken, and badly mistaken at that. In rejecting atomism he made a critical (though understandable) error; and when one combines the rejection of atomism with the antiquated belief in the four elements, it is easy to conclude that his views are purely of scholarly interest with no real relevance to contemporary concerns. But even though his views may be much further removed from reality than those of modern science, they are much closer in many ways to common sense. In the laboratory we do not suppose that every part of some butter is butter. But in the kitchen we do; and it is convenient, though erroneous, assumptions of this sort that guide us in our everyday life. This therefore suggests that we treat these views of Aristotle as having their most direct bearing, not on the nature of reality, but on the structure of common sense.

    There have been recent attempts in cognitive science to formalize the content of folk or naive physics; such a physics is meant to provide the principles that would enable one to construct a robot that could deal with the everyday world in much the same way as we do. If I am not mistaken, the contemporary interest of Aristotle's scientific views may lie as much in their connection with these developments within cognitive science as it does with the content of the established sciences. I might add that the recent attempt to rehabilitate the notion of capacity by Cartwright (1989) and others also gives a topical interest to Aristotle's general views on capacities and on the way they might compose or interact within a mixture.

    The paper is in six sections. In the first, I state the problem with which Aristotle opens his discussion of mixture in Generation and Corruption: how is mixture possible? Aristotle thinks he has a solution; and our problem is to understand what that solution is. In the next section, I consider three interpretations of his views on mixture, those of Sharvy (1983), Gill (1989) and Bogen (1995), and find all of them wanting. The main defect with these proposals, from my own point of view, is that they do not take Aristotle's hylomorphic outlook sufficiently seriously. In the third section, I provide a sketch of that outlook and set out the two main accounts of mixture that are in conformity with it, Leveling and Ascent; one places mixture at the same level as the elements, the other at a higher level. The next two sections are the heart of the paper and constitute a sustained argument in favor of Leveling. It is shown how two doctrines -- the doctrines of intermediates and of derived parts -- enable Aristotle to avoid the apparently insuperable difficulties that lie in the way of its acceptance. The final section considers the problem of how mixing, as opposed to mixture, is possible and argues that Aristotle is also in a position to solve this problem." (pp. 82-83).


    Bogen, 1995 "Fire in the belly: Aristotelian elements, organisms, and chemical compounds", this volume [pp. 183-216]

    Gill, M. 1989 Aristotle on Substance: The Paradox of Unity, New Jersey: Pennsylvania University Press

    Maier, A. 1982 On the Threshold of Exact Science, Philadelphia: University of Pennsylvania Press

    Sharvy, R. 1983 "Aristotle on Mixtures", Journal of Philosophy, 80, 439-457.

  15. ———. 1995. "Ontological Dependence." Proceedings of the Aristotelian Society no. 95:269-290.

    "T'here appears to be a distinctively ontological sense in which one thing may be said to depend upon another. What the one thing is will depend upon the other thing, upon what it is. It is in this sense that one is tempted to say that a set depends upon its members or that a particularized feature, such as a smile, upon the particular in which it is found. For what the set is will depend upon its members; and what the feature is will depend upon the particular that instantiates it. (1)

    Granted that there is an intelligible notion of ontological dependence, it would appear to be of great importance to the study of metaphysics. Metaphysics has two main areas of concern: one is with the nature of things, with what they are; and the other is with the existence of things, with whether they are. Considerations of dependence are relevant to both. For central to the question of the nature of any item is the determination of what it depends upon; and if something is taken to exist, then so must any thing upon which it depends. Indeed, it has often been maintained that it is only those things which do not depend upon anything else that can properly be said to exist at all." (p. 269)


    "But how is the notion of dependence itself to be understood? The idea of what something is, its identity or being, is notoriously obscure; and the idea of the being of one thing depending upon that of another is doubly obscure. A natural suggestion at this point is to take the being of something simply to be its existence. Thus in saying that a set depends upon its members, or a feature upon its instantiator, we are taking the existence of the one to depend upon that of the other. Call this the existential construal of dependence. Another natural suggestion is to take the dependence between the beings of the two items, as opposed to the items themselves, to be modal in character. The being of the one will depend upon that of the other in the sense that it is necessary that if the one item has its ‘being’ then so does the other. Call this the modal construal of dependence." (p. 270)

    (1) This paper derives from an earlier paper ‘Dependent Objects’ , that was written in 1982 but remained unpublished. Some of the issues raised are discussed at greater length in Fine [1995b]; and no attempt is here made to settle the methodological, as opposed to the conceptual, issues. I should like to thank Ruth Chang and the members of the Wednesday Group at Oxford for helpful comments.


    Fine K. [1995b] ‘Senses of Essence’, to appear in Festschrift for Ruth Barcan Marcus.

  16. ———. 1995. "Senses of Essence." In Modality, Morality and Belief. Essays in Honor of Ruth Barcan Marcus, edited by Sinnott-Armstrong, Walter, 53-73. Cambridge: Cambridge University Press.

    "One may distinguish between tbe essential and accidental properties of an object. A property of an object is essential if it must have the property to be what it is; otherwise the property is accidental.

    But what exactly is meant by this account? It has been common to give a further explanation in modal terms. A property is taken to be essential when it is necessary that the object have the property or, alternatively, when it is necessary that it have tbe property if it exist. For reasons that I have already given in my paper “Essence and Modality,’’ I doubt whether this or any other modal explanation of the notion can succeed. Indeed, I doubt whether there exists any explanation of the notion in fundamentally different terms. But this is not to deny the possibility of further clarification; and it is the aim of the present paper to provide it.

    What I shall do is to distinguish some of the closely related ways in which the notion may be understood. This will be important for getting clearer both on which claims can be made with its help and on which concepts can be defined with its help. In particular, we shall see that several different senses of ontological dependence correspond to the different senses of essence. The task is also important for the purpose of developing a logic of essentialist reasoning; for most of the different senses of essence that we distinguish will make a difference to the resulting logic. My main concern in this paper has been with making the distinctions, and not with drawing out their implications; but I hope it is clear from the examples what some of these implications are." (p. 53)

  17. Fine, Kit, and Schurz, Gerhard. 1996. "Transfer Theorems for Multimodal Logics." In Logic and Reality: Essays on the Legacy of Arthur Prior, edited by Copeland, Jack, 169-214. Oxford: Oxford University Press.

    "Many of the modal logics that have been developed contain two or more modal operators. A notable example is the tense logic of Prior, which contains operators for both the past and the future. A more recent example is the logic of programs, which contains infinitely many operators, one for each program.

    A multimodal logic will have various monomodal fragments; and in the simplest case, it will be the join of these fragments -- there will be no interactive axioms. Our concern in the present chapter is to investigate the question of when certain properties of the monomodal logics transfer to their join. To answer this question, we develop a very general proof method, which allows us to piece together models for different logics. The resulting theorems provide very general answers to our question, which are positive in most cases, but not in all.

    Our investigation is a natural continuation of those begun by Prior.

    For he was interested both in the development of multimodal logics and in their relationship to monomodal logics. It is therefore, with a keen sense of his own contribution to the subject that we have pursued the present line of research." (p. 169)

    [Note:] Some of the initial ideas behind this chapter were contained in a letter from Fine to Schurz in 1990. The subsequent work has been joint, with Fine writing up sections 1 and 6 and Schurz writing up the rest. The result on strong completeness transfer has been obtained independantly by Valentin Goranko and Solomon Passy; the results on transfer of strong and weak completeness, f.m.p., and of decidability (under the assumption of weak completeness) have 'been obtained independently by Marcus Kracht and Frank Wolter. Our own proof of decidability transfer is based upon ideas in their proof.

  18. Fine, Kit. 1998. "Mixing Matters." Ratio no. 11:278-288.

    Reprinted in: David Oderberg, Form and Matter. Themes in Contemporary Metaphysics, Oxford: Blackwell. 1999 pp. 65-75.

    Abstract: "Aristotle raised a puzzle about the possibility of mixing whose solution is by no means obvious. I here explicate his solution to the puzzle and attempt to make it plausible within the context of his thought. Although we now know that his specific views on mixing were mistaken, his discussion of the topic raises questions concerning the role of capacities and the relationship of part to whole that are still of interest."

    "The topic of mixture plays a central role in Aristotle's metaphysics (1). For every concrete substance is composed of mixtures and underlying every substantial change is a process of mixing.

    Thus no understanding of substance or of substantial change is complete without an understanding of mixtures and mixing.

    Aristotle's account of mixture may also be of some contemporary interest. For it depends upon a view, still worthy of attention, of how dispositions may conflict.

    The main text in which mixture is discussed is chapter I.10 of Generation and Corruption. Aristotle there raises two puzzles that purport to show that mixing is impossible.

    (1) The present paper is a much abridged version of Fine [95].

    Many people have helped me develop the ideas in these two papers; and I am especially indebted to the work of Boguen [95] and Code [95].


    Bogen [95] J., 'Fire in the Belly; Aristotelian Elements, Organisms, and Chemical Compounds', Pacific Philosophical Quarterly, v. 76, nos 3&4, pp. 370-404.

    Code A., [95] 'Potentiality in Aristotle's Science and Metaphysics', Pacific Philosophical Quarterly, v. 76, nos 3 & 4, pp. 405-418.

  19. ———. 1998. "Cantorian Abstraction: A Reconstruction and Defense." Journal of Philosophy no. 95:599-634.

    "In what follows I shall concentrate on the views of Cantor, though it should be clear how what I say will can be modifed to apply to the views of Dedekind. I have not attempted to capture all of the nuances or tensions in Cantor's thought but merely to develop what I take to be its spirit, or central idea. And in developing this idea, I have been guided more by what the idea itself requires than by Cantor's own writings.

    The plan of the paper is as follows. I begin by setting out what appear to be decisive objections to the Cantorian account. I then show how these objections can be overcome by making use of the theory of arbitrary objects developed in my book 'Reasoning with Arbitrary Objects' [Chapter VII. The relevant parts of the theory are outlined in section 2; and the application to Cantor's account of number is made in section 3. I show, in section 4, how the approach may be extended to order types and to structure types in general. In the final two sections, I first compare the Cantorian approach to abstraction with the standard approaches of von Neumann and Zermelo, on the one side, and of Russell and Frege, on the other; and I then consider to what extent the Cantorian approach is capable of yielding a structuralist conception of number and order type. In a formal appendix, I briefly indicate how the present theory might be formalized within an extension of ZF [Zermelo-Frankel]." (p. 603)

  20. ———. 1998. "The Limits of Abstraction." In The Philosophy of Mathematics Today, edited by Schirn, Matthias, 503-630. Oxford: Oxford University Press.

    "This paper has been written more from a sense of curiosity than commitment. I was fortunate enough to attend the Munich Conference on the Philosophy of Mathematics in the Summer of 1993 and to overhear a discussion of recent work on Frege's approach to the foundations of mathematics. This led me to investigate certain technical problems connected with the approach; and these led me, in their turn, to reflect on certain philosophical aspects of the subject. I was concerned to see to what extent a Fregean theory of abstraction could be developed and used as a foundation for mathematics and to place the development of such a theory within a general framework for dealing with questions of abstraction. My conclusions were somewhat mixed: a theory of abstraction could be developed somewhat along the lines that Frege has envisaged; and it could indeed be used as a basis for both arithmetic and analysis. When wedded to a suitable version of the context principle, the theory was capable of accounting for our reference to numbers and other abstract objects. But without the support of the principle, it was not clear that the theory had any great advantage over its rivals. Thus my results would be congenial to someone already committed to the Fregean approach though unconvincing to someone who was not. I therefore present them in somewhat the same spirit as someone who sends off a message in a bottle. I have no desire to announce my communication to the world; but if someone stumbles across it and finds it to be of interest, I shall be pleased.

    The paper is in three parts. The first is devoted to philosophical matters, which help explain the motivation for the subsequent technical work and also its significance. It is centred on three abstracts with which they deal? And to what extent can they provide a foundation for mathematics? The second part proposes and investigates a set of necessary and sufficient conditions for an abstraction principle to be acceptable. The acceptable principles, according to this criterion, are precisely determined and it is shown, in particular, that there is a strongest such principle. The third part attempts to develop a general theory of abstraction within the technical limitations set out by the second part; the theory is equipped with a natural class of models; and it is shown to provide a foundation for both arithmetic and analysis.

    The original version of the paper contained a lengthy section on the context principle. But this acquired a life of its own (just as reference does under the principle); and it has therefore been omitted. I hope to be able to present the material elsewhere." (pp. 503-504)

  21. ———. 1999. "Things and their Parts." Midwest Studies in Philosophy no. 23:61-74.

    "I wish to sketch a theory of the general nature of material things. It is a theory on which I have been working for some time; and what I present here is the merest sketch. Details are slid over, significant questions not raised, and controversial assumptions left undefended. But I hope, all the same, that enough is said to indicate the relevance of the theory to questions concerning the nature of material things and the plausibility of its answers.

    One way into the theory is through consideration of part-whole. Things have parts; and so we are led to consider how they are capable of having the parts that they do. What in their nature accounts for their division into parts? It has often been supposed that we may give an adequate answer to this question by conceiving of a material thing as the material content of a space-time region or as a successive stream of matter. But I believe that there are enormous difficulties with these positions and that, once they are taken into account, we are led to adopt a very different conception of a material thing and of its relationship to its parts.

    Central to the paper is a distinction between two different ways in which one thing can be part of another. It can, in the first place, be apart in a way that is relative to a time. It is in this way, for example, that a newly installed carburetor is now apart of my car, whereas earlier it was not, or that certain molecules are now parts of my body though later, through the exercise of natural bodily functions, they no longer will be.

    In the second place, one object can be a part of another in a way that is not relative to a time. For something that is a part in this way, it is not appropriate to ask when, or for how long, it is a part; it just is a part. It is in such a way that the pants and the jacket, for example, are parts of a suit or various atoms are parts of a water molecule, or two particular pints of milk are parts of a quart of milk, or various time-slices, if there are such things, are parts of a persisting individual." (p. 61)

  22. ———. 2000. "Semantics for the Logic of Essence." Journal of Philosophical Logic no. 29:543-584.

    "In a previous paper 'The Logic of Essence’, I presented a system for the logic of essence. In this paper, I present a semantics for a variant of the system and prove it complete with respect to that semantics.


    The basic idea behind the semantics is that a statement should be taken to be true in virtue of the nature of certain objects if it is true in any world compatible with the nature of those objects. We shall make the simplifying assumption that each world is compatible with the nature of all and only those objects that it contains. Thus the condition for a statement to be true in virtue of the nature of certain objects is that it should be true in all those worlds that contain those objects. However, the presence of an object in a world is not taken to guarantee its existence but merely its possibility.

    Thus each world will be taken to embody its own ‘view’ of which objects are possible and which are not.


    The first two sections are devoted to the language of the logic (Section 1) and the system of proof (Section 2). The next section gives the semantics (Section 3). The remaining six sections develop the completeness proof. The first three (Sections 4–6) provide lemmas crucial to the construction of the canonical model. The next two sections (Sections 7, 8) show how to build up a ‘diagram’ of the model; and the last section (Section 9) shows how to obtain the model itself. The reader might find it helpful to have the previous paper ‘The Logic of Essence’ at hand (henceforth abbreviated to ‘LE’) and also to consult the papers ‘Essence and Modality’ and ‘Senses of Essence’ for further explanation of the notion of essence and for general philosophical motivation." (pp. 543-544)

  23. ———. 2000. "Neutral Relations." The Philosophical Review no. 109:1-33.

    "There is a standard view of relations, held by philosophers and logicians alike, according to which we may meaningfully talk of a relation holding of several objects in a given order. Thus it is supposed that we may meaningfully - indeed, correctly - talk of the relation loves holding of Anthony and Cleopatra or of the relation between holding of New York, Washington, and Boston. But innocuous as this view might appear to be, it cannot be accepted as applying to all relations whatever. For there is an important class of metaphysical and linguistic contexts which call for an alternative conception of relation, one for which the order of the relata plays no role and in which the application of the relation to its relata is achieved by other means.

    My argument for this conclusion will be roughly Hegelian in form (though not at all in content). I begin with a thesis, the standard view on relations, and consider various problems to which it gives rise (§ 1). After considering what is required of a solution to these problems (§ 2), I propose an antithesis, the positionalist view, according to which each relation is taken to be endowed with a given number of argument-places, or positions, in no specified order (§ 3). But this view is beset with certain ontological and substantive problems; and I conclude with a synthesis, the antipositionalist view, which combines the virtues of the two previous accounts (§ 4) and is seen to lead to a distinctive conception of relations (§ 5).

    I have largely confined my attention to metaphysical issues; and as a consequence, two important topics have not been pursued.

    One is the logic of complex neutral relations; and the other is the role of neutral relations in the interpretation of language (and in our mental representation of reality). However, I hope enough has been said on the metaphysics of the issue to make clear why these topics are of interest and how they might be developed." (pp. 1-2)

  24. ———. 2000. "A Counter-Exemple to Locke's Thesis." The Monist no. 83:357-361.

    "Locke's thesis states that no two things of the same sort can be in the same place at the same time. The thesis has recently received extensive discussion, with some philosophers attempting to find arguments in its favour and others attempting to provide counter-examples.(1) However, neither the arguments nor the counter-examples have been especially convincing;and it is my aim, in this short note, to present what I believe is a more convincing counter-example to the thesis." (p. 357)


    "Many philosophers have thought that no two things can necessarily always coincide even if they are not of the same sort. But if this second example is correct, it shows that things may necessarily coincide even when they are of the same sort. (2)" (p. 361)

    (1) The detractors include Hughes [97a, b, c], Shorter[77], and Simons ([85], [87], [97]).The defenders include Wiggins ([68], [75], [80]),Odergard [96] and also, of course, all those who hold that no two things can coincide,whether of the same sort or not.


    Hughes, C. [97a] "Same Kind Coincidents and the Ship of Theseus," Mind, vol. 106, 53-68.

    _ [97b] "An IncredibleCoincidence,"Mind, vol. 106,769-72.

    Leibniz,G.W. [81] New Essays on Human Understanding (trans,and ed. Peter Remnant and Jonathon Bennett), Cambridge: Cambridge University Press.

    Locke, J. [75] An Essay Concerning Human Understanding (ed. P.H. Nidditch), Oxford: Clarendon.

    Odergard,D. [96] "Coincidence Under a Sortal," Philosophical Review,vol. 105, 145-72.

    Rea, M. [97] "Material Constitution: A Reader," Boston, MA: Rowman & Littlefield.

    Shorter, J.M. [77] "On Coinciding in Space and Time," Philosophy 52, 399-408.

    Simons,P. [85] "Coincidence of Things of a Kind," Mind 94, 70-75.

    _[87] Parts: A Study in Ontology, Oxford: Clarendon.

    _ [97] "On Being the Same Ship(s)? or Electron(s): Reply to Hughes,"Mind 106, 761-68.

    Wiggins, D. [68] "On Being in the Same Place at the Same Time," Philosophical Review 77: 90-95, reprintedin Rea [97].

    _ [80] Sameness and Substance, Cambridge,MA: Harvard University Press.

  25. ———. 2002. "The Question of Realism." In Individuals, Essence and Identity. Themes of Analytic Metaphysics, edited by Bottani, Andrea, Carrara, Massimiliano and Giaretta, Pierdaniele, 3-48. Dordrecht: Kluwer.

    Also published in Philosophers' Imprint, vol. I, 1, 2001, pp. 1-30.

    "My aim in this paper is to help lay the conceptual and methodological foundations for the study of realism. I come to two main conclusions: first, that there is a primitive metaphysical concept of reality, one that cannot be understood in fundamentally different terms; and second, that questions of what is real are to be settled upon the basis of considerations of ground. The two conclusions are somewhat in tension with one another, for the lack of a definition of the concept of reality would appear to stand in the way of developing a sound methodology for determining its application; and one of my main concerns has been to show how the tension between the two might be resolved.

    The paper is in two main parts. In the first, I point to the difficulties in making out a metaphysical conception of reality.

    I begin by distinguishing this conception from the ordinary conception of reality (§ 1) and then show how the two leading contenders for the metaphysical conception -- the factual and the irreducible-both appear to resist formulation in other terms. This leads to the quietist challenge, that questions of realism are either meaningless or pointless (§ 4); and the second part of the paper (§§ 5-10) is largely devoted to showing how this challenge might be met. I begin by introducing the notion of ground (§ 5) and then show how it can be used as a basis for resolving questions both of factuality (§§ 6-7) and of irreducibility (§§ 8-9). I conclude with some remarks on the essential unity of these two questions and of the means by which they are to be answered (§ 10)." (pp. 3-4)

  26. ———. 2002. "The Varieties of Necessity." In Conceivability and Possibility, edited by Gendler, Tamar Szabo and Hawthorne, John, 253-282. New York: Oxford University Press.

    Reprinted in: Modality and Tense. Philosophical Papers, as chapter 7, pp. 235-260.

    "Necessity abounds. There are the necessary truths of logic, mathematics and metaphysics, the necessary connections among events in the natural world, the necessary or unconditional principles of ethics, and many other forms of necessary truth or connection. But how much diversity is there to this abundance?

    Are all necessary truths and connections reducible to a single common form of necessity? And if not, then what are the different ways in which a truth might be necessary or a necessary connection might hold?

    It is the aim of this paper to show that diversity prevails.

    I shall argue 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. Thus what it is for a necessity or possibility of any of these forms to obtain does not consist in the obtaining of some other form or forms of necessity or possibility.

    Although the focus of the paper falls squarely within the philosophy of modality, some of my arguments may be of broader interest. For certain currently fashionable views on scientific essentialism and ethical naturalism entail the collapse of forms of necessity that I would wish to keep distinct. Thus I have found it essential to indicate what it is in these views that I take to be in error; and this has required consideration of questions from within the metaphysics of natural kinds and the epistemology of ethical belief." (p. 253)

  27. ———. 2003. "The Role of Variables." Journal of Philosophy no. 50:605-631.

    Reprinted in the Philosopher's Annual 2003; revised in Joseph Almog, Paolo Leonardi (eds.), The Philosophy of David Kaplan, New York: Oxford University Press, 2009 pp. 109-133.

    "It is generally supposed - by logicians and philosophers alike - that we now possess a perfectly good understanding of how variables work in the symbolism of logic and mathematics.

    Once Gottlob Frege had provided a clear syntactic account of variables and once Alfred Tarski had supplemented this with a rigorous semantic account, it would appear that there was nothing more of any significance to be said. It seems to me, however, that this common view is mistaken. There are deep problems concerning the role of variables that have never been properly recognized, let alone solved, and once we attempt to solve them we see that they have profound implications not only for our understanding of variables but also for our understanding of other forms of expression and for the general nature of semantics.

    It is my aim here to say what these problems are and how they are to be solved, and to indicate the implications fo the rest of semantics. I begin with an antimony concerning the role of variables which I believe any satisfactory account of them should solve (section 1). I then argue that the three main semantical schemes currently on the market - the Tarskian, the instantial and the algebraic -- are unsuccessful in solving the puzzle (sections II-III) or in providing a satisfactory semantics for first-order logic (Sections IV-V). Finally, I offer an alternative scheme that it is capable of solving the antimony (section VI) and of providing a more satisfactory semantics for first-order logic (section VII). It is based upon a new approach to representational semantics, which I call semantic relationism; and I conclude by discussing the implications of this approach for the semantics of names and belief-reports." (p. 605)

  28. ———. 2003. "The Non-Identity of a Material Thing and Its Matter." Mind no. 112:195-234.

    "Many philosophers have thought that a material thing is, or may be, one and the same as its matter - that a statue, for example, may be the same as the clay from which it is made or a river the same as the water which flows through it. There appears to be a powerful argument against such views, for the thing in each of these cases would appear to have properties not possessed by its matter.

    Thus the clay of a statue may exist even though the statue itself has ceased to exist and the river may be composed of different water at different times even though this cannot be true of the water that composes it at any given time. However, these philosophers have responded to this argument by claiming that the apparent difference in properties represents, not a difference in the objects themselves, but a difference in the descriptions under which they may be conceived. We may conceive of a given thing as a statue or some clay or as a river or a body of water, for example, and, depending upon how the object is conceived, we will say one thing about it rather than another.

    It is the aim of this paper to show that this counter-response cannot be sustained and that the original argument against identity should therefore be allowed to stand. This is no easy task since there would appear to be nothing in the immediate linguistic data to settle the question one way or the other.

    However, by working through the consequences of the counter-response for the rest of our language, I think it may be shown to be extremely implausible. The paper is in two main parts. The first (§§1-4) is largely concerned with setting up the problem. We characterize the different forms the identity theory can take (§1), explain how the argument in favor of non-identity might in principle break down (§2), present the most plausible versions of such arguments (§3), and then consider the most plausible counter-response to them (§4). The second part (§§5-8) embarks on a detailed investigation of the difficulties with the counter-response. It is shown to be unable to account for a wide variety of different linguistic data, that is loosely classified according as to how reference to a material thing might be achieved. Four main kinds of case will be considered: those in which a sort is explicitly invoked (§5); those in which it is implicitly invoked (§6); those in which the very notion of reference is itself used in securing reference(§7); and those in which there is reference to a plurality of things (§8)." (p. 195)

  29. ———. 2005. "The Problem of Possibilia." In The Oxford Handbook of Metaphysics, edited by Loux, Michael J. and Zimmerman, Dean, 161-179. Oxford: Oxford University Press.

    Reprinted in: Modality and Tense. Philosophical Papers, as chapter 6, pp. 214-231.

    "Are there, in addition to the various actual objects that make up the world, various possible objects? Are there merely possible people, for example, or merely possible electrons, or even merely possible kinds?

    We certainly talk as if there were such things. Given a particular sperm and egg, I may wonder whether that particular child which would result from their union would have blue eyes.

    But if the sperm and egg are never in fact brought together, then there is no actual object that my thought is about.(1) Or again, in the semantics for modal logic we presuppose an ontology of possibilia twice over.(2) For first, we coutenance various possible worlds, in addition to the actual world; and second, each of these worlds is taken to be endowed with its own domain of objects. These will be the actual objects of the world in question, but they need not be actual simpliciter, i.e., actual objects of our world. What are we to make of such discourse? There are four options:

    (i) the discourse is taken to be unintelligible; (ii) it is taken to be intelligible but nonfactual, i.e. as not in the business of stating facts; (iii) it is taken to be factual but reducible to discourse involving no reference to possibilia; (iv) it is taken to be both factual and irreducible.(3) These options range from a fullblooded form of actualism at one extreme to a full-blooded form of possibilism at the other. The two intermediate positions are possibilist in that they accept the intelligibility of possibilist discourse but actualist in that they attempt to dispense with its prima facie commitment to possibilia. All four positions have found advocates in the literature. Quine, in his less irenic moments, favours option (i); Forbes ([85], p. 94) advocates option (ii), at least for certain parts of possibilist discourse; many philosophers, including Adams [74] and myself, opt for (iii); while Lewis [86] and Stalnaker [75] have endorsed versions of (iv), that differ in how full-blooded they take the possible objects to be.

    My focus in the present article is on the third option. I wish to see to what extent reference to possibilia might be understood in other terms. Can we regard talk of possibilia as a mere facon de parler, perhaps somewhat in the same manner as talk of the average man or of infinitesimals? (4) I shall not be concerned to argue directly against any of the other options.

    However, any argument for the viability of (iii) is indirectly an argument against the plausibility of these other options.

    For (iv), especially in its more extreme forms, offends against what Russell has called our 'robust sense of reality', (i) offends against our even more robust sense of what is intelligible, while (ii) offends against our somewhat less robust sense of what is factual. It is therefore preferable to go with the third option, if we possibly can." (pp. 161-162)

    (1) Cf Gupta ([80], 20, n.15.

    (2) See Kripke [63] for a standard exposition of the semantics.

    (3) See Fine [01] for a general discussion of what these various options amount to.

    (4) As should be clear from Fine [01], the viability of any reduction will also depend upon its success in accounting for our understanding of modal discourse and our knowledge of modal

    truth. See Peacocke [01] for a broader discussion along these lines.


    Fine K., [01] 'The Question of Realism', to appear in Imprint. [see Fine 2002]

    Gupta A., [80] 'The Logic of Common Nouns', Yale University Press, 1980.

    Kripke S., [63] 'Semantical Considerations on Modal Logic', Acta Philosophica Fennica 16, 83-94, reprinted in 'Reference and Modality' (ed. L. Linsky), Oxford: Oxford Univ. Press, 1971.

    Peacocke C., [01] 'Principles for Possibilia', to appear. [Noûs, vol. 36, 2002, pp. 486-508]

  30. ———. 2005. "Replies." Philosophical Studies no. 122:367-395.

    Replies to critics about The Limits of Abstraction.

    "I am extremely grateful to the contributors for their careful, perceptive and sympathetic discussion of my book. For the most part, they have chosen not to criticize what I say but to see how the doctrines of the book might be developed or be used to throw light on other questions. A defense of the book is therefore out of place; and I can do no better than to continue the discussion of some of the questions that they raise. There is perhaps only one point on which there is a substantive disagreement; and this concerns the status of second-order logic. Weir takes it to be epistemologically problematic; I do not. This issue was not discussed in the book, and I have here attempted to explain the grounds upon which I think its epistemic innocence might be defended." (p. 367)

  31. ———. 2005. "Précis [of "The Limits of Abstraction"]." Philosophical Studies no. 122:305-313.

    Symposium on Kit' Fine's book The Limits of Abstraction.

    "Before dealing with the contributors’ comments, I would like to provide a selective summary of the book. I will focus on two main themes: the development of a general theory of abstraction; and the critique of Hume’s principle as a form of definition. There are several other topics from the book that I would have liked to have covered. They include the question of the identity of abstracts and the viability of the context principle, on the philosophical side (§1.5, §§11.3-5) and the analysis of invariance and the proofs of categoricity, on the technical side (§§6,7). But in the interests of brevity, I have had to exclude them.

    The general idea of abstraction is one that has been discussed by philosophers throughout the ages but it was Frege who first showed how the idea could be put on a rigorous footing. For Frege, the idea of abstraction had two main components. The first related to the items upon which the abstraction was to be performed. These were to be taken to be related by an equivalence relation, i.e. by a relation that was reflexive, symmetric and transitive. As examples, we have the relation of parallelism on lines or the relation of equinumerosity on concepts. The second component related to the abstracts themselves. These were to be obtained from the items by means of a suitable operation of abstraction - the operation of forming directions in the case of parallel lines and of forming numbers in the case of equinumerous concepts. These two components, the equivalence relation and the operation of abstraction, were then to be connected by a principle relating the identity of the abstracts to the equivalence of the items from which they were formed." (p. 305)

  32. ———. 2005. "Class and Membership." Journal of Philosophy no. 102:547-572.

    Abstract: "I wish to describe a construction that is capable of yielding a new solution to the set-theoretic paradoxes. Perhaps what is most dis- tinctive about the construction is the reversal in the roles of the predicate of membership and the ontology of sets. On the usual conception of the cumulative hierarchy of Zermelo-Fraenkel set theory (ZF), we think of the membership predicate as given and of the ontology of sets or classes as something to be made out. Thus given an understanding ofmembership, we successively carve out the ontology of sets by using the membership predicate to specify which further sets should be added to those that are already taken to exist. Under the present approach, by contrast, we think of the ontology of classes as given and of the membership predicate as something to be made out. Thus given an understanding of the ontology of classes, we successively carve out extensions of the membership predicate by using conditions on the domain of classes to specify which further membership relationships should obtain. What unfolds is not the ontology of sets or classes but the meaning of membership. This “Copernican revolution” in our conception of class membership, once properly implemented, is capable of yielding a theory of classes that is just as natural as the standard theory of ZF and yet far more powerful in the strength of its principles and the scope of its applications."

  33. ———. 2005. "Reference, Essence, and Identity." In Modality and Tense. Philosophical Papers, 19-39. New York: Oxford University Press.

    Previously unpublished and written up in the spring of 1984 as a talk for the conference ‘Themes from Kaplan’.

    Chris Peacocke was the commentator.

    "There are three main concerns within current thinking on modality. One relates to the problem of essentialism, of making sense of de re modal discourse. Another relates to the problem of transworld identification, of individuating objects across possible worlds. The third relates to the problem of direct reference, of whether any terms can refer to their bearers independently of how they are described.

    It has commonly been supposed that these various problems are connected and that a solution to the one will push us in a certain direction in regard to another. But I shall argue that, once the problems are properly understood, it will be seen that they are quite distinct and that the supposed connections among them are illusory." (p. 19)

  34. ———. 2005. "Necessity and Non-existence." In Modality and Tense. Philosophical Papers, 321-354. New York: Oxford University Press.

    Previously unpublished.

    "Is it possible for Socrates to be a man and yet not exist? This is the kind of question that is likely to strike someone from outside philosophy as preposterous and that may not be taken seriously even by philosophers themselves. But I believe that the answer to this question has profound implications for our understanding of the concepts of existence, identity, and modality and for how these concepts connect to one another and to the world.

    It is my central contention that, just as there is a distinction between tensed and tenseless sentences, so there is a distinction between worldly and unworldly sentences, between sentences that depend for their truth upon the worldly circumstances and those that do not. It is in terms of such a distinction that we should assess the possibility that Socrates might be a man and yet not exist, since his non-existence will be a matter of the circumstances while his being a man will not. But once the distinction is drawn, it will be seen to have consequences for a wide range of further questions. It will lead us to distinguish, within the realm of what are normally regarded as necessary truths, between the necessary truths proper, those that hold whatever the circumstances, and the transcendent truths, those that hold regardless of the circumstances. It will also lead us to make an analogous distinction, within the realm of what are normally regarded as necessary existents, between the necessary existents proper, those that exist whatever the circumstances, and the transcendent objects, those that exist regardless of the circumstances. Thus some objects will not properly be in the world just as it has been supposed that some objects are not properly in time. Finally, it will be suggested that the identity of an object—what it is—is not, at bottom, a worldly matter; essence will precede existence in the sense that the identity of an object may be fixed by its unworldly features even before any questionof its existence or other worldly features is considered." (p. 321)

  35. ———. 2006. "The Reality of Tense." Synthese no. 150:399-414.

    "Is reality somehow tensed? Or is tense a feature of how we represent reality and not properly a feature of reality itself? Although this question is often raised, it is very hard to say what it comes to. For both sides to the debate can agree to certain tensed claims. They can agree that I am sitting right now, for example, or that Queen Ann is dead. So in a clear and obvious sense there are tensed facts. And so how can it sensibly be denied that reality is tensed?

    My own view is that the question can only be made clear by drawing a distinction between how things are (mere reality) and how things are in reality (metaphysical reality). Thus what the antirealist about tense wishes to dispute is not how things are, which should be common ground between him and his opponent, but how things are in reality. Of course, he will say, Queen Ann is dead but this representation of the facts is not faithful to how things are in reality; and this is so, not because of the reference to Queen Ann or to her being dead, but because of the tense. In a faithful representation of how things are in reality, there will be nothing that corresponds to our use of tense. (1)"

    (1) The more formal minded reader may suppose that there is a sentential operator 'in reality,_' by means of which the various realist claims are to be made (Fine 2000). I should add that this paper is a summary of views which are elaborated at much greater length in Fine (2005). In the interests of brevity, I have made no attempt to engage with the extensive literature on the topic.


    Fine. K.: 2000, 'The Question of Reality', Philosophers Imprint 1 (1).

    Fine. K.: 2005, 'Tense and Reality', in Papers on Modality and Tense, Clarendon Press, Oxford, 2005.

  36. ———. 2006. "Our Knowledge of Mathematical Objects." In Oxford Studies in Epistemology. Vol. 1, edited by Gendler, Tamar Szabo and Hawthorne, John, 89-110. Oxford: Clarendon Press.

    "I have recently been attempting to provide a new approach to the philosophy of mathematics, which I call ‘proceduralism’ or ‘procedural postulationism’.(1) It shares with traditional forms of postulationism, advocated by Hilbert (1930) and Poincaré (1952), the belief that the existence of mathematical objects and the truth of mathematical propositions are to be seen as the product of postulation. But it takes a very different view of what postulation is. For it takes the postulates from which mathematics is derived to be imperatival, rather than indicative, in form; what are postulated are not propositions true in a given mathematical domain, but procedures for the construction of that domain.

    This difference over the status of the posulates has enormous repercussions for the development and significance of such a view. The philosophy of mathematics is faced with certain fundamental problems.

    How are we capable of acquiring an understanding of mathematical terms? How do we secure reference to mathematical objects? What is the nature of these objects? Do they exist independently of us or are they somehow the products of our minds? What accounts for the possibility of applying mathematics to the real world? And how are we able of acquire knowledge of mathematical truths? The procedural form of postulationism, in contrast to the propositional form, is capable of providing plausible answers to each of these questions. By going procedural, we convert a view that is beset with pitfalls to one that is worthy of serious consideration.

    In what follows I shall focus on the last question concerning our knowledge of mathematics (although this will inevitably involve the other questions). I do this not because this question is the most interesting or even because it provides the most convincing illustration

    of the value of our approach, but because it helps to bring out what is most distinctive—and also most problematic—about the approach. If one can go along with what it recommends in this particular case, then one is well on the way to accepting the view in its entirety.

    As with the ‘big three’ traditional approaches to the philosophy of mathematics—logicism, formalism, and intuitionism—the present approach rests upon a certain technical program within the foundation of mathematics. It attempts to derive the whole of mathematics—or a significant part thereof—within the limitations imposed by its underlying philosophy. Since the viability of the underlying philosophical view largely depends upon the possibility of carrying out such a program, it will be helpful to give a sketch—if only in the barest form—of what the program is and of how it is to be executed. I hope elsewhere to provide a much more extensive development of the view in both its philosophical and technical aspects." (pp. 90-90)

    (1) First broached in Fine (2002: 36, 56, 100).


    Hilbert, D. (1930) Grundlagen der Geometrie, 7th edn. (Leipzig: Open Court Press).

    Poincaré, H. (1952) Science and Method (New York: Dover).

  37. ———. 2006. "Modal Logic and Its Application." EOLSS Survey of Mathematical Logic.

  38. ———. 2006. "Arguing for Non-Identity: A Response to King and Frances." Mind no. 115:1059-1082.

    "Jeffrey King and Bryan Frances are both critical of my paper, 'The Nonidentity of a Thing and its Matter' (Fine 2003), though in rather different ways. King engages in carpet bombing; his aim is to destroy every argument in sight, even to the extent of showing that the linguistic data cited by the paper favours the monist rather than the pluralist. Frances, by contrast, engages in strategic warfare; by 'taking out' certain key arguments, he attempts to demolish the paper as a whole.

    I remain unmoved -- and, I hope, unscathed -- by their attacks.

    King's carpet bombing may cause a great deal of collateral damage but not to its intended target; and Frances's strategic bombing may hit its target but without inflicting much harm. Still, their papers raise many interesting issues not discussed -- or, at least, not properly discussed -- in my original paper; and I am grateful to them for providing me with the opportunity to take these issues into account.

    My response will be in three main parts: I begin by outlining the central line of argument of my original paper (Sect. 1); I then discuss King's criticisms of the paper (Sects 2, 3, 4); and finally I turn to Frances's criticisms (Sect. 5). I have tried to make my response reasonably self-contained and to bring out the independent significance of the issues under discussion but it would be helpful, all the same, if the reader had all three papers at hand." (p. 187)

    Fine, K. 2003: 'The Non-identity of a Material Thing and its Matter' Mind 112, pp. 195-234.

    Frances, Bryan 2006: 'The New Leibniz's Law Arguments for Pluralism' Mind 115, pp. 1007-1022.

    King, Jeffrey C. 2006: 'Semantics for Monists'. Mind 115, pp. 1023-1058.

  39. ———. 2006. "In Defence of Three-Dimensionalism." Journal of Philosophy no. 103:699-714.

    Reprinted in: Robin Le Poidevin (ed.), Being: Developments in Contemporary Metaphysics, Cambridge: Cambridge University Press, 2008, pp. 1-16.

    "Let us use the term 'present' in such a way that a material thing can be said to be present both in space and in time. Thus on this usage we can say that the desk in front of me is present at any moment at which it exists and also that it is present at any position within its spatial location at that moment. We might similarly talk of presence throughout a period of time or a region of space and of the presence of other categories of objects, such as states or events.

    Some philosophers, the "three-dimensionalists," have thought that there is a distinctive way in which material things are present in time as opposed to space. They have thought that a thing is somehow "stretched out" through its location at a given time though not through the period of during which it exists and that it is somehow present in its entirety at any moment at which it exists though not at any position at which it is located. Other philosophers, the "four dimensionalists," have denied that this was so; they have thought

    that a material thing is as equally "stretched out" in time as it is in space and that there is no special way in which it is entirely present at a moment rather than at a position.

    We might use the term 'existence' for the way in which 3D-ers have thought that a thing is present in time and 'extension' or 'location' for the way in which 4D-ers have thought that a thing is present in space. The 3D-ers have then held that things exist in time but are extended in space while the 4D-ers hold that things are extended both in space and in time. (1)" (p. 699)

    (1) My terms 'presence', 'existence', and 'extension' (deriving from my paper, "Compounds and Aggregates," Nous, xxviii, 2 (1994): 137-58) correspond to the more familiar terminology of 'persistence', 'endurance', and 'perdurance'. I prefer my own terminology since it is somewhat more general, allowing one to talk of existence or extension at a moment when one cannot very well talk of endurance or perdurance at a moment and allowing one to talk of existence or extension in space when one cannot very well talk of endurance or perdurance in space.

  40. ———. 2006. "Relatively Unrestricted Quantification." In Absolute Generality, edited by Rayo, Agustin and Uzquiano, Gabriel, 20-44. New York: Oxford University Press.

    "There are four broad grounds upon which the intelligibility of quantification over absolutely everything has been questioned-one based upon the existence of semantic indeterminacy, another on the relativity of ontology to a conceptual scheme, a third upon the necessity of sortal restriction, and the last upon the possibility of indefinite extendibility. The argument from semantic indeterminacy derives from general philosophical considerations concerning our understanding of language. For the Skolem-Lowenheim Theorem appears to show that an understanding of quantification over absolutely everything (assuming a suitably infinite domain) is semantically indistinguishable from the understanding of quantification over something less than absolutely everything; the same first-order sentences are true and even the same first-order conditions will be satisfied by objects from the narrower domain. From this it is then argued that the two kinds of understanding are indistinguishable tout court and that nothing could count as having the one kind of understanding as opposed to the other.

    The second two arguments reject the bare idea of an object as unintelligible, one taking it to require supplementation by reference to a conceptual scheme and the other taking it to require supplementation by reference to a sort. Thus we cannot properly make sense of quantification over mere objects, but only over objects of such and such a conceptual scheme or of such and such a sort. The final argument, from indefinite extendibility, rejects the idea of a completed totality. For if we take ourselves to be quantifying over all objects, or even over all sets, then the reasoning of Russell's paradox can be exploited to demonstrate the possibility of quantifying over a more inclusive domain. The intelligibility of absolutely unrestricted quantification, which should be free from such incompleteness, must therefore be rejected.

    The ways in which these arguments attempt to the undermine the intelligibility of absolutely unrestricted quantification are very different; and each calls for extensive discussion in its own right. However, my primary concern in the present paper is with the issue of indefinite extendibility; and I shall only touch upon the other arguments in so far as they bear upon this particular issue. I myself am not persuaded by the other arguments and I suspect that, at the end of day, it is only the final argument that will be seen to carry any real force. If there is a case to be made against absolutely unrestricted quantification, then it will rest here, upon logical considerations of extendibility, rather than upon the nature of understanding or the metaphysics of identity." (pp. 20-21)