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Fine, Kit. 1970. "Propositional Quantifiers in Modal Logic." Theoria no. 36:336-346.
"Propositional quantifiers are added to S5, S4, T and B etc. The cases in which any truth-functional formula, any formula whatever, and any set of possible worlds correspond to a proposition are distinguished. Canonical models, a translation argument and quantifier elimination, respectively, are used to show, for the first two cases, that the logics are axiomatizable and that most of the modally weak logics are undecidable and, for all cases, that the S5 logics are decidable."
———. 1971. "The Logics Containing S4.3." Zeitschrift für Mathematische Logik und Grundlagen der Mathematik no. 17:371-376.
———. 1971. "Counting, Choice and Undecidability." Manifold no. 11:71-82.
———. 1972. "In So Many Possible Worlds." Notre Dame Journal of Formal Logic no. 13:516-520.
"Ordinary modal logic deals with the notion of a proposition being true at least one possible world. This makes it natural to consider the notion of a proposition being true in k possible worlds for any nonnegative integer k. Such a notion would stand to Tarski's numerical quantifiers as ordinary possibility stands to the existential quantifier.
In this paper (1) I present several logics for numerical possibility. First I give the syntax and semantics for a minimal such logic (sections 1 and 2); then I prove its completeness (sections 3 and 4); and finally I show how to extend this result to other logics (section 5)."
(1) The results of this paper are contained in my doctorate thesis, submitted to the University of Warwick in 1969. I am greatly indebted to my supervisor, the late Arthur Prior. Without his help and encouragement this paper would never have been written.
———. 1972. "For So Many Individuals." Notre Dame Journal of Formal Logic no. 13:569-572.
"In his 'Introduction to logic', Tarski introduces the numerical quantifiers 'there are at least K individuals x such that', K a natural number. This paper proves completeness for a predicate calculus that contains each of these quantifiers but no sign for identity."
———. 1972. "Logics Containing S4 without the Finite Model Property." In Conference in Mathematical Logic, London '70, edited by Hodges, Wifrid, 98-102. Berlin: Springer Verlag.
———. 1972. "Some Necessary and Sufficient Conditions for Representative Decision on Two Alternatives." Econometrica no. 40:1083-1090.
———. 1973. "Conditions for the Existence of Cycles under Majority Non-Minority Rules." Econometrica no. 41:889-899.
———. 1973. "Surveys on Deontic Logic, Mathematical Logic and the Philosophy of Mathematics." In Unesco Survey of the Social Sciences.
———. 1974. "An Ascending Chain of S4 Logics." Theoria no. 40:110-116.
"This paper shows that there are infinite ascending chains of modal logics containing S4. The proof uses possible world semantics. A consequence of the proof is that there is a continuum of logics containing S4."
———. 1974. "Models for Entailment." Journal of Philosophical Logic no. 3:347-372.
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.
———. 1974. "An Incomplete Logic Containing S4." Theoria no. 40:23-29.
"This paper exhibits a modal logic that is finitely axiomatized, stronger than S4, yet not complete for any Kripke semantics. The proof shows that a particular formula is valid in all frames of the logic but is not itself a theorem. The paper ends with some questions about the extent to which modal logics can be incomplete."
———. 1974. "Logics Containing K4. Part I." Journal of Symbolic Logic no. 39:31-42.
"This paper gives a general completeness result in modal logic. Let i(n) be the axiom that says there are at most n incomparable points related to a given point. then the result is that all logics containing K4 and i(n) are complete. The proof is a variant on the method of maximally consistent theories; it shows that a frame for any such logic results from dropping certain points from the canonical frame."
———. 1974. "Social Choice and Individual Ranking I." Review of Economic Studies no. 41:303-322.
With Ben J. Fine
———. 1974. "Social Choice and Individual Ranking Ii." Review of Economic Studies no. 41:459-475.
———. 1975. "Vagueness, Truth and Logic." Synthese no. 30:265-300.
Reprinted in: Rosanna Keefe and Peter Smith - Vagueness: a reader - Cambridge, MIT Press, 1996, pp. 119-150.
"This paper deals with the truth-conditions and the logic for vague languages. The use of supervaluations and of classical logic is defended; and other approaches are criticized. the truth-conditions are extended to a language that contains a definitely operator and that is subject
to higher order vagueness."
———. 1975. "Normal Forms in Modal Logic." Notre Dame Journal of Formal Logic no. 16:229-237.
"There are two main methods of completeness proof in modal logic.
One may use maximally consistent theories or their algebraic counterparts, on the one hand, or semantic tableaux and their variants, on the other hand. The former method is elegant but not constructive, the latter method is constructive but not elegant.
Normal forms have been comparatively neglected in the study of modal sentential logic. Their champions include Carnap [3], von Wright [10], Anderson [l] and Cresswell [4]. However, normal forms can provide elegant and constructive proofs of many standard results. They can also provide proofs of results that are not readily proved by standard means.
Section 1 presents preliminaries. Sections 2 and 3 establish a reduction to normal form and a consequent construction of models. Section 4 contains a general completeness result. Finally, section 5 provides normal formings for the logics T and K4."
[1] Anderson, A. R., "Improved decision procedures for Lewis's calculus S4 and Van Wright's calculus M," The Journal of Symbolic Logic, vol. 34 (1969), pp. 253-255.
[2] Bull, R. A., "On the extension of S4 with CLMpMLp," Notre Dame Journal of Formal Logic, vol. VIII (1967), pp. 325-329.
[3] Carnap, R., "Modalities and quantification," The Journal of Symbolic Logic, vol. 11 (1946), pp. 33-64.
[4] Cresswell, M. J., "A conjunctive normal form for S3.5," The Journal of Symbolic Logic, vol. 34 (1969), pp. 253-255.
[10] Wright, G. H. von, An Essay in Modal Logic, Amsterdam (1951).
———. 1975. "Review of David Lewis Counterfactuals." Mind no. 84:451-458.
———. 1975. "Some Connections between Elementary and Modal Logic." In Proceedings of the Third Scandinavian Logic Symposium, edited by Kanger, Stig, 15-31. Amsterdam: North-Holland.
———. 1976. "Review of the Nature of Necessity (A. Plantinga)." The Philosophical Review no. 86:562-566.
Reprinted in: Modality and tense. Philosophical papers as chapter 11.
———. 1976. "Completeness for the Semi-Lattice Semantics. Abstract." Journal of Symbolic Logic no. 41:560.
———. 1976. "Completeness for the S5 Analogue of E_{i}." Journal of Symbolic Logic no. 41:559-560.
———. 1977. "Properties, Propositions and Sets." Journal of Philosophical Logic no. 6:135-191.
"This paper presents a theory of extensional and intensional entities. It takes a possible-worlds account of these entities for granted and, in terms of that account, attempts to characterize and investigate various features of the entities. tTese features include existence in a world, being purely general or qualitative, being logical, having an individual as a constituent, and being essentially modal. the characterizations are given abstractly, in terms of a relevant notion of isomorphism, and linguistically, in terms of expressibility within an ideal language."
———. 1977. World, Times and Selves. London: Duckworth.
Co-author: Arthur Norman Prior
———. 1977. "Postscript to Worlds, Times and Selves by Arthur Norman Prior." In Worlds, Times and Selves. London: Duckworth.
Reprinted in: Modality and tense. Philosophical papers as chapter 4.
———. 1978. "Model Theory for Modal Logic Part I: The 'De Re / De Dicto' Distinction." Journal of Philosophical Logic no. 7:125-156.
" This series attempts to bring the methods of model theory closer to certain philosophical concerns in modal logic. In the first part, I deal with two related philosophical positions, "de re" scepticism and anti-haecceitism. The main result is that a sentence is equivalent to a "de dicto" one if and only if its truth-value does not turn on the identity of individuals across possible worlds. However, there are also extensions of the result to different languages, different logics, generalisations of the concept of "de dicto"."
———. 1978. "Model Theory for Modal Logic Part Ii: The Elimination of 'De Re' Modality." Journal of Philosophical Logic no. 7:277-306.
"A modal theory is said to permit formula (sentence) eliminability if each formula (sentence) is equivalent, in the theory, to a "de dicto" formula. Various particular and general results on theories which permit eliminability are established. it is shown, for example, that no consistent theory with "de dicto" axioms permits sentence eliminability and that there is only one natural which permits formula eliminability."
———. 1979. "Failures of the Interpolation Lemma in Quantified Modal Logic." Journal of Symbolic Logic no. 44:201-206.
" It is shown that Beth's definability theorem and its corollary, the interpolation lemma, fail for quantified S5, with or without constant domain, and for all systems with constant domain that lie between K and S5."
———. 1979. "Analytic Implication." In Papers on Language and Logic, edited by Dancy, Jonathan, 64-70. Keele: Keele University Library.
Reprinted in: Notre Dame Journal of Formal Logic, 27, 1986, pp. 169-179.
"Parry presented a system of analytic implication in [7] and [8], Dunn [2] gave an algebraic completeness proof for an extension of this system and Urquhart [10] later gave a semantic completeness proof for Dunn's system with necessity. This paper establishes completeness for Parry's original system, (*) thereby answering a question of Gödel [6], and then, on the basis of the completeness result, derives decidability; it also deals with quantificational versions and other modifications of his system.
Section 1 contains some informal remarks on the notion of analytic implication.
They are not strictly relevant to the later analysis, although they may help to place it in perspective. Section 2 presents the semantics and Section 3 exhibits a system of analytic implication. Section 4 helps to demonstrate that the system is equivalent to Parry's, and Section 5 establishes completeness. Finally, Section 6 outlines the theory for some related systems."
(*) I mean the full system of [7] with adjunction, A14 and A15.
[1] Anderson A. R. and N. D. Belnap, Jr., "A simple treatment of truth-functions," The Journal of Symbolic Logic, vol. 25 (1959), pp. 301-302.
[2] Dunn, J. M., "A modification of Parry's analytic implication," Notre Dame Journal of Formal Logic, vol. 13, no. 2 (1972), pp. 195-205.
[3] Epstein, D., "The semantic foundations of logic," to appear.
[4] Hughs, G. E. and M. J. Cresswell, An Introduction to Modal Logic, Methuen, London, 1968.
[5] Kielkopf, C. F., Formal Sentential Entailment, University Press of America, Washington, D.C., 1977.
[6] Parry, W. T., "Ein Axiomsystem fur eine neue Art von Implication (analytische Implication)," Ergebrisse eines Mathematischen Colloquiums, vol. 4 (1933), pp. 5-6.
[7] Parry, W. T., "The logic of C. I. Lewis," pp. 115-154 in The Philosophy of C. I. Lewis, ed., P. A. Schilpp, Cambridge University Press, 1968.
[8] Parry, W. T., "Comparison of entailment theories," The Journal of Symbolic Logic, vol. 37 (1972), pp. 441 f.
[9] Post, E. L., The Two-Valued Iterative Systems of Mathematical Logic, Princeton, University Press, Princeton, New Jersey, 1941.
[10] Urquhart, A., "A semantical theory of analytical implication," Journal of Philosophical Logic, vol. 2 (1973), pp. 212-219.
———. 1980. "First-Order Modal Theories. Ii: Propositions." Studia Logica no. 39:159-202.
"This paper is part of a general programme of developing and investigating particular first-order modal theories. In the paper, a modal theory of propositions is constructed under the assumption that there are genuinely singular propositions, i.e., ones that contain individuals as constituents. Various results on decidability, axiomatizability and definability are established."
———. 1981. "First-Order Modal Theories. I: Sets." Noûs no. 15:177-205.
"This paper is the first part of a general program to develop different existentialist theories and deals with the special topic of sets. various essentialist axioms are discussed, and an attempt is made to formalize correct modal systems for sets. These systems are then investigated metatheoretically. The topics considered include: class abstracts in a modal setting; the deductive
equivalence of the different systems; embedding of the possible worlds semantics within a first-order modal theory; the modal adequacy of the formalizations; and the identity of sets as part of a general account of the identity of objects."
———. 1981. "Model Theory for Modal Logic. Part Iii: Existence and Predication." Journal of Philosophical Logic no. 10:293-307.
"This paper is concerned with the technical implications of the requirement that the predicates of a modal language be true only of the existents of each world. a preservation result for formulas in which the predicates are made to conform to the requirement is established, and sufficient conditions for the predicates of a theory to admit of an analysis in terms of those that meet the
requirement are laid down.
This paper is the third and final part of a series. It was completed and submitted to the Journal of Philosophical Logic in 1977, at about the same time as the other parts. But because of some mishap in the mail, its publication was delayed. The present part is independent from the other parts in its results, but draws upon the terminology of Section 2 of Part I."
———. 1982. "The Problem of Non-Existents. I: Internalism." Topoi no. 1:97-140.
"I describe a particular theory of non-existent objects and point out what seem to be its principal defects. An attempt is made, on the way, to set up a more general framework for the consideration of questions in object theory."
———. 1982. "First-Order Modal Theories. Iii: Facts." Synthese no. 53:43-122.
"This paper gives a philosophical and technical account of the essentialist properties of facts."
———. 1982. "Acts, Events and Things." In Sprache Und Ontologie. Akten Des Sechsten Internationalen Wittgenstein-Symposiums, 23. Bis 30. August 1981, Kirchberg Am Wechsel (Osterreich), edited by Leinfellner, Werner, Kraemer, Eric and Schank, Jeffrey, 97-105. Wien: Holder-Pichler-Tempsky.
———. 1983. "The Permutation Principle in Quantificational Logic." Journal of Philosophical Logic no. 12:33-37.
———. 1983. "Symposium. A Defence of Arbitrary Objects: I." Proceedings of the Aristotelian Society no. Supplementary volume 57:55-77.
Reprinted in: Fred Landman, Frank Veltman (eds.) - Varieties of formal semantics. Proceedings of the fourth Amsterdam colloquium, September 1982 - Dordrecht,: Foris Publications, 1984.
"A theory of arbitrary objects is defended against various philosophical objections. Several applications of the theory to the study of generality are outlined."
———. 1984. "Critical Review of T. Parsons' Nonexistent Objects." Philosophical Studies no. 45:95-142.
Review of: Terence Parsons - Nonexistent objects - New Haven, Yale University Press, 1980.
"There has recently been a rebellion within the ranks of analytic philosophy. It has come to be appreciated that, in the debate between Russell and Meinong, Russell was perhaps mistaken in his criticisms and Meinong was perhaps correct in his views. As a consequence, an attempt was made to rehabilitate the Meinongian position, to defend it against the most obvious attacks and to develop it in the most plausible ways. T. Parsons was among the first of the contemporary philosophers to make this attempt,' and so it is especially appropriate that his views should now be set out in a book.
I should say, at the outset, that I thoroughly approve of the Meinongian project. As Parsons makes clear (pp. 32-38), we refer to non-existents in much the same way as we refer to other objects. It is therefore incumbent upon the philosopher to work out the principles by which our discourse concerning such objects is governed. Not that this is necessarily to endorse a realist position towards the objects of the resulting theory. Nominalists and Platonists alike may attempt to set out the principles that govern arithmetical discourse; and it is in the same spirit that the realist or anti-realist may attempt to set out the principles of our fictional discourse.
Despite my approval of the project, I must admit to some misgivings as to how Parsons has carried it out. These misgivings are of two kinds. There are first some internal criticisms, requiring only change within Parsons' basic approach. There are then some external criticisms, requiring change to the basic approach.
These criticisms, though, should not be though.. to detract from the merits of Parsons' book. It is, in many ways, an admirable contribution to the field. It gives weight both to the interest and the legitimacy of the Meinongian enterprise; it pinpoints the difficulties which any satisfactory theory must deal with; and in its solution to those difficulties, it sets up a theory with a degree of rigour and systematicity that should serve as a model for years to come. As a well worked-out and accessible contribution to object theory, there is no better book."
———. 1984. "Truth without Satisfaction." Journal of Philosophical Logic no. 13:397-421.
With Timothy McCarthy.
"Tarski defined truth in terms of satisfaction. but is this necessary? We give some answers to this question and thereby solve a problem of Kripke's and of Tharp's."
———. 1985. "Natural Deduction and Arbitrary Objects." Journal of Philosophical Logic no. 14:57-107.
Reprinted in Philosopher's Annual - vol. 8, 1985.
"I sketch a theory of arbitrary or variable objects and then use it in interpreting systems of natural deduction that contain a rule of existential instantiation. Such an interpretation is able to motivate the restrictions on the rules and to provide simple and natural proofs of soundness. it also seems to correspond quite well to our actual understanding of quantificational reasoning."
———. 1985. "Logics Containing K4. Part Ii." Journal of Symbolic Logic no. 50:619-651.
"This paper deals with logics containing K4 that are complete for a class of frames that contains any subframe of its members. A uniform axiomatization of such logics is given; it is shown that they all have the finite model properly; and tests for compactness are developed. Various other results on p-morphism, definability and decidability are also established."
———. 1985. Reasoning with Arbitrary Objects. Oxford: Basil Blackwell.
Contents: Preface VII; Introduction 1; 1. The general framework 5; 2. Some standard systems 61; 3. Systems in general 147; 4. Non standard-systems 177; Bibliography 210; General Index 215; Index of symbols 219-220.
———. 1985. "Plantinga on the Reduction of Possibilist Discourse." In Alvin Plantinga, edited by Tomberlin, James and Inwagen, Peter van, 145-186. Dordrecht: Reidel.
Reprinted in: Modality and tense. Philosophical papers as chapter 5.
"What is the modal actualist to make of apparently intelligible discourse concerning possible worlds and individuals? I compare Plantinga's and my own views on this question. I also discuss some related questions on the connection between existence and predication, the necessary existence of propositions, and the Priorian perspective on modality."
———. 1988. "Semantics for Quantified Relevance Logic." Journal of Philosophical Logic no. 17:27-59.
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. 235-262..
"It is known that quantified R and related systems are not complete for the standard versions of the operational or ternary relation semantics. I provide a version of these semantics for which such systems are complete. It employs an unorthodox clause for the quantifiers: a universally quantified statement is true iff the corresponding condition is true of an arbitrary individual."
———. 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.
"Propositional relevance logic is complete for a certain relational semantics. It is shown that the natural extension of the logic to quantifiers is not complete for the natural extension of the semantics."
———. 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.
"This paper attempts to evaluate Quine's arguments against quantifying into modal contexts and, as such, both complements and expands on my paper "Quine on Quantifying In". Special attention is given to the conditions for quantification to be intelligible and the question of whether quantification must be referential."
———. 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."
———. 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.
"The paper attempts to evaluate Quine's argument against quantifying into modal contexts. Two versions of the argument are distinguished, one of a broadly logical sort and the other relating to the nature of necessity. The first version is seen to depend upon an assumption of linguistic uniformity, which may be reasonable for certain ideal formal languages but which is problematic for natural languages; and the second version is seen to have some force in application to a metaphysical conception of modality, but to have none in application to a logical or analytic
conception of modality."
———. 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."
———. 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.
———. 1992. "Aristotle on Matter." Mind no. 101:35-57.
"This paper attempts to give a systematic account of Aristotle's view on the relationship between a thing and the matter of which it is composed."
———. 1992. "Transparency." In Proceedings of the Conference on Logic in Computer Science 89. New York: Springer.
———. 1994. "Essence and Modality." In Philosophical Perspectives 8: Logic and Language, edited by Tomberlin, James, 1-16. Atascadero: Ridgeview Publishing Co.
"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
———. 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."
———. 1994. "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.
"The notion of essence is clarified in an attempt to provide a firm foundation for the theory of essence"
———. 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: Oxford University 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."
(1) Furth, M. Transtemporal Stability in Aristotelian Substances, Journal of Philosophy, 75 (1978), 624-646; repeated in Substance, Form and Psyche: An Aristotelian Metaphysics, Cambridge University Press: Cambridge, 1988. (note abbreviated).
———. 1994. "Ontological Dependence." Proceedings of the Aristotelian Society no. 95:269-290.
"The usual account of ontological dependence in terms of necessity is criticized; and an alternative account of terms of essence is proposed. Different notions of dependence are seen to correspond to different notions of essence."
———. 1995. "The Logic of Essence." Journal of Philosophical Logic no. 24:241-273.
———. 1995. "Part-Whole." In The Cambridge Companion to Husserl, edited by Smith, Barry and Smith, David Woodruff, 463-485. Cambridge: Cambridge University Press.
———. 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. 82-93.
References:
Bogen, 1995 "Fire in the belly: Aristotelian elements, organisms, and chemichal compounds", this volume
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
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