Heil wants us to be ‘ontologically serious’. Because if we’re ontologically serious we won’t take relations seriously. Here’s one of the lines of thought that runs through Heil’s Relations. It’s go...

There is no single problem of universals but a family of difficulties that treat of a variety of interwoven metaphysical, epistemological, logical and semantic themes. This makes the problem of universals resistant to canonical reduction (to a ‘once-and-for-all’ concern). In particular, the problem of universals cannot be reduced to the problem of supplying truth-makers for sentences that express sameness of type. This is (in part) because the conceptual distinction between numerical and qualitative identity must first be drawn before a sentence (...) is eligible to be supplied with truth-makers. The case is made through a consideration of a recent argument by Gonzalo Rodriguez-Pereyra. (shrink)

Philosophical Papers Vol.31(1) 2002: 49-61.

This chapter contains sections titled: Genesis Logical Constants Converse Relations Acknowledgments References.

According to neo-Fregeans, an expression that is syntactically singular and figures in a true sentence is guaranteed to have some existing thing in the world to pick out. But this approach is confronted by a dilemma. If reality is crystalline, has a structure fixed independently of language, then the view that reality is guaranteed to contain a sufficient plenitude of objects to supply referents for the relevant expressions is left hostage to cosmological fortune. Whereas if reality is plastic then it (...) becomes dubiously coherent to conceive of our ordinary, scientific, and mathematical claims about a diversity of objects as being genuinely true or false of an independent reality. To avoid this dilemma, the neo-Fregeans must abandon the dichotomy that says either our true sentences must ‘mirror’ the structure of a crystalline reality or ‘impose’ structure upon a plastic one. If we can legitimately deny that there is an intelligible question to be raised of how language hooks onto reality, then prima facie we can grant that a sentence S is true without thereby becoming embroiled in the uncomfortable consequences of having to say what makes S true. So ontological quietism holds out the last, best hope for neo-Fregeanism. (shrink)

According to philosophical folklore Ramsey maintained three propositions in his famous 1925 paper “Universals”: (i) there is no subject-predicate distinction; (ii) there is no particular-universal distinction; (iii) there is no particular-universal distinction because there is no subject-predicate distinction. The ‘first generation’ of Ramsey commentators dismissed “Universals” because they held that whereas predicates may be negated, names may not and so there is a subject-predicate distinction after all. The ‘second generation’ of commentators dismissed “Universals because they held that the absence of (...) a merely linguistic distinction between subject and predicate does not provide any kind of reason for doubting that a truly ontological (i.e. non-linguistic) distinction obtains between particulars and universals. But both first and second-generation criticisms miss their marks because Ramsey did not maintain the three identified propositions. The failure of commentators to appreciate the point and purpose of the position Ramsey actually advanced in “Universals” results from (a) failing to consider the range of different arguments advanced there, (b) looking at “Universals” in isolation from Ramsey’s other papers and (c) failing to consider Ramsey’s writings in the context of the views that Russell and Wittgenstein held during the early 1920s. Seen from this wider perspective Ramsey arguments in “Universals” take on an altogether different significance. They not only anticipate important contemporary developments⎯the resurgence of Humeanism and the doctrine that the existence of universals can only be established a posteriori⎯but also point beyond them. (shrink)

There cannot be a reductive theory of modality constructed from the concepts of sparse particular and sparse universal. These concepts are suffused with modal notions. I seek to establish this conclusion by tracing out the pattern of modal entanglements in which these concepts are involved. In order to appreciate the structure of these entanglements a distinction must be drawn between the lower-order necessary connections in which particulars and universals apparently figure, and higher-order necesary connections. The former type of connection relates (...) specific entities. By contrast, the latter type of connection is unspecific: it relates entities to some others. I argue that whilst there may be techniques that succeed in providing reductive truth conditions for sentences that say particulars and universals figure in lower-order necessary connections, such techniques cannot succeed in providing reductive truth conditions for sentences that say these entities figure in higher-order necessary connections. I conclude that this situation leaves reductionists with a dilemma. If they wish to affirm that there are particulars and universals then the project of reducing modality by positing these entities must be abandoned. Alternatively, they may continue to deploy their usual reductive techniques but then they must abandon the doctrine that there is more than one fundamental category of entity. (shrink)

Ante rem structuralism is the doctnne that mathematics descubes a realm of abstract (structural) universab. According to its proponents, appeal to the exutence of these universab provides a source distinctive insight into the epistemology of mathematics, in particular insight into the so-called 'access problem' of explaining how mathematicians can reliably access truths about an abstract realm to which they cannot travel andfiom which they recave no signab. Stewart Shapiro offers the most developed version of this view to date. Through an (...) examination of Shapiro's proposed structuralist epistemology for mathematics I argue that ante rem structuralism faib to provide the ingredients for a satisfactory resolution of the access problem for infinite structures (whether small or large). (shrink)

There is no such thing as , conceived as a special discipline with its own distinctive subject matter or peculiar method. But there is an analytic task for philosophy that distinguishes it from other reflective pursuits, a global or synoptic commission: to establish whether the final outputs of other disciplines and common sense can be fused into a single periscopic vision of the Universe. And there is the hard-won insight that thought and language aren't transparent but stand in need of (...) analysis an insight that threatens to be lost once philosophers appeal to intuitions. (shrink)

In this review, as well as discussing the pedagogical of this text book, I also discuss Linnebo's approach to the Caesar problem and the use of metaphysical notions to explicate mathematics.

In this paper I provide a state of the art survey and assessment of the contemporary debate about relations. After (1) distinguishing different varieties of relations, symmetric from non-symmetric, internal from external relations etc. and relations from their set-theoretic models or sequences, I proceed (2) to consider Bradley’s regress and whether relations can be eliminated altogether. Next I turn (3) to the question whether relations can be reduced, bringing to bear considerations from the philosophy of physics as well as metaphysics. (...) Finally, (3) I consider in what sense relations have order, and whether to make sense of this we are required to conceive of relations as having direction or argument positions. (shrink)

In ‘Putnam’s Paradox’, Lewis defended global descriptivism and reference magnetism. According to Schwarz [2014], Lewis didn’t mean what he said there, and really held neither position. We present evidence from Lewis’s correspondence and publications which shows conclusively that Lewis endorsed both.

This article for the Stanford Encyclopedia for Philosophy provides a state of the art survey and assessment of the contemporary debate about truth-makers, covering both the case for and against truth-makers. It explores 4 interrelated questions about truth-makers, (1) What is it to be a truth-maker? (2) Which range, or ranges, of truths are eligible to be made true (if any are)? (3) What kinds of entities are truth-makers? (4) What is the motivation for adopting a theory of truth-makers? And (...) adds that there's another question to often put aside by metaphysicians but has critical consequences for truth-makers: (5) What are the truth-bearers? (shrink)

Is the assumption of a fundamental distinction between particulars and universals another unsupported dogma of metaphysics? F. P. Ramsey famously rejected the particular – universal distinction but neglected to consider the many different conceptions of the distinction that have been advanced. As a contribution to the piecemeal investigation of this issue three interrelated conceptions of the particular – universal distinction are examined: universals, by contrast to particulars, are unigrade; particulars are related to universals by an asymmetric tie of exemplification; universals (...) are incomplete whereas particulars are complete. It is argued that these conceptions are wanting in several respects. Sometimes they fail to mark a significant division amongst entities. Sometimes they make substantial demands upon the shape of reality; once these demands are understood aright it is no longer obvious that the distinction merits our acceptance. The case is made via a discussion of the possibility of multigrade universals. (shrink)

We argue that Lewis would have rejected recent appeals to the notions of ‘metaphysical dependency’, ‘grounding’ and ‘ontological priority’, because he would have held that they’re not needed and they’re not intelligible. We argue our case by drawing upon Lewis’s views on supervenience, the metaphysics of singletons and the dubiousness of Kripke’s essentialism.

According to the species of neo-logicism advanced by Hale and Wright, mathematical knowledge is essentially logical knowledge. Their view is found to be best understood as a set of related though independent theses: (1) neo-fregeanism-a general conception of the relation between language and reality; (2) the method of abstraction-a particular method for introducing concepts into language; (3) the scope of logic-second-order logic is logic. The criticisms of Boolos, Dummett, Field and Quine (amongst others) of these theses are explicated and assessed. (...) The issues discussed include reductionism, rejectionism, the Julius Caesar problem, the Bad Company objections, and the charge that second-order logic is set theory in disguise. (shrink)

The contemporary Humean programme that seeks to combine property realism with the denial of necessary connections between distinct existences is flawed. Objects and properties by their very natures are entangled in such connections. It follows that modal notions cannot be reductively analysed by appeal to the concept property, not even if the reducing theory posits an abundant supply of entities to fall under that concept.

The concepts of particular and universal have grown so familiar that their significance has become difficult to discern, like coins that have been passed back and forth too many times, worn smooth so their values can no longer be read. On the Genealogy of Universals seeks to overcome our sense of over-familiarity with these concepts by providing a case study of their evolution during the late nineteenth century and early twentieth century, a study that shows how the history of these (...) concepts is bound up with the origins and development of analytic philosophy itself. Understanding how these concepts were taken up, transfigured, and given up by the early analytic philosophers, enables us to recover and reanimate the debate amongst them that otherwise remains Delphic. This book begins from the early, originating texts of analytic philosophy that have hitherto baffled commentators, including Moore's early papers, and engages afresh with the neglected contributions of philosophical figures that historians of analytic philosophy have mostly since forgotten, including Stout and Whitehead. This sheds new light upon the relationships of Moore to Russell, Russell to Wittgenstein, and Wittgenstein to Ramsey. (shrink)

Frege attempted to provide arithmetic with a foundation in logic. But his attempt to do so was confounded by Russell's discovery of paradox at the heart of Frege's system. The papers collected in this special issue contribute to the on-going investigation into the foundations of mathematics and logic. After sketching the historical background, this introduction provides an overview of the papers collected here, tracing some of the themes that connect them.

There are three different degrees to which we may allow a systematic theory of the world to embrace the idea of relatedness—supposing realism about non-symmetric relations as a background requirement. (First Degree) There are multiple ways in which a non-symmetric relation may apply to the things it relates—for the binary case, aRb ≠ bRa. (Second Degree) Every such relation has a distinct converse—for every R such that aRb there is another relation R* such that bR*a. (Third Degree) Each one of (...) them applies in an order to the things it relates—with regard to the state that results from R's applying to a and b, either R applies to a first and b second, or it applies to b first and a second. Whereas the first degree is near-indubitable, embracing the second or third generates unwholesome consequences. The second degree embodies a commitment to the existence of a superfluity of distinct converses and states to which such relations give rise. The third degree embodies commitment to recherché facts of the matter about how the states that arise from the application of one non-symmetric relation compare to any other. It is argued that accounts that purport to offer an analysis of the first degree generate unwelcome second or third degree consequences. This speaks in favour of our adopting an account of the application of relations that's not an analysis at all, an account that takes the first degree as primitive. (shrink)

Modality is standardly thought to come in two varieties: de dicto and de re. De re modality concerns the attribution of modal features to things or individuals, and enshrines a commitment to Aristotelian essentialism. This chapter considers how David Lewis's conception of de re modality fits into his overall metaphysics. The hypothesis is that the driving force behind his metaphysics in general, and his adherence to counterpart theory in particular, is the distinctly Humean thought that necessary connections between distinct existences (...) are literally unintelligible. Lewis's appeal to counterpart theory in his account of truthmakers is explicitly aimed at delivering a truthmaker principle that eschews necessary connections. Lewis's attitude towards several well‐rehearsed debates in contemporary ontology and the reasons underlying that attitude closely mirror Hume's incendiary verdict on "divinity and school metaphysics." Finally, de re modality is connected with his adherence to the doctrine of "Humean supervenience". (shrink)

Do non‐symmetric relations apply to the objects they relate in an order? According to the standard view of relations, the difference between aRb and bRa obtaining, where R is non‐symmetric, corresponds to a difference in the order in which the non‐symmetric relation R applies to a and b. Recently Kit Fine has challenged the standard view in his important paper ‘Neutral Relations’ arguing that non‐symmetric relations are neutral, lacking direction or order. In this paper I argue that Fine cannot account (...) for the application of non‐symmetric relations to their relata; so far from being neutral, these relations are inherently directional. (shrink)

Can Bradley's Regress be solved by positing relational tropes as truth-makers? No, no more than Russell's paradox can be solved by positing Fregean extensions. To call a trope relational is to pack into its essence the relating function it is supposed to perform but without explaining what Bradley's Regress calls into question, viz. the capacity of relations to relate. This problem has been masked from view by the (questionable) assumption that the only genuine ontological problems that can be intelligibly raised (...) are those that can be answered by providing a schedule of truthmakers. (shrink)

The basic relations and functions that mathematicians use to identify mathematical objects fail to settle whether mathematical objects of one kind are identical to or distinct from objects of an apparently different kind, and what, if any, intrinsic properties mathematical objects possess. According to one influential interpretation of mathematical discourse, this is because the objects under study are themselves incomplete; they are positions or akin to positions in patterns or structures. Two versions of this idea are examined. It is argued (...) that the evidence adduced in favor of the incompleteness of mathematical objects underdetermines whether it is the objects themselves or our knowledge of them that is incomplete. Also, holding that mathematical objects are incomplete conflicts with the practice of mathematics. The objection that structuralism is committed to the identity of indiscernibles is evaluated and it is also argued that the identification of objects with positions is metaphysically suspect. (shrink)

According to the species of neo‐logicism advanced by Hale and Wright, mathematical knowledge is essentially logical knowledge. Their view is found to be best understood as a set of related though independent theses: (1) neo‐fregeanism—a general conception of the relation between language and reality; (2) the method of abstraction—a particular method for introducing concepts into language; (3) the scope of logic—second‐order logic is logic. The criticisms of Boolos, Dummett, Field and Quine (amongst others) of these theses are explicated and assessed. (...) The issues discussed include reductionism, rejectionism, the Julius Caesar problem, the Bad Company objections, and the charge that second‐order logic is set theory in disguise.The irresistible metaphor is that pure abstract objects […] are no more than shadows cast by the syntax of our discourse. And the aptness of the metaphor is enhanced by the reflection that shadows are, after their own fashion, real. (Crispin Wright [1992], p. 181–2)But I feel conscious that many a reader will scarcely recognise in the shadowy forms which I bring before him his numbers which all his life long have accompanied him as faithful and familiar friends; (Richard Dedekind [1963], p. 33)1 Introduction2 Logical‐historical preliminaries3 The linguistic turn4 Reductionism5 Rejectionism6 The ‘Julius Caesar’ problem7 Second‐order logic8 Bad company objections9 Conclusion. (shrink)

In ‘Putnam’s Paradox’, Lewis defended global descriptivism and reference magnetism. According to Schwarz [2014], Lewis didn’t mean what he said there, and really held neither position. We present evidence from Lewis’s correspondence and publications which shows conclusively that Lewis endorsed both.

The early David Lewis was a staunch critic of the Truthmaker Principle. To endorse the principle, he argued, is to accept that states of affairs are truthmakers for contingent predications. But states of affairs violate Hume's prohibition of necessary connections between distinct existences. So Lewis offered to replace the Truthmaker Principle with the weaker principle that ‘truth supervenes upon being’. This chapter argues that even this principle violates Hume's prohibition. Later Lewis came to ‘withdraw’ his doubts about the Truthmaker Principle, (...) invoking counterpart theory to show how it is possible to respect the principle whilst admitting only things that do not violate Hume's prohibition. What this really reveals is that the Truthmaker Principle is no explanatory advance on the supervenience principle. Extending Lewis's use of counterpart theory also allows us to explain away the necessary connections that threatened to undermine his earlier statements of supervenience. (shrink)

Whether a predicate is a referential expression depends upon what reference is conceived to be. Even if it is granted that reference is a relation between words and worldly items, the referents of expressions being the items to which they are so related, this still leaves considerable scope for disagreement about whether predicates refer. One of Frege's great contributions to the philosophy of language was to introduce an especially liberal conception of reference relative to which it is unproblematic to suppose (...) that predicates are referring expressions. According to this liberal conception, each significant expression in a language has its own distinctive semantic role or power, a power to effect the truth-value of the sentences in which it occurs. (shrink)

According to Armstrong (amongst others) ‘any truth, should depend for its truth for something “outside” it’ where this one-way dependency is explained in terms of the asymmetric relationship that obtains between a truth and its truth-maker. But there’s no need to appeal to truth-makers to make sense of this dependency. The truth of a proposition is essentially determined by the interlocking semantic mechanism of reference and satisfaction which already ensures that the truth-value of a proposition depends on how things stand (...) outside it. By contrast, how things stand outside of a proposition is determined by other worldly mechanisms that have nothing to do with truth. (shrink)

In 1901 Russell had envisaged the new analytic philosophy as uniquely systematic, borrowing the methods of science and mathematics. A century later, have Russell’s hopes become reality? David Lewis is often celebrated as a great systematic metaphysician, his influence proof that we live in a heyday of systematic philosophy. But, we argue, this common belief is misguided: Lewis was not a systematic philosopher, and he didn’t want to be. Although some aspects of his philosophy are systematic, mainly his pluriverse of (...) possible worlds and its many applications, that systematicity was due to the influence of his teacher Quine, who really was an heir to Russell. Drawing upon Lewis’s posthumous papers and his correspondence as well as the published record, we show that Lewis’s non- Quinean influences, including G.E. Moore and D.M. Armstrong, led Lewis to an anti- systematic methodology which leaves each philosopher’s views and starting points to his or her own personal conscience. (shrink)

Is the truthmaker principle a development of the correspondence theory of truth? So Armstrong introduced the truthmaker principle to us, but Lewis (2001. Forget about the ‘correspondence theory of truth’. Analysis 61: 275–80.) influentially argued that it is neither a correspondence theory nor a theory of truth. But the truthmaker principle can be correctly understood as a development of the correspondence theory if it’s conceived as incorporating the insight that truth is a relation between truth-bearers and something worldly. And we (...) strengthen rather than weaken the plausibility of the truthmaker principle if we conceive of truth as performing a substantial rather than deflationary role in the truthmaker principle. (shrink)

Is there a particular-universal distinction? Is there a difference of kind between all the particulars on the one hand and all the universals on the other? Can we demonstrate that there is such a difference without assuming what we set out to show? In 1925 Frank Ramsey made a famous attempt to answers these questions. He came to the sceptical conclusion that there was no particularuniversal distinction, the theory of universals being merely “a great muddle”. Following Russell, Ramsey identified three (...) kinds of distinction, psychological, physical and logical, in terms of which the particular-universal distinction might be understood. Ramsey argued that the particular-universal distinction could not be understood in terms of any of these kinds of distinction. Ramsey concluded that the particular-universal distinction, being neither psychological, physical or logical, was no distinction at all. The conclusion that there is no particular-universal distinction cannot be substantiated on the basis of the arguments that Ramsey provides. At least one of these arguments, the argument that the particular-universal distinction cannot be a ‘physical’ distinction, is flawed. (shrink)

The eleven new papers in this volume address fundamental and interrelated philosophical issues concerning modality and identity, issues that were pivotal to the development of analytic philosophy in the twentieth century, and remain a key focus of debate in the twenty-first. Identity and Modality brings together leading researchers in metaphysics, the philosophy of mind, the philosophy of science, and the philosophy of mathematics.

A priori reflection, common sense and intuition have proved unreliable sources of information about the world outside of us. So the justification for a theory of the categories must derive from the empirical support of the scientific theories whose descriptions it unifies and clarifies. We don’t have reliable information about the de re modal profiles of external things either because the overwhelming proportion of our knowledge of the external world is theoretical—knowledge by description rather than knowledge by acquaintance. This undermines (...) the traditional idea that to be an object of category C is to be an object with such- and-such characteristic possibilities of combination. But this is no loss because de re modal thought lacks utility for creatures like us. (shrink)

Frank Plumpton Ramsey (1903–30) made seminal contributions to philosophy, mathematics and economics. Whilst he was acknowledged as a genius by his contemporaries, some of his most important ideas were not appreciated until decades later; now better appreciated, they continue to bear an influence upon contemporary philosophy. His historic significance was to usher in a new phase of analytic philosophy, which initially built upon the logical atomist doctrines of Bertrand Russell and Ludwig Wittgenstein, raising their ideas to a new level of (...) sophistication, but ultimately he became their successor rather than remain a mere acolyte. (shrink)

This paper provides a new solution to the concept horse paradox. Frege argued no name co-refers with a predicate because no name can be inter-substituted with a predicate. This led Frege to embrace the paradox of the concept horse. But Frege got it wrong because predicates are impurely referring expressions and we shouldn’t expect impurely referring expressions to be intersubstitutable even if they co-refer, because the contexts in which they occur are sensitive to the extra information they carry about their (...) referents. (shrink)

In this paper I contribute a further element to the case for admitting non-symmetric relations by dismantling the case against them. Armstrong and Dorr have both argued (1) that asymmetric relations give rise to ‘brute necessities’, whilst Dorr further argues (2) that admitting non-symmetric relations generates spurious possibilities and (3) that exploiting work of Goodman and Hazen, we can do without non-symmetric relations anyway. Against (1) I argue that neither Armstrong nor Dorr succeed in avoiding brute necessities themselves. Against (2) (...) and (3) I argue that admitting non-symmetric relations doesn’t give rise to spurious possibilities and Goodman and Hazen’s work cannot be used to establish that non-symmetric relations are dispensable to science and mathematics. (shrink)

In an unpublished speech from 1991, David Lewis told his audience that he counted ‘the metaphysician Carnap ’ amongst his historical ancestors. Here I provide a novel interpretation of the Aufbau that allows us to make sense of Lewis’s claim. Drawing upon Lewis’s correspondence, I argue it was the Carnap of the Aufbau whom Lewis read as a metaphysician, because Carnap’s appeal to the notion of founded relations in the Aufbau echoes Lewis’s own appeal to the metaphysics of natural properties. (...) I further maintain that Lewis was right to read Carnap this way and that the notion of a founded relation has a legitimate claim to be both logical and metaphysical. I also argue that Carnap’s initial response to Goodman’s puzzle about ‘grue’ relies upon a metaphysics of simple properties which also prefigures Lewis’s own response to Goodman invoking natural properties. (shrink)

This paper investigates the meta-ontological problem, what is the Julius Caesar objection? I distinguish epistemic, metaphysical and semantic versions. I argue that neo-Fregean and supervaluationist solutions to the Caesar objection fails because, amongst other flaws, they fail to determine which version of the problem is in play.