In his ‘Ambitious, Yet Modest, Metaphysics’, Hofweber puts forward arguments against positions in metaphysics that he describes as ‘immodest’; a position he identifies as defended by Jonathan Lowe. In this paper I reply to Hofweber’s arguments, offering a defence of immodest metaphysics of the type practiced by Lowe inter alia.

I argue that mereological nihilism fails because it cannot answer the special arrangement question: when is it true that the xs are arranged F-wise? I suggest that the answers given in the literature fail and that the obvious responses that could be made look to undermine the motivations for adopting nihilism in the first place.

I propose that constitution is a case of composition in which, for example, the lump of clay composes the statue. In other words, we can reduce constitution to composition. Composition does all of the work that we want from an account of constitution, and we do not need two separate relations. Along the way, I offer reasons to reject weak supplementation. Acknowledgments (which by my mistake were not included in the journal publication): Many people have given me feedback over the (...) years on this paper or an ancestor of it, and I apologize for oversights in my acknowledgments here. Special thanks to Trenton Merricks for comments on several drafts of this paper. Thanks also for helpful comments and discussions to Eugene Mills, Donald Smith, Peter Sutton, David Liebesman, Charlie Tanksley, Amanda Hicks, Kristl Laux, and to an audience at the University at Buffalo conference in honor of E. J. Lowe, an audience at Amherst College, and an audience at the 2017 APA Eastern Division Meeting. Thank you also to multiple anonymous referees along the way. (shrink)

The stage theory is a four-dimensional account of persistence motivatedby the worm theory's inability to account for our intuitions in thecases involving coinciding objects. Like the worm theory, it claimsthat there are objects spread out in time, but unlike the worm theory,it argues that these spacetime worms are not familiar particulars liketables and chairs. Rather, familiar particulars are the instantaneoustemporal slices of worms. In order to explain our intuitions that particulars persist for more than an instant, the stage theory drawson (...) the counterpart theory of modal possibilism, which it is supposedto parallel. In this paper I show how the stage theory presupposes thattime can be divided into instants, which I call the atomistic view oftime. I do this by laying out an alternative theory of the nature oftime, the gunky view, and show that if time is gunky the stage theorycollapses into the worm theory. The deeper problem is that the merepossibility of gunky time would cause the stage theory's parallels topossibilism to break down. I therefore conclude that the stage theoryis committed to the view that time is necessarily atomistic. Finally,in the last section I argue that the fact that the stage theory rulesout a priori the possibility of time being gunky gives us reason toreject it as an account of persistence. (shrink)

‘Ahab is a whaler’ and ‘Holmes is a whaler’ express different propositions, even though neither ‘Ahab’ nor ‘Holmes’ has a referent. This seems to constitute a theoretical puzzle for the Russellian view of propositions. In this paper, I develop a variant of the Russellian view, Plenitudinous Russellianism. I claim that ‘Ahab is a whaler’ and ‘Holmes is a whaler’ express distinct gappy propositions. I discuss key metaphysical and semantic differences between Plenitudinous Russellianism and Traditional Russellianism and respond to objections that (...) stem from those differences. (shrink)

In this paper I present two new arguments against the possibility of an omniscient being. My new arguments invoke considerations of cardinality and resemble several arguments originally presented by Patrick Grim. Like Grim, I give reasons to believe that there must be more objects in the universe than there are beliefs. However, my arguments will rely on certain mereological claims, namely that Classical Extensional Mereology is necessarily true of the part-whole relation. My first argument is an instance of a problem (...) first noted by Gideon Rosen and requires an additional assumption about the mereological structure of certain beliefs. That assumption is that an omniscient being’s beliefs are mereological simples. However, this assumption is dropped when I present my second argument. Thus, I hope to show that if Classical Extensional Mereology is true of the part-whole relation, there cannot be an omniscient being. (shrink)

The general composition question asks “what are the necessary and jointly sufficient conditions any xs and any y must satisfy in order for it to be true that those xs compose that y?” Although this question has received little attention, there is an interesting and theoretically fruitful answer. Namely, strong composition as identity (SCAI): necessarily, for any xs and any y, those xs compose y iff those xs are identical to y. SCAI is theoretically fruitful because if it is true, (...) then there is an answer to one of the most difficult and intractable questions of mereology (The Simple Question). In this paper, I introduce the identity account of simplicity and argue that if SCAI is true then this identity account of simplicity is as well. I consider an objection to the identity account of simplicity. Ultimately, I find this objection unsuccessful. (shrink)

Strong Composition as Identity is the thesis that necessarily, for any xs and any y, those xs compose y iff those xs are non-distributively identical to y. Some have argued against this view as follows: if some many things are non-distributively identical to one thing, then what’s true of the many must be true of the one. But since the many are many in number whereas the one is not, the many cannot be identical to the one. Hence is mistaken. (...) Although I am sympathetic to this objection, in this paper, I present two responses on behalf of the theorist. I also show that once the defender of accepts one of these two responses, that defender will be able to answer The Special Composition Question. (shrink)

A material simple is a material object that has no proper parts. Some philosophers have argued for the possibility of extended simples. Some have even argued for the possibility of heterogeneous simples or simples that have intrinsic variations across their surfaces. There is a puzzle, though, that is meant to show that extended, heterogeneous simples are impossible. Although several plausible responses have been given to this puzzle, I wish to reopen the case against extended, heterogeneous simples. In this paper, I (...) briefly canvass responses to this puzzle which may be made in defense of extended, heterogeneous simples. I then present a new version of this puzzle which targets simples that occupy atomic yet extended regions of space. It seems that none of the traditional responses can be used to successfully save this particular kind of extended simple from the new puzzle. I also consider some non-traditional defenses of heterogeneous extended simples and argue that they too are unsuccessful. Finally, I will argue that a substantial case can be made against the possibility of extended heterogeneous simples of any kind. (shrink)

Some philosophers say that a whole is “nothing over and above” its parts. Most also take general extensilonal mereology to be treating wholes as “nothing over and above” their parts. It is not always clear, however, what exactly is meant by the phrase “nothing over and above.” Nor is it obvious why the phrase is associated with mereology, and what purpose it serves there. In the words of Peter Van Inwagen : “This slippery phrase has had a lot of employment (...) in philosophy, but what it means is never explained by its employers.” This paper sheds light on the various senses in which one might hold that a whole is “nothing over and above” its parts, and on how these senses are related both to each other and to mereology. (shrink)

Lewis famously argued that mereology is ontologically innocent. Many who have considered this claim believe he was mistaken. Mereology is not innocent, because its acceptance entails the acceptance of sums, new objects that were not previously part of one’s ontology. This argument, the argument from ontological parsimony, has two versions: a qualitative and a quantitative one. I argue that the defender of mereology can neutralize both arguments by holding that, given mereology, a commitment to the parts of an object is (...) not an extra ontological commitment, made in addition to the commitment to the object; and that if the parts of an object are ‘ontologically innocent’, then sums cannot fail to be innocent either. (shrink)

European Journal of Philosophy, EarlyView.

Standard principles of mereology, such as the transitivity and asymmetry of proper parthood, have been questioned, using various multi-location scenarios. The most famous of these is Borges’s Aleph, although the literature is rife with other examples that allegedly show that some mereological principle is at odds with some form of multi-location. However, the scenarios only support this conclusion given various bridge principles that link location to parthood. I argue that the bridge principles that guarantee the desired conclusion are controversial partly (...) because they give the wrong result in other situations, in particular cases of co-location. Moreover, less controversial bridge principles do not provide an incompatibility result between standard mereological principles and multi-location. Hence, multi-location does not threaten any standard mereological principles. (shrink)

W.V. Quine is a well-known proponent of naturalism, the view on which reality is described only in science. He is also well-known for arguing that our current scientific theories commit us to the existence of abstract objects. It is tempting to believe that the naturalistic philosopher should think scientists outside of philosophy are in the best position to assess the merits of revising our current commitment to abstract objects. But Quine rejects this deferential view. On the reading of Quine’s philosophical (...) methodology that I defend in this paper, the naturalistic philosopher not only may assess the merits of revising the commitments of our scientific theories, but also will recommend we make such revisions if doing so simplifies and clarifies our science. To develop my reading, I will examine John Burgess and Gideon Rosen’s naturalism in ontology that includes the deferential view Quine rejects. By explaining how Quine’s naturalism differs from the anti-revisionist, deferential naturalism in philosophy of mathematics that Burgess and Rosen advance, I seek to clarify and advance contemporary debates on naturalism. (shrink)

The consensus in the philosophical literature on joint action is that, sometimes at least, when agents intentionally jointly φ, this is explicable by their intending that they φ, for a period of time prior to their φ-ing. If this be granted, it poses a dilemma. For agents who so intend either severally or jointly intend that they φ. The first option is ruled out by two stipulations that we may consistently make: (i) that at least one of the agents non-akratically (...) believes that, all things considered, the agents ought not to φ, and (ii) that an agent is akratic, if she intends a thing that she believes, all things considered, ought not to be done. But the second option seems to entail the existence of a mental state with multiple subjects, which, in turn, seems to commit us to the existence of a group mind modified by that state: an incautious posit to say the least. I resolve the dilemma by noting that ‘They jointly intend’ is indeterminate between ‘They intend, jointly’, which does indeed entail that some mental state is an intention with multiple subjects, and ‘Jointly, they intend’, which entails a weaker claim, viz. that some mental state or states is an intention with multiple subjects. I then sketch an account of how a plurality of mental states, distributed among subjects, might, collectively, do service as their intention that they φ. It makes novel use of notions of participation and of doing a thing jointly with others. A corollary is that either intentions are not attitudes towards propositions, or propositions are individuated more finely than is often assumed. (shrink)

The mereological predicate ‘is part of’ can be used to define the predicate ‘is identical with’. I argue that this entails that mereological theories can be ideologically simpler than nihilistic theories that do not use the notion of parthood—contrary to what has been argued by Ted Sider. Moreover, if one accepts an extensional mereology, there are good philosophical reasons apart from ideological simplicity to give a mereological definition of identity.

In this paper, I consider ways of responding to critiques of natural kinds monism recently suggested from the pluralist camp. Even if monism is determined to be untenable in certain domains (say, about species), it might well be tenable in others. Chemistry is suggested to be such a monist‐friendly domain. Suggestions of trouble for chemical kinds can be defused by attending to the difference between monism as a metaphysical thesis and as a claim about classification systems. Finally, I consider enantiomers (...) as a test case for the monism/pluralism debate. The question of whether enantiomers differ in kind does not appear easily answerable. I suggest that this legislates for pluralism in chemistry. (shrink)

'Philosophy arises through misconceptions of grammar', said Wittgenstein. Few people have believed him, and probably none, therefore, working in the area of the philosophy of mathematics. Yet his assertion is most evidently the case in the philosophy of Set Theory, as this paper demonstrates (see also Rodych 2000). The motivation for twentieth century Set Theory has rested on the belief that everything in Mathematics can be defined in terms of sets [Maddy 1994: 4]. But not only are there notable items (...) which cannot be so defined, including numbers and mereological sums, the very notion of a set, as formalized within this tradition, is based on a series of grammatical confusions. (shrink)

Maddy's (1990) arguments against Aggregate Theory were undermined by the shift in her position in 1997. The present paper considers Aggregate Theory in the light of this, and the recent search for `New Axioms for Mathematics'. If Set Theory is the part-whole theory of singletons, then identifying singletons with their single members collapses Set Theory into Aggregate Theory. But if singletons are not identical to their single members, then they are not extensional objects and so are not a basis for (...) Science. Either way, the Continuum Hypothesis has no physical interest. (shrink)

We often speak of an object being composed of various other objects. We say that the deck is composed of the cards, that a road is the sum total of its sections, that a house is composed of its walls, ceilings, floors, doors, etc. Suppose we have some material objects. Here is a philosophical question: what conditions must obtain for those objects to compose something? In his recent book Material Beings, Peter van Inwagen addresses this question, which he calls the (...) ‘special composition question’; his answer is:1 (1) For any material objects X , the X s compose something iff the activity of the X s constitutes a life, or there is only one of the Xs. Additionally, he accepts a simpler thesis that follows from (1):2 (2) Every material object is either a mereological atom or a living thing, where a mereological atom is an object lacking proper parts. (2) may seem radical. If it is true then there are no tables, chairs, planets, protons, galaxies, gas stations, etc. But van Inwagen does not hold it lightly— there are serious difficulties with alternate views. Moreover, he claims that.. (shrink)

There will be a few themes. One to get us going: expansion versus contraction. About an object, o, and the region, R, of space(time) in which o is exactly located,1 we may ask: i) must there exist expansions of o: objects in filled superregions2 of R? ii) must there exist contractions of o: objects in filled subregions of..

Peter Forrest and D.M. Armstrong have given an argument against a theory of naturalness proposed by David Lewis based on the fact that ordered pairs can be constructed from sets in any of a number of different ways. 1. I think the argument is good, but requires a more thorough defense. Moreover, the argument has important consequences that have not been noticed. I introduce a version of Lewis’s proposal in section one, and then in section two I present and defend (...) my version of the argument. After addressing a worry about my argument in section three, in section four I argue that a similar “argument from arbitrariness” jeopardizes Lewis’s solution to the Kripke/Wittgenstein puzzle of the content of thought. (shrink)

The core idea of David Armstrong’s combinatorial theory of possibility is attractive. Rearrangement is the key to modality; possible worlds result from scrambling bits and pieces of other possible worlds. Yet I encounter great difficulty when trying to formulate the theory rigorously, and my best attempts are vulnerable to counterexamples. The Leibnizian biconditionals relate possibility and necessity to possible world and true in.

Analytic Philosophy, Volume 62, Issue 3, Page 275-294, September 2021.

Some philosophers of biology state that the metaphysical status of biological species is context determined by the use different branches of biology make of their corresponding proper names, so that one and the same biological species can be both an individual and a natural kind. In this paper, I aim to undermine the idea, often associated with the present thesis, according to which the debate about the metaphysical status of biological species should be deflated, since it would be possible to (...) translate every sentence from natural-kind talk to individual-talk and vice versa. I offer a charitable interpretation of the principle grounding such an idea and show how it is in tension with independent theoretical biological notions. (shrink)

Late Lowe’s metaphysics of material objects is an interesting multi-thingist theory that still attracts interest from various authors. The core idea is that ifxmaterially constitutesy, thexis a proper part ofy. I discuss some mereological issues that arise from the approach and propose a revision of the mereology associated. Particularly, I examine the tenability of a number of supplementation principles and conclude that just one may serve the theory adequately. Still, the endorsement of such a principle does not come for free. (...) Successively, I address the derivability of an important extensionality theorem and conclude that the theorem must be taken as an axiom in the mereology at stake. Lastly, I discuss two notable definitions of mereological fusions to assess which one best suits the present theory. The result is that authors sharing Lowe’s multi-thingist conception of material objects can still enjoy a moderately strong mereology. (shrink)

The Razor commands us not to multiply entities without necessity. I argue for an alternative principle—The Laser—which commands us not to multiply fundamental entities without necessity.

Consider a circle and a pair of its semicircles. Which is prior, the whole or its parts? Are the semicircles dependent abstractions from their whole, or is the circle a derivative construction from its parts? Now in place of the circle consider the entire cosmos (the ultimate concrete whole), and in place of the pair of semicircles consider the myriad particles (the ultimate concrete parts). Which if either is ultimately prior, the one ultimate whole or its many ultimate parts?

‘‘Thus I believe that there is no part of matter which is not—I do not say divisible—but actually divided; and consequently the least particle ought to be considered as a world full of an infinity of different creatures.’’ (Leibniz, letter to Foucher).

Mereological nihilism is the view that all concrete objects are simple. Existence monism is the view that the only concrete object is one big simple: the world. I will argue that nihilism culminates in monism. The nihilist demands the simplest sufficient ontology, and the monist delivers it.

This article looks at recent work in cognitive science on mathematical cognition from the perspective of history and philosophy of mathematical practice. The discussion is focused on the work of Lakoff and Núñez, because this is the first comprehensive account of mathematical cognition that also addresses advanced mathematics and its history. Building on a distinction between mathematics as it is presented in textbooks and as it presents itself to the researcher, it is argued that the focus of cognitive analyses of (...) historical developments of mathematics has been primarily on the former, even if they claim to be about the latter. (shrink)

The paper argues that no second order theory is ontologically commited to anything beyond what its individual variables range over.

As I will use the term, an object is a mereological sum of some things just in case those things compose it simply in virtue of existing. In the first half of this paper, I argue that there are no sums. The key premise for this conclusion relies on a constraint on what, in certain cases, it takes for something to ground, or metaphysically explain, something else. In the second half, I argue that in light of my argument against sums, (...) Universalism, which is perhaps the most widely accepted answer to the Special Composition Question, is false. (shrink)

Some hold that the lesson of Russell’s paradox and its relatives is that mathematical reality does not form a ‘definite totality’ but rather is ‘indefinitely extensible’. There can always be more sets than there ever are. I argue that certain contact puzzles are analogous to Russell’s paradox this way: they similarly motivate a vision of physical reality as iteratively generated. In this picture, the divisions of the continuum into smaller parts are ‘potential’ rather than ‘actual’. Besides the intrinsic interest of (...) this metaphysical picture, it has important consequences for the debate over absolute generality. It is often thought that ‘indefinite extensibility’ arguments at best make trouble for mathematical platonists; but the contact arguments show that nominalists face the same kind of difficulty, if they recognize even the metaphysical possibility of the picture I sketch. (shrink)

The existence of mereological sums can be derived from an abstraction principle in a way analogous to numbers. I draw lessons for the thesis that “composition is innocent” from neo-Fregeanism in the philosophy of mathematics.

When do the folk think that mereological composition occurs? Many metaphysicians have wanted a view of composition that fits with folk intuitions, and yet there has been little agreement about what the folk intuit. We aim to put the tools of experimental philosophy to constructive use. Our studies suggest that folk mereology is teleological: people tend to intuit that composition occurs when the result serves a purpose. We thus conclude that metaphysicians should dismiss folk intuitions, as tied into a benighted (...) teleological view of nature. (shrink)

C. S. Jenkins has recently proposed an account of arithmetical knowledge designed to be realist, empiricist, and apriorist: realist in that what’s the case in arithmetic doesn’t rely on us being any particular way; empiricist in that arithmetic knowledge crucially depends on the senses; and apriorist in that it accommodates the time-honored judgment that there is something special about arithmetical knowledge, something we have historically labeled with ‘a priori’. I’m here concerned with the prospects for extending Jenkins’s account beyond arithmetic—in (...) particular, to set theory. After setting out the central elements of Jenkins’s account and entertaining challenges to extending it to set theory, I conclude that a satisfactory such extension is unlikely. (shrink)

In this paper, we consider the implications of Grace de Laguna and Joel Katzav's work for the charge of conservatism against the analytic tradition. We differentiate that conservatism into three kinds: starting place; path dependency; and modesty. We also think again about gender in philosophy, consider the positive account of speculative philosophy presented by de Laguna and Katzav in comparison to some other naturalist trajectories, and conclude with a brief Australian addendum that reflects on a similar period in our own (...) country which was also associated with the professional institutionalisation of analytic philosophy. (shrink)

ABSTRACT Historical structuralist views have been ontological. They either deny that there are any mathematical objects or they maintain that mathematical objects are structures or positions in them. Non-ontological structuralism offers no account of the nature of mathematical objects. My own structuralism has evolved from an early sui generis version to a non-ontological version that embraces Quine’s doctrine of ontological relativity. In this paper I further develop and explain this view.

This is a survey of the concept of continuity. Efforts to explicate continuity have produced a plurality of philosophical conceptions of continuity that have provably distinct expressions within contemporary mathematics. I claim that there is a divide between the conceptions that treat the whole continuum as prior to its parts, and those conceptions that treat the parts of the continuum as prior to the whole. Along this divide, a tension emerges between those conceptions that favor philosophical idealizations of continuity and (...) those that are more readily available for mathematico-scientific use. (shrink)

Forthcoming in Philosophical Compass. I explain why plural quantifiers and predicates have been thought to be philosophically significant.

Simon Evnine’s Making Objects and Events: A Hylomorphic Theory of Artifacts develops amorphic hylomorphism. I critically discuss three of its main themes. One theme is its attempt to do the work of form without forms. A second theme is the requirement that hylomorphs have ‘metabolisms at work’. A third theme is the use of artifacts as the paradigms for hylomorphs. I will raise some criticisms of each of these themes. Although the themes might at first appear disconnected, I believe the (...) third underwrites the first two. So the criticisms of the third theme also bear on the rest. (shrink)

The point of this paper is to bring together three topics: non-existent objects, mereology, and nothing. There are important inter-connections, which it is my aim to spell out, in the service of an account of the last of these.

This note examines the mereological component of Geoffrey Hellman's most recent version of modal structuralism. There are plausible forms of agnosticism that benefit only a little from Hellman's mereological turn.

This essay defends the following two claims: (1) liraitation-of-size reasoning yields enough sets to meet the needs of most mathematicians; (2) set formation and mereological fusion share enough logical features to justify placing both in the genus composition (even when the components of a set are taken to be its members rather than its subsets).

Competent speakers of natural languages can borrow reference from one another. You can arrange for your utterances of ‘Kirksville’ to refer to the same thing as my utterances of ‘Kirksville’. We can then talk about the same thing when we discuss Kirksville. In cases like this, you borrow “ aboutness ” from me by borrowing reference. Now suppose I wish to initiate a line of reasoning applicable to any prime number. I might signal my intention by saying, “Let p be (...) any prime.” In this context, I will be using the term ‘p’ to reason about the primes. Although ‘p’ helps me secure the aboutness of my discourse, it may seem wrong to say that ‘p’ refers to anything. Be that as it may, this paper explores what mathematical discourse would be like if mathematicians were able to borrow freely from one another not just the reference of terms that clearly refer, but, more generally, the sort of aboutness present in a line of reasoning leading up to a universal generalization. The paper also gives reasons for believing that aboutness of this sort really is freely transferable. A key implication will be that the concept “set of natural numbers” suffers from no mathematically significant indeterminacy that can be coherently discussed. (shrink)

We contribute to the ongoing discussion on mathematical structuralism by focusing on a question that has so far been neglected: when is a structure part of another structure? This paper is a first step towards answering the question. We will show that a certain conception of structures, abstractionism about structures, yields a natural definition of the parthood relation between structures. This answer has many interesting consequences; however, it conflicts with some standard mereological principles. We argue that the tension between abstractionism (...) about structure and classical mereology is an interesting result and conclude that the mereology of abstract structures is a subject that deserves further exploration. We also point out some connections between our discussion of the mereology of structures and recent work on non-well-founded mereologies. (shrink)