A number of philosophers think that grounding is, in some sense, well-founded. This thesis, however, is not always articulated precisely, nor is there a consensus in the literature as to how it should be characterized. In what follows, I consider several principles that one might have in mind when asserting that grounding is well-founded, and I argue that one of these principles, which I call ‘full foundations’, best captures the relevant claim. My argument is by the process of elimination. For (...) each of the inadequate principles, I illustrate its inadequacy by showing either that it excludes cases that should not be ruled out by a well-foundedness axiom for grounding, or that it admits cases that should be ruled out. (shrink)

Alex Oliver and Timothy Smiley provide a new account of plural logic. They argue that there is such a thing as genuinely plural denotation in logic, and expound a framework of ideas that includes the distinction between distributive and collective predicates, the theory of plural descriptions, multivalued functions, and lists.

It is customary practice to define ‘x is composed of the ys’ as ‘x is a sum of the ys and the ys are pairwise disjoint ’. This predicate has played a central role in the debate on the special composition question and on related metaphysical issues concerning the mereological structure of objects. In this note we show that the customary characterization is nonetheless inadequate. We do so by constructing a mereological model where everything qualifies as composed of atoms even (...) though some elements in the domain are gunky, i.e., can be divided indefinitely into smaller and smaller proper parts. (shrink)

General discussion of grounding, including its formal features, relations to other notions, and applications. (Originally published 2014; revised 2021).

Can there be grounding without necessitation? Can a fact obtain wholly in virtue of metaphysically more fundamental facts, even though there are possible worlds at which the latter facts obtain but not the former? It is an orthodoxy in recent literature about the nature of grounding, and in first-order philosophical disputes about what grounds what, that the answer is no. I will argue that the correct answer is yes. I present two novel arguments against grounding necessitarianism, and show that grounding (...) contingentism is fully compatible with the various explanatory roles that grounding is widely thought to play. (shrink)

Contemporary metaphysicians have been drawn to a certain attractive picture of the structure of the world. This picture consists in classical mereology, the priority of parts over wholes, and the well-foundedness of metaphysical priority. In this short note, I show that this combination of theses entails superatomism, which is a significant strengthening of mereological atomism. This commitment has been missed in the literature due to certain sorts of models of mereology being overlooked. But the entailment is an important one: we (...) must either accept superatomism or reject one (or other) of the most widespread theses of contemporary metaphysics. (shrink)

Although the relationship of part to whole is one of the most fundamental there is, this is the first full-length study of this key concept. Showing that mereology, or the formal theory of part and whole, is essential to ontology, Simons surveys and critiques previous theories--especially the standard extensional view--and proposes a new account that encompasses both temporal and modal considerations. Simons's revised theory not only allows him to offer fresh solutions to long-standing problems, but also has far-reaching consequences for (...) our understanding of a host of classical philosophical concepts. (shrink)

The topic of this book is material objects. Like most interesting concepts, the concept of a material object is one without precise boundaries.

Classical mereology is a formal theory of the part-whole relation, essentially involving a notion of mereological fusion, or sum. There are various different definitions of fusion in the literature, and various axiomatizations for classical mereology. Though the equivalence of the definitions of fusion is provable from axiom sets, the definitions are not logically equivalent, and, hence, are not inter-changeable when laying down the axioms. We examine the relations between the main definitions of fusion and correct some technical errors in prominent (...) discussions of the axiomatization of mereology. We show the equivalence of four different ways to axiomatize classical mereology, using three different notions of fusion. We also clarify the connection between classical mereology and complete Boolean algebra by giving two "neutral" axiom sets which can be supplemented by one or the other of two simple axioms to yield the full theories; one of these uses a notion of "strong complement" that helps explicate the connections between the theories. (shrink)

Those who wish to claim that all facts about grounding are themselves grounded (“the meta-grounding thesis”) must defend against the charge that such a claim leads to infinite regress and violates the well-foundedness of ground. In this paper, we defend. First, we explore three distinct but related notions of “well-founded”, which are often conflated, and three corresponding notions of infinite regress. We explore the entailment relations between these notions. We conclude that the meta-grounding thesis need not lead to tension with (...) any of the three notions of “well-founded”. Finally, we explore the details of and motivations for further conditions on ground that one might add to generate a conflict between the meta-grounding thesis and a well-founded constraint. We explore these topics by developing and utilizing a formal framework based on the notion of a grounding structure. (shrink)

Philosophical questions concerning parts and wholes have received a tremendous amount of the attention of contemporary analytic metaphysicians. In what follows, I discuss some of the central questions. The questions to be discussed are: how general is parthood? Are there different kinds of parthood or ways to be a part? Can two things be composed of the same parts? When does composition occur? Can material objects gain or lose parts? What is the logical form of the parthood relation enjoyed by (...) material objects? (shrink)

An overview of contemporary part-whole theories, with reference to both their axiomatic developments and their philosophical underpinnings.

Fundamentality plays a pivotal role in discussions of ontology, supervenience, and possibility, and other key topics in metaphysics. However, there are two different ways of characterising the fundamental: as that which is not grounded, and as that which is the ground of everything else. I show that whether these two characterisations pick out the same property turns on a principle—which I call “Dichotomy”—that is of independent interest in the theory of ground: that everything is either fully grounded or not even (...) partially grounded. I then argue that Dichotomy fails: some facts have partial grounds that cannot be complemented to a full ground. Rejecting Dichotomy opens the door to recognising a bifurcation in our notion of fundamentality. I sketch some of the far-reaching metaphysical consequences this might have, with reference to big-picture views such as Humeanism. Since Dichotomy is entailed by the standard account of partial ground, according to which partial grounds are subpluralities of full grounds, a non-standard account is needed. In a technical “Appendix”, I show that truthmaker semantics furnishes such an account, and identify a semantic condition that corresponds to Dichotomy. (shrink)

Atomism is the thesis that every object is composed of atoms. This principle is generally regimented by means of an atomicity axiom according to which every object has atomic parts. But there appears to be a sense that something is amiss with atomistic mereology. We look at three concerns, which, while importantly different, involve infinite descending chains of proper parts and have led some to question standard formalizations of atomism and composition in mereology.

Mereological atomism is the thesis that everything is ultimately composed of atomic parts, i.e., parts lacking proper parts. Standardly, this thesis is characterized by an axiom that says, more simply, that everything has atomic parts. Anthony Shiver has argued that this characterization is satisfied by models that are not atomistic, and is therefore inadequate. I argue that Shiver’s conclusion can and ought to be resisted, for the models in question are atomistic in the intended sense, and even though the standard (...) characterization does not say that everything is composed of atoms, it implies so. If there is a sense in which the relevant models are problematic, it lies elsewhere. (shrink)

Ordinary English contains different forms of quantification over objects. In addition to the usual singular quantification, as in 'There is an apple on the table', there is plural quantification, as in 'There are some apples on the table'. Ever since Frege, formal logic has favored the two singular quantifiers ∀x and ∃x over their plural counterparts ∀xx and ∃xx (to be read as for any things xx and there are some things xx). But in recent decades it has been argued (...) that we have good reason to admit among our primitive logical notions also the plural quantifiers ∀xx and ∃xx. More controversially, it has been argued that the resulting formal system with plural as well as singular quantification qualifies as ‘pure logic’; in particular, that it is universally applicable, ontologically innocent, and perfectly well understood. In addition to being interesting in its own right, this thesis will, if correct, make plural quantification available as an innocent but extremely powerful tool in metaphysics, philosophy of mathematics, and philosophical logic. For instance, George Boolos has used plural quantification to interpret monadic second-order logic and has argued on this basis that monadic second-order logic qualifies as “pure logic.” Plural quantification has also been used in attempts to defend logicist ideas, to account for set theory, and to eliminate ontological commitments to mathematical objects and complex objects. (shrink)

Since the publication of Peter van Inwagen's book, Material Beings,1 there has been a growing body of philosophical literature on the topic of composition. The main question addressed in both van Inwagen's book and subsequent discussions of the topic is a question that van Inwagen calls "the Special Composition Question." The Special Composition Question is, roughly, the question Under what circumstances do several things compose, or add up to, or form, a single object? For the purposes of formulating a more (...) precise version of the Special Composition Question, we can adopt the following technical terms. (shrink)

The standard definition of atomicity—the thesis that everything is ultimately composed of entities that lack proper parts—is satisfied by a model that is not atomistic. The standard definition is therefore an incorrect characterization of atomicity. I show that the model satisfies the axioms of all but the strongest mereology and therefore that the standard definition of atomicity is only adequate given some controversial metaphysical assumptions. I end by proposing a new definition of atomicity that does not require extensionality or unrestricted (...) summation. (shrink)

Using only uncontentious principles from the logic of ground I construct an infinitely descending chain of ground without a lower bound. I then compare the construction to the constructions due to Dixon and Rabin and Rabern.

Reviewed Works:John R. Steel, A. S. Kechris, D. A. Martin, Y. N. Moschovakis, Scales on $\Sigma^1_1$ Sets.Yiannis N. Moschovakis, Scales on Coinductive Sets.Donald A. Martin, John R. Steel, The Extent of Scales in $L$.John R. Steel, Scales in $L$.