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Abstraction principles and grounding can be combined in a natural way Modality: metaphysics, logic, and epistemology, Oxford University Press, Oxford, pp 109–136, 2010; Schwartzkopff in Grazer philosophische studien 82:353–373, 2011). However, some groundtheoretic abstraction principles entail that there are circles of partial ground :775–801, 2017). I call this problem autoabstraction. In this paper I sketch a solution. Sections 1 and 2 are introductory. In Sect. 3 I start comparing different solutions to the problem. In Sect. 4 I contend that the (...) 

Sometimes a fact can play a role in a grounding explanation, but the particular content of that fact make no difference to the explanation—any fact would do in its place. I call these facts vacuous grounds. I show that applying the distinction betweenvacuous grounds allows us to give a principled solution to Kit Fine and Stephen Kramer’s paradox of ground. This paradox shows that on minimal assumptions about grounding and minimal assumptions about logic, we can show that grounding is reflexive, (...) 

There is a puzzle concerning the essences of fundamental entities that arises from considerations about essence, on one hand, and fundamentality, on the other. The EssenceDependence Link (EDL) says that if x figures in the essence of y, then y is dependent upon x. EDL is prima facie plausible in many cases, especially those involving derivative entities. But consider the property negative charge. A negatively charged object exhibits certain behaviors that a positively charged object does not: it moves away from (...) 

A fundamental entity is an entity that is ‘ontologically independent’; it does not depend on anything else for its existence or essence. It seems to follow that a fundamental entity is ‘modally free’ in some sense. This assumption, that fundamentality entails modal freedom (or ‘FEMF’ as I shall label the thesis), is used in the service of other arguments in metaphysics. But as I will argue, the road from fundamentality to modal freedom is not so straightforward. The defender of FEMF (...) 

Discussion of atomistic and monistic theses about abstract reality. 

Identity and distinctness facts are ones like “The Eiffel Tower is identical to the Eiffel Tower,” and “The Eiffel Tower is distinct from the Louvre.” This paper concerns one question in the metaphysics of identity: Are identity and distinctness facts metaphysically fundamental or are they nonfundamental? I provide an overview of answers to this question. 

This paper offers a metaphysical explanation of the identity and distinctness of concrete objects. It is tempting to try to distinguish concrete objects on the basis of their possessing different qualitative features, where qualitative features are ones that do not involve identity. Yet, this criterion for object identity faces counterexamples: distinct objects can share all of their qualitative features. This paper suggests that in order to distinguish concrete objects we need to look not only at which properties and relations objects (...) 

One conception of the Principle of Sufficient Reason maintains that every fact is metaphysically explained. There are different ways to challenge this version of the PSR; one type of challenge involves pinpointing a specific set of facts that resist metaphysical explanation. Certain identity and distinctness facts seem to constitute such a set. For example, we can imagine a scenario in which we have two qualitatively identical spheres, Castor and Pollux. Castor is distinct from Pollux but it is unclear what could (...) 



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 neoFregeanism in the philosophy of mathematics. 

This paper sets out a new framework for discussing a longstanding problem in the philosophy of mathematics, namely the connection between the physical world and a mathematical domain when the mathematics is applied in science. I argue that considering counterfactual situations raises some interesting challenges for some approaches to applications, and consider an approach that avoids these challenges. 

Contingent negative existentials give rise to a notorious paradox. I formulate a version in terms of metaphysical grounding: nonexistence can't be fundamental, but nothing can ground it. I then argue for a new kind of solution, expanding on work by Kit Fine. The key idea is that negative existentials are contingently zerogrounded – that is to say, they are grounded, but not by anything, and only in the right conditions. If this is correct, it follows that grounding cannot be an (...) 

In this paper, we try to establish that some mathematical theories, like Ktheory, homology, cohomology, homotopy theories, spectral sequences, modern Galois theory (in its various applications), representation theory and character theory, etc., should be thought of as (abstract) machines in the same way that there are (concrete) machines in the natural sciences. If this is correct, then many epistemological and ontological issues in the philosophy of mathematics are seen in a different light. We concentrate on one problem which immediately follows (...) 

Seemingly natural principles about the logic of ground generate cycles of ground; how can this be if ground is asymmetric? The goal of the theory of decycling is to find systematic and principled ways of getting rid of such cycles of ground. In this paper—drawing on graphtheoretic and topological ideas—I develop a general framework in which various theories of decycling can be compared. This allows us to improve on proposals made earlier by Fine and Litland. However, it turns out that (...) 

I systematically defend a novel account of the grounds for identity and distinct ness facts: they are all uniquely zerogrounded. First, the Null Account is shown to avoid a range of problems facing other accounts: a relation satisfying the Null Account would be an excellent candidate for being the identity relation. Second, a plenitudinist view of relations suggests that there is such a relation. To flesh out this plenitudinist view I sketch a novel framework for expressing real definitions, use this (...) 

Though the divide between reasonbased and causalexplanatory approaches in psychiatry and psychopathology is old and deeply rooted, current trends involving multifactorial explanatory models and evidencebased approaches to interpersonal psychotherapy, show that it has already been implicitly bridged. These trends require a philosophical reconsideration of how reasons can be causes. This paper contributes to that trajectory by arguing that Donald Davidson’s classic paradigm of 1963 is still a valid option. 

This is part two of a twopart paper in which we develop an axiomatic theory of the relation of partial ground. The main novelty of the paper is the of use of a binary ground predicate rather than an operator to formalize ground. In this part of the paper, we extend the base theory of the first part of the paper with hierarchically typed truthpredicates and principles about the interaction of partial ground and truth. We show that our theory is (...) 

An argument going back to Russell shows that the view that propositions are structured is inconsistent in standard type theories. Here, it is shown that such type theories may nevertheless provide entities which can serve as proxies for structured propositions. As an illustration, such proxies are applied to the case of grounding, as standard views of grounding require a degree of propositional structure which suffices for a version of Russell’s argument. While this application solves some of the problems grounding faces, (...) 

A brief review of Øystein Linnebo's Thin Objects. The review ends with a brief discussion of cardinal number and metaphysical ground. 

We discuss abstraction principles in the context of modal and temporal logic. It is argued that abstractionism conflicts with both serious presentism and serious actualism. 

Hume’s Principle states that the cardinal number of the concept F is identical with the cardinal number of G if and only if F and G can be put into onetoone correspondence. The SchwartzkopffRosen Principle is a modification of HP in terms of metaphysical grounding: it states that if the number of F is identical with the number of G, then this identity is grounded by the fact that F and G can be paired onetoone, 353–373, 2011, 362). HP is (...) 

This essay aims to redress the contention that epistemic possibility cannot be a guide to the principles of modal metaphysics. I introduce a novel epistemic twodimensional truthmaker semantics. I argue that the interaction between the twodimensional framework and the mereological parthood relation, which is superrigid, enables epistemic possibilities and truthmakers with regard to parthood to be a guide to its metaphysical profile. I specify, further, a twodimensional formula encoding the relation between the epistemic possibility and verification of essential properties obtaining (...) 

This paper develops a novel theory of abstraction—what we call collective abstraction. The theory solves a notorious problem for noneliminative structuralism. The noneliminative structuralist holds that in addition to various isomorphic systems there is a pure structure that can be abstracted from each of these systems; but existing accounts of abstraction fail for non rigid systems like the complex numbers. The problem with the existing accounts is that they attempt to define a unique abstraction operation. The theory of collective abstraction (...) 

Platonism about mathematics (or mathematical platonism) isthe metaphysical view that there are abstract mathematical objectswhose existence is independent of us and our language, thought, andpractices. Just as electrons and planets exist independently of us, sodo numbers and sets. And just as statements about electrons and planetsare made true or false by the objects with which they are concerned andthese objects' perfectly objective properties, so are statements aboutnumbers and sets. Mathematical truths are therefore discovered, notinvented., Existence. There are mathematical objects. 



I explore proposals for stating identity criteria in terms of ground. I also address considerations for and against taking identity and distinctness facts to be ungrounded. 