What is the source of logical and mathematical truth? This book revitalizes conventionalism as an answer to this question. Conventionalism takes logical and mathematical truth to have their source in linguistic conventions. This was an extremely popular view in the early 20th century, but it was never worked out in detail and is now almost universally rejected in mainstream philosophical circles. Shadows of Syntax is the first book-length treatment and defense of a combined conventionalist theory of logic and mathematics. It (...) argues that our conventions, in the form of syntactic rules of language use, are perfectly suited to explain the truth, necessity, and a priority of logical and mathematical claims, as well as our logical and mathematical knowledge. (shrink)

Wright claims that “the epistemology of good abstraction principles should be assimilated to that of basic principles of logical inference”. In this paper I follow Wright’s recommendation, but I consider a different epistemology of logic, namely anti-exceptionalism. Anti-exceptionalism’s main contention is that logic is not a priori, and that the choice between rival logics should be based on abductive criteria such as simplicity, adequacy to the data, strength, fruitfulness, and consistency. This paper’s goal is to lay down the foundations for (...) an application of the anti-exceptionalist methodology to abstraction principles. In Sect. 1 I outline my strategy. I show that anti-exceptionalism has a bearing on the so-called Bad Company problem, and explore some versions of anti-exceptionalism about abstraction. I then consider new criteria for choosing between rival abstraction principles, and, in particular, between consistent revisions of Frege’s Basic Law V. I finally consider how the abstractionist can compare between competing criteria, and argue that anti-exceptionalists should be pluralists about abstraction. (shrink)

Are there different sizes of infinity? That is, are there infinite sets of different sizes? This is one of the most natural questions that one can ask about the infinite. But it is of course generally taken to be settled by mathematical results, such as Cantor’s theorem, to the effect that there are infinite sets without bijections between them. These results settle the question, given an almost universally accepted principle relating size to the existence of functions. The principle is: for (...) any sets A and B, if A is the same size as B, then there is a bijection from A to B. The aim of the paper, however, is to argue that this question is in fact wide open: to argue that we are not in a position to know the answer, because we are not in one to know the principle. The aim, that is, is to argue that for all we know there is only one size of infinity. (shrink)

The notion of a proposition is central to philosophy. But it is subject to paradoxes. A natural response is a hierarchical account and, ever since Russell proposed his theory of types in 1908, this has been the strategy of choice. But in this paper I raise a problem for such accounts. While this does not seem to have been recognized before, it would seem to render existing such accounts inadequate. The main purpose of the paper, however, is to provide a (...) new hierarchical account that solves the problem. (shrink)

What is the explanatory role of ‘status-truths’ such as essence-truths, necessity-truths and law-truths? A plausible principle, suggested by various authors, is Ground by Status, according to which status truths ground their prejacents. For instance, if it is essential to a that p, then this grounds the fact that p. But Ground by Status faces a forceful objection: it is inconsistent with widely accepted principles regarding the logic of grounding (Glazier in Philos Stud 174(11):2871–2889, 2017a, Synthese 174(198):1409–1424, 2017b; Kappes in Synthese (...) 199(1–2):2575–2595, 2020, Philos Stud 178(4):1267–1284, 2021). I defend Ground by Status against this objection. (shrink)

According to constitution views of persons, we are constituted by spatially coinciding human animals. Constitution views face an ‘overpopulation’ puzzle: if the animal has my brain, there is another thinker where I am. An influential solution to this problem distinguishes between derivative and non‐derivative property possession: persons non‐derivatively have their personal properties, while inheriting others from their constituters. I will show that this solution raises a new problem, by constructing a puzzle with the absurd result that we instantiate certain properties (...) incompatibly. In setting up the puzzle, I demonstrate the relevance of the bodily awareness and self‐awareness literatures to overpopulation puzzles. (shrink)

In The Construction of Logical Space, Agustín Rayo defends trivialism, according to which number-involving truths are trivially equivalent to other, non-number-involving truths; picturesquely, ‘I have five fingers on my hand’ and ‘the number of fingers on my hand is five’ express the same fact, but carved up in different ways. A single fact thus has multiple structures. I distinguish two ways this might go: on the deflationary picture, facts get their structures from our linguistic practices, while on an inflationary picture, (...) facts have multiple structures independently of language. I argue that Rayo’s view is best interpreted as deflationary. Thus interpreted, it blocks off an attractive solution to the old problems of intensionality. I further argue a that a semi-deflationary variant of Rayo’s view can make use of the attractive solution—but it thereby sacrifices the supposed mathematical benefits of trivialism. (shrink)

Discussions of “indeterminacy” customarily distinguish two putative types: semantic indeterminacy (SI)—indeterminacy that’s somehow the product of the semantics of our words/concepts—and metaphysical indeterminacy (MI)—indeterminacy that exists as a mind/language-independent feature of reality itself. A popular and influential thought among philosophers is that all indeterminacy must be SI. In this paper we challenge this thought. Our challenge is guided by the question: What, exactly, does it take for a case of indeterminacy to count as SI? We argue that the only satisfactory (...) answer to this question must take SI to be grounded in a more basic type of MI. We conclude that SI cannot be made sense of without implicating MI. If there’s any indeterminacy, there must be indeterminacy in the world itself. (shrink)

When a train operator tells us that our train will be late ‘because of delays’, their attempt at explanation fails because there is insufficient distance between the explanans and the explanandum. In this paper, I motivate and defend an account of ‘explanatory distance’, based on the idea that explanations give information about dependence. I show that this account offers useful resources for addressing problem cases, including recent debates about grounding explanation, and the historical case of Molière’s dormitive virtue.

One of the central puzzles in ontology concerns the relation between apparently innocent sentences and their ontologically loaded counterparts. In recent work, Agustín Rayo has developed the insight that such cases can be usefully described with the help of the ‘just is’ operator: plausibly, for there to be a table just is for there to be some things arranged tablewise; and for the number of dinosaurs to be Zero just is for there to be no dinosaurs. How does the operator (...) relate to another prominent notion that is frequently put to similar use: metaphysical grounding? In this paper I show that despite what has been argued in the literature the ‘just is’ operator can be spelled out in terms of grounding: roughly, as having the same ultimate grounds. This is good news for Rayo, for it broadens his target audience. It is even better news for the friends of ground. For it exemplifies the immense fruitfulness of the notion of grounding in its ability to incorporate philosophically highly significant subtheories. (shrink)

When axiomatizing a body of truths, one first concentrates on obtaining a set of axioms that entail all and only those truths. The theorist expects that this complete system will have some...

Subverting a once widely held Quinean paradigm, there is a growing consensus among philosophers of logic that higher-order quantifiers (which bind variables in the syntactic position of predicates and sentences) are a perfectly legitimate and useful instrument in the logico-philosophical toolbox, while neither being reducible to nor fully explicable in terms of first-order quantifiers (which bind variables in singular term position). This article discusses the impact of this quantificational paradigm shift on metaphysics, focussing on theories of properties, propositions, and identity, (...) as well as on the metaphysics of modality. (shrink)

Are there any disjunctive properties—features of things such as being either red or round, or Nelson Goodman’s infamous example of being grue? As esoteric as the question may seem at first, central issues about the metaphysics of properties hinge upon its answer, such as whether reductive views about special science properties can handle the phenomenon of multiple realizability. A familiar argument for a negative answer is that disjunctive properties fail to guarantee that their instances are similar in some genuine respect. (...) In this paper, I respond to a novel, sophisticated version of this argument developed in recent work by Paul Audi. Along the way, I develop two new accounts of what it is for a property to be disjunctive—which rely on important recent work on the nature of essence and analysis—and clarify what one is committed to in believing that there are any disjunctive properties at all. (shrink)

This paper argues that the semantic facts about ‘because’ are best explained via a metaphorical treatment of metaphysical explanation that treats causal explanation as explanation par excellence. Along the way, it defends a commitment to a unified causal sense of ‘because’ and offers a proprietary explanation of grounding skepticism. With the causal metaphor account of metaphysical explanation on the table, an extended discussion of the relationship between conceptual structure and metaphysics ends with a suggestion that the semantic facts about ‘because’ (...) tell against grounding-causation unity. (shrink)

This paper presents evidence that ‘because’ is importantly ambiguous between two closely related senses covering what are usually called causal explanations, on the one hand, and grounding or metaphysical explanations, on the other hand. To this end, it introduces the lexical categories of monosemy, polysemy and homonymy; describes a test for polysemy; and discusses the results of the test when applied to ‘because’. It also shows how to understand so-called hybrid explanations in light of the semantic facts established by the (...) analysis. (shrink)

A thriving literature has developed over logical and mathematical pluralism – i.e. the views that several rival logical and mathematical theories can be equally correct. These have unfortunately grown separate; instead, they both could gain a great deal by a closer interaction. Our aim is thus to present some novel forms of abstractionist mathematical pluralism which can be modeled on parallel ways of substantiating logical pluralism (also in connection with logical anti-exceptionalism). To do this, we start by discussing the Good (...) Company Problem for neo-logicists recently raised by Paolo Mancosu (2016), concerning the existence of rival abstractive definitions of cardinal number which are nonetheless equally able to reconstruct Peano Arithmetic. We survey Mancosu’s envisaged possible replies to this predicament, and suggest as a further path the adoption of some form of mathematical pluralism concerning abstraction principles. We then explore three possible ways of substantiating such pluralism—Conceptual Pluralism, Domain Pluralism, Pluralism about Criteria—showing how each of them can be related to analogous proposals in the philosophy of logic. We conclude by considering advantages, concerns, and theoretical ramifications for these varieties of mathematical pluralism. (shrink)

The aim of this paper is to explore the possibility that, at least, some metaphysical debates are ‘metalinguistic negotiations’. I will take the dispute between the dominant approaches of realism and the anti-realism ones about the ontological status of scientific models as a case-study. I will argue that such a debate may be better understood as a disagreement, at bottom normatively, motivated, insofar as a normative and non-factual question may be involved in it: how the relevant piece of language ought (...) to be used. Even though I will generally assess the prospects for a broadly deflationist approach, I shall outline a sense in which the dispute can be recast as ‘minimally substantive’. (shrink)

I examine three ‘anti-object’ metaphysical views: nihilism, generalism, and anti-quantificationalism. After setting aside nihilism, I argue that generalists should be anti-quantificationalists. Along the way, I attempt to articulate what a ‘metaphysically perspicuous’ language might even be.

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.

Some metaphysicians believe that metaphysical modality is explainable by the essences of objects. In §II, I spell out the definitional view of essence, and in §III, a working notion of metaphysical explanation. Then, in §IV, I consider and reject five natural ways to explain necessity by essence: in terms of the principle that essential properties can't change, in terms of the supposed obviousness of the necessity of essential truth, in terms of the logical necessity of definitions, in terms of Fine's (...) logic of essence, and in terms of the theory of real definitions. I will conclude that the present evidence favours rejecting the hypothesis that modality is explainable by essence. (shrink)

It is common to think that grounding is necessary in the sense that: if P grounds Q, then necessarily: if P, then Q. Though most accept this principle, some give counterexamples to it. Instead of straightforwardly arguing for, or against, necessity, I explain the sense in which grounding is necessary and contingent. I argue that there are two kinds of grounding: what-grounding and why-grounding, where the former kind is necessary while the latter is contingent.

Critical social ontology is any study of social ontology that is done in order to critique ideology or end social injustice. The goal of this paper is to outline what I call the fundamentality approach to critical social ontology. On the fundamentality approach, social ontologists are in the business of distinguishing between appearances and (fundamental) reality. Social reality is often obscured by the acceptance of ideology, where an ideology is a distorted system of beliefs that leads people to promote or (...) accept widespread social injustices. Social reality is also obscured in cases where ordinary thought and language simply is not perspicuous enough to represent the social objects, kinds, and structures that are central to understanding social injustice. In both cases, I argue that the critical social ontologist will benefit from using the tools and concepts of fundamental metaphysics. (shrink)

This paper extracts some of the main theses in the philosophy of mathematics from my book, The Construction of Logical Space. I show that there are important limits to the availability of nominalistic paraphrase functions for mathematical languages, and suggest a way around the problem by developing a method for specifying nominalistic contents without corresponding nominalistic paraphrases. Although much of the material in this paper is drawn from the book — and from an earlier paper — I hope the present (...) discussion will earn its keep by motivating the ideas in a new way, and by suggesting further applications. (shrink)

I argue for a conception of essence that does not rely on distinctions of metaphysical fundamentality.

Meinongians in general, and Routley in particular, subscribe to the principle of the independence of Sosein from Sein. In this paper, I put forward an interpretation of the independence principle that philosophers working outside the Meinongian tradition can accept. Drawing on recent work by Stephen Yablo and others on the notion of subject matter, I offer a new account of the notion of Sosein as a subject matter and argue that in some cases Sosein might be independent from Sein. The (...) question whether numbers exist, for instance, is not part of the question of how numbers are, which is the topic mathematicians are interested in. (shrink)

In the recent literature there has been some debate between advocates of deflationist and fictionalist positions in metaontology. The purpose of this paper is to advance the debate by reconsidering one objection presented by Amie Thomasson against fictionalist strategies in metaontology. The objection can be reconstructed in the following way. Fictionalists need to distinguish between the literal and the real content of sentences belonging to certain areas of discourse. In order to make that distinction, they need to assign different truth-conditions (...) to the real and the literal content. But it is hard to see what more is required for the literal content to be true than for the real content to be true. So, fictionalism is an unsatisfactory position. Here I offer a novel reply to Thomasson’s challenge. I argue that the literal and the real content need not be distinguished in terms of their truth-conditions; rather, they can be distinguished in terms of their different subject-matters, leaving it open whether their truth-conditions coincide or not. I explain how replying to Thomasson’s objection is crucial for deepening our understanding of fictionalist strategies in metaontology. (shrink)

I identify two reasons for believing in the objectivity of mathematical knowledge: apparent objectivity and applications in science. Focusing on arithmetic, I analyze platonism and cognitive nativism in terms of explaining these two reasons. After establishing that both theories run into difficulties, I present an alternative epistemological account that combines the theoretical frameworks of enculturation and cumulative cultural evolution. I show that this account can explain why arithmetical knowledge appears to be objective and has scientific applications. Finally, I will argue (...) that, while this account is compatible with platonist metaphysics, it does not require postulating mind-independent mathematical objects. (shrink)

Logical realism is the view that there is logical structure in the world. I argue that, if logical realism is true, then we are deeply ignorant of that logical structure: either we can’t know which of our logical concepts accurately capture it, or none of our logical concepts accurately capture it at all. I don’t suggest abandoning logical realism, but instead discuss how realists should adjust their methodology in the face of this ignorance.

In this short paper we consider Linnebo's thin/thick dichotomy: first, we show that it does not overlap with the very common one between abstract/concrete objects; second, on the basis of some difficulties with the distinction, we propose, as a possible way out, to move from thin/thick objects to thin/thick concepts.

Intrinsicality is a central notion in metaphysics that can do important work in many areas of philosophy. It is not widely appreciated, however, that there are in fact a number of different notions of intrinsicality, and that these different notions differ in what work they can do. This paper discusses what these notions are, describes how they are related to each other, and argues that each of them can be analysed in terms of a single notion of intrinsic aboutness that (...) relates states of affairs to the things they are intrinsically about. (shrink)

Deflationary positions have been defended in many areas of philosophy. Most prominent are semantic deflationism about truth and reference, and meta-ontological deflationism, according to which existence has no deep nature and the standard neo-Quinean approach to ontology is misguided. Although both kinds of views have generated much discussion, surprisingly little attention has been paid to the question of how they relate to each other. Are they independent, is it advisable to hold them all at once, or do they even entail (...) each other? One exception is Amie Thomasson, who has argued that semantic deflationism actually entails meta-ontological deflationism. This is unexpected, since semantic deflationism is usually regarded as much less controversial than meta-ontological deflationism. In our paper, we will argue that Thomasson’s argument fails though, and that the connection between the views is in fact weaker than she makes them out to be. (shrink)

Peacocke’s recent The Primacy of Metaphysics covers a wide range of topics. This critical discussion focuses on the book’s novel account of extensive magnitudes and numbers. First, I further develop and defend Peacocke’s argument against nominalistic approaches to magnitudes and numbers. Then, I argue that his view is more Aristotelian than Platonist because reified magnitudes and numbers are accounted for via corresponding properties and these properties’ application conditions, and because the mentioned objects have a “shallow nature” relative to the corresponding (...) properties. The result is an asymmetric conception of abstraction, which contrasts with the neo-Fregeans’ but has important tenets in common with an approach that I have recently developed. (shrink)

The literature suggests two main answers to the question of what it is for a material object to be located at a region of spacetime. Both have a number of virtues. However, both suffer from well-known problems. According to one answer, location is a primitive relation with no informative metaphysical analysis. But this makes a number of necessary truths seem mysterious and leaves them unexplained. According to the other answer, to be located at a region is just to be identical (...) to that region. But this is inconsistent with a number of independently plausible theses about material objects and their locations. In this paper, I explore a new theory of location and argue that it has the virtues of these familiar theories but not their vices. I then explore some further connections the new theory has with some contemporary issues in metaphysics. (shrink)

One well-known objection to supersubstantivalism is that it is inconsistent with the contingency of location. This paper presents a new objection to supersubstantivalism: it is inconsistent with the vagueness of location. Though contingency and vagueness are formally similar, there are important philosophical differences between the two. As a result, the objection from vague location will be structurally different than the objection from contingent location. The paper explores these differences and then defends the argument that supersubstantivalism is inconsistent with the plausible (...) thesis that it is vague where I am located. (shrink)

An essentialist theory of modality claims that the source of possibility and necessity lies in essence, where essence is then not to be defined in terms of necessity. Hence such theories owe us an account of why it is that the essences of things give rise to necessities in the way required. A new approach to understanding essence in terms of the notion of generalized identity promises to answer this challenge by appeal to the necessity of identity. I explore the (...) prospects for this approach, and argue that it fails. If one favours an account of essence in terms of generalized identity, then one will not, I argue, be able to satisfactorily defend an essentialist theory of modality against the challenge; if one wishes to defend an essentialist theory of modality, and thereby to give an explanation of how necessity arises from essence, one should not understand essence in terms of generalized identity. (shrink)

During the last quarter of a century, a number of philosophers have become attracted to the idea that necessity can be analyzed in terms of a hyperintensional notion of essence. One challenge for proponents of this view is to give a plausible explanation of our modal knowledge. The goal of this paper is to develop a strategy for meeting this challenge. My approach rests on an account of modality that I developed in previous work, and which analyzes modal properties in (...) terms of the notion of a metaphysical law. I discuss what information about the metaphysical laws is required for modal knowledge. Moreover, I describe two ways in which we might be able to acquire this information. The first way employs inference to the best explanation. The metaphysical laws, including the essential truths, play a crucial role in causal and grounding explanations and we can gain knowledge of these laws by abductive inferences from facts of which we have perceptual or a priori knowledge. The second way of gaining information about the metaphysical laws rests on knowledge that is partly constitutive of competence with the concepts that are needed to express the relevant information. Finally, I consider how knowledge of the metaphysical laws can be used to establish modal claims, paying special attention to the much-discussed connection between conceiving and possibility. (shrink)

Some views articulate reality's hierarchical structure using relations from the fundamental to representations of reality. Other views instead use relations from the fundamental to constituents of non-representational reality. This paper argues against the first kind of view.

Serious actualism is the prima facie plausible thesis that things couldn’t have been related while being nothing. The thesis plays an important role in a number of arguments in metaphysics, e.g., in Plantinga’s argument for the claim that propositions do not ontologically depend on the things that they are about and in Williamson’s argument for the claim that he, Williamson, is necessarily something. Salmon has put forward that which is, arguably, the most pressing challenge to serious actualists. Salmon’s objection is (...) based on a scenario intended to elicit the judgment that merely possible entities may nonetheless be actually referred to, and so may actually have properties. It is shown that predicativism, the thesis that names are true of their bearers, provides the resources for replying to Salmon’s objection. In addition, an argument for serious actualism based on Stephanou, 219–250 2007) is offered. Finally, it is shown that once serious actualism is conjoined with some minimal assumptions, it implies property necessitism, the thesis that necessarily all properties are necessarily something, as well as a strong comprehension principle for higher-order modal logic according to which for every condition there necessarily is the property of being a thing satisfying that condition. (shrink)

A central question for ontology is the question of whether numbers really exist. But it seems easy to answer this question in the affirmative. The truth of a sentence like ‘Seven students came to the party’ can be established simply by looking around at the party and counting students. A trivial paraphrase of is ‘The number of students who came to the party is seven’. But appears to entail the existence of a number, and so it seems that we must (...) conclude that numbers exist. This is sometimes called the puzzle of how we can get something from nothing. Most extant attempts to solve the puzzle take it for granted that is ontologically innocent, and focus their attention either on or on the transition from to. We argue that both attempts go wrong at the first step: the assumption that is ontologically innocent is undermined by a highly attractive and independently well-motivated degree-based account of number word constructions. Thus the degree-based account provides a straightforward linguistic resolution of the puzzle of how we can get something from nothing. But the paper also has a second aim. The semantics we present treats ‘seven’ as a referring expression that refers to a degree of a certain sort. But what are degrees? We consider various anti-platonist proposals that seek to account for degrees in terms of relations between concrete entities, and argue that they are incompatible with the Universal Density of Measurement hypothesis of Fox and Hackl. While the UDM cannot yet claim to be the consensus view among degree-based semanticists, our aim is to use it to illustrate how views about the nature of degrees can be evaluated by considering the properties degrees must have if they are to play the explanatory roles they are called upon to play in linguistics. In the present state of development of degree-based semantics there are difficult open questions about what these properties are. These questions need to be addressed if we are to develop a clear picture of what natural language semantics has to contribute to ontology and metaphysics. (shrink)

We prove Yablo’s paradox without the diagonal lemma or the recursion theorem. Only a disquotation schema and axioms for a serial and transitive ordering are used in the proof. The consequences for the discussion on whether Yablo’s paradox is circular or involves self-reference are evaluated.

Propositions represent the entities from which they are formed. This fact has puzzled philosophers and some have put forward radical proposals in order to explain it. This paper develops a primitivist account of the representational properties of propositions that centers on the operation of application. As we will see, this theory wins out over its competitors on grounds of strength, systematicity and unifying power.

What is the connection between having a phenomenal property and knowing that one has that property? A traditional view on the matter takes the connection to be quite intimate. Whenever one has a phenomenal property, one knows that one does. Recently most authors have denied this traditional view. The goal of this paper is to defend the traditional view. In fact, I will defend something much stronger: I will argue that what it is for a property to be phenomenal is (...) for it to be a property one must know oneself to have when on has it. As we will see, this theory has a number of surprising and welcome upshots, suggesting that the traditional view has been unjustly maligned. (shrink)

Agustín Rayo’s The Construction of Logical Space offers an exciting and ambitious defense of a broadly Carnapian approach to metaphysics. This essay will focus on one of the main differences between Rayo’s and Carnap’s approaches. Carnap distinguished between analytic, a priori “meaning postulates”, and empirical claims, which were both synthetic and knowable only a posteriori. Like meaning postulates, they determine the boundaries of logical space. But Rayo is skeptical that the a priori/a posteriori or analytic/synthetic distinctions can do the work (...) Carnap wanted them to, so unlike meaning postulates, ‘just is’-statements aren’t assumed to be analytic or knowable a priori. This essay will concern the epistemology of ‘just is’-statements in Rayo’s picture. If not by a priori reflection, how can we determine which ones to accept? I’ll distinguish two competing strands in Rayo’s work. The less radical, Lewisian strand holds that the question of whether to accept a ‘just is’-statement can be addressed in a neutral, non-question-begging way, by a kind of cost-benefit analysis. The more radical, Kuhnian strand holds that there can be no ‘just is’-statement-independent, rational choice of which ‘just is’-statements to accept. I argue that Rayo faces strong internal pressure to adopt the Kuhnian picture. While it is possible for Rayo to resist these Kuhnian pressures, natural strategies for doing so leave his view more similar to Carnap’s than the above gloss suggested. (shrink)

The identity predicate can be defined using second-order quantification: a=b =df ∀F(Fa↔Fb). Less familiarly, a dyadic sentential operator analogous to the identity predicate can be defined using third-order quantification: ϕ≡ψ =df ∀X(Xϕ↔Xψ), where X is a variable of the same syntactic type as a monadic sentential operator. With this notion in view, it is natural to ask after general principles governing its application. More grandiosely, how fine-grained is reality? -/- I will argue that reality is not structured in anything like (...) the way that the sentences we use to talk about it are structured. I do so by formulating a higher-order analogue of Russell’s paradox of structured propositions. I then relate this argument to the Frege-Russell correspondence. When confronted with the alleged paradox, Frege agreed that reality was not structured, but maintained that propositions (i.e. thoughts) were structured all the same. Russell replied that his paradox showed Frege’s theory of structured thoughts to be inconsistent, to which Frege replied that Russell’s argument failed to heed the distinction between sense and reference. Most recent commentators have sided with Russell. In defense of Frege, I establish the consistency of one version of his rejoinder. I then consider and reject some ways of resisting the argument against a structured conception of reality. I conclude that, if propositions are structured, this is because they correspond not to distinctions in reality, but rather to ways in which those distinctions can be represented. (shrink)

According to Originalism, word types are non-eternal continuants which are individuated by their causal-historical lineage and have a unique possible time of origination. This view collides with the intuition that individual words can be added to the lexicon of a language at different times, and generates other problematic consequences. The paper shows that such undesired results can be accommodated without abandoning Originalism.