“Rayo's The Construction of Logical Space” forthcoming in Inquiry

A critical discussion of Rayo's recent book. I ask which one of a series of characters this Agustin Rayo really is. It makes sense once you look at the paper.

“Carnap's Big Idea” forthcoming in a volume on Carnap (ed. S. Blatti and S. LaPointe)

Carnap has a great insight about ontology, his Big Idea. But the reason why Carnap thought the Big Idea was true, and what he thought followed from it, where both mistaken. Nonetheless, the Big Idea is still true, and significant things follow for metaphysics and ontology from it. This paper focuses on Carnap’s Big Idea, and hopes to work out why on Carnap’s own account it should be seen as being false, why it is true nonetheless, and what follows from it.

“Extraction, displacement, and focus: a reply to Balcerak Jackson” forthcoming in Linguistics and Philosophy

This paper is a reply to Brendan Balcerak Jackson's criticisms of my view, defended in "Innocent statements and their metaphysically loaded counterparts," that on standard uses, "the number of moons of Jupiter is four" is not an identity statement. I respond to some of his objections and clarify the position defended in the earlier paper.

“Is subjectivity required in a material world?” (Submitted)

An under-explored intermediate position between traditional materialism and traditional idealism is the view that although the spatiotemporal world is purely material, minds nonetheless have a metaphysically special place in it. One such intermediate position is that minds must exist, by metaphysical necessity, in any material world, and thus a mindless material world is impossible. This position, labeled The Subjectivity Thesis by Anton Friedrich Koch, was defended by him with an intriguing, purely metaphysical argument that is largely neglected in the contemporary debate. This paper is a critical examination of Koch’s argument, as well as of the larger position it would lead to.

Cardinality arguments against regular probability measures” conditionally forthcoming in Thought

Cardinality arguments against regular probability measures aim to show that no matter which ordered field H we select as the measures for probability, we can find some event space F of sufficiently large cardinality such that there can be no regular probability measure from F into H. In particular, taking H to be hyperreal numbers won’t help to guarantee that probability measures can always be regular. I argue that such cardinality arguments fail, since they rely on the wrong conception of the role of numbers as measures of probability. With the proper conception of their role we can see that for any event space F, of any cardinality, there are regular hyperreal-valued probability measures.

“Hyperreal-valued probability measures approximating a real-valued measure”  (with Ralf Schindler) in Notre Dame Journal of Formal Logic Forthcoming

We give a direct and elementary proof of the fact that every real-valued probability measure can be approximated up to an infinitesimal by a hyperreal-valued one which is regular and defined on the whole powerset of the sample space.

Infinitesimal Chances The Philosophers’ Imprint vol. 14 no. 2 (February 2014): http://www.philosophersimprint.org/014002/

It is natural to think that questions in the metaphysics of chance are independent of the mathematical representation of chance in probability theory. After all, chance is a feature of events that comes in degrees and the mathematical representation of chance concerns these degrees but leaves the nature of chance open. The mathematical representation of chance could thus, un-controversially, be taken to be what it is commonly taken to be: a probability measure satisfying Kolmogorov’s axioms. The metaphysical questions about chance seem to be left open by all this. I argue that this is a mistake. The employment of real numbers as measures of chance in standard probability theory brings with it commitments in the metaphysics of (objective) chance that are not only substantial but also mistaken. To measure chance properly we need to employ extensions of the real numbers that contain infinitesimals: positive numbers that are infinitely small. But simply using infinitesimals alone is not enough, as a number of arguments show. Instead we need to put three ideas together: infinitesimals, the non-locality of chance and flexibility in measurement. Only those three together give us a coherent picture of chance and its mathematical representation.

“Are there completely ineffable aspects of reality?” (Submitted, presently in revisions)

Should we think that some aspects of reality are simply beyond us, in the sense that creatures like us are in principle incapable of representing them in thought or language? What should we think follow for the project of metaphysics from our limitations or lack thereof? I will argue that on standard assumptions the answer should be that we are limited, and that this has significant consequences for metaphysics. However, we have good reasons to think that these standard assumptions are false, and that if so then the situation will be quite different. (This paper is a follow-up on “Inexpressible properties and propositions”)

“How to Endure”  (with J. David Velleman) in Philosophical Quarterly. vol. 61.1. January 2011. Pages 37-57.

We argue that the standard way to try to understand the intuitive difference between endurance and perdurance is based on a confusion. According to the standard, temporal parts based way we don’t get two conceptually coherent options about how to persist, but rather we get one side which is a conceptual truth, and one which is a conceptual falsehood, Thus there can be no coherent metaphysical debate about which side wins. Instead we propose a new way to spell out the difference that gives us two conceptually coherent options about persistence. An enduring object, we propose,  is wholly present or “all there” at a moment in the sense that which object exists at this moment is a fact local to that moment. To endure is to persist and to have ones identity determined by properties local to every moment over which one endures. The difference between endurance and perdurance is thus not one about temporal parts, but about identity. We spell out how this is to be understood more precisely, what follows from it, and why the other, temporal parts based option, seems coherent even though it isn’t.

“Inferential Role and the Ideal of Deductive Logic” in The Baltic International Yearbook of Cognition, Logic and Communication. Volume 5: Meaning, Understanding and Knowledge. 2010. Pages 1-26.

Although there is a prima facie strong case for a close connection between the meaning  and inferential role for certain expressions, this connection seems seriously threatened by the semantic and logical paradoxes which rely on these inferential roles. Some philosophers have drawn radical conclusions from the paradoxes for the theory of meaning in general, and for which sentences in our language are true. I criticize these overreactions, and instead propose to distinguish two conceptions of inferential role. This distinction is closely tied to two conceptions of deductive logic, and it is the key, I argue, for understanding first the connection between meaning and inferential role, and second what the paradoxes show more generally. (This paper is a follow up on my paper “Validity, Paradox and the Ideal of Deductive Logic”.)

“Formal Tools and the Philosophy of Mathematics” in New Waves in the Philosophy of Mathematics. O. Bueno and O. Linnebo (eds.). Palgrave Macmillan. Pages 197-210. 2009.

I argue that contrary to current practice formal tools only have a limited role to play in the philosophy of mathematics, and that many of the harder questions empirical questions about language and mind. However, for those who hold certain philosophical views (which I do hold) formal tools do have a important role, while for most philosophers they do not.

“Review of John Burgess’ Mathematics, Models, and Modality” in Notre Dame Philosophical Reviews. January 2010.

A review of the collection of philosophical papers by John Burgess. I in particular criticize his critique of nominalism, and his positive proposal about meta-ontology.

“My answers to 5 questions” in Metaphysics: 5 Questions. A. Steglich-Petersen (ed.). 2010.

My answers to the 5 questions in the 5 questions series. About metaphysics in particular.

“Ambitious, yet modest, metaphysics”  in Chalmers, Manley, and Wasserman (eds.) Metametaphysics. Pages 260-289. 2009.

I discuss some general constraints that metaphysics has to meet, and reject one recently not uncommon way to meet them. Then I outline another way to carry out metaphysics, mostly for the case of ontology. This paper outlines the main thesis of my book manuscript Ontology and the Ambitions of Metaphysics, as well as my critique of esoteric metaphysics.

“Review of Graham Priest’s Towards Non-Being”  in the Bulletin of Symbolic Logic.  vol 14:1. Pages 116-18. 2008.

A review of Priest’s recent book on non-existent objects. Besides the praise I complain that he is too quick to draw metaphysical conclusions from his clever semantics of intensional transitive verbs, and too negligent with the linguistic literature on the same topic.

“The Meta-Problem of Change” in Noûs. vol. 43.2. Pages 286-314. 2009.

The problem of change plays a central role in the metaphysics of time and material objects, and whoever does best in solving this problem has a leg up when it comes to choosing a metaphysics of time and material objects. But whether this central role of the problem of change in metaphysics is legitimate is not at all clear. This is in part since it is not clear what the problem of change is, and why it is a problem in metaphysics. I investigate what metaphysical problem the problem of change might be, and how it relates to various other problems related to change that are studied in the empirical sciences. The problem of change can thus be a case study of what makes a problem a metaphysical one and how metaphysics relates to the empirical sciences. I conclude that the central role the problem of change has in the metaphysics of time is not justified.

“Review of Jody Azzouni’s Deflating Existential Consequence” in The Philosophical Review, vol. 116.3. 2007. Pages 465-67.

As the title says, this is a book review of Azzouni’s book. I complain that Azzouni proposes an answer to a question, but it is unclear what question he is trying to answer.

“Validity, Paradox, and the Ideal of Deductive Logic” in Revenge of the Liar, JC Beall (ed.) Oxford University Press 2007.

I express my dissatisfaction with the common ways to treat the semantic paradoxes. Not only do they give rise to revenge paradoxes, they ignore the wisdom contained in the ordinary reaction to paradoxes. I instead propose an account that vindicates the ordinary reaction to paradox by putting the blame on us philosophers. It is the wrong conception of what a valid inference is, one that is central to “the ideal of deductive logic” that gives rise to the problem. The solution outlined gives us a new way to accept defeat in light of the paradoxes: the arguments that lead to them are based on valid forms of reasoning, but their conclusions are nonetheless rationally rejected.

“From Remnants to Things, and back again” forthcoming in Meanings and other Things: essays on Stephen Schiffer, Gary Ostertag (ed.) MIT Press 2007. 2008. 2009  2010 2011

Schiffer substantially changed his view about propositions and that-clauses somewhere between his two most recent books: Remnants of Meaning and The Things We Mean. I look at what problems his earlier view had, and what reason Schiffer gives for giving it up in favor of his more recent view. I argue that Schiffer’s reasons are not very good reasons, and that instead the problems for Remnants can be solved, contrary to the ones Things faces. I outline how a view in the spirit of the one Schiffer held in Remnants can be formulated and defended against the problems that his version faces. In the end we should go back to a view like the one he held in Remnants.

“Innocent Statements and Their Metaphysically Loaded Counterparts” The Philosophers’ Imprint vol. 7 no. 1 (February 2007): http://www.philosophersimprint.org/007001/

Reprinted in the Philosophers’ Annual vol. XXVII. 2008.

One puzzling feature of talk about properties, propositions and natural numbers is that statements that are explicitly about them can be introduced apparently without change of truth conditions from statements that don't mention them at all. Thus it seems that the existence of numbers, properties and propositions can be established `from nothing'. This metaphysical puzzle is tied to a series of syntactic and semantic puzzles about the relationship between ordinary, metaphysically innocent statements and their metaphysically loaded counterparts, statements that explicitly mention numbers, properties and propositions, but nonetheless appear to be equivalent to the former. I argue that the standard solutions to the metaphysical puzzles make a mistaken assumption about the semantics of the loaded counterparts. Instead I propose a solution to the syntactic and semantic puzzles, and argue that this solution also gives us a new solution to the metaphysical puzzle. I argue that instead of containing more semantically singular terms that aim to refer to extra entities, the loaded counterparts are focus constructions. Their syntactic structure is in the service of presenting information with a focus, but not to refer to new entities. This will allow us to spell out Frege's metaphor of content carving.

“Number Determiners, Numbers, and Arithmetic” in The Philosophical Review vol. 114.2, pp. 179-225. April 2005. (actual publication date is sometime Fall 2006).

Number words like "two" and "four" occur in natural language in at least two, apparently incompatible ways. Sometimes they appear to be singular terms, at other times they appear to be adjectives, or parts of quantifiers. How these two occurrences relate to each other is somewhat mysterious, as is how they relate to symbolic uses of numerals. In this paper we will first investigate and reject some proposals that have been made about their relationship, and then propose a new account of it. This new account will give us a unified view about the different uses of number words in natural language, and it is, in part, motivated by widely held views in natural language semantics and by a solution to certain cognitive problems that we face in learning basic arithmetic. According to this account all number words are determiners in all of these occurrences. Finally, I outline a view in the philosophy of arithmetic which holds that arithmetic truth is literal and objective truth, but it does not depend on what or how many objects exists. This gives us a non-Fregean form of logicism.

“Review of Wolfgang Künne’s  Conceptions of Truth” in The Philosophical Review, vol. 114.1, January 2005. pp. 136-39. (actual publication date is sometime Fall 2006).

   

This review mostly discusses Künne's positive proposal about truth, his Modest Account. In particular, I discuss propositional quantification, which is required for Künne's formulation of the Modest Account, and under what conditions this kind of quantification is acceptable. I argue that it requires a view of propositions which he rejects, (but I accept).

“Schiffer’s New Theory of Propositions” in Philosophy and Phenomenological Research. vol. LXXIII. July 2006. Pages 211 - 17.

This paper is a critical discussion of Schiffer's new book The Things we Mean, and part of a symposium on this book. I in particular discuss the relation between Schiffer's new pleonastic theory and his older no-reference theory. I focus on his discussion of substitution failure of that-clauses (I fear that p vs. I fear the proposition that p), and on the question whether non-existent objects might be pleonastic entities, and whether pleonastic entities might be non-existent objects.

“Encuneral Noun Phrases” (with Jeff Pelletier) draft (Fall 2005 version)

We argue that noun phrases should not be seen as coming in only three kinds: referential, predicative and quantificational. We in particular discuss whether there is some kind of methodological privilege for assuming that there are only as few kinds of NPs as are proven to be necessary, and other issues about the methodology of semantics. We end with a list of examples that are prima facie candidates for being an encuneral NP.

       

   

“Supervenience and Object Dependent Properties” in Journal of Philosophy vol. CII.1 pp. 5-32. January 2005

I argue that the semantic thesis of direct reference and the metaphysical thesis of the supervenience of the non-physical on the physical cannot both be true. The argument first develops a necessary condition for supervenience, a so-called conditional locality requirement, which is then shown to be incompatible with some physical object having object dependent properties, which in turn is required for the thesis of direct reference to be true. I apply this argument to formulate a new argument against the claim that a thisness is analyzable in purely general terms, one that does not rely on complete symmetry nor the falsity of the identity of indiscernibles. At the end I consider what options the argument leaves one with.

“Inexpressible Properties and Propositions” in Oxford Studies in Metaphysics vol. 2. Dean Zimmerman (ed.) Oxford University Press 2006. pp. 155-206. Winner of the Oxford Studies Younger Metaphysician Prize. Winner of the APA Article Prize.

The paper starts out with wondering whether it could be that talk about properties and propositions is literally true, but there is no substantial metaphysical project of finding out what they are. I hold this to be true. To see how that can be I formulate an internalist conception of talk about properties and propositions, according to which such talk is literally true, but not about any entities. This is contrasted with an externalist conception, according to which such talk is about a language independent domain of entities. The internalist conception of quantification over properties and propositions takes quantification over them to be a generalization over the instances, and not as ranging over a language independent domain of entities. This internalist view seems to be easily refuted by taking recourse to inexpressible properties and propositions. In this paper I discuss what arguments we have for thinking that there are inexpressible properties and propositions, and I formulate a version of internalism that can accommodate them. This version of internalism suggest a view about how and why different languages differ in expressive power, which I call the expressibility hypothesis which is formulated and discussed. The resulting internalist view has the idealist sounding consequence that all the properties of all objects can be expressed by us in our present language, while at the same time having the realist consequence that what properties objects have is independent of us.

“A Puzzle about Ontology” in Noûs vol 39.2. pp. 256-83. 2005. (Reprinted in Italian translation (!) in a special issue of Rivista di Estetica)

Ontology, as it is usually practiced, gives rise to a puzzle. This paper formulates and discusses this puzzle, and proposes a solution to it. A solution to the puzzle requires us to investigate the function of quantifiers in ordinary communication, and the relationship between syntactic form and semantic function, in particular the relationship between syntactic form and information structure. The solution proposed leads to a distinction between internal and external questions about what there is, a distinction going back to Carnap, but without rejecting either one of them as meaningless. I argue that a Quinean approach to ontology has to be rejected in favor of a neo-Carnapian one, properly formulated. A strategy for answering ontological questions is outlined at the end.

“Logic and Ontology” in the Stanford Encyclopedia of Philosophy 2004.

A survey article on logic and ontology, in particular how they should be understood and how they relate to each other. I distinguish different conceptions of “logic” and of “ontology” and discuss several areas of overlap.

“Proof-Theoretic Reduction as a Philosopher’s Tool” in Erkenntnis vol. 53. 2000. pp. 127-46. Reprinted in The Philosopher’s Annual vol. XXIII. 2001.

This paper deals with the philosophical relevance of certain technical results, namely proof-theoretic reductions and closely related relative consistency proofs. Such results were the goal of Hilbert's Program in the philosophy of mathematics. The particular result that Hilbert aimed for is known to be impossible, but closely related theorems have been proven in recent years, and used in so-called relativized versions of Hilbert's Program. I argue that one the one hand, they do not have the particular philosophical significance that they are sometimes claimed to have. However, on the other hand, I make a proposal about what large scale significance they do have, and outline a position in the philosophy of mathematics were they play a central constructive role. This position requires some other work in the philosophy of mathematics, some of which is discussed in "Number determiners, numbers and arithmetic" (see above).

“Quantification and Non-Existent Objects” in Empty Names, Fiction and the Puzzles of Non-Existence Anthony Everett and Thomas Hofweber (eds.) CSLI Publications. 2000. pp. 249-73.

Sometimes it seems we use quantifiers that range over things that don't exist. And sometimes we use them such that only existing things are allowed in the domain of quantification. A Meinongean argues that the latter are really contextual restrictions of the former, and that the true domain of quantification involves existing as well as non-existing objects. I argue that we indeed use quantifiers that range over non-existing objects, but that the difference between them and uses where only existing things count is not one of contextual restriction. The difference is rather of a different kind, and we can see that this is so from a general need we have for quantifiers in communication. I propose that quantifiers are semantically underspecified, and that they have a domain conditions reading and an inferential role reading. The difference between them is not one of contextual restriction. I also discuss the relationship between quantification and ontology, where I reject Quine's approach in favor of a version of Carnap's.

         

“Contextualism and the Meaning-Intention Problem” in Cognition, Agency and Rationality, edited by K. Korta, E. Sosa and J. Arrozola, Kluwer, 1999.

The paper discusses whether contextualist theories of knowledge are in trouble because of limited cognitive access of speakers to the (alleged) context sensitivity of their utterances about knowledge. I argue that they aren't, and discuss some other related issues.

My Dissertation:

Here is my 1999 Stanford University dissertation. (It was jointly supervised by Solomon Feferman and John Perry.)

                Ontology and Objectivity    (as a pdf, 892 KB, 268 pages)

The official abstract is as follows:

Ontology is the study of what there is, what kinds of things make up reality. Ontology seems to be a very difficult, rather speculative discipline. However, it is trivial to conclude that there are properties, propositions and numbers, starting from only necessarily true or analytic premises. This gives rise to a puzzle about how hard ontological questions are, and relates to a puzzle about how important they are. And it produces the ontology-objectivity dilemma: either (certain) ontological questions can be trivially answered using only uncontroversial premises, or the uncertainties of ontology are really a threat to the truth of basically everything we say or believe.

The main aim of this dissertation is to resolve these puzzles and to shed some light on the discipline of ontology. I defend a view inspired by Carnap’s internal-external distinction about what there is, but one according to which both internal and external questions are fully factual and meaningful. In particular, I argue that the trivial arguments are valid, but they do not answer any ontological questions. Furthermore, I propose an account of the function of our talk about properties, propositions and natural numbers. According to this account our talk about them has no ontological presuppositions for its literal and objective truth. This avoids the ontology-objectivity dilemma, and solves the puzzles about ontology.

To do this I look at quantification and noun phrases in general, and at their relation

to ontology. I argue that quantifiers are semantically underspecified in a certain respect, and play two different roles in communication. I discuss the relation between syntactic form and information structure, the function of certain non-referential, non-quantificational noun phrases, the uses of bare number determiners, and how arithmetic truths are learned and taught.

The more metaphysical issues discussed include: inexpressible properties, logicism about arithmetic, nominalism, Carnap’s view about ontology, the problem of universals, the relationship between ontology and objectivity, different projects within ontology, non-existent objects, and others.

A technical appendix deals with the relation that certain uses of quantifiers have to

small fragments of infinitary logic.