Thomas Hofweber

Although there is a prima facie strong case for a close connection between the meaning and inferential role of 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.

forthcoming in Meanings and other Things: essays on Stephen Schiffer Gary Ostertag (ed.) MIT Press 2007. 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.

The relevant alternatives approach in epistemology1 arose some years ago partly out of the hope to be able to reconcile our ordinary claims of knowledge with our inability to answer the skeptic. It was supposed to give rise to an account of knowledge according to which our ordinary claims of knowledge are true, even though the claims about our lack of knowledge that the skeptics make in one of their more persuasive moments are also true. To know, according to such an account, is to have evidence sufficient to rule out all the relevant alternatives. In ordinary life few alternatives are relevant. For example, whether or not we are brains in a vat is not a relevant alternative that we have to be able to rule out. In the debate with the skeptic it may become relevant, and accordingly we might not know something any more then, even though we have the same evidence as in ordinary life. The skeptics cleverly make more and more alternatives relevant, and that is how they succeed. But their success in the philosophy seminar is no threat to our ordinary claims of knowledge, or so the theory goes.

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 so in part since it is not clear what the problem of change is, and why it is a problem in metaphysics. We will 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 other parts of inquiry. We conclude that the central role the problem of change is given in the contemporary metaphysics of time is not justified.

Hilbert’s program in the philosophy of mathematics comes in two parts. One part is a technical part. To carry out this part of the program one has to prove a certain technical result. The other part of the program is a philosophical part. It is concerned with philosophical questions that are the real aim of the program. To carry out this part one, basically, has to show why the technical part answers the philosophical questions one wanted to have answered. Hilbert probably thought that he had completed the philosophical part of his program, maybe up to a few details. What was left to do was the technical part. To carry it out one, roughly, had to give a precise axiomatization of mathematics and show that it is consistent on purely finitistic grounds. This would come down to giving a relative consistency proof of mathematics in finitist mathematics, or to give a proof-theoretic reduction of mathematics on to finitist mathematics (we will look at these notions in more detail soon). It is widely believed that Gödel’s theorems showed that the technical part of Hilbert’s program could not be carried out. Gödel’s theorems show that the consistency of arithmetic can not even be proven in arithmetic, not to speak of by finitistic means alone. So, the technical part of Hilbert’s program is hopeless, and since Hilbert’s program essentially relied on both the technical and the philosophical part, Hilbert’s program as a whole is hopeless. Justified as this attitude is, it is a bit unfortunate. It is unfortunate because it takes away too much attention from the philosophical part of Hilbert’s program. And this is unfortunate for two reasons.

In his groundbreaking Grundlagen, Frege (1884) pointed out that number words like ‘four’ occur in ordinary language in two quite different ways and that this gives rise to a philosophical puzzle. On the one hand ‘four’ occurs as an adjective, which is to say that it occurs grammatically in sentences in a position that is commonly occupied by adjectives. Frege’s example was (1) Jupiter has four moons, where the occurrence of ‘four’ seems to be just like that of ‘green’ in (2) Jupiter has green moons. On the other hand, ‘four’ occurs as a singular term, which is to say that it occurs in a position that is commonly occupied by paradigmatic cases of singular terms, like proper names: (3) The number of moons of Jupiter is four. Here ‘four’ seems to be just like ‘Wagner’ in (4) The composer of Tannhäuser is Wagner, and both of these statements seem to be identity statements, ones with which we claim that what two singular terms stand for is identical. But that number words can occur both as singular terms and as adjectives is puzzling. Usually adjectives cannot occur in a position occupied by a singular term, and the other way round, without resulting in ungrammaticality and nonsense. To give just one example, it would be ungrammatical to replace ‘four’ with ‘the number of moons of Jupiter’ in (1): (5) *Jupiter has the number of moons of Jupiter moons. This ungrammaticality results even though ‘four’ and ‘the number of moons of Jupiter’ are both apparently singular terms standing for the same object in (3). So, how can it be that number words can occur both as singular terms and as adjectives, while other adjectives cannot occur as singular terms, and other singular terms cannot occur as adjectives?

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.

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.

Philosophers and theorists have long been puzzled by humans' ability to talk about things that do not exist, or to talk about things that they think exist but, in fact, do not. _Empty Names, Fiction, and the Puzzles of Non-Existence_ is a collection of 13 new works concerning the semantic and metaphysical issues arising from empty names, non-existence, and the nature of fiction. The contributors include some of the most important researchers working in these fields. Some of the papers develop and defend new positions on these matters, while others offer important new perspectives and criticisms of the existing approaches. The volume contains a comprehensive introductory essay by the editors, which provides a survey of the philosophical issues concerning empty names, the various responses to these issues, and the literature on the subject to date

There is a long history of worrying about whether or not metaphysics is a legitimate philosophical discipline. Traditionally such worries center around issues of meaning and epistemological concerns. Do the metaphysical questions have any meaning? Can metaphysical methodology lead to knowledge? But these questions are, in my opinion, not as serious as they have sometimes (historically) been taken to be. What is much more concerning is another set of worries about metaphysics, which I take to the greatest threat to metaphysics as a philosophical discipline. These worries, in effect, hold that the questions that metaphysics tries to answer have long been answered in other parts of inquiry, ones that have much greater authority. And if they haven’t been answered yet then one should not look to philosophy for an answer. What metaphysics tries to do has been or will be done by the sciences. There is nothing left to do for philosophy, or so the worry. Let me illustrate this with two examples, one of which is our main concern here.

I argue that the semantic thesis of direct reference and the meta- physical 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. We 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. I outline a strategy at the end how the conclusion could be avoided, at a price.

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.

Ontology is the philosophical discipline that tries to find out what there is: what entities make up reality, what is the stuff the world is made from? Thus, ontology is part of metaphysics, and in fact it seems to be about half of all of metaphysics. It tries to establish what (kinds of) things there are, the other half tries to find out what the (general) properties of these things are and what (general) relations they have to each other. Settling questions in ontology would bring with it major progress in metaphysics. And it would bring with it major progress in a variety of areas in philosophy outside of metaphysics as well. Many philosophical debates outside of metaphysics are quite directly influenced by how things turn out in ontology. Whether or not there are certain entities will give rise to quite different answers in various philosophical debates. I would like to very briefly describe three debates where ontological questions play a central role. These debates are either directly from metaphysics or from other areas of philosophy and they will be of central importance throughout this paper.

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 ontologyobjectivity 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....

This paper investigates the connection of intellectual humility to a somewhat neglected form of a limitation of human knowledge—a limitation in which facts or truths we human beings can in principle represent conceptually. I consider some arguments for such a limitation, and argue that, under standard assumptions, the sub-algebra hypothesis is the best hypothesis about how the facts we can represent relate to the ones that we can not. This hypothesis has a consequence for intellectual humility in that it supports it in metaphysics, but not in ordinary inquiry.

The semantics of noun phrases (NPs) is of crucial importance for both philosophy and linguistics. Throughout much of the history of the debate about the semantics of noun phrases there has been an implicit assumption about how they are to be understood. Basically, it is the assumption that NPs come only in two kinds. In this paper we would like to make that assumption explicit and discuss it and its status in the semantics of natural language. We will have a look at how the assumption is to be understood more precisely, what its methodological status should be, whether it has been abandoned in recent work in semantics, and whether it should be abandoned in future work. To do all this, it’s best to start with some historical context.

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.

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

On the one hand they seem to be quite obviously truth conditionally equivalent, but on the other hand they seem to be about different things. Whereas (1) is about Jupiter and its moons, (2) is about numbers. In particular, the word ‘four’ appears in (1) in the position of an adjective or determiner, whereas it seems to be a name for a number in (2). Furthermore, (2) appears to be an identity statement claiming that what two number terms stand for is the same thing. Several authors have proposed answers to this puzzle, including Frege, by either pinning the issue on the nature of numbers, pretense, fictionalism, or the nature of reference, but all these proposals agreed that (2) is an identity statement and that in it ‘four’ is a name for an object. In [Hofweber, 2007] I argued that (2) is not an identity statement and that ‘four’ in (2) is not a name for an object. The argument for it was this: When we look at what role (2) has in actual communication we can see that (2) has a focus effect on a discourse that arises from the syntax without special intonation

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 way this can be is via a special role that subjects have in the metaphysics of material objects. Some metaphysical aspect of material objects might require the existence of subjects. This would support that minds must exist if material objects exist and thus that a mindless material world is impossible. This view, labeled the subjectivity thesis by Anton Friedrich Koch, was defended by him with an intriguing, purely metaphysical argument connected to the individuation of material objects in space and time. The present paper hopes to make progress on assessing the viability of such a position. It starts by critically examining Koch's argument for the subjectivity thesis, as well as similar arguments that give minds a central place in the metaphysics of material objects via considerations about identity and difference. It then compares these ideas to similar ones in the philosophy of time, and concludes with an outlook on whether such a position is viable and what needs to be done to fill the gaps unearthed along the way