Matti Eklund

Neo-Fregeanism in the philosophy of mathematics consists of two main parts: the logicist thesis, that mathematics (or at least branches thereof, like arithmetic) all but reduce to logic, and the platonist thesis, that there are abstract, mathematical objects. I will here focus on the ontological thesis, platonism. Neo-Fregeanism has been widely discussed in recent years. Mostly the discussion has focused on issues specific to mathematics. I will here single out for special attention the view on ontology which underlies the neo-Fregeans’ claims about mathematical objects, and discuss this view in a broader setting

In his recent article "Carnapian Frameworks" (Synthese, 2021), Gabriel Broughton criticizes my discussions of Carnap on ontology and puts forward his own interpretation of what Carnap’s external/internal distinction amounts to. I here first argue that Broughton’s main claims about me are based on a misinterpretation. Then I turn to some issues of broader interest. I argue that Broughton’s own, potentially interesting interpretation of Carnap’s external/internal distinction does not work. And in light of Broughton’s discussion I present a sharpened version of what I have earlier said about Carnap’s this distinction.

In recent work, Bengson, Cuneo, and Shafer‐Landau (2020) develop a new social version of moral intuitionism that promises to explain why our moral intuitions are trustworthy. In this paper, we raise several worries for their account and present some general challenges for the broader class of views we call Social Moral Intuitionism. We close by reflecting on Bengson, Cuneo, and Shafer‐Landau's comparison between what they call the “perceptual practice” and the “moral intuition practice”, which we take to raise some difficult normative and meta‐normative questions for theorists of all stripes.

Vagueness, as discussed in the philosophical literature, is the phenomenon that paradigmatically rears its head in the sorites paradox, one prominent version of which is: One grain of sand does not make a heap. For any n, if n grains of sand do not make a heap, then n + 1 grains of sand do not make a heap. So, ten billion grains of sand do not make a heap. It is common ground that the different versions of the sorites paradox arise because of vagueness in a key expression, in this case ‘heap’. One central concern in the literature on vagueness is to find a solution to the sorites paradox. Vagueness also gives rise to borderline cases. Since ‘heap’ is a vague expression, ‘heap’ also gives rise to borderline cases: there are some possible entities such that they are neither clearly heaps nor clearly non-heaps, but instead are borderline heaps. Borderline cases can seem intuitively to present counter-examples to bivalence and the law of excluded middle . If Harry is a borderline case of baldness, ‘Harry is bald’ can seem neither true nor false, whence it presents doubts concerning bivalence. Similarly, one can find the corresponding instance of LEM, ‘Either Harry is bald or Harry is not bald’, suspect. There are three main theories that involve departures from bivalence, and two of them involve rejection of LEM as well. Standard three-valued logic invokes the idea of a third truth-value or truth-value gaps; fuzzy logic invokes the idea of continuum-many truth-values intermediate between truth and falsity. Both these views preserve truth-functionality. Traditional supervaluationism involves rejection of bivalence, but adherence to LEM. The idea is that if an expression is vague there is a range of precisifications associated with it, where, roughly, precisifications are ways the expression could be …

In this paper I outline an alternative to hermeneutic fictionalism, an alternative I call indifferentism, with the same advantages as hermeneutic fictionalism with respect to ontological issues but avoiding some of the problems that face fictionalism. The difference between indifferentism and fictionalism is this. The fictionalist about ordinary utterances of a sentence S holds, with more orthodox views, that the speaker in some sense commits herself to the truth of S. It is only that for the fictionalist this is truth in the relevant fiction. According to the indifferentist, by contrast, we are simply non-committal – or indifferent – with respect to some aspects of what is literally said in our assertive utterances

In (2001), (2003), and elsewhere, Ted Sider presents two arguments concerning the existential quantifier which are justly central to the recent discussion of metaontology. What we will call Sider's indeterminacy argument is an attempted reductio of the suggestion that the existential quantifier might be semantically indeterminate. What we will call Sider's naturalness argument is an argument for the claim that the semantic value of the existential quantifier is the most eligible existence-like meaning there is, à la David Lewis' eligibility theory of meaning. We will argue that these arguments cannot be jointly maintained: Sider must give up at least one. Before arguing this, we will present Sider's two arguments in a bit more detail, and discuss their relationship. A few remarks on the broader significance of our conclusions are in order at the outset. One may think that since one successful argument for a given conclusion is sufficient the point that Sider's arguments cannot both work is purely academic. But we think that Sider's two arguments at bottom reflect different ways of thinking about metaphysics. Moreover, we think that it is only the naturalness argument that promises to deliver all that Sider wants when it comes to metaontology, and it is only the indeterminacy argument that promises to deliver all that Sider wants when it comes to ontology

I shall here discuss some matters related to the so-called radical indeterminacy or inscrutability arguments due to, e.g., Willard v. O. Quine, Hilary Putnam, John Wallace and Donald Davidson.1 These are arguments that, on the face of it, demonstrate that there is radical indeterminacy in what the expressions in a theory refer to and in what the ontology of the theory is. I will use “inscrutability argument” as a general label for these arguments. My main topic – after I have dealt with some issues that in the context are mere preliminaries – will be what the consequences of inscrutability for ontology might be. (The label ‘inscrutability’ is not ideal, as it suggests that the problem raised is primarily epistemic. But it is common to use the label in the context of Quine’s arguments. And it has the advantage over the alternative suggestion “indeterminacy” that it signals that we are here dealing with a special kind of indeterminacy, not only more widespread but also in principle irremediable.).

The main question of the paper is that ofwhat vagueness consists in. This question must be distinguished from other questions about vagueness discussed in the literature. It is argued that familiar accounts of vagueness for general reasons failto answer the question ofwhat vagueness consists in. A positive view is defended, according to which, roughly, the vagueness of an expression consists in it being part ofsemantic competence to accept a tolerance principle for the expression. Since tolerance principles are inconsistent, this is an inconsistency view on vagueness.

Mark Johnston and Eric Olson have both pressed what Johnston has dubbed the personite problem. Personites, if they exist, are person-like entities whose lives extend over a continuous proper part of a person’s life. They are so person-like that they seem to have moral status if persons do. But this threatens to wreak havoc with ordinary moral thinking. For example, simple decisions to suffer some short-term hardship for long-term benefits become problematic. And ordinary punishment is always also punishment of the innocent, since it punishes personites that didn’t exist when the crime was committed. An initially attractive way around the personite problem may be to simply deny that personites exist. But as I discuss in this talk, relating to contemporary discussions in metaontology, this response for principled reasons doesn’t work. The problems I discuss illustrate the significance of metaontological considerations for issues in ethics and metaethics, and generalize widely beyond the personite problem.

The problem, or cluster of problems, of the unity of the proposition, along with the cluster of problems that tend to go under the name of Bradley’s regress, has recently again become a going concern for philosophers, after having for some time been regarded as primarily of historical interest. In this paper, I distinguish between the different problems that tend to be brought up under the heading of the unity of the proposition, and between different related regress arguments. I present my favored solutions to these problems.

I here critically discuss Hilary Putnam's views on ontology, especially as recently expounded in his Ethics without Ontology. In particular, I discuss Putnam's thesis of conceptual relativity and his criticism of the thesis that objectivity requires objects. Although I think that much of what Putnam says is important, and that there are important elements of truth to it, my points will largely be negative. Along the way I will discuss Putnam's and Wittgenstein's views in the philosophy of mathematics, and I will compare Putnam's metaontological views with those of William James, Michael Dummett, Crispin Wright and Simon Blackburn

In his recent Analysis article (2012), Robert Williams considers two puzzles relating to indeterminacy. On the basis of these puzzles, he defends a seemingly radical view on the normative role of indeterminacy. He speaks of indeterminacy as ‘normatively silent’. There are two ways of understanding the view that Williams defends. On one understanding, the view ends up being indistinguishable from one of the more traditional views Williams rejects, the view that phenomena of different kinds fall under the umbrella level ‘indeterminacy’. On the other understanding, Williams’s view is genuinely radical but his arguments don't adequately support it