There is no concept more central to logic and critical thinking than the concept of an argument. I here address the definition of ‘argument’ in the logical sense of the term and defend the claim that many current proposals, once they are interpreted in a way that makes them sufficiently precise, are extensionally inadequate. Definitions found in some contemporary, prominent critical thinking textbooks will serve as a springboard. I claim that each may be interpreted in an absolutist way or a (...) relativistic way, yet all turn out to be objectionable no matter which route is taken. I finish with a proposal on which the definition of ‘argument’ is an absolutist one, yet one that avoids the problems discussed for the earlier proposals. (shrink)

This paper argues for the thesis that, roughly put, it is impossible to talk about absolutely everything. To put the thesis more precisely, there is a particular sense in which, as a matter of semantics, quantifiers always range over domains that are in principle extensible, and so cannot count as really being ‘absolutely everything’. The paper presents an argument for this thesis, and considers some important objections to the argument and to the formulation of the thesis. The paper also offers (...) an assessment of just how implausible the thesis really is. It argues that the intuitions against the thesis come down to a few special cases, which can be given special treatment. Finally, the paper considers some metaphysical ideas that might surround the thesis. Particularly, it might be maintained that an important variety of realism is incompatible with the thesis. The paper argues that this is not the case. (shrink)

The paper contains a general argument for linguistic idealism, which it approaches by way of some considerations relating to the unity of the proposition and Tractarian metaphysics. Language exhibits a function–argument structure, but does it do so because it is reflecting how things are in the world, or does the relation of dependence run in the other direction? The paper argues that the general structure of the world is asymmetrically dependent on a metaphysically prior fact about language, namely that it (...) exhibits subject–predicate structure. (shrink)

This book summarizes the intense research that the author performed for his Ph.D. thesis , revised and with the addition of an intuitionistic critique of Husserl's concept of number. His starting point consisted of a double conviction: 1) Brouwerian intuitionism is a valid way of doing mathematics but is grounded on a weak philosophy; 2) Husserlian phenomenology can provide a suitable philosophical ground for intuitionism. In order to let intuitionism and phenomenology match, he had to solve in general two problems: (...) 1) the question of the reciprocal indifference that the authors had toward each other's theorizing which indeed they knew; 2) Husserl's general attitude of accepting classical mathematics, which contrasts with the critical attitude of the intuitionists.Moreover, in the specific case focused on by this book—concerning choice sequences, that is, sequences that can be completely lawless and that were admitted as mathematical entities by Brouwer—van Atten had to handle a further problem: such sequences do not fit the characteristic of omnitemporality that the late Husserl seemed to consider a necessary attribute of entities if they were to be considered mathematical. In as far as they are lawless we cannot predict at any moment how they will develop in the future, hence they are not determined at any particular time—they will be determined only in the future.Let us begin with van Atten's first conviction, i.e., that Brouwerian intuitionism is grounded on a weak philosophy. We have to recall that Brouwer provided a mystical attitude for proposing his intuitionism: man can obtain happiness only by keeping himself closed inside the inner Self. Any attempted movement towards the exterior world is a source of pain: in particular language and the sciences. Mathematics, in order to be morally acceptable …. (shrink)

Quantifier variance faces a number of difficulties. In this paper we first formulate the view as holding that the meanings of the quantifiers may vary, and that languages using different quantifiers may be charitably translated into each other. We then object to the view on the basis of four claims: (i) quantifiers cannot vary their meaning extensionally by changing the domain of quantification; (ii) quantifiers cannot vary their meaning intensionally without collapsing into logical pluralism; (iii) quantifier variance is not an (...) ontological doctrine; (iv) quantifier variance is not compatible with charitable translation and as such is internally inconsistent. In light of these troubles, we recommend the dissolution of quantifier variance and suggest that the view be laid to rest. (shrink)

A central element in neo-Fregean philosophy of mathematics is the focus on abstraction principles, and the use of abstraction principles to ground various areas of mathematics. But as is well known, not all abstraction principles are in good standing. Various proposals for singling out the acceptable abstraction principles have been presented. Here I investigate what philosophical underpinnings can be provided for these proposals; specifically, underpinnings that fit the neo-Fregean's general outlook. Among the philosophical ideas I consider are: general views on (...) a priori justification; the idea of abstraction as reconceptualization, the idea that truth is prior to reference in the sense associated with Frege's context principle; and various broadly relativistic views. The conclusions are by and large negative. (shrink)

This paper raises and then discusses a puzzle concerning the ontological commitments of mathematical principles. The main focus here is Hume's Principle—a statement that, embedded in second-order logic, allows for a deduction of the second-order Peano axioms. The puzzle aims to put pressure on so-called epistemic rejectionism, a position that rejects the analytic status of Hume's Principle. The upshot will be to elicit a new and very basic disagreement between epistemic rejectionism and the neo-Fregeans, defenders of the analytic status of (...) Hume's Principle, which will provide a new angle from which properly to assess and re-evaluate the current debate. (shrink)

The syntactic priority thesis (henceforth SP) asserts that the truth of appropriate sentential contexts containing what are, by syntactic criteria, singular terms, is sufficient to justify the attribution of objectual reference to such terms (Wright, 1983, 24). One consequence that the neo-Fregean draws from SP is that it is through an analysis of the syntactic structure of true statements that 'ontological questions are to be understood and settled' (Wright, 1983, 25). Despite the significant literature on SP, little consideration has been (...) given to this bold meta-ontological claim.1 My concern here is accordingly not with specific applications of SP to debates in the philosophy of mathematics, but rather with the .. (shrink)

RÉSUMÉ: Selon une ontologie platonicienne, il faut qu’une exemplification platonicienne lie des particuliers physiques et un universel non localisé pour qu’i! y ait connexion entre propriété et choses. Dans cet article, je discute du lien d’exemplification platonicien, lequel a l’intéressante faculté de lier des entités localisées à une entité non localisée et donc, pour reprendre les mots d’Armstrong, la faculté de traverser le domaine du non spatialement localisé et celui du spatialement localisé. La littérature ne contient à peu près aucune (...) discussion de l’exemplification. J’en discute et signale une nouveau problème relatif à la connexion entre un universel platonicien et des particuliers physiques. (shrink)

Auf Kants berühmte Frage "Wie ist Metaphysik möglich?" wird eine bejahende Antwort gegeben - eine, die Metaphysik als eine selbständige und unentbehrliche Disziplin darstellt, deren Aufgabe es ist, das Reich der wirklichen Möglichkeiten zu erforschen. Die Begriffe der "wirklichen" oder "metaphysischen" Möglichkeit und Notwendigkeit werden verteidigt und von den Begriffen verschiedener anderer Arten von Modalität unterschieden, z.B. physischer, logischer und begrifflicher Möglichkeit oder Notwendigkeit. Es wird dargelegt, daß die Gegner der Metaphysik, von den Relativisten bis zu denen, welche die Metaphysik (...) den empirischen Wissenschaften, der Erkenntnislehre oder der Sprachphilosophie unterordnen möchten, inkohärente Auffassungen annehmen. (shrink)

In recent discussions concerning the definition of argument, it has been maintained that the word ‘argument’ exhibits the process-product ambiguity, or an act/object ambi-guity. Drawing on literature on lexical ambiguity we argue that ‘argument’ is not ambiguous. The term ‘argument’ refers to an object, not to a speech act. We also examine some of the important implications of our argument by considering the question: what sort of abstract objects are arguments?

This paper gives a characterization of the ontology implicit in natural language and the entities it involves, situates natural language ontology within metaphysics, and responds to Chomskys' dismissal of externalist semantics.

In this dissertation I examine the NeoFregean metaontology of mathematics. I try to clarify the relationship between what is sometimes called Priority Thesis and Platonism about mathematical entities. I then present three coherent ways in which one might endorse both these stances, also answering some possible objections. Finally I try to show which of these three ways is the most promising.

This dissertation is centered around a set of apparently conflicting intuitions that we may have about mathematics. On the one hand, we are inclined to believe that the theorems of mathematics are true. Since many of these theorems are existence assertions, it seems that if we accept them as true, we also commit ourselves to the existence of mathematical objects. On the other hand, mathematical objects are usually thought of as abstract objects that are non-spatiotemporal and causally inert. This makes (...) it difficult to understand how we can have knowledge of them and how they can have any relevance for our mathematical theories. I begin by characterizing a realist position in the philosophy of mathematics and discussing two of the most influential arguments for that kind of view. Next, after highlighting some of the difficulties that realism faces, I look at a few alternative approaches that attempt to account for our mathematical practice without making the assumption that there exist abstract mathematical entities. More specifically, I examine the fictionalist views developed by Hartry Field, Mark Balaguer, and Stephen Yablo, respectively. A common feature of these views is that they accept that mathematics interpreted at face value is committed to the existence of abstract objects. In order to avoid this commitment, they claim that mathematics, when taken at face value, is false. I argue that the fictionalist idea of mathematics as consisting of falsehoods is counter-intuitive and that we should aim for an account that can accommodate both the intuition that mathematics is true and the intuition that the causal inertness of abstract mathematical objects makes them irrelevant to mathematical practice and mathematical knowledge. The solution that I propose is based on Rudolf Carnap's distinction between an internal and an external perspective on existence. I argue that the most reasonable interpretation of the notions of mathematical truth and existence is that they are internal to mathematics and, hence, that mathematical truth cannot be used to draw the conclusion that mathematical objects exist in an external/ontological sense. (shrink)

Against non-analytic naturalism and quietist realism, I defend a robust form of non-naturalism. The argument proceeds as follows: In the face of extensional underdetermination, quietist realism cannot non-question-beggingly respond to alternative accounts that offer formally identical but substantively different interpretations of what reasons are. They face what we might call the reasons appropriation problem. In light of this problem, quietists ought to abandon their view in favor of robust realism. By permitting substantive metaphysical claims we can then argue, based on (...) reasonhood being a relation, that reasonhood is an abstract universal. If reasonhood is an abstract universal, then we can non-question-beggingly assert that the counting in favor of relation is a general kind or genus. This poses a dilemma for non-analytic naturalists: either they need to give the same reductive analysis for epistemic and practical reasons, or they can give a different analyses by treating epistemic and practical reasons as a species of the larger genus. However, the former looks extensionally implausible epistemic reasons are not desire-based and the latter entails that the reduction, via a violation of irreflexivity, fails to ground reasonhood. Naturalistic reductions of the normative, accordingly, face a damning dilemma. We should, in the face of this argument, thus accept a robust form of non-naturalist realism. (shrink)