For several decades, Carnap's philosophy of mathematics used to be either dismissed or ignored. It was perceived as a form of linguistic conventionalism and thus taken to rely on the bankrupt notion of truth by convention. However, recent scholarship has revealed a more subtle picture. It has been forcefully argued that Carnap is not a linguistic conventionalist in any straightforward sense, and that supposedly decisive objections against his position target a straw man. This raises two questions. First, how exactly should (...) we characterise Carnap's actual philosophy of mathematics? Secondly, is his position an attractive alternative to established views? I will tackle these issues by looking at Carnap's response to the incompleteness theorems. Drawing on arguments put forward by Gödel and Beth, I show that some crucial aspects of Carnap's positive account have remained underdeveloped. Suggestions on what a full evaluation of Carnap's position requires are made. (shrink)

In her paper “Neo-positivist metaphysics” (Philosophical Studies, 160(1), 53–78, 2012), Alyssa Ney promises a naturalized metaphysics that is acceptable even by positivists’ – and specifically Carnap’s – standards. This neo-positivist metaphysics takes its outset in the findings of our best science and relies on them to inform a metaphysics that can avoid the dependence on linguistic frameworks that is inherent to Carnapian deflationism. Neo-positivist metaphysics attempts to sidestep these problems by inheriting its semantic credentials directly from science itself. This paper (...) argues that such attempts are unsuccessful since science contains no resources with which to answer Carnap’s challenge either, and a science-based metaphysics is therefore just as vulnerable to Carnapian deflationism as traditional metaphysics. Consequently, neo-positivist metaphysics does not provide the promised metaphysics that can avoid Carnapian deflationism. While this conclusion focuses on Ney’s neo-positivist metaphysics, its scope includes any attempt to avoid Carnapian deflationism by a naturalized metaphysics that relies on strict deference to the findings of science. Substantial metaphysics – naturalized or not – is impossible unless or until Carnapian deflationism is refuted, and the resources for such a refutation cannot be found in naturalized metaphysics. (shrink)

One dimension of cognitive success concerns getting it right: having many true beliefs and no false ones. Another dimension of cognitive success concerns using the right concepts. For example, using a concept of a person that systematically excludes people of certain demographics from its extension is a sort of cognitive deficiency. This view, if correct, tasks inquirers with critically examining the concepts they are using and perhaps replacing those concepts with new and better ones. This task is often referred to (...) as “conceptual engineering”. However, so far it is unclear what exactly happens in cases of conceptual engineering. How does language change when we engineer a concept? This article offers an answer. I propose a view on which, when speakers assess the truth of propositions, they often rely on assumptions with regard to what is required for their truth. For example, when speakers assess whether unborn fetuses are people, they rely on assumptions with regard to what is required to be a person. Based on this idea, I develop a model of conceptual engineering according to which speakers “engineer concepts” when they change how they assess the truth of propositions. For example, speakers engineer the concept of a person when they change how they assess the truth of the proposition that unborn fetuses are people. (shrink)

A definition of a property P is impredicative if it quantifies over a domain to which P belongs. Due to influential arguments by Ramsey and Gödel, impredicative mathematics is often thought to possess special metaphysical commitments. It seems that an impredicative definition of a property P does not have the intended meaning unless P already exists, suggesting that the existence of P cannot depend on its explicit definition. Carnap (1937 [1934], p. 164) argues, however, that accepting impredicative definitions amounts to (...) choosing a "form of language" and is free from metaphysical implications. This paper explains this view in its historical context. I discuss the development of Carnap’s thought on the foundations of mathematics from the mid-1920s to the mid-1930s, concluding with an account of Carnap’s (1937 [1934]) non-Platonistic defense of impredicativity. This discussion is also important for understanding Carnap’s influential views on ontology more generally, since Carnap’s (1937 [1934]) view, according to which accepting impredicative definitions amounts to choosing a "form of language", is an early precursor of the view Carnap presents in "Empiricism, Semantics and Ontology" (1956 [1950]), according to which referring to abstract entities amounts to accepting a "linguistic framework". (shrink)

Let “explanationism” be the view that ontology is fundamentally an explanatory enterprise. What it does is “on a par” with natural science, as Quine put it. Carnap appears to offer a “lighter weight” alternative in “Empiricism, Semantics, and Ontology”: ontology is concerned with semantics and language choice. This paper argues that Carnap’s account of the internal/external distinction is of less use than Carnap suggests for diagnosis of disputes in ontology. But he largely agrees with Quine about explanationism. I propose that (...) explanationism is an attractive metametaphysical position between “heavy weight” and “light weight” views. Its method is abductive inference, which is broader than “light weight” methods. Since it is “on a par” with natural science, ontology contributes nothing beyond the claim that what there is, is what our best theories say there is. Hence, it is not “heavy weight”. (shrink)

What are scientific models? Philosophers of science have been trying to answer this question during the last three decades by putting forward a number of different proposals. Some say that models are best understood as abstract Platonic objects or fictional entities akin to Sherlock Holmes, while others focus on their mathematical nature and see them as set theoretical structures. Although each account has its own strengths in offering various insights on the nature of models, several objections have been raised against (...) these views which still remain unanswered, making the debate on the ontology of models seem unresolvable. The primary aim of this paper is to show that a large part of these difficulties stems from an inappropriate reading of the main question on the ontology of models as a purely metaphysical question. Building on Carnap, it is argued that the question of the ontology of scientific models is either an internal theoretical question within an already accepted linguistic framework or an external practical question regarding the choice of the most appropriate form of language in order to describe and explain the practice of scientific modelling. The main implication of this view is that the question of the ontology of models becomes a means of probing other related questions regarding the overall practice of scientific modelling, such as questions on the capacity of models to provide knowledge and the relation of models with background theories. (shrink)

Carnap was one of the first to use the term 'non-cognitivism'. His linguistic pluralism and voluntarism, and his deflationary views of ontology and semantics, are highly congenial to those of us who want to take non-cognitivism in the direction of global expressivism. In his own case, however, this move is in tension with his continued endorsement of what he calls 'the general thesis of logical empiricism', that 'there is no third kind of knowledge besides empirical and logical knowledge.’ So while (...) Carnap clears a path towards global expressivism, he doesn't seem to appreciate what it requires him to leave behind. (shrink)

This chapter analyzes several key themes in Kant’s views about modality. We begin with the pre-critical Only Possible Argument in Support of a Demonstration of the Existence of God, in which Kant distinguishes between formal and material elements of possibility, claims that all possibility requires an actual ground, and argues for the existence of a single necessary being. We then briefly consider how Kant’s views change in his mature period, especially concerning the role of form and thought in defining modality. (...) Kant’s mature views, however, present two difficult interpretive puzzles. The first puzzle concerns whether Kant has a generally reductive view of modality. While Kant’s views on logical modality, the role of actuality in grounding possibility, and the relation of modality to cognition all suggest reduction, we argue that the categorial status of modal concepts and the difficulty in even identifying amodal grounds for modal facts all suggest a non-reductive view. The second puzzle concerns whether Kant accepts modal facts or properties at the noumenal level. While Kant’s appeal to noumenal necessary connections, the contingency of noumenal willing, and the idea of a necessary noumenal being suggest that he endorses noumenal modality, his claims that modal concepts express only relations to the faculty of cognition and his claim that modal concepts arise from our distinctive psychological structures, we argue, suggest that he rejects noumenal modality. We conclude by considering potential solutions to these puzzles. (shrink)