The foremost aim of this paper is to realize the fourth part of the Aufbau. This part, which provides an actual phenomenalistic constitution system, is interpretable from a Kantian perspective (§§1-4). But Carnap plotted to overcome Kant’s old style of philosophy as well. We review this aspect of his constitution, focusing on space (§§7-13) and time (§§5-6), especially.

In a famous critique, Goodman dismissed similarity as a slippery and both philosophically and scientifically useless notion. We revisit his critique in the light of important recent work on similarity in psychology and cognitive science. Specifically, we use Tversky’s influential set-theoretic account of similarity as well as Gärdenfors’s more recent resuscitation of the geometrical account to show that, while Goodman’s critique contained valuable insights, it does not warrant a dismissal of similarity.

The aim of this paper is to propose a qualitative approach to the theory of conceptual spaces, in contrast to the usual metric framework. This requires qualitative notions of similarity, simple concepts, prototypes and conceptual categorisation. For this purpose, I will introduce three mathematical models for conceptual spaces. The first one is topological and has been proposed by Mormann. The other two are new and are based on atomistic orders and similarity relations. I will discuss how each of them deals (...) with the Design Principles proposed by Douven and Gärdenfors and with further Adequacy Conditions. Despite being apparently different, I will show that these three models are mathematically equivalent. Finally, I will address three objections to the present approach. The first one says that the qualitative notion of a prototype is a bad analogue of the metric one. The second one suggests that, in contrast to the Voronoi construction, the function qualitatively representing the conceptual categorisation process is arbitrary. The last one appeals to Goodman’s companionship and imperfect community problems to show that there is a flaw in defining simple concepts from similarity relations. (shrink)

Rudolf Carnap's Der logische Aufbau der Welt (The Logical Structure of the World) is generally conceived of as being the failed manifesto of logical positivism. In this paper we will consider the following question: How much of the Aufbau can actually be saved? We will argue that there is an adaptation of the old system which satisfies many of the demands of the original programme. In order to defend this thesis, we have to show how a new 'Aufbau-like' programme may (...) solve or circumvent the problems that affected the original Aufbau project. In particular, we are going to focus on how a new system may address the well-known difficulties in Carnap's Aufbau concerning abstraction, dimensionality, and theoretical terms. (shrink)

How should we understand the relationship between the contents of our color, causal, modal, and evaluative beliefs, on the one hand, and color, causal, modal, and evaluative properties, on the other? According to Barry Stroud (2011), because of the nature of the contents of those types of beliefs, we should also think that what he calls a “negative metaphysical verdict” on the latter is not one that we could consistently maintain. The metaphysical project aims to arrive at an improved conception (...) of ourselves and our relation the world, no matter if that conception is positive or negative. But if Stroud is right that we cannot consistently arrive at the view that all of our causal, modal, and evaluative beliefs are systematically false, we will see that we cannot consistently reach the negative verdict. But failure to reach the negative verdict doesn’t mean that we have reached the positive verdict. Stroud calls this philosophical failure “metaphysical dissatisfaction”. In this paper, I argue that we can appropriate a metaepistemological response to the problem of the external world which shares its core features with Stroud’s (2000, 2011) arguments, but which nevertheless leaves us with a distinctive kind of epistemological dissatisfaction. (shrink)

This thesis focuses on models of conceptual change in science and philosophy. In particular, I developed a new bootstrapping methodology for studying conceptual change, centered around the formalization of several popular models of conceptual change and the collective assessment of their improved formal versions via nine evaluative dimensions. Among the models of conceptual change treated in the thesis are Carnap’s explication, Lakatos’ concept-stretching, Toulmin’s conceptual populations, Waismann’s open texture, Mark Wilson’s patches and facades, Sneed’s structuralism, and Paul Thagard’s conceptual revolutions. (...) -/- In order to analyze and compare the conception of conceptual change provided by these different models, I rely on several historical reconstructions of episodes of scientific conceptual change. The historical episodes of scientific change that figure in this work include the emergence of the morphological concept of fish in biological taxonomies, the development of scientific conceptions of temperature, the Church-Turing thesis and related axiomatizations of effective calculability, the history of the concept of polyhedron in 17th and 18th century mathematics, Hamilton’s invention of the quaternions, the history of the pre-abstract group concepts in 18th and 19th century mathematics, the expansion of Newtonian mechanics to viscous fluids forces phenomena, and the chemical revolution. I will also present five different formal and informal improvements of four specific models of conceptual change. I will first present two different improvements of Carnapian explication, a formal and an informal one. My informal improvement of Carnapian explication will consist of a more fine-grained version of the procedure that adds an intermediate, third step to the two steps of Carnapian explication. I will show how this novel three-step version of explication is more suitable than its traditional two-step relative to handle complex cases of explications. My second, formal improvement of Carnapian explication will be a full explication of the concept of explication itself within the theory of conceptual spaces. By virtue of this formal improvement, the whole procedure of explication together with its application procedures and its pragmatic desiderata will be reconceptualized as a precise procedure involving topological and geometrical constraints inside the theory of conceptual spaces. My third improved model of conceptual change will consist of a formal explication of Darwinian models of conceptual change that will make vast use of Godfrey-Smith’s population-based Darwinism for targeting explicitly mathematical conceptual change. My fourth improvement will be dedicated instead to Wilson’s indeterminate model of conceptual change. I will show how Wilson’s very informal framework can be explicated within a modified version of the structuralist model-theoretic reconstructions of scientific theories. Finally, the fifth improved model of conceptual change will be a belief-revision-like logical framework that reconstructs Thagard’s model of conceptual revolution as specific revision and contraction operations that work on conceptual structures. -/- At the end of this work, a general conception of conceptual change in science and philosophy emerges, thanks to the combined action of the three layers of my methodology. This conception takes conceptual change to be a multi-faceted phenomenon centered around the dynamics of groups of concepts. According to this conception, concepts are best reconstructed as plastic and inter-subjective entities equipped with a non-trivial internal structure and subject to a certain degree of localized holism. Furthermore, conceptual dynamics can be judged from a weakly normative perspective, bound to be dependent on shared values and goals. Conceptual change is then best understood, according to this conception, as a ubiquitous phenomenon underlying all of our intellectual activities, from science to ordinary linguistic practices. As such, conceptual change does not pose any particular problem to value-laden notions of scientific progress, objectivity, and realism. At the same time, this conception prompts all our concept-driven intellectual activities, including philosophical and metaphilosophical reflections, to take into serious consideration the phenomenon of conceptual change. An important consequence of this conception, and of the analysis that generated it, is in fact that an adequate understanding of the dynamics of philosophical concepts is a prerequisite for analytic philosophy to develop a realistic and non-idealized depiction of itself and its activities. (shrink)

Traditional approaches to the semantics of questions analyze questions indirectly, via the notion of an answer. In recent work on inquisitive semantics, a different perspective is taken: the meaning of a question is equated with its resolution conditions, just like the meaning of a statement is traditionally equated with its truth-conditions. In this paper I argue that this proposal improves on previous approaches, combining the formal elegance and explanatory power of Groenendijk and Stokhof’s partition theory with the greater generality afforded (...) by answer-set theories. (shrink)

This paper contains answers to the following Five questions, posed by the editors are answered: (1) Why were you initially drawn to the foundations of mathematics and/or the philosophy of mathematics? (2) What example(s) from your work (or the work of others) illustrates the use of mathematics for philosophy? (3) What is the proper role of philosophy of mathematics in relation to logic, foundations of mathematics, the traditional core areas of mathematics, and science? (4) What do you consider the most (...) neglected topics and/or contributions in late 20th century philosophy of mathematics? (5) What are the most important open problems in the philosophy of mathematics and what are the prospects for progress? (shrink)

The paper outlines a novel version of mathematical structuralism related to invariants. The main objective here is twofold: first, to present a formal theory of structures based on the structuralist methodology underlying work with invariants. Second, to show that the resulting framework allows one to model several typical operations in modern mathematical practice: the comparison of invariants in terms of their distinctive power, the bundling of incomparable invariants to increase their collective strength, as well as a heuristic principle related to (...) the search for new invariants. (shrink)

In Our Knowledge of the Internal World, Robert Stalnaker describes two opposed perspectives on the relation between the internal and the external. According to one, the internal world is taken as given and the external world as problematic, and according to the other, the external world is taken as given and the internal world as problematic. Analytic philosophy moved from the former to the latter, from problems of world-construction to problems of self-locating beliefs. I argue in this paper that these (...) problems are equivalent: both arise because experience and objective, external facts jointly underdetermine their relation. Both can be seen as a problem of expressive completeness; of the internal language in the former case, and of the non-indexical language in the second. (shrink)

This paper argues for the theoretical and practical validity of similarity as a useful epistemological tool in scientific knowledge generation, specifically in chemistry. Classical analyses of similarity in philosophy of science do not account for the concept’s practical significance in scientific activities. We recur to examples from chemistry to counter the claim of authors like Quine or Goodman to the effect that similarity must be excluded from scientific practices . In conclusion we argue that more recent conceptualizations of the notion (...) of similarity, particularly Giere’s one, are appropriate for a philosophical analysis that considers scientific practices on equal terms with scientific theory. (shrink)