‘Mapping accounts’ of applied mathematics hold that the application of mathematics in physical science is best understood in terms of ‘mappings’ between mathematical structures and physical structures. In this paper, I suggest that mapping accounts rely on the assumption that the mathematics relevant to any application of mathematics in empirical science can be captured in an appropriate mathematical structure. If we are interested in assessing the plausibility of mapping accounts, we must ask ourselves: how plausible is this assumption as a (...) working hypothesis about applied mathematics? In order to do so, we examine the role played by mathematics in the multiscalar modelling of sea ice melting behaviour and examine whether we can indeed capture the mathematics involved in the kind of mathematical structure employed by the mapping account. Along the way, we note that the cases of applied mathematics that appear in discussions of mapping accounts almost exclusively involve the employment of a single clearly circumscribed mathematical field or domain. While the core assumption of mapping accounts may appear plausible in such situations, we ultimately suggest that the mapping account is not able to handle the important added complexities involved in our sea ice case study. In particular, the notion of mathematical structure around which such accounts are framed does not seem to be able to capture the way in which some applications of mathematics require that very different pieces of mathematics be related to one another on the basis of both mathematical and empirical information. (shrink)

The quality of philosophical diagnosis within the philosophy of science will be greatly improved if the original distinctions of applied mathematics are employed instead of the inadequate substitutes provided by the logical empiricists. The problem of evaluating counterfactual claims is examined from this point of view.

What are the pillars on which the success of modern science rest? Although philosophers have much discussed what is behind science’s success, this paper argues that much of the discussion is misdirected. The extant literature rightly regards the semantic and inferential tools of formal logic and probability theory as pillars of scientific rationality, in the sense that they reveal the justificatory structure of important aspects of scientific practice. As key elements of our rational reconstruction toolbox, they make a fundamental contribution (...) to our understanding of the success of science.At the same time, any science, however exact, is dominated by approximation, error, and uncertainty, a fact that makes one wonder how science can be so successful. This paper articulates and illustrates general themes—e.g., that truth-preserving arguments often fail to preserve approximate truth—that highlight the need for additional semantic resources. Thus, our proposal is that persistent failures to unravel the reasons behind the success of science in the face of pervasive error and uncertainty should be attributed to an insufficiently rich way of rationally reconstructing scientific and mathematical knowledge. What is missing? This paper claims that there is a third formal method of reasoning that constitutes a distinct pillar on which rests the success of science, namely, perturbation theory. The paper outlines how the representational and inferential tools of perturbation theory differ from those of logic and probability theory, and how they enable us to understand the apparently elusive aspects of the success of science.However, compared to its peers, perturbative reasoning has not received the attention it deserves. As the paper explains, this partly results from the circumstances in which perturbation theory is taught, and partly from the fact that perturbation theory first appears to be a vaguely related collection of methods offering no systematic semantic insight. In an attempt to show that this first impression is wrong, this paper presents its contribution to the semantic dimension of scientific representation and inference in terms of what I call “semantic layering.”. (shrink)

Mark Wilson presents a highly original account of conceptual behavior that challenges many received views about concepts in analytic philosophy. Few attempts have been made to rationally reconstruct Wilson’s framework of patches and facades within a precise semantic framework. I will show how a modified version of the structuralist framework offers a semantic reconstruction of scientific theories capable of modeling Wilson’s ideas about conceptual behavior. Specifically, I will argue that Theory-Elements and a modified version of Theory-Nets explicate respectively Wilson’s patches (...) and facades. I will also demonstrate how several wandering phenomena described by Wilson can be adequately reconstructed within my framework. (shrink)

A common strategy for simplifying complex systems involves partitioning them into subsystems whose behaviors are roughly independent of one another at shorter timescales. Dynamic causal models clarify how doing so reveals a system’s nonequilibrium causal relationships. Here I use these models to elucidate the idealizations and abstractions involved in representing a system at a timescale. The models reveal that key features of causal representations—such as which variables are exogenous—may vary with the timescale at which a system is considered. This has (...) implications for debates regarding which systems can be represented causally. (shrink)

As a philosophical paradigm, differential heterogenesis offers us a novel descriptive vantage with which to inscribe Deleuze’s virtuality within the terrain of “differential becoming,” conjugating “pure saliences” so as to parse economies, microhistories, insurgencies, and epistemological evolutionary processes that can be conceived of independently from their representational form. Unlike Gestalt theory’s oppositional constructions, the advantage of this aperture is that it posits a dynamic context to both media and its analysis, rendering them functionally tractable and set in relation to other (...) objects, rather than as sedentary identities. Surveying the genealogy of differential heterogenesis with particular interest in the legacy of Lautman’s dialectic, I make the case for a reading of the Deleuzean virtual that departs from an event-oriented approach, galvanizing Sarti and Citti’s dynamic a priori vis-à-vis Deleuze’s philosophy of difference. Specifically, I posit differential heterogenesis as frame with which to examine our contemporaneous epistemic shift as it relates to multi-scalar computational modeling while paying particular attention to neuro-inferential modes of inductive learning and homologous cognitive architecture. Carving a bricolage between Mark Wilson’s work on the “greediness of scales” and Deleuze’s “scales of reality”, this project threads between static ecologies and active externalism vis-à-vis endocentric frames of reference and syntactical scaffolding. (shrink)

Recent work in the philosophy of scientific concepts has seen the simultaneous revival of operationalism and development of patchwork approaches to scientific concepts. We argue that these two approaches are natural allies. Both recognize an important role for measurement techniques in giving meaning to scientific terms. The association of multiple techniques with a single term, however, raises the threat of proliferating concepts (Hempel, 1966). While contemporary operationalists have developed some resources to address this challenge, these resources are inadequate to account (...) for the full range of complex behaviors of scientific concepts. We adopt show how the patchwork approach’s repertoire of inter-patch relations can expand the resources available to the operationalist. We focus on one especially important type of inter-patch relation: sharing a general reasoning strategy. General reasoning strategies serve two important functions: (1) they bind together distinct patches of scientific concepts, and (2) they provide normative guidance for extending concepts to new domains. (shrink)

The word “effective” has become the standard label attached to scientific theories these days. An effective theory allows us to make accurate predictions about a physical system at a certain (energy, length) scale while being largely ignorant of the details at more fundamental levels. One does not need to know anything about the deeper, quantum structure of water molecules to describe the macroscopic behaviour of waves or water in a glass. Although effective descriptions so broadly construed have been part of (...) research in physics since the earliest stages of modern science, it is particle physics that has most clearly relied on and brought to the fore some of the most interesting and admittedly puzzling aspects of this way of looking at theories. Indeed, the effective field theory (EFT) program in QFT has established itself as the most natural way to understand renormalisation and dissipate initial reservations about the status of these techniques by treating higher-order processes as contributions suppressed at lower energy scales. QFT is thus treated as the “effective” framework par excellence with the decoupling of scales constituting its permeating tenet. The goal of this project is to attempt a philosophical appraisal of EFTs as currently used in high energy physics as well as assess the possibility that the whole program eventually breaks down, i.e. fails to apply when certain preconditions do not hold. Accordingly, the dissertation is logically divided into two parts with the first two chapters dedicated to discussion of the relation between EFTs and traditional questions in the philosophy of science concerning the structure of scientific theories, the formulation and defence of scientific realism as well as its connection to possible ontological readings of EFTs. The second part constitutes an analysis of two well-known problems that have been accorded the status of crises in the physics literature: the hierarchy problem and the cosmological constant problem. Our main focus will be to uncover those assumptions responsible for undermining the validity of the EFT techniques in their respective context. In light of this analysis, we will ultimately lean towards a more cautionary or “reserved” approach to EFTs. (shrink)

Are plants conscious? Most knowledgeable people say they aren't. A small minority say they are. Others say we don't know. Virtually all assume the predicate '– is conscious' is fully determinate; plants are or aren't in its extension. Appealing to Mark Wilson's work on predicates and concepts, I challenge that assumption, proposing that the predicate isn't determinate for plants. I offer the start of an explanation for why this is so. We tacitly rely on many empirical correlations when we correctly (...) characterize creatures as conscious, but we have limited knowledge of those facts, and plants differ significantly from animals, while also being substantively similar to them. We don't yet know what it would be for them to be conscious. (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)

Despite being one of the most dependable methods used by applied mathematicians and engineers in handling complex systems, the finite element method commits variational crimes. This paper contextualizes the concept of variational crime within a broader account of mathematical practice by explaining the tradeoff between complexity and accuracy involved in the construction of numerical methods. We articulate two standards of accuracy used to determine whether inexact solutions are good enough and show that, despite violating the justificatory principles of one, the (...) finite element method nevertheless succeeds in obtaining its legitimacy from the other. (shrink)

Original explorers often see a puzzling conceptual landscape more vividly than jaded later travelers. This essay surveys several ways in which Descartes and Leibniz recognized descriptive problems within applied mathematics more clearly than later commentators have appreciated.

Contrary to the common-sense view and positivist aspirations, scientific concepts are often imprecise. Many of these concepts are ambiguous, vague, or have an under-specified meaning. In this paper, I discuss how imprecise concepts promote integration in biology and thus benefit science. Previous discussions of this issue focus on the concepts of molecular gene and evolutionary novelty. The concept of molecular gene helps biologists integrate explanatory practices, while the notion of evolutionary novelty helps them integrate research questions into an interdisciplinary problem (...) New directions in the philosophy of science, Springer, Dordrecht, 2014). In what follows, I compare molecular gene and evolutionary novelty to another imprecise concept, namely biological lineage. This concept promotes two other types of scientific integration: it helps biologists integrate theoretical principles and methodologies into different areas of biology. The concept of biological lineage facilitates these types of integration because it is broad and under-specified in ways that the concepts of molecular gene and evolutionary novelty are not. Hence, I use the concept of biological lineage as a case study to reveal types of integration that have been overlooked by philosophers. This case study also shows that even very imprecise concepts can be beneficial to scientific practice. (shrink)

Multiscale modeling techniques have attracted increasing attention by philosophers of science, but the resulting discussions have almost exclusively focused on issues surrounding explanation (e.g., reduction and emergence). In this paper, I argue that besides explanation, multiscale techniques can serve important exploratory functions when scientists model systems whose organization at different scales is ill-understood. My account distinguishes explanatory and descriptive multiscale modeling based on which epistemic goal scientists aim to achieve when using multiscale techniques. In explanatory multiscale modeling, scientists use multiscale (...) techniques to select information that is relevant to explain a particular type of behavior of the target system. In descriptive multiscale modeling scientists use multiscale techniques to explore lower-scale features which could be explanatorily relevant to many different types of behavior, and to determine which features of a target system an upper-scale data pattern could refer to. Using multiscale models from data-driven neuroscience as a case study, I argue that descriptive multiscale models have an exploratory function because they are a sources of potential explanations and serve as tools to reassess our conception of the target system. (shrink)