Understanding scientific modelling can be divided into two sub-projects: analysing what model-systems are, and understanding how they are used to represent something beyond themselves. The first is a prerequisite for the second: we can only start analysing how representation works once we understand the intrinsic character of the vehicle that does the representing. Coming to terms with this issue is the project of the first half of this chapter. My central contention is that models are akin to places and characters (...) of literary fictions, and that therefore theories of fiction play an essential role in explaining the nature of model-systems. This sets the agenda. Section 2 provides a statement of this view, which I label the fiction view of model-systems, and argues for its prima facie plausibility. Section 3 presents a defence of this view against its main rival, the structuralist conception of models. In Section 4 I develop an account of model-systems as imagined objects on the basis of the so-called pretence theory of fiction. This theory needs to be discussed in great detail for two reasons. First, developing an acceptable account of imagined objects is mandatory to make the fiction view acceptable, and I will show that the pretence theory has the resources to achieve this goal. Second, the term ‘representation’ is ambiguous; in fact, there are two very different relations that are commonly called ‘representation’ and a conflation between the two is the root of some of the problems that beset scientific representation. Pretence theory provides us with the conceptual resources to articulate these two different forms of representation, which I call p-representation and t-representation respectively. Putting these elements together provides us with a coherent overall picture of scientific modelling, which I develop in Section 5. (shrink)

We develop a new metaphor account where metaphors become surrogate variables for different but related phenomena. As we will argue, subrogation is the result of the interplay between the things inspired by the metaphor and the empirical dynamics that result from such inspiration. In particular, we focus on adaptive radiation, a major concept of evolutionary biology. Our study suggests that there is no distinct phenomenon, process, or pattern in nature than can be identified as adaptive radiation. What we have instead (...) is a grouping variable that has surrogated different evolutionary phenomena into one expansive label. We believe this analysis of metaphors helps better understand the value of metaphors for science not only as a provider of epistemic and cognitive virtues but most importantly, as a crucial research tool that can both help and divert scientific experimentation. (shrink)

This paper discusses Baker’s Enhanced Indispensability Argument for mathematical realism on the basis of the indispensable role mathematics plays in scientific explanations of physical facts, along with various responses to it. I argue that there is an analogue of causal explanation for mathematics which, of several basic types of explanation, holds the most promise for use in the EIA. I consider a plausible case where mathematics plays an explanatory role in this sense, but argue that such use still does not (...) support realism about mathematical objects. (shrink)

I argue that everyday folk-psychological skill might best be explained in terms of the deployment of something like a model, in a specific sense drawn from recent philosophy of science. Theoretical models in this sense do not make definite commitments about the systems they are used to understand; they are employed with a particular kind of flexibility. This analysis is used to dissolve the eliminativism debate of the 1980s, and to transform a number of other questions about the status and (...) role of folk psychology. (shrink)

In this paper, I briefly present the regularity and necessity views and assess their difficulties. I construe scientific laws as universal propositions satisfied by empirically successful scientific models and made — approximately — true by the real systems represented, albeit partially, by these models. I also conceive a scientific theory as a set of models together with a set of propositions, some of which are laws. A scientific law is a universal proposition or statement that belongs to a scientific theory. (...) Scientific laws also are laws of nature since we can provide arguments in favour of natural causal powers that ground the truth of laws. I argue that the truth of counterfactual conditional statements and the occurrence of regularities in nature provide good reasons to believe that real causal powers exist in nature and that the truth of scientific laws is based on a metaphysics of nature. (shrink)

The context of an operational description is given by the distinction between what we consider as relevant and what as irrelevant for a particular experiment or observation. A rigorous description of a context in terms of a mathematically formulated context-independent fundamental theory is possible by the restriction of the domain of the basic theory and the introduction of a new coarser topology. Such a new topology is never given by first principles, but depends in a crucial way on the abstractions (...) made by the cognitive apparatus or the pattern recognition devices used by the experimentalist. A consistent mathematical formulation of a higher-level theory requires the closure of the restriction of the basic theory in the new contextual topology. The validity domain of the so constructed higher-level theory intersects nontrivially with the validity domain of the basic theory: neither domain is contained in the other. Therefore, higher-level theories cannot be totally ordered and theory reduction is not transitive. The emergence of qualitatively new properties is a necessary consequence of such a formulation of theory reduction (which does not correspond to the traditional one). Emergent properties are not manifest on the level of the basic theory, but they can be derived rigorously by imposing new, contextually selected topologies upon context-independent first principles. Most intertheoretical relations are mathematically describable as singular asymptotic expansions which do not converge in the topology of the primary theory, or by choosing one of the infinitely many possible, physically inequivalent representations of the primary theory (Gelfand–Naimark–Segal-construction of algebraic quantum mechanics). As examples we discuss the emergence of shadows, inductors, capacitors and resistors from Maxwell’s electrodynamics, the emergence of order parameters in statistical mechanics, the emergence of mass as a classical observable in Galilei-relativistic theories, the emergence of the shape of molecules in quantum mechanics, the emergence of temperature and other classical observables in algebraic quantum mechanics. (shrink)

This is a defense of the doctrine of scientific realism. SR is defined through the following two claims: Most essential unobservables posited by the well-established current scientific theories exist independently of our minds. We know our well-established scientific theories to be approximately true. I first offer positive argumentation for SR. I begin with the so-called 'success arguments' for SR: 1) scientific theories most of the times entail successful predictions; 2) science is methodologically successful in generating empirically successful theories. SR explains (...) these facts via inference to the best explanation. I combine Hacking's experimental argument for entity realism with Salmon's common-cause principle. I take entity realism to be foundational to SR: one may believe in the existence of some theoretical entities without believing in any particular theory in which these are embedded. Its motivation comes from experimental practice, where the manipulation of these entities often relies on incompatible theoretical accounts. The underdetermination topic is thereafter discussed. Several attempts to distinguish between an observable and an unobservable realm are critically discussed, as well as the possibility that for any given theory, there are empirically equivalents generated by means of algorithms. I present extensive argumentation to the effect that such algorithmic rivals are not to be taken seriously. Social constructivism is being critically treated. I proceed by distinguishing between a metaphysical, a semantic, and an epistemic variant of SC. I conclude that only a moderate metaphysical constructivism can stand on its own feet. Its claim is merely that some facts about the world are socially constructed. I finish with a plea for a selective SR, able to do justice to the presence of both instrumentalism and modest constructivism in scientific practice. (shrink)

Examining the role of dispositions (potentials and propensities) in both physics and psychology reveals that they are commonly derivative dispositions, so called because they derive from other dispositions. Furthermore, when they act, they produce further propensities. Together, therefore, they appear to form discrete degrees within a structure of multiple generative levels. It is then constructively hypothesized that minds and physical nature are themselves discrete degrees within some more universal structure. This gives rise to an effective dualism of mind and nature, (...) but one according to which they are still constantly related by causal connections. I suggest a few of the unified principles of operation of this more complicated but universal structure. (shrink)

The central question of this thesis is how one can learn about particular targets by using models of those targets. A widespread assumption is that models have to be representative models in order to foster knowledge about targets. Thus the thesis begins by examining the concept of representation from an epistemic point of view and supports an account of representation that does not distinguish between representation simpliciter and adequate representation. Representation, understood in the sense of a representative model, is regarded (...) as a success term. That is, a representative model is one relatum in a relation of adequate representation (Chapter 2). When a representative model represents a target, it allows users of this model to learn something about the target. It is argued that a representative model has this epistemic function because it shares relevant features with the target. This presupposes a similarity view of representation. Similarity views of representation face serious objections, which will be rebutted (Chapter 3). One way of spelling out a similarity view of representation is to defend an indirect view of representation. In this thesis, which does not argue for an indirect view, it is assumed that the indirect view is a good option, if not the best, for articulating the similarity view. It is demonstrated how such an indirect view can be expanded to account for cases of technological modeling. A case study in bioengineering is used to show that the indirect view of representation must acknowledge a distinction between two directions of fit in relations between vehicles and targets. In this context the notion of design is interpreted as a relation between a vehicle and a target, thereby connecting ideas from philosophy of science with ideas from philosophy of technology (Chapter 4). Fictionalist accounts of models are intended to tackle the issue of the ontology of models. In this thesis, however, two prominent fictionalist accounts are discussed from an epistemological point of view in light of the central question regarding how one can learn about targets by using models. This question is addressed from the standpoint of Waltonian fictionalism. The result of the discussion is that the two discussed Waltonian fictionalist accounts cannot sufficiently answer the question. These accounts are criticized for their inability to deliver a satisfactory epistemology of representation (Chapter 5). Although Waltonian fictionalism is criticized, the present thesis also shows that the foundational theory of Waltonian fictionalism, the theory of make-believe can nevertheless be used to account for the distinction between projections and predictions that is made by the Intergovernmental Panel on Climate Change (Chapter 6). (shrink)

What if your peers tell you that you should disregard your perceptions? Worse, what if your peers tell you to disregard the testimony of your peers? How should we respond if we get evidence that seems to undermine our epistemic rules? Several philosophers have argued that some epistemic rules are indefeasible. I will argue that all epistemic rules are defeasible. The result is a kind of epistemic particularism, according to which there are no simple rules connecting descriptive and normative facts. (...) I will argue that this type of particularism is more plausible in epistemology than in ethics. The result is an unwieldy and possibly infinitely long epistemic rule — an Uber-rule. I will argue that the Uber-rule applies to all agents, but is still defeasible — one may get misleading evidence against it and rationally lower one’s credence in it. (shrink)

The discovery of high-level causal relations seems a central activity of the special sciences. Those same sciences are less successful in formulating strict laws. If causation must be underwritten by strict laws, we are faced with a puzzle, which might be dubbed the 'no strict laws' problem for high-level causation. Attempts have been made to dissolve this problem by showing that leading theories of causation do not in fact require that causation be underwritten by strict laws. But this conclusion has (...) been too hastily drawn. Philosophers have tended to equate non-strict laws with ceteris paribus laws. I argue that there is another category of non-strict law that has often not been properly distinguished: namely, minutiae rectus laws. If, as it appears, many special science laws are minutiae rectus laws, then this poses a problem for their ability to underwrite causal relations in a way that their typically ceteris paribus nature does not. I argue that the best prospect for resolving the resurgent 'no strict laws' problem is to argue that special science laws are in fact typically probabilistic, rather than being minutiae rectus laws. (shrink)

In the face of causal complexity, scientists reconstitute phenomena in order to arrive at a more simplified and partial picture that ignores most of the 'bigger picture.' This paper will distinguish between two modes of reconstituting phenomena: one moving down to a level of greater decomposition (toward organizational parts of the original phenomenon), and one moving up to a level of greater abstraction (toward different differences regarding the phenomenon). The first aim of the paper is to illustrate that phenomena are (...) moving targets, i.e., they are not fixed once and for all, but are adapted, if necessary, on the basis of the preferred perspective adopted for pragmatic reasons. The second aim is to analyze in detail the second mode of reconstituting phenomena. This includes an exposition of the kind of pragmatic-pluralistic picture resulting from the fact that phenomena are reconstituted by a move up to a level of greater abstraction. (shrink)

Associate Professor | Director and President Department of Philosophy | Molinari Institute 6080 Haley Center, Auburn University Auburn AL 36849 USA email: [email protected] URL: praxeology.net..

The frame problem is a problem in artificial intelligence that a number of philosophers have claimed has philosophical relevance. The structure of this paper is as follows: (1) An account of the frame problem is given; (2) The frame problem is distinguished from related problems; (3) The main strategies for dealing with the frame problem are outlined; (4) A difference between commonsense reasoning and prediction using a scientific theory is argued for; (5) Some implications for the..

Contemporary sociology of scientific knowledge (SSK) is defined by its relativist trend. Its programme often calls for the support of philosophers, such as Duhem, Quine, and Wittgenstein. A critical re-reading of key texts shows that the main principles of relativism are only derivable with difficulty. The thesis of the underdetermination of theory doesn't forbid that Duhem, in many places, validates a correspondence-consistency theory of truth. He never said that social beliefs and interests fill the lack of underdetermination. Quine's idea of (...) a selective revision of hypotheses, as well as the neat incompatibility between holism and conventionalism, openly challenges the principles of relativism. Wittgenstein's work, which is not presented in book-form but rather as a tree, forces us to avoid aphoristic choices that credit any text-excising. This remark allows us to tackle the passages that sociological relativism is based on.Mathematical conventions are not anthropological objects. When Wittgenstein examines the "language-games," he only speaks of the functioning of natural language, not to be confused with scientific formal languages. We then should render the formula "language-game" by "well-defined, explicit and compulsory rules of communication", which is a much less attractive formula for relativism. Consequently, there does not exist a real continuity between the epistemologies of Duhem, Quine and Wittgenstein, and the recent works of the SSK. (shrink)

Key words: the continuum, structuralism, conceptual structuralism, basic structural conceptions, Euclidean geometry, Hilbertian geometry, the real number system, settheoretical conceptions, phenomenological conceptions, foundational conceptions, physical conceptions.

The talk given on 10 January 2017 during the workshop "The Arbitrariness of the Sign" at "Le cours de linguistique générale 1916-2016" conference in Geneva.

Fundamental theories are hard to come by. But even if we had them, they would be too complicated to apply. Quantum chromodynamics is a case in point. This theory is supposed to govern all strong interactions, but it is extremely hard to apply and test at energies where protons, neutrons and ions are the effective degrees of freedom. Instead, scientists typically use highly idealized models such as the MIT Bag Model or the Nambu Jona-Lasinio Model to account for phenomena in (...) this domain, to explain them and to gain nderstanding. Based on these models, which typically isolate a single feature of QCD and disregard many others, scientists attempt to get a better understanding of the physics of strong interactions. But does this practice make sense? Is it justified to use these models for the purposes at hand? Interestingly, these models do not even provide an accurate description of the mass spectrum of protons, neutrons and pions and their lowest lying excitations well - despite several adjustable parameters. And yet, the models are heavily used. I'll argue that a qualitative story, which establishes an explanatory link between the fundamental theory and a model, plays an important role in model acceptance in these cases. (shrink)

Traditional accounts of explanation fail to illuminate the explanatory relevance of “models that are descriptively false” in the sense that the regularities they entail fail to obtain. In this paper, I propose an account of explanation, which I call ‘explanation by concretization’, that serves to explicate the explanatory relevance of such models. Starting from a highly abstract and idealized model, causal explanations of the absence of regularities are sought by adding complexity to the model or by concretizing it. Whether this (...) process is successful depends on whether the abstractions and idealizations in the basic model succeed in isolating a mechanism, i.e. in representing how it operates when interfering factors are absent. This account is developed in the context of economics and contrasted to those of Daniel Hausman and Nancy Cartwright. I go on to provide an account of how unrealistic models can be used for providing understanding of the way mechanisms work. (shrink)

The paper discusses major implications of high energy physics for the scientific realism debate. The first part analyses the ways in which aspects of the empirically well-confirmed standard model of particle physics are relevant for a reassessment of entity realism, ontological realism and structural realism. The second part looks at the implications of more far-reaching concepts like string theory. While those theories have not found empirical confirmation, if they turned out viable, their implications for the realism debate would be more (...) substantial than those of the standard model. (shrink)

You are asked to call out the letters on a chart during an eyeexamination: you see and then read out the letters ‘U’, ‘R’, and ‘X’. Commonsense says that your perceptual experiences causally control your calling out the letters. Or suppose you are playing a game of chess intent on winning: you plan your strategy and move your chess pieces accordingly. Again, commonsense says that your intentions and plans causally control your moving the chess pieces. These causal judgements are as (...) plain and evident as any can be. (shrink)

In this paper I propose an account of representation for scientific models based on Kendall Walton’s ‘make-believe’ theory of representation in art. I first set out the problem of scientific representation and respond to a recent argument due to Craig Callender and Jonathan Cohen, which aims to show that the problem may be easily dismissed. I then introduce my account of models as props in games of make-believe and show how it offers a solution to the problem. Finally, I demonstrate (...) an important advantage my account has over other theories of scientific representation. All existing theories analyse scientific representation in terms of relations, such as similarity or denotation. By contrast, my account does not take representation in modelling to be essentially relational. For this reason, it can accommodate a group of models often ignored in discussions of scientific representation, namely models which are representational but which represent no actual object. (shrink)

Darcy's law is a phenomenological relationship for fluid flow rate that finds one of its principle applications in hydrology. Theoretical hydrologists rely upon a multiplicity of conceptual models to carry out approximate derivations of Darcy's law. These derivations provide structural explanations of the law; they require the application of fundamental principles, such as conservation of momentum, to idealized models of the porous media within which the flow occurs. In practice, recognition of the idealized conditions incorporated into models facilitates the empirical (...) clarification of the domain within which the law remains accurate. Structural explanations also contribute to the physical interpretation of phenomenological parameters. (shrink)

I am arguing that it is only by concentrating on the role of models in theory construction, interpretation and change, that one can study the progress of science sensibly. I define the level at which these models operate as a level above the purely empirical (consisting of various systems in reality) but also indeed below that of the fundamental formal theories (expressed linguistically). The essentially multi-interpretability of the theory at the general, abstract linguistic level, implies that it can potentially make (...) claims about systems in reality, other than the particular one which originally induced it. Any so-called correspondence relation between (systems in) reality and the entities and relations in some scientific theory, thus consists of two jumps or interpretations: from the theory (linguistic level) to some model of it (constructural level); and from there to some system in reality. Clearly then the level of fundamental theories cannot be ignored la Nancy Cartwright - in studying the relations between a theory and reality, because the particular features of the theory (the various systems in reality onto which the theory can be mapped) cannot be studied without the underlying knowledge that these systems have one common feature, namely that each of them is the range (or other pole) of a mapping of a context-specific model of the theory - which in itself, is a mapping, or more specifically, an interpretation of the theory. I am also claiming that the nature of these levels and the relations between them necessitate an epistemological rather than an ontological notion of truth criteria, and a referential rather than a representational link between science and reality. (shrink)

The use of MABS (Multi-Agent Based Simulations) is analysed as the modelling of distributed (usually social) systems using MAS as the model structure. It is argued that rarely is direct modelling of target systems attempted but rather an abstraction of the target systems is modelled and insights gained about the abstraction then applied back to the target systems. The MABS modelling process is divided into six steps: abstraction, design, inference, analysis, interpretation and application. Some types of MABS papers are characterised (...) in terms of the steps they focus on and some criteria for good MABS formulated in terms of the soundness with which the steps are established. Finally some practical proposals that might improve the informativeness of the field are suggested. (shrink)

The paper bridges between a science-based metamathematical model of emerging truth and truth emerging from inquiry within ordinary contexts of argumentation. This requires that the underlying intuitions driving the notion of truth in the scientific image be made clear and analogues identified in a manner that permits their application within the ordinary contexts found in the manifest image.

According to Zurek, decoherence is a process resulting from the interaction between a quantum system and its environment; this process singles out a preferred set of states, usually called “pointer basis”, that determines which observables will receive definite values. This means that decoherence leads to a sort of selection which precludes all except a small subset of the states in the Hilbert space of the system from behaving in a classical manner: environment-induced-superselection (einselection) is a consequence of the process of (...) decoherence. The aim of this paper is to present a new approach to decoherence, different from the mainstream approach of Zurek and his collaborators. We will argue that this approach offers conceptual advantages over the traditional one when problems of foundations are considered; in particular, from the new perspective, decoherence in closed quantum systems becomes possible and the preferred basis acquires a well founded definition. (shrink)

John Earman and John T. Roberts advocate a challenging and radical claim regarding the semantics of laws in the special sciences: the statistical account. According to this account, a typical special science law “asserts a certain precisely defined statistical relation among well-defined variables” and this statistical relation does not require being hedged by ceteris paribus conditions. In this paper, we raise two objections against the attempt to cash out the content of special science generalizations in statistical terms.

In the philosophical tradition, the notions of determinism and causality are strongly linked: it is assumed that in a world of deterministic laws, causality may be said to reign supreme; and in any world where the causality is strong enough, determinism must hold. I will show that these alleged linkages are based on mistakes, and in fact get things almost completely wrong. In a deterministic world that is anything like ours, there is no room for genuine causation. Though there may (...) be stable enough macro-level regularities to serve the purposes of human agents, the sense of “causality” that can be maintained is one that will at best satisfy Humeans and pragmatists, not causal fundamentalists. (shrink)

Learning to construct good scientific explanations is an important aspect of learning science. To this end it is important to also consider that the detailed standards for good explanations differ across the sciences. Practitioners face these differences, for instance, when interdisciplinary work is attempted. This paper reports on a comparative qualitative study of exemplar explanations on polymers from molecular biology and polymer physics aiming to map the differences in standards for good explanations between the two domains. The study gives detail (...) to the theoretical expectation that mechanistic explanations are the ideal in molecular biology whereas derivations play the central role in polymer physics. Mechanistic explanations in molecular biology focus on material objects with a function-determining structure. In polymer physics derivations are the preferred kind of explanation. Derivations focus on variables, particularly, physical quantities like energy and entropy, whereas the three dimensional structure of polymers is often ignored. Differences in the kinds of explanations-seeking questions deemed relevant within the two domains are also identified. (shrink)

Josiah Parsons Cooke established chemistry education at Harvard University, initiated an atomic weight research program, and broadly impacted American chemical education through his students, the introduction of laboratory instruction, textbooks, and influence on Harvard's admissions requirements. The devoutly Unitarian Cooke also articulated and defended a biogeochemical natural theology, which he defended by arguing for commonalities between the epistemologies of science and religion. Cooke's pre-Mendeleev classification scheme for the elements and atomic weight research were motivated by his interest in numerical order (...) in nature, which reflected his belief in a divine lawgiver. (shrink)

Philosophical interpretations of theories generally presuppose that a theory can be presented as a consistent mathematical formulation that is interpreted through models. Algebraic quantum field theory (AQFT) can fit this interpretative model. However, standard Lagrangian quantum field theory (LQFT), as well as quantum electrodynamics and nuclear physics, resists recasting along such formal lines. The difference has a distinct bearing on ontological issues. AQFT does not treat particle interactions or the standard model. This paper develops a framework and methodology for interpreting (...) such informal theories as LQFT and the standard model. We begin by summarizing two minimal epistemological interpretation of non-relativistic quantum mechanics (NRQM): Bohrian semantics, which focuses on communicables; and quantum information theory, which focuses on the algebra of local observables. Schwinger's development of quantum field theory supplies a unique path from NRQM to QFT, where each step is conceptually anchored in local measurements. LQFT and the standard model rely on postulates that go beyond the limits set by AQFT and Schwinger's anabatic methodology. The particle ontology of the standard model is clarified by regarding the standard model as an informal modular theory with a limited range of validity. (shrink)

This paper analyses and criticizes the idea that powers are representable as vectors. Mumford and Anjum have recently developed a vector model of powers as part of their account of dispositional causation. The purpose of this model is to represent dispositionality, i.e. a sui generis type of modality introduced by their power-based ontology, as well as to explain various features of their account of causation. In this paper, we criticise both the claim that powers are vectors and the concomitant claim (...) that the composition of causes can be understood as vector addition. We argue that powers cannot be thought of as even analogous to vectors, and that the vector model is simply misleading. We show that the root of the problem is in Mumford and Anjum’s thought that powers have magnitude and direction. (shrink)

Polygenic effects have more than one cause. They testify to the fact that several causal contributors are sometimes simultaneously involved in causation. The importance of polygenic causation was noticed early on by Mill (1893). It has since been shown to be a problem for causal-law approaches to causation and accounts of causation cast in terms of capacities. However, polygenic causation needs to be examined more thoroughly in the emerging literature on causal mechanisms. In this paper I examine whether an influential (...) theory of mechanisms proposed by Peter Machamer, Lindley Darden and Carl Craver can accommodate polygenic effects and other forms of causal interaction. This theory is problematic, I will argue, because it ascribes a central role to activities. In it, activities are needed not only to constitute mechanisms but also to perform the causal role of mechanisms. Any such mechanism-as-activity will be incompatible with causal situations where either no or merely another kind of activity occurs. But, as I will try to illustrate in this paper, both kinds of situation may be frequent. If I am right, the view that Machamer and colleagues suggest leads to an impoverished conception of mechanism. (shrink)

This paper argues that there is no conflict between quantum theory and relativity, and that quantum theory itself helps us explain puzzling “non-local” correlations in a way that contradicts neither Bell’s intuitive locality principle nor his local causality condition. The argument depends on understanding quantum theory along pragmatist lines I have outlined elsewhere, and on a more general view of how that theory helps us explain. The key counterfactuals that hold in such cases manifest epistemic rather than causal connections between (...) distant events. Quantum theory exploits the possibility of private informational links between an agent and events he neither observes nor brings about, in ways that are strikingly independent of the spatiotemporal relations between them. This possibility has interesting implications for theories of chance in a relativistic world. (shrink)

Scientific models need to be investigated if they are to provide valuable information about the systems they represent. Surprisingly, the epistemological question of what enables this investigation has hardly been investigated. Even authors who consider the inferential role of models as central, like Hughes or Bueno and Colyvan, content themselves with claiming that models contain mathematical resources that provide inferential power. We claim that these notions require further analysis and argue that mathematical formalisms contribute to this inferential role. We characterize (...) formalisms, illustrate how they extend our mathematical resources, and highlight how distinct formalisms offer various inferential affordances. (shrink)

The aim of this paper is to re-emphasise that the purpose of formal systems is to provide something to map into and to stem the tide of unjustified formal systems. I start by arguing that expressiveness alone is not a sufficient justification for a new formal system but that it must be justified on pragmatic grounds. I then deal with a possible objection as might be raised by a pure mathematician and after that to the objection that theory can be (...) later used by more specific models. I go on to compare two different methods of developing new formal systems: by a priori principles and intuitions; and by post hoc generalisation from data and examples. I briefly describe the phenomena of “social embedding” and use it to explain the social processes that underpin “normal” and “revolutionary” science. This suggests social grounds for the popularity of normal science. I characterise the “foundational” and “empirical” approaches to the use of formal systems and situate these with respect to “normal” and “revolutionary” modes of science. I suggest that successful sciences (in the sense of developing relevant mappings to formal systems) bare either more tolerant of revolutionary ideas or this tolerance is part of the reason they are successful. I finish by enumerating a number of ‘tell-tale’ signs that a paper is presenting an unjustified formal system. (shrink)