Shared structure need not be shared set-structure

Recent semantic approaches to scientific structuralism, aiming to make precise the concept of shared structure between models, formally frame a model as a type of set-structure. This framework is then used to provide a semantic account of (a) the structure of a scientific theory, (b) the applicability of a mathematical theory to a physical theory, and (c) the structural realist’s appeal to the structural continuity between successive physical theories. In this paper, I challenge the idea that, to be so used, the concept of a model and so the concept of shared structure between models must be formally framed within a single unified framework, set-theoretic or other. I first investigate the Bourbaki-inspired assumption that structures are types of set-structured systems and next consider the extent to which this problematic assumption underpins both Suppes’ and recent semantic views of the structure of a scientific theory. I then use this investigation to show that, when it comes to using the concept of shared structure, there is no need to agree with French that “without a formal framework for explicating this concept of ‘structure-similarity’ it remains vague, just as Giere’s concept of similarity between models does ...” (French, 2000, Synthese, 125, pp. 103–120, p. 114). Neither concept is vague; either can be made precise by appealing to the concept of a morphism, but it is the context (and not any set-theoretic type) that determines the appropriate kind of morphism. I make use of French’s (1999, From physics to philosophy (pp. 187–207). Cambridge: Cambridge University Press) own example from the development of quantum theory to show that, for both Weyl and Wigner’s programmes, it was the context of considering the ‘relevant symmetries’ that determined that the appropriate kind of morphism was the one that preserved the shared Lie-group structure of both the theoretical and phenomenological models. I wish to thank Katherine Brading, Anjan Chakravartty, Steven French, Martin Thomson-Jones, Antigone Nounou, Stathis Psillos, Dean Rickles, Mauricio Suarez and two anonymous referees for valuable comments and criticisms, and Gregory Janzen for editorial suggestions. Research for this paper was funded by a generous SSHRC grant for which I am grateful     

Hybrid Indexicals and Ellipsis

In this essay, I explain how certain suggestions put forth by Frege, Wittgenstein, and Schlick regarding the interpretation of indexical expressions may be incorporated within a systematic semantic account. I argue that the ‘hybrid’ approach they propose is preferable to more conventional systems, in particular when it comes to the interpretation of cases of cross-contextual ellipsis. I also explain how the hybrid view entails certain important and independently motivated distinctions among contextually dependent expressions, for instance between ‘here’ and ‘local’.     

A teleological account of Cartesian sensations?

Alison Simmons, in Simmons (1999), argues that Descartes in Meditation Six offered a teleological account of sensory representation. According to Simmons, Descartes’ view is that the biological function of sensations explains both why sensations represent what they do (i.e., their referential content) and why they represent their objects the way they do (i.e., their presentational content). Moreover, Simmons claims that her account has several advantages over other currently available interpretations of Cartesian sensations. In this paper, I argue that Simmons’ teleological account cannot be sustained for both theoretical and textual reasons and that it does not have the advantages it is claimed to have.     

Chains of meaning: A model for concept formation in contemporary physics theories

The rationality of scientific concept formation in theory transitions, challenged by the thesis of semantic incommensurability, can be restored by theChains of Meaning approach to concept formation. According to this approach, concepts of different, succeeding theories may be identified with respect to referential meaning, in spite of grave diversity of the mathematical structures characterizing them in their respective theories. The criterion of referential identity for concepts is that they meet a relation ofsemantic embedding, i.e. that the embedding concept can be substituted by the embedded one in classical limit situations. Three case studies from contemporary physics theories will be used to show that the Chains of Meaning approach not only yields meaning comparisons for already established concepts (as for Newtonian and Schwarzschild mass) but is also well suited to characterize actual scientific strategies of concept formation in yet open cases such as black hole entropy or relativistic thermodynamics.     

The structure of lexical concepts

Jerry Fodor (Concepts: Where cognitive science went wrong. New York: Oxford University Press, 1998) famously argued that lexical concepts are unstructured. After examining the advantages and disadvantages of both the classical approach to concepts and Fodor’s conceptual atomism, I argue that some lexical concepts are, in fact, structured. Roughly stated, I argue that structured lexical concepts bear a necessary biconditional entailment relation to their structural constituents. I develop this account of the structure of lexical concepts within the framework of Pavel Tichy’s (The foundations of Frege’s logic. Berlin, New York: De Gruyter, 1988) theory of constructions. I argue that concepts are constructions which can be combined by way of Tichy’s construction-forming operations of composition and closure and an additional operation, simplification, which I propose in section 6. The last of these construction-forming operations plays a central role in my account of lexical concept structure. Stated generally, structured lexical concepts are a result of simplifying their structural constituents.     

Reduction,externalism and immanence in Husserl and Heidegger

This paper argues that the Husserl–Heidegger relationship is systematically misunderstood when framed in terms of a distinction between internalism and externalism. Both philosophers, it is argued, employ the phenomenological reduction to immanence as a fundamental methodological instrument. After first outlining the assumptions regarding inner and outer and the individual and the social from which recent epistemological interpretations of phenomenology begin, I turn to the question of Husserl’s internalism. I argue that Husserl can only be understood as an internalist on the assumption that immanence equates with internal. This, however, is not the case as can be seen once the reduction is understood not as setting aside the existence of the world, but rather a reflection on its meaning. Turning to Heidegger, I argue that his commitment to a form of the phenomenological reduction precludes him from being either a semantic or a social externalist. The place of authenticity and the first person perspective in his work derive from his phenomenological commitments, which can be seen in his accounts of discourse and language and of falling (Verfallen). I then go on to briefly outline a more plausible basis for understanding the difference between Husserl’s and Heidegger’s phenomenologies in terms of their respective emphases on logic and on poetics.     

From philosophy to criticism of myth: Cassirer’s concept of myth

This article discusses the question whether or not Cassirer’s philosophical critique of technological use of myth in The Myth of the State implies a revision of his earlier conception and theory of myth as provided by The Philosophy of Symbolic Forms. In the first part, Cassirer’s early theory of myth is compared with other approaches of his time. It is claimed that Cassirer’s early approach to myth has to be understood in terms of a transcendental philosophical approach. In consequence, myth is conceived as a form of cultural consciousness which is constituted by specific symbolic processes. In the second part, the theoretical assumptions underlying Cassirer’s criticism of myth are discussed and compared with his earlier theory. It is argued that there is a strong conceptual and theoretical continuity between Cassirer’s early views on myth as a symbolic form and his later critique of technological use of myth.     

Hindriks on Rule-Following*

This paper is a reply to Frank Hindriks’ paper “A Modest Solution to the Problem of Rule-Following”. Hindriks claims to find room for what he calls a modest solution to the Kripkensteinian problem of rule-following, different from both straight and sceptical solutions. Hindriks criticises Philip Pettit’s “ethocentric” solution and goes on to provide his own, “modest” one. My paper is in two parts. In the first part, I argue that there is no room for a “modest” solution to sceptical problems: depending on how one reads Kripke, Hindriks’ “modest” solution is always going to turn out either straight or sceptical. In the second part, I defend the ethocentric solution against Hindriks’ arguments. In particular, I argue that the topic-neutral specifications of favourable conditions which Pettit uses are superior to Hindriks’ topic-specific ones. *I want to thank Frank Hindriks for comments on an earlier version, but I take full responsibility for any remaining errors or misunderstandings. This work has been financially supported by the Academy of Finland (project 202513).     

Saving the intuitions: polylithic reference

My main aim in this paper is to clarify the concepts of referential success and of referential continuity that are so crucial to the scientific realism debate. I start by considering the three dominant theories of reference and the intuitions that motivate each of them. Since several intuitions cited in support of one theory conflict with intuitions cited in support of another something has to give way. The traditional policy has been to reject all intuitions that clash with a chosen theory. A more radical policy, tied to some experimental philosophers, has called for the rejection of any evidential role for intuitions. I explore a largely ignored third alternative, i.e. saving intuitions (and their evidential role) even when they are at odds. To accommodate conflicting intuitions different sets of internally consistent (yet externally inconsistent) intuitions are taken to lend credence to different concepts of reference. In the current context, this means that the concepts of referential success and referential continuity are not monolithic. They are what I call ‘polylithic’. This paper is as much about meta-philosophical concerns with the role of intuitions as it is about reference and the scientific realism debate. Regarding the former I hope that a blueprint will emerge for similar projects in other philosophical domains. Regarding the latter, I hope that polylithicity helps disentangle claims about referential success and continuity in the scientific realism debate by making perspicuous which concepts are best equipped to evaluate the realist’s epistemic claims against the historical record of science.     

Remembering (Short-Term) Memory: Oscillations of an Epistemic Thing

This paper provides an interpretation of Hans-J?rg Rheinberger’s notions of epistemic things and historical epistemology. I argue that Rheinberger’s approach articulates a unique contribution to current debates about integrated HPS, and I propose some modifications and extensions of this contribution. Drawing on examples from memory research, I show that Rheinberger is right to highlight a particular feature of many objects of empirical research (“epistemic things”)—especially in the contexts of exploratory experimentation—namely our lack of knowledge about them. I argue that this analysis needs to be supplemented with an account of what scientists do know, and in particular, how they are able to attribute rudimentary empirical contours to objects of research. These contours are closely connected to paradigmatic research designs, which in turn are tied to basic methodological rules for the exploration of the purported phenomena. I suggest that we engage with such rules in order to develop our own normative (epistemological) categories, and I tie this proposal to the idea of a methodological naturalism in philosophy of science.     

Quantifiers and propositional attitudes: Quine revisited

Quine introduced a famous distinction between the ‘notional’ sense and the ‘relational’ sense of certain attitude verbs. The distinction is both intuitive and sound but is often conflated with another distinction Quine draws between ‘dyadic’ and ‘triadic’ (or higher degree) attitudes. I argue that this conflation is largely responsible for the mistaken view that Quine’s account of attitudes is undermined by the problem of the ‘exportation’ of singular terms within attitude contexts. Quine’s system is also supposed to suffer from the problem of ‘suspended judgement with continued belief’. I argue that this criticism fails to take account of a crucial presupposition of Quine’s about the connection between thought and language. The aim of the paper is to defend the spirit of Quine’s account of attitudes by offering solutions to these two problems. See also chapters four and five of Word and Object (Quine, 1960) and ‘Intensions Revisited’ (Quine, 1977).     

Zwart and Franssen’s impossibility theorem holds for possible-world-accounts but not for consequence-accounts to verisimilitude

Zwart and Franssen’s impossibility theorem reveals a conflict between the possible-world-based content-definition and the possible-world-based likeness-definition of verisimilitude. In Sect. 2 we show that the possible-world-based content-definition violates four basic intuitions of Popper’s consequence-based content-account to verisimilitude, and therefore cannot be said to be in the spirit of Popper’s account, although this is the opinion of some prominent authors. In Sect. 3 we argue that in consequence-accounts, content-aspects and likeness-aspects of verisimilitude are not in conflict with each other, but in agreement. We explain this fact by pointing towards the deep difference between possible-world- and the consequence-accounts, which does not lie in the difference between syntactic (object-language) versus semantic (meta-language) formulations, but in the difference between ‘disjunction-of-possible-worlds’ versus ‘conjunction-of-parts’ representations of theories. Drawing on earlier work, we explain in Sect. 4 how the shortcomings of Popper’s original definition can be repaired by what we call the relevant element approach. We propose a quantitative likeness-definition of verisimilitude based on relevant elements which provably agrees with the qualitative relevant content-definition of verisimilitude on all pairs of comparable theories. We conclude the paper with a plea for consequence-accounts and a brief analysis of the problem of language-dependence (Sect. 6).     

On universals: an extensionalist alternative to Quine’s resemblance theory

The notion of similarity plays a central role in Quine’s theory of Universals and it is with the help of this notion that Quine intends to define the concept of kind which also plays a central role in the theory. But as Quine has admitted, his attempts to define kinds in terms of similarities were unsuccessful and it is mainly because of this shortcoming that Quine’s theory has been ignored by several philosophers (see, e.g., Armstrong, D. M. (1978a). Nominalism and realism: Universals and Scientific realism (Vol. I). Cambridge: Cambridge University Press). In the present paper, I propose an alternative framework that accounts for the phenomena that Quine intends to explain with his resemblance theory. The framework agrees with Quine’s austere ontology; in particular, it does not assume the existence of properties and of possible worlds. (I will mention below Quine’s reason for rejecting properties and possible worlds. For a theory of Universals that assumes possible worlds, see, e.g., Rodriguez-Pereyra, G. (2002). Resemblance nominalism: A solution to the problem of Universals. Oxford: Clarendon Press.) Moreover, the framework is extensionalist since the abstract entities it assumes are classes and these can be individuated extensionally, for classes are identical if their members are identical. Finally, I will refute some of the objections to Quine’s approach that have been raised by Armstrong and Oliver [(1996). The metaphysics of properties. Mind, 105, 1–80.] and I will argue that, contrary to what has been claimed by Oliver in a comment on Lewis [(1986). On the plurality of worlds. Oxford: Blackwell.], Quine is able to specify an important set of sparse properties. Editor’s Note: Nathan Stemmer died on 6 April 2007. Due to this, the proofreading was only done by the editors. All colleagues being acquainted with Nathan Stemmers work are deeply concerned about the loss.     

How to Define a Number? A General Epistemological Account of Simon Stevin’s Art of Defining

This paper explores Simon Stevin’s l’Arithmétique of 1585, where we find a novel understanding of the concept of number. I will discuss the dynamics between his practice and philosophy of mathematics, and put it in the context of his general epistemological attitude. Subsequently, I will take a close look at his justificational concerns, and at how these are reflected in his inductive, a postiori and structuralist approach to investigating the numerical field. I will argue that Stevin’s renewed conceptualisation of the notion of number is a sort of “existential closure” of the numerical domain, founded upon the practice of his predecessors and contemporaries. Accordingly, I want to make clear that l’Aritmetique have to be read not as an ontological analysis or exploration of the numerical field, but as an explication of a mathematical ethos. In this sense, this article also intends to make a specific contribution to the broader issue of the “ethics of geometry.”     

A survey of some recent results on Spectrum Exchangeability in Polyadic Inductive Logic

The discussion presents a framework of concepts that is intended to account for the rationality of semantic change and variation, suggesting that each scientific concept consists of three components of content: (1) reference, (2) inferential role, and (3) the epistemic goal pursued with the concept’s use. I argue that in the course of history a concept can change in any of these components, and that change in the concept’s inferential role and reference can be accounted for as being rational relative to the third component, the concept’s epistemic goal. This framework is illustrated and defended by application to the history of the gene concept. It is explained how the molecular gene concept grew rationally out of the classical gene concept despite a change in reference, and why the use and reference of the contemporary molecular gene concept may legitimately vary from context to context.     

A puzzle about visualization

Visual imagination (or visualization) is peculiar in being both free, in that what we imagine is up to us, and useful to a wide variety of practical reasoning tasks. How can we rely upon our visualizations in practical reasoning if what we imagine is subject to our whims? The key to answering this puzzle, I argue, is to provide an account of what constrains the sequence in which the representations featured in visualization unfold—an account that is consistent with its freedom. Three different proposals are outlined, building on theories that link visualization to sensorimotor predictive mechanisms (e.g., “efference copies,” “forward models”). Each sees visualization as a kind of reasoning, where its freedom consists in our ability to choose the topic of the reasoning. Of the three options, I argue that the approach many will find most attractive—that visualization is a kind of “off-line” perception, and is therefore in some sense misrepresentational—should be rejected. The two remaining proposals both conceive of visualization as a form of sensorimotor reasoning that is constitutive of one’s commitments concerning the way certain kinds of visuomotor scenarios unfold. According to the first, these commitments impinge on one’s web of belief from without, in the manner of normal perceptual experience; according to the second, these commitments just are one’s (occurrent) beliefs about such generalizations. I conclude that, despite being initially counterintuitive, the view of visualization as a kind of occurrent belief is the most promising.