Musical formalism, which strictly limits the type of thing any description of the music can tell us, is ill-equipped to account for contemporary performance practice. If performative interpretations are in a position to tell us something about musical works—that is if performance is a kind of description, as Peter Kivy argues—then we have to loosen the restrictions on notions of musical relevance to make sense of performance. I argue that musical formalism, which strictly limits the type of thing (...) any description of the music can tell us, is inconsistent with Kivy's quite compelling account of performance. This shows the difficulty that actual performances pose to overly rigid conceptions of music. Daniel Barenboim unannounced performance of Wagner in Israel in 2001 shows that the problem of the boundaries of musical relevance is no mere philosophical puzzle. It is a pressing problem in the musical public sphere. (shrink)
In this paper I present a formalist philosophy mathematics and apply it directly to Arithmetic. I propose that formalists concentrate on presenting compositional truth theories for mathematical languages that ultimately depend on formal methods. I argue that this proposal occupies a lush middle ground between traditional formalism, fictionalism, logicism and realism.
Musical formalism is often portrayed as the enemy of artistic freedom. Its main representative, Eduard Hanslick, is seen as a purist who, by emphasizing musical rules, aims at restricting music criticism and even musical practices themselves. It may also seem that formalism is depriving music of its ability to have moral significance, as the semantic connection to the extramusical is denied by the formalistic view. In my paper, I defend formalism by placing Hanslick’s argument in a Kantian (...) framework. It is not hard to find Kantian elements in Hanslick’s work, such as his emphasis on the contemplative and disinterested nature of the aesthetic judgment, the nonconceptuality of music’s content, and his insistence that “beauty has no purpose.” I argue further that Hanslick’s formalism is in fact motivated by and manifests the Kantian conception of freedom as self-legislation. Thus understood, the kind of moral significance music may have rests upon its own autonomous rules. (shrink)
Moderate formalism is the view that all artworks which have aesthetic properties have formal aesthetic properties, and some but not all of those works also have non-formal aesthetic properties. Nick Zangwill develops this view in his Metaphysics of Beauty after having argued against its alternatives – extreme formalism and anti-formalism. This article reviews his arguments against the rivals of moderate formalism, and argues that the rejection of anti-formalism is unjustified. Zangwill does not succeed in proving (...) that the broadly determined (context-determined) properties of artworks are in some cases irrelevant to their aesthetic properties – and following that, interpretation and assessment. A historical argument presented here shows how aesthetic properties of every work must partly supervene on this work’s contextual properties. In particular, this disproves Zangwill’s claim that epistemological matters are unessential in determining the artwork’s properties, and exposes some problems his account has with explaining relations between nonaesthetic and aesthetic properties. (shrink)
Despite the divide between American formalism and theoreticians of minimalism, Barnett Newman’s art received great acclaim from both schools of thought. Attempting to unearth the philosophical preconditions of this strange constellation, this article argues that the closeness between minimalism and formalism is due to their mutual reliance upon phenomenology and ordinary language philosophy. However, their proximity also conveys their distance, since they imply different interpretations and applications of the philosophical schools in question. Such theoretical differences shed light on (...) Newman’s paintings: both minimalism and formalism are right in their accounts – yet not exclusively so. What arguably makes up the distinctive fascination of Newman’s paintings is their incessant oscillation between empty physicality and powerful meaning. (shrink)
It has been contended that it is unjustified to believe, as Weyl did, that formalism's victory against intuitionism entails a defeat of the phenomenological approach to mathematics. The reason for this contention, recently put forth by Paolo Mancosu and Thomas Ryckman, is that, unlike intuitionistic Anschauung, phenomenological intuition could ground classical mathematics. I argue that this indicates a misinterpretation of Weyl's view, for he did not take formalism to prevail over intuitionism with respect to grounding classical mathematics. I (...) also point out that the contention is false: if intuitionism fails, in the way Weyl thought it did, i.e., with respect to supporting scientific objectivity, then one should also reject the phenomenological approach, in the same respect. (shrink)
In 1939, Curry proposed a philosophy of mathematics he called formalism. He made this proposal in two works originally written then, although one of them was not published until 1951. These are the two philosophical works for which Curry is known, and they have left a false impression of his views. In this article, I propose to clarify Curry’s views by referring to some of his later writings on the subject. I claim that Curry’s philosophy was not what is (...) now usually called formalism, but is really a form of structuralism. (shrink)
We show that it is possible to generalize the Ursell–Mayer cluster formalism so that it may cover also the statistics of Internet websites. Our starting point is the introduction of an extra variable that is assumed to take account, as will be explained, of the nature of the Internet statistics. We then show, following the arguments in Mayer, that one may obtain a phase transition-like phenomena.
The objective of this paper is to introduce a flexible approach to the structuring of negotiations. The process of negotiations with its intricacies is discussed, and drawbacks of quantitative methods are analyzed. The decomposition of the negotiation process into a certain hierarchical structure is presented. This structure is represented with ‘and/or’ trees used for knowledge representation in artificial intelligence. The definitions of flexibility and reactions to the opponent's moves are introduced with the help of a rule-based formalism. The implications (...) of these definitions for the analysis of the negotiation process are presented. The approach is illustrated with a set of hypothetical examples. (shrink)
Hegel’s aesthetic ideal is the perfect integration of form and content within a work of art. This ideal is incompatible with the predominant 20th-century principle of formalist criticism, that form is the sole important factor in a work of art. Although the formalist dichotomy between form and content has been criticized on philosophical grounds, that does not suffice to justify Hegel’s ideal. Justifying Hegel’s ideal requires detailed art criticism that shows how form and content are, and why they should be, (...) integrated in good works of art. This essay provides some of this criticism. By focusing on the work of the contemporary artist, Robert Turner, this criticism further suggests that Hegel’s aesthetic ideal is still relevant. Moreover, the nature of Turner’s work suggests that art is still relevant in our day in ways Hegel did not expect. (shrink)
I consider the relationship of Badiou’s schematism of the event to critical thought following the linguistic turn as well as to the mathematical formalisms of set theory. In Being and Event, Badiou uses formal argumentation to support his sweeping rejection of the linguistic turn as well as much of contemporary critical thought. This rejection stems from his interpretation of set theory as barring thought from the 'One-All' of totality; but I argue that, by interpreting it differently, we can understand this (...) implication in a way that is in fact consistent with the critical and linguistic methods Badiou wishes to reject. (shrink)
Quantum Mechanics can be viewed as a linear dynamical theory having a familiar mathematical framework but a mysterious probabilistic interpretation, or as a probabilistic theory having a familiar interpretation but a mysterious formal framework. These points of view are usually taken to be somewhat in tension with one another. The first has generated a vast literature aiming at a “realistic” and “collapse-free” interpretation of quantum mechanics that will account for its statistical predictions. The second has generated an at least equally (...) large literature aiming to derive, or at any rate motivate, the formal structure of quantum theory in probabilistically intelligible terms. In this paper I explore, in a preliminary way, the possibility that these two programmes have something to offer one another. In particular, I show that a version of the measurement problem occurs in essentially any non-classical probabilistic theory, and ask to what extent various interpretations of quantum mechanics continue to make sense in such a general setting. I make a start on answering this question in the case of a rudimentary version of the Everett interpretation. (shrink)
I identify two mutually exclusive notions of formalism in Kant’s Critique of Aesthetic Judgement: a thin concept of aesthetic formalism and a thick concept of aesthetic formalism. Arguably there is textual support for both concepts in Kant’s third critique. I offer interpretations of three key elements in the Critique of Aesthetic Judgement which support a thick formalism. The three key elements are: Harmony of the Faculties, Aesthetic Ideas and Sensus Communis. I interpret these concepts in relation (...) to the conditions for theoretical Reason, the conditions for moral motivation and the conditions for intersubjectivity, respectively. I conclude that there is no support for a thin concept of aesthetic formalism when the key elements of Kant’s Critique of Aesthetic Judgement are understood in the context of his broader critical aims. (shrink)
We present an alternative to the Copenhagen interpretation of the formalism of nonrelativistic quantum mechanics. The basic difference is that the new interpretation is formulated in the language of epistemological realism. It involves a change in some basic physical concepts. Elementary particles are considered as extended objects and nonlocal effects are included. The role of the new concepts in the problems of measurement and of the Einstein–Podolsky–Rosen correlations is described. Experiments to distinguish the proposed interpretation from the Copenhagen one (...) are pointed out. (shrink)
The Ghirardi–Rimini–Weber (GRW) theory of spontaneous wave function collapse is known to provide a quantum theory without observers, in fact two different ones by using either the matter density ontology (GRWm) or the flash ontology (GRWf). Both theories are known to make predictions different from those of quantum mechanics, but the difference is so small that no decisive experiment can as yet be performed. While some testable deviations from quantum mechanics have long been known, we provide here something that has (...) until now been missing: a formalism that succinctly summarizes the empirical predictions of GRWm and GRWf. We call it the GRW formalism. Its structure is similar to that of the quantum formalism but involves different operators. In other words, we establish the validity of a general algorithm for directly computing the testable predictions of GRWm and GRWf. We further show that some well-defined quantities cannot be measured in a GRWm or GRWf world. (shrink)
I outline a variant on the formalist approach to mathematics which rejects textbook formalism's highly counterintuitive denial that mathematical theorems express truths while still avoiding ontological commitment to a realm of abstract objects. The key idea is to distinguish the sense of a sentence from its explanatory truth conditions. I then look at various problems with the neo-formalist approach, in particular at the status of the notion of proof in a formal calculus and at problems which Gödelian results seem (...) to pose for the tight link assumed between truth and proof. (shrink)
The guiding idea behind formalism is that mathematics is not a body of propositions representing an abstract sector of reality but is much more akin to a game, bringing with it no more commitment to an ontology of objects or properties than ludo or chess. This idea has some intuitive plausibility: consider the tyro toiling at multiplication tables or the student using a standard algorithm for differentiating or integrating a function. It also corresponds to some aspects of the practice (...) of advanced mathematicians in some periods—for example, the treatment of imaginary numbers for some time after Bombelli's introduction of them, and perhaps the attitude of some contemporary mathematicians towards the higher flights of set theory. Finally, it is often the position to which philosophically naïve respondents will gesture towards, when pestered by questions as to the nature of mathematics. (shrink)
The Ghirardi–Rimini–Weber (GRW) theory of spontaneous wave function collapse is known to provide a quantum theory without observers, in fact two different ones by using either the matter density ontology (GRWm) or the flash ontology (GRWf). Both theories are known to make predictions different from those of quantum mechanics, but the difference is so small that no decisive experiment can as yet be performed. While some testable deviations from quantum mechanics have long been known, we provide here something that has (...) until now been missing: a formalism that succinctly summarizes the empirical predictions of GRWm and GRWf. We call it the GRW formalism. Its structure is similar to that of the quantum formalism but involves different operators. In other words, we establish the validity of a general algorithm for directly computing the testable predictions of GRWm and GRWf. We further show that some well-defined quantities cannot be measured in a GRW world, for example the number of collapses in a system during a chosen time interval. (shrink)
Aesthetic Formalism has fallen on hard times. At best it receives unsympathetic discussion and swift rejection. At worst it is the object of abuse and derision. But I think that there is something to be said for it. In this paper, I shall try to find and secure the truth in formalism. I shall not try to defend formalism against all of the objections to it.1 Instead I shall articulate a moderate formalist view that draws on aesthetic0nonaesthetic (...) determination and Kant’s distinction between free and dependent beauty. I shall examine four central art forms—painting, sculpture, lit-. (shrink)
Hegel famously argued that Kantian Moralität is an empty formalism. This article offers a defense of Kant’s formalism and suggests that it is crucial to Hegel’s own idealism. My defense, however, depends on reading Kantian morality non-morally, as a theory of normative authority. Through a reading of the Grundlegung and Religion, the article delineates Kant’s hyperbolic formalism—the insistence on giving an account of the form of rational agency by isolating willing from all content. The article accordingly assesses (...) Kant’s understanding of autonomy as a matter of institution-subjection. It also critically engages Henry Allison’s groundbreaking work on Kant. Hegel follows Kant in arguing that determinacy is a matter of institution-subjection, and in the Logic provides a radically formalist justification of the role of normative authority in determinacy. Unlike Kant, who articulates institution-subjection as a matter of an isolated subject, Hegel shows that institution-subjection is a matter of social practices. (shrink)
Recently, several authors have defended a new version of formalism in the aesthetics of nature and attempted to refute earlier arguments against the doctrine. In this essay, we assess this new formalism by reconsidering the force of antiformalist arguments against both traditional formalism and new formalism. While we find that these arguments remain effective against traditional formalism, new formalism falls largely beyond their scope. We therefore provide a novel line of argument for the insignificance (...) of the formal appreciation of nature. This argument suggests that new formalism is inadequate as a theory of the aesthetics of nature. (shrink)
In a recent article, Azzouni has argued in favor of a version of formalism according to which ordinary mathematical proofs indicate mechanically checkable derivations. This is taken to account for the quasi-universal agreement among mathematicians on the validity of their proofs. Here, the author subjects these claims to a critical examination, recalls the technical details about formalization and mechanical checking of proofs, and illustrates the main argument with aanalysis of examples. In the author's view, much of mathematical reasoning presents (...) genuine meaning-dependent mathematical characteristics that cannot be captured by formal calculi. ‘…there is a conflict between mathematical practice and the formalist doctrine.’ [Kreisel, 1969, p. 39]. (shrink)
Most of the debate for and against aesthetic formalism in the twentieth century has been little more than a sequence of assertions, on both sides. But there is one discussion that stands out for its argumentative subtlety and depth, and that is Kendall Walton’s paper ‘Categories of Art’.1 In what follows I shall defend a certain version of formalism against the antiformalist arguments which Walton deploys. I want to show that while Walton’s arguments do indeed create insurmountable diﬃculties (...) for an extreme version of formalism, he has not shown that a moderate version is problematic or inadequate. (I have no space to address anti-formalist arguments other than Walton’s.2) I shall defend moderate formalism rather than put forward positive considerations in its favour, although some of its attractions will become apparent as a side-eﬀect. I pursue the positive case for moderate formalism elsewhere.3 I. FORMAL PROPERTIES AND FORMALISMS I.1. Walton begins his paper by raising an issue about whether those who make aesthetic judgements should only be concerned with what can be directly perceived in works of art. The issue of formalism has often been described in these terms. But Walton rightly distances himself from setting up a debate in that way. He moves on to take as his target the view that ‘Circumstances connected with a work’s origin ... have no essential bearing on an assessment of its aesthetic nature’ (p. 334). (shrink)
In recent articles, Zangari (1994) and Karakostas (1997) observe that while an &unknown;-extended version of the proper orthochronous Lorentz group O + (1,3) exists for values of &unknown; not equal to zero, no similar &unknown;-extended version of its double covering group SL(2, C) exists (where &unknown;=1-2&unknown; R , with &unknown; R the non-standard simultaneity parameter of Reichenbach). Thus, they maintain, since SL(2, C) is essential in describing the rotational behaviour of half-integer spin fields, and since there is empirical evidence for (...) such behaviour, &unknown;-coordinate transformations for any value of &unknown;<>0 are ruled out empirically. In this article, I make two observations:(a)There is an isomorphism between even-indexed 2-spinor fields and Minkowski world-tensors which can be exploited to obtain generally covariant expressions of such spinor fields.(b)There is a 2-1 isomorphism between odd-indexed 2-spinor fields and Minkowski world-tensors which can be exploited to obtain generally covariant expressions for such spinor fields up to a sign. Evidence that the components of such fields do take unique values is not decisive in favour of the realist in the debate over the conventionality of simultaneity in so far as such fields do not play a role in clock synchrony experiments in general, and determinations of the one-way speed of light in particular.I claim that these observations are made clear when one considers the coordinate-independent 2-spinor formalism. They are less evident if one restricts oneself to earlier coordinate-dependent formalisms. I end by distinguishing these conclusions from those drawn by the critique of Zangari given by Gunn and Vetharaniam (1995). (shrink)
Machine generated contents note: Introduction: The Rise of Philosophical Art Criticism 1 -- Chapter 1. In the Beginning Was Formalism 17 -- Chapter 2. The Structuralist Adventure 33 -- Chapter 3. The Historicist, Antiessentialist Definition of Art 55 -- Chapter 4. Resentment and Its Discontents 71 -- Chapter 5. The Deconstruction of Structuralism 87 -- Afterword: The Fate of Philosophical Art Criticism 111.
The relationship between mathematical formalism, physical interpretation and epistemological appraisal in the practice of physical theorizing is considered in the context of Bohmian mechanics. After laying outthe formal mathematical postulates of thetheory and recovering the historical roots ofthe present debate over the meaning of Bohmianmechanics from the early debate over themeaning of Schrödinger's wave mechanics,several contemporary interpretations of Bohmianmechanics in the literature are discussed andcritiqued with respect to the aim of causalexplanation and an alternative interpretationis proposed. Throughout, the over-arching (...) aimis to exhibit the connections betweenmathematical, ontological and methodologicalquestions in physical theory and to reflect onthe rationality of physical theorizing in lightof the present case. (shrink)
ANTI-FORMALISM has become the consensus in aesthetics. But in my view anti-formalism is not true to our aesthetic experience; it gives a revisionary account of the aesthetic properties that we think we find in works of art. The thesis I think we should hold is not extreme formalism—the view that all or almost all aesthetic properties are formal—but the moderate thesis that many are. This view has not been given its due because so many aestheticians have been (...) convinced by anti-formalist arguments. In this short paper, I propose a systematic method for resisting anti-formalist arguments. The method is to apply one of three strategies. These strategies are repeatable archetypes. I shall show these neutralizing strategies at work with seven objections to formalism. (shrink)
Formalism shares with nominalism a distaste for abstracta. But an honest exposition of the former position risks introducing abstracta as the stuff of syntax. This article describes the dangers, and offers a new escape route from platonism for the formalist. It is explained how the needed role of derivations in mathematical practice can be explained, not by a commitment to the derivations themselves, but by the commitment of the mathematician to a practice which is in accord with a theory (...) of derivations. (shrink)
Customary discussions of quantum measurements are unrealistic, in the sense that they do not reflect what happens in most actual measurements even under ideal circumstances. Even theories of measurement which discard the projection postulate tend to retain two unrealistic assumptions of the von Neumann theory: that a measurement consists of a single physical interaction, and that the topic of every measurement is information wholly contained in the quantum state of the object of measurement. I suggest that these unrealistic assumptions originate (...) from an overly literal interpretation of the operator formalism of quantum mechanics. I also suggest, following Park, that some issues can be clarified by distinguishing the sense of the term ''''measurement'''' occurring in the quantum-mechanical operator formalism, and the sense of ''''measurement'''' that refers to actual processes of gaining information about the physical world. (shrink)
The main thesis of this paper is that, Contrary to general belief, George berkeley did in fact express a coherent philosophy of mathematics in his major published works. He treated arithmetic and geometry separately and differently, And this paper focuses on his philosophy of arithmetic, Which is shown to be strikingly similar to the 19th and 20th century philosophies of mathematics known as 'formalism' and 'instrumentalism'. A major portion of the paper is devoted to showing how this philosophy of (...) mathematics follows directly from berkeley's theory of signs and his philosophy of language, And from his discovery of an alternative to the correspondence theory of truth used by most of his predecessors. (shrink)
I reinterpret Bohr's attitude towards quantum mechanical formalism and its empirical content, based on his understanding of the correspondence principle and its approximate applicability. I suggest that Bohr understood complementarity as a limitation imposed by the commutation relations upon the applicability of the idealizations which had grounded the use of the correspondence principle. By discussing this interpretation against the contemporary background of discussions regarding “naïve realism” about operators (as observables), I suggest that a Bohrian view on the empirical content (...) of quantum mechanical operators may provide a middle ground between complete contextualism and an untenable realism about quantum properties. (shrink)
We introduce a new “positive formalism” for encoding quantum theories in the general boundary formulation, somewhat analogous to the mixed state formalism of the standard formulation. This makes the probability interpretation more natural and elegant, eliminates operationally irrelevant structure and opens the general boundary formulation to quantum information theory.
The analysis of atomic sentences and their subatomic components poses a special problem for proof-theoretic approaches to natural language semantics, as it is far from clear how their semantics could be explained by means of proofs rather than denotations. The paper develops a proof-theoretic semantics for a fragment of English within a type-theoretical formalism that combines subatomic systems for natural deduction  with constructive (or Martin-Löf) type theory [8, 9] by stating rules for the formation, introduction, elimination and equality (...) of atomic propositions understood as types (or sets) of subatomic proof-objects. The formalism is extended with dependent types to admit an interpretation of non-atomic sentences. The paper concludes with applications to natural language including internally nested proper names, anaphoric pronouns, simple identity sentences, and intensional transitive verbs. (shrink)
We outline the rationale and preliminary results of using the State Context Property (SCOP) formalism, originally developed as a generalization of quantum mechanics, to describe the contextual manner in which concepts are evoked, used, and combined to generate meaning. The quantum formalism was developed to cope with problems arising in the description of (1) the measurement process, and (2) the generation of new states with new properties when particles become entangled. Similar problems arising with concepts motivated the formal (...) treatment introduced here. Concepts are viewed not as fixed representations, but entities existing in states of potentiality that require interaction with a context---a stimulus or another concept---to `collapse' to observable form as an exemplar, prototype, or other (possibly imaginary) instance. The stimulus situation plays the role of the measurement in physics, acting as context that induces a change of the cognitive state from superposition state to collapsed state. The collapsed state is more likely to consist of a conjunction of concepts for associative than analytic thought because more stimulus or concept properties take part in the collapse. We provide two contextual measures of conceptual distance---one using collapse probabilities and the other weighted properties---and show how they can be applied to conjunctions using the pet fish problem. (shrink)
I defend extreme formalism about inorganic nature against arguments put forward by Glenn Parsons. I begin by laying out the general issue over aesthetic formalism, and I describe the position of extreme formalism about inorganic nature. I then reconsider -Ronald Hepburn's beach/seabed example. Next I discuss the notions of function in play in our thinking about inorganic nature. And lastly I consider Parsons's flooding river example. I conclude that extreme formalism about inorganic nature is safe from (...) Parsons's arguments. (shrink)
Abstract Economic formalism crowds out the analysis of change and adjustments to change under capitalism. The style of analytical narrative that was practiced by the first generation of neoclassical economists, in contrast, is more productive of genuine economic understanding. Despite Daniel Haus?man's challenging argument to the contrary, I maintain that Joseph Stiglitz's work is formalist at its core. While I agree with Robert Heilbroner's critique of contemporary economics, there is a limited sense in which nonformalist economics can rely on (...) universalistic assumptions. And Thomas Mayer has provided useful guidelines for focusing nonformalist analysis on real?world economic problems. (shrink)
Contemporary Austrian?school economists reject neoclassical welfare theory for being founded on the benchmark of a perfectly competitive general equilibrium, and instead favor a formal theory deemed consistent with the notions of radical subjectivism and disequilibrium analysis. Roy Cordato advances a bold free?market benchmark by which to formally assess social welfare, economic efficiency, and externalities issues. Like all formalist, a priori theory, however, Cordato's reformulation cannot meet its own standards, being theoretically and empirically flawed, and perhaps ideologically suspect.
Goodman’s account of the ‘grue’ paradox stands at a crossroads in the history of twentieth century epistemology. Published in 1954, Fact, Fiction, and Forecast is a reaction to the logical empiricist views that held sway in the first half of the last century and anticipates many of the conventionalist and/or relativist moves popular throughout the second half. Through his evaluation of Hume’s problem of induction, as well as his own novel reformulation of it, Goodman comes to reject a number of (...) the fundamental parts of logical empiricism. In particular, Goodman argues that the formal epistemic methods the logical empiricists wanted to rely upon are insufficient. This leads him to turn towards conventionalism, which is the basis of his rejection of the objective view of knowledge. In his conventionalism he is a precursor of writers such as Hanson, Kuhn and Feyerabend, who, seeing the inadequacy of formalism, sought to fill the gaps it left in epistemic methodology with scientific values, tacit knowledge and linguistic practices. Making use of Susan Haack’s distinction between three different kinds of foundationalism, we analyse Goodman’s position and its relation to the views of the logical empiricists. The two are reflections of each other in that, where the logical empiricists are foundationalists in their views on empirical evidence, methods used and objective criteria of justification, Goodman consistently opts for the corresponding coherentist options. As it turns out, this choice of options makes it impossible for Goodman to deal with the very objections he raises against the logical empiricists. In adding the new problem of induction to the old one, Goodman adds a problem which clearly can not be resolved by a purely syntactic solution. The charge Goodman raises is that logical empiricists cannot determine which predictions are sound and which are not. We argue that his method of identifying acceptable predictions based on the use of entrenchment is, in the end, arbitrary and only postpones the underlying problem.. (shrink)
The paper discusses the emergence of Frege's puzzle and the introduction of the celebrated distinction between sense and reference in the context of Frege's logicist project. The main aim of the paper is to show that not logicism per se is mainly responsible for this introduction, but Frege's constant struggle against formalism. Thus, the paper enlarges the historical context, and provides a reconstruction of Frege's philosophical development from this broader perspective.
Morphogenesis is a key process in developmental biology. An important issue is the understanding of the generation of shape and cellular organisation in tissues. Despite of their great diversity, morphogenetic processes share common features. This work is an attempt to describe this diversity using the same formalism based on a cellular description. Tissue is seen as a multi-cellular system whose behaviour is the result of all constitutive cells dynamics. Morphogenesis is then considered as a spatiotemporal organization of cells activities. (...) We show how this formalism relies on Reaction–Diffusion/Positional Information approach and how it permits to generalize its modelling possibilities. Three quite different applications for concrete morphogenetic processes are presented. The first one is a model for epithelial invagination, the second is a model of cellular differentiation by local cell–cell signalling. The last example is the secondary radial growth of conifer trees. From the mathematical point of view, different modelling tools are used according to the specificity of each process. (shrink)
The constraint formalism of classical mechanics is extended to field theories with gauge groups. Explicit examples of Klein-Gordon and Maxwell fields are presented. The symmetry properties of the Maxwell fields have the unexpcted feature in this formalism of forming a first-class algebra which is not Lie, a situation already encountered in the general theory of relativity.
We suggest a general formalism of four-valued reasoning, called biconsequence relations, intended to serve as a logical framework for reasoning with incomplete and inconsistent data. The formalism is based on a four-valued semantics suggested by Belnap. As for the classical sequent calculus, any four-valued connective can be defined in biconsequence relations using suitable introduction and elimination rules. In addition, various three-valued and partial logics are shown to be special cases of this formalism obtained by imposing appropriate additional (...) logical rules. We show also that such rules are instances of a single logical principle called coherence. The latter can be considered a general requirement securing that the information we can infer in this framework will be classically coherent. (shrink)
Abstract Contrary to Peter J. Boettke's essay, ?What Went Wrong with Economics??, there is no connection between ?formalism? and the alleged inability of mainstream economists to regard theoretical models as anything other than either depictions of real market economies or bases for criticizing market economies and justifying government intervention. Although Boettke's criticisms of the excesses of formalism are justified, Austrian economists such as Boettke need to justify their view that government interventions into economic affairs are inevitably harmful.
The objective of this article is to provide a formalism to deal with the special theory of relativity (STR, in short) as riewed by Reichenbach, according to which STR involves an ineradicableconventionality of simultaneity. One of the two postulates of STR asserts that, in empty space, the one-way speed of light relative to inertial frames is constant. Experimental evidence, however, is related to the constancy of the round-trip speed of light and has no bearing on one-way speeds. Following Reichenbach's (...) viewpoint, we relax the second postulate of STR, abandoning the constancy of the one-way speed of light to the more realistic one asserting the constancy of the round-trip speed of light. This, in turn, results in a formalism to deal with Reichenbach's special theory of relativity (RSTR, in short) in which the two one-way speeds of light in empty space, C±, in the two senses of a round-trip are arbitrarily selected in such a way that their harmonic mean is the measurable round-trip speed of light, c. Experimentally, RSTR and STR are indistinguishable and, hence, represent the same physical theory. It is only the formalism that we use to deal with STR which is extended in RSTR to accommodate the immeasurability of one-way velocities. The usefulness of the proposed formalism to study special relativity is demonstrated. (shrink)