Legal decisions and theories are frequently condemned as formalistic, yet little discussion has occurred regarding exactly what the term "'formalism" means. In this Article, Professor Schauer examines divergent uses of the term to elucidate its descriptive content. Conceptions offormalism, he argues, involve the notion that rules constrict the choice of the decisionmaker. Our aversion to formalism stems from denial that the language of rules either can or should constrict choice in this way. Yet Professor Schauer argues that this (...) aversion to formalism should be rethought: At times language both can and should restrict decisionmakers. Consequently, the term "'formalistic" should not be used as a blanket condemnation of a decisionmaking process; instead the debate regarding decision according to rules should be confronted on its own terms. (shrink)

We present an alternative to the Copenhagen interpretation of the formalism of nonrelativistic quantum mechanics. The basic difference is that the new inter- pretation 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)

This book has three main parts. The first, longer, part is a reprint of the author's Deviant Logic, which initially appeared as a book by itself in 1974. The second and third parts include reprints of five papers originally published between 1973 and 1980. Three of them focus on the nature and justification of deductive reasoning, which are also a major concern of Deviant Logic. The other two are on fuzzy logic, and make up for a major omission of Deviant (...) Logic. (shrink)

It seems necessary to introduce the basic concepts used in this article i.e. formalism, anti-formalism and moderate formalism. Formalists believe that the aesthetic appreciation of an art work generally involves an attentive awareness of its sensory or conceptual qualities and does not require knowledge about its non-perceptual properties. Anti-formalists on the hand hold that noon of the aesthetic properties in the work of art are formal. A number of philosophers have recently advocated a more moderate formalism. (...) According to this view although not all aesthetic properties are formal, many are, and some artworks possess only formal aesthetic qualities. The quarrel among these three rival views concerns what sort of knowledge, if any, is required for appropriate aesthetic appreciation of an art work. In what follows, we will give a brief exposition of these three view points. Subsequently we will give our preferred position with regard to these views. (shrink)

This article defends a formalist interpretation of Wittgenstein’s later thought on music by comparing it with Eduard Hanslick’s musical formalism. In doing so, it returns to a disagreement I have had with Bela Szabados who, in his book Wittgenstein as a Philosophical Tone-Poet, claims that the attribution of formalism obscures the role that music played in the development of Wittgenstein’s thought. The paper scrutinizes the four arguments Szabados presents to defend his claim, pertaining to alleged differences between Wittgenstein (...) and Hanslick on their accounts of theory, beauty, rules, and the broader significance of music. I will argue that in each case the similarities between Wittgenstein’s and Hanslick’s respective views outshine possible differences. Ultimately, I will argue that instead of rendering music a marginal phenomenon suited for mere entertainment, formalism –as presented by Hanslick and Wittgenstein, whom I read as influenced by Kant’s aesthetics– underscores music’s ability to show fundamental features of reality and our relation to it. Music does this precisely by being treated as a sensuous yet structured medium that is irreducible to any conceptually determined domain. (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)

Frege says, at the end of a discussion of formalism in the Foundations of Arithmetic, that his own foundational program ``could be called formal'' but is ``completely different'' from the view he has just criticized. This essay examines Frege's relationship to Hermann Hankel, his main formalist interlocutor in the Foundations, in order to make sense of these claims. The investigation reveals a surprising result: Frege's foundational program actually has quite a lot in common with Hankel's. This undercuts Frege's claim (...) that his own view is completely different from Hankel's formalism, and motivates a closer examination of where the differences lie. On the interpretation offered here, Frege shares important parts of the formalist perspective, but differs in recognizing a kind of content for arithmetical terms which can only be made available via proof from prior postulates. (shrink)

The paper deals with the formalistic view on music presented in Eduard Hanslick’s treatise On the Musically Beautiful, which is taken to be the foundingwork of the aesthtetics of music. In the paper I propose an interpretation of Hanslick’s treatise which differs on many points from the interpretations displayed in the works of several most influential contemporary aestheticians of music. My main thesis is that Hanslick’s treatise is misunderstood and incorrectly presented by these authors. I try to demonstrate this thesis (...) by referring to Hanslick’s original formulations in the German edition and by showing that my interpretation renders Hanslick’s view far more coherent and his arguments successful in showing his main conclusions. Accepting this alternative interpretation should have further implications on many contemporary theories in the aesthetics of music that reckon on the failure of Hanslick’s arguments as presented by usual interpretations. (shrink)

The formalist philosophy of mathematics (in its purest, most extreme version) is widely regarded as a “discredited position”. This pure and extreme version of formalism is called by some authors “game formalism”, because it is alleged to represent mathematics as a meaningless game with strings of symbols. Nevertheless, I would like to draw attention to some arguments in favour of game formalism as an appropriate philosophy of real mathematics. For the most part, these arguments have not yet (...) been used or were neglected in past discussions. (shrink)

Book information: Deviant Logic, Fuzzy Logic: Beyond The Formalism. By SUSAN HAACK. Chicago, Ill.: University of Chicago Press, 1996. Pp. xxvi, 291.

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)

Right after the elaboration and success of general relativity (GR), alternative theories for gravity began to appear. In order to verify and classify all these theories, specific tests have been developed, based on self-consistency and on completeness. In the field of experimental gravity, one of the important applications is formalism. For the evaluation of gravity models, several sets of tests have been proposed. Parameterized post-Newtonian formalism considers approximations of Einstein's gravity equations by the lowest order deviations from Newton's (...) law for weak fields. DOI: 10.13140/RG.2.2.25994.82881. (shrink)

The problem of measurement in economic models and the possibility of their quantum-mechanical description are considered. It is revealed that the apparent paradox of such a description is associated with a priori requirement of conformity of the model to all the alternatives of free choice of the observer. The measurement of the state of a trader on a stock exchange is formally defined as his responses to the proposals of sale at a fixed price. It is shown that an analogue (...) of Bell's inequalities for this measurement model is violated at the most general assumptions related to the strategy of the trader and requires a quantummechanical description of the dynamics of his condition. In the framework of the theory of weak continuous quantum measurements, the equation of stock price dynamics and the quantum-mechanical generalization of the F. Black and M. Scholes model for pricing options are obtained. The fundamental distinctions between the obtained model and the classical one are discussed. (shrink)

The conventional notion of a formal system is adapted to conform to the sound deductive inference model operating on finite strings. Finite strings stipulated to have the semantic value of Boolean true provide the sound deductive premises. Truth preserving finite string transformation rules provide the valid deductive inference. Sound deductive conclusions are the result of these finite string transformation rules.

Forty-two years ago, Capra published “The Tao of Physics” (Capra, 1975). In this book (page 17) he writes: “The exploration of the atomic and subatomic world in the twentieth century has …. necessitated a radical revision of many of our basic concepts” and that, unlike ‘classical’ physics, the sub-atomic and quantum “modern physics” shows resonances with Eastern thoughts and “leads us to a view of the world which is very similar to the views held by mystics of all ages and (...) traditions.“ This article stresses an analogous situation in biology with respect to a new theoretical approach for studying living systems, Integral Biomathics (IB), which also exhibits some resonances with Eastern thought. Stepping on earlier research in cybernetics1 and theoretical biology,2 IB has been developed since 2011 by over 100 scientists from a number of disciplines who have been exploring a substantial set of theoretical frameworks. From that effort, the need for a robust core model utilizing advanced mathematics and computation adequate for understanding the behavior of organisms as dynamic wholes was identified. At this end, the authors of this article have proposed WLIMES (Ehresmann and Simeonov, 2012), a formal theory for modeling living systems integrating both the Memory Evolutive Systems (Ehresmann and Vanbremeersch, 2007) and the Wandering Logic Intelligence (Simeonov, 2002b). Its principles will be recalled here with respect to their resonances to Eastern thought. (shrink)

The default theory of aesthetic value combines hedonism about aesthetic value with strict perceptual formalism about aesthetic value, holding the aesthetic value of an object to be the value it has in virtue of the pleasure it gives strictly in virtue of its perceptual properties. A standard theory of aesthetic value is any theory of aesthetic value that takes the default theory as its theoretical point of departure. This paper argues that standard theories fail because they theorize from the (...) default theory. (shrink)

Immanuel Kant's moral thesis is that reason alone must identify moral laws. Examining various interpretations of his ethics, this essay shows that the thesis fails. G. W. F. Hegel criticizes Kant's Formula of Universal Law as an empty formalism. Although Christine Korsgaard's Logical and Practical Contradiction Interpretations, Barbara Herman's contradiction in conception and contradiction in will tests, and Kenneth Westphal's paired use of Kant's universalization test all refute what Allen Wood calls a stronger form of the formalism charge, (...) they are not free from a weaker form of it. Some philosophers try to avoid both forms of the formalism charge in the following ways: First, some underline the roles of Kant's other formulas. Second, some interpret the Formula of Universal Law teleologically. Third, some claim that a maxim must be something all those potentially affected by it can rationally accept. Fourth, Robert Louden introduces the empirical to evaluate a maxim. All those attempts introduce heteronomy into Kant's ethics. Besides, on the third response, from the fact that all those potentially affected accept a maxim, it does not follow that it is morally right. It is impossible to avoid the formalism charge without making his ethics heteronomous. Thus, Kant's ethics is either empty or heteronomous. Either way it fails to identify moral laws by reason alone. (shrink)

A formalism is introduced to represent the connective organization of an evolving neuronal network and the effects of environment on this organization by stabilization or degeneration of labile synapses associated with functioning. Learning, or the acquisition of an associative property, is related to a characteristic variability of the connective organization: the interaction of the environment with the genetic program is printed as a particular pattern of such organization through neuronal functioning. An application of the theory to the development of (...) the neuromuscular junction is proposed and the basic selective aspect of learning emphasized. (shrink)

The study is focused on analysing formalism which is a strategy of applying laws by stressing the formal features of the law, even if the consequences of the strategy like that are difficult to accept in light of legal principles and the general requirement of equity. Contrary to the common view presented in the legal literature, the study sets out arguments that the formalism is neither justified in the tradition of legal positivism, neither in the idea of the (...) rule of law. In particular it is not true that formalism secures stability and predictability of laws application. On the other hand, a non-formalistic approach to applying laws, consisting in a simultaneous application of strict rules and general principles and in acknowledging the purpose and the function of the law as important factors, allows for realising the values that are traditionally linked with legal positivism. That non-formalistic approach to applying laws, called in the study 'interpretative holism', was supported by a wide use of contemporary philosophy of language, in particular the Kripke-Putnam semantics and the findings of the contemporary philosophy of law and legal theory. -/- Praca jest poświęcona analizie zjawiska formalizmu, które jest strategią stosowania prawa, podlegająca na podkreśleniu wagi formalnych cech prawa, nawet jeśli strategia taka prowadzi do rezultatów trudnych do zaakceptowania z punktu widzenia zasad prawa albo ogólnych wymogów słuszności. Przeciwnie do dotychczasowych stanowisk reprezentowanych w literaturze, w pracy przedstawione są argumenty, że formalistyczne podejście do stosowania prawa nie ma uzasadnienia, ani w koncepcji pozytywizmu prawniczego, ani w koncepcji rządów prawa. Z drugiej strony nieformalistyczne podejście do stosowania prawa, które polega głównie na współstosowaniu reguł i zasad oraz na uwzględnianiu celu i funkcji prawa, pozwala na realizację wartości tradycyjnie przypisywanych koncepcji pozytywizmu prawniczego. Ta nieformalistyczna strategia stosowania prawa, nazywana w pracy holizmem interpretacyjnym, została w pracy uzasadniona poprzez szerokie wykorzystanie współczesnej filozofii języka, w szczególności tzw. semantyki Kripkego-Putnama oraz współczesnego dorobku polskiej i zagranicznej teorii i filozofii prawa.". (shrink)

The computational argument for individualism, which moves from computationalism to individualism about the mind, is problematic, not because computationalism is false, but because computational psychology is, at least sometimes, wide. The paper provides an early, or perhaps predecessor, version of the thesis of extended cognition.

The hermeneutic pragmatism explored in this article timely examines how “post-truth” claims over-estimate semantic freedoms while at the same time underestimating semantic and pre-semantic restraints. Such pragmatism also timely examines how formalists err by committing the reverse errors. Drawing on insights from James, Peirce, Putnam, Rorty, Gadamer, Derrida, and others, such hermeneutic pragmatism explores (1) the necessary role of both internal and objective experience in meaning, (2) the resulting instrumental nature of concepts required to deal with such experience, (3) the (...) related need for workability to apply to the “the collectivity of experience’s demands, nothing being omitted,” (4) the inherent role of morality and other norms in measuring such workability, (5) the semantic as well as experiential nature of our workable realities, (6) the semantic freedoms involved in constructing, framing, and retaining our workable realities and concepts, and (7) the semantic, pre-semantic, and other restraints on constructing, framing, and retaining our workable realities and concepts. -/- Such hermeneutic pragmatism also introduces Eunomia, a real-world alternative to Dworkin’s superhuman judge Hercules. Named after the Greek goddess of good order, the human Eunomia represents the reasonable judge excellently versed in (among other things) legal theory, legal practice, linguistics, and philosophy of language. Additionally, in its appendices, this article surveys the pragmatic restraints of “implementives” and provides a detailed overview of pragmatic “workability” restraints for both law and fact. -/- (By “sense” the title of this article means not only “meaning conveyed or intended” but also “capacity for effective application of the powers of the mind as a basis for action or response.” See Sense, MERRIAM-WEBSTER’S COLLEGIATE DICTIONARY (11th ed. 2014) “Workable” has the broad meaning discussed in Sections II, IV, and Appendix C of the Article, and "good" is further explored in the section on Eunomia, namesake of the Greek goddess of good order.) -/- Keywords: Pragmatism, Hermeneutic, Truth, Rule of Law, William James, C.S. Peirce, Hilary Putnam, Richard Rorty, Gadamer, Habermas, Derrida, Lon Fuller, H.L.A. Hart, Post-truth, Postmodernism, Trump, Rhetoric, Meaning, Interpretation, Metaphor, Category, Lifeworld, Formalism, Framing, Deconstruction. (shrink)

Published in 1903, this book was the first comprehensive treatise on the logical foundations of mathematics written in English. It sets forth, as far as possible without mathematical and logical symbolism, the grounds in favour of the view that mathematics and logic are identical. It proposes simply that what is commonly called mathematics are merely later deductions from logical premises. It provided the thesis for which _Principia Mathematica_ provided the detailed proof, and introduced the work of Frege to a wider (...) audience. In addition to the new introduction by John Slater, this edition contains Russell's introduction to the 1937 edition in which he defends his position against his formalist and intuitionist critics. (shrink)

In this paper, I consider the use of mathematical results in philosophical arguments arriving at conclusions with non-mathematical content, with the view that in general such usage requires additional justification. As a cautionary example, I examine Kreisel’s arguments that the Continuum Hypothesis is determined by the axioms of Zermelo-Fraenkel set theory, and interpret Weston’s 1976 reply as showing that Kreisel fails to provide sufficient justification for the use of his main technical result. If we take the perspective that mathematical results (...) are used in the context of a modelling of something not necessarily mathematical, then the situation is clarified somewhat, and the procedure for arriving at justification for the use of such results becomes clear. I give an example of a particularly strong form this justification might take, using the idea of formalism independence due to Gödel and Kennedy. (shrink)

In this paper I present an account of musical arousal that takes into account key demands of formalist philosophers such as Peter Kivy and Nick Zangwill. Formalists prioritise our understanding and appreciation of the music itself. As a result, they demand that any feelings we have in response to music must be directed at the music alone, without being distracted by non-musical associations. To accommodate these requirements I appeal to a mechanism of contagion which I synthesize with the expectation-based arousal (...) mechanism proposed by Leonard Meyer. This account connects musical expressivity and arousal in a way that formalists have rejected, but I argue that it provides the best explanation of our observations of listener responses while also focusing on the music itself. (shrink)

In this study we offer a new way of applying Kendall Walton’s theory of make-believe to musical experiences in terms of psychologically inhibited games of make-believe, which Walton attributes chiefly to ornamental representations. Reading Walton’s theory somewhat against the grain, and supplementing our discussion with a set of instructive examples, we argue that there is clear theoretical gain in explaining certain important aspects of composition and performance in terms of psychologically inhibited games of make-believe consisting of two interlaced game-worlds. Such (...) complex games can accommodate a continuous rich spectrum of congruent modes of listening, which broaches both the formalist-type and the narrativist-type. We conclude that this sort of oblique reading of Walton’s original theory actually complements and completes Walton’s recent theoretic angle concerning thoughtwriting in music by way of affording it with a suitable conception for a mechanism of appropriation for music. (shrink)

[A Czech Greenberg? Mukařovský and Aesthetic Formalism] This article revisits Tomáš Pospiszyl’s discussion of the split between the North American and the Czechoslovak postwar modernism as a difference between the views of two critics who dominated the American and the Czechoslovak art scene, respectively--Clement Greenberg and Jindřich Chalupecký. Pospiszyl convincingly traces the evolution of American art to what has been called Greenberg’s “formalism,” and the developments on the Czechoslovak scene to Chalupecký’s ideas about art as part of social (...) social interactions. Though the author of the article agrees with this analysis of Czechoslovak modernism as anti-formalist, he seeks to draw attention to the writings of the Czech literary theorist Jan Mukařovský, which were contemporaneous with Chalupecký’s and Greenberg’s--in particular Mukařovský’s 1944 lecture “The Essence of the Visual Arts.” The author provides a comparative analysis of Mukařovský and Greenberg, suggesting that the former was quite close to the latter’s “formalism.” This might seem incorrect, given that Mukařovský is considered to be a precursor of the semiotic theory of art, which is generally understood as antithetical to formalism. The solution, he argues, is to realize that Greenberg is subtler, hence not so "formalist” after all. At any rate, it turns out that in addition to Chalupecký’s “social” theory of art, Mukařovský had a more “formalist” alternative which – for well-known historical reasons – had no effect on the subsequent development of Czechoslovak modernism. (shrink)

A study of the making of George Peacock's highly influential, yet disturbingly split, 1830 account of algebra as an entanglement of two separate undertakings: arithmetical and symbolical or formal.

This book analyses the impact computerization has had on contemporary science and explains the origins, technical nature and epistemological consequences of the current decisive interplay between technology and science: an intertwining of formalism, computation, data acquisition, data and visualization and how these factors have led to the spread of simulation models since the 1950s. -/- Using historical, comparative and interpretative case studies from a range of disciplines, with a particular emphasis on the case of plant studies, the author shows (...) how and why computers, data treatment devices and programming languages have occasioned a gradual but irresistible and massive shift from mathematical models to computer simulations. -/- . (shrink)

On one popular view, the general covariance of gravity implies that change is relational in a strong sense, such that all it is for a physical degree of freedom to change is for it to vary with regard to a second physical degree of freedom. At a quantum level, this view of change as relative variation leads to a fundamentally timeless formalism for quantum gravity. Here, we will show how one may avoid this acute ‘problem of time’. Under our (...) view, duration is still regarded as relative, but temporal succession is taken to be absolute. Following our approach, which is presented in more formal terms in, it is possible to conceive of a genuinely dynamical theory of quantum gravity within which time, in a substantive sense, remains. 1 Introduction1.1 The problem of time1.2 Our solution2 Understanding Symmetry2.1 Mechanics and representation2.2 Freedom by degrees2.3 Voluntary redundancy3 Understanding Time3.1 Change and order3.2 Quantization and succession4 Time and Gravitation4.1 The two faces of classical gravity4.2 Retaining succession in quantum gravity5 Discussion5.1 Related arguments5.2 Concluding remarks. (shrink)

Conversational exculpature is a pragmatic process whereby information is subtracted from, rather than added to, what the speaker literally says. This pragmatic content subtraction explains why we can say “Rob is six feet tall” without implying that Rob is between 5'0.99" and 6'0.01" tall, and why we can say “Ellen has a hat like the one Sherlock Holmes always wears” without implying Holmes exists or has a hat. This article presents a simple formalism for understanding this pragmatic mechanism, specifying (...) how, in context, the result of such subtractions is determined. And it shows how the resulting theory of conversational exculpature accounts for a varied range of linguistic phenomena. A distinctive feature of the approach is the crucial role played by the question under discussion in determining the result of a given exculpature. (shrink)

Does the notion of ground, as it has recently been employed by metaphysicians, point to a single unified phenomenon? Jonathan Schaffer holds that the phenomenon of grounding exhibits the unity characteristic of a single genus. In defense of this hypothesis, Schaffer proposes to take seriously the analogy between causation and grounding. More specifically, Schaffer argues that both grounding and causation are best approached through a single formalism, viz., that utilized by structural equation models of causation. In this paper, I (...) present several concerns which suggest that the structural equation model does not transfer as smoothly from the case of causation to the case of grounding as Schaffer would have us believe. If it can in fact be shown that significant differences surface in how the formalism in question applies to the two types of phenomena in question, Schaffer’s attempt at establishing an analogy between grounding and causation has thereby been weakened and, as a result, the application of the Unity Hypothesis to the case of grounding once again stands in need of justification. (shrink)

The relationship between abstract formal procedures and the activities of actual physical systems has proved to be surprisingly subtle and controversial, and there are a number of competing accounts of when a physical system can be properly said to implement a mathematical formalism and hence perform a computation. I defend an account wherein computational descriptions of physical systems are high-level normative interpretations motivated by our pragmatic concerns. Furthermore, the criteria of utility and success vary according to our diverse purposes (...) and pragmatic goals. Hence there is no independent or uniform fact to the matter, and I advance the ‘anti-realist’ conclusion that computational descriptions of physical systems are not founded upon deep ontological distinctions, but rather upon interest-relative human conventions. Hence physical computation is a ‘conventional’ rather than a ‘natural’ kind. (shrink)

I argue for an enactive account of musical experience — that is, the experience of listening ‘deeply’(i.e., sensitively and understandingly) to a piece of music. The guiding question is: what do we do when we listen ‘deeply’to music? I argue that these music listening episodes are, in fact, doings. They are instances of active perceiving, robust sensorimotor engagements with and manipulations of sonic structures within musical pieces. Music is thus experiential art, and in Nietzsche’s words, ‘we listen to music with (...) our muscles’. This paper attempts to explicate and defend this claim. First, I discuss enactive approaches to consciousness and cognition generally. Next, I apply an enactive model of perceptual consciousness to the experience of listening to music. To clarify what is at stake, I use Peter Kivy’s ‘enhanced formalism’ as a philosophical foil. I then look at how the animate body shapes musical experience. (shrink)

The Foundational Model of Anatomy (FMA) symbolically represents the structural organization of the human body from the macromolecular to the macroscopic levels, with the goal of providing a robust and consistent scheme for classifying anatomical entities that is designed to serve as a reference ontology in biomedical informatics. Here we articulate the need for formally clarifying the is-a and part-of relations in the FMA and similar ontology and terminology systems. We diagnose certain characteristic errors in the treatment of these relations (...) and show how these errors can be avoided through adoption of the formalism we describe. We then illustrate how a consistently applied formal treatment of taxonomy and partonomy can support the alignment of ontologies. (shrink)

Detlefsen (1986) reads Hilbert's program as a sophisticated defense of instrumentalism, but Feferman (1998) has it that Hilbert's program leaves significant ontological questions unanswered. One such question is of the reference of individual number terms. Hilbert's use of admittedly "meaningless" signs for numbers and formulae appears to impair his ability to establish the reference of mathematical terms and the content of mathematical propositions (Weyl (1949); Kitcher (1976)). The paper traces the history and context of Hilbert's reasoning about signs, which illuminates (...) Hilbert's account of mathematical objectivity, axiomatics, idealization, and consistency. (shrink)

True beliefs are better guides to the world than false ones. This is the common-sense assumption that undergirds theorizing in evolutionary epistemology. According to Alvin Plantinga, however, evolution by natural selection does not care about truth: it cares only about fitness. If our cognitive faculties are the products of blind evolution, we have no reason to trust them, anytime or anywhere. Evolutionary naturalism, consequently, is a self-defeating position. Following up on earlier objections, we uncover three additional flaws in Plantinga's latest (...) formulation of his argument: a failure to appreciate adaptive path dependency, an incoherent conception of content ascription, and a conflation of common-sense and scientific beliefs, which we diagnose as the ‘foundationalist fallacy’. More fundamentally, Plantinga's reductive formalism with respect to the issue of cognitive reliability is inadequate to deal with relevant empirical details. (shrink)

We argue that philosophers ought to distinguish epistemic decision theory and epistemology, in just the way ordinary decision theory is distinguished from ethics. Once one does this, the internalist arguments that motivate much of epistemic decision theory make sense, given specific interpretations of the formalism. Making this distinction also causes trouble for the principle called Propriety, which says, roughly, that the only acceptable epistemic utility functions make probabilistically coherent credence functions immodest. We cast doubt on this requirement, but then (...) argue that epistemic decision theorists should never have wanted such a strong principle in any case. (shrink)

2nd edition. Many-valued logics are those logics that have more than the two classical truth values, to wit, true and false; in fact, they can have from three to infinitely many truth values. This property, together with truth-functionality, provides a powerful formalism to reason in settings where classical logic—as well as other non-classical logics—is of no avail. Indeed, originally motivated by philosophical concerns, these logics soon proved relevant for a plethora of applications ranging from switching theory to cognitive modeling, (...) and they are today in more demand than ever, due to the realization that inconsistency and vagueness in knowledge bases and information processes are not only inevitable and acceptable, but also perhaps welcome. The main modern applications of (any) logic are to be found in the digital computer, and we thus require the practical knowledge how to computerize—which also means automate—decisions (i.e. reasoning) in many-valued logics. This, in turn, necessitates a mathematical foundation for these logics. This book provides both these mathematical foundation and practical knowledge in a rigorous, yet accessible, text, while at the same time situating these logics in the context of the satisfiability problem (SAT) and automated deduction. The main text is complemented with a large selection of exercises, a plus for the reader wishing to not only learn about, but also do something with, many-valued logics. (shrink)

We expound 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. The ψ function is no longer interpreted as a probability amplitude of the observed behaviour of elementary particles but as an objective physical field representing the particles themselves. The particles are thus extended objects whose extension varies in time according (...) to the variation of ψ. They are considered as fundamental regions of space with some kind of nonlocality. Special consideration is given to the Heisenberg relations, the Einstein-Podolsky- Rosen correlations, the reduction process, the problem of measurement, and the quantum-statistical distributions. (shrink)

Several prominent philosophers of art have worried about whether Kant has a coherent theory of music on account of two perceived tensions in his view. First, there appears to be a conflict between his formalist and expressive commitments. Second (and even worse), Kant defends seemingly contradictory claims about music being beautiful and merely agreeable, that is, not beautiful. Against these critics, I show that Kant has a consistent view of music that reconciles these tensions. I argue that, for Kant, music (...) can be experienced as either agreeable or beautiful depending on the attitude we take toward it. Although it is tempting to think he argues that we experience music as agreeable when we attend to its expressive qualities and as beautiful when we attend to its formal properties, I demonstrate that he actually claims that we are able to judge music as beautiful only if we are sensitive to the expression of emotion through musical form. With this revised understanding of Kant's theory of music in place, I conclude by sketching a Kantian solution to a central problem in the philosophy of music: given that music is not sentient, how can it express emotion? (shrink)

A new form of skepticism is described, which holds that objectivity and understanding are incompossible ideals of modern science. This is attributed to Weyl, hence its name: Weylean skepticism. Two general defeat strategies are then proposed, one of which is rejected as a failure.

Walter Dubislav (1895–1937) was a leading member of the Berlin Group for scientific philosophy. This “sister group” of the more famous Vienna Circle emerged around Hans Reichenbach’s seminars at the University of Berlin in 1927 and 1928. Dubislav was to collaborate with Reichenbach, an association that eventuated in their conjointly conducting university colloquia. Dubislav produced original work in philosophy of mathematics, logic, and science, consequently following David Hilbert’s axiomatic method. This brought him to defend formalism in these disciplines as (...) well as to explore the problems of substantiating (Begründung) human knowledge. Dubislav also developed elements of general philosophy of science. Sadly, the political changes in Germany in 1933 proved ruinous to Dubislav. He published scarcely anything after Hitler came to power and in 1937 committed suicide under tragic circumstances. The intent here is to pass in review Dubislav’s philosophy of logic, mathematics, and science and so to shed light on some seminal yet hitherto largely neglected currents in the history of philosophy of science. (shrink)

Our conscious minds exist in the Universe, therefore they should be identified with physical states that are subject to physical laws. In classical theories of mind, the mental states are identified with brain states that satisfy the deterministic laws of classical mechanics. This approach, however, leads to insurmountable paradoxes such as epiphenomenal minds and illusionary free will. Alternatively, one may identify mental states with quantum states realized within the brain and try to resolve the above paradoxes using the standard Hilbert (...) space formalism of quantum mechanics. In this essay, we first show that identification of mind states with quantum states within the brain is biologically feasible, and then elaborating on the mathematical proofs of two quantum mechanical no-go theorems, we explain why quantum theory might have profound implications for the scientific understanding of one's mental states, self identity, beliefs and free will. (shrink)

We argue that the mathematization of science should be understood as a normative activity of advocating for a particular methodology with its own criteria for evaluating good research. As a case study, we examine the mathematization of taxonomic classification in systematic biology. We show how mathematization is a normative activity by contrasting its distinctive features in numerical taxonomy in the 1960s with an earlier reform advocated by Ernst Mayr starting in the 1940s. Both Mayr and the numerical taxonomists sought to (...) formalize the work of classification, but Mayr introduced a qualitative formalism based on human judgment for determining the taxonomic rank of populations, while the numerical taxonomists introduced a quantitative formalism based on automated procedures for computing classifications. The key contrast between Mayr and the numerical taxonomists is how they conceptualized the temporal structure of the workflow of classification, specifically where they allowed meta-level discourse about difficulties in producing the classification. (shrink)

Abstract: One of the institutional highlights of the encounter between Austrian “wissen¬schaftliche Philosophie” and French “philosophie scientifique” in the first half of the 20th century was the “First International Congress for Unity of Science” that took place 1935 in Paris. In my contribution I deal with an episode of the philosophical mega-event whose protagonist was the American philosopher and semiotician Charles William Morris. At the Paris congress he presented his programme of a comprehensive, practice-oriented scientific philosophy and, in a more (...) elaborated version he published it two years later in Logical Positivism, Pragmatism and Scientific Empiricism (Morris 1937). Morris aimed at a synthesis of formalism, pragmatism, and traditional empiricism that combined the virtues of these accounts while avoided their shortocmings. The core of approach was a comprehensive theory of the concept of meaning. Through an analysis of the concept of meaning he sought to sort out the existing differences and the options for a possible future rapprochment between logical empiricism and pragmatism. Against the overly narrow logical empiricist understanding of philosophy as the syntax of the language of science Morris argued for a “scientific pragmatism” that comprised four levels: (1) Philosophy as Logic of Science, (2) Philosophy as Clarification of Meaning (Peirce), (3) Philosophy as Empirical Axiology (Dewey), and (4) Philosophy as Empirical Cosmology (Whitehead). (shrink)

Although Kant (1998) envisaged a prominent role for logic in the argumentative structure of his Critique of Pure Reason, logicians and philosophers have generally judged Kantgeneralformaltranscendental logics is a logic in the strict formal sense, albeit with a semantics and a definition of validity that are vastly more complex than that of first-order logic. The main technical application of the formalism developed here is a formal proof that Kants logic is after all a distinguished subsystem of first-order logic, namely (...) what is known as geometric logic. (shrink)

“Second-order Logic” in Anderson, C.A. and Zeleny, M., Eds. Logic, Meaning, and Computation: Essays in Memory of Alonzo Church. Dordrecht: Kluwer, 2001. Pp. 61–76. -/- Abstract. This expository article focuses on the fundamental differences between second- order logic and first-order logic. It is written entirely in ordinary English without logical symbols. It employs second-order propositions and second-order reasoning in a natural way to illustrate the fact that second-order logic is actually a familiar part of our traditional intuitive logical framework and (...) that it is not an artificial formalism created by specialists for technical purposes. To illustrate some of the main relationships between second-order logic and first-order logic, this paper introduces basic logic, a kind of zero-order logic, which is more rudimentary than first-order and which is transcended by first-order in the same way that first-order is transcended by second-order. The heuristic effectiveness and the historical importance of second-order logic are reviewed in the context of the contemporary debate over the legitimacy of second-order logic. Rejection of second-order logic is viewed as radical: an incipient paradigm shift involving radical repudiation of a part of our scientific tradition, a tradition that is defended by classical logicians. But it is also viewed as reactionary: as being analogous to the reactionary repudiation of symbolic logic by supporters of “Aristotelian” traditional logic. But even if “genuine” logic comes to be regarded as excluding second-order reasoning, which seems less likely today than fifty years ago, its effectiveness as a heuristic instrument will remain and its importance for understanding the history of logic and mathematics will not be diminished. Second-order logic may someday be gone, but it will never be forgotten. Technical formalisms have been avoided entirely in an effort to reach a wide audience, but every effort has been made to limit the inevitable sacrifice of rigor. People who do not know second-order logic cannot understand the modern debate over its legitimacy and they are cut-off from the heuristic advantages of second-order logic. And, what may be worse, they are cut-off from an understanding of the history of logic and thus are constrained to have distorted views of the nature of the subject. As Aristotle first said, we do not understand a discipline until we have seen its development. It is a truism that a person's conceptions of what a discipline is and of what it can become are predicated on their conception of what it has been. (shrink)

Does it make sense to employ modern logical tools for ancient philosophy? This well-known debate2 has been re-launched by the indologist Piotr Balcerowicz, questioning those who want to look at the Eastern school of Jainism with Western glasses. While plainly acknowledging the legitimacy of Balcerowicz's mistrust, the present paper wants to propose a formal reconstruction of one of the well-known parts of the Jaina philosophy, namely: the saptabhangi, i.e. the theory of sevenfold predication. Before arguing for this formalist approach to (...) philosophy, let us return to the reasons to be reluctant at it. (shrink)