A comprehensive historical overview of formalist ideas in the philosophy of mathematics.

Joe L. Kincheloe (1950-2008) was one of North America's leading critical pedagogy scholars. He defined post-formalist thought in terms of deconstruction, affectivity, and non-linearity. His deconstruction focused on the context of ideas, ideologies, and teaching. It was a form of sociological deconstruction, and as such, inspired by Derrida, but different from him as well. In effect, Kincheloe was trying to marry Derrida to Foucault by making deconstruction see power in thought, relationships, and the world. Kincheloe's 'turn to affect' was inspired (...) by feminism and radical pedagogy. It was 'affect' focused on (in)justice and the social practices of repression. His 'self-other' construct was inherently politicized by his identification of 'unfreedom' with capitalism and the assumption that this link determines affect. Kincheloe assumed that linear rationality was inadequate to understanding human needs and hopes. Freedom as dynamism was seen to be inherently non-linear. The prison of rationality (it can only repeat the same, over and over again) was the crux of his critique of Newtonian-Cartesian linearity. Kincheloe attempted to construct a concept of 'place'--such as the classroom. But it was a particular, concrete classroom and not an abstract or theoretical one. Here, the three concepts could come together. 'Place' is context, and to understand it, deconstruction is needed. 'Place' exists as it is felt and requires affectivity; it is eventful, alive, and dynamic. It requires non-linearity to be understood. Post-formalism, Pedagogy Lives (in memory of Kincheloe's contribution) encompasses each of the basic principles of Kincheloe's post-formal thought. (shrink)

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)

Introductory Remarks IN A MAJOR WORK planned for the near future I will attempt to develop a non-formal ethics of Values on the broadest possible basis of ...

It is sometimes claimed that formalism and the logical incompatibility thesis together imply that fouls cannot be part of the game. Some philosophers think this proves that therefore strategic fouls are always morally wrong, but other philosophers think this result undermines formalism itself, since strategic fouls clearly are part of the game and are at least sometimes morally permissible. I show that formalism in fact does accommodate strategic fouls and that it is neutral about whether strategic fouls (...) are morally permissible or not. (shrink)

When discussing Wilfrid Sellars’s philosophy, very little work has been done to offer a developmental account of his systematic views. More often than not, Sellars’s complex views are presented in a systematic and holistic fashion that ignores any periodization of his work. I argue that there is a metaphilosophical shift in Sellars’s early philosophy that results in substantive changes to his conception of language, linguistic rules, and normativity. Specifically, I claim that Sellars’s shift from a formalist metaphilosophy to one more (...) closely aligned with psychology allows for the construction of a normative conception of language. My central claim is that without his abandonment of earlier metaphilosophical commitments, Sellars could not hold what I call an external conception of normativity. It is this move away from a formalist notion of philosophy that allows Sellars to construct a normative picture of language. I conclude that because this substantive shift in philosophical commitments results from changes in Sellars’s metaphilosophical views, there is insight to be found in a meticulous periodization of his work. (shrink)

Constitutivists have tried to answer Enoch’s “schmagency” objection by arguing that Enoch fails to appreciate the inescapability of agency. Although these arguments are effective against some versions of the objection, I argue that they leave constitutivism vulnerable to an important worry; namely, that constitutivism leaves us alienated from the moral norms that it claims we must follow. In the first part of the paper, I try to make this vague concern more precise: in a nutshell, it seems that constitutivism cannot (...) provide an adequate account of the relation between the constitutive norms of agency and the particular ends the agent pursues. I then provide a broad outline of an interpretation of Kant’s formalism that is immune to this objection. I conclude that constitutivism is best understood as the upshot of a formalist view of categorical practical principles. (shrink)

This chapter contains sections titled: The Project of Formalism The Nature of Justification The Structures of Justification The Ground of Justification The Immanent Intelligibility of Law Conclusion References.

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)

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)

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)

Social network research is widely considered atheoretical. In contrast, in this article I argue that network analysis often mixes two distinct theoretical frameworks, creating a logically inconsistent foundation. Relationalism rejects essentialism and a priori categories and insists upon the intersubjectivity of experience and meaning as well as the importance of the content of interactions and their historical setting. Formalism is based on a structuralist interpretation of the theoretical works of Georg Simmel. Simmel laid out a neo-Kantian program of identifying (...) a priori categories of relational types and patterns that operate independently of cultural content or historical setting. Formalism and relationalism are internally consistent theoretical perspectives, but there are tensions between them. To pave the way for stronger middle-range theoretical development, I disaggregate the two approaches and highlight the contradictions that must be addressed or resolved for the construction of any general and inclusive theory. (shrink)

The structure of the rate of variation of the atomic energy for an arbitrary stationary motion of the atom in interaction with a quantum electromagnetic field is investigated. Our main purpose is to rewrite the formalism in Zhu et al. and to deduce the general expressions of the Einstein A coefficients of an atom on an arbitrary stationary trajectory. The total rate of change of the energy and Einstein coefficients of the atom near a plate with finite temperature or (...) acceleration are also investigated. (shrink)

In a narrow sense, the formalistic conception of art cannot range and explain a wide variety of contemporary art phenomena. In a wide sense, formalism – rejecting the reductionist definition of the essence of art, involving the conceptual dimension of the artwork, and expanding the dimension of sensibility – becomes a productive philosophical art theory allowing one to explain and investigate some part of the contemporary art (modern and postmodern) phenomena. In the expanded conception, the basic principles of aesthetic (...) formalism include a wide scale of the principles of the creation and comprehension of the artwork – from an abstract form (perceived by senses) to a conceptual form. The article gives an illustration of these principles discussing abstractionism and surrealism as two different types of the contemporary formalistic visual art. (shrink)

In his remarkable paper Formalism 64, Robinson defends his eponymous position concerning the foundations of mathematics, as follows:Any mention of infinite totalities is literally meaningless.We should act as if infinite totalities really existed. Being the originator of Nonstandard Analysis, it stands to reason that Robinson would have often been faced with the opposing position that ‘some infinite totalities are more meaningful than others’, the textbook example being that of infinitesimals. For instance, Bishop and Connes have made such claims regarding (...) infinitesimals, and Nonstandard Analysis in general, going as far as calling the latter respectively a debasement of meaning and virtual, while accepting as meaningful other infinite totalities and the associated mathematical framework. We shall study the critique of Nonstandard Analysis by Bishop and Connes, and observe that these authors equate ‘meaning’ and ‘computational content’, though their interpretations of said content vary. As we will see, Bishop and Connes claim that the presence of ideal objects in Nonstandard Analysis yields the absence of meaning. We will debunk the Bishop–Connes critique by establishing the contrary, namely that the presence of ideal objects in Nonstandard Analysis yields the ubiquitous presence of computational content. In particular, infinitesimals provide an elegant shorthand for expressing computational content. To this end, we introduce a direct translation between a large class of theorems of Nonstandard Analysis and theorems rich in computational content, similar to the ‘reversals’ from the foundational program Reverse Mathematics. The latter also plays an important role in gauging the scope of this translation. (shrink)

A simple mathematical extension of quantum theory is presented. As well as opening the possibility of alternative methods of calculation, the additional formalism implies a new physical interpretation of the standard theory by providing a picture of an external reality. The new formalism, developed first for the single-particle case, has the advantage of generalizing immediately to quantum field theory and to the description of relativistic phenomena such as particle creation and annihilation.

The development and applicability of complex numbers is often cited in defence of the formalist philosophy of mathematics. This view is rejected through an examination of hamilton's development of the notion of complex numbers as ordered pairs of reals, And his later development of the quaternion theory, Which subsequently formed the basis of vector analysis. Formalism, By protecting informal assumptions from critical scrutiny, Constrained rather than encouraged the development of mathematics.

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.

Rosenberg concludes with a critical reassessment of widely accepted views regarding the relationships among natural languages, mathematical formalisms, and philosophical commitments. The culmination of twenty years' reflection, Beyond Formalism is an original and sophisticated book of importance to both philosophers and linguists.

This paper objectively defines the three main contemporary philosophies of mathematics: formalism, logicism, and intuitionism. Being the three leading scientists of each: Hilbert (formalist), Frege (logicist), and Poincaré (intuitionist).

Mīmāṁsā, an Indian hermeneutics provides an exhaustive methodology to interpret Vedic statements. A formalism namely, Mīmāṁsā Inspired Representation of Actions has already been proposed in a preliminary manner. This paper expands the formalism logically and includes Syntax and Semantics covering Soundness and Completeness. Here, several interpretation techniques from Mīmāṁsā have been considered for formalising the statements. Based on these, instructions that denote actions are categorized into positive and prohibitive unconditional imperatives and conditional imperatives that enjoin reason, temporal action (...) and goal. These instructions are evaluated to three values S, V and N. If the instruction is executed with the intention of goal, then it acquires the value of S; if the intention of goal is present and the instruction is not executed, then it assumes the value of V; and if there is no intention of goal, then the instruction is evaluated to N. This formalism has also been applied in different computational settings such as AI planning, Robotics, task analysis and classification of natural language instructions. An outline of these applications and the comparison of this formalism with other relevant theories are also presented in this paper. (shrink)

According to long-established narratives, legal thinking in Germany, France and the U.S.A. was shaped by formalist legal cultures for the most part of the nineteenth century until the respective legal sciences embraced their social responsibility in the early twentieth century. Recently, legal historians have begun to question these narratives. In separate analyses, they have shown that the critics of ‘Legal Formalism’ exerted a lasting influence on historical research since the early twentieth century, thereby fostering a deeply charged understanding of (...) nineteenth century jurisprudence. What went largely unnoticed, however, was the transnational dimension of this false narrative. Due to the transnational ties of the critics of ‘Legal Formalism’, a powerful misrepresentation of nineteenth century Western legal thought emerged that still influences contemporary global legal history. Dismantling the prejudices surrounding the Western jurisprudence of the nineteenth century causes crucial challenges for conceptualising nineteenth century Western legal thought. (shrink)

The traditional exposition of Kantian ethical theory in the business ethics literature is abstract, esoteric, and impractical compared to the more usable presentations of utilitarianism. This situation can be improved by identifying and describing the conceptual dimensions of formalistic ethical reasoning, as contained in the interplay between case and principle, with examples from the business/society literature.

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)

This chapter contains sections titled: 1 2 3 4 5.

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)

A current focus of legal debate is the proper role of the courts in the interpretation of statutes and the Constitution. Are judges to look solely to the naked language of an enactment, then logically deduce its application in simple syllogistic fashion, as legal formalists had purported to do? Or may the inquiry into meaning be informed by perhaps unbridled and unaccountable judicial notions of public policy, using legal realism to best promote the general welfare? Judge Posner considers the concepts (...) of formalism and realism to be meaningful and useful in common law reasoning but in interpretation to be useless and, worse, forbidden. He analogizes unclear "orders" from a legislature to garbled battlefield communications, and argues that the duty of the recipient of those orders (the judge) is to advance as best he can the enterprise set on foot by the superiors. Case studies elaborate this thesis. Judicial decisions interpreting fixed texts, Judge Posner concludes, can be neither logically correct or incorrect, philosophically sound or unsound, until the ultimate jurist, time, has adjudged their results. (shrink)

In his work, Bernard Suits presents and pursues a stated objective: to define ‘game’ or, more precisely, ‘game-playing’. In The Grasshopper: Games, Life and Utopia, the author seeks a definition not as a ‘commitment to the universal fruitfulness of definition construction’, but rather with the idea ‘that some things are definable, and some are not’. This is something he believed could resolve many of the issues surrounding the debate on ‘game’ and ‘play’, such as those with Huizinga (in Homo Ludens) (...) or proposed by the anti-definitionism of Wittgenstein, a philosopher who did not accept that it was possible to define ‘game’. In this article, we will trace Suits’ definitional steps and aim to critique his resolution as a kind of ‘formalism’, as it tended to prioritize rules. Furthermore, notwithstanding the merit of his theoretical endeavor – seen in the attempt to define a social component that is so complex and the target of the most diverse interpretations and misconceptions –, it seems to us that, with his theoretical unifying element (lusory attitude), the author has summoned another problem to the debate, that of ‘subjectivism’, rather than a solution (especially to his formalism), even subjecting himself to comparisons with other conceptions (e.g. Fichte) that are also problematic. This aspect will also be criticized. The attention of this article will shift to these two lines of critique, drawing on an insightful analysis of Malaby’s work at a specific juncture, aiming to delve further into the subject and taking an additional step. (shrink)

In this paper we isolate a notion that we call “formalism freeness” from Gödel's 1946 Princeton Bicentennial Lecture, which asks for a transfer of the Turing analysis of computability to the cases of definability and provability. We suggest an implementation of Gödel's idea in the case of definability, via versions of the constructible hierarchy based on fragments of second order logic. We also trace the notion of formalism freeness in the very wide context of developments in mathematical logic (...) in the 20th century. (shrink)

ABSTRACT In a recent essay, Sören Stenlund tries to align Wittgenstein’s approach to the foundations and nature of mathematics with the tradition of symbolic mathematics. The characterization of symbolic mathematics made by Stenlund, according to which mathematics is logically separated from its external applications, brings it closer to the formalist position. This raises naturally the question whether Wittgenstein holds a formalist position in philosophy of mathematics. The aim of this paper is to give a negative answer to this question, defending (...) the view that Wittgenstein always thought that there is no logical separation between mathematics and its applications. I will focus on Wittgenstein’s remarks about arithmetic during his middle period, because it is in this period that a formalist reading of his writings is most tempting. I will show how his idea of autonomy of arithmetic is not to be compared with the formalist idea of autonomy, according to which a calculus is “cut off” from its applications. The autonomy of arithmetic, according to Wittgenstein, guarantees its own applicability, thus providing its own raison d’être. RESUMO Em um recente artigo, Sören Stenlund procura alinhar a abordagem de Wittgenstein em relação aos fundamentos e à natureza da matemática com a tradição da matemática simbólica. A caracterização da matemática simbólica feita por Stenlund, de acordo com a qual a matemática é logicamente separada de suas aplicações externas, a aproxima da posição formalista. Isto naturalmente levanta a questão de se Wittgenstein defende uma posição formalista em filosofia da matemática. O objetivo deste artigo é dar uma resposta negativa a esta questão, ao defender que Wittgenstein sempre pensou não haver separação lógica entre a matemática e suas aplicações. Atenção especial será dada às observações de Wittgenstein sobre a aritmética pertencentes ao seu período intermediário, pois é neste período que uma leitura formalista de seus escritos é mais sedutora. Mostrarei como sua ideia de autonomia da aritmética não deve ser comparada à ideia formalista de autonomia, segundo a qual um cálculo é “cortado” de suas aplicações. A autonomia da aritmética, para Wittgenstein, garante ela própria sua aplicabilidade, provendo, assim, sua própria raison d’être. (shrink)

In this paper I begin to fashion a theory of musical form that I call historical formalism. Historical formalism posits that our perception of the formal properties of a musical work is informed by considerations not only of artistic categories but also of the historical, sociopolitical, and cultural circumstances within which that work was composed.

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)

Carnap's position on mathematical truth in The Logical Syntax of Language has been attacked from two sides: Kreisel argues that it is formalistic but should not be, and Friedman argues that it is not formalistic but needs to be. In this paper I argue that the Carnap of Syntax does not eliminate our ordinary notion of mathematical truth in favour of a formal analogue; so Carnap's notion of mathematical truth is not formalistic. I further argue that there is no conflict (...) between Carnap's use of informal notions and his principle of tolerance; so Carnap's definition of mathematical truth need not be formalistic. CiteULike Connotea Del.icio.us What's this? (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.

In this paper we isolate a notion that we call "formalism freeness" from Gödel's 1946 Princeton Bicentennial Lecture, which asks for a transfer of the Turing analysis of computability to the cases of definability and provability We suggest an implementation of Gödel's idea in the case of definability, via versions of the constructible hierarchy based on fragments of second order logic. We also trace the notion of formalism freeness in the very wide context of developments in mathematical logic (...) in the 20th century. (shrink)

This dissertation is intended to provide a formalism for those generics that trigger nonmonotonic inferences. The formalism is to reflect intentionality and exception-tolerating features of generics, and has an emphasis on the axiomatization of generic reasoning that encodes nonmonotonicity. ;A modal conditional approach is taken to formalize the nonmonotonic reasoning in general at the level of object language. A serial of logic systems---MN, NID, NCUM, N STCUM---are constructed in an increasing strength of the characterized nonmonotonic inference relation. In (...) these systems, two binary modal operators ⩾ and > are introduced in their syntax, and a ⊛ function lifted from the traditional * function is deployed in their semantics. These systems are shown to be sound and complete with respect to certain classes of frames defined in the semantics. They are decidable as well. The nonmonotonic inference is argued to be a ternary relation "[phi], Gamma |∼ alpha", and is defined in the system NSTCUM. Many widely discussed nonmonotonic inference patterns such as Defeasible Modus Ponens, Defeasible Transitivity, the Penguin Principle etc. are justified. The specificity rule is proved to be a theorem of the system N STCUM. The impact of negated defaults on an inference is also investigated and accounted for. ;A canonical form to read off generics is proposed: All generic sentences with subject-predicate structure can be re-written into their canonical form S . If S is a plural noun phrase, it can be further refined to be . Normal objects are selected based on the "meaning" of the subject and predicate terms. The second parameter provides an aspect with respect to which certain objects of a kind are considered normal. Due to such a way to select normal objects, the drowning problem is solved. ;The inference behaviors of generics are axiomatized in the system G, which is a quantificational extension of the system NSTCUM. It is proved to be sound and complete with respect to the class of L⩾,G -frames. Those benchmark examples of generic inferences are examined in the system G. (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)

This essay presents the Aestheticism of the 19th century as the foundational movement of modernist-formalist aesthetics of the 20th century. The main principle of this movement is what I denominate “productive opacity”. Aestheticism has not been recognized as a philosophical aesthetic theory. However, its definition of artwork as an exclusive kind of form—a deep, opaque form—is among the most precise ever given in the discipline. This essay offers an interpretation of aestheticism as a formalist theory, referred to here as “deep (...) formalism”, focusing on the thinking of leading aestheticists, Walter Pater, Oscar Wilde, and James Whistler. These three thinkers defined artwork as a form saturated with an inextricable content, viz. opaque form. (shrink)

LEGO tells about not just LEGO architecture but architecture generally: its objects, its aesthetic properties, and how people judge them. To illustrate how thinking about LEGO can help people with such matters, this chapter considers some scenarios. These scenarios illustrate two very different ways of thinking about architecture. On the one hand, people might think architectural objects (more commonly, "works of architecture"), like buildings, bridges, and aqueducts, have forms that stand on their own, and which thereby do not depend on (...) historical, environmental, or any other contexts. On the other hand, they might think that architectural objects are best understood (maybe only understood) if they have one or more kinds of contextual information. From a different angle, some might see formalism as a better fit with original LEGO world design than with real‐world architectural design. Proponents of formalism take note of what makes architectural objects distinctive. (shrink)

This book revisits the theory of the sources of international law from the perspective of formalism.

Coordinate formalism on Hilbert manifolds developed in \cite{Kryukov} is reviewed. The results of \cite{Kryukov} are applied to the simpliest case of a Hilbert manifold: the abstract Hilbert space. In particular, functional transformations preserving properties of various linear operators on Hilbert spaces are found. Any generalized solution of an arbitrary linear differential equation with constant coefficients is shown to be related to a regular solution by a (functional) coordinate transformation. The results also suggest a way of using generalized functions to (...) solve nonlinear problems on Hilbert spaces. (shrink)

Coordinate formalism on Hilbert manifolds developed in \cite{Kryukov}, \cite{Kryukov1} is further analyzed. The main subject here is a comparison of the ordinary and the string bases of eigenvectors of a linear operator as introduced in \cite{Kryukov}. It is shown that the string basis of eigenvectors is a natural generalization of its classical counterpart. It is also shown that the developed formalism forces us to consider any Hermitian operator with continuous spectrum as a restriction to a space of square (...) integrable functions of a self-adjoint operator defined on a space of generalized functions. In the formalism functional coordinate transformations preserving the norm of strings are now linear isometries rather than the unitary transformations. (shrink)

Placing the work of key figures in context and addressing such issues as aesthetics, linguistics and the category of literature, form and function or literary ...

. This paper endeavors to formalize imperatives that convey actions. Imperatives, unlike propositions, do not hold the value of true or false. Peter Vranas proposed an alternate logical formalism in the literature of imperative logic with three values, namely: Satisfaction (), Violation () and Avoidance (). Although this formalism takes into account the conditional imperatives, it does not address imperatives from the perspective of actions. According to Mīmāṁsā, the prime motive of an imperative is to carry out action (...) so as to reach the goal. This paper modifies the notion of Vranas' imperative logic using Mīmāṁsā principles. The resulting imperative formalism, focusing on action representation, is presented with syntax, deduction rules and semantic tables. The effectiveness of this representation is demonstrated in the area of artificial intelligence planning. (shrink)

The ramified legacy of Bernard Berenson’s writings within 20th century art historiography is both celebrated and maligned. In an effort to help reconcile this situation, this essay argues for the partial validity of Berenson’s peculiar version of art historical formalism by detailing its historical connections to the Pragmatist philosophy and psychology of William James and by analytically correlating Berenson’s arguments with recent work in aesthetics and the philosophy of perception. The essay examines the specific example of Berenson’s analysis of (...) Giotto’s paintings and leverages a Pragmatist interpretation of Berenson’s writings to frame Berenson’s known connections with other writers: including Adolf Hildebrand, Giovanni Morelli, and Walter Pater. In conclusion, the failure, potential, reception, and legacy of Berenson’s art historical scholarship are assessed in relation to Pragmatist ideas. Der vielfältige Einfluss von Bernard Berensons Schriften auf die Kunstgeschichte des 20. Jahrhunderts wird ebenso geschätzt wie verachtet. In dem Bestreben, diese Divergenzen zu berichtigen, versucht dieser Beitrag den Nachweis für die bedingte Gültigkeit von Berensons eigentümlicher Variante eines kunsthistorischen Formalismus zu erbringen, indem er einerseits seine historischen Verbindungen zur pragmatischen Philosophie und Psychologie von William James aufzeigt und indem er andererseits Berensons Argumentation ins Verhältnis zu aktuellen Debatten der wahrnehmungstheoretischen Ästhetik und Philosophie setzt. Am Beispiel von Berensons Interpretation der Gemälde Giottos führt dieser Essay eine pragmatische Analyse von Berensons Schriften durch und stellt diese ins Umfeld seiner Kontakte zu anderen Autoren: darunter Adolf Hildebrand, Giovanni Morelli und Walter Pater. Schließlich soll das Scheitern, das Potenzial, die Rezeption und das Erbe von Berensons kunsthistorischen Studien unter pragmatischen Gesichtspunkten bewertet werden. (shrink)

The recent discussions on “The Right and the Good” show that the reconciliation between formalism and teleology is still a problem. Some of the contending parties lean more strongly towards formalism, others towards teleology; but neither side has, I believe, done equal justice to formalism and teleology. To review the whole discussion is beyond the scope of this paper. Instead, I propose to suggest in outline a theory which may possibly harmonize the essential tenets of both parties.