Formal languages are widely regarded as being above all mathematical objects and as producing a greater level of precision and technical complexity in logical investigations because of this. Yet defining formal languages exclusively in this way offers only a partial and limited explanation of the impact which their use actually has. In this book, Catarina Dutilh Novaes adopts a much wider conception of formal languages so as to investigate more broadly what exactly is going (...) on when theorists put these tools to use. She looks at the history and philosophy of formal languages and focuses on the cognitive impact of formal languages on human reasoning, drawing on their historical development, psychology, cognitive science and philosophy. Her wide-ranging study will be valuable for both students and researchers in philosophy, logic, psychology and cognitive and computer science. (shrink)

Abstract:This article analyzes some of the issues raised by historians after turning to computers for historical research in the 1960s and 1970s. The main point is to enrich this context by looking into the debates computer programmers were having in their own field at the same time. In particular, the use of formal languages to enhance the theoretical basis of both practices is discussed. A second point, the debates in programming, is also highlighted: as historians were turning to (...) computer programming, programmers were becoming historians of their own practice, engaged in methodological discussions on how to write their history. (shrink)

I present a formal language that imposes a structure on processes in macro-chemistry. Each symbol in the language invites a type of analysis that is carried out either by looking into the semantics if the language or by looking at the context. Every formal language has assumptions underlying it. The assumptions made in developing the formal language are meant to help with conceptual analysis by inviting certain types of question.

I present a formal language that imposes a structure on processes in macro-chemistry. Each symbol in the language invites a type of analysis that is carried out either by looking into the semantics if the language or by looking at the context. Every formal language has assumptions underlying it. The assumptions made in developing the formal language are meant to help with conceptual analysis by inviting certain types of question.

I present a formal language that imposes a structure on processes in macro-chemistry. Each symbol in the language invites a type of analysis that is carried out either by looking into the semantics if the language or by looking at the context. Every formal language has assumptions underlying it. The assumptions made in developing the formal language are meant to help with conceptual analysis by inviting certain types of question.

History and Philosophy of Logic, Volume 35, Issue 1, Page 108-110, February 2014.

Summary In this work we elaborate on the idea of a formal theory for a limited but important part of structural chemistry, that described by Lewis’ methods and VSEPR (Valence Shell Electron Pair Repulsion). For this purpose, recursive functions and propositional functions are defined, that apply to formal expressions of the structure, based on a finite set of symbols. This approach allows for the expression of numerous questions of chemical interest. The formalization of basic structural chemistry based on (...) Lewis/VSEPR method is potentially useful for the automation of the related procedures, but possibly also of some use as complementary material in teaching and as a heuristic tool in structural chemistry. (shrink)

This book is a running commentary of Tarski’s momentous monograph ‘The Concept of Truth in Formalized Languages’, published in Polish in 1933, with special focus on discrepancies...

Broadly, the subject of this paper is the relation between logic and linguistics. More narrowly, it concentrates on formal semantics. The first part of the text discusses the topics and methods of formal semantics, and the second part the history of formal semantics. Formal semantic analysis has not been widely known and applied in our research community, and formal methods have been applied extremely rarely in linguistic analyses. This is why it is useful to point (...) out the significant achievements of formal semantics. This inspiring interdisciplinary field of research has been successfully connecting research in linguistics, logic and philosophy since the early 1970s. (shrink)

We show that, contrary to long-standing assumptions, syntactic traits, modeled here within the generative biolinguistic framework, provide insights into deep-time language history. To support this claim, we have encoded the diversity of nominal structures using 94 universally definable binary parameters, set in 69 languages spanning across up to 13 traditionally irreducible Eurasian families. We found a phylogenetic signal that distinguishes all such families and matches the family-internal tree topologies that are safely established through classical etymological methods and datasets. We (...) have retrieved “near-perfect” phylogenies, which are essentially immune to homoplastic disruption and only moderately influenced by horizontal convergence, two factors that instead severely affect more externalized linguistic features, like sound inventories. This result allows us to draw some preliminary inferences about plausible/implausible cross-family classifications; it also provides a new source of evidence for testing the representation of diversity in syntactic theories. (shrink)

Is medieval logic formal? And if yes, in what sense? There are striking affinities between medieval and contemporary theories of language. Authors from the two periods share formal ambitions and maintain complex, and at time uneasy, relations with natural language. However, modern scholars became careful not to overlook the specificities of theories developed more than five hundred years apart, in particular with respect to their 'formal' character. In 1972, Alfonso Maieru noted that the efforts of medieval logicians (...) to identify logical structures in language formal enough to become objects of scientific consideration. He also stressed that the language investigated is a historical one, Latin, so that one can legitimately wonder to which extent... one is allowed to speak of 'formal logic' in the middle ages. In other words, medieval logic is characterized by a tension between 'formalist ambitions' and constraints proper to natural language. Today, our knowledge of the field has considerably expanded, calling for a new assessment of the question. (shrink)

In the history of formal semantics, the successful joining of linguistic and philosophical work brought with it some difficult foundational questions concerning the nature of meaning and the nature of knowledge of language in the domain of semantics: questions in part about “what’s in the head” of a competent language-user. This paper, part of a project on the history of formal semantics, revisits the central issues of (Partee, 1979) in a historical context, as a clash between two traditions, (...) Fregean and Chomskyan, a clash that accompanied early work combining Montague’s semantics with Chomskyan syntax. Recent advances in philosophy of mind (from, e.g., Stalnaker and Burge) go a long way towards changing the framework of arguments about “psychological reality” and “competence”, challenging the suppositions on which the original dichotomy rested, thus largely defusing the tension. (shrink)

There is a standard story told about the rise and fall of ordinary language philosophy: it was a widespread, if not dominant, approach to philosophy in Great Britain in the aftermath of World War II up until the early 1960s, but with the development of systematic approaches to the study of language—formal semantic theories on one hand and Gricean pragmatics on the other—ordinary language philosophy more or less disappeared. In this paper we present quantitative evidence to evaluate the standard (...) story of the rise and fall of ordinary language philosophy, building on the topic model of over 30,000 philosophy articles in Weatherson (2022). Using a combination of qualitative judgment and a topic-model-based measurement of similarity between individual articles, we find evidence that supports the first part of the standard story, according to which ordinary language philosophy arises in the 1940s, peaks between the early 1950s and the late 1960s, and then rapidly declines. But we argue that there is also evidence of a "new wave" of ordinary language philosophy in the early 21st century that defies the second part of the standard story. (shrink)

A wide-ranging history of the intellectual developments that produced the modern idea of the algorithm. Bringing together the histories of mathematics, computer science, and linguistic thought, Language and the Rise of the Algorithm reveals how recent developments in artificial intelligence are reopening an issue that troubled mathematicians long before the computer age. How do you draw the line between computational rules and the complexities of making systems comprehensible to people? Here Jeffrey M. Binder offers a compelling tour of four visions (...) of universal computation that addressed this issue in very different ways: G. W. Leibniz's calculus ratiocinator; a universal algebra scheme Nicolas de Condorcet designed during the French Revolution; George Boole's nineteenth-century logic system; and the early programming language ALGOL, whose name is short for algorithmic language. These episodes show that symbolic computation has repeatedly become entangled in debates about the nature of communication. To what extent can meaning be controlled by individuals, like the values of a and b in algebra, and to what extent is meaning inevitably social? By attending to this long-neglected question, we come to see that the modern idea of the algorithm is implicated in a long history of attempts to maintain a disciplinary boundary separating technical knowledge from the languages people speak day to day. Machine learning, in its increasing dependence on words, now places this boundary in jeopardy, making its stakes all the more urgent to understand. The idea of the algorithm is a levee holding back the social complexity of language, and it is about to break. This book is about the flood that inspired its construction. (shrink)

The chapter looks at an aspect of David Lewis’s work on language that has been important for the foundation and history of formal semantics as a discipline practiced by both linguists and philosophers of language: a referential semantics over possible worlds that is connected to linguistically plausible syntactic structures. Lewis’s original contributions are placed within their historical context: Church’s typed lambda calculus, Carnapian intensions, the categorial grammars of Ajdukiewicz, and Chomsky’s theories of the relation between syntax and semantics. Relying (...) on Lewis’s letters, the chapter identifies the works of Stenius, Davidson, and Katz as triggering Lewis’s interest in formal theories of natural language semantics and clarifies the relation between his and Montague’s contributions to the foundation of the discipline. (shrink)

Over the past half-century, formal, machine-executable proofs have been developed for an impressive range of mathematical theorems. Formalists argue that such proofs should be seen as providing the fully worked out proofs of which mathematicians’ proofs are sketches. Nonformalists argue that this conception of the relationship of formal to informal proofs cannot explain the fact that formal proofs lack essential virtues enjoyed by mathematicians’ proofs, the fact, for example, that formal proofs are not convincing and lack (...) the explanatory power of their informal counterparts. Formal proofs do not yield mathematical insight or understanding, and they are not fruitful in the way that informal proofs can be, for instance, in suggesting novel approaches to old problems. And yet, there is a clear sense in which the formalist is right: Formal proofs do seem to make explicit what is otherwise taken for granted in the mathematician’s reasoning. Very recent work uncovers the source of the dilemma by showing that rigor does not entail formalism insofar as rigor, unlike formalism, is compatible with contentfulness. Mathematical proofs, were they to be recast in a Leibnizian language, at once a characteristica and a calculus, would be, or could be made to be, completely gap-free and hence machine checkable. Because as so recast they would be grounded in mathematical ideas, they would not be machine executable. It is on just this basis that a compelling account can be given of the fact that formal proofs are mostly irrelevant to mathematicians in their practice. (shrink)

This book presents novel formalizations of three of the most important medieval logical theories: supposition, consequence and obligations. In an additional fourth part, an in-depth analysis of the concept of formalization is presented - a crucial concept in the current logical panorama, which as such receives surprisingly little attention.Although formalizations of medieval logical theories have been proposed earlier in the literature, the formalizations presented here are all based on innovative vantage points: supposition theories as algorithmic hermeneutics, theories of consequence analyzed (...) with tools borrowed from model-theory and two-dimensional semantics, and obligations as logical games. For this reason, this is perhaps the first time that these medieval logical theories are made fully accessible to the modern philosopher and logician who wishes to obtain a better grasp of them, but who has always been held back by the lack of appropriate ‘translations' into modern terms.Moreover, the book offers a reflection on the very nature of logic, a reflection that is prompted by the comparisons between medieval and modern logic, their similarities and dissimilarities. It is thus a contribution not only to the history of logic, but also to the philosophy of logic, the philosophy of language and semantics.The analysis of medieval logic is also relevant for the modern philosopher and logician in that, being the unifying methodology used across all disciplines at that time, logic really provided unity to science. It thus presents a unified model of scientific investigation, where logic plays the aggregating role. (shrink)

The papers collected in this volume exemplify some of the trends in current approaches to logic, language and computation. Written by authors with varied academic backgrounds, the contributions are intended for an interdisciplinary audience. The first part of this volume addresses issues relevant for multi-agent systems: reasoning with incomplete information, reasoning about knowledge and beliefs, and reasoning about games. Proofs as formal objects form the subject of Part II. Topics covered include: contributions on logical frameworks, linear logic, and different (...) approaches to formalized reasoning. Part III focuses on representations and formal methods in linguistic theory, addressing the areas of comparative and temporal expressions, modal subordination, and compositionality. (shrink)

Like Spanish moss on a live oak tree, the scientific study of meaning in language has expanded in the last 100 years, and continues to expand steadily. In this essay I want to chart some central themes in that expansion, including their histories and their important figures. Our attention will be directed toward what is called 'formal semantics', which is the adaptation to natural language of analytical techniques from logic.[1] The first, background, section of the paper will survey the (...) changing attitudes of linguists toward semantics into the last third of the century. The second and third sections will examine current formal approaches to meaning. In the final section I will summarize some of the common assumptions of the approaches examined in the middle sections of the paper, sketch a few alternatives, and make some daring predictions. (shrink)

As idealized descriptions of mathematical language, there is a sense in which formal systems specify too little, and there is a sense in which they specify too much. On the one hand, formal languages fail to account for a number of features of informal mathematical language that are essential to the communicative and inferential goals of the subject. On the other hand, many of these features are independent of the choice of a formal foundation, so grounding (...) their analysis on a particular choice of a formal system introduces unnecessary specificity. This chapter begins to map out the design features of mathematical language without descending to the level of formal implementation, drawing on examples from the mathematical literature and insights from the design of computational proof assistants and their libraries. (shrink)

This thesis is on the history and philosophy of logic and semantics. Logic can be described as the ‘science of reasoning’, as it deals primarily with correct patterns of reasoning. However, logic as a discipline has undergone dramatic changes in the last two centuries: while for ancient and medieval philosophers it belonged essentially to the realm of language studies, it has currently become a sub-branch of mathematics. This thesis attempts to establish a dialogue between the modern and the medieval traditions (...) in logic, by means of ‘translations’ of the medieval logical theories into the modern framework of symbolic logic, i.e. formalizations. One of its conclusions is that, when properly understood within their own framework, the interest of medieval logical theories for modern investigations go beyond mere historical interest, but that a thorough conceptual analysis of such theories must be undertaken in order to avoid conceptual misprojections. While such translations of medieval into modern logic have been attempted before, the approach presented here is innovative in that attention is paid to the similarities as well as to the dissimilarities between the two traditions, and to what can be learned from the medieval masters for modern investigations in logic and semantics. (shrink)

Proof and Disproof in Formal Logic is a lively and entertaining introduction to formal logic providing an excellent insight into how a simple logic works. Formal logic allows you to check a logical claim without considering what the claim means. This highly abstracted idea is an essential and practical part of computer science. The idea of a formal system-a collection of rules and axioms, which define a universe of logical proofs-is what gives us programming languages (...) and modern-day programming. This book concentrates on using logic as a tool: making and using formal proofs and disproofs of particular logical claims. The logic it uses-natural deduction-is very small and very simple; working with it helps you see how large mathematical universes can be built on small foundations. The book is divided into four parts: Part I "Basics" gives an introduction to formal logic with a short history of logic and explanations of some technical words. Part II "Formal Syntactic Proof" show you how to do calculations in a formal system where you are guided by shapes and never need to think about meaning. Your experiments are aided by Jape, which can operate as both inquisitor and oracle. Part III "Formal Semantic Disproof" shows you how to construct mathematical counterexamples to shoe that proof is impossible. Jape can check the counterexamples you build. Part IV " Program Specification and Proof" describes how to apply your logical understanding to a real computer science problem, the accurate description and verification of programs. Jape helps, as far as arithmetic allows. Aimed at undergraduates and graduates in computer science, logic, mathematics and philosophy, the text includes reference to and exercises based on the computer software package Jape, an interactive teaching and research tool designed and hosted by the author that is freely available on the web. (shrink)

"Logic", one of the central words in Western intellectual history, compre hends in its meaning such diverse things as the Aristotelian syllogistic, the scholastic art of disputation, the transcendental logic of the Kantian critique, the dialectical logic of Hegel, and the mathematical logic of the Principia Mathematica of Whitehead and Russell. The term "Formal Logic", following Kant is generally used to distinguish formal logical reasonings, precisely as formal, from the remaining universal truths based on reason. (Cf. SCHOLZ, (...) 1931). A text-book example of a formal-logical inference which from "Some men are philosophers" and "All philosophers are wise" concludes that "Some men are wise" is called formal, because the validity of this inference depends only on the form ofthe given sentences -in particular it does not depend on the truth or falsity of these sentences. (On the dependence of logic on natural language, English, for example, compare Section 1 and 8). The form of a sentence like "Some men are philosophers", is that which remains preserved when the given predicates, here "men" and "philosophers" are replaced by arbitrary ones. The form itself can thus be represented by replacing the given predicates by variables. Variables are signs devoid of meaning, which may serve merely to indicate the place where meaningful constants (here the predicates) are to be inserted. As variables we shall use - as did Aristotle - letters, say P, Q and R, as variables for predicates. (shrink)

Traditional logical reconstruction of arguments aims at assessing the validity of ordinary language arguments. It involves several tasks: extracting argumentations from texts, breaking up complex argumentations into individual arguments, framing arguments in standard form, as well as formalizing arguments and showing their validity with the help of a logical formalism. These tasks are guided by a multitude of partly antagonistic goals, they interact in various feedback loops, and they are intertwined with the development of theories of valid inference and adequate (...) formalization. This paper explores how the method of reflective equilibrium can be used for modelling the complexity of such reconstructions and for justifying the various steps involved. The proposed approach is illustrated and tested in a detailed reconstruction of the beginning of Anselm’s De casu diaboli. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The History of Ideas:Precept and Practice, 1950–2000 and BeyondAnthony GraftonIn the middle years of the twentieth century, the history of ideas rose like a new sign of the zodiac over large areas of American culture and education. In those happy days, Dwight Robbins, the president of a fashionable progressive college, kept "copies of Town and Country, the Journal of the History of Ideas, and a small magazine—a little magazine—that (...) had no name" on the table in his waiting room. True, Robbins did not exist: he was the fictional president of Randall Jarrell's equally fictional Benton, a liberal arts dystopia where "[h]alf of the college was designed by Bottom the Weaver, half by Ludwig Mies van der Rohe."1 But Jarrell's notation of the Journal's status was accurate nonetheless.2The Journal, in the twenty years or so after its foundation, attracted attention from many quarters, some of them unexpected. And it occupied a unique position, between the technical journals of history and philology, [End Page 1] each firmly identified with a discipline, in which professional humanists normally published their results, and the quarterlies, often based not in disciplines but in liberal arts colleges and universities, which cultivated a mixed readership to which they offered fiction and poetry as well as essays. By contrast with both, the JHI fifty years ago ran on a rich mix of technical articles and wide-ranging essays that could easily have attracted the attention of a sophisticated administrator—or at least made a good impression on his coffee table. Bliss was it to be a subscriber in that happy day when the JHI glowed with something of the luster that haloed Representations in the 1980s and Critical Inquiry more recently.3The main reason for the Journal's prominence was that it represented a new field, appealingly located between disciplines as the Journal was between other sorts of periodical. In its postwar heyday, the history of ideas was not a dim subdivision of history, itself a discipline whose luster has worn off with time, but an intellectual seismic zone where the tectonic plates of disciplines converged and rubbed against one another, producing noises of all sorts. In recent years, it has sometimes seemed impossible, even to the best informed observers, that intellectual history, or the history of ideas, ever enjoyed this sort of prestige. A quarter century ago, Robert Darnton surveyed the state of intellectual and cultural history in the United States in an informative and influential essay. Using a language more resonant of the historical President Carter than the fictional President Robbins, Darnton detected "malaise" everywhere he looked. In the fifties, he noted, intellectual historians had seen "their discipline as the queen of the historical sciences. Today she seems humbled." True, desperate cries for help were not yet called for. Historians continued to write histories of ideas, and even to cast them in the technical languages of A.O. Lovejoy or Perry Miller: "one still finds 'unit-ideas' and 'mind' among the trendier terms." The just-published Dictionary of the History of Ideas, moreover, offered a vast selection of Lovejoyan formal analyses, systematically organized, to the reading public.4 [End Page 2]But for the last ten years, Darnton argued, younger scholars, especially graduate students, had been scrambling over the gunwales of the good ship History of Ideas, abandoning the effort to converse abstractly with the mighty dead, and clambering in hordes over the side of a newer vessel, Social History, which boasted a Hogarthian passenger list of heretics, misfits, and military women. At the level of the dissertations written in history departments, social history was outpacing intellectual, by a proportion of three to one. At the level of the scholarly journal, too, social history had forged ahead, though by a smaller margin. In the murkier, but no less significant, world of opinion, finally, the decline of intellectual history appeared clearest. History of ideas no longer occupied the cutting edge in young scholars' mental vision of their discipline.Social history, after all, had captured the minds of a generation—or a large percentage of it—in the 1960s, thanks both to the power of... (shrink)

The Sentence in Language and Cognition is about the significant role of the sentence in linguistic cognition and in the practical domains of human existence. Dr. Tista Bagchi has written a comprehensive assessment of the structure and cognitive function of the sentence and the clause in the context of real-world discourse and activities.The notions of sentencehood and clausehood with special reference to the semantic histories of the terms sentence and clause, including their ethical, legal, and administrative uses, are assessed. This (...) is followed by a concise historical survey of the treatment of the sentence in a few of the ancient linguistic traditions, notably the Greek, Roman(-Alexandrian), Arab, and Sanskrit scholastic traditions. A wide variety of sentence types, from a cross-section of languages spoken in Asia, Europe, and the Americas, are presented by way of factual evidence for sentences and clauses as linguistic units. Formally defined notions of the sentence and the clause as syntactic constituents in major theoretical frameworks are examined and assessed for their essential properties and points of convergence. The Sentence in Language and Cognition is an essential book for advanced students and researchers of linguistics. (shrink)

The article presents a formalization of Thomas Aquinas proof for the indestructibility of the human soul. The author of the formalization—the first of its kind in the history of philosophy—is Father Joseph Maria Bocheński. The presentation involves no more than updating the logical symbolism used and accompanies the logical formulae with ordinary language paraphrases in order to ease the reader’s understanding of the formulae. “The fundamental idea of the Thomist proof is of utmost simplicity: things which are destructible are destructible (...) either per se or per accidens; but the human soul is destructible neither per se nor per accidens: therefore the human soul is not destructible”. Bochenski’s words required him to devote considerable effort for the sake of precision of the symbolic language that would be maximally adequate to Thomas’ discourse. Moreover, I have thought it necessary to provide an ample commentary to the traditional and contemporary semantical presuppositions of Aquinas philosophical anthropology in light of Bocheński’s interpretation thereof. (shrink)

Olympiodorus led the Platonist school of philosophy at Alexandria for several decades in the sixth century, and both Platonic and Aristotelian commentaries ascribed to him survive. During this time the school’s attitude to the teaching of Aristotelian syllogistic, originally owing something to Ammonius, changed markedly, with an early tendency to reinforce the teaching of syllogistic even in Platonist lectures giving way to a greater awareness of its limitations. The vocabulary for arguments and their construction becomes far commoner than the language (...) of syllogistic and syllogistic figures, and also of demonstration. I discuss the value of these changes for the dating of certain works, especially where the text lectured on does not demand different emphases. The commitment to argument rather than to authority continues, but a greater emphasis eventually falls on the establishment of the premises than on formal validity. (shrink)

When one looks into the role of artificial languages in philosophy of language it seems appropriate to start with making a distinction between philosophy of language proper and formal semantics of natural language. Although the distinction between the two disciplines may not always be easy to make since there arguably exist substantial historical and systematic relationships between the two, it nevertheless pays to keep the two apart, at least initially, since the motivation commonly given for the use of (...) artificial languages in philosophy of language is often rather different from the one that drives the use of such languages in semantics. Of course, this difference in motivation should not blind us for the commonalities that exists between the two disciplines. Philosophy of language and formal semantics have a common history, and arguably also share some of their substance. Philosophy of language is by and large an outgrowth of work in the analytical tradition in philosophy in the first half of the twentieth century. Both ordinary language philosophy, with its emphasis on the description of actual language use, as well as the more logic-oriented and formally inclined school of logical positivism contributed to the definition of philosophy of language as a separate philosophical discipline, with its own set of problems and methods to solve them. Another major contributor to the establishment of philosophy of language as a distinct discipline has been modern linguistics, in particular generative grammar in the tradition of Chomsky that became the dominant paradigm in linguisticsin the fifties and sixties of the previous century. And as it happens, both the generative tradition of Chomsky and analytic philosophy in its formal and less formal guises have been important factors in the development of formal semantics as well. Thus, it should come as no surprise that the two have something in common. That the communalities go beyond a common ancestry, but are reflected in substance and methods as well, will be argued later on. However, be that as it may, it is still a good idea to keep philosophy of language and formal semantics separate, at least initially, since the role that is assigned to artificial languages and the ways in which these languages are employed in both does differ in a number of respects that are worth keeping in mind.. (shrink)

Finland is internationally known as one of the leading centers of twentieth century analytic philosophy. This volume offers for the first time an overall survey of the Finnish analytic school. The rise of this trend is illustrated by original articles of Edward Westermarck, Eino Kaila, Georg Henrik von Wright, and Jaakko Hintikka. Contributions of Finnish philosophers are then systematically discussed in the fields of logic, philosophy of language, philosophy of science, history of philosophy, ethics and social philosophy. Metaphilosophical reflections on (...) the nature of philosophy are highlighted by the Finnish dialogue between analytic philosophy, phenomenology, pragmatism, and critical theory. (shrink)

This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes that we view mathematics as a system of conventions and norms that is designed to help us make sense of the world and reason efficiently. Like any designed system, it can perform well or poorly, and the philosophy of mathematics has a role to play in (...) helping us understand the general principles by which it serves its purposes well. (shrink)

Wittgenstein explores learning through practice in the Philosophical Investigations by means of an extended analogy with games. However, does this concern with learning also necessarily extend to education, in our institutional understanding of the word? While Wittgenstein's examples of language learning and use are always shared or social, he does not discuss formal educational institutions as such. He does not wish to found a ‘school of thought’, and is suspicious of philosophy acting as a theory that can be applied (...) to other areas of life. While Wittgenstein's focus on developing independent thinking was neither individualistic nor anti-institutional, it did, however, focus on developing the thinking of his students rather than theorising about how this could be applied on a large scale. An analysis of Hermann Hesse's novel, The Glass Bead Game will help us to pick up where Wittgenstein deliberately left off—thinking about how (or if) one can institutionalise learning methods that encourage thinking for oneself. These differences in the writers’ treatment of education will become evident in the differences between their game analogies. While language-games combat our ‘craving for generality’ in Philosophical Investigations, the Glass Bead Game represents this craving, and how it manifests itself throughout history in disciplines other than logic and philosophy of language. It also represents the potential for institutions to become insular, exclusive communities. (shrink)

How does one formalize the structure of structures necessary for the foundations of physics? This work is an attempt at conceptualizing the metaphysics of pregeometric structures, upon which new and existing notions of quantum geometry may find a foundation. We discuss the philosophy of pregeometric structures due to Wheeler, Leibniz as well as modern manifestations in topos theory. We draw attention to evidence suggesting that the framework of formal language, in particular, homotopy type theory, provides the conceptual building blocks (...) for a theory of pregeometry. This work is largely a synthesis of ideas that serve as a precursor for conceptualizing the notion of space in physical theories. In particular, the approach we espouse is based on a constructivist philosophy, wherein ``structureless structures'' are syntactic types realizing formal proofs and programs. Spaces and algebras relevant to physical theories are modeled as type-theoretic routines constructed from compositional rules of a formal language. This offers the remarkable possibility of taxonomizing distinct notions of geometry using a common theoretical framework. In particular, this perspective addresses the crucial issue of how spatiality may be realized in models that link formal computation to physics, such as the Wolfram model. (shrink)

A scholarly and superbly done history of formal logic, devoted mainly to four movements: the Greek; the scholastic; modern mathematical logic; and Indian Logic. Father Bochenski makes extensive use of direct quotation--in German translation by himself, when the original language is not German. The translations are sound, the documentation precise, and the organization lucid. The treatment is balanced and unified; the selection of passages to be quoted is judicious. All in all, a masterly work. Criticism will probably focus more (...) on his views of the relation of formal logic to philosophical logic, than on the factual accuracy of his account.--R. W. (shrink)

In June 22-27,1970, an International Working Symposium on Pragmatics of Natural Languages took place in Jerusalem under the auspices of The Israel Academy of Sciences and Humanities and the Division of Logic, Methodology and Philosophy of Science of the International Union of History and Philosophy of Science.! Some thirty philosophers, logicians, linguists, and psychologists from Israel, U.S.A., West-Germany, England, Belgium, France, Scotland, and Denmark met in seven formal and a number of informal sessions in order to discuss some (...) ofthe problems around the use and acquisition oflanguage which in the eyes of an increasing number of scholars have been left under treated in the recent upsurge ofinterest in theoretical linguistics and philos ophy of language. More specifically, during the formal sessions the following topics were discussed: The validity of the syntactics-seman tics-pragmatics trichotomy The present state of the competence-performance issue Logic and linguistics The New Rhetoric Speech acts Language acquisition. The participants in the Symposium distributed among themselves re prints and preprints of relevant material, partly in advance of the meeting, partly at its beginning. Each session was introduced by one or two modera tors, and summaries of each day's proceedings were prepared and distri buted the next day. The participants were invited to submit papers after the symposium, written under its impact. The eleven essays published here are the result. (shrink)

The project of integrated HPS has occupied philosophers of science in one form or another since at least the 1960s. Yet, despite this substantial interest in bringing together philosophical and historical reflections on the nature of science, history of science and formal philosophy of science remain as divided as ever. In this paper, I will argue that the continuing separation between historical and formal philosophy of science is ill-founded. I will argue for this in both abstract and concrete (...) terms. At the abstract level, I reconstruct two possible arguments for the incompatibility of historical and formal philosophy of science and argue that they are both wanting. At the concrete level, I discuss how historical and formal philosophy of science have been brought together in practice, namely: in the form of a largely forgotten research tradition that I will refer to here as the study of formalized macro-units. After a brief exposition, I argue that this research tradition has been unduly overlooked by historically minded philosophers of science. Bringing together these observations, I argue that the divide between historical and formal philosophy of science is not grounded in any substantive arguments, but can be primarily attributed to disciplinary happenstance. (shrink)

In this essay, an attempt is made to formalize the idea of analogy in a way which is as faithful as possible to Thomas Aquinas’ theory of analogy. To accomplish this, we must first present Aquinas’ theory of analogy as it appears in his main works; we then express the contents of Aquinas’ theory of analogy using Leśniewski’s Ontology, a symbolic language which is both rigorous and true to the spirit of Aquinas’ philosophy. In doing this we present definitions and (...) theorems lying outside the scope of Leśniewski’s Elementary Ontology and we demostrate that the notion of “to be the definition of” is not an extensional functor. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:History of Philosophy and the Reflective Society by Riccardo PozzoRobert R. ClewisPOZZO, Riccardo. History of Philosophy and the Reflective Society. Berlin: Walter de Gruyter, 2021. vi + 231 pp. Cloth, $94.99In a forward-looking proposal, Pozzo lays out his vision for a multidisciplinary history of philosophy "from a global perspective." This book is "a long position paper, an extended essay dedicated to twenty-first century policies of philosophical research from (...) a global perspective." The chosen format is a Denkschrift, that is, a memorandum in the sense of a document that experts lay out for their government to ponder. Perhaps, Pozzo suggests, the history of philosophy could even have an impact on economic authorities and policymakers. Indeed, the work seems driven by the laudable aim of promoting access and equality around the world. The author reveals a just concern for migrants in particular, since they bring [End Page 156] with them their intellectual traditions and philosophical texts, which can be translated and thereby foster intercultural dialogue.The book consists of an introduction (chapter 1) followed by nine chapters. It has a thirty-page references list as well as subject and name indexes. In part one, Pozzo argues for the need for new narratives in the history of philosophy (chapter 2), in order to establish its role in addressing migration (chapter 3). The second part concerns reflective society (chapter 4). It considers societal readiness (chapter 5) and cultural innovation (chapter 6). Part three explores the paradigm shift from a close reading of texts to a "distant" reading of corpora (chapter 7), a shift Pozzo endorses. It examines implications for the translation of languages (chapter 8) and the translation of studies (knowledge) and competencies (chapter 9). Chapter 10 concludes by briefly reflecting on the notions of the "fluidity" of peoples and their ideas, biodiversity (and food), and spiritual humanism based on dignity.Scholars in the history of philosophy "should be open to the idea of a pluriversum of a history of facts and places, whereby history of philosophy finds its grounding in spatial heterogeneity." Nowadays, when people migrate and transfer competencies at increasing velocity, the "history of philosophy can be usefully reinvented on the basis of its consideration of intercultural dialogue." Pozzo considers the World Digital Library to be "one of the most exciting examples of corpora that talk to each other"—an idea he uses not merely metaphorically. By "corpora" is meant not just the sum of separate books, but XML-accessible complete collections of traditions of texts, with corresponding dictionaries, thesauri, and reference works, which make it possible to analyze a number of original texts as well as transliterations into other alphabets or hanzi characters. The result would be a "data-driven" history of philosophy.Given that history of philosophy is a product of culture, it is influenced by migrating peoples, who bring philosophical ideas and religious traditions with them. Research on migration thus ought to also consider translations of texts and competencies from one to another context, be it linguistic, economic, political, or cultural. The humanities, and a reflective society more generally, might provide a partial basis for intercultural dialogue. The history of philosophy might even thereby improve the quality of life of citizens.Pozzo rightly emphasizes that we need multilingual philosophers and historians of philosophy. History of philosophy ought to also be based on robust lexical and historical considerations, and historians of philosophy should be trained in a number of the world's languages as well as face the challenge of dealing with multilingualism and with validating translations. Pozzo's proposed methodology, informed by computational techniques, relies on tools such as vocabularies, ontologies, concordances, frequencies, or the analysis of texts and corpora, which integrates quantitative and formal methods into the portfolio of the methods of history of philosophy and intellectual history. Since Pozzo has published [End Page 157] widely on Kant, it is fitting that he explores Kant on migration as well as the editorial contexts and translation projects concerning the philosopher's writings.As for aesthetics, Pozzo notes that the history of philosophy can reflect on migrants' cultural and artistic creations. Historians of philosophy should thus start observing and interpreting phenomena created by... (shrink)

Over the last decades, migration across Europe has continued to increase. Consequently, offering educational support for migrant students in the schools of host countries has been an extensively debated issue across Europe and further afield, especially in countries with a history of immigration. However, less is known about how education systems in the ‘new’ immigration countries have responded to the needs of recently arrived migrants. This article focuses on language support measures set up for migrant students in state-funded schools in (...) the Republic of Ireland and Spain – both multilingual countries with more than one official language and with a heterogeneous migrant population. In reviewing educational policy and practice in these jurisdictions in the areas of language support for migrants, this article seeks to contribute to the debate on challenges involved in supporting language acquisition by migrant students in formal educational settings. (shrink)

This short monograph laudably presents itself as a lucid introduction for the plain man and schoolboy to the problems of language, with which contemporary British philosophers from Moore to Wittgenstein’s disciples have been preoccupied. Mr. Wilson, an experienced teacher of semantics, holds that the solution of human problems and disputes other than through force must be based upon that science of linguistic communication. If we are to be saved from excessive propaganda and demagogy, we must first understand the meaning and (...) precise verification of words. Hence he offers this introduction to the current method and findings of linguistic analysis. His survey in the pattern of function, types and mistakes moves from the analysis of words to statements and their special relation to truth through verification. This poses the question of meaning, in the familiar Humean and dogmatic disjunction of factual or purely formal statement, and leads inevitably to the crucial meaning of value and metaphysical statements. (shrink)

The mnemonic arts and the idea of a universal language that would capture the essence of all things were originally associated with cryptology, mysticism, and other occult practices. And it is commonly held that these enigmatic efforts were abandoned with the development of formal logic in the seventeenth century and the beginning of the modern era. In his distinguished book, Logic and the Art of Memory Italian philosopher and historian Paolo Rossi argues that this view is belied by an (...) examination of the history of the idea of a universal language. Based on comprehensive analyses of original texts, Rossi traces the development of this idea from late medieval thinkers such as Ramon Lull through Bruno, Bacon, Descartes, and finally Leibniz in the seventeenth century. The search for a symbolic mode of communication that would be intelligible to everyone was not a mere vestige of magical thinking and occult sciences, but a fundamental component of Renaissance and Enlightenment thought. Seen from this perspective, modern science and combinatorial logic represent not a break from the past but rather its full maturity. Available for the first time in English, this book (originally titled Clavis Universalis ) remains one of the most important contributions to the history of ideas ever written. In addition to his eagerly anticipated translation, Steven Clucas offers a substantial introduction that places this book in the context of other recent works on this fascinating subject. A rich history and valuable sourcebook, Logic and the Art of Memory documents an essential chapter in the development of human reason. (shrink)

The paper discusses in how far medieval logic can appropriately be characterized as a formal science. In this respect, the special mediecal approach to logic as a scientia sermocinalis is examined as well as its main doctrines, namely the theories of supposition and of consequences, and the famous characterization of logic as an ars artium or scientia scientiarum. It is pointed out that medieval logic is not devoted to the setting up of formal systems or any metalogical analysis (...) of formal structures. Logic in the medieval sense of the discipline is necessarily connected with semantical aspects of natural language. Accordingly, we are confronted with a discipline going far beyond the formal structures of discourse. The classification of medieval logic as a formal science is appropriate only under selected perspectives. (shrink)

The mnemonic arts and the idea of a universal language that would capture the essence of all things were originally associated with cryptology, mysticism, and other occult practices. And it is commonly held that these enigmatic efforts were abandoned with the development of formal logic in the seventeenth century and the beginning of the modern era. In his distinguished book, Logic and the Art of Memory Italian philosopher and historian Paolo Rossi argues that this view is belied by an (...) examination of the history of the idea of a universal language. Based on comprehensive analyses of original texts, Rossi traces the development of this idea from late medieval thinkers such as Ramon Lull through Bruno, Bacon, Descartes, and finally Leibniz in the seventeenth century. The search for a symbolic mode of communication that would be intelligible to everyone was not a mere vestige of magical thinking and occult sciences, but a fundamental component of Renaissance and Enlightenment thought. Seen from this perspective, modern science and combinatorial logic represent not a break from the past but rather its full maturity. Available for the first time in English, this book (originally titled Clavis Universalis) remains one of the most important contributions to the history of ideas ever written. In addition to his eagerly anticipated translation, Steven Clucas offers a substantial introduction that places this book in the context of other recent works on this fascinating subject. A rich history and valuable sourcebook, Logic and the Art of Memory documents an essential chapter in the development of human reason. (shrink)

The leading philosophers of science of the first half of the twentieth century had little use for the history of science. There are several possible explanations for this. One is that philosophers of science sometimes (knowingly or not) mimic the methodological habits and values of scientists. Many philosophers of science are motivated by admiration for the perceived rigor and intellectual hygiene of the exact sciences. Historical sense is not normally a cardinal virtue among physicists. Hence, those philosophers who take their (...) methodological cues from their scientific heroes are unlikely to think of philosophy as a historical discipline. Indeed, the idea of a close relationship between history and philosophy may have fallen into disrepute as a consequence of its association with idealist philosophers, of whom Hegel is the most notorious. Then there is Feyerabend's explanation, which is that the philosophy of science was transformed by the spectacular advances in formal logic which took place in the late nineteenth century. The development of modern formal logic made possible a range of hitherto inconceivable projects in the philosophy of science. The most radical of these was the positivist attempt to replace philosophy with the logical analysis of scientific language. Equally dependent on the new logic was Popper's attempt to explain the workings of empirical science using only deductive patterns of inference. According to Feyerabend, the philosophical projects engendered by the advances in formal logic came to dominate so thoroughly that everything else was marginalized (see feyerabend). It was not necessary for philosophers to know anything about the history of science, but they did have to be competent logicians: “As always maturity in a narrow domain means illiteracy elsewhere” (Feyerabend 1981, p. 20). (shrink)

The paper addresses the question how descriptive language is used to express legal norms. Sentences we find in legislative acts, i.e. statutes, constitutions and regulations, express legal norms. Linguistically speaking, there are various grammatical and lexical ways of expressing norms, such as imperative mood, modal verbs, deontic verbs, etc. However, norms may also be expressed by descriptive sentences, namely sentences in present or future tense and indicative (declarative) mood (i.e. _The minister determines the tax rate_). In many civil law countries (...) (including Poland), this is a very common, if not the default, form of expressing norms in legislative texts. Often presented as a legal peculiarity, this phenomenon has yet to draw much academic attention. The normative meaning of descriptive sentences is usually attributed to purely pragmatic factors stemming from our shared assumptions about the legal system. However, a closer look reveals that similar grammatical constructions are ubiquitous in everyday communication and in different languages. We tend to utter various sorts of directives using descriptive sentences (_Now we add a spoon of salt to the sauce_; _credit cards are not accepted_). This suggests the possibility for a linguistic (as opposed to exclusively legal) explanation. This paper aims to offer such an explanation. Rather than resorting to formal semantics, so prevalent in legal theory, it borrows from Cognitive Linguistics to reveal the cognitive underpinnings of our surprising tendency to express normativity in descriptive terms. This involves four different, yet complementary, theories. Firstly, the theory of conceptual metaphor by George Lakoff and Mark Johnson which explains the phenomenon in question in terms of the metaphor “ ought is is ”; with “ ought ” as the more abstract target domain and “ is ” as the more concrete, cognitively simpler source domain. Secondly, the theory of speech act metonymy by Panther and Thornburg which presents descriptive legal sentences as referring to various components of the underlying cognitive scenario of obligation. Thirdly, Ronald Langacker’s notion of the virtuality of language as the explanation for non-present, including future, perpetual and directive, uses of the present tense. Fourtly, the notion of normative generics which points to the nominal, as opposed to verbal, structure of descriptive legal sentences as the source of their normativity. (shrink)