The advantages and disadvantages of formalization in philosophy are summarized. It is concluded that formalized philosophy is an endangered speciality that needs to be revitalized and to increase its interactions with non-formalized philosophy. The enigmatic style that is common in philosophical logic must give way to explicit discussions of the problematic relationship between formal models and the philosophical concepts and issues that motivated their development.

John Norton’s argument that all formal theories of induction fail raises substantive questions about the philosophical analysis of scientific reasoning. What are the criteria of adequacy for philosophical theories of induction, explanation, or theory structure? Is more than one adequate theory possible? Using a generalized version of Norton’s argument, I demonstrate that the competition between formal and material theories in philosophy of science results from adhering to different criteria of adequacy. This situation encourages an interpretation of “formal” and “material” (...) as indicators of divergent criteria that accompany different philosophical methodologies. I characterize another criterion of adequacy associated with material theories, the avoidance of imported problems, and conclude that one way to negotiate between conflicting criteria is to adopt a pluralist stance toward philosophical theories of scientific reasoning. (shrink)

The paper offers a historical survey of the emergence of logical formalization in twentieth-century analytically oriented philosophy of religion. This development is taken to have passed through three main ?stages?: a pioneering stage in the late nineteenth and early twentieth centuries (led by Frege and Russell), a stage of crisis in the 1920s and early 1930s (occasioned by Wittgenstein, logical positivists such as Carnap, and neo-Thomists such as Maritain), and a stage of rehabilitation in the 1930s, 1940s, and (...) 1950s (led by the Cracow Circle and Quine). (shrink)

This essay addresses the methodology of philosophy of science and illustrates how formal and empirical methods can be fruitfully combined. Special emphasis is given to the application of experimental methods to confirmation theory and to recent work on the conjunction fallacy, a key topic in the rationality debate arising from research in cognitive psychology. Several other issue can be studied in this way. In the concluding section, a brief outline is provided of three further examples.

The title of this book refers to the tension between formal and informal elements in the ways analytical philosophy is practiced. The authors examine questions of the scopes and limits of both kinds of research methods.

Challenging Formalization in Education and Beyond addresses the effects of today's attempts to organize knowledge, processes, and performance in education, particularly in its ever-growing digital environments. As on-site, blended, and fully online learning become deeply interdependent, secondary and higher education managers and instructors who seek to integrate, apply, and teach within these formats using standardized rules, assessments, algorithms, and accountability structures may be doing unintended harm to their students. Focusing on students' performance, health, cognition, behavior, and learning outcomes, this (...) book analyses how current trends, methods, and policies in formalization can be challenged and corrected to ensure high-quality education. Scholars, educators, administrators, and designers of traditional, asynchronous, precision, automated and micro-learning formats will come away with new insights and pragmatic solutions for engaging students in more active, participatory, and creative activities. (shrink)

Introduction to the Special Issue containing selected contributions to the conference "Formal Methods and Science in Philosophy IV", Inter-University Center, Dubrovnik, April 11-13, 2019.

Suppose we have two false hypotheses H1 and H2. Sometimes, we would like to be able to say that H1 is closer to the truth than H2 (e.g., Newton’s hypothesis vs. Ptolemy’s).

Traditionally, logic has been the dominant formal method within philosophy. Are logical methods still dominant today, or have the types of formal methods used in philosophy changed in recent times? To address this question, we coded a sample of philosophy papers from the late 2000s and from the late 2010s for the formal methods they used. The results indicate that the proportion of papers using logical methods remained more or less constant over that time period but the (...) proportion of papers using probabilistic methods was approximately three times higher in the late 2010s than it was in the late 2000s. Further analyses explored this change by looking more closely at specific methods, specific levels of technical engagement, and specific subdisciplines within philosophy. These analyses indicate that the increasing proportion of papers using probabilistic methods was pervasive, not confined to particular probabilistic methods, levels of sophistication, or subdisciplines. (shrink)

This paper examines Heidegger’s account of the proper relation between philosophy and theology, and Dietrich Bonhoeffer’s critique thereof. Part I outlines Heidegger’s proposal for this relationship in his lecture “Phenomenology and Theology,” where he suggests that philosophy might aid theology by means of ‘formal indication.’ In that context Heidegger never articulates what formal indication is, so Part II exposits this obscure notion by looking at its treatment in Heidegger’s early lecture courses, as well as its roots in Husserl. (...) Part III presents Bonhoeffer’s theological response, which challenges Heidegger’s attempt to maintain a neutral ontology that remains unaffected by both sin and faith. (shrink)

The tools of logic are used properly or improperly relative to two interrelated purposes. Logic is both a symbolism for the expression of the formal structures of thought and an inference mechanism. Formalization in philosophical logic is justified to the extent that it contributes to our understanding of logical properties and the conceptual problems they may help to state, clarify, or resolve. This view of the value and limits of formalization in logic affords a pragmatic perspective that in (...) principle should selectively support the development of particular formal systems, while excluding others as unjustified. Yet the pragmatic grounds are so liberal as to disallow virtually no exercises in formalization as entirely useless. Logic is abused in another sense, when it is wrongly used, not by violating logical canons generally, but by presupposing that substantive metaphysical, normative, or scientific content can be derived from purely formal logical relations. (shrink)

Formal ontology combines two ideas, one originating with Husserl, the other with Frege: that of ontology of the formal aspects of all objects, irrespective of their particular nature, and ontology pursued by employing the tools of modern formal disciplines, notably logic and semantics. These two traditions have converged in recent years and this is the first collection to encompass them as a whole in a single volume. It assembles essays from authors around the world already widely known for their work (...) in formal ontology, and illustrates that through the application of formal methods the ancient discipline of ontology may be put on a firm methodological basis. The essays not only illuminate the nature of ontology and its relation to other areas, in language, logic and everyday life, but also demonstrate that common issues from the analytical and phenomenological traditions may be discussed without ideological barriers. Audience: advanced students of and specialists in philosophy, linguistics, cognitive science, computer science, database engineering. (shrink)

"Foundations of the Formal Sciences" is a series of interdisciplinary conferences in mathematics, philosophy, computer science and linguistics. The main goal is to reestablish the traditionally strong links between these areas of research that have been lost in the past decades. The second conference in the series had the subtitle "Applications of Mathematical Logic in Philosophy and Linguistics" and brought speakers from all parts of the Formal Sciences together to give a holistic view of how mathematical methods can (...) improve our philosophical and technical understanding of language and scientific discourse, ranging from the theoretical level up to applications in language recognition software. Audience: This volume is of interest to all formal philosophers and theoretical linguists. In addition to that, logicians interested in the applications of their field and logic students in mathematics, computer science, philosophy and linguistics can use the volume to broaden their knowledge of applications of logic. (shrink)

The present paper argues that ‘mature mathematical formalisms’ play a central role in achieving representation via scientific models. A close discussion of two contemporary accounts of how mathematical models apply—the DDI account (according to which representation depends on the successful interplay of denotation, demonstration and interpretation) and the ‘matching model’ account—reveals shortcomings of each, which, it is argued, suggests that scientific representation may be ineliminably heterogeneous in character. In order to achieve a degree of unification that is compatible with successful (...) representation, scientists often rely on the existence of a ‘mature mathematical formalism’, where the latter refers to a—mathematically formulated and physically interpreted—notational system of locally applicable rules that derive from (but need not be reducible to) fundamental theory. As mathematical formalisms undergo a process of elaboration, enrichment, and entrenchment, they come to embody theoretical, ontological, and methodological commitments and assumptions. Since these are enshrined in the formalism itself, they are no longer readily obvious to either the novice or the proficient user. At the same time as formalisms constrain what may be represented, they also function as inferential and interpretative resources. (shrink)

1 Logic in philosophy The century that was Logic has played an important role in modern philosophy, especially, in alliances with philosophical schools such as the Vienna Circle, neopositivism, or formal language variants of analytical philosophy. The original impact was via the work of Frege, Russell, and other pioneers, backed up by the prestige of research into the foundations of mathematics, which was fast bringing to light those amazing insights that still impress us to-day. The Golden Age (...) of the 1930s deeply affected philosophy, and heartened the minority of philosophers with a formalanalytical bent. As Brand Blanshard writes in Reason and Analysis (1964) – I quote from memory here, to avoid the usual disappointment when re-reading an original text. (shrink)

Every university student has his or her nemesis. Biology and social science students anticipate with great apprehension their required statistics course, while many philosophy students live in fear of formal logic. Math anxiety is the common thread uniting all of them. This article argues that since formal logic is an algebra requiring similar kinds of symbol-manipulation skills needed to succeed in a basic mathematics course, then if logic students have math anxiety, this can impede their progress. Further, it argues (...) that math anxiety is primarily caused by and exacerbated by poor instruction. Formal logic instructors who employ effective instructional techniques for reducing it can help their students overcome math anxiety to foster learning. Methods of instruction leading to anxiety reduction and evidence supporting their efficacy are discussed, including co-operative learning, the mastery goal approach, and self-paced learning. None of these methods holds back more advanced students. (shrink)

Major figures of twentieth-century philosophy were enthralled by the revolution in formal logic, and many of their arguments are based on novel mathematical discoveries. Hilary Putnam claimed that the Löwenheim-Skølem theorem refutes the existence of an objective, observer-independent world; Bas van Fraassen claimed that arguments against empiricism in philosophy of science are ineffective against a semantic approach to scientific theories; W. V. O. Quine claimed that the distinction between analytic and synthetic truths is trivialized by the fact that (...) any theory can be reduced to one in which all truths are analytic. This book dissects these and other arguments through in-depth investigation of the mathematical facts undergirding them. It presents a systematic, mathematically rigorous account of the key notions arising from such debates, including theory, equivalence, translation, reduction, and model. The result is a far-reaching reconceptualization of the role of formal methods in answering philosophical questions. (shrink)

The chapter argues that a model‐building methodology like that widespread in contemporary natural and social science already plays a significant role in philosophy. One neglected form of progress in philosophy over the past fifty years has been the development of better and better formal models of significant phenomena. Examples are given from both philosophy of language and epistemology. Philosophy can do still better in the future by applying model‐building methods more systematically and self‐consciously, with consequent readjustments (...) to its methodology. Although it is neither likely nor desirable for model‐building to become the sole or even main philosophical method, its use enhances the power and reliability of philosophical thinking. (shrink)

"Foundations of the Formal Sciences" is a series of interdisciplinary conferences in mathematics, philosophy, computer science and linguistics. The main goal is to reestablish the traditionally strong links between these areas of research that have been lost in the past decades. The second conference in the series had the subtitle "Applications of Mathematical Logic in Philosophy and Linguistics" and brought speakers from all parts of the Formal Sciences together to give a holistic view of how mathematical methods can (...) improve our philosophical and technical understanding of language and scientific discourse, ranging from the theoretical level up to applications in language recognition software. Audience: This volume is of interest to all formal philosophers and theoretical linguists. In addition to that, logicians interested in the applications of their field and logic students in mathematics, computer science, philosophy and linguistics can use the volume to broaden their knowledge of applications of logic. (shrink)

On an ordinary view of the relation of philosophy of science to science, science serves only as a topic for philosophical reflection, reflection that proceeds by its own methods and according to its own standards. This ordinary view suggests a way of writing a global history of philosophy of science that finds substantially the same philosophical projects being pursued across widely divergent scientific eras. While not denying that this view is of some use regarding certain themes of and (...) particular time periods, this essay argues that much of the epistemology and philosophy of science in the early twentieth century in a variety of projects looked to the then current context of the exact sciences, especially geometry and physics, not merely for its topics but also for its conceptual resources and technical tools. This suggests a more variable project of philosophy of science, a deeper connection between early twentieth-century philosophy of science and its contemporary science, and a more interesting and richer history of philosophy of science than is ordinarily offered. (shrink)

Questions about the relation between identity and discernibility are important both in philosophy and in model theory. We show how a philosophical question about identity and dis- cernibility can be ‘factorized’ into a philosophical question about the adequacy of a formal language to the description of the world, and a mathematical question about discernibility in this language. We provide formal definitions of various notions of discernibility and offer a complete classification of their logical relations. Some new and surprising facts (...) are proved; for instance, that weak dis- cernibility corresponds to discernibility in a language with constants for every object, and that weak discernibility is the most discerning nontrivial discernibility relation. (shrink)

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)

In this article, we reflect on the use of formal methods in the philosophy of science. These are taken to comprise not just methods from logic broadly conceived, but also from other formal disciplines such as probability theory, game theory, and graph theory. We explain how formal modelling in the philosophy of science can shed light on difficult problems in this domain.

Philosophy and science employ abstract hypothetical scenarios- thought experiments - to illustrate, defend, and dispute theoretical claims. Since thought experiments furnish no new empirical observations, the method prompts two epistemological questions: whether anything may be learnt from the merely hypothetical, and, if so, how. Various sceptical arguments against the use of thought experiments in philosophy are discussed and criticized. The thesis that thought experiments in science provide a priori knowledge through non-sensory grasping of abstract entities is discussed and (...) rejected. The thesis that thought experimentation consists in manipulations of mental models is examined and found to be of limited epistemological relevance. It is argued that thought experiments are associated with characteristic arguments in a manner similar to ordinary experiments. It is further argued that thought experiments function in the same way as experiments in general: by providing premises for their associated arguments. Like other experiments, a thought experiment is successful when the premises it provides are true. This holds both for philosophical and scientific thought experiments. An argument schema is proposed and shown to be a formal analogue to that associated with ordinary experiments; similar in being subject to epistemological holism; but differing in being modal: in employing statements about possibility and necessity. The evaluation of thought experiments thus depends on how modal statements may be justified. Intuition and conceivability are discussed as sources of modal justification and found problematic. Instead it is suggested that evaluation proceed by accommodation of the statements describing the experiment's hypothetical scenario. The method of accommodation is developed and applied to five influential thought experiments in philosophy: the brain in a vat; Putnam's Twin Earth; Burge's arthritis example; Searle's Chinese Room; and Newcomb's problem. Its application shows some of these to be failed, others to be successful only relative to controversial philosophical doctrines. (shrink)

This article is concerned with the development of philosophy of science in the 1970s. The explanatory framework is the picture of two fundamental split-offs: the controversial establishment of history and sociology of science and of formal philosophy of science as independent disciplines, against the background of more traditional “conceptual” varieties of philosophy of science. I illustrate these developments, which finally led to somewhat “purified” versions of the respective accounts, by examining a case study, namely, that of the (...) structuralist school, which emerged in the 1970s as an attempt to reconcile historical and formal approaches in philosophy of science. I try to explain the failure of this initial program of “Kuhn Sneedified” and its transition to a more purified formalist version, on the basis of the fact that the former attempt was caught somewhere amid the purism of conceptual, historical, and formal accounts of philosophy of science. (shrink)

The eighteenth and nineteenth centuries witnessed a change in the perception of the arts and of philosophy. In the arts this transition occurred around 1800, with, for instance, the breakdown of Vitruvianism in architecture, while in philosophy the foundationalism of which Descartes and Spinoza were paradigmatic representatives, which presumed that philosophy and the sciences possessed a method of ensuring the demonstration of truths, was undermined by the idea, asserted by Nietzsche and Wittgenstein, that there exist alternative styles (...) of enquiry among which a choice is open. The essays in this book examine the circumstances, features, and consequences of this historical transition, exploring in particular new aspects and instances of the inter-relatedness of content and its formal representation in both the arts and philosophy. (shrink)

The eighteenth and nineteenth centuries witnessed a change in the perception of the arts and of philosophy. In the arts this transition occurred around 1800, with, for instance, the breakdown of Vitruvianism in architecture, while in philosophy the foundationalism of which Descartes and Spinoza were paradigmatic representatives, which presumed that philosophy and the sciences possessed a method of ensuring the demonstration of truths, was undermined by the idea, asserted by Nietzsche and Wittgenstein, that there exist alternative styles (...) of enquiry among which a choice is open. The essays in this book examine the circumstances, features, and consequences of this historical transition, exploring in particular new aspects and instances of the inter-relatedness of content and its formal representation in both the arts and philosophy. (shrink)

It is sometimes said that questions of form are questions of logic or language. In his "Logical Investigations" Husserl, however, clearly distinguished formal ontology from formal grammar and formal logic. The article attempts to explain Husserl's notion of formal ontology. It investigates the relation between formal and material ontology as well as the relation between epistemic and metaphysical necessity. The article provides an interpretation of Husserl's claim that there are metaphysical necessities which are necessarily recognized by the human mind on (...) the basis of Husserl's well-known distinction between the meanings of mental acts and their objective correlates. (shrink)

In a free society, it is common to hear the request that one â ~keep an open mind.â Just what exactly is it, however, to keep an open-mind? How does open-mindedness function? How does it square with important personal commitments? These issues are particularly acute when it comes to matters of religious belief in which open-mindedness can sound to the pious a bit too much like doubt. Certainly, in a discipline whose discourse remains rational dialogue, effort should be spent discerning (...) the contours of this virtue, especially in light of its formal role in establishing responsiveness to new inquiries in matters philosophical and religious. This book provides a collection of essays serving to promote conversation about open-mindedness, its virtue, and its role and application in problems in the philosophy of religion in particular. (shrink)

This is an outstanding contribution to Scotistic scholarship in English. A distinguished array of Scotus and medieval philosophy scholars have served up polished essays to mark this the seventh centenary of the birth of the "Subtle Doctor." Allan Wolter writes on "The Formal Distinction," Timotheus A. Barth on "Being, Univocity, and Analogy According to Duns Scotus," Heiko Oberman on "Duns Scotus, Nominalism, and the Council of Trent," Efrem Bettoni on "The Originality of the Scotistic Synthesis," Bonansea on "Duns Scotus' (...) Voluntarism," Felix Alluntis on Scotus' treatment of "Demonstrability and Demonstration of the Existence of God." There are nine other contributions, most of uniformly high quality, including extended notes by Charles Balic on "The Life and Works of John Duns Scotus" and "The Nature and Value of a Critical Edition of the Complete Works of John Duns Scotus."—E. A. R. (shrink)

Forthcoming guide with brief introductions on methods in analytic philosophy by experts on the relevant topics. With sections on: formal methods, argumentation, inferential methods, thought experiments, intuition, ordinary language philosophy, conceptual analysis, conceptual engineering, naturalism, analytic feminism, experimental philosophy, and progress and disagreement in philosophy.

After several decades during which formalization has flourished it now becomes possible to detect its shortcomings. A definition of formalization is given at the outset. It is next shown that the main justification of formalization as making explicit the form of a proof has serious difficulties. An important shortcoming is found in the fact that many validation procedures in logic and mathematics are not adequately represented deductively. Several such procedures relating to the validation of logical and mathematical (...) sentences are examined. It is concluded that formalization is materially inadequate. (shrink)

The purpose of this paper is twofold. First, it aims at introducing the ontological argument through the analysis of five historical developments: Anselm’s argument found in the second chapter of his Proslogion, Gaunilo’s criticism of it, Descartes’ version of the ontological argument found in his Meditations on First Philosophy, Leibniz’s contribution to the debate on the ontological argument and his demonstration of the possibility of God, and Kant’s famous criticisms against the (cartesian) ontological argument. Second, it intends to critically (...) examine the enterprise of formally analyzing philosophical arguments and, as such, contribute in a small degree to the debate on the role of formalization in philosophy. My focus will be mainly on the drawbacks and limitations of such enterprise; as a guideline, I shall refer to a Carnapian, or Carnapian-like theory of argument analysis. (shrink)

An in-depth history of the linguistic turn in analytic philosophy, from a leading philosopher of language This is the second of five volumes of a definitive history of analytic philosophy from the invention of modern logic in 1879 to the end of the twentieth century. Scott Soames, a leading philosopher of language and historian of analytic philosophy, provides the fullest and most detailed account of the analytic tradition yet published, one that is unmatched in its chronological range, (...) topics covered, and depth of treatment. Focusing on the major milestones and distinguishing them from detours, Soames gives a seminal account of where the analytic tradition has been and where it appears to be heading. Volume 2 provides an intensive account of the new vision in analytical philosophy initiated by Ludwig Wittgenstein’s Tractatus Logico-Philosophicus, its assimilation by the Vienna Circle of Moritz Schlick and Rudolf Carnap, and the subsequent flowering of logical empiricism. With this “linguistic turn,” philosophical analysis became philosophy itself, and the discipline’s stated aim was transformed from advancing philosophical theories to formalizing, systematizing, and unifying science. In addition to exploring the successes and failures of philosophers who pursued this vision, the book describes how the philosophically minded logicians Kurt Gödel, Alfred Tarski, Alonzo Church, and Alan Turing discovered the scope and limits of logic and developed the mathematical theory of computation that ushered in the digital era. The book’s account of this pivotal period closes with a searching examination of the struggle to preserve ethical normativity in a scientific age. (shrink)

Three leading philosopher-logicians present a clear and concise overview of formal theories of truth, explaining key logical techniques. Truth is as central topic in philosophy: formal theories study the connections between truth and logic, including the intriguing challenges presented by paradoxes like the Liar.

1. One sometimes finds, in popular literature, the statement that formal logic is called formal because it studies the forms of thought: concepts, judgments, inferences. To confine the definition in this way would, to say the least, be an inaccuracy. Study of concepts and other forms of thought is generally assumed to be a task of philosophy; and it attains its highest development in dialectical philosophy. The fact is that statements such as the one we have cited are (...) usually followed by the explanation that formal logic studies thoughts — concepts, judgments, inferences — in terms of their formal structure and construction, that is, of various general ways of connecting parts of their concrete content. And it is observed that the logical structure of thought emerges as the result of abstraction, the identification and separation of the general from a multiplicity of individual facts differing in content, and that it is then recorded in terms of formulas. (shrink)

The subject of research in this article is the question of the possibility of formalizing the general theory of systems, that is, turning it into a language for describing systems of any nature with unambiguously defined lexical units and rules. To answer this question, the author considers the phenomenon of semantic indeterminacy of languages, which ensures the flexibility of formed lexical constructions due to the multivalence of lexical units. Also the subject of the research is the practice of quoting out (...) of context – a phenomenon, the admissibility of which is conditioned by the isomorphism of lexical constructions, as well as by the creative nature of the cognitive process, in which the result of cognition is unknown in advance, and thus the change of interpretation of the used concepts is inevitable. The conducted research allows us to state that the general theory of systems cannot be exclusively an applied theory, but should be supplemented with an ontological component. In this case, it becomes a philosophical theory, for which full formalization is impossible without loss of functionality. As a result, general systems theory must inevitably retain a certain semantic uncertainty. This uncertainty, however, can be reduced by translation into universality and generalization of concepts. Besides, it is possible and in some cases necessary to formalize separate components of the general theory of systems, in particular, its ontological component - the metaphysics of material existence. (shrink)

This paper addresses the question of understanding of language expressions. We argue that understanding of language expressions can be successfully studied within a general approach of formal semantics and pragmatics. We show how three types of meanings of expressions (truth conditional meaning, presuppositional component and implicatures) contribute to our general understanding of what was said and how those meanings can be studied within the formal approach.