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)

Since the beginning of the 20th Century to the present day, it has rarely been doubted that whenever formal aesthetic methods meet their iconological counterparts, the two approaches appear to be mutually exclusive. In reality, though, an ahistorical concept is challenging a historical analysis of art. It is especially Susanne K. Langer´s long-overlooked system of analogies between perceptions of the world and of artistic creations that are dependent on feelings which today allows a rapprochement of these positions. Krois’s insistence on (...) a similar point supports this analysis. - I - Unbestritten bis heute gilt, formwissenschaftliche und ikonologische Methoden scheinen sich grundsätzlich auszuschließen, da die ersteren auf ahistorischen und die letzteren auf historischen Grundlagen aufbauen. Dem entgegen soll mit diesem Beitrag gezeigt werden, wie insbesondere die Forschungen Susanne K. Langers und ergänzend diejenigen von John M. Krois eine Annäherung beider Positionen ermöglichen. (shrink)

Formal epistemology is just what it sounds like: epistemology done with formal tools. Coinciding with the general rise in popularity of experimental philosophy, formal epistemologists have begun to apply experimental methods in their own work. In this entry, I survey some of the work at the intersection of formal and experimental epistemology. I show that experimental methods have unique roles to play when epistemology is done formally, and I highlight some ways in which results from formal epistemology have been (...) used fruitfully to advance epistemically-relevant experimental work. The upshot of this brief, incomplete survey is that formal and experimental methods often constitute mutually informative means to epistemological ends. (shrink)

In his paper “Flaws of Formal Relationism”, Mahrad Almotahari argues against the sort of response to Frege's Puzzle I have defended elsewhere, which he dubs ‘Formal Relationism’. Almotahari argues that, because of its specifically formal character, this view is vulnerable to objections that cannot be raised against the otherwise similar Semantic Relationism due to Kit Fine. I argue in response that Formal Relationism has neither of the flaws Almotahari claims to identify.

A brief review of Carnap's formal program in philosophy of science.

The task of this essay is to put biological individuals in formal terms. This approach is not directly interested in matters of time (for example, in evolution), but rather in the formal shape of biological objects. So it is different from, but not opposed to, natural science. In his later years, Wittgenstein made similar investigations in psychology and mathematics. Unfortunately, he found no time to make extensive remarks on philosophy of biology. This is what we are going to advance (...) here. (shrink)

A collection of material on Husserl's Logical Investigations, and specifically on Husserl's formal theory of parts, wholes and dependence and its influence in ontology, logic and psychology. Includes translations of classic works by Adolf Reinach and Eugenie Ginsberg, as well as original contributions by Wolfgang Künne, Kevin Mulligan, Gilbert Null, Barry Smith, Peter M. Simons, Roger A. Simons and Dallas Willard. Documents work on Husserl's ontology arising out of early meetings of the Seminar for Austro-German Philosophy.

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)

This paper introduces the special issue on Formal Approaches to the Ontological Argument of the Journal of Applied Logics (College Publications). The issue contains the following articles: Formal Approaches to the Ontological Argument, by Ricardo Sousa Silvestre and Jean-Yves Béziau; A Brief Critical Introduction to the Ontological Argument and its Formalization: Anselm, Gaunilo, Descartes, Leibniz and Kant, by Ricardo Sousa Silvestre; A Mechanically Assisted Examination of Begging the Question in Anselm’s Ontological Argument, by John Rushby; A Tractarian Resolution to (...) the Ontological Argument, by Erik Thomsen; On Kant’s Hidden Ambivalence Toward Existential Generalization in his Critique of the Ontological Argument, by Giovanni Mion; The Totality of Predicates and the Possibility of the Most Real Being, by Srećko Kovač; An Even More Leibnizian Version of Gödel’s Ontological Argument, by Kordula Świętorzecka and Marcin Łyczak; A Case Study On Computational Hermeneutics: E. J. Lowe’s Modal Ontological Argument, by David Fuenmayor. (shrink)

Over the years many mathematicians have voiced a preference for proofs that stay “close” to the statements being proved, avoiding “foreign”, “extraneous”, or “remote” considerations. Such proofs have come to be known as “pure”. Purity issues have arisen repeatedly in the practice of arithmetic; a famous instance is the question of complex-analytic considerations in the proof of the prime number theorem. This article surveys several such issues, and discusses ways in which logical considerations shed light on these issues.

A central aim for philosophers of science has been to understand scientific theory change, or more specifically the rationality of theory change. Philosophers and historians of science have suggested that not only theories but also scientific methods and standards of rational inquiry have changed through the history of science. The topic here is methodological change, and what kind of theory of rational methodological change is appropriate. The modest ambition of this paper is to discuss in what ways results in formal (...) theories of belief revision can throw light on the question of what an appropriate theory of methodological change would look like. (shrink)

I submit that epistemic progress in key areas of contemporary academic philosophy has been compromised by politically correct ideology. First, guided by an evolutionary account of ideology, results from social and cognitive psychology and formal philosophical methods, I expose evidence for political bias in contemporary Western academia and sketch a formalization for the contents of beliefs from the PC worldview taken to be of core importance, the theory of social oppression and the thesis of anthropological mental egalitarianism. Then, (...) aided by discussions from contemporary epistemology on epistemic values, I model the problem of epistemic appraisal using the frameworks of multi-objective optimization theory and multi-criteria decision analysis and apply it to politically correct philosophy. I conclude that philosophy guided by politically correct values is bound to produce constructs that are less truth-conducive and that spurious values which are ideologically motivated should be abandoned. Objections to my framework stemming from contextual empiricism, the feminine voice in ethics and political philosophy are considered. I conclude by prescribing the epistemic value of empirical adequacy, the contextual value of political diversity and the moral virtue of moral courage to reverse unwarranted trends in academic philosophy due to PC ideology. (shrink)

he general theme of this paper is the issue of formalization in philosophy; in a more specific way, it deals with the issue of formalization of arguments in analytic philosophy of religion. One argument in particular – Anselm’s Proslogion II ontological argument – and one specific attempt to formalize it – Robert Adams’ formalization found in his paper “The Logical Structure of Anselm’s Arguments”, published in The Philosophical Review in 1971 – are taken as study cases. The (...) purpose of the paper is to critically analyze Adams’ formalization with the intent to shed some light on the following questions: What are the virtues of formally analyzing arguments and the contributions, if any, of such an enterprise to the debate on Anselm’s argument? Which lessons can Adam’s work teach us about the dangers and limitations of formalization? Do these virtues and dangers teach us something about analysis of arguments in general? (shrink)

Carnap and Twentieth-Century Thought: Explication as En lighten ment is the first book in the English language that seeks to place Carnap's philosophy in a broad cultural, political and intellectual context. According to the author, Carnap synthesized many different cur rents of thought and thereby arrived at a novel philosophical perspective that remains strik ing ly relevant today. Whether the reader agrees with Carus's bold theses on Carnap's place in the landscape of twentieth-century philosophy, and his even bolder (...) claims concerning the role that philosophy in Carnap's style should play in the thought of our century, does not matter so much as the excellent opportunity Carus's book offers to thoroughly rethink one's ideas about Carnap's philosophy. One reason why Carnap and Twentieth-Century Thought might change one's ideas is that Carus has unearthed much hitherto unknown material from the archives that sheds new light on Carnap's early life and thought. Indeed, the many archival findings presented in CTT for the first time suffice to make the book re warding reading for philosophers and historians of philosophy alike. CTT exhibits a high standard of historical scholarship, and the book itself is a beautiful example of high-quality academic publishing. Up to now, Carnap has remained a controversial figure on the philo sophical scene. On the one hand, he has a solid reputation as a leading figure of logical positivism . According to conventional wisdom, this was a school of thought characterized by its formal and technical philosophy, as well as being rather dismissive of other ways of doing philosophy, dogmatically sticking to its own theses. As a typical example of this arrogant logical empiricist attitude, one usually refers to Carnap's notorious Overcoming Metaphysics by Logical Analysis of Language , written when the Vienna Circle's Logical Empiricism had entered its most radical phase. Self-proclaimed postpositivist philosophers of science dismissed logical positivism, in particular Carnap's, as the dogmatic and orthodox “received view.” The tendency to portray logical empiricism as an obsolete doctrine centering around certain “dogmas” started with Quine's Two Dogmas of Empiricism and reached its somewhat ridiculous culmination in the early 1980s when allegedly “six or seven dogmas” were discovered . Thereby an allegedly un brid geable gap between classical “dogmatic” logical em pi ricism and its modern “enlightened” suc ces sors was construed. (shrink)

I review Michael T. Ferejohn's "Formal Causes: Definition, Explanation, and Primacy in Socratic and Aristotelian Thought".

(This is for the Cambridge Handbook of Analytic Philosophy, edited by Marcus Rossberg) In this handbook entry, I survey the different ways in which formal mathematical methods have been applied to philosophical questions throughout the history of analytic philosophy. I consider: formalization in symbolic logic, with examples such as Aquinas’ third way and Anselm’s ontological argument; Bayesian confirmation theory, with examples such as the fine-tuning argument for God and the paradox of the ravens; foundations of mathematics, with (...) examples such as Hilbert’s programme and Gödel’s incompleteness theorems; social choice theory, with examples such as Condorcet’s paradox and Arrow’s theorem; ‘how possibly’ results, with examples such as Condorcet’s jury theorem and recent work on intersectionality theory; and the application of advanced mathematics in philosophy, with examples such as accuracy-first epistemology. (shrink)

In this paper we examine whether and how powers ontologies can back formal causation. We attempt to answer three questions: i) what is formal causation; ii) whether we need formal causation, and iii) whether formal causation need powers and whether it can be grounded in powers. We take formal causal explanations to be explanations in which something's essence features prominently in the explanans. Three kinds of essential explanations are distinguished: constitutive, consequential, and those singling out something's propria. This last kind (...) of explanation has been somewhat overlooked in the literature, but we argue that it features in much of the most relevant uses of formal explanations in philosophy and science. These are the explanations for why an object has certain propertis that are not, properly speaking, parts of its essence, but that belong to it more intimately than just being part of its consequential essence: they are the properties that ‘flow’ from something's essence. It is argued that a powers metaphysics is uniquely placed to make sense of this last phenomenon. We then distinguish three grades of involvement in which powers might be salient for formal causal explanations: i) powers might be the subject matter of the essence operator, ii) the essence of something might include (or be exhausted) by powers, or iii) powers can explain how propria can flow from something's constitutive existence. (shrink)

I argue that normative formal epistemology (NFE) is best understood as modelling, in the sense that this is the reconstruction of its methodology on which NFE is doing best. I focus on Bayesianism and show that it has the characteristics of modelling. But modelling is a scientific enterprise, while NFE is normative. I thus develop an account of normative models on which they are idealised representations put to normative purposes. Normative assumptions, such as the transitivity of comparative credence, are characterised (...) as modelling idealisations motivated normatively. I then survey the landscape of methodological options: what might formal epistemologists be up to? I argue the choice is essentially binary: modelling or theorising. If NFE is theorising it is doing very poorly: generating false claims with no clear methodology for separating out what is to be taken seriously. Modelling, by contrast, is a successful methodology precisely suited to the management of useful falsehoods. Regarding NFE as modelling is not costless, however. First, our normative inferences are less direct and are muddied by the presence of descriptive idealisations. Second, our models are purpose-specific and limited in their scope. I close with suggestions for how to adapt our practice. (shrink)

In the era of “big data,” science is increasingly information driven, and the potential for computers to store, manage, and integrate massive amounts of data has given rise to such new disciplinary fields as biomedical informatics. Applied ontology offers a strategy for the organization of scientific information in computer-tractable form, drawing on concepts not only from computer and information science but also from linguistics, logic, and philosophy. This book provides an introduction to the field of applied ontology that is (...) of particular relevance to biomedicine, covering theoretical components of ontologies, best practices for ontology design, and examples of biomedical ontologies in use. After defining an ontology as a representation of the types of entities in a given domain, the book distinguishes between different kinds of ontologies and taxonomies, and shows how applied ontology draws on more traditional ideas from metaphysics. It presents the core features of the Basic Formal Ontology (BFO), now used by over one hundred ontology projects around the world, and offers examples of domain ontologies that utilize BFO. The book also describes Web Ontology Language (OWL), a common framework for Semantic Web technologies. Throughout, the book provides concrete recommendations for the design and construction of domain ontologies. (shrink)

Edward Nieznański developed two logical systems to deal with the problem of evil and to refute religious determinism. However, when formalized in first-order modal logic, two axioms of each system contradict one another, revealing that there is an underlying minimal set of axioms enough to settle the questions. In this article, we develop this minimal system, called N3, which is based on Nieznański’s contribution. The purpose of N3 is to solve the logical problem of evil through the defeat of a (...) version of religious determinism. On the one hand, these questions are also addressed by Nieznański’s systems, but, on the other hand, they are obtained in N3 with fewer assumptions. Our approach can be considered a case of logic of religion, that is, of logic applied to religious discourse, as proposed by Józef Maria Bocheński; in this particular case, it is a discourse in theodicy, which is situated in the context of the philosophy of religion. (shrink)

This commentary is a reflection on a collaboration with the artist Rossella Biscotti and comments on how artistic research and logico-mathematical methods can be used to contribute to the development of critical perspectives on contemporary data practices.

This paper reviews the central points and presents some recent developments of the epistemic approach to paraconsistency in terms of the preservation of evidence. Two formal systems are surveyed, the basic logic of evidence (BLE) and the logic of evidence and truth (LET J ), designed to deal, respectively, with evidence and with evidence and truth. While BLE is equivalent to Nelson’s logic N4, it has been conceived for a different purpose. Adequate valuation semantics that provide decidability are given for (...) both BLE and LET J . The meanings of the connectives of BLE and LET J , from the point of view of preservation of evidence, is explained with the aid of an inferential semantics. A formalization of the notion of evidence for BLE as proposed by M. Fitting is also reviewed here. As a novel result, the paper shows that LET J is semantically characterized through the so-called Fidel structures. Some opportunities for further research are also discussed. (shrink)

The formal sciences - mathematical as opposed to natural sciences, such as operations research, statistics, theoretical computer science, systems engineering - appear to have achieved mathematically provable knowledge directly about the real world. It is argued that this appearance is correct.

This essay discusses Wittgenstein's conception of logic, early and late, and some of the types of logical system that he constructed. The essay shows that the common view according to which Wittgenstein had stopped engaging in logic as a philosophical discipline by the time of writing Philosophical Investigations is mistaken. It is argued that, on the contrary, logic continued to figure at the very heart of later Wittgenstein's philosophy; and that Wittgenstein's mature philosophy of logic contains many interesting (...) thoughts that have gone widely unnoticed. (shrink)

In the past few years, social epistemologists have developed several formal models of the social organisation of science. While their robustness and representational adequacy has been analysed at length, the function of these models has begun to be discussed in more general terms only recently. In this article, I will interpret many of the current formal models of the scientific community as representing the latest development of what I will call the ‘Kuhnian project’. These models share with Kuhn a number (...) of questions about the relation between individuals and communities. At the same time, they also inherit some of Kuhn’s problematic characterisations of the scientific community. In particular, current models of the social organisation of science represent the scientific community as essentially value-free. This may put into question both their representational adequacy and their normative ambitions. In the end, it will be shown that the discussion on the formal models of the scientific community may contribute in fruitful ways to the ongoing debates on value judgements in science. (shrink)

In this paper I try to answer four basic questions: (1) How the concept of God is to be represented? (2) Are there any logical principles governing it? (3) If so, what kind of logic lies behind them? (4) Can there be a logic of the concept of God? I address them by presenting a formal-logical account to the concept of God. I take it as a methodological desideratum that this should be done within the simplest existing logical formalism. I (...) start with first-order logic (FOL) with identity, and then show that its simplest modal extension (SQML, or the simplest quantified modal logic) is enough for us to formalize a minimally satisfactory theory of the concept of God. I focus exclusively on the monotheistic concept of God. (shrink)

It is commonly said that some standards, such as morality, are ‘normatively authoritative’ in a way that other standards, such as etiquette, are not; standards like etiquette are said to be ‘not really normative’. Skeptics deny the very possibility of normative authority, and take claims like ‘etiquette is not really normative’ to be either empty or confused. I offer a different route to defeat skeptics about authority: instead of focusing on what makes standards like morality special, we should focus on (...) what makes standards like etiquette ‘not really normative’. I defend a fictionalist theory on which etiquette is ‘not really normative’ in roughly the same way that Sherlock is ‘not really a detective’, and show that fictionalism about some normative standards helps us explain the possibility of normative authority. (shrink)

This paper introduces new logical systems which axiomatize a formal representation of inconsistency (here taken to be equivalent to contradictoriness) in classical logic. We start from an intuitive semantical account of inconsistent data, fixing some basic requirements, and provide two distinct sound and complete axiomatics for such semantics, LFI1 and LFI2, as well as their first-order extensions, LFI1* and LFI2*, depending on which additional requirements are considered. These formal systems are examples of what we dub Logics of Formal Inconsistency (LFI) (...) and form part of a much larger family of similar logics. We also show that there are translations from classical and paraconsistent first-order logics into LFI1* and LFI2*, and back. Hence, despite their status as subsystems of classical logic, LFI1* and LFI2* can codify any classical or paraconsistent reasoning. (shrink)

This paper formalizes part of the cognitive architecture that Kant develops in the Critique of Pure Reason. The central Kantian notion that we formalize is the rule. As we interpret Kant, a rule is not a declarative conditional stating what would be true if such and such conditions hold. Rather, a Kantian rule is a general procedure, represented by a conditional imperative or permissive, indicating which acts must or may be performed, given certain acts that are already being performed. These (...) acts are not propositions; they do not have truth-values. Our formalization is related to the input/ output logics, a family of logics designed to capture relations between elements that need not have truth-values. In this paper, we introduce KL3 as a formalization of Kant’s conception of rules as conditional imperatives and permissives. We explain how it differs from standard input/output logics, geometric logic, and first-order logic, as well as how it translates natural language sentences not well captured by first-order logic. Finally, we show how the various distinctions in Kant’s much-maligned Table of Judgements emerge as the most natural way of dividing up the various types and sub-types of rule in KL3. Our analysis sheds new light on the way in which normative notions play a fundamental role in the conception of logic at the heart of Kant’s theoretical philosophy. (shrink)

Hilbert arithmetic in a wide sense, including Hilbert arithmetic in a narrow sense consisting by two dual and anti-isometric Peano arithmetics, on the one hand, and the qubit Hilbert space (originating for the standard separable complex Hilbert space of quantum mechanics), on the other hand, allows for an arithmetic version of Gentzen’s cut elimination and quantum measurement to be described uniformy as two processes occurring accordingly in those two branches. A philosophical reflection also justifying that unity by quantum neo-Pythagoreanism links (...) it to the opposition of propositional logic, to which Gentzen’s cut rule refers immediately, on the one hand, and the linguistic and mathematical theory of metaphor therefore sharing the same structure borrowed from Hilbert arithmetic in a wide sense. An example by hermeneutical circle modeled as a dual pair of a syllogism (accomplishable also by a Turing machine) and a relevant metaphor (being a formal and logical mistake and thus fundamentally inaccessible to any Turing machine) visualizes human understanding corresponding also to Gentzen’s cut elimination and the Gödel dichotomy about the relation of arithmetic to set theory: either incompleteness or contradiction. The metaphor as the complementing “half” of any understanding of hermeneutical circle is what allows for that Gödel-like incompleteness to be overcome in human thought. (shrink)

This article discusses a relation between the formal science of logical semantics and some monotheistic, polytheistic and Trinitarian Christian notions. This relation appears in the use of the existential quantifier and of logical-modal notions when some monotheistic and polytheistic concepts and, principally, the concept of Trinity Dogma are analyzed. Thus, some presupposed modal notions will appear in some monotheistic propositions, such as the notion of “logically necessary”. From this, it will be shown how the term “God” is a polysemic term (...) and is often treated as both subject and predicate. This will make it clear that there is no plausible intellectual justification for believing that the term “God” can only be used as a name and never as a predicate, and vice versa. After that analysis, I will show that the conjunction of the “Trinity Dogma” with some type of “monotheistic position” would necessarily imply some class of absurdity and/or semantic “oddity”. (shrink)

There are two fundamentally distinct kinds of biological theorizing. "Formal biology" focuses on the relations, captured in formal laws, among mathematically abstracted properties of abstract objects. Population genetics and theoretical mathematical ecology, which are cases of formal biology, thus share methods and goals with theoretical physics. "Compositional biology," on the other hand, is concerned with articulating the concrete structure, mechanisms, and function, through developmental and evolutionary time, of material parts and wholes. Molecular genetics, biochemistry, developmental biology, and physiology, which are (...) examples of compositional biology, are in serious need of philosophical attention. For example, the very concept of a "part" is understudied in both philosophy of biology and philosophy of science. ;My dissertation is an attempt to clarify the distinction between formal biology and compositional biology and, in so doing, provide a clear philosophical analysis, with case studies, of compositional biology. Given the social, economic, and medical importance of compositional biology, understanding it is urgent. For my investigation, I draw on the philosophical fields of metaphysics and epistemology, as well as philosophy of biology and philosophy of science. I suggest new ways of thinking about some classic philosophy of science issues, such as modeling, laws of nature, abstraction, explanation, and confirmation. I hint at the relevance of my study of two kinds of biological theorizing to debates concerning the disunity of science. (shrink)

Revised version of chapter in J. N. Mohanty and W. McKenna (eds.), Husserl’s Phenomenology: A Textbook, Lanham: University Press of America, 1989, 29–67. -/- Logic for Husserl is a science of science, a science of what all sciences have in common in their modes of validation. Thus logic deals with universal laws relating to truth, to deduction, to verification and falsification, and with laws relating to theory as such, and to what makes for theoretical unity, both on the side of (...) the propositions of a theory and on the side of the domain of objects to which these propositions refer. This essay presents a systematic overview of Husserl’s views on these matters as put forward in his Logical Investigations. It shows how Husserl’s theory of linguistic meanings as species of mental acts, his formal ontology of part, whole and dependence, his theory of meaning categories, and his theory of categorial intuition combine with his theory of science to form a single whole. Finally, it explores the ways in which Husserl’s ideas on these matters can be put to use in solving problems in the philosophy of language, logic and mathematics in a way which does justice to the role of mental activity in each of these domains while at the same time avoiding the pitfalls of psychologism. (shrink)

In the paper, various notions of the logical semiotic sense of linguistic expressions – namely, syntactic and semantic, intensional and extensional – are considered and formalised on the basis of a formal-logical conception of any language L characterised categorially in the spirit of certain Husserl's ideas of pure grammar, Leśniewski-Ajdukiewicz's theory of syntactic/semantic categories and, in accordance with Frege's ontological canons, Bocheński's and some of Suszko's ideas of language adequacy of expressions of L. The adequacy ensures their unambiguous syntactic and (...) semantic senses and mutual, syntactic and semantic correspondence guaranteed by the acceptance of a postulate of categorial compatibility of syntactic and semantic categories of expressions of L. This postulate defines the unification of these three logical senses. There are three principles of compositionality which follow from this postulate: one syntactic and two semantic ones already known to Frege. They are treated as conditions of homomorphism of partial algebra of L into algebraic models of L: syntactic, intensional and extensional. In the paper, they are applied to some expressions with quantifiers. Language adequacy connected with the logical senses described in the logical conception of language L is, obviously, an idealisation. The syntactic and semantic unambiguity of its expressions is not, of course, a feature of natural languages, but every syntactically and semantically ambiguous expression of such languages may be treated as a schema representing all of its interpretations that are unambiguous expressions. (shrink)

There is an old meta-philosophical worry: very roughly, metaphysical theories have no observational consequences and so the study of metaphysics has no value. The worry has been around in some form since the rise of logical positivism in the early twentieth century but has seen a bit of a renaissance recently. In this paper, I provide an apology for metaphysics in the face of this kind of concern. The core of the argument is this: pure mathematics detaches from science in (...) much the same manner as metaphysics and yet it is valuable nonetheless. The source of value enjoyed by pure mathematics extends to metaphysics as well. Accordingly, if one denies that metaphysics has value, then one is forced to deny that pure mathematics has value. The argument places an added burden on the sceptic of metaphysics. If one truly believes that metaphysics is worthless (as some philosophers do), then one must give up on pure mathematics as well. (shrink)

I defend the thesis that Kantian analytic judgments are about objects (as opposed to concepts) against two challenges raised by recent scholars. First, can it accommodate cases like “A two-sided polygon is two-sided”, where no object really falls under the subject-concept as Kant sees it? Second, is it compatible with Kant’s view that analytic judgments make no claims about objects in the world and that we can know them to be true without going beyond the given concepts? I address these (...) challenges in two steps. First, given Kant’s distinction between an object in general = x from an object of sensible intuition, I argue that analytic judgments are about objects in the former sense, no matter whether the purported objects can be given in our intuition. Second, using Kant’s method of representing certain logical relations of concepts with such figures as circles, I construct a model to show that analytic truths are truths about objects in general = x and yet can be determined solely by the intensional relation between the given concepts plus certain Kantian-logical laws. Analytic truths are thus shown as formal in the Kantian sense that they do not presuppose the purported objects as givable in our intuition. This account of the formality of analytic truths captures Kant’s diagnosis of the Leibnizian illusion that we can make material claims about the world by analytically true judgments. (shrink)

This short article pairs the realms of “Mathematics”, “Philosophy”, and “Poetry”, presenting some corners of intersection of this type of scientocreativity. Poetry have long been following mathematical patterns expressed by stern formal restrictions, as the strong metrical structure of ancient Greek heroic epic, or the consistent meter with standardized rhyme scheme and a “volta” of Italian sonnets. Poetry was always connected to Philosophy, and further on, notable mathematicians, like the inventor of quaternions, William Rowan Hamilton, or Ion Barbu, (...) the creator of the Barbilian spaces, have written appreciated poems. We will focus here on an avant-garde movement in literature, art, philosophy, and science, called Paradoxism, founded in Romania in 1980 by a mathematician, philosopher and poet, and on the laboured writing exercises of the Oulipo group, founded in Paris in 1960 by mathematicians and poets, both of them still in act. (shrink)

This submission constitutes six (core) pages in literary prose expounding the philosophy of Parmenides of Elea outside the reductionist framework based in formal logic that has become de rigeur in philosophy departments of the English language world — at least prior to Dr. Papa-Grimaldi’s research. To this end, my paper, in chronological order, by way of introduction simulates Plato’s Parmenides; in the main body reconstructs Taran’s argument in “Much Ado About ‘Nothing,’” in Apeiron, Vol. XXXV, No. 2, June (...) 2002, pp. 87-104; and in the final section which will be presented at the conference, breaks away into an original hermeneutics in dialogical format featuring Socrates as a guest dramatis personae charged with the task of reconstructing in a new key, on behalf of the author, Parmenides’s philosophy. (shrink)

Reasons-based accounts of our normative conclusions face difficulties in distinguishing between what ought to be done and what is required. This article addresses this problem from a formal perspective. I introduce a rudimentary formalization of a reasons-based account and demonstrate that that the model faces difficulties in accounting for the distinction between oughts and requirements. I briefly critique attempts to distinguish between oughts and requirements by appealing to a difference in strength or weight of reasons. I then present a (...) formalized reasons-based account of permissions, oughts and requirements. The model exploits Joshua Gert (2004; 2007) and Patricia Greenspan’s (2005; 2007; 2010) suggestion that some reasons perform a purely justificatory function. I show that the model preserves the standard entailment relationships between requirements, oughts and permissions. (shrink)

In this text I propose a formal framework for the study of phenomenal objectness - the distinction in an a priori undifferenciated experience of the phenomenal field of certain 'objects'. The purpose of this framework is to represent (even partially) the reality of phenomenal experience in its structure (which participates conceptually to consciousness as such) and at the same time to allow the production of a tractable formalism in order to search for a mathematical explanation for the fundamental phenomenon of (...) objectness. The constitution of this framework is based on intuitions from consciousness literature as well as the recent integrated information theory. Before coming to the framework's definition, I analyse this theory from the point of view of the discourse, through concepts that I introduce here (statical and dynamical phases of the discourse), and explain some severe epistemic difficulties it encounters. The definition of a general combination criterion for the inter-discourse between philosophy and mathematics (which is necessary for the project of explaining consciousness scientifically) in these terms leads in this text to disentangle this theory into the proposed framework. (shrink)

Formal relationism in the philosophy of mind is the thesis that folk psychological states should be individuated, at least partially, in terms of the purely formal inference-licensing relations between underlying mental representations. It's supposed to provide a Russellian alternative to a Fregean theory of propositional attitudes. I argue that there's an inconsistency between the motivation for formal relationism and the use to which it's put in defense of Russellian propositions. Furthermore, I argue that formal relationism is committed to epiphenomenalism (...) about singular mental content. (shrink)

This publication defends a phenomenalist interpretation of Kant’s idealism, which, however, deviates from usual phenomenalist interpretations in several respects. According to my reading, appearances are the content of representations, but not the true object of cognition. The object to which our cognition refers is rather the thing itself as the transcendental object. Nonetheless, we only cognize them as they appear and not as they are in themselves. Thus the unknowability of things as they are in themselves is retained. In the (...) course of my presentation, I discuss a number of aspects of Kant’s philosophy, among which are the distinction between appearances and things in themselves, Kant’s relationship to Cartesian epistemology, the refutation of idealism, and not least his theory of synthesis. My aim is not only to show that Kant is a phenomenalist, but also to characterize the kind of his phenomenalism. (shrink)

Formal systems are standardly envisaged in terms of a grammar specifying well-formed formulae together with a set of axioms and rules. Derivations are ordered lists of formulae each of which is either an axiom or is generated from earlier items on the list by means of the rules of the system; the theorems of a formal system are simply those formulae for which there are derivations. Here we outline a set of alternative and explicitly visual ways of envisaging and analyzing (...) at least simple formal systems using fractal patterns of infinite depth. Progressively deeper dimensions of such a fractal can be used to map increasingly complex wffs or increasingly complex 'value spaces', with tautologies, contradictions, and various forms of contingency coded in terms of color. This and related approaches, it turns out, offer not only visually immediate and geometrically intriguing representations of formal systems as a whole but also promising formal links (1) between standard systems and classical patterns in fractal geometry, (2) between quite different kinds of value spaces in classical and infinite-valued logics, and (3) between cellular automata and logic. It is hoped that pattern analysis of this kind may open possibilities for a geometrical approach to further questions within logic and metalogic. (shrink)

The primary function that philosophy has to perform is analysis of meanings. Contemporary philosophy is a story of the idea of meaning, in the words of Gilbert Ryle. The study of meaning in our time takes several ways. Two ways come in the forefront. The first relates to the formal theories proposed by Frege, earlier Wittgenstein, Quine, Chomsky and Dummmett. The second relates to the theories of use suggested by the later Wittgenstein, Austin, Ryle, Strawson, Grice and Searle. (...) Formal theories are concerned with the formal structure of languages, and the interrelationships between sentences, while the use theories emphasize the role of speakers in determining and understanding the meaning. This book provides an analytical and critical study of the theory communication- intention in meaning according to Paul Grice (1913-1988), which gave speakers and their intentions a central place in the interpretation of meaning, and also aims to formulate the links between theory of communication- intention in semantics and the theory of conversational implicature in pragmatics. الوظيفة الأساسية التي يتعين على الفلسفة القيام بها هي تحليل المعاني. والفلسفة المعاصرة قصة لفكرة المعني على حد تعبير جيلبرت رايل. وتسلك دراسة المعنى في عصرنا عدة طرائق. تأتي في طليعتها طريقتان. ترتبط الأولي بالنظريات الصورية التي اقترحها فريجه، وفتجنشتين المبكر، وكواين، وتشومسكي، ودميت. وترتبط الثانية بنظرية الاستعمال التي اقترحها فتجنشتين المتأخر، وأوستن، ورايل، وستراوسون، وجرايس، وسيرل وتحفل النظريات الصورية بالبنية الصورية للغات، والعلاقات المتبادلة بين الجمل،على حين تؤكد نظريات الاستعمال على دور المتكلمين في تحديد المعنى وفهمه. ويقدم هذا الكتاب دراسة تحليلية نقدية لنظرية قصد الاتصال (النظرية القصدية) في المعنى عند جرايس (1988-1913) الذي أعطى المتكلمين ومقاصدهم مكانة محورية في تفسير المعنى، ويهدف أيضا إلى صياغة الروابط بين نظرية قصد الاتصال في علم الدلالة ونظرية الاقتضاء التخاطبي في علم الاستعمال المعنى، علم الدلالة، علم الاستعمال، المعنى لدى المتكلم، الاقتضاء التخاطبي، قواعد المحادثة، النظريات الصورية، نظريات الاستعمال، فريجه، جرايس، سيرل . (shrink)

In his book, History as a Science and the System of the Sciences, Thomas Seebohm articulates the view that history can serve to mediate between the sciences of explanation and the sciences of interpretation, that is, between the natural sciences and the human sciences. Among other things, Seebohm analyzes history from a phenomenological perspective to reveal the material foundations of the historical human sciences in the lifeworld. As a preliminary to his analyses, Seebohm examines the formal and material presuppositions of (...) phenomenological epistemology, as well as the emergence of the human sciences and the traditional distinctions and divisions that are made between the natural and the human sciences. -/- As part of this examination, Seebohm devotes a section to discussing Husserl’s formal mereology because he understands that a reflective analysis of the foundations of the historical sciences requires a reflective analysis of the objects of the historical sciences, that is, of concrete organic wholes (i.e., social groups) and of their parts. Seebohm concludes that Husserl’s mereological ontology needs to be altered with regard to the historical sciences because the relations between organic wholes and their parts are not summative relations. Seebohm’s conclusion is relevant for the issue of the reducibility of organic wholes such as social groups to their parts and for the issue of the reducibility of the historical sciences to the lower-order sciences, that is, to the sciences concerned with lower-order ontologies. -/- In this paper, I propose to extend Seebohm’s conclusion to the ontology of chemical wholes as object of quantum chemistry and to argue that Husserl’s formal mereology is descriptively inadequate for this regional ontology as well. This may seem surprising at first, since the objects studied by quantum chemists are not organic wholes. However, my discussion of atoms and molecules as they are understood in quantum chemistry will show that Husserl’s classical summative and extensional mereology does not accurately capture the relations between chemical wholes and their parts. This conclusion is relevant for the question of the reducibility of chemical wholes to their parts and of the reducibility of chemistry to physics, issues that have been of central importance within the philosophy of chemistry for the past several decades. (shrink)

Should we believe our controversial philosophical views? Recently, several authors have argued from broadly conciliationist premises that we should not. If they are right, we philosophers face a dilemma: If we believe our views, we are irrational. If we do not, we are not sincere in holding them. This paper offers a way out, proposing an attitude we can rationally take toward our views that can support sincerity of the appropriate sort. We should arrive at our views via a certain (...) sort of ‘insulated’ reasoning – that is, reasoning that involves setting aside certain higher-order worries, such as those provided by disagreement – when we investigate philosophical questions. (shrink)

ABSTRACT. May scientists rely on substantive, a priori presuppositions? Quinean naturalists say "no," but Michael Friedman and others claim that such a view cannot be squared with the actual history of science. To make his case, Friedman offers Newton's universal law of gravitation and Einstein's theory of relativity as examples of admired theories that both employ presuppositions (usually of a mathematical nature), presuppositions that do not face empirical evidence directly. In fact, Friedman claims that the use of such presuppositions is (...) a hallmark of "science as we know it." But what should we say about the special sciences, which typically do not rely on the abstruse formalisms one finds in the exact sciences? I identify a type of a priori presupposition that plays an especially striking role in the development of empirical psychology. These are ontological presuppositions about the type of object a given science purports to study. I show how such presuppositions can be both a priori and rational by investigating their role in an early flap over psychology's contested status as a natural science. The flap focused on one of the field's earliest textbooks, William James's Principles of Psychology. The work was attacked precisely for its reliance on a priori presuppositions about what James had called the "mental state," psychology's (alleged) proper object. I argue that the specific presuppositions James packed into his definition of the "mental state" were not directly responsible to empirical evidence, and so in that sense were a priori; but the presuppositions were rational in that they were crafted to help overcome philosophical objections (championed by neo-Hegelians) to the very idea that there can be a genuine science of mind. Thus, my case study gives an example of substantive, a priori presuppositions being put to use—to rational use—in the special sciences. In addition to evaluating James's use of presuppositions, my paper also offers historical reflections on two different strands of pragmatist philosophy of science. One strand, tracing back through Quine to C. S. Peirce, is more naturalistic, eschewing the use of a priori elements in science. The other strand, tracing back through Kuhn and C. I. Lewis to James, is more friendly to such presuppositions, and to that extent bears affinity with the positivist tradition Friedman occupies. (shrink)

The formal and empirical-generative perspectives of computation are demonstrated to be inadequate to secure the goals of simulation in the social sciences. Simulation does not resemble formal demonstrations or generative mechanisms that deductively explain how certain models are sufficient to generate emergent macrostructures of interest. The description of scientific practice implies additional epistemic conceptions of scientific knowledge. Three kinds of knowledge that account for a comprehensive description of the discipline were identified: formal, empirical and intentional knowledge. The use of formal (...) conceptions of computation for describing simulation is refuted; the roles of programming languages according to intentional accounts of computation are identified; and the roles of iconographic programming languages and aesthetic machines in simulation are characterized. The roles that simulation and intentional decision making may be able to play in a participative information society are also discussed. (shrink)

Photomechanical reprint of papers from 1970 to 1992 mostly in English, some in German or French: Foreword 1–4; LAW AS PRACTICE ‘La formation des concepts en sciences juridiques’ 7–33, ‘Geltung des Rechts – Wirksamkeit des Rechts’ 35–42, ‘Macrosociological Theories of Law’ 43–76, ‘Law & its Inner Morality’ 77–89, ‘The Law & its Limits’ 91–96; LAW AS TECHNIQUE ‘Domaine »externe« & domaine »interne« en droit’ 99–117, ‘Die ministerielle Begründung’ 119–139, ‘The Preamble’ 141–167, ‘Presumption & Fiction’ 169–185, ‘Legal Technique’187–198; LAW AS LOGIC (...) ‘Moderne Staatlichkeit und modernes formales Recht’ 201–207, ‘Heterogeneity & Validity of Law’ 209–218, ‘Leibniz & die Frage der rechtlichen Systembildung’ 219–232, ‘Law & its Approach as a System’ 233–255, ‘Logic of Law & Judicial Activity’ 258–288, ‘Kelsen’s Pure Theory of Law’ 289–293, ‘The Nature of the Judicial Application of Norms’ 295–314; LAW AS EXPERIENCE ‘The Socially Determined Nature of Legal Reasoning’317–374, ‘The Ontological Foundation of Law’ 375–390, ‘Is Law a System of Enactments?’ 391–398, ‘The Uniqueness of National Legal Cultures’ 399–411, ‘Institutions as Systems’ 413–424; LAW AS HISTORY ‘From Legal Customs to Legal Folkways’ 427–436, ‘Anthropological Jurisprudence?’ 437–457, ‘Law as a Social Issue’ 459–475, ‘Law as History?’477–484, ‘Rechtskultur – Denkkultur’ 485–489; w/ Curriculum Vitae & Bibliography, as well as Index & Indexes of normative materials & of names. (shrink)

Judaic Logic is an original inquiry into the forms of thought determining Jewish law and belief, from the impartial perspective of a logician. Judaic Logic attempts to honestly estimate the extent to which the logic employed within Judaism fits into the general norms, and whether it has any contributions to make to them. The author ranges far and wide in Jewish lore, finding clear evidence of both inductive and deductive reasoning in the Torah and other books of the Bible, and (...) analyzing the methodology of the Talmud and other Rabbinic literature by means of formal tools which make possible its objective evaluation with reference to scientific logic. The result is a highly innovative work – incisive and open, free of clichés or manipulation. Judaic Logic succeeds in translating vague and confusing interpretative principles and examples into formulas with the clarity and precision of Aristotelean syllogism. Among the positive outcomes, for logic in general, are a thorough listing, analysis and validation of the various forms of a-fortiori argument, as well as a clarification of dialectic logic. However, on the negative side, this demystification of Talmudic/Rabbinic modes of thought (hermeneutic and heuristic) reveals most of them to be, contrary to the boasts of orthodox commentators, far from deductive and certain. They are often, legitimately enough, inductive. But they are also often unnatural and arbitrary constructs, supported by unverifiable claims and fallacious techniques. Many other thought-processes, used but not noticed or discussed by the Rabbis, are identified in this treatise, and subjected to logical review. Various more or less explicit Rabbinic doctrines, which have logical significance, are also examined in it. In particular, this work includes a formal study of the ethical logic (deontology) found in Jewish law, to elicit both its universal aspects and its peculiarities. With regard to Biblical studies, one notable finding is an explicit formulation (which, however, the Rabbis failed to take note of and stress) of the principles of adduction in the Torah, written long before the acknowledgement of these principles in Western philosophy and their assimilation in a developed theory of knowledge. Another surprise is that, in contrast to Midrashic claims, the Tanakh (Jewish Bible) contains a lot more than ten instances of qal vachomer (a-fortiori) reasoning. In sum, Judaic Logic elucidates and evaluates the epistemological assumptions which have generated the Halakhah (Jewish religious jurisprudence) and allied doctrines. Traditional justifications, or rationalizations, concerning Judaic law and belief, are carefully dissected and weighed at the level of logical process and structure, without concern for content. This foundational approach, devoid of any critical or supportive bias, clears the way for a timely reassessment of orthodox Judaism (and incidentally, other religious systems, by means of analogies or contrasts). Judaic Logic ought, therefore, to be read by all Halakhists, as well as Bible and Talmud scholars and students; and also by everyone interested in the theory, practise and history of logic. (shrink)