Only by classifying things into kinds can we gain knowledge beyond memory and perception. Eric Funkhouser uncovers a logical structure that is common to many, if not all, classificatory systems, given by the determination dimensions of kinds. His account of multiple realizability provides standards for establishing the autonomy of the sciences.

The Logic & Structure project is about the language of mathematical logic and how it can be of use in the visual arts. It involves a conversation between a mathematical logician and a group of artists. The project is ongoing, and this is a report on its first two phases. This text has two parts. The first, “Logic”, is a short introduction to certain aspects of logic, as it was presented to the participants. The second part, “Structures”, describes some (...) of the outcomes.The inspiration for the project comes from modern model theory whose advances revealed the extent to which formal methods may be helpful in describing and analysing mathematical structures. While the structures that are studied are often immensely complex, the formal language in which their properties can be expressed is simple. Its syntax is precisely defined and well understood, and this understanding often successfully guides us in our explorations of the rich world of mathematical objects. Our goal is to see the extent to which a similar approach could be of value when talking about works of art as structures. To this end, one could try to describe existing art objects in terms of suitably chosen formal languages, but we follow a reverse route. The language is described first, and the participating artists are asked to come up with artwork in which formal elements and their relations are chosen in advance, making it easier to identify those features of the created pieces that can be formally expressed. In other words, we are not thinking of applying formal methods to create art; rather we want to begin with samples that can serve as material for discussion. (shrink)

Available for the first time in 20 years, here are two important works from the 1920s by the best-known representative of the Vienna Circle.

In the present article the logical structure of applied social sciences will be discussed. Applied sciences don't regard causes and effects but only means and ends. Therefore the logical structure of means-end-argumentations in social sciences will be shown. One can perceive also the important part of normative statements. In summarizing, we can declare that in social sciences there is partly a need to reflect on the postulate of a value-free social science. But it is not our (...) purpose to introduce normative statements as scientific ones. What counts is a liberal attitude towards all realizable norms. (shrink)

Available for the first time in 20 years, here are two important works from the 1920s by the best-known representative of the Vienna Circle.

Structuralism has recently moved center stage in philosophy of mathematics. One of the issues discussed is the underlying logic of mathematical structuralism. In this paper, I want to look at the dual question, namely the underlying structures of logic. Indeed, from a mathematical structuralist standpoint, it makes perfect sense to try to identify the abstract structures underlying logic. We claim that one answer to this question is provided by categorical logic. In fact, we claim that the latter can be seen—and (...) probably should be seen—as being a structuralist approach to logic and it is from this angle that categorical logic is best understood. (shrink)

A survey of just war theory literature reveals the existence of quite different lists of principles. This apparent arbitrariness raises a number of questions: What is the relation between ad bellum and in bello principles? Why are there so many of the former and so few of the latter? What order is there among the various principles? To answer these questions, I first draw on some recent work by Jeff McMahan to show that ad bellum and in bello principles are (...) not, as often portrayed, independent—the justice of conduct in war largely presupposes the justice of the recourse to war. Undermining this independence claim is one important step toward revealing the unified logical structure of just war theory. I then argue that we can see the dependence of the jus in bello upon the jus ad bellum , not just in the content of certain principles, but also in the structure of the two sets of principles: I construct a one-to-one mapping between ad bellum and in bello principles. In doing so, I argue also that the shared structure successfully finds place for the questions central to the evaluation of the morality of war: what is a sufficient provocation to use force, what objectives may be sought by force, why or for what ends, who has authority to decide to use force, and when or in what circumstances? Despite variations in expression, the theory allows for a coherent and comprehensive evaluation of morality in warfare. (shrink)

In "The Logical Structure of Linguistic Commitment I" (The Journal of Philosophical Logic 23 (1994), 369-400), we sketch a linguistic theory (inspired by Brandom's Making it Explicit) which includes an "expressivist" account of the implication connective, →: the role of → is to "make explicit" the inferential proprieties among possible commitments which proprieties determine, in part, the significances of sentences. This motivates reading (A → B) as "commitment to A is, in part, commitment to B". Our project is (...) to study the logic of →. LSLC I approximates (A → B) as "anyone committed to A is committed to B", ignoring issues of whether A is relevant to B. The present paper includes considerations of relevance, motivating systems of relevant commitment entailment related to the systems of commitment entailment of LSLC I. We also consider the relevance logics that result from a commitment reading of Fine's semantics for relevance logics, a reading that Fine suggests. (shrink)

The Logical Structure of Kinds, by FunkhouserEric. Oxford: Oxford University Press, 2014. Pp. 182.

In this work we discuss logical structures related to indistinguishable particles. Most of the framework used to develop these structures was presented in [17, 28] and in [20, 14, 15, 16]. We use these structures and constructions to discuss possible ontologies for identical particles. In other words, we use these structures in order to characterize the logical structure of quantum systems for the case of indistinguishable particles, and draw possible philosophical implications. We also review some proposals available (...) in the literature which may be considered within the framework of the quantum logical tradition regarding the problem of indistinguishability. Besides these discussions and constructions, we advance novel technical results, namely, a lattice theoretical structure for identical particles for the finite dimensional case. This kind of approach was not present in the scarcely literature of quantum logic and indistinguishable particles. (shrink)

In a nutshell, this dissertation builds a bridge between an informal psychological model of emotions on the one hand, and implementation of emotions in robots and virtual characters on the other hand. This is done by formalizing a psychological model of emotions. With that we1 mean translating the concepts used in the psy- chological model to a logical language with unambiguous semantics. The resulting formalization of emotions will give rise to theorems that can be proved to be true. These (...) theorems are properties of the formal model and can be checked against the original psychological model of emotions. If they match, this will mean that the formalization is truthful with respect to the psychological model. The description of the model of emotions in this formal language can then be used as a foundation for implementing emotions in robots and virtual characters. (shrink)

This paper: (1) gives a schema of the logical structure of functional explanation in biology; (2) shows that it falls under the covering law model of explanation by proving that the explanandum follows from the explanans; and (3) supports the claim that it captures the logical structure underlying the biological usage by analyzing in detail two cases from biology.

1. Dialectic, in the sense of Hegel and Marx, is a dynamic process in which contradictions arise and are aufgehoben—an impossible word to translate into English, since it means both removed and pre...

Socrates’ expert-analogies is frequent both in Plato’s dialogues and in the Socratic writings of Xenophon, and is also ascribed to Socrates by Aristotle and Aeschines. Socrates makes an analogy from a non-controversial expert (or an expertise) like the cobbler or ship-captain, to another (often controversial) expert (or expertise) like the statesman. This paper defends an interpretation of the expert-analogy as valid deductions. It infers from one type of expert (such as the ship-captain) to another type of expert (such as the (...) statesman), and the attribute inferred (for instance ‘should not be selected by lot’) belongs to these types of experts because they are experts. The general logical form, which makes no mention of the expert and which is valid in virtue of its form, infers from one or more species to another species of the same genus, and the attribute inferred is presupposed to belong as such to the genus and only accidentally to the species. (shrink)

This article uncovers the logical structure of Russell’s negative facts, which he postulated in his 1919 lectures on logical atomism as a way of accounting for the truth of negative propositions. It is argued that he subsequently abandoned his belief in the existence of negative facts because the latter could not be reconciled with his Principle of Acquaintance, a fundamental corner stone of his logical atomism. A proposed fine tuning of this Principle shows that the postulation (...) of negative facts represents the best solution to the problem of negation which his logical atomism must face. (shrink)

This paper offers a critical analysis of the logical structure of principles proposed by Robert Alexy and, in particular, of their structure as optimisation commands. Its first part dwells on the question whether the optimisation element in the logical structure should be understood as part of modalisation, as part of the consequent, or as an independent element. In the second part, the author analyses possible forms of inter-definability of deontic operators. Finally, some questions are raised (...) on the conditional structure proposed by Alexy for principles. (shrink)

We present a reconstruction of so-called classical, formal or Mendelian genetics using a notation which we believe is more legible than that of earlier accounts, and lends itself easily to computer implementation, for instance in PROLOG. By drawing from, and emending, earlier work of Balzer and Dawe (1986,1997), the present account presents the three most important lines of development of classical genetics: the so-called Mendel's laws, linkage genetics and gene mapping, in the form of a theory-net. This shows that the (...) set theoretic representation format used in the structuralist approach to the philosophy of science also applies to the domain of genetic theories. There construction is intended to lend more clarity to theme thodological, philosophical and didactical discussions of the foundations of genetics, and on the other hand to defend a formally, logically minded view of theories which seems to have become contested through the work of Feyerabend, Kuhn and Kitcher. (shrink)

We present a logically detailed case-study of explanation and prediction in Newtonian mechanics. The case in question is that of a planet's elliptical orbit in the Sun's gravitational field. Care is taken to distinguish the respective contributions of the mathematics that is being applied, and of the empirical hypotheses that receive a mathematical formulation. This enables one to appreciate how in this case the overall logical structure of scientific explanation and prediction is exactly in accordance with the hypotheticodeductive (...) model. (shrink)

Curiously, though he provides in Making It Explicit (MIE) elaborate accounts of various representational idioms, of anaphora and deixis, and of quantification, Robert Brandom nowhere attempts to lay out how his understanding of content and his view of the role of logical idioms combine in even the simplest cases of what he calls paradigmatic logical vocabulary. That is, Brandom has a philosophical account of content as updating potential - as inferential potential understood in the sense of commitment or (...) entitlement preservation - and says that the point of logical vocabulary is to make available the expressive resources to make explicit such semantic structures as arise from discursive scorekeeping practice. Thus, one would expect an account of the updating or inferential potential of sentences involving logical vocabulary, an account which is such as to assign to those sentences the inferential significance necessary for this expressive job. In short, one would expect a semantics of logical vocabulary - &, ν, ∼ → - in terms of the difference an assertion of a sentence involving it makes to the atomic score of a linguistic agent, and a completeness proof for the logic generated by this semantics. Despite this, no such semantics is given in MIE. It is in the current paper. (shrink)

This paper aims to reconstruct the overarching logical structure of Michael Williams's response to philosophical skepticism. One goal is to forestall overhasty dismissals of his position based on failures to understand the logical relations among his various anti‐skeptical claims and arguments. In many places, Williams suggests that the strategy he calls “theoretical diagnosis” is sufficient to defuse the skeptical challenge and that, accordingly, his anti‐skeptical strategy consists solely in developing theoretical diagnoses. According to the account developed here, (...) this claim is misleading—in need of significant qualification, if not outright false. Even so, the paper concludes that, in its essentials, Williams's response is structurally sound, given his understanding of the problem posed by skepticism. The paper ends with a brief assessment of the merits of that response. (shrink)

In contemporary social ontology, normative attitudes are often regarded as the essential element to account for the existence of the social/normative realm. However, by emphasizing their foundational explanatory role, philosophers have been led to overlook or misrepresent some aspects of their structure. The first part of this paper attempts to offer a more proportioned analysis of the structure of normative attitudes; according to it, normative attitudes are essentially _sanctions_ that have a _projective_ or _generalizing_ aim, that is, sanctions (...) that manage to point beyond the acts they directly target. The second part of the paper engages in a polemic with two prominent authors in the social-ontology/normativity debate, Brandom and Searle, and shows that, by building their views on normative attitudes with the almost exclusive purpose of meeting foundational explanatory constraints, they fail to adequately conceptualize crucial aspects that make normative attitudes normative at all. (shrink)

Some commentators argue that the Laws does not have a clear organization, and use this as evidence to show that Plato left the dialogue incomplete or that old age had decreased the philosophical quality of his writing. However, the Laws can be shown to be answering a lucid question according to a discernable logical structure, and the specific proposals set forth can be understood as corresponding to this structure. The Laws constitutes part of an actual political founding. (...) As such, the dialogue treats the acts of lawgiving, and not the nature of laws themselves. The Athenian stranger, evidently a philosopher, presents an account of lawgiving that is alternative to the traditional understanding of lawgiving as transmitted by divinely inspired poetry (624b, 747e). (shrink)

When a person hopes something, this means that he or she hopes some proposition will be true. Thus, hope is a type of modality on propositions. Hope logic is the study of the logical structure among propositions with hope modalities. Rational hope is deductively enclosed, consistent, self-affirmed, etc. These properties can be regarded as axioms of hope logic. An important property of hope is that hope is not necessarily true, but it is hoped that that hope is true. (...) This is a property particular to hope, and it can be regarded as ‘the hope axiom’. Using possible world semantics, different hope logic systems, which are sound and complete with respect to their frames, can be obtained by selecting different hope axioms. (shrink)

A hundred years ago, Ramsey (1927) devised a new system of notation to more perspicuously represent the idea that ‘p’ and ‘¬¬p’ express the same fact. Recently, Monroy Pérez (2023) has argued that we can apply Ramsey’s insight to solve a recalcitrant problem for logical elitism — the thesis, most famously defended by Sider (2011), that the world’s fundamental metaphysical structure includes logical structure. Here, I discuss the general role of language in the framing of (...) class='Hi'>logical elitism and present four arguments that show that the Ramseyan strategy for defending logical elitism fails. First, it does not eliminate all arbitrariness even for zeroth-order classical logic (§3). Second, it is a case of a more general strategy that exploits the fact that classical negation is an involution; then, choosing the Ramseyan proposal among the other cases is arbitrary (§4). Third, there are proposals to solve the riddle that are simpler than every case of the involutory strategy (§5). The discussion has consequences for logical elitism at large: in my fourth argument I contend, contrary to a fairly favoured opinion, that logical elitism should not be thought of as a thesis about languages, but as a thesis about joints in metaphysical structure (§6). (shrink)

This paper studies the structure of semantic theories over modular computational systems and applies the algebraic Theory of Institutions to provide a logical representation of such theories. A modular semantic theory is here defined by a cluster of semantic theories, each for a single program's module, and by a set of relations connecting models of different semantic theories. A semantic theory of a single module is provided in terms of the set of ∑‐models mapped from the category Th (...) of ∑‐theories and generating a hierarchy of structures from an abstract model to a concrete model of data. The collection of abstract models representing different modules of a program is formalised as the category of institutions INS, where theory morphisms express refinements, integrations, and compositions between couples of modules. Finally, it is required that a morphism in INS at any level occurs iff the same morphism occurs at the lower level alongside the Th hierarchy. (shrink)

In this paper I examine a cluster of concepts relevant to the methodology of truth theories: 'informative definition', 'recursive method', 'semantic structure', 'logical form', 'compositionality', etc. The interrelations between these concepts, I will try to show, are more intricate and multi-dimensional than commonly assumed.

We characterize semantically quantified subjects, type (et,t), in English and show that the Boolean closure of the generalized existential and universal quantifiers is exactly the conservative ones. We prove that all subjects are expressible as Boolean functions of Montagovian individuals and that all mathematically extend to objects, type (eet,et). But quantified objects also include many functions that are not subject extensions, contrary to usual textbook assumptions. This is because two-place predicates (P2s) have more structure than one-place ones (P1s), so (...) quantified objects have more to vary with/depend on. For example, we illustrate how lexical P2s in English can force their models to be infinite; P1s provably cannot. (shrink)

There are two general questions which many views in the philosophy of mathematics can be seen as addressing: what are mathematical objects, and how do we have knowledge of them? Naturally, the answers given to these questions are linked, since whatever account we give of how we have knowledge of mathematical objects surely has to take into account what sorts of things we claim they are; conversely, whatever account we give of the nature of mathematical objects must be accompanied by (...) a corresponding account of how it is that we acquire knowledge of those objects. The connection between these problems results in what is often called "Benacerraf's Problem", which is a dilemma that many philosophical views about mathematical objects face. It will be my goal here to present a view, attributed to Richard Dedekind, which approaches the initial questions in a different way than many other philosophical views do, and in doing so, avoids the dilemma given by Benacerraf's problem. (shrink)

The papers in this volume are contributions to a comparative semantics, understood in the context of the theory of Logical Form as a branch of comparative syntax. In contrastively exploring a wide range of languages, including Arabic, Chinese, English, Hungarian, Italian, Japanese, Navajo, Spanish and Toba Batak, the authors provide new insights into our understanding of the nature of quantificational, WH and anaphoric phenomena, and into the form of constraints, including subjacency and ECP, on the structure of binding (...) at Logical Form. -- Back cover. (shrink)

We present a logically detailed case-study of Darwinian evolutionary explanation. Special features of Darwin’s explanatory schema made it an unusual theoretical breakthrough, from the point of view of the philosophy of science. The schema employs no theoretical terms, and puts forward no theoretical hypotheses. Instead, it uses three observational generalizations—Variability, Heritability and Differential Reproduction—along with an innocuous assumption of Causal Efficacy, to derive Adaptive Evolution as a necessary consequence. Adaptive Evolution in turn, with one assumption of scale (‘Deep Time’), implies (...) the observational generalization of Adaptation. It is a fascinating methodological task to regiment the premises and make the reasoning both rigorous and clear. Doing so reveals how surprisingly small an amount of mathematics is needed in order to carry out the argument. The investigation also reveals the crucial role played by heritability, and how heritability itself admits of Darwinian explanation. (shrink)

The distinction between normative arguments and normative judgements or statements has been developed as a reconstruction of Dworkin’s thesis that rules and principles are logically distinct types of norms. His approach that principles are reasons to be balanced against competing principles, whilst rules are applied in an all-or-nothing fashion, links a normtheoretical feature to a specific method of application. However, whether such a distinction is tenable is a matter of dispute. The most prominent attempt to present a structural distinction of (...) rules and principles is Alexy’s account of principles as requirements of optimisation, in contrast to rules as definitive norms or as norms with a special prima facie character. However, Alexy’s approach is contested, and indeed it does not explain how principles can figure as reasons for balancing judgements. The prevailing opinion seems to be that there is no structural difference between rules and principles, but, if at all, only a gradual one. (shrink)

This paper is an investigation in the use of truthmaker theory for exploring the relation of logic to world, and as a tool for metaphysics. A variant of truthmaker theory, which we call the simple theory, is defined and defended against objections. It is characterized formally, and its central features are derived. As part of this project, we give a formal metaphysics based on nondeterministic necessitation relations among possible entities. In what is called the fundamental theorem of truthmaking, it is (...) shown that, as long as a logic is sound and complete, its inferential structure will be isomorphic to the necessitation structure of our metaphysics. We thus arrive at a purely structural logic–world relationship which can be used for metaphysical investigations. Other products of our investigation are a sound and complete semantics for first-order logic with identity and a solution to a result of Restall which has threatened to make truthmaker theory trivial. (shrink)

: Usually, when studying schematism we devote almost exclusive attention to the study of the modifications that the categories suffer when combined with time. Instead, we have focused our attention on the determinations that time receives when combined with the categories. Departing from the definition of the transcendental schemata as “determinations of time”, an attempt is made to establish the various determinations that time receives from each one of the categories, as these perform the determination of time in schematism. The (...) categories of quantity allow us to think of time as a series of homogeneous unities; the categories of quality show each instant of time as a receptacle able to receive the different intensities of the real; the categories of relation establish a rule-dependent order on the flow of time; finally, the categories of modality determine the whole of time forming a collective unity that gathers or embraces each one of the instants of time preserving its specificity. (shrink)

This short article aims to illustrate the mutually question-begging arguments that are often presented in debates between opponents and defenderss of McTaggart’s “proof” that A-properties (pastness, presentness and futurity) are logically incoherent. A sample of such arguments is taken from a recent debate between L. Nathan Oaklander (a defender of McTaggart) and myself (an opponent of McTaggart) and a method of escaping the impasse that is often reached in such debates is suggested.

In this paper the structuralist approach of theory reconstruction is applied to International Trade Theory. In the basic element the universal laws of the theory are stated and the general concepts are defined in terms of three sets and seven functions. Ricardo’s Theory of Comparative Advantage and the Factor Proportions Theory by Heckscher and Ohlin are reconstructed as specialisations of the basic element. Two intratheoretical constraints are formulated in order to ensure the consistency of the theory. A number of empirical (...) studies are shown to be paradigmatic, successful or questionable applications of International Trade Theory. The reconstruction allows the assessment of the theory from a metatheoretical angle and illuminates the logical interdependencies of its components. (shrink)