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 book uncovers a logical structure that is common to many, if not all, of the kinds posited by scientific taxonomies. Specification relations, such as those holding between determinates and determinables (determination), are central to this logical investigation of kinds. The species–genus relation is a familiar specification relation for substantival kinds, but this book focuses on adjectival kinds—whose instances are properties—instead. Determination relations are then used to structure kinds at the same level of abstraction into property (...) spaces, which in turn leads to a theory for individuating properties (tropes). These determination relations are contrasted with realization relations, the latter being the favored way of understanding the connection between the mental and the physical. Particular attention is given to the distinction between multiple realizability and multiple determination, and it is argued that determination and realization are mutually exclusive. The claim that multiple realizability entails various senses of autonomy is defended from various reductionist challenges. These theories of determination and realization then provide general standards for establishing the autonomy of the special sciences or, conversely, their reduction. (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.

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)

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.

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 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)

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.

Eva Cassirer; X—On Logical Structure, Proceedings of the Aristotelian Society, Volume 64, Issue 1, 1 June 1964, Pages 177–198, https://doi.org/10.1093/aristotel.

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)

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)

This exposition of ockham's theory of (common, Personal) supposition involves the logical form of the four descent/ascent conditions and the logical relations of these with the three main modes of supposition. Central theses: each condition is a one-Way entailment, Each mode is a truth-Functional combination of conditions, Two of the three modes are not even coextensive with the two-Way entailments commonly taken as their definitions. Ockham's idea of "the singulars" of a general proposition is vague and problematic and (...) the entailment used in the descent/ascent conditions probably cannot be taken to be logical consequence in any strict sense. (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)

At the onset of quantum mechanics, it was argued that the new theory would entail a rejection of classical logic. The main arguments to support this claim come from the non-commutativity of quantum observables, which allegedly would generate a non-distributive lattice of propositions, and from quantum superpositions, which would entail new rules for quantum disjunctions. While the quantum logic program is not as popular as it once was, a crucial question remains unsettled: what is the relationship between the logical (...) structures of classical and quantum mechanics? In this essay we answer this question by showing that the original arguments promoting quantum logic contain serious flaws, and that quantum theory does satisfy the classical distributivity law once the full meaning of quantum propositions is properly taken into account. Moreover, we show that quantum mechanics can generate a distributive lattice of propositions, which, unlike the one of quantum logic, includes statements about expectation values which are of undoubtable physical interest. Lastly, we show that the lattice of statistical propositions in classical mechanics follows the same structure, yielding an analogue non-commutative sublattice of classical propositions. This fact entails that the purported difference between classical and quantum logic stems from a misconstructed parallel between the two theories. (shrink)

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)

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)

: 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.

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)

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 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)

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