The article presents proofs of the context freeness of a family of typelogical grammars, namely all grammars that are based on a uni- ormultimodal logic of pure residuation, possibly enriched with thestructural rules of Permutation and Expansion for binary modes.

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.

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.

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)

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)

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...

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)

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)

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)

Any arbitrarily complicated non-oriented graph, that is a graph of arbitrarily large genus, can be encoded in a cut-free proof. This unpublished result of Statman was shown in the early seventies. We provide a proof of it, and of a number of other related facts.

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)

: 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)

Sittlichkeit seduces: Hegel’s third category of Right, intended to synthesize impartially derived rights with a subjectively centered morality of the good, understandably piques the hopes of his modern readers. How could it not? Sittlichkeit, Ethical Life, holds out the prospect of so much that we still seek. It promises to reconcile welfare and autonomy while guaranteeing concrete content for their product. By combining legal duty with a place for conscience and freedom, it could solve a central problem of politics. Most (...) broadly, Sittlichkeit would graft Enlightenment individualism onto a more Aristotelian conception of social order, merging the benefits of ancient virtue and modern liberty. Who would not want to have their cake and eat it in this way? (shrink)

It has been noticed by several authors that the colloquial understanding of anonymity as mere unknown-ness is insufficient. This common-sense notion of anonymity does not recognize the role of the goal for which the anonymity is sought. Starting with the distinction between the intentional and unintentional anonymity (which are usually taken to be the same) and the general concept of the non-coordinatability of traits, we offer a logical analysis of anonymity and identification (understood as de-anonymization). In our enquiry, we (...) focus on the intentional aspect of anonymity and develop a metaphor of “anonymity game” between “perpetrator” and “detective”. Beginning from common-sense intuitions, we provide a formalized, critical notion of anonymity. (shrink)

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)

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)

The place of science.--The structure of science.--Nature: occurrents.--Nature: complexes.--Awareness.--Operations.--Meaning.--Meaning: correlational symbols.--Meaning: constructs and hypotheses.--The development of knowledge.--Models.--Description.--Explanation.--Quantitative methods.

Sittlichkeit seduces: Hegel’s third category of Right, intended to synthesize impartially derived rights with a subjectively centered morality of the good, understandably piques the hopes of his modern readers. How could it not? Sittlichkeit, Ethical Life, holds out the prospect of so much that we still seek. It promises to reconcile welfare and autonomy while guaranteeing concrete content for their product. By combining legal duty with a place for conscience and freedom, it could solve a central problem of politics. Most (...) broadly, Sittlichkeit would graft Enlightenment individualism onto a more Aristotelian conception of social order, merging the benefits of ancient virtue and modern liberty. Who would not want to have their cake and eat it in this way? (shrink)

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 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: (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.

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)

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

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)

This book addresses the argument in the history of the philosophy of science between the positivists and the anti-positivists. The author starts from a point of firm conviction that all science and philosophy must start with the given... But that the range of the given is not definite. He begins with an examination of science from the outside and then the inside, explaining his position on metaphysics and attempts to formulate the character of operational acts before a general theory of (...) symbolism is explored. The last five chapters constitute a treatise to show that the development from one stage of symbolismto the next is inevitable, consequently that explanatory science represents the culmination of knowledge. (shrink)