Semilattice-based dualities

The paper discusses regularisation of dualities. A given duality between (concrete) categories, e.g. a variety of algebras and a category of representation spaces, is lifted to a duality between the respective categories of semilattice representations in the category of algebras and the category of spaces. In particular, this gives duality for the regularisation of an irregular variety that has a duality. If the type of the variety includes constants, then the regularisation depends critically on the location or absence of constants within the defining identities. The role of schizophrenic objects is discussed, and a number of applications are given. Among these applications are different forms of regularisation of Priestley, Stone and Pontryagin dualities.     

Pierre de La Ramée et le déclin de la rhétorique

This article provides a basic general introduction to Ramus, and evaluates his role in the history of logic and rhetoric, especially with relation to the study of argumentation. The author agrees with Ong and other historians of logic that Ramus is not to be taken seriously as a logician, and that his undoubted importance in the history of ideas is to be found elsewhere.Ramus advocates a belief in nature, experience and reason, and rejects the reliance on the authority of ancient philosophers, above all Aristotle, though experience does not mean scientific experiment and, paradoxically, includes the example of great philosophers and writers. In the end Ramus is seen as responsible for substituting for ancient classical rhetoric an entirely ornamental rhetoric of figures which was to take over education (with the exception of the Jesuit schools) almost until our own day. This curtailing and diminishing of rhetoric is seen as a degeneration. Ancient five-part rhetoric had been concerned with convincing and persuading: Aristotle distinguished the analytic, scientific reasoning of logic, from dialectic which was based on opinion and probability and had close links with rhetoric; by the time of Cicero and Quintilian, who addressed themselves to jurists and politicians, logic has given way to dialectic. In the Middle Ages and the Renaissance the two become assimilated; the evolution of this is traced here through the thirteenth-century Summulae logicales of Peter of Spain to the fifteenth-century German humanist logician Rudolph Agricola, who influenced Ramus partly through the intermediary of Johann Sturm. Ramus took over their topical theories but restricted them to logic/dialectic, and left rhetoric with little more than tropes and figures. He believed that there was only one method for teaching all the arts, and one dialectic common to them all. The distinction between analytical and dialectical has disappeared, with far-reaching consequences for the study of argumentation. Over the centuries logic has lost its connection with controversy and persuasion. With the development of the post-Cartesian, post-Baconian emphasis on the clarity of scientific discourse, and the mid-nineteenth-century interest in mathematical and formal logic, the process was complete. Argumentation, or the new rhetoric, aims to fill the gap thus created.

     

Perception as abduction: turning sensor data into meaningful representation

This article presents a formal theory of robot perception as a form of abduction. The theory pins down the process whereby low-level sensor data is transformed into a symbolic representation of the external world, drawing together aspects such as incompleteness, top-down information flow, active perception, attention, and sensor fusion in a unifying framework. In addition, a number of themes are identified that are common to both the engineer concerned with developing a rigorous theory of perception, such as the one on offer here, and the philosopher of mind who is exercised by questions relating to mental representation and intentionality.     

Proof-Theoretic Modal PA-Completeness III: The Syntactic Proof

This paper is the final part of the syntactic demonstration of the Arithmetical Completeness of the modal system G; in the preceding parts [9] and [10] the tools for the proof were defined, in particular the notion of syntactic countermodel. Our strategy is: PA-completeness of G as a search for interpretations which force the distance between G and a GL-LIN-theorem to zero. If the GL-LIN-theorem S is not a G-theorem, we construct a formula H expressing the non G-provability of S, so that ⊢_GL-LIN ∼ H and so that a canonical proof T of ∼ H in GL-LIN is a syntactic countermodel for S with respect to G, which has the height θ(T) equal to the distance d(S, G) of S from G. Then we define the interpretation ξ of S which represents the proof-tree T in PA. By induction on θ(T), we prove that ⊢_PA S^ξ and d(S, G) > 0 imply the inconsistency of PA. This revised version was published online in June 2006 with corrections to the Cover Date.     

Second order inductive logic and Wilmers' principle

We extend the framework of Inductive Logic to Second Order languages and introduce Wilmers' Principle, a rational principle for probability functions on Second Order languages. We derive a representation theorem for functions satisfying this principle and investigate its relationship with the first order principles of Regularity and Super Regularity.     

Reflecting rules: A note on generalizing the deduction theorem

The purpose of this brief note is to prove a limitative theorem for a generalization of the deduction theorem. I discuss the relationship between the deduction theorem and rules of inference. Often when the deduction theorem is claimed to fail, particularly in the case of normal modal logics, it is the result of a confusion over what the deduction theorem is trying to show. The classic deduction theorem is trying to show that all so-called ‘derivable rules’ can be encoded into the object language using the material conditional. The deduction theorem can be generalized in the sense that one can attempt to encode all types of rules into the object language. When a rule is encoded in this way I say that it is reflected in the object language. What I show, however, is that certain logics which reflect a certain kind of rule must be trivial. Therefore, my generalization of the deduction theorem does fail where the classic deduction theorem didn't.     

Peer Assessment of Aviation Performance: Inconsistent for Good Reasons

Research into expertise is relatively common in cognitive science concerning expertise existing across many domains. However, much less research has examined how experts within the same domain assess the performance of their peer experts. We report the results of a modified think‐aloud study conducted with 18 pilots (6 first officers, 6 captains, and 6 flight examiners). Pairs of same‐ranked pilots were asked to rate the performance of a captain flying in a critical pre‐recorded simulator scenario. Findings reveal (a) considerable variance within performance categories, (b) differences in the process used as evidence in support of a performance rating, (c) different numbers and types of facts (cues) identified, and (d) differences in how specific performance events affect choice of performance category and gravity of performance assessment. Such variance is consistent with low inter‐rater reliability. Because raters exhibited good, albeit imprecise, reasons and facts, a fuzzy mathematical model of performance rating was developed. The model provides good agreement with observed variations.     

How Hume’s Philosophy Informed Radical Behaviorism

The present paper analyzes consistencies between the philosophical systems of David Hume and B. F. Skinner, focusing on their conceptualization of causality and attitudes about scientific behavior. The ideas that Hume initially advanced were further developed in Skinner’s writings and shaped the behavior-analytic approach to scientific behavior. Tracing Skinner’s logical antecedents allows for additional historical and philosophical clarity when examining the development of radical behaviorism.     

An observation on Carnapʼs Continuum and stochastic independencies

We characterize those identities and independencies which hold for all probability functions on a unary language satisfying the Principle of Atom Exchangeability. We then show that if this is strengthen to the requirement that Johnson?s Sufficientness Principle holds, thus giving Carnap?s Continuum of inductive methods for languages with at least two predicates, then new and somewhat inexplicable identities and independencies emerge, the latter even in the case of Carnap?s Continuum for the language with just a single predicate.