In a recent paper Horsten embarked on a journey along the limits of the domain of the unknowable. Rather than knowability simpliciter, he considered a priori knowability, and by the latter he meant absolute provability, i.e. provability that is not relativized to a formal system. He presented an argument for the conclusion that it is not absolutely provable that there is a natural number of which it is true but absolutely unprovable that it has a certain property. The argument depends (...) on a description principle. I will argue that the latter principle implies the knowability of all arithmetical truths. Therefore, Horsten's argument is either sound but its conclusion is trivial, or his argument is unsound. (shrink)

The subject of the first section is Carnapian modal logic. One of the things I will do there is to prove that certain description principles, viz. the ''self-predication principles'', i.e. the principles according to which a descriptive term satisfies its own descriptive condition, are theorems and that others are not. The second section will be devoted to Carnapian modal arithmetic. I will prove that, if the arithmetical theory contains the standard weak principle of induction, modal truth collapses to truth. Then (...) I will propose a different formulation of Carnapian modal arithmetic and establish that it is free of collapse. Noteworthy is that one can retain the standard strong principle of induction. I will occupy myself in the third section with Carnapian epistemic logic and arithmetic. Here too it is claimed that the standard weak principle of induction is invalid and that the alternative principle is valid. In the fourth and last section I will get back to the self-predication principles and I will point to some of the consequences if one adds them to Carnapian Epistemic arithmetic. The interaction of self-predication principles and the strong principle of induction results in a collapse of de re knowability. (shrink)

I will examine three claims made by Ackerman and Kripke. First, they claim that not any arithmetical terms is eligible for universal instantiation and existential generalisation in doxastic or epistemic contexts. Second, Ackerman claims that Peano numerals are eligible for universal instantiation and existential generalisation in doxastic or epistemic contexts. Kripke's position is a bit more subtle. Third, they claim that the successor relation and the smaller-than relation must be effectively calculable. These three claims will be examined from the framework (...) of modal-epistemic arithmetic, i.e. arithmetic extended with certain modal, epistemic and modal-epistemic principles. I will present theorems that give support to the claims made by Ackerman and Kripke. (shrink)

Jan Heylen and Leon Horsten object to my proposed analysis of ordinary-language conditionals by appealing to certain putative counter-examples. In this reply, I explain how, by ignoring my reading of the indicative/subjunctive distinction, their objection misses its target. I also criticize their underlying methodology.

In Lowe (1995), instead of endorsing a Stalnaker/Lewis-style account of counterfactuals, E. J. Lowe claims that a variation of C. I. Lewis’s strict implication alone captures the essence of everyday conditionals and avoids the paradoxes of strict implication. However, Lowe’s approach fails to account for the validity of simple and straightforward arguments such as ‘if 2=3 then 2+1=3+1’, and Heylen & Horsten (2006) even claims that no variation of strict implication can successfully describe the logical behavior of natural language (...) conditionals. By incorporating the German logician O. Becker’s modal intuition with the insight of Ramsey’s Test, we show that there does exist a unified, strict-conditional based account of everyday conditionals, which withstands all attacks previously raised against truth-conditional accounts of conditionals. Furthermore, a subtle distinction between autistic and realistic readings of the indexical ‘I’ involved in a conditional helps us resolve a recent debate concerning the Thomason conditionals. (shrink)

No detailed description available for "From Axiom to Dialogue".

We represent shape in both sight and touch, but how do these abilities relate to one another? This issue has been discussed in the context of Molyneux's question of whether someone born blind could, upon being granted sight, identify shapes visually. Some have suggested that we might look to real‐world cases of sight restoration to illuminate the relation between visual and tactual shape representations. Here, I argue that newly sighted perceivers should not be relied on in this way because they (...) are unlikely to form the kinds of shape representations responsible for cross‐modal recognition in normally sighted perceivers. I then argue that the available evidence makes a compelling case for the type identity view, on which the visual and tactual representations responsible for cross‐modal recognition are type‐identical. (shrink)

Contents Include: The Early Life of Socrates - The Later Life of Socrates: His Trial and Death - The Thought of Socrates.

Most authors who work with moral status automatically dismiss the possibility that plants are the kinds of entities that have moral status. This dismissal coheres with our intuitions about common-sense morality: if plants do not have moral status then we do not have any direct moral obligations to plant life. An implication of such a view is that any suggestion otherwise commits one to be in favour of an absurd conclusion. However, given the recent literature and empirical evidence on plant (...) minds, there are reasons to accept a different perspective that finds the absurd conclusion plausible. (shrink)

Legislation usually lacks a systematic organization which makes the management and the access to norms a hard problem to face. A more analytic semantic unit of reference (provision) for legislative texts was identified. A model of provisions (provisions types and their arguments) allows to describe the semantics of rules in legislative texts. It can be used to develop advanced semantic-based applications and services on legislation. In this paper an automatic bottom-up strategy to qualify existing legislative texts in terms of provision (...) types is described. (shrink)

The first main result isolates some conditions which fail for the class of graphs and hold for the class of Abelian p-groups, the class of Abelian torsion groups, and the special class of "rank-homogeneous" trees. We consider these conditions as a possible definition of what it means for a class of structures to have "Ulm type". The result says that there can be no Turing computable embedding of a class not of Ulm type into one of Ulm type. We apply (...) this result to show that there is no Turing computable embedding of the class of graphs into the class of "rank-homogeneous" trees. The second main result says that there is a Turing computable embedding of the class of rank-homogeneous trees into the class of torsion-free Abelian groups. The third main result says that there is a "rank-preserving" Turing computable embedding of the class of rank-homogeneous trees into the class of Boolean algebras. Using this result, we show that there is a computable Boolean algebra of Scott rank ${\mathrm{\omega }}_{1}^{\mathrm{C}\mathrm{K}}$. (shrink)

E. Jayne Whitea, Catherine Matsuob and Fiona WestbrookcaUniversity of Canterbury; bFukuoka University; cAuckland University of Technology (AUT)This collective writing piece takes its points of depa...

Decisions related to animal welfare standards depend on farmer’s multiple goals and values and are constrained by a wide range of external and internal forces. The aim of this paper is twofold, i.e., to develop a theoretical framework for farmers’ AW decisions that incorporates farmers’ goals, use and non-use values and to present an approach to empirically implement the theoretical framework. The farmer as a head of the farm household makes choices regarding production to maximize the utility of the household. (...) The overall utility of the farmer is determined by his multiple objectives. For the analysis of multi-objective problems, the multiple criteria decision - making paradigm provides an appropriate theoretical framework. However, theories from the field of social-psychology are needed to facilitate the identification of all relevant aspects in the decision making. The practical use of the conceptual framework is demonstrated using a simple numerical application of a multi-objective programming model. Two workshops were devoted to examining the scientific consistency and the practical usefulness of the approach. Implementing this approach will increase knowledge of the main factors and barriers that determine farmers’ decisions with regard to AW standards. This knowledge is relevant during the development of new AW concepts that aims to supply products that comply with above-legal AW standards for middle-market segments. (shrink)

In the fourth section of Goethe’s Zahme Xenien we find the quatrain from which I have taken the theme of such an old and new controversy, which, as I hope, concerns both Germanic studies and the other humanities: “What was it that kept you from us so apart?” I always read Plutarch again and again. “And what was the lesson he did impart?” “They were all human beings—so much is plain.”1 In the very years when Goethe wrote these lines, that (...) is in the 1820s, Hegel repeatedly gave his lectures on the philosophy of history. Right at the beginning he formulated the opposite view which I should like briefly to characterize as “cultural relativism.”Every age has such peculiar circumstances, such individual conditions that it must be interpreted, and can only be interpreted, by reference to itself…. Nothing is shallower in this respect than the frequent appeal to Greek and Roman example which so often occurred among the French at the time of their Revolution. Nothing could be more different than the nature of these peoples and the nature of our own times.2 What is at issue here is not, of course, Hegel’s assertion that ages and peoples differ from each other. We all know that, and Goethe, the attentive reader and traveler, also knew, for instance, that the Roman carnival differed in its character from the celebrations of the Feast of Saint Rochus at Bingen, both of which he had described so lovingly. What makes the cultural historian into a cultural relativist is only the conclusion which we saw Hegel draw, that cultures and styles of life are not only different but wholly incommensurable, in other words that it is absurd to compare the peoples of a region or an age with human beings of other zones because there is no common denominator that would justify us in doing so. 1. ‘Was hat dich nun von uns entfernt?’ Hab immer den Plutarch gelesen. ‘Was has du den dabei gelernt?’ Sind eben alles Menschen gewesen.’ Johann Wolfgang von Goethe, Sämtlich Werke. Jubiläums-ausgabe in 40 Bänden 4:73; with commentary.2. See Georg Wilhelm Friedrich Hegel, Vorselungen über die Philosophie der Geschichte, Werke, 20 vols. , 12:17. E. H. Gombrich was director of the Warburg Institute and Professor of the History of the Classical Tradition at the University of London from 1959 to 1976. His many influential works include The Story of Art, Art and Illusion, Meditations on a Hobby Horse, The Sense of Order, Ideals and Idols, The Image and the Eye, Tributes, Aby Warburg, and New Light on Old Masters. His previous contributions to Critical Inquiry include “The Museum: Past, Present and Future” , “Standards of Truth: The Arrested Image and the Moving Eye” , and “Representation and Misrepresentation”. (shrink)

Although students of the fifth century A.D. have not been slow to recognize the merits of the ͉στορα Βυζαντιακ of Priscus, few efforts seem to have been made to under-stand this historian's methods of composition. The purpose of the present note is to indicate that the literary fashions of his time have exercised an unfortunate influence on at least one part of Priscus' work.

Rescher has presented a proof that a completed science is logically impossible; not every truth can be known. I show that the proof is valid only if it is read de re. One of its premises, however, is an obvious truth only on a de dicto reading; read de re it is false. What the proof shows, therefore, is that science has no limits and any true proposition can be known. We can, however, know it only in the meagre de (...) re, and not in the informationally rich de dicto, sense of 'know'. (shrink)

This is a progressive text that explores the relationship between psychology, science and morality, to address fundamental questions about the foundations of psychological research and its relevance for the development of these disciplines.

Epistemological issues associated with Cantorian set theory were at the center of the foundational debates from 1900 onward. Hermann Weyl, as a central actor, saw this as a smoldering crisis that burst into flames after World War I. The historian Herbert Mehrtens argued that this “foundations crisis” was part of a larger conflict that pitted moderns, led by David Hilbert, against various counter-moderns, who opposed the promotion of set theory and trends toward abstract theories. Among counter-moderns, L.E.J. Brouwer went a (...) step further by proposing new foundational principles based on his philosophy of intuitionism. Meanwhile, Felix Hausdorff emerged as a leading proponent of the new modern style. In this essay, I offer a reassessment of the foundations crisis that stresses the marginal importance of the various intellectual issues involved. Instead, I offer an interpretation that focuses on tensions within the German mathematical community that led to a dramatic power struggle for control of the journal Mathematische Annalen. (shrink)