My purpose in this brief paper is to consider the implications of a radically different computer architecure to some fundamental problems in the foundations of Cognitive Science. More exactly, I wish to consider the ramifications of the 'Gödel-Minds-Machines' controversy of the late 1960s on a dynamically changing computer architecture which, I venture to suggest, is going to revolutionize which 'functions' of the human mind can and cannot be modelled by (non-human) computational automata. I will proceed on the presupposition that the (...) reader is familiar with some of the fundamentals of computational theory and mathematical logic. (shrink)

In this paper we interpret a characterization of the Gödel speed-up phenomenon as providing support for the ‘Nagel-Newman thesis’ that human theorem recognizers differ from mechanical theorem recognizers in that the former do not seem to be limited by Gödel's incompleteness theorems whereas the latter do seem to be thus limited. However, we also maintain that (currently non-existent) programs which are open systems in that they continuously interact with, and are thus inseparable from, their environment, are not covered by the (...) above (or probably any other recursion-theoretic) argument. (shrink)

In this paper we interpret a characterization of the Gödel speed-up phenomenon as providing support for the ‘Nagel-Newman thesis’ that human theorem recognizers differ from mechanical theorem recognizers in that the former do not seem to be limited by Gödel's incompleteness theorems whereas the latter do seem to be thus limited.However, we also maintain that (currently non-existent) programs which are open systems in that they continuously interact with, and are thus inseparable from, their environment, are not covered by the above (...) (or probably any other recursion-theoretic) argument. (shrink)

This paper studies a propositional logic which is obtained by interpreting implication as formal provability. It is also the logic of finite irreflexive Kripke Models.A Kripke Model completeness theorem is given and several completeness theorems for interpretations into Provability Logic and Peano Arithmetic.

In the recent literature on concepts, two extreme positions concerning animal minds are predominant: the one that animals possess neither concepts nor beliefs, and the one that some animals possess concepts as well as beliefs. A characteristic feature of this controversy is the lack of consensus on the criteria for possessing a concept or having a belief. Addressing this deficit, we propose a new theory of concepts which takes recent case studies of complex animal behavior into account. The main aim (...) of the paper is to present an epistemic theory of concepts and to defend a detailed theory of criteria for having concepts. The distinction between nonconceptual, conceptual, and propositional representations is inherent to this theory. Accordingly, it can be reasonably argued that some animals, e.g., grey parrots and apes, operate on conceptual representations. (shrink)

This paper challenges the traditional assumption that descriptive and prescriptive sciences are essentially distinct by presenting a study on the implicit normativity of the production and presentation of biomedical scientific facts within evidence-based medicine. This interdisciplinary study serves as an illustration of the potential worth of the concept of implicit normativity for bioethics in general and for integrated empirical ethics research in particular. It demonstrates how both the production and presentation of scientific information in an evidence-based decision-support contain implicit presuppositions (...) and values, which pre-structure the moral environment of the clinical process of decision-making. As a consequence, the evidence-based decision support did not only support the clinical decision-making process; it also transformed it in a morally significant way. This phenomenon undermines the assumption within much of the literature on patient autonomy that information disclosure is a conditional requirement before patient autonomy even starts; patient autonomy is already influenced during the production and presentation of information. These results imply an increased responsibility of those who produce and present evidence-based facts(i.e. scientists in general and physicians in particular). The insights of this study not only involve a different focus on both theory and practice of patient autonomy and informed consent, but they also call for a broader scope of morality than does traditional empirical research in bioethics. The concept of implicit normativity within integrated empirical ethics research calls for a strong cooperation between bioethicists and descriptive scientists, i.e., a cooperation that goes beyond the discipline-specific epistemic values and that takes place during all phases of the research process. (shrink)

Two leaves of typescript and 7 leaves of galley proofs with corrections in Einstein's hand for the article "Relativity" in American Peoples Encyclopedia.

Introduction Watching the Doctor In some cultures, it is said, villagers cluster around a healer and a patient, eagerly listening to their conversation and ...

Corporate transgression is a well-known phenomenon in today's business world. Some corporations are involved in violations of law and moral rules that produce organizational practices and products that take a toll on the public. Social cognitive theory of moral agency provides a conceptual framework for analyzing how otherwise pro-social managers adopt socially injurious corporate practices. This is achieved through selective disengagement of moral self-sanctions from transgressive conduct. This article documents moral disengagement practices in four famous cases of corporate transgressions and (...) discusses some implications for business ethics on how to counteract organizational use of moral disengagement strategies. (shrink)

The question “What are cognitive processes?” can be understood variously as meaning “What is the nature of cognitive processes?”, “Can we distinguish epistemically cognitive processes from physical and biochemical processes on the one hand, and from mental or conscious processes on the other?”, and “Can we establish a fruitful notion of cognitive process?” The present aim is to deliver a positive answer to the last question by developing criteria for what would count as a paradigmatic exemplar of a cognitive process, (...) and then to offer the comparator mechanism as a convincing paradigmatic example. Thus, the paper argues, given the current state of science, we can indeed establish a fruitful scientific notion of a cognitive process. Nevertheless, it is left open whether the example-based characterization ends up as merely highlighting a fruitful convention within the early-twentyfirst century interdisciplinary investigation of intelligent behaviour in humans, animals, and robots, or whether the examples determine a natural kind or a property cluster. (shrink)

What has moral theory to do with practical judgment? The practical ethicist can move by analogy from case to case, saying of most new cases, “Oh, I think I've been here before.” Theory, ascending to a broader view, can provide directions when the ethicist finds herself in unfamiliar territory.

This paper contains a careful derivation of principles of Interpretability Logic valid in extensions of I0+1.

In this paper we study proofs of some general forms of the Second Incompleteness Theorem. These forms conform to the Feferman format, where the proof predicate is fixed and the representation of the set of axioms varies. We extend the Feferman framework in one important point: we allow the interpretation of number theory to vary.

In this paper I give a characterization of the closed fragment of the provability logic of $I \triangle_0 + \mathrm{EXP}$ with a propositional constant for $\mathrm{EXP}$. In three appendices many details on arithmetization are provided.

In this paper, we characterize the strength of the predicative Frege hierarchy, , introduced by John Burgess in his book [J. Burgess, Fixing frege, in: Princeton Monographs in Philosophy, Princeton University Press, Princeton, 2005]. We show that and are mutually interpretable. It follows that is mutually interpretable with Q. This fact was proved earlier by Mihai Ganea in [M. Ganea, Burgess’ PV is Robinson’s Q, The Journal of Symbolic Logic 72 619–624] using a different proof. Another consequence of the our (...) main result is that is mutually interpretable with Kalmar Arithmetic . The fact that interprets EA was proved earlier by Burgess. We provide a different proof. Each of the theories is finitely axiomatizable. Our main result implies that the whole hierarchy taken together, , is not finitely axiomatizable. What is more: no theory that is mutually locally interpretable with is finitely axiomatizable. (shrink)

A theory T is trustworthy iff, whenever a theory U is interpretable in T, then it is faithfully interpretable. In this paper we give a characterization of trustworthiness. We provide a simple proof of Friedman’s Theorem that finitely axiomatized, sequential, consistent theories are trustworthy. We provide an example of a theory whose schematic predicate logic is complete Π20.

We show that a consistent, finitely axiomatized, sequential theory cannot prove its own inconsistency on every definable cut. A corollary is that there are at least three degrees of global interpretability of theories equivalent modulo local interpretability to a consistent, finitely axiomatized, sequential theory U.

In this paper we study essential hereditary undecidability. Theories with this property are a convenient tool to prove undecidability of other theories. The paper develops the basic facts concerning essentially hereditary undecidability and provides salient examples, like a construction of essentially hereditarily undecidable theories due to Hanf and an example of a rather natural essentially hereditarily undecidable theory strictly below. We discuss the (non-)interaction of essential hereditary undecidability with recursive boolean isomorphism. We develop a reduction relation essential tolerance, or, in (...) the converse direction, lax interpretability that interacts in a good way with essential hereditary undecidability. We introduce the class of $$\Sigma ^0_1$$ Σ 1 0 -friendly theories and show that $$\Sigma ^0_1$$ Σ 1 0 -friendliness is sufficient but not necessary for essential hereditary undecidability. Finally, we adapt an argument due to Pakhomov, Murwanashyaka and Visser to show that there is no interpretability minimal essentially hereditarily undecidable theory. (shrink)

In this paper we study the idea of theories with containers, like sets, pairs, sequences. We provide a modest framework to study such theories. We prove two concrete results. First, we show that first-order theories of finite signature that have functional non-surjective ordered pairing are definitionally equivalent to extensions in the same language of the basic theory of non-surjective ordered pairing. Second, we show that a first-order theory of finite signature is sequential (is a theory of sequences) iff it is (...) definitionally equivalent to an extension in the same language of a system of weak set theory called WS. (shrink)

This paper is concerned with notions of consequence. On the one hand, we study admissible consequence, specifically for substitutions of Σ 1 0 -sentences over Heyting arithmetic . On the other hand, we study preservativity relations. The notion of preservativity of sentences over a given theory is a dual of the notion of conservativity of formulas over a given theory. We show that admissible consequence for Σ 1 0 -substitutions over HA coincides with NNIL -preservativity over intuitionistic propositional logic . (...) Here NNIL is the class of propositional formulas with no nestings of implications to the left . The identical embedding of IPC -derivability into a consequence relation has in many cases a left adjoint. The main tool of the present paper will be an algorithm to compute this left adjoint in the case of NNIL -preservativity. In the last section, we employ the methods developed in the paper to give a characterization the closed fragment of the provability logic of HA. (shrink)

The narrow-the-scope proposal for defining racism posits that a narrow definition is preferable to a wide definition because the former better facilitates interracial dialogue. Important critiques of the narrow-the-scope proposal have so far focused on the content of narrow definitions. This paper argues that it is important to critique the use of narrow definitions, as well. An examination of white uses of the term “racism” reveals that narrow definitions tend to be interchangeable with individualist definitions, as individualism is an effective (...) framework for white co-optation in the service of white interests. Consequently, philosophers interested in theorizing racism for racial justice purposes ought to reject the narrow-the-scope proposal. Individualist forms of racism should be accommodated within a wide conception of racism that centers the phenomenon of white racism. (shrink)

For the last century, moral philosophy has stressed theory for the analysis of moral argument and concepts. In the last decade, interest in the ethical issues of health care has stimulated attention to cases and particular instances. This has revealed the gap between ethical theory and practice. This article reviews the history and method of casuistry which for many centuries provided an approach to practical ethics. Its strengths and weaknesses are noted and its potential for contemporary use explored.

Most models of lexical access assume that bilingual speakers activate their two languages even when they are in a context in which only one language is used. A critical piece of evidence used to support this notion is the observation that a given word automatically activates its translation equivalent in the other language. Here, we argue that these findings are compatible with a different account, in which bilinguals “carry over” the structure of their native language to the non-native language during (...) learning, and where there is no activation of translation equivalents. To demonstrate this, we describe a model in which language learning involves mapping native language phonological relationships to the non-native language, and we show how it can explain the results attributed to automatic activation of translation equivalents. (shrink)

In this paper we study local induction w.r.t. Σ1‐formulas over the weak arithmetic. The local induction scheme, which was introduced in, says roughly this: for any virtual class that is progressive, i.e., is closed under zero and successor, and for any non‐empty virtual class that is definable by a Σ1‐formula without parameters, the intersection of and is non‐empty. In other words, we have, for all Σ1‐sentences S, that S implies, whenever is progressive. Since, in the weak context, we have (at (...) least) two definitions of Σ1, we obtain two minimal theories of local induction w.r.t. Σ1‐formulas, which we call Peano Corto and Peano Basso.In the paper we give careful definitions of Peano Corto and Peano Basso. We establish their naturalness both by giving a model theoretic characterization and by providing an equivalent formulation in terms of a sentential reflection scheme.The theories Peano Corto and Peano Basso occupy a salient place among the sequential theories on the boundary between weak and strong theories. They bring together a powerful collection of principles that is locally interpretable in. Moreover, they have an important role as examples of various phenomena in the metamathematics of arithmetical (and, more generally, sequential) theories. We illustrate this by studying their behavior w.r.t. interpretability, model interpretability and local interpretability. In many ways the theories are more like Peano arithmetic or Zermelo Fraenkel set theory, than like finitely axiomatized theories as Elementary Arithmetic, and. On the one hand, Peano Corto and Peano Basso are very weak: they are locally cut‐interpretable in. On the other hand, they behave as if they were strong: they are not contained in any consistent finitely axiomatized arithmetical theory, however strong. Moreover, they extend, the theory of parameter‐free Π1‐induction. (shrink)

In this paper we study 1. the frame-theory of certain bimodal provability logics involving the reflection principle and we study2. certain specific bimodal logics with a provability predicate for a subtheory of Peano arithmetic axiomatized by a non-standardly finite number of axioms.

A Kripke model ? is a submodel of another Kripke model ℳ if ? is obtained by restricting the set of nodes of ℳ. In this paper we show that the class of formulas of Intuitionistic Predicate Logic that is preserved under taking submodels of Kripke models is precisely the class of semipositive formulas. This result is an analogue of the Łoś-Tarski theorem for the Classical Predicate Calculus.In Appendix A we prove that for theories with decidable identity we can take (...) as the embeddings between domains in Kripke models of the theory, the identical embeddings. This is a well known fact, but we know of no correct proof in the literature. In Appendix B we answer, negatively, a question posed by Sam Buss: whether there is a classical theory T, such that ℋT is HA. Here ℋT is the theory of all Kripke models ℳ such that the structures assigned to the nodes of ℳ all satisfy T in the sense of classical model theory. (shrink)

In this note we derive Robinson???s Arithmetic from Hume???s Principle in the context of very weak theories of classes and relations.

In this paper we introduce a notion of context for Groenendijk & Stokhof's Dynamic Predicate Logic DPL. We use these contexts to give a characterization of the relations on assignments that can be generated by composition from tests and random resettings in the case that we are working over an infinite domain. These relations are precisely the ones expressible in DPL if we allow ourselves arbitrary tests as a starting point. We discuss some possible extensions of DPL and the way (...) these extensions interact with our notion of context. (shrink)

In this paper we study the interpretations of a weak arithmetic, like Buss’s theory $\mathsf{S}^{1}_{2}$, in a given theory $U$. We call these interpretations the arithmetics of $U$. We develop the basics of the structure of the arithmetics of $U$. We study the provability logic of $U$ from the standpoint of the framework of the arithmetics of $U$. Finally, we provide a deeper study of the arithmetics of a finitely axiomatized sequential theory.

In this paper we formulate a version of Second Incompleteness Theorem. The idea is that a sequential sentence has ‘consistency power’ over a theory if it enables us to construct a bounded interpretation of that theory. An interpretation of V in U is bounded if, for some n , all translations of V -sentences are U -provably equivalent to sentences of complexity less than n . We call a sequential sentence with consistency power over T a pro-consistency statement for T (...) . We study pro-consistency statements. We provide an example of a pro-consistency statement for a sequential sentence A that is weaker than an ordinary consistency statement for A . We show that, if A is $${{\sf S}^{1}_{2}}$$ , this sentence has some further appealing properties, specifically that it is an Orey sentence for EA . The basic ideas of the paper essentially involve sequential theories. We have a brief look at the wider environment of the results, to wit the case of theories with pairing. (shrink)

This article explores emotions and their relationship to ‘somatic responses’, i.e., one’s automatic responses to sensations of pain, cold, warmth, sudden intensity. To this end, it undertakes a Husserlian phenomenological analysis of the first-hand experience of eight basic emotions, briefly exploring their essential aspects: their holistic nature, their identifying dynamic transformation of the lived body, their two-layered intentionality, their involuntary initiation and voluntary espousal. The fact that the involuntary tensional shifts initiating emotions are irreplicatable voluntarily, is taken to show that (...) all emotions have an innate core, a conclusion corroborated by their strong similarities to somatic responses in dynamics, hedonic tone, and topology. The fact that emotions may be culturally reworked, is shown to be explicable in terms of their complex nature: their dependence on belief, their voluntary espousal, and their ready social transmittability. Finally, it is argued that emotions may plausibly be deemed the evolutionary descendants of somatic responses. (shrink)

In his 1967 paper Vaught used an ingenious argument to show that every recursively enumerable first order theory that directly interprets the weak system VS of set theory is axiomatizable by a scheme. In this paper we establish a strengthening of Vaught's theorem by weakening the hypothesis of direct interpretability of VS to direct interpretability of the finitely axiomatized fragment VS2 of VS. This improvement significantly increases the scope of the original result, since VS is essentially undecidable, but VS2 has (...) decidable extensions. We also explore the ramifications of our work on finite axiomatizability of schemes in the presence of suitable comprehension principles. (shrink)

Vardanyan's theorem states that the set of PA-valid principles of Quantified Modal Logic, QML, is complete Π0 2. We generalize this result to a wide class of theories. The crucial step in the generalization is avoiding the use of Tennenbaum's Theorem.

As the youngest work in the Platonic corpus, the Axiochus interacts with other texts in the corpus as well as with its contemporary philosophical milieu. How it does so, however, and what the purpose of the work is, is still unclear. This paper proposes a new theoretical approach to this text, arguing that the Axiochus anchors a number of innovations. It discusses three innovations in particular: the introduction of philosophical therapy in Platonism, the use of Epicurean arguments in Academic philosophy, (...) and a renovated Platonism on the contemporary philosophical scene. The Axiochus aims, so this paper argues, to make these innovations acceptable to different audiences by anchoring them in the Socratic dialogue and the therapeutic paradigm of philosophy, respectively. (shrink)