The main result proved in the paper is that on every recursive structure the intrinsically hyperarithmetical sets coincide with the relatively intrinsically hyperarithmetical sets. As a side effect of the proof an effective version of the Kueker's theorem on definability by means of infinitary formulas is obtained.

An external characterization of the inductive sets on countable abstract structures is presented. The main result is an abstract version of the classical Suslin-Kleene characterization of the hyperarithmetical sets.

We prove that there is a structure, indeed a linear ordering, whose degree spectrum is the set of all non-hyperarithmetic degrees. We also show that degree spectra can distinguish measure from category.

A generic computation of a subsetAof ℕ is a computation which correctly computes most of the bits ofA, but which potentially does not halt on all inputs. The motivation for this concept is derived from complexity theory, where it has been noticed that frequently, it is more important to know how difficult a type of problem is in the general case than how difficult it is in the worst case. When we study this concept from a recursion theoretic point of (...) view, to create a transitive relationship, we are forced to consider oracles that sometimes fail to give answers when asked questions. Unfortunately, this makes working in the generic degrees quite difficult. Indeed, we show that generic reduction is$\Pi _1^1$―complete. To help avoid this difficulty, we work with the generic degrees of density-1 reals. We demonstrate how an understanding of these degrees leads to a greater understanding of the overall structure of the generic degrees, and we also use these density-1 sets to provide a new a characterization of the hyperartithmetical Turing degrees. (shrink)

A mass problem is a set of Turing oracles. If P and Q are mass problems, we say that P is weakly reducible to Q if for all Y ∈ Q there exists X ∈ P such that X is Turing reducible to Y. A weak degree is an equivalence class of mass problems under mutual weak reducibility. Let [Formula: see text] be the lattice of weak degrees of mass problems associated with nonempty [Formula: see text] subsets of the Cantor (...) space. The lattice [Formula: see text] has been studied in previous publications. The purpose of this paper is to show that [Formula: see text] partakes of hyperarithmeticity. We exhibit a family of specific, natural degrees in [Formula: see text] which are indexed by the ordinal numbers less than [Formula: see text] and which correspond to the hyperarithmetical hierarchy. Namely, for each [Formula: see text], let hα be the weak degree of 0, the αth Turing jump of 0. If p is the weak degree of any mass problem P, let p* be the weak degree of the mass problem P* = {Y | ∃X ⊆ BLR )} where BLR is the set of functions which are boundedly limit recursive in X. Let 1 be the top degree in [Formula: see text]. We prove that all of the weak degrees [Formula: see text], [Formula: see text], are distinct and belong to [Formula: see text]. In addition, we prove that certain index sets associated with [Formula: see text] are [Formula: see text] complete. (shrink)

We construct a class of relations on computable structures whose degree spectra form natural classes of degrees. Given any computable ordinal and reducibility r stronger than or equal to m-reducibility, we show how to construct a structure with an intrinsically invariant relation whose degree spectrum consists of all nontrivial r-degrees. We extend this construction to show that can be replaced by either or.

A statement of hyperarithmetic analysis is a sentence of second order arithmetic S such that for every Y⊆ω, the minimum ω-model containing Y of RCA0 + S is HYP, the ω-model consisting of the sets hyperarithmetic in Y. We provide an example of a mathematical theorem which is a statement of hyperarithmetic analysis. This statement, that we call INDEC, is due to Jullien [13]. To the author's knowledge, no other already published, purely mathematical statement has been found with this property (...) until now. We also prove that, over RCA0, INDEC is implied by [Formula: see text] and implies ACA0, but of course, neither ACA0, nor ACA 0+ imply it. We introduce five other statements of hyperarithmetic analysis and study the relations among them. Four of them are related to finitely-terminating games. The fifth one, related to iterations of the Turing jump, is strictly weaker than all the other statements that we study in this paper, as we prove using Steel's method of forcing with tagged trees. (shrink)

Millar showed that for each n<ω, there is a complete decidable theory having precisely eighteen nonisomorphic countable models where some of these are decidable exactly in the hyperarithmetic set H. By combining ideas from Millar's proof with a technique of Peretyat'kin, the author reduces the number of countable models to five. By a theorem of Millar, this is the smallest number of countable models a decidable theory can have if some of the models are not 0″-decidable.

We study arithmetic and hyperarithmetic degrees of categoricity. We extend a result of E. Fokina, I. Kalimullin, and R. Miller to show that for every computable ordinal $\alpha$, $\mathbf{0}^{}$ is the degree of categoricity of some computable structure $\mathcal{A}$. We show additionally that for $\alpha$ a computable successor ordinal, every degree $2$-c.e. in and above $\mathbf{0}^{}$ is a degree of categoricity. We further prove that every degree of categoricity is hyperarithmetic and show that the index set of structures with degrees (...) of categoricity is $\Pi_{1}^{1}$-complete. (shrink)

Recent work in computability theory has focused on various notions of asymptotic computability, which capture the idea of a set being “almost computable.” One potentially upsetting result is that all four notions of asymptotic computability admit “almost computable” sets in every Turing degree via coding tricks, contradicting the notion that “almost computable” sets should be computationally close to the computable sets. In response, Astor introduced the notion of intrinsic density: a set has defined intrinsic density if its image under any (...) computable permutation has the same asymptotic density. Furthermore, introduced various notions of intrinsic computation in which the standard coding tricks cannot be used to embed intrinsically computable sets in every Turing degree. Our goal is to study the sets which are intrinsically small, i.e. those that have intrinsic density zero. We begin by studying which computable functions preserve intrinsic smallness. We also show that intrinsic smallness and hyperimmunity are computationally independent notions of smallness, i.e. any hyperimmune degree contains a Turing-equivalent hyperimmune set which is “as large as possible” and therefore not intrinsically small. Our discussion concludes by relativizing the notion of intrinsic smallness and discussing intrinsic computability as it relates to our study of intrinsic smallness. (shrink)

"In recent years, design has grown in importance for economic and technical development projects. This increase is in turn associated with very topical social issues. Yet, how can this dimension of design, i.e. "social design", be researched and made visible? This was the question that was tackled by the authors of this book to shed light on the specific rationalities of the processes and methods of design. Based on eight selected projects of applied design at the Zurich University of the (...) Arts, from the areas of Industrial design, Interaction design and Game design, various networks of heterogeneous actors are described and discussed from various academic perspectives. The investigated design productions represent an intrinsic logic than can neither be limited to standardized sets of methods within the discipline nor to established methods outside it. At the same time, decoding the complexity of singular design processes contributes to the advancement of the formulation of design theory."--Site Web de l'éditeur. (shrink)

We first summarize and comment upon a 'calculus of intrinsic preferability' which we have presented in detail elsewhere. 1 Then we set forth 'the problem of supererogation' - a problem which, according to some, has presented difficulties for deontic logic. And, finally, we propose a moral or deontic interpretation of the calculus of intrinsic preferability which, we believe, enables us to solve the problem of supererogation.

In this essay I propose an environmental ethic in the pragmatic vein. I begin by suggesting that the contemporary debate in environmental ethics is forced into a familiar but highly restrictive set of distinctions and problems by the traditional notion of intrinsic value, particularly by its demands that intrinsic values be self-sufficient, abstract, and justified in special ways. I criticize this notion and develop an alternativewhich stresses the interdependent structure of values, a structure which at once roots them deeply in (...) our selves and at the same time opens them to critical challenge and change. Finally, I apply this alternative view back to environmental ethics. It becomes easy to justify respect for other life forms and concern for the natural environment, and indeed many of the standard arguments only become stronger, once the demand to establish intrinsic values is removed. (shrink)

In this essay I propose an environmental ethic in the pragmatic vein. I begin by suggesting that the contemporary debate in environmental ethics is forced into a familiar but highly restrictive set of distinctions and problems by the traditional notion of intrinsic value, particularly by its demands that intrinsic values be self-sufficient, abstract, and justified in special ways. I criticize this notion and develop an alternativewhich stresses the interdependent structure of values, a structure which at once roots them deeply in (...) our selves and at the same time opens them to critical challenge and change. Finally, I apply this alternative view back to environmental ethics. It becomes easy to justify respect for other life forms and concern for the natural environment, and indeed many of the standard arguments only become stronger, once the demand to establish intrinsic values is removed. (shrink)

There are many computational problems which are generally “easy” to solve but have certain rare examples which are much more difficult to solve. One approach to studying these problems is to ignore the difficult edge cases. Asymptotic computability is one of the formal tools that uses this approach to study these problems. Asymptotically computable sets can be thought of as almost computable sets, however every set is computationally equivalent to an almost computable set. Intrinsic density was introduced as a way (...) to get around this unsettling fact, and which will be our main focus.Of particular interest for the first half of this dissertation are the intrinsically small sets, the sets of intrinsic density $0$. While the bulk of the existing work concerning intrinsic density was focused on these sets, there were still many questions left unanswered. The first half of this dissertation answers some of these questions. We proved some useful closure properties for the intrinsically small sets and applied them to prove separations for the intrinsic variants of asymptotic computability. We also completely separated hyperimmunity and intrinsic smallness in the Turing degrees and resolved some open questions regarding the relativization of intrinsic density.For the second half of this dissertation, we turned our attention to the study of intermediate intrinsic density. We developed a calculus using noncomputable coding operations to construct examples of sets with intermediate intrinsic density. For almost all $r\in $, this construction yielded the first known example of a set with intrinsic density r which cannot compute a set random with respect to the r-Bernoulli measure. Motivated by the fact that intrinsic density coincides with the notion of injection stochasticity, we applied these techniques to study the structure of the more well-known notion of MWC-stochasticity.prepared by Justin Miller.E-mail: [email protected]: https://curate.nd.edu/show/6t053f4938w. (shrink)

We exploit properties of certain directed graphs, obtained from the families of sets with special effective enumeration properties, to generalize several results in computable model theory to higher levels of the hyperarithmetical hierarchy. Families of sets with such enumeration features were previously built by Selivanov, Goncharov, and Wehner. For a computable successor ordinal α, we transform a countable directed graph into a structure such that has a isomorphic copy if and only if has a computable isomorphic copy.A computable structure (...) is categorical if for all computable isomorphic copies of , there is an isomorphism from onto , which is . We prove that for every computable successor ordinal α, there is a computable, categorical structure, which is not relatively categorical. This generalizes the result of Goncharov that there is a computable, computably categorical structure, which is not relatively computably categorical.An additional relation R on the domain of a computable structure is intrinsically on if in all computable isomorphic copies of , the image of R is . We prove that for every computable successor ordinal α, there is an intrinsically relation on a computable structure, which not relatively intrinsically . This generalizes the result of Manasse that there is an intrinsically computably enumerable relation on a computable structure, which is not relatively intrinsically computably enumerable.The dimension of a structure is the number of computable isomorphic copies, up to isomorphisms. We prove that for every computable successor ordinal α and every n≥1, there is a computable structure with dimension n. This generalizes the result of Goncharov that there is a structure of computable dimension n for every n≥1.Finally, we prove that for every computable successor ordinal α, there is a countable structure with isomorphic copies in just the Turing degrees of sets X such that relative to X is not . In particular, for every finite n, there is a structure with isomorphic copies in exactly the non- Turing degrees. This generalizes the result obtained by Wehner, and independently by Slaman, that there is a structure with isomorphic copies in exactly the nonzero Turing degrees. (shrink)

What is the most general common set of attributes that characterises something as intrinsically valuable and hence as subject to some moral respect, and without which something would rightly be considered intrinsically worthless or even positively unworthy and therefore rightly to be disrespected in itself? This paper develops and supports the thesis that the minimal condition of possibility of an entity's least intrinsic value is to be identified with its ontological status as an information object. All entities, even (...) when interpreted as only clusters of information, still have a minimal moral worth qua information objects and so may deserve to be respected. The paper is organised into four main sections. Section 1 models moral action as an information system using the object-oriented programming methodology (OOP). Section 2 addresses the question of what role the several components constituting the moral system can have in an ethical analysis. If they can play only an instrumental role, then Computer Ethics (CE) is probably bound to remain at most a practical, field-dependent, applied or professional ethics. However, Computer Ethics can give rise to a macroethical approach, namely Information Ethics (IE), if one can show that ethical concern should be extended to include not only human, animal or biological entities, but also information objects. The following two sections show how this minimalist level of analysis can be achieved. Section 3 provides an axiological analysis of information objects. It criticises the Kantian approach to the concept of intrinsic value and shows that it can be improved by using the methodology introduced in the first section. The solution of the Kantian problem prompts the reformulation of the key question concerning the moral worth of an entity: what is the intrinsic value of x qua an object constituted by its inherited attributes? In answering this question, it is argued that entities can share different observable properties depending on the level of abstraction adopted,and that it is still possible to speak of moral value even at the highest level of ontological abstraction represented by the informational analysis. Section 4 develops a minimalist axiology based on the concept of information object. It further supports IE's position by addressing five objections that may undermine its acceptability. (shrink)

Our intuitions concerning cultures show that we are committed to thinking that they are intrinsically valuable. I set out the conditions under which we attribute such value to cultures, and show that coming to possess intrinsic value is a matter of having the right kind of causal history.

This paper claims that a particular interpretation of Kant`s legal-political philosophy, as it is presented in his Doctrine of Right, provides us with the much needed resolution to the question of the normativity of law, precisely because it brings in a perspective that avoids both positivism and ethicism. This particular interpretation follows a strategy of argumentation that I call the “argument for the intrinsic normativity of law”, i.e., the argument that law is defined and justified on its own grounds, without (...) any need to refer to ethics, or rational/enlightened self-interest. This argument highlights the concept of legal person with the innate right to freedom as the necessary presupposition of legal practices, and sets forth a fundamental sense of justice inherent to the concept of law that consists in the reciprocal recognition of legal personality. In the end, I come up with a distinctive conception of law that I formulate as a last resort of normativity in the face of a conflict wherein an ethical solution does not appeal to all parties. (shrink)

Since the choice of a particular loss function strongly influences the resulting inference, it seems necessary to rely on “intrinsic” losses when no information is available about the utility function of the decision-maker, rather than to call for classical losses like the squared error loss. Since this setting is quite similar to the derivation of noninformative priors in Bayesian analysis, we first recall the conditions of this derivation and deduce from these conditions some requirements on the intrinsic losses. It then (...) appears that these loss functions should only depend on the sampling distribution and that they should be independent of the parameterization of the distribution. The resulting estimators are therefore transformation equivariant. We study the properties of two natural intrinsic losses, namely entropy and Hellinger losses, and show that they can be expressed in closed form for exponential families. Moreover, the entropy loss also provides analytic expressions of Bayes estimators under conjugate priors; the derivation of Bayes estimators associated with the Hellinger loss is more cumbersome, as shown in Poisson and Gamma cases, while leading to similar estimators. (shrink)

The heart has a high‐metabolic rate, and its “around‐the‐clock” vital role to sustain life sets it apart in a regenerative setting from other organs and appendages. The landscape of vertebrate species known to perform intrinsic heart regeneration is strongly biased toward ectotherms—for example, fish, salamanders, and embryonic/neonatal ectothermic mammals. It is hypothesized that intrinsic heart regeneration is exclusively limited to the low‐metabolic hearts of ectotherms. The biomedical field of regenerative medicine seeks to devise biologically inspired regenerative therapies to diseased human (...) hearts. Falsification of the ectothermy dependency for heart regeneration hypothesis may be a crucial prerequisite to meaningfully seek inspiration in established ectothermic regenerative animal models. Otherwise, engineering approaches to construct artificial heart components may constitute a more viable path toward regenerative therapies. A more strict definition of regenerative phenomena is generated and several testable sub‐hypotheses and experimental avenues are put forward to elucidate the link between heart regeneration and metabolism. Also see the video abstract here https://youtu.be/fZcanaOT5z8. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Martin Steinmann INTRINSIC MERIT AND MULTICULTURALISM O OME proponents of multiculturalism argue as follows: There is no such thing as intrinsic merit. Therefore, the hegemony ofwestern culture in America is not due to its intrinsic merit. Therefore, it is due only to the political and economic power of white Americans of European ancestry, especially males. Therefore, it might yield to a new order in which all cultures represented in (...) America, whatever dieir origin, have equal authority, influence, and status in schools, colleges, and universities, in theaters and concert halls, in museums and galleries, and in libraries. Is this a good argument for multiculturalism? I propose to examine not only its validitybutits assumptions and what impels diese multiculturalists to make it. Is there such a thing as intrinsic merit? A famous and influential argument that there is—W K. Wimsatt and Monroe C. Beardsley's "The Affective Fallacy" (1949)—argues that the merit (or lack of merit) of literature, and by extension the other arts, is intrinsic. Actually—what comes to much the same thing—this essay attacks die belief that merit is extrinsic, in particular that it inheres in effects upon readers. The Affective Fallacy, they claim, "is a confusion between the poem [where poem is synecdoche for work of literature] and its results (what it is and Philosophy and Literature, © 1994, 18: 253-264 254Philosophy and Literature what it does).... It begins by trying to derive die standards of criticism from the psychological effects of the poem and ends in impressionism and relativism." The standards ofcriticism ought to be derived, Wimsatt and Beardsley say, from "cognitive analysis ofparadox, ambiguity, irony, and symbol"—that is, intrinsic features of the poem itself. Are Wimsatt and Beardsley right? I think not. For one tiling, the weight of opinion, of both critics and writers, is against diem. For Aristode, the point of a tragedy was to arouse pity and fear in the audience. For Horace, die point of poetry was to please and instruct readers (dulce et utile). For Dickens, die point of his novels was to make readers laugh and cry. For Henry James, every choice he made as a novelist—of characters, incidents, setting, point ofview—he made widi effects upon readers in mind. Even for Romantic poets, diough die merit of a poem did not lie in its effects upon readers, it did not lie in its intrinsic features either, but in its effects upon the poet himself (for Wordswordi, occasioning "die spontaneous overflow of powerful feelings "). Indeed, not until the advent, in the late thirties, of the school of which Wimsatt and Beardsley were die chief theoreticians—die New Criticism—did critics locate merit in intrinsic features. Critics and writers, of course, often speak of intrinsic features but only, as James does, to relate them to somediing extrinsic. Aristode, for instance, says diat a tragedy can arouse pity and fear only if its hero is a person of middling virtue who undeservedly goes from good fortune to bad in die course of the play. Books of literature are created by humans for humans, and whatever merit (or lack of merit) they may have humans confer upon them. Far from being an intrinsic merit, paradox or ambiguity or irony or symbol or any intrinsic feature of a work is no merit at all unless readers count it as a merit; readers may disagree about whether it is a merit (the relativism thatWimsatt and Beardsley deplore) ; every standard to which diey may appeal to settle disputes is a standard created by humans; and they may have various reasons for counting it as a merit (or a defect). The most common reason, of course, commits the Affective Fallacy: the feature affects readers in a way they find desirable. (As I shall note later, in section III, diere can be other reasons less direcdy related to the effect of the work.) It is not easy for readers (or theorists of literary value) to sayjust what die effect is ofan intrinsic feature or why readers count this effect as desirable or even what feature of the work causes this effect. But, though Wimsatt and Beardsley, in arguing dieir case for the Affective Fallacy, make... (shrink)

ABSTRACT We shall defend three philosophical theses about the extent of intrinsic justification based on various technical results. We shall present a set of theorems which indicate intriguing structural similarities between a family of “weak” reflection principles roughly at the level of those considered by Tait and Koellner and a family of “strong” reflection principles roughly at the level of those of Welch and Roberts, which we claim to lend support to the view that the stronger reflection principles are (...) class='Hi'>intrinsically justified as well as the weaker ones. We consider connections with earlier work of Marshall. (shrink)

Various tests have been proposed as helps to identify intrinsic properties. This paper compares three prominent tests and shows that they fail to pass adequate verdicts on a set of three properties. The paper examines whether improved versions of the tests can reduce or remove these negative outcomes. We reach the sceptical conclusion that whereas some of the tests must be discarded as inadequate because they don’t yield definite results, the remaining tests depend for their application on the details of (...) fundamental particle physics so much so that they cannot be relied upon. (shrink)

– Common to most realist accounts of powers is the claim that they are intrinsic properties. Most arguments presented in defence of the intrinsicality thesis have as their targets reductive treatments of powers that conceive of powers as relations between the object described as possessing the power and either some previous manifestation event or the laws of nature. However, even if these arguments are successful, they fail to establish that powers are intrinsic properties; at best they demonstrate the irreducibility of (...) powers. In order to take the further step to intrinsicality, these arguments need to be supplemented by an argument to the effect that powers are not relations that hold between pairs or sets of objects. This paper aims to supply that missing argument. (shrink)

Principia Ethica set the agenda for analytical metaethics. Moore’s unrelenting focus on fundamentals both brought metaethics into view as a potentially separate area of philosophical inquiry and provided a model of the analytical techniques necessary to pursue it.1 Moore acknowledged that he wasn’t the first to insist on a basic irreducible core of all ethical concepts. Although he seems not to have appreciated the roots of this thought in eighteenth-century intuitionists like Clarke, Balguy, and Price, not to mention sentimentalists like (...) Hutcheson and Hume, Moore gave full marks to Sidgwick. According to Moore, Sidgwick was the “only . . . ethical writer” to have clearly seen the irreducibility of ethics’ defining notion.2 Nevertheless, twentieth-century meta-. (shrink)

This is the introductory installment in a projected series of articles in which I shall be advancing the positive case for the "intrinsic" kind of explanatory account of "consciousness4." "Consciousness4" has reference to a property of individual mental-occurrence instances wherein there takes place an immediate awareness of them either upon their occurrence or as part of their very occurrence. The immediacy or directness of such inner awareness amounts to the absence of mental mediation by any other occurrent awareness. An account (...) of consciousness4 that properly comes under the heading of "intrinsic theory" is distinguished by the thesis that a mental-occurrence instance’s being conscious4 is an intrinsic property, rather than an external-relational property of that mental-occurrence instance. My hope for the present series of articles is that, by the end, the case for intrinsic theory will he so evidently strong, or at least so vivid, that all psychologists of consciousness will have to address intrinsic theory and its explanandum of consciousness4. In this article, I set the stage by rendering some of the relevant meanings explicit, spelling out my purpose and approach to making the case for intrinsic theory, providing some context for the discussions to follow, and mentioning important objections to intrinsic theory that have been voiced in the literature. (shrink)

The infinite pigeonhole principle for 2-partitions asserts the existence, for every set A, of an infinite subset of A or of its complement. In this paper, we study the infinite pigeonhole pr...

In recent metaethical debate over ways to justify the notion of intrinsic natural value, some neopragmatists have challenged realist conceptions of scientific and moral truth. Holmes Rolston defends a critical-realist epistemology as the basis for a metaphysics of "projective nature" and a cosmological narrative--both of which set up a historical ontology of objective natural value. Pure ecological science informs the wilderness experience of Rolston's ideal epistemic subject, the "sensitive naturalist." The author argues that Rolston's account of the relation between knowing (...) and valuing can be clarified and strengthened by appropriating Bernard Lonergan's transcendental method. Conversely, Lonergan's view of moral self-transcendence can be developed further in light of Rolston's virtue epistemology, which is embodied in the figure of the sensitive naturalist. (shrink)

In his book, Earth and Other Ethics, Christopher Stone attempts to account for the moral dimension of our lives insofar as it extends to nonhuman animals, plants, species, ecosystems, and even inanimate objects. In his effort to do this, he introduces a technical notion, the moral plane. Moral planes are defined both by the ontological commitments they make and by the governance mIes that pertain to the sorts of entities included in the plane. By introducing these planes, Stone is left (...) with a set of problems. Do the planes provide anything more objective than a set of alternative ways of looking at moral problems? How can one resolve apparent conflicts between the recommendations forthcoming from distinct planes? Why do certain entities constitute moral planes; and how do we decide which planes to “buy into?” Stone’s answers to these questions endorse aseries of concessions to moral relativism. In this paper I outline an alternative to Stone’s moral planes which, while sympathetic to his ethical concerns, comes down squarelyon the side of moral realism. (shrink)

A Π01 class is an effectively closed set of reals. We study properties of these classes determined by cardinality, measure and category as well as by the complexity of the members of a class P. Given an effective enumeration {Pe:e < ω} of the Π01 classes, the index set I for a certain property is the set of indices e such that Pe has the property. For example, the index set of binary Π01 classes of positive measure is Σ02 complete. (...) Various notions of boundedness are discussed and classified. For example, the index set of the recursively bounded classes is Σ03 complete and the index set of the recursively bounded classes which have infinitely many recursive members is Π04 complete. Consideration of the Cantor-Bendixson derivative leads to index sets in the transfinite levels of the hyperarithmetic hierarchy. (shrink)

This article considers 3 claims that cognitive sex differ- ences account for the differential representation of men and women in high-level careers in mathematics and sci- ence: (a) males are more focused on objects from the beginning of life and therefore are predisposed to better learning about mechanical systems; (b) males have a pro- file of spatial and numerical abilities producing greater aptitude for mathematics; and (c) males are more variable in their cognitive abilities and therefore predominate at the upper (...) reaches of mathematical talent. Research on cogni- tive development in human infants, preschool children, and students at all levels fails to support these claims. Instead, it provides evidence that mathematical and scientific rea- soning develop from a set of biologically based cognitive capacities that males and females share. These capacities lead men and women to develop equal talent for mathe- matics and science. (shrink)

We show that for every c.e. degree a > 0 there exists an intrinsically c.e. relation on the domain of a computable structure whose degree spectrum is {0, a}. This result can be extended in two directions. First we show that for every uniformly c.e. collection of sets S there exists an intrinsically c.e. relation on the domain of a computable structure whose degree spectrum is the set of degrees of elements of S. Then we show that if (...) α ∈ ω∪{ω } then for any α-c.e. degree a > 0 there exists an intrinsically α-c.e. relation on the domain of a computable structure whose degree spectrum is {0, a}. All of these results also hold for m-degree spectra of relations. (shrink)

This paper examines the debate as to whether something can have final value in virtue of its relational (i.e., non-intrinsic) properties, or, more briefly put, whether final value must be intrinsic. The paper adopts the perspective of the fitting-attitude analysis (FA analysis) of value, and argues that from this perspective, there is no ground for the requirement that things may have final value only in virtue of their intrinsic properties, but that there might be some grounds for the alternate requirement (...) that final value be grounded only in the essential properties of their bearers. First, the paper introduces the key elements of the FA analysis, and sets aside an obvious but unimportant way in which this analysis makes all final values relational. Second, it discusses some classical counterexamples to the view that final value must be intrinsic. Third, it discusses the relation between final, contributive, and signatory value. Fourth, it examines Zimmerman’s defense of the requirement that final value must be intrinsic on the grounds that final value cannot be derivative. And finally, it explores the alternative requirement that something may have final value in virtue of its essential properties. (shrink)

In his book, Earth and Other Ethics, Christopher Stone attempts to account for the moral dimension of our lives insofar as it extends to nonhuman animals, plants, species, ecosystems, and even inanimate objects. In his effort to do this, he introduces a technical notion, the moral plane. Moral planes are defined both by the ontological commitments they make and by the governance mIes (moral maxims) that pertain to the sorts of entities included in the plane. By introducing these planes, Stone (...) is left with a set of problems. (1) Do the planes provide anything more objective than a set of alternative ways of looking at moral problems? (2) How can one resolve apparent conflicts between the recommendations forthcoming from distinct planes? (3) Why do certain entities constitute moral planes; and how do we decide which planes to “buy into?” Stone’s answers to these questions endorse aseries of concessions to moral relativism. In this paper I outline an alternative to Stone’s moral planes which, while sympathetic to his ethical concerns, comes down squarelyon the side of moral realism. (shrink)

The thesis deals with the concept of truth and the paradoxes of truth. Philosophical theories usually consider the concept of truth from a wider perspective. They are concerned with questions such as - Is there any connection between the truth and the world? And, if there is - What is the nature of the connection? Contrary to these theories, this analysis is of a logical nature. It deals with the internal semantic structure of language, the mutual semantic connection of sentences, (...) above all the connection of sentences that speak about the truth of other sentences and sentences whose truth they speak about. Truth paradoxes show that there is a problem in our basic understanding of the language meaning and they are a test for any proposed solution. It is important to make a distinction between the normative and analytical aspect of the solution. The former tries to ensure that paradoxes will not emerge. The latter tries to explain paradoxes. Of course, the practical aspect of the solution is also important. It tries to ensure a good framework for logical foundations of knowledge, for related problems in Artificial Intelligence and for the analysis of the natural language. Tarski’s analysis emphasized the T-scheme as the basic intuitive principle for the concept of truth, but it also showed its inconsistency with the classical logic. Tarski’s solution is to preserve the classical logic and to restrict the scheme: we can talk about the truth of sentences of a language only inside another essentially richer metalanguage. This solution is in harmony with the idea of reflexivity of thinking and it has become very fertile for mathematics and science in general. But it has normative nature | truth paradoxes are avoided in a way that in such frame we cannot even express paradoxical sentences. It is also too restrictive because, for the same reason we cannot express a situation in which there is a circular reference of some sentences to other sentences, no matter how common and harmless such a situation may be. Kripke showed that there is no natural restriction to the T-scheme and we have to accept it. But then we must also accept the riskiness of sentences | the possibility that under some circumstances a sentence does not have the classical truth value but it is undetermined. This leads to languages with three-valued semantics. Kripke did not give any definite model, but he gave a theoretical frame for investigations of various models | each fixed point in each three-valued semantics can be a model for the concept of truth. The solutions also have normative nature | we can express the paradoxical sentences, but we escape a contradiction by declaring them undetermined. Such a solution could become an analytical solution only if we provide the analysis that would show in a substantial way that it is the solution that models the concept of truth. Kripke took some steps in the direction of finding an analytical solution. He preferred the strong Kleene three-valued semantics for which he wrote it was "appropriate" but did not explain why it was appropriate. One reason for such a choice is probably that Kripke finds paradoxical sentences meaningful. This eliminates the weak Kleene three valued semantics which corresponds to the idea that paradoxical sentences are meaningless, and thus indeterminate. Another reason could be that the strong Kleene three valued semantics has the so-called investigative interpretation. According to this interpretation, this semantics corresponds to the classical determination of truth, whereby all sentences that do not have an already determined value are temporarily considered indeterminate. When we determine the truth value of these sentences, then we can also determine the truth value of the sentences that are composed of them. Kripke supplemented this investigative interpretation with an intuition about learning the concept of truth. That intuition deals with how we can teach someone who is a competent user of an initial language (without the predicate of truth T) to use sentences that contain the predicate T. That person knows which sentences of the initial language are true and which are not. We give her the rule to assign the T attribute to the former and deny that attribute to the latter. In that way, some new sentences that contain the predicate of truth, and which were indeterminate until then, become determinate. So the person gets a new set of true and false sentences with which he continues the procedure. This intuition leads directly to the smallest fixed point of strong Kleene semantics as an analytically acceptable model for the logical notion of truth. However, since this process is usually saturated only on some transfinite ordinal, this intuition, by climbing on ordinals, increasingly becomes a metaphor. This thesis is an attempt to give an analytical solution to truth paradoxes. It gives an analysis of why and how some sentences lack the classical truth value. The starting point is basic intuition according to which paradoxical sentences are meaningful (because we understand what they are talking about well, moreover we use it for determining their truth values), but they witness the failure of the classical procedure of determining their truth value in some "extreme" circumstances. Paradoxes emerge because the classical procedure of the truth value determination does not always give a classically supposed (and expected) answer. The analysis shows that such an assumption is an unjustified generalization from common situations to all situations. We can accept the classical procedure of the truth value determination and consequently the internal semantic structure of the language, but we must reject the universality of the exterior assumption of a successful ending of the procedure. The consciousness of this transforms paradoxes to normal situations inherent to the classical procedure. Some sentences, although meaningful, when we evaluate them according to the classical truth conditions, the classical conditions do not assign them a unique value. We can assign to them the third value, \undetermined", as a sign of definitive failure of the classical procedure. An analysis of the propagation of the failure in the structure of sentences gives exactly the strong Kleene three-valued semantics, not as an investigative procedure, as it occurs in Kripke, but as the classical truth determination procedure accompanied by the propagation of its own failure. An analysis of the circularities in the determination of the classical truth value gives the criterion of when the classical procedure succeeds and when it fails, when the sentences will have the classical truth value and when they will not. It turns out that the truth values of sentences thus obtained give exactly the largest intrinsic fixed point of the strong Kleene three-valued semantics. In that way, the argumentation is given for that choice among all fixed points of all monotone three-valued semantics for the model of the logical concept of truth. An immediate mathematical description of the fixed point is given, too. It has also been shown how this language can be semantically completed to the classical language which in many respects appears a natural completion of the process of thinking about the truth values of the sentences of a given language. Thus the final model is a language that has one interpretation and two systems of sentence truth evaluation, primary and final evaluation. The language through the symbol T speaks of its primary truth valuation, which is precisely the largest intrinsic fixed point of the strong Kleene three valued semantics. Its final truth valuation is the semantic completion of the first in such a way that all sentences that are not true in the primary valuation are false in the final valuation. (shrink)

This paper suggests that libertarians should avail themselves of a system of natural and autonomy-friendly motivational foundations—intrinsic motives. A psyche equipped with intrinsic motives could allow for some degree of character-formation that is genuinely and robustly autonomous. Such autonomy would rest on motives that are one’s own in the most direct way: they are part of one’s natural make-up. A model with intrinsic motives can help libertarians in multiple ways: to deal with skeptics regarding the very idea of robust self-making; (...) to explain the importance of autonomy (it helps explain how the agent can set her dominant life-goals on the basis of her own motives); to explain why an artificially induced, albeit rational, autonomy is less than genuine (it would not rely on the agent’s own motives). (shrink)

ABSTRACT Most theorists agree that our social order includes a distinctive legal dimension. A fundamental question is that of whether reference to specific legal phenomena always involves a commitment to a particular moral view. Whereas many philosophers advance the ‘positivist’ claim that any correspondence between morality and the law is just a function of political circumstance, natural law theorists insist that law is intrinsically moral. Each school claims the crucial advantage of consistency with our folk concept. Drawing on the (...) notion of dual character concepts, we develop a set of hypotheses about the intuitive relation between a rule’s moral and legal aspects. We then report a set of studies that conflict unexpectedly with the predictions by legal positivists. Intuitively, an evil rule is not a fully-fledged instance of law. (shrink)

Discussion continues here of a theory I have previously described as being an equivocal remembrance theory of inner awareness, the direct appre-hension of one’s own mental-occurrence instances . O’Shaughnessy claims that we acquire knowledge of each of our experiences as it occurs, yet any occurrent cognitive awareness of it that we may have comes later and is mediated by memory. Thus, acquiring knowledge of an experience firsthand is automatic and silent, not a matter of experientially apprehending the experience. Although O’Shaughnessy (...) does hold that every experience has itself as an object, this is not a matter of a cognitive self-apprehension . O’Shaughnessy’s grounds for his proposal of a nonexperiential acquisition of knowledge of one’s experiences amounts to the claim that to hold otherwise would imply an infinite regress of experiences, for the experience by which we would know of an experience would be itself the object of experience, etc. I argue that neither an appendage theory nor an intrinsic theory of inner awareness, both of which are experiential, sets an experiential regress going. Then, I argue that something experiential would seem to be essential to acquiring firsthand knowledge of one’s experiences according to O’Shaughnessy’s own account of environmental perception. At its core is the thesis that the basic perceptual experience, the primary component of a perception, is a nonconceptual and noncognitive noticing of present sensations produced by environmental items. This first component evokes a second, cognitive component of the experience that is a recognitional awareness of the first component. Only in this way could perception perform its cognitive function, according to the theory, which is to yield knowledge of sensations and their causes in the environment. But the recognitional awareness, the “interpretative” component, clearly is experiential and an inner awareness. Moreover, O’Shaughnessy does not appear to view this component as resulting in an infinite number of inner awarenesses because implicitly he considers it, perhaps, to be intrinsic to the perceptual experience. (shrink)

The position of some environmental ethicists that some non-humans have intrinsic value as a mind-independent property is seriously flawed. This is because human beings lack any evidence for this position and hence are unjustified in holding it. For any possible world that is alleged to have this kind of intrinsic value, it is possible to conceive an observationally identical world that lacks intrinsic value. Hence, one is not justified in inferring the intrinsic value of some non-human from any set of (...) observable properties, since that same set of properties could just as well exist in a world that lacks intrinsic value. However, since human beings do not have a faculty of intuition that would allow them to .. (shrink)

This book represents the most comprehensive account to date of an important but widely contested approach to ethics--intuitionism, the view that there is a plurality of moral principles, each of which we can know directly. Robert Audi casts intuitionism in a form that provides a major alternative to the more familiar ethical perspectives. He introduces intuitionism in its historical context and clarifies--and improves and defends--W. D. Ross's influential formulation. Bringing Ross out from under the shadow of G. E. Moore, he (...) puts a reconstructed version of Rossian intuitionism on the map as a full-scale, plausible contemporary theory. A major contribution of the book is its integration of Rossian intuitionism with Kantian ethics; this yields a view with advantages over other intuitionist theories and over Kantian ethics taken alone. Audi proceeds to anchor Kantian intuitionism in a pluralistic theory of value, leading to an account of the perennially debated relation between the right and the good. Finally, he sets out the standards of conduct the theory affirms and shows how the theory can help guide concrete moral judgment. The Good in the Right is a self-contained original contribution, but readers interested in ethics or its history will find numerous connections with classical and contemporary literature. Written with clarity and concreteness, and with examples for every major point, it provides an ethical theory that is both intellectually cogent and plausible in application to moral problems. (shrink)

Rough sets are used in numerous knowledge representation contexts and are then empowered with varied ontologies. These may be intrinsically associated with ideas of rationality under certain conditions. In recent papers, specific granular generalisations of graded and variable precision rough sets are investigated by the present author from the perspective of rationality of approximations (and the associated semantics of rationality in approximate reasoning). The studies are extended to ideal-based approximations (sometimes referred to as subsethood-based approximations). It is additionally shown (...) that co-granular or point-wise approximations defined by σ-ideals/filters (for an arbitrary relation σ) fit easily into the entire scheme. Concepts of the rationality of objects (vague or crisp) and their types are introduced and are shown to be applicable to most general rough sets by the present author. Surprising results on these are proved on these by her in this part of the research paper. The present paper is the first of a three part study on the topic. (shrink)

Research suggests that attitudes guide individuals’ thinking and actions. In this study, we explore the monetary intelligence construct and investigate the relationships between a formative model of money attitudes involving affective, behavioral, and cognitive components and several sets of outcome variables—unethical intentions, intrinsic and extrinsic job satisfaction, and coping strategies. Based on 515 managers in the Republic of Macedonia, we test our model for the whole sample and also cross sector and gender. Managers’ negative stewardship behavior and positive cognitive meaning (...) of money define MI which, in turn, is related to unethical intentions. Positive cognition in the public sector and poor stewardship behavior in the private sector contribute to unethical intentions, respectively. Good stewards have higher intrinsic and lower extrinsic job satisfaction, those in the private sector, in particular. Affective motive and stewardship behavior are related to their stronger “approach” coping strategies and weaker “avoidance” coping strategies. Affective motive and stewardship behavior contribute to coping responses for managers in the public and private sectors, respectively. Further, the relationship between stewardship behavior and coping mechanisms exists for females, but not for males. We demonstrate that MI, a type of social intelligence, allows individuals to monitor their own emotions, behaviors, and cognitions and guides their thinking and actions. (shrink)

Presents a new framework for the complexity of algorithms, for all readers interested in the theory of computation.

In [7], a naive set theory is introduced based on a polynomial time logical system, Light Linear Logic (LLL). Although it is reasonably claimed that the set theory inherits the intrinsically polytime character from the underlying logic LLL, the discussion there is largely informal, and a formal justification of the claim is not provided sufficiently. Moreover, the syntax is quite complicated in that it is based on a non-traditional hybrid sequent calculus which is required for formulating LLL.In this paper, (...) we consider a naive set theory based on Intuitionistic Light Affine Logic (ILAL), a simplification of LLL introduced by [1], and call it Light Affine Set Theory (LAST). The simplicity of LAST allows us to rigorously verify its polytime character. In particular, we prove that a function over {0, 1}* is computable in polynomial time if and only if it is provably total in LAST. (shrink)

The axiom of infinity states that infinite sets exist. I will argue that this axiom lacks justification. I start by showing that the axiom is not self-evident, so it needs separate justification. Following Maddy’s :481–511, 1988) distinction, I argue that the axiom of infinity lacks both intrinsic and extrinsic justification. Crucial to my project is Skolem’s From Frege to Gödel: a source book in mathematical logic, 1879–1931, Cambridge, Harvard University Press, pp. 290–301, 1922) distinction between a theory of real sets, (...) and a theory of objects that theory calls “sets”. While Dedekind’s argument fails, his approach was correct: the axiom of infinity needs a justification it currently lacks. This epistemic situation is at variance with everyday mathematical practice. A dilemma ensues: should we relax epistemic standards or insist, in a skeptical vein, that a foundational problem has been ignored? (shrink)

I discuss three potential sources of evidence for truth in set theory, coming from set theory’s roles as a branch of mathematics and as a foundation for mathematics as well as from the intrinsic maximality feature of the set concept. I predict that new non first-order axioms will be discovered for which there is evidence of all three types, and that these axioms will have significant first-order consequences which will be regarded as true statements of set theory. The bulk of (...) the paper is concerned with the Hyperuniverse Programme, whose aim is to discover an optimal mathematical principle for expressing the maximality of the set-theoretic universe in height and width. (shrink)