Özet Şii-İmamiyye’nin usûlde Mu’tezilenin etkisinde kaldığı iddiaları, hicri dördüncü asırdan itibaren dile getirilmektedir. Buna karşılık usûlî düşüncenin ilk mümessili sayılan Şeyh Müfîd’den itibaren mezhep içinden yükselen sesler bu iddiaları şiddetle reddetmişlerdir. Biz bu çalışmada Mu’tezile kelamına sistematik hüviyet kazandıran ve yazdığı eserlerle Mu’tezile kelamının bugüne ulaşmasında büyük pay sahibi olan Kâdî Abdülcebbâr ile İmamiyye’nin kelam düşüncesinin istikrar bulmasında ve Şeyh Müfîd’le başlatılan usûlî yaklaşımın benimsenip yaygınlaşmasında büyük bir yeri olan Ebû Ca’fer et-Tûsî arasında adalet ilkesi üzerinden bir karşılaştırma yaparak, söz (...) konusu iddiaların ne kadar sübut bulduğunu tespit etmeye çalıştık. Kısmi farklı izahları bir kenara bırakırsak, adalet ilkesinin ispat ve yorumlanmasında iki kelamcı arasında kayda değer bir farklılığın olmadığı görülmektedir. Abstract The claim that the Shi’i Imamite thought is heavily influenced by the Mu’tazilite outlook has been alleged since the fouth century of hijra. However, beginning with Shaikh Mufid, the first representative of the Usuli branch of Shi’a, the Shi’is vehemently denied this allegation. In this article, this issue is dealt with by making a comparison between the idea of Qadi Abd al-Jabbar, the prominent Mu’tazilite scholar who made a major contribution to the consolidation of the schools’ theaching and that of al-Tusi, who also made a contrubitued to the integration of the Shi’ite kalam and the spreading of the usuli approach initiated by Shaikh Mufid. Leaving aside the differences in deatil, it seems that there is no noteworthy difference between their approcah to the issue of justice. Key Words: Qâdî Abd al-Jabbâr, Abû Ja’far al-Tûsî, Husn-Qubh, Divine Justice, Free Will. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:When Our Fathers Fall:A Thomistic-Confudan Approach to Lay Moral Correction of ClergyJoshua R. BrownIn this article, I seek to draw upon the resources of Thomas Aquinas and early Confucian philosophy in order to answer the following question: what are the responsibilities of lay Catholics to our priests and bishops as regards their personal moral rectification? This justifiably provokes two questions in reaction: why is this question worth pursuing, and (...) why pursue it via a comparative reading of Aquinas and Confucian philosophy?As to the first of these, the question I pose here is a specification of the larger responsibilities that fall to Christians according to the Scriptures. Galatians 5:1–2 puts the matter this way: "Brothers, even if a person is caught in some transgression, you who are spiritual should correct that one in a gentle spirit, looking to yourself, so that you may also not be tempted. Bear one another's burdens and so you will fulfill the law of Christ."1 In the theological tradition, "bearing one another's burdens" has been neatly and aptly represented in the principle of fraternal correction. The question I am focused on here, then, is how is fraternal correction properly offered from laity to clerics.Ultimately, articulating the shape or form of virtuous lay correction of clergy is actually a rather knotty problem. This is because the manner of the relationship between laity and clergy is not simply understood in terms [End Page 1025] of the bonds of Christian fraternity. Certainly, all Christians are brothers and sisters in Christ, for through His grace we have been adopted into the inheritance of the Kingdom of God as children of God (see Eph 5:1–5; 1 John 3:1–3). Yet the Church also recognizes that priests and bishops possess not simply a fraternal but also a paternal relationship to laity. As St. Paul again puts it to the church in Corinth, "I became your father in Christ Jesus through the gospel. Therefore, I urge you, be imitators of me" (1 Cor 4:15–16).I propose here that, although fraternal correction is a still useful concept for understanding how laity can morally correct clergy, it has an obvious weakness in that it corresponds to a particular relational analogy, that of fraternity, within which the difference in authority is not as great as the parent–child bond. Thus, fraternal correction is exceptionally useful for understanding how relationships with more or less equal rank of authority can function in terms of moral remonstration, such as how a lay Christian might fraternally correct another lay Christian, or a cleric fraternally correct a cleric. However, when it comes to clergy–laity relations, the shape of fraternal correction is far less clear, for there is a just and genuine disparity between them in the order of ecclesial, magisterial authority underlying the relationship, even if there is equality in other important respects.I argue here that lay responsibilities for correcting clergy can be fruitfully understood in terms of filial remonstration as understood by the Confucian philosophical tradition. Of course, there is one tremendous dissimilarity between Confucian views on the responsibilities for filial remonstration and those pertaining to the laity–clergy relationship: the former occur within and flow from the natural foundation of the parent–child bond, while the latter are not based on blood relations and natural duties. Yet, the same can be said about the language of fraternal correction, which draws upon the analogous duties of blood-kin applied to the spiritual fraternity of the Christian life. And so, it must be admitted that although the father–child relationship is used only analogously to describe the priest–laity relationship, it also accurately depicts the reality of that relationship. As John Paul II observed, priestly celibacy entails "a singular sharing in God's fatherhood and in the fruitfulness of the Church."2 The call of the priest to the celibate life is thus a call to fatherhood, indeed, a call to imitate and participate in the paternity of the triune God in a special and spiritual way. It seems clear that only a materialistic conception of things that denies the spiritual its proper... (shrink)

We work with a large spatialized array of individuals in an environment of drifting food sources and predators. The behavior of each individual is generated by its simple neural net; individuals are capable of making one of two sounds and are capable of responding to sounds from their immediate neighbors by opening their mouths or hiding. An individual whose mouth is open in the presence of food is “fed” and gains points; an individual who fails to hide when a predator (...) is present is “hurt” by losing points. Opening mouths, hiding, and making sounds each exact an energy cost. There is no direct evolutionary gain for acts of cooperation or “successful communication” per se. In such an environment we start with a spatialized array of neural nets with randomized weights. Using standard learning algorithms, our individuals “train up” on the behavior of successful neighbors at regular intervals. Given that simple setup, will a community of neural nets evolve a simple language for signaling the presence of food and predators? With important qualifications, the answer is “yes.” In a simple spatial environment, pursuing individualistic gains and using partial training on successful neighbors, randomized neural nets can learn to communicate. (shrink)

A number of ways of taxonomizing human learning have been proposed. We examine the evidence for one such proposal, namely, that there exist independent explicit and implicit learning systems. This combines two further distinctions, (1) between learning that takes place with versus without concurrent awareness, and (2) between learning that involves the encoding of instances (or fragments) versus the induction of abstract rules or hypotheses. Implicit learning is assumed to involve unconscious rule learning. We examine the evidence for implicit learning (...) derived from subliminal learning, conditioning, artificial grammar learning, instrumental learning, and reaction times in sequence learning. We conclude that unconscious learning has not been satisfactorily established in any of these areas. The assumption that learning in some of these tasks (e.g., artificial grammar learning) is predominantly based on rule abstraction is questionable. When subjects cannot report the rules that govern stimulus selection, this is often because their knowledge consists of instances or fragments of the training stimuli rather than rules. In contrast to the distinction between conscious and unconscious learning, the distinction between instance and rule learning is a sound and meaningful way of taxonomizing human learning. We discuss various computational models of these two forms of learning. (shrink)

Originally published in 1920, this collection of essays presents and discusses some of the principal subjects addressed in the Report of the Committee on Adult Education in 1919. The authors examine topics such as women and adult education, and the democratic foundations and implications of further education for those past school-leaving age. One essay is written by an adult student from Southport who is a self-described 'working-man'. This book will be of value to anyone with an interest in the history (...) of education. (shrink)

The chapters published in this volume developed from presentations, and their associated discussions at a conference organised by the Scottish Branch of the British Psychological Society, held at Rothesay, Isle of Bute, Scotland in September 1987. The goal of the conference was to bring together workers across a wide area of neuropsychological research to discuss recent technological advances, developments in assessment and rehabilitation, and to address theoretical issues of current interest. Thus, the chapters in this book include contributions on the (...) use of Magnetic Resonance Imaging and Single Photon Emission Computed Tomography in neuropsychological research, studies of hemi spheric specialisation and cooperation, alcoholic and Alzheimer type dementia, prosopagnosia and facial processing, the assessment, management and rehabilitation of memory problems, the assessment of premorbid intellectual status and issues in developmental neuropsychology. Many of those engaged in research and clinical practice in neuropsychology encounter a range of topic at least as wide as this in their professional lives. The opportunity for researchers and clinicians to discuss some of the key issues in the field was invaluable and we hope that readers gain as much from the material presented here as the participants did from the meeting itself. (shrink)

It is human nature to wonder how things might have turned out differently--either for the better or for the worse. For the past two decades psychologists have been intrigued by this phenomenon, which they call counterfactual thinking. Specifically, researchers have sought to answer the "big" questions: Why do people have such a strong propensity to generate counterfactuals, and what functions does counterfactual thinking serve? What are the determinants of counterfactual thinking, and what are its adaptive and psychological consequences? This important (...) work brings together a collection of thought-provoking papers by social and cognitive psychologists who have made important theoretical and empirical contributions to our understanding of this topic. The essays in this volume contain novel theoretical insights, and, in many cases descriptions of previously unpublished empirical studies. The Psychology of Counterfactual Thinking provides an excellent overview of this fascinating topic for researchers, as well as advanced undergraduates and graduates in psychology--particularly those with an interest in social cognition, social judgment, decision judgment, decision making, thinking and reasoning. (shrink)

In the original target article (Shanks & St. John 1994), one of our principal conclusions was that there is almost no evidence that learning can occur outside awareness. The continuing commentaries raise some interesting questions, especially about the definition of learning, but do not lead us to abandon our conclusion.

This book is an introduction, entirely by example, to the possibilities of using computer models as tools in phosophical research in general and in philosophical logic in particular. Topics include chaos, fractals, and the semantics of paradox; epistemic dynamics; fractal images of formal systems; the evolution of generosity; real-valued game theory; and computation and undecidability in the spatialized Prisoner's Dilemma.

The goal of philosophy of information is to understand what information is, how it operates, and how to put it to work. But unlike ‘information’ in the technical sense of information theory, what we are interested in is meaningful information. To understand the nature and dynamics of information in this sense we have to understand meaning. What we offer here are simple computational models that show emergence of meaning and information transfer in randomized arrays of neural nets. These we take (...) to be formal instantiations of a tradition of theories of meaning as use. What they offer, we propose, is a glimpse into the origin and dynamics of at least simple forms of meaning and information transfer as properties inherent in behavioral coordination across a community. (shrink)

Background: Studies on autistic strengths are often focused on what they reveal about autistic intelligence and, in some cases, exceptional and atypical reasoning abilities. An emerging research trend has demonstrated how interests and strengths often evident in autism can be harnessed in interventions to promote the well-being, adaptive, academic and professional success of autistic people. However, abilities in certain domains may be accompanied by major limitations in others, as well as psychiatric and behavioral issues, which may challenge their inclusion in (...) support programs. Objectives: To provide an in-depth, pragmatic, real-life example of the psychological and psychiatric management of interests and strengths in an autistic adolescent. Method: An autistic teenager, C.A., with above-average calendar calculation and musical abilities, received psychiatric, neuropsychological, and language standardized and clinical assessments, combined with a measurement of his musical and calendar calculation abilities. C.A. and his parents then received psychiatric and psychological support over a 14-month period, targeting their perceptions of C.A.’s interests, strengths, and co-occurring difficulties. Results: C.A. had a verbal IQ within the intellectual disability range and a non-verbal IQ in the low mean range. Modest calendar calculation, absolute pitch, and matrix abilities coexisted with severe receptive and expressive language disorder. The discrepancy between his abilities in areas of strengths and his limitations in other domains led to anxiety, frustration, and sometimes behavioral issues. Displacing the focus from academic performance to interests, as well as promoting the use of his strengths to develop new skills independently of their short-term adaptive benefits yielded positive effects on C.A.’s self-assessment, quality of life, and behavior at follow up. Discussion: The appealing idea that abilities mostly found in autistic people, such as calendar calculation, can be directly harnessed into academic achievement and lead to paid employment may have detrimental effects, especially when such abilities are modest and associated with other limitations. These abilities should be primarily used to maximize well-being and quality of life, independently of their short-term adaptive function, which may or may not be positive. (shrink)

James Collins has turned his talent for painstaking and definitive scholarship to the philosophy of religion, and nobody with an interest in this particular area of philosophy, or in the general development of modern philosophy in the hands of Hume, Kant, and Hegel, can afford to miss consulting this book. The philosophy of religion, as distinct from the older style natural theology, theodicy, and straight theological treatments of religion, is a discipline whose need was first felt when the scientific picture (...) of the universe began to declare its independence from, and possible ascendency over, the theistically ordered anthropological and cosmological harmony of the universe. As Collins details in a balanced manner, it was Hume who first formulated a program to meet this need. He did it in such a way, however, that he made religion a legitimate object of, but wholly external and even inimical in content to, philosophy, particularly epistemology and ethics. Building upon Hume, Kant defined the epistemological issue more precisely—"I have denied knowledge to save belief"—and reinterpreted the relation between morality and religion as one of complementarity rather than contradictoriness. It remained for Hegel to internalize the relation between the content of religion and the content of philosophy and thus to reduce the former to an anticipation of the latter. Collins' exposition is interpenetrated by a critical concern supplied by the dialectical development of the idea of the philosophy of religion from Hume through Kant to Hegel, and by his own proposal for integrating the genuine and irreducible insights of each of these three classical philosophies within a realistic philosophy of religion that remains basically theistic. The book is an expanded form of Collins' St. Thomas More Lectures at Yale University; it would be an impressive addition to any series of lectures.—E. A. R. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Book Reviews St. Auc~stine and Being: A Me$aphyM,cal Essay. By James F. Anderson. (The Hague: Martinus Nijhoff, 1965.Pp. viii [i] + 76. Guilders 9.90.) Contemporary students of medieval philosophy, especially those influenced by the writings of Gilson, usually view Augustine as primarily an essentialist in metaphysics, while Aquinas is viewed as some sort of existentialist. This is taken to mean that, whereas Augustine seems to identify being with essence (...) or wha~ a thing is, Aquinas distinguishes between what a thing is and its act of existence. The major contribution of Aquinas to later philosophy is often depicted as this distinction between essence and existence. Perhaps the major interest and value of Professor Anderson's essay is that it contests this currently predominant opinion of the essentialist character of Augustinian metaphysics and calls for a re-evaluation of the supposedly revohi~ionary character of the Thomistic concentration upon the act of existence. It is quite evident that Augustine broke with Plotinus when he asserted that the first principle of all things was God, being itself (ipsum esse), rather than the One, which transcends being. The controversy arises over Augustine's view of the nature of being (esse). For Gilson the notion of being remained for Augustine Neoplatonic, while for Anderson Augustine introduced an existential aspect to the notion of being lacking in Neoplatonic thought. Citing the same texts for support Gilson maintains that Augustine interprets the name of God given in Exodus as "I am he who never changes," while Anderson maintains that Augustine interprets Exodus as asserting that God is being, in the sense of existence, itself. The major point of disagreement between Gilson and Anderson is not whether Augustine regarded being as pre~ dominant, but how Augustine interpreted the notion of being. In some texts Augustine maintsSns that being and immutability mean the same thing, in others he argues that a thing truly is 'because it is immutable, and in yet others he argues that a thing is immutable because it truly is. The first opinion seems to be the one frequently favored as an interpretation of Augustine by Gilson. The second is usually regarded as Neoplatonic. The third is the opinion which Professor Anderson argues was most accurately Augustine's. According to Professor Anderson the first two opinions reflect for Augustine a merely factual connection between being and immutability, whereas the third reflects a metaphysical entailment. I should like to mention three points in Professor Anderson's discussion which seem to me weak. Firstly, as Augustine remarks that being is the name for unchangeableness we cannot take this as asserting a merely factual relationship. Secondly, to say that 'being' and 'immutability ~mean the same thing to Augustine or that being and immutability are identical to him does not necessitate, as Professor Andersen claims, denying the primacy of being. If 'being' and 'immutability' mean the same thing, then it is very peculiar to ask which is primary. If it is remarked that 'triangleI means the same thing as 'three sided figure', what sense does it make to ask which notion is primary? I suspect that Professor Anderson's contention makes sense only if one believes that there is a difference in the meanings of 'being' and 'immutability ', but whether or not there was such a difference for Augustine is precisely the point at issue. Professor Anderson asserts that it would be a "metaphysical inconsistency" to claim that God is both being and immutability, but it is not clear why such a claim would be inconsistent if the two terms in fact mean the same thing (p. 30). Thirdly, if, as is in fact the case, Augustine's remarks on the relationship between immutability and being are inconsistent perhaps we should accept the possibility that Augustine himself never came to a clear view on this matter rather than attempt to surmise what Augustine "must have meant." Of course, such inconsistency in Augustine's writings would tend to support the thesis of Gilson that Augustine has difficulties reconciling his theology and metaphysics. Moreover, the analogy Professor Anderson suggests between the Augustinian mutability-immutability contrast and the Thomistic potency-act contrast could only be a very rough one... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Book Reviews St. Auc~stine and Being: A Me$aphyM,cal Essay. By James F. Anderson. (The Hague: Martinus Nijhoff, 1965.Pp. viii [i] + 76. Guilders 9.90.) Contemporary students of medieval philosophy, especially those influenced by the writings of Gilson, usually view Augustine as primarily an essentialist in metaphysics, while Aquinas is viewed as some sort of existentialist. This is taken to mean that, whereas Augustine seems to identify being with essence (...) or wha~ a thing is, Aquinas distinguishes between what a thing is and its act of existence. The major contribution of Aquinas to later philosophy is often depicted as this distinction between essence and existence. Perhaps the major interest and value of Professor Anderson's essay is that it contests this currently predominant opinion of the essentialist character of Augustinian metaphysics and calls for a re-evaluation of the supposedly revohi~ionary character of the Thomistic concentration upon the act of existence. It is quite evident that Augustine broke with Plotinus when he asserted that the first principle of all things was God, being itself (ipsum esse), rather than the One, which transcends being. The controversy arises over Augustine's view of the nature of being (esse). For Gilson the notion of being remained for Augustine Neoplatonic, while for Anderson Augustine introduced an existential aspect to the notion of being lacking in Neoplatonic thought. Citing the same texts for support Gilson maintains that Augustine interprets the name of God given in Exodus as "I am he who never changes," while Anderson maintains that Augustine interprets Exodus as asserting that God is being, in the sense of existence, itself. The major point of disagreement between Gilson and Anderson is not whether Augustine regarded being as pre~ dominant, but how Augustine interpreted the notion of being. In some texts Augustine maintsSns that being and immutability mean the same thing, in others he argues that a thing truly is 'because it is immutable, and in yet others he argues that a thing is immutable because it truly is. The first opinion seems to be the one frequently favored as an interpretation of Augustine by Gilson. The second is usually regarded as Neoplatonic. The third is the opinion which Professor Anderson argues was most accurately Augustine's. According to Professor Anderson the first two opinions reflect for Augustine a merely factual connection between being and immutability, whereas the third reflects a metaphysical entailment. I should like to mention three points in Professor Anderson's discussion which seem to me weak. Firstly, as Augustine remarks that being is the name for unchangeableness we cannot take this as asserting a merely factual relationship. Secondly, to say that 'being' and 'immutability ~mean the same thing to Augustine or that being and immutability are identical to him does not necessitate, as Professor Andersen claims, denying the primacy of being. If 'being' and 'immutability' mean the same thing, then it is very peculiar to ask which is primary. If it is remarked that 'triangleI means the same thing as 'three sided figure', what sense does it make to ask which notion is primary? I suspect that Professor Anderson's contention makes sense only if one believes that there is a difference in the meanings of 'being' and 'immutability ', but whether or not there was such a difference for Augustine is precisely the point at issue. Professor Anderson asserts that it would be a "metaphysical inconsistency" to claim that God is both being and immutability, but it is not clear why such a claim would be inconsistent if the two terms in fact mean the same thing (p. 30). Thirdly, if, as is in fact the case, Augustine's remarks on the relationship between immutability and being are inconsistent perhaps we should accept the possibility that Augustine himself never came to a clear view on this matter rather than attempt to surmise what Augustine "must have meant." Of course, such inconsistency in Augustine's writings would tend to support the thesis of Gilson that Augustine has difficulties reconciling his theology and metaphysics. Moreover, the analogy Professor Anderson suggests between the Augustinian mutability-immutability contrast and the Thomistic potency-act contrast could only be a very rough one... (shrink)

We investigate the complexity of various combinatorial theorems about linear and partial orders, from the points of view of computability theory and reverse mathematics. We focus in particular on the principles ADS (Ascending or Descending Sequence), which states that every infinite linear order has either an infinite descending sequence or an infinite ascending sequence, and CAC (Chain-AntiChain), which states that every infinite partial order has either an infinite chain or an infinite antichain. It is well-known that Ramsey's Theorem for pairs (...) (RT₂²) splits into a stable version (SRT₂²) and a cohesive principle (COH). We show that the same is true of ADS and CAC, and that in their cases the stable versions are strictly weaker than the full ones (which is not known to be the case for RT₂² and SRT₂²). We also analyze the relationships between these principles and other systems and principles previously studied by reverse mathematics, such as WKL₀, DNR, and BΣ₂. We show, for instance, that WKL₀ is incomparable with all of the systems we study. We also prove computability-theoretic and conservation results for them. Among these results are a strengthening of the fact, proved by Cholak, Jockusch, and Slaman, that COH is Π₁¹-conservative over the base system RCA₀. We also prove that CAC does not imply DNR which, combined with a recent result of Hirschfeldt, Jockusch, Kjos-Hanssen, Lempp, and Slaman, shows that CAC does not imply SRT₂² (and so does not imply RT₂²). This answers a question of Cholak, Jockusch, and Slaman. Our proofs suggest that the essential distinction between ADS and CAC on the one hand and RT₂² on the other is that the colorings needed for our analysis are in some way transitive. We formalize this intuition as the notions of transitive and semitransitive colorings and show that the existence of homogeneous sets for such colorings is equivalent to ADS and CAC, respectively. We finish with several open questions. (shrink)

Formal systems are standardly envisaged in terms of a grammar specifying well-formed formulae together with a set of axioms and rules. Derivations are ordered lists of formulae each of which is either an axiom or is generated from earlier items on the list by means of the rules of the system; the theorems of a formal system are simply those formulae for which there are derivations. Here we outline a set of alternative and explicitly visual ways of envisaging and analyzing (...) at least simple formal systems using fractal patterns of infinite depth. Progressively deeper dimensions of such a fractal can be used to map increasingly complex wffs or increasingly complex 'value spaces', with tautologies, contradictions, and various forms of contingency coded in terms of color. This and related approaches, it turns out, offer not only visually immediate and geometrically intriguing representations of formal systems as a whole but also promising formal links (1) between standard systems and classical patterns in fractal geometry, (2) between quite different kinds of value spaces in classical and infinite-valued logics, and (3) between cellular automata and logic. It is hoped that pattern analysis of this kind may open possibilities for a geometrical approach to further questions within logic and metalogic. (shrink)

The relationship between animal ownership and owners' health has received increasing attention in the recent human-companion animal literature. This article considers a new aspect of the human-companion animal relationship, that of compatibility between pet and owner. Compatibility is viewed as the fit between the animal and the owner on physical, behavioral, and psychological dimensions. A postal survey was used to test the hypothesis that compatibility has influences on physical and mental health that are independent of those due to owners' level (...) ofpet attachment and human social support. A sample group of 176 pet owners completed a questionnaire containing a new measure of compatibility as well as standard measures of pet attachment, human social support, and mental and physical health. Results of multiple regression analyses indicated that people who are relatively more compatible with their pets report better mental health overall and fewer physical symptoms. Social support was positively associated with mental health. Pet attachment was also positively associated with mental health, but negatively with physical health. (shrink)

We give some new examples of possible degree spectra of invariant relations on Δ 0 2 -categorical computable structures, which demonstrate that such spectra can be fairly complicated. On the other hand, we show that there are nontrivial restrictions on the sets of degrees that can be realized as degree spectra of such relations. In particular, we give a sufficient condition for a relation to have infinite degree spectrum that implies that every invariant computable relation on a Δ 0 2 (...) -categorical computable structure is either intrinsically computable or has infinite degree spectrum. This condition also allows us to use the proof of a result of Moses [23] to establish the same result for computable relations on computable linear orderings. We also place our results in the context of the study of what types of degree-theoretic constructions can be carried out within the degree spectrum of a relation on a computable structure, given some restrictions on the relation or the structure. From this point of view we consider the cases of Δ 0 2 -categorical structures, linear orderings, and 1-decidable structures, in the last case using the proof of a result of Ash and Nerode [3] to extend results of Harizanov [14]. (shrink)

Whenever a structure with a particularly interesting computability-theoretic property is found, it is natural to ask whether similar examples can be found within well-known classes of algebraic structures, such as groups, rings, lattices, and so forth. One way to give positive answers to this question is to adapt the original proof to the new setting. However, this can be an unnecessary duplication of effort, and lacks generality. Another method is to code the original structure into a structure in the given (...) class in a way that is effective enough to preserve the property in which we are interested. In this paper, we show how to transfer a number of computability-theoretic properties from directed graphs to structures in the following classes: symmetric, irreflexive graphs; partial orderings; lattices; rings ; integral domains of arbitrary characteristic; commutative semigroups; and 2-step nilpotent groups. This allows us to show that several theorems about degree spectra of relations on computable structures, nonpreservation of computable categoricity, and degree spectra of structures remain true when we restrict our attention to structures in any of the classes on this list. The codings we present are general enough to be viewed as establishing that the theories mentioned above are computably complete in the sense that, for a wide range of computability-theoretic nonstructure type properties, if there are any examples of structures with such properties then there are such examples that are models of each of these theories. (shrink)

There is a common misconception that our genomes - all unique, except for those in identical twins - have the upper hand in controlling our destiny. The latest genetic discoveries, however, do not support that view. Although genetic variation does influence differences in various human behaviours to a greater or lesser degree, most of the time this does not undermine our genuine free will. Genetic determinism comes into play only in various medical conditions, notably some psychiatric syndromes. Denis Alexander (...) here demonstrates that we are not slaves to our genes. He shows how a predisposition to behave in certain ways is influenced at a molecular level by particular genes. Yet a far greater influence on our behaviours is our world-views that lie beyond science - and that have an impact on how we think the latest genetic discoveries should, or should not, be applied. Written in an engaging style, Alexander's book offers tools for understanding and assessing the latest genetic discoveries critically. (shrink)

We build an א₁-categorical but not א₀-categorical theory whose only computably presentable model is the saturated one. As a tool, we introduce a notion related to limitwise monotonic functions.

This article represents comments arising from The Compatibility of Evolution and Design by Rope Kojonen (Palgrave Macmillan, 2021) concerning the role of chance and randomness in evolution (citations from this book are shown as page numbers in brackets). The various meanings of chance and randomness as used in descriptions of biological evolution are discussed and contrasted with their meanings in mathematics and metaphysics. The discussion relates to the role of contingency in evolution and to ideological and rhetorical extrapolations from biology (...) into philosophical world views. Overall it is concluded that evolution is not a chance process, except in the epistemic sense of “chance.” Theologically, this has implications for the idea that God creates through “a free evolutionary process” and may also influence our perspectives on divine action and intentionality in evolutionary history. (shrink)

Several notions of computability-theoretic reducibility between [Formula: see text] principles have been studied. This paper contributes to the program of analyzing the behavior of versions of Ramsey’s Theorem and related principles under these notions. Among other results, we show that for each [Formula: see text], there is an instance of RT[Formula: see text] all of whose solutions have PA degree over [Formula: see text] and use this to show that König’s Lemma lies strictly between RT[Formula: see text] and RT[Formula: see (...) text] under one of these notions. We also answer two questions raised by Dorais, Dzhafarov, Hirst, Mileti, and Shafer on comparing versions of Ramsey’s Theorem and of the Thin Set Theorem with the same exponent but different numbers of colors. Still on the topic of the effect of the number of colors on the computable aspects of Ramsey-theoretic properties, we show that for each [Formula: see text], there is an [Formula: see text]-coloring [Formula: see text] of [Formula: see text] such that every [Formula: see text]-coloring of [Formula: see text] has an infinite homogeneous set that does not compute any infinite homogeneous set for [Formula: see text], and connect this result with the notion of infinite information reducibility introduced by Dzhafarov and Igusa. Next, we introduce and study a new notion that provides a uniform version of the idea of implication with respect to [Formula: see text]-models of RCA0, and related notions that allow us to count how many applications of a principle [Formula: see text] are needed to reduce another principle to [Formula: see text]. Finally, we fill in a gap in the proof of Theorem 12.2 in Cholak, Jockusch, and Slaman. (shrink)

This study examines the socioeconomic and familial background of Irish Catholic priests born between 1867 and 1911. Previous research has hypothesized that lack of marriage opportunities may influence adoption of celibacy as part of a religious institution. The present study traced data from Irish seminary registries for 46 Catholic priests born in County Limerick, Ireland, using 1901 Irish Census returns and Land Valuation records. Priests were more likely to originate from landholding backgrounds, and with landholdings greater in size and wealth (...) than the local average. Priests were found to originate from families with more sons than the national average, but with similar numbers of daughters. These findings are discussed in relation to competition for resources and lineage survival strategies. (shrink)

For [Formula: see text], the coarse similarity class of A, denoted by [Formula: see text], is the set of all [Formula: see text] such that the symmetric difference of A and B has asymptotic density 0. There is a natural metric [Formula: see text] on the space [Formula: see text] of coarse similarity classes defined by letting [Formula: see text] be the upper density of the symmetric difference of A and B. We study the metric space of coarse similarity classes (...) under this metric, and show in particular that between any two distinct points in this space there are continuum many geodesic paths. We also study subspaces of the form [Formula: see text] where [Formula: see text] is closed under Turing equivalence, and show that there is a tight connection between topological properties of such a space and computability-theoretic properties of [Formula: see text]. We then define a distance between Turing degrees based on Hausdorff distance in the metric space [Formula: see text]. We adapt a proof of Monin to show that the Hausdorff distances between Turing degrees that occur are exactly 0, [Formula: see text], and 1, and study which of these values occur most frequently in the senses of Lebesgue measure and Baire category. We define a degree a to be attractive if the class of all degrees at distance [Formula: see text] from a has measure 1, and dispersive otherwise. In particular, we study the distribution of attractive and dispersive degrees. We also study some properties of the metric space of Turing degrees under this Hausdorff distance, in particular the question of which countable metric spaces are isometrically embeddable in it, giving a graph-theoretic sufficient condition for embeddability. Motivated by a couple of issues arising in the above work, we also study the computability-theoretic and reverse-mathematical aspects of a Ramsey-theoretic theorem due to Mycielski, which in particular implies that there is a perfect set whose elements are mutually 1-random, as well as a perfect set whose elements are mutually 1-generic. Finally, we study the completeness of [Formula: see text] from the perspectives of computability theory and reverse mathematics. (shrink)

Cholak, Goncharov, Khoussainov, and Shore [1] showed that for each k > 0 there is a computably categorical structure whose expansion by a constant has computable dimension k. We show that the same is true with k replaced by ω. Our proof uses a version of Goncharov's method of left and right operations.

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)

There has been increasing interest over the last few decades in the study of the effective content of Mathematics. One field whose effective content has been the subject of a large body of work, dating back at least to the early 1960s, is model theory. Several different notions of effectiveness of model-theoretic structures have been investigated. This communication is concerned withcomputablestructures, that is, structures with computable domains whose constants, functions, and relations are uniformly computable.In model theory, we identify isomorphic structures. (...) From the point of view of computable model theory, however, two isomorphic structures might be very different. For example, under the standard ordering of ω the success or relation is computable, but it is not hard to construct a computable linear ordering of type ω in which the successor relation is not computable. In fact, for every computably enumerable degree a, we can construct a computable linear ordering of type ω in which the successor relation has degree a. It is also possible to build two isomorphic computable groups, only one of which has a computable center, or two isomorphic Boolean algebras, only one of which has a computable set of atoms. Thus, for the purposes of computable model theory, studying structures up to isomorphism is not enough. (shrink)

A number of ways of taxonomizing human learning have been proposed. We examine the evidence for one such proposal, namely, that there exist independent explicit and implicit learning systems. This combines two further distinctions, between learning that takes place with versus without concurrent awareness, and between learning that involves the encoding of instances versus the induction of abstract rules or hypotheses. Implicit learning is assumed to involve unconscious rule learning. We examine the evidence for implicit learning derived from subliminal learning, (...) conditioning, artificial grammar learning, instrumental learning, and reaction times in sequence learning. We conclude that unconscious learning has not been satisfactorily established in any of these areas. The assumption that learning in some of these tasks is predominantly based on rule abstraction is questionable. When subjects cannot report the “implicitly learned” rules that govern stimulus selection, this is often because their knowledge consists of instances or fragments of the training stimuli rather than rules. In contrast to the distinction between conscious and unconscious learning, the distinction between instance and rule learning is a sound and meaningful way of taxonomizing human learning. We discuss various computational models of these two forms of learning. (shrink)

We show that for every computably enumerable degree a > 0 there is an intrinsically c.e. relation on the domain of a computable structure of computable dimension 2 whose degree spectrum is { 0 , a } , thus answering a question of Goncharov and Khoussainov 55–57). We also show that this theorem remains true with α -c.e. in place of c.e. for any α∈ω∪{ω} . A modification of the proof of this result similar to what was done in Hirschfeldt (...) shows that for any α∈ω∪{ω} and any α -c.e. degrees a 0 ,…, a n there is an intrinsically α -c.e. relation on the domain of a computable structure of computable dimension n+1 whose degree spectrum is { a 0 ,…, a n } . These results also hold for m-degree spectra of relations. (shrink)