Presenting the cultural and neuronal forces that power our distinctively human modes of awareness, the author proposes that the human mind is a hybrid product of interweaving a super-complex form of matter (the brain) with an invisible symbolic web (culture) to form a cognitive network. Reprint. 11,500 first printing.

This bold and brilliant book asks the ultimate question of the life sciences: How did the human mind acquire its incomparable power? In seeking the answer, Merlin Donald traces the evolution of human culture and cognition from primitive apes to the era of artificial intelligence, and presents an original theory of how the human mind evolved from its presymbolic form. In the emergence of modern human culture, Donald proposes, there were three radical transitions. During the first, our (...) bipedal but still apelike ancestors acquired "mimetic" skill—the ability to represent knowledge through voluntary motor acts—which made Homo erectus successful for over a million years. The second transition—to "mythic" culture —coincided with the development of spoken language. Speech allowed the large-brained Homo sapiens to evolve a complex preliterate culture that survives in many parts of the world today. In the third transition, when humans constructed elaborate symbolic systems ranging from cuneiforms, hieroglyphics, and ideograms to alphabetic languages and mathematics, human biological memory became an inadequate vehicle for storing and processing our collective knowledge. The modern mind is thus a hybrid structure built from vestiges of earlier biological stages as well as new external symbolic memory devices that have radically altered its organization. According to Donald, we are symbol-using creatures, more complex than any that went before us, and we may have not yet witnessed the final modular arrangement of the human mind. (shrink)

This book proposes a theory of human cognitive evolution, drawing from paleontology, linguistics, anthropology, cognitive science, and especially neuropsychology. The properties of humankind's brain, culture, and cognition have coevolved in a tight iterative loop; the main event in human evolution has occurred at the cognitive level, however, mediating change at the anatomical and cultural levels. During the past two million years humans have passed through three major cognitive transitions, each of which has left the human mind with a new way (...) of representing reality and a new form of culture. Modern humans consequently have three systems of memory representation that were not available to our closest primate relatives: mimetic skill, language, and external symbols. These three systems are supported by new types of “hard” storage devices, two of which (mimetic and linguistic) are biological, one technological. Full symbolic literacy consists of a complex of skills for interacting with the external memory system. The independence of these three uniquely human ways of representing knowledge is suggested in the way the mind breaks down after brain injury and confirmed by various other lines of evidence. Each of the three systems is based on aninventivecapacity, and the products of those capacities – such as languages, symbols, gestures, social rituals, and images – continue to be invented and vetted in the social arena. Cognitive evolution is not yet complete: the externalization of memory has altered the actual memory architecture within which humans think. This is changing the role of biological memory and the way in which the human brain deploys its resources; it is also changing the form of modern culture. (shrink)

Hominid-like morphology in habiline cranial endocasts does not necessarily imply the presence of language capacity. The cortical zone in question is not associated exclusively with language in humans, and its emergence in habilines might indicate the evolution of other cognitive functions special to humans that were preconditions for the later evolution of language.

Images of mindmarks a new era in human cognitive neuroscience. Despite the difficult conceptual problems associated with using group-averaged data and paired subtractions, human PET images converge well with existing data from other areas of cognitive neuroscience while opening up new theoretical and experimental possibilities. However, greater attention to individual differences might prove necessary in the study of culturally driven adaptations such as literacy.

One central tenet of the Modern Evolutionary Synthesis , and the consensus view among biologists until now, is that all genetic mutations occur by “chance” or at “random” with respect to adaptation. However, the discovery of some molecular mechanisms enhancing mutation rate in response to environmental conditions has given rise to discussions among biologists, historians and philosophers of biology about the “chance” vs “directed” character of mutations . In fact, some argue that mutations due to a particular kind of mutator (...) mechanisms challenge the Modern Synthesis because they are produced when and where needed by the organisms concerned. This paper provides a defense of the Modern Synthesis’ consensus view about the chance nature of all genetic mutations by reacting to Jablonka and Lamb’s analysis of genetic mutations and the explicit Lamarckian flavor of their arguments. I argue that biologists can continue to talk about chance mutations according to what I call and define as the notion of “evolutionary chance,” which I claim is the Modern Synthesis’ consensus view and a reformulation of Darwin’s most influential idea of “chance” variation. Advances in molecular genetics are therefore significant but not revolutionary with respect to the Modern Synthesis’ paradigm. (shrink)

Ordinal Computability discusses models of computation obtained by generalizing classical models, such as Turing machines or register machines, to transfinite working time and space. In particular, recognizability, randomness, and applications to other areas of mathematics, including set theory and model theory, are covered.

We consider the following problem for various infinite-time machines. If a real is computable relative to a large set of oracles such as a set of full measure or just of positive measure, a comeager set, or a nonmeager Borel set, is it already computable? We show that the answer is independent of ZFC for ordinal Turing machines with and without ordinal parameters and give a positive answer for most other machines. For instance, we consider infinite-time Turing machines, unresetting and (...) resetting infinite-time register machines, and α-Turing machines for countable admissible ordinals α. (shrink)

The frame concept from linguistics, cognitive science and artificial intelligence is a theoretical tool to model how explicitly given information is combined with expectations deriving from background knowledge. In this paper, we show how the frame concept can be fruitfully applied to analyze the notion of mathematical understanding. Our analysis additionally integrates insights from the hermeneutic tradition of philosophy as well as Schmid’s ideal genetic model of narrative constitution. We illustrate the practical applicability of our theoretical analysis through a case (...) study on extremal proofs. Based on this case study, we compare our analysis of proof understanding to Avigad’s ability-based analysis of proof understanding. (shrink)

This study contains a critical edition of Ibn al-Jawzī’s Kitāb Akhbār as-Sifāt along with an annotated translation and introduction. KAS is primarily a critique of anthropomorphic conceptions of God, directed against fellow Hanbalis and traditionalists generally. It sheds important new light on the intellectual fault-lines within medieval Hanbalism, and reveals the extent to which kalām had penetrated the school by the 12th century.

Infinite Time Register Machines are a well-established machine model for infinitary computations. Their computational strength relative to oracles is understood, see e.g. , and . We consider the notion of recognizability, which was first formulated for Infinite Time Turing Machines in [6] and applied to ITRM 's in [3]. A real x is ITRM -recognizable iff there is an ITRM -program P such that PyPy stops with output 1 iff y=xy=x, and otherwise stops with output 0. In [3], it is (...) shown that the recognizable reals are not contained in the ITRM -computable reals. Here, we investigate in detail how the ITRM -recognizable reals are distributed along the canonical well-ordering shrink)

Deep brain stimulation as investigational intervention for symptomatic relief from Alzheimer disease has generated big expectations. Our aim is to discuss the ethical justification of this research agenda by examining the underlying research rationale as well as potential methodological pitfalls. The shortcomings we address are of high ethical importance because only scientifically valid research has the potential to be ethical. We performed a systematic search on MEDLINE and EMBASE. We included 166 publications about DBS for AD into the analysis of (...) research rationale, risks and ethical aspects. Fifty-eight patients were reported in peer-reviewed journals with very mixed results. A grey literature search revealed hints for 75 yet to be published, potentially enrolled patients. The results of our systematic review indicate methodological shortcomings in the literature that are both scientific and ethical in nature. According to our analysis, research with human subjects was performed before decisive preclinical research was published examining the specific research question at stake. We also raise the concern that conclusions on the potential safety and efficacy have been reported in the literature that seem premature given the design of the feasibility studies from which they were drawn. In addition, some publications report that DBS for AD was performed without written informed consent from some patients, but from surrogates only. Furthermore, registered ongoing trials plan to enroll severely demented patients. We provide reasons that this would violate Art. 28 of the Declaration of Helsinki, because DBS for AD involves more than minimal risks and burdens, and because its efficacy and safety are not yet empirically established to be likely. Based on our empirical analysis, we argue that clinical research on interventions of risk class III should not be exploratory but grounded on sound, preclinically tested, and disease-specific a posteriori hypotheses. This also applies to DBS for dementia as long as therapeutic benefits are uncertain, and especially when research subjects with cognitive deficits are involved, who may foreseeably progress to full incapacity to provide informed consent during the required follow-up period. (shrink)

The work done so far on the understanding of mathematical (proof) texts focuses mostly on logical and heuristical aspects; a proof text is considered to be understood when the reader is able to justify inferential steps occurring in it, to defend it against objections, to give an account of the “main ideas”, to transfer the proof idea to other contexts etc. (see, e.g., Avigad in The philosophy of mathematical practice, Oxford University Press, Oxford, 2008). In contrast, there is a rich (...) philosophical tradition dealing with the concept of understanding and interpreting texts, namely philosophical hermeneutics, represented, e.g., by Schleiermacher, Dilthey, Heidegger or Gadamer. In this tradition, “understanding” generally refers to the integration in a comprehensive (historical, existential, life-worldly,...) context. In this article, we take some first steps towards exploring the question how the ideas from philosophical hermeneutics presented in Gadamer’s “Truth and Method” apply to mathematical texts and what (if anything) can be learned from these for the didactics and presentation of mathematics. (shrink)

Infinite time register machines (ITRMs) are register machines which act on natural numbers and which are allowed to run for arbitrarily many ordinal steps. Successor steps are determined by standard register machine commands. At limit times register contents are defined by appropriate limit operations. In this paper, we examine the ITRMs introduced by the third and fourth author (Koepke and Miller in Logic and Theory of Algorithms LNCS, pp. 306–315, 2008), where a register content at a limit time is set (...) to the lim inf of previous register contents if that limit is finite; otherwise the register is reset to 0. The theory of these machines has several similarities to the infinite time Turing machines (ITTMs) of Hamkins and Lewis. The machines can decide all ${\Pi^1_1}$ sets, yet are strictly weaker than ITTMs. As in the ITTM situation, we introduce a notion of ITRM-clockable ordinals corresponding to the running times of computations. These form a transitive initial segment of the ordinals. Furthermore we prove a Lost Melody theorem: there is a real r such that there is a program P that halts on the empty input for all oracle contents and outputs 1 iff the oracle number is r, but no program can decide for every natural number n whether or not ${n \in r}$ with the empty oracle. In an earlier paper, the third author considered another type of machines where registers were not reset at infinite lim inf’s and he called them infinite time register machines. Because the resetting machines correspond much better to ITTMs we hold that in future the resetting register machines should be called ITRMs. (shrink)

What is the relation between a reason and an action when the reason explains the action by giving the agent's reason for doing what he did? We may call such explanations rationalizations, and say that the reason rationalizes the action. In this paper I want to defend the ancient - and common-sense - position that rationalization is a species of ordinary causal explanation. The defense no doubt requires some redeployment, but not more or less complete abandonment of the position, as (...) urged by many recent writers. (shrink)

In this section, we apply the notions obtained above to a famous historical example of a false proof. Our goal is to demonstrate that this proof shows a sufficient degree of distinctiveness for a formalization in a Naproche-like system and hence that automatic checking could indeed have contributed in this case to the development of mathematics. This example further demonstrates that even incomplete distinctivication can be sufficient for automatic checking and that actual mistakes may occur already in the margin between (...) the degree of distinctiveness necessary for formalization and complete distinctiveness. (shrink)

Cantor argued that absolute infinity is beyond mathematical comprehension. His arguments imply that the domain of mathematics cannot be grasped by mathematical means. We argue that this inability constitutes a foundational problem. For Cantor, however, the domain of mathematics does not belong to mathematics, but to theology. We thus discuss the theological significance of Cantor’s treatment of absolute infinity and show that it can be interpreted in terms of negative theology. Proceeding from this interpretation, we refer to the recent debate (...) on absolute generality and argue that the method of diagonalization constitutes a modern version of the vianegativa. On our reading, negative theology can evoke an attitude of humility with respect to the boundedness of the human condition. Along these lines, we think that the foundational problem of mathematics concerning its domain can be addressed through a methodological attitude of humility. (shrink)

Ayn Rand's use of “selfishness” and “altruism” was polarizing and contrary to common usage. With the help of Venn diagrams, this essay compares and even reconciles the divergent meanings of egoism and altruism. It cites Rand's usage of “traditional egoism,” a term she used in correspondence but in none of her books or periodicals. This term helps to understand Rand's meaning of egoism. It also comments on earlier essays in this periodical about egoism.

Recently, the term ‘aphantasia’ has become current in scientific and public discourse to denote the absence of mental imagery. However, new terms for aphantasia or its subgroups have recently been proposed, e.g. ‘dysikonesia’ or ‘anauralia’, which complicates the literature, research communication and understanding for the general public. Before further terms emerge, we advocate the consistent use of the term ‘aphantasia’ as it can be used flexibly and precisely, and is already widely known in the scientific community and among the general (...) public. (shrink)

The problem with authenticity—the idea of being “true to one’s self”—is that its somewhat checkered reputation garners a complete range of favorable and unfavorable reactions. In educational settings, authenticity is lauded as one of the top two traits students desire in their teachers. Yet, authenticity is criticized for its tendency towards narcissism and self-entitlement. So, is authenticity a good or a bad thing? The purpose of this article is to develop an intimate understanding of authenticity by investigating its current interpretation (...) and criticisms, its struggle with narcissism and relation to freedom. Examining authenticity as multilayered self-exploration reveals a composite of understanding, care, and acceptance. While a side current of acceptable tension shifts our understanding of authenticity from the security of self-determination to the messy interplay involved in being “true to one’s self” and being “in-the-world”. (shrink)

The acquisition of English noun and verb morphology is modeled using a single-system connectionist network. The network is trained to produce the plurals and past tense forms of a large corpus of monosyllabic English nouns and verbs. The developmental trajectory of network performance is analyzed in detail and is shown to mimic a number of important features of the acquisition of English noun and verb morphology in young children. These include an initial error-free period of performance on both nouns and (...) verbs followed by a period of intermittent over-regularization of irregular nouns and verbs. Errors in the model show evidence of phonological conditioning and frequency effects. Furthermore, the network demonstrates a strong tendency to regularize denominal verbs and deverbal nouns and masters the principles of voicing assimilation. Despite their incorporation into a single-system network, nouns and verbs exhibit some important differences in their profiles of acquisition. Most importantly, noun inflections are acquired earlier than verb inflections. The simulations generate several empirical predictions that can be used to evaluate further the suitability of this type of cognitive architecture in the domain of inflectional morphology. (shrink)