We present a model of computation for string functions over single-sorted, total algebraic structures and study some basic features of a general theory of computability within this framework. Our concept generalizes the Blum-Shub-Smale setting of computability over the reals and other rings. By dealing with strings of arbitrary length instead of tuples of fixed length, some suppositions of deeper results within former approaches to generalized recursion theory become superfluous. Moreover, this gives the basis for introducing computational complexity in a (...) BSS-like manner. Relationships both to classical computability and to Friedman's concept of eds computability are established. Two kinds of nondeterminism as well as several variants of recognizability are investigated with respect to interdependencies on each other and on properties of the underlying structures. For structures of finite signatures, there are universal programs with the usual characteristics. For the general case of not necessarily finite signature, this subject will be studied in a separate, forthcoming paper. (shrink)

Functional explanation in the social sciences is the focal point for conflict between individualistic and social modes of explanation. While the agent thought she was acting for reasons, the functional explanation seems to reveal the hidden strings of the puppet master. This essay argues that the conflict is merely apparent. The erotetic model of explanation is used to analyze the forms of intentional action and functional explanations. Two explanations conflict if either the presuppositions of their respective why-questions conflict or the (...) typical answers identified by their relevance criteria conflict. While a functional explanation may have the same topic and foil as an intentional action explanation, both the why-questions and their typical answers are compatible. (shrink)

I argue that neural activity, strictly speaking, is not computation. This is because computation, strictly speaking, is the processing of strings of symbols, and neuroscience shows that there are no neural strings of symbols. This has two consequences. On the one hand, the following widely held consequences of computationalism must either be abandoned or supported on grounds independent of computationalism: (i) that in principle we can capture what is functionally relevant to neural processes in terms of some formalism taken from (...) computability theory (such as Turing Machines), (ii) that it is possible to design computer programs that are functionally equivalent to neural processes in the same sense in which it is possible to design computer programs that are functionally equivalent to each other, (iii) that the study of neural (or mental) computation is independent of the study of neural implementation, (iv) that the Church-Turing thesis applies to neural activity in the sense in which it applies to digital computers. On the other hand, we need to gradually reinterpret or replace computational theories in psychology in terms of theoretical constructs that can be realized by known neural processes, such as the spike trains of neuronal ensembles. (shrink)

Multidisciplinary studies have led to the discovery and characterization of cysteine string proteins (csps) in both Drosophila and Torpedo. Phenotypic analysis of csp mutants in Drosophila demonstrates a crucial role for csp in synaptic transmission. Expression studies of Torpedo csp (Tcsp) in Xenopus oocytes suggests that the protein has some role in the function of presynaptic Ca2+ channels. However, biochemical purification of Tcsp indicates that is associated with synaptic vesicles rather than with the plasma membrane of presynaptic terminals (...) where Ca2+ channels reside. These results suggest a model in which csps serve as a link by which docked synaptic vesicles could modulate the activity of presynaptic Ca2+ channels. (shrink)

It has been recently argued that some machine learning techniques known as Kernel methods could be relevant for capturing cognitive and neural mechanisms (Jäkel, Schölkopf, & Wichmann, 2009). We point out that ‘‘String kernels,’’ initially designed for protein function prediction and spam detection, are virtually identical to one contending proposal for how the brain encodes orthographic information during reading. We suggest some reasons for this connection and we derive new ideas for visual word recognition that are successfully put (...) to the test. We argue that the versatility and performance of String kernels makes a compelling case for their implementation in the brain. (shrink)

Coordinate formalism on Hilbert manifolds developed in \cite{Kryukov}, \cite{Kryukov1} is further analyzed. The main subject here is a comparison of the ordinary and the string bases of eigenvectors of a linear operator as introduced in \cite{Kryukov}. It is shown that the string basis of eigenvectors is a natural generalization of its classical counterpart. It is also shown that the developed formalism forces us to consider any Hermitian operator with continuous spectrum as a restriction to a space of square (...) integrable functions of a self-adjoint operator defined on a space of generalized functions. In the formalism functional coordinate transformations preserving the norm of strings are now linear isometries rather than the unitary transformations. (shrink)

There is a long history of cryptographic hash functions, i.e. functions mapping variable-length strings to fixed-length strings, and such functions are also expected to enjoy certain security properties. Hash functions can be effected via modular arithmetic, permutation-based schemes, chaotic mixing, and so on. Herein we introduce the notion of an artificial-life (ALife) hash function (ALHF), whereby the requisite mixing action of a good hash function is accomplished via ALife rules that give rise to complex evolution of a given (...) system. Various security tests have been run, and the results reported for examples of ALHFs. (shrink)

This paper offers an account of what it is for a physical system to be a computing mechanism—a mechanism that performs computations. A computing mechanism is any mechanism whose functional analysis ascribes it the function of generating outputs strings from input strings in accordance with a general rule that applies to all strings. This account is motivated by reasons that are endogenous to the philosophy of computing, but it may also be seen as an application of recent literature on (...) mechanisms. The account can be used to individuate computing mechanisms and the functions they compute and to taxonomize computing mechanisms based on their computing power. This makes it ideal for grounding the comparison and assessment of computational theories of mind and brain. (shrink)

Inspired from a joint work by A. Beckmann, S. Buss and S. Friedman, we propose a class of set-theoretic functions, predicatively computable set functions. Each function in this class is polynomial time computable when we restrict to finite binary strings.

A recursive enumerator for a function h is an algorithm f which enumerates for an input x finitely many elements including h(x), f is a k(n)-enumerator if for every input x of length n, h(x) is among the first k(n) elements enumerated by f. If there is a k(n)-enumerator for h then h is called k(n)-enumerable. We also consider enumerators which are only A-recursive for some oracle A. We determine exactly how hard it is to enumerate the Kolmogorov (...) class='Hi'>function, which assigns to each string x its Kolmogorov complexity: • For every underlying universal machine U, there is a constant a such that C is k(n)-enumerable only if k(n) ≥ n/a for almost all n. • For any given constant k, the Kolmogorov function is k-enumerable relative to an oracle A if and only if A is at least as hard as the halting problem. • There exists an r.e., Turing-incomplete set A such for every non-decreasing and unbounded recursive function k, the Kolmogorov function is k(n)-enumerable relative to A. The last result is obtained by using a relativizable construction for a nonrecursive set A relative to which the prefix-free Kolmogorov complexity differs only by a constant from the unrelativized prefix-free Kolmogorov complexity. Although every 2-enumerator for C is Turing hard for K, we show that reductions must depend on the specific choice of the 2-enumerator and there is no bound on the quantity of their queries. We show our negative results even for strong 2-enumerators as an oracle where the querying machine for any x gets directly an explicit list of all hypotheses of the enumerator for this input. The limitations are very general and we show them for any recursively bounded function g: • For every Turing reduction M and every non-recursive set B, there is a strong 2-enumerator f for g such that M does not Turing reduce B to f. • For every non-recursive set B, there is a strong 2-enumerator f for g such that B is not wtt-reducible to f. Furthermore, we deal with the resource-bounded case and give characterizations for the class ${\rm S}_{2}^{{\rm P}}$ introduced by Canetti and independently Russell and Sundaram and the classes PSPACE, EXP. • ${\rm S}_{2}^{{\rm P}}$ is the class of all sets A for which there is a polynomially bounded function g such that there is a polynomial time tt-reduction which reduces A to every strong 2-enumerator for g. • PSPACE is the class of all sets A for which there is a polynomially bounded function g such that there is a polynomial time Turing reduction which reduces A to every strong 2-enumerator for g. Interestingly, g can be taken to be the Kolmogorov function for the conditional space bounded Kolmogorov complexity. • EXP is the class of all sets A for which there is a polynomially bounded function g and a machine M which witnesses A ∈ PSPACEf for all strong 2-enumerators f for g. Finally, we show that any strong O(log n)-enumerator for the conditional space bounded Kolmogorov function must be PSPACE-hard if P = NP. (shrink)

We consider total well-founded orderings on monadic terms satisfying the replacement and full invariance properties. We show that any such ordering on monadic terms in one variable and two unary function symbols must have order typeω,ω2orωω. We show that a familiar construction gives rise to continuum many such orderings of order typeω. We construct a new family of such orderings of order typeω2, and show that there are continuum many of these. We show that there are only four such (...) orderings of order typeωω, the two familiar recursive path orderings and two closely related orderings. We consider also total well-founded orderings onNnwhich are preserved under vector addition. We show that any such ordering must have order typeωkfor some 1 ≤k≤n. We show that ifkshrink)

We consider total well-founded orderings on monadic terms satisfying the replacement and full invariance properties. We show that any such ordering on monadic terms in one variable and two unary function symbols must have order type $\omega, \omega^2$ or $\omega^\omega$. We show that a familiar construction gives rise to continuum many such orderings of order type $\omega$. We construct a new family of such orderings of order type $\omega^2$, and show that there are continuum many of these. We show (...) that there are only four such orderings of order type $\omega^\omega$, the two familiar recursive path orderings and two closely related orderings. We consider also total well-founded orderings on $\mathbf{N}^n$ which are preserved under vector addition. We show that any such ordering must have order type $\omega^k$ for some $1 \leq k \leq n$. We show that if $k < n$ there are continuum many such orderings, and if $k = n$ there are only $n$!, the $n$! lexicographic orderings. (shrink)

Winner, 2020 Body and Embodiment Best Publication Award, given by the American Sociological Association Honorable Mention, 2020 Sociology of Sex and Gender Distinguished Book Award, given by the American Sociological Association How the female body has been racialized for over two hundred years There is an obesity epidemic in this country and poor Black women are particularly stigmatized as “diseased” and a burden on the public health care system. This is only the most recent incarnation of the fear of fat (...) Black women, which Sabrina Strings shows took root more than two hundred years ago. Strings weaves together an eye-opening historical narrative ranging from the Renaissance to the current moment, analyzing important works of art, newspaper and magazine articles, and scientific literature and medical journals—where fat bodies were once praised—showing that fat phobia, as it relates to Black women, did not originate with medical findings, but with the Enlightenment era belief that fatness was evidence of “savagery” and racial inferiority. The author argues that the contemporary ideal of slenderness is, at its very core, racialized and racist. Indeed, it was not until the early twentieth century, when racialized attitudes against fatness were already entrenched in the culture, that the medical establishment began its crusade against obesity. An important and original work, Fearing the Black Body argues convincingly that fat phobia isn’t about health at all, but rather a means of using the body to validate race, class, and gender prejudice. (shrink)

In modern physics, various fundamental problems have become topics of debate. There was the 20th century climb to a Standard Model, still accurate at the highest energy levels obtainable so far. But, since the 1970's, a different approach to physics advocates for theories such as string theory, known for their mathematical elegance, even though they either cannot be verified in data or contradict presently known experimental results. In philosophy of physics, there is a gradually emerging consensus that philosophy of (...) physics and physics somehow contribute to a common enterprise. But, there is little sign of progress toward consensus about the nature of that unity. All the while, it is generally recognized that physics is interdisciplinary. There are, of course, differences in focus. But, implicitly at least, there are no "sharp dividing lines" between physics and philosophy of physics; pure and applied physics; physical chemistry; biophysics; medical physics; history and philosophy of physics; physics and society; physics education; and so on. What, then, is progress in physics? The question here is not about ideal structures, but asks about what is going on in physics. Beginnings in discerning the presence of eight main tasks help reveal the (pre-) emergence of a normative omni-disciplinary basis for collaboration that, once adverted to, promises to be constitutive of a new and increasingly effective control of meaning. Originally discovered by Bernard Lonergan in 1965, progress in the new collaboration will not seek to eliminate specialized expertise. It will, though, divide tasks within an eightfold functional division of labor. This book invites attention to data for each of the eight main tasks evident and self-evident in existing scholarship in the community. (shrink)

In this note we consider register-machines with symbol manipulation capabilities. They can form words over a given alphabet in their registers by appending symbols to the strings already stored. These machines are similar to Post's normal systems and the related machine-models discussed in the literature. But unlike the latter devices they are deterministic and are not allowed to read symbols from the front of the registers. Instead they can compare registers and erase them. At first glance it is surprising that (...) in general these devices are as powerful as the seemingly stronger models. Here we investigate the borderline of universality for these machines. (shrink)

Let g be a map defined as the Nisan–Wigderson generator but based on an NP ∩ coNP -function f. Any string b outside the range of g determines a propositional tautology τb expressing this fact. Razborov [27] has conjectured that if f is hard on average for P/poly then these tautologies have no polynomial size proofs in the Extended Frege system EF. We consider a more general Statement that the tautologies have no polynomial size proofs in any propositional (...) proof system. This is equivalent to the statement that the complement of the range of g contains no infinite NP set. We prove that Statement is consistent with Cook' s theory PV and, in fact, with the true universal theory T PV in the language of PV. If PV in this consistency statement could be extended to "a bit" stronger theory then Razborov's conjecture would follow, and if TPV could be added too then Statement would follow. We discuss this problem in some detail, pointing out a certain form of reflection principle for propositional logic, and we introduce a related feasible disjunction property of proof systems. (shrink)

In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a variable that depends in an arbitrary manner on another variable. The change was required when mathematicians discovered that analytic expressions were not sufficient to represent physical phenomena such as the vibration of (...) a string and heat conduction. The introduction of generalized functions or distributions is shown to stem partly from the development of new theories of physics such as electrical engineering and quantum mechanics that led to the use of improper functions such as the delta function that demanded a proper foundation. We argue that the development of student understanding of mathematics and its nature is enhanced by embedding mathematical concepts and theories, within an explicit–reflective framework, into a rich historical context emphasizing its interaction with other disciplines such as physics. Students recognize and become engaged with meta-discursive rules governing mathematics. Mathematics teachers can thereby teach inquiry in mathematics as it occurs in the sciences, as mathematical practice aimed at obtaining new mathematical knowledge. We illustrate such a historical teaching and learning of mathematics within an explicit and reflective framework by two examples of student-directed, problem-oriented project work following the Roskilde Model, in which the connection to physics is explicit and provides a learning space where the nature of mathematics and mathematical practices are linked to natural science. (shrink)

Church's Thesis asserts that the only numeric functions that can be calculated by effective means are the recursive ones, which are the same, extensionally, as the Turing-computable numeric functions. The Abstract State Machine Theorem states that every classical algorithm is behaviorally equivalent to an abstract state machine. This theorem presupposes three natural postulates about algorithmic computation. Here, we show that augmenting those postulates with an additional requirement regarding basic operations gives a natural axiomatization of computability and a proof of Church's (...) Thesis, as Gödel and others suggested may be possible. In a similar way, but with a different set of basic operations, one can prove Turing's Thesis, characterizing the effective string functions, and--in particular--the effectively-computable functions on string representations of numbers. (shrink)

Recently, G. ASSER has obtained two interesting characterizations of the class of unary primitive recursive string-functions over a fixed alphabet as Robinson algebras. Both characterizations use a somewhat artificial string-function, namely the string-function lexicographically associated with the number-theoretical excess-over-a-square function. Our aim is to offer two new and natural Robinson algebras which are equivalent to ASSER’S algebras.

The standard formulation of quantum gauge theories results from the Lagrangian (functional integral) quantization of classical gauge theories. A more intrinsic quantum theoretical access in the spirit of Wigner’s representation theory shows that there is a fundamental clash between the pointlike localization of zero mass (vector, tensor) potentials and the Hilbert space (positivity, unitarity) structure of QT. The quantization approach has no other way than to stay with pointlike localization and sacrifice the Hilbert space whereas the approach built on the (...) intrinsic quantum concept of modular localization keeps the Hilbert space and trades the conflict creating pointlike generation with the tightest consistent localization: semiinfinite spacelike string localization. Whereas these potentials in the presence of interactions stay quite close to associated pointlike field strengths, the interacting matter fields to which they are coupled bear the brunt of the nonlocal aspect in that they are string-generated in a way which cannot be undone by any differentiation.The new stringlike approach to gauge theory also revives the idea of a Schwinger-Higgs screening mechanism as a deeper and less metaphoric description of the Higgs spontaneous symmetry breaking and its accompanying tale about “God’s particle” and its mass generation for all the other particles. (shrink)

The crossing property is perhaps the most subtle aspect of the particle-field relation. Although it is not difficult to state its content in terms of certain analytic properties relating different matrixelements of the S-matrix or formfactors, its relation to the localization- and positive energy spectral principles requires a level of insight into the inner workings of QFT which goes beyond anything which can be found in typical textbooks on QFT. This paper presents a recent account based on new ideas derived (...) from “modular localization” including a mathematic appendix on this subject. Its main achievement is the proof of the crossing property from a two-algebra generalization of the KMS condition.The main content is an in-depth criticism of the dual model and its string theoretic extension. The conceptual flaws of these models are closely related to misunderstandings of crossing. The correct interpretation of string theory is that of a dynamic infinite component one particle space where “dynamic” means that, unlike a mere collection of independent free fields, the formalism contains also operators which communicate between the different irreducible Poincaré representations and set the mass/spin spectrum. Whereas in pre-string times there were unsuccessful attempts to achieve this in analogy to the O(4,2) hydrogen spectrum by the use of higher noncompact groups, the superstring in d=9+1, which uses instead (bosonic/fermionic) oscillators obtained from multicomponent chiral currents, is the only known solution of the dynamical infinite component pointlike field (or pointlike generated wave function) project. (shrink)

This article addresses the question of the mechanisms of the emergence of structure and meaning in the biological and physical sciences. It proceeds from an examination of the concept of intentionality and proposes a model of intentional behavior on the basis of results of computer simulations of structural and functional self-organization. Current attempts to endow intuitive aspects of meaningful complexity with operational content are analyzed and the metaphor of DNA as a computer program (the `genetic program') is critically examined in (...) relation to an alternative metaphor of DNA as data. It is argued that relatively simple networks of boolean automata can classify and recognize patterns of binary strings on the basis of non-programmed, self-generated criteria, but lack a capacity for self-observation and interpretation. To overcome this problem it is necessary to clarify the relationships between the goals and underlying mechanisms of a process and between a system and its environment. It will be shown that memory devices that record the histories of interactions are essential for models of conscious and unconscious intentional behavior and that the possibility of infinitely sophisticated - and therefore unprogrammable - machines cannot be avoided. It will be argued that the notion of infinite sophistication allows the ideas of self-organization and physical determinism to be reconciled. These models will be used to suggest how the voluntary aspect of decision-making in general can emerge out of functional self-organizing processes. The conclusion will introduce the notion of `underdetermination' of theories, which imposes an intrinsic limitation on models of complex natural systems - a limitation that, at the same time, may be precisely what makes possible mutual understanding and intersubjectivity. (shrink)

We extend Meyer's 1972 investigation of sets of minimal indices. Blum showed that minimal index sets are immune, and we show that they are also immune against high levels of the arithmetic hierarchy. We give optimal immunity results for sets of minimal indices with respect to the arithmetic hierarchy, and we illustrate with an intuitive example that immunity is not simply a refinement of arithmetic complexity. Of particular note here are the fact that there are three minimal index sets located (...) in Π3 − Σ3 with distinct levels of immunity and that certain immunity properties depend on the choice of underlying acceptable numbering. We show that minimal index sets are never hyperimmune; however, they can be immune against the arithmetic sets. Lastly, we investigate Turing degrees for sets of random strings defined with respect to Bagchi's size-function s. (shrink)

In “Function and Concept” and “On Concept and Object”, Frege argued that certain differences between dependent and independent meanings were inviolable and “founded deep in the nature of things” but, in those articles, he was not explicit about the actual consequences of violating such differences. However, since by creating a law that permitted one to pass from a concept to its extension, he himself mixed dependent and independent meanings, we are in a position to study some of the actual (...) consequences of his having done so. To make certain of Frege’s ideas about the inviolability of logical form more tangible, I describe a string of very interrelated consequences that his attempt to transform dependent meanings into independent meanings actually brought in its wake. (shrink)

In the present study, using event-related functional magnetic resonance imaging, we investigated a group of participants on a grammaticality classification task after they had been exposed to well-formed consonant strings generated from an artificial regular grammar. We used an implicit acquisition paradigm in which the participants were exposed to positive examples. The objective of this studywas to investigate whether brain regions related to language processing overlap with the brain regions activated by the grammaticality classification task used in the present study. (...) Recent meta-analyses of functional neuroimaging studies indicate that syntactic processing is related to the left inferior frontal gyrus (Brodmann's areas 44 and 45) or Broca's region. In the present study, we observed that artificial grammaticality violations activated Broca's region in all participants. This observation lends some support to the suggestions that artificial grammar learning represents a model for investigating aspects of language learning in infants [TICS 4 (2000) 178] and adults [Proceedings of the National Academy of Sciences of United States of America 99 (2002) 529]. (shrink)

In the present study, using event-related functional magnetic resonance imaging, we investigated a group of participants on a grammaticality classification task after they had been exposed to well-formed consonant strings generated from an artificial regular grammar. We used an implicit acquisition paradigm in which the participants were exposed to positive examples. The objective of this studywas to investigate whether brain regions related to language processing overlap with the brain regions activated by the grammaticality classification task used in the present study. (...) Recent meta-analyses of functional neuroimaging studies indicate that syntactic processing is related to the left inferior frontal gyrus (Brodmann's areas 44 and 45) or Broca's region. In the present study, we observed that artificial grammaticality violations activated Broca's region in all participants. This observation lends some support to the suggestions that artificial grammar learning represents a model for investigating aspects of language learning in infants [TICS 4 (2000) 178] and adults [Proceedings of the National Academy of Sciences of United States of America 99 (2002) 529]. (shrink)

Novel functions, which emerge by reusing existing resources formerly adapted to other original usages, cannot be anticipated before the need eventually arises. Simple reuse must be accidental. However, to survive the evolutionary race, one cannot merely keep hoping for a string of good fortune. So, successful species might be gifted with and biological mechanisms to prepare for future reuse. Neural reuse must be extrapolated from such mechanisms.

The sequential patterns of the sixty-four hexagrams in the Yijing, variously known as I Ching (the Book of Changes) are structured to embrace the universe of possibilities, scenarios and probabilities. Each hexagram equates to each moment in space-time. With the arrow of time, a string of hexagrams represent a string of moments. A probability curve can be formed from the string of hexagrams. Physicists call this mathematical entity a wave function which is constantly changing and proliferating. (...) A wave function is mathematical representation of all possibilities that can happen to an observed entity when it interacts with an observer. The form of the wave function can be calculated by the Schrodinger wave equation for any part of the range of moments. The string of hexagrams deal with probabilities. Physicists deal mainly with two wave forms and functions – dynamic wave that follows the Schrodinger wave equation and the second phenomenon is the “collapse of the wave function” which is abrupt and discontinuous. Which part of the wave collapses is a matter of probability and chance. The wave transition from the first to the second is call the quantum jump. This exhibited phenomenon is very similar to how the hexagram in the Yijing. When unobserved, the sequential formation of the hexagrams, moment by moment, form a probability wave but when it is observed, it abruptly collapses. It is the abrupt collapse of all the development aspects of the wave function except the one that actualizes and that particular hexagram is therefore the mathematical representation of the observed entity. What spurs all the changes is the energy that flows through the system and all the interacting waves are interconnected and interdependent and they form the energy fields. Emphasis is on the stringed hexagrams, each possesses a sophisticated mathematical structure, suggesting at the same time that it would hold great significance as an integral part of the whole of the wave or energy field. The subject of this paper is on the quantum- informational theoretical framework of Yijing. (shrink)

There has been much discussion recently about the scope and limits of purely symbolic models of the mind and about the proper role of connectionism in cognitive modeling. This paper describes the symbol grounding problem : How can the semantic interpretation of a formal symbol system be made intrinsic to the system, rather than just parasitic on the meanings in our heads? How can the meanings of the meaningless symbol tokens, manipulated solely on the basis of their shapes, be grounded (...) in anything but other meaningless symbols? The problem is analogous to trying to learn Chinese from a Chinese/Chinese dictionary alone. A candidate solution is sketched: Symbolic representations must be grounded bottom-up in nonsymbolic representations of two kinds: iconic representations, which are analogs of the proximal sensory projections of distal objects and events, and categorical representations, which are learned and innate feature-detectors that pick out the invariant features of object and event categories from their sensory projections. Elementary symbols are the names of these object and event categories, assigned on the basis of their categorical representations. Higher-order symbolic representations, grounded in these elementary symbols, consist of symbol strings describing category membership relations. Connectionism is one natural candidate for the mechanism that learns the invariant features underlying categorical representations, thereby connecting names to the proximal projections of the distal objects they stand for. In this way connectionism can be seen as a complementary component in a hybrid nonsymbolic/symbolic model of the mind, rather than a rival to purely symbolic modeling. Such a hybrid model would not have an autonomous symbolic module, however; the symbolic functions would emerge as an intrinsically dedicated symbol system as a consequence of the bottom-up grounding of categories ' names in their sensory representations. Symbol manipulation would be governed not just by the arbitrary shapes of the symbol tokens, but by the nonarbitrary shapes of the icons and category invariants in which they are grounded. (shrink)

If the cortex is an associative memory, strongly connected cell assemblies will form when neurons in different cortical areas are frequently active at the same time. The cortical distributions of these assemblies must be a consequence of where in the cortex correlated neuronal activity occurred during learning. An assembly can be considered a functional unit exhibiting activity states such as full activation (“ignition”) after appropriate sensory stimulation (possibly related to perception) and continuous reverberation of excitation within the assembly (a putative (...) memory process). This has implications for cortical topographies and activity dynamics of cell assemblies forming during language acquisition, in particular for those representing words. Cortical topographies of assemblies should be related to aspects of the meaning of the words they represent, and physiological signs of cell assembly ignition should be followed by possible indicators of reverberation. The following postulates are discussed in detail: (1) assemblies representing phonological word forms are strongly lateralized and distributed over perisylvian cortices; (2) assemblies representing highly abstract words such as grammatical function words are also strongly lateralized and restricted to these perisylvian regions; (3) assemblies representing concrete content words include additional neurons in both hemispheres; (4) assemblies representing words referring to visual stimuli include neurons in visual cortices; and (5) assemblies representing words referring to actions include neurons in motor cortices. Two main sources of evidence are used to evaluate these proposals: (a) imaging studies focusing on localizing word processing in the brain, based on stimulus-triggered event-related potentials (ERPs), positron emission tomography (PET), and functional magnetic resonance imaging (fMRI), and (b) studies of the temporal dynamics of fast activity changes in the brain, as revealed by high-frequency responses recorded in the electroencephalogram (EEG) and magnetoencephalogram (MEG). These data provide evidence for processing differences between words and matched meaningless pseudowords, and between word classes, such as concrete content and abstract function words, and words evoking visual or motor associations. There is evidence for early word class-specific spreading of neuronal activity and for equally specific high-frequency responses occurring later. These results support a neurobiological model of language in the Hebbian tradition. Competing large-scale neuronal theories of language are discussed in light of the data summarized. Neurobiological perspectives on the problem of serial order of words in syntactic strings are considered in closing. Key Words: associative learning; cell assembly; cognition; cortex; ERP; EEG; fMRI; language; lexicon; MEG; PET; word category. (shrink)

We begin by distinguishing computationalism from a number of other theses that are sometimes conflated with it. We also distinguish between several important kinds of computation: computation in a generic sense, digital computation, and analog computation. Then, we defend a weak version of computationalism—neural processes are computations in the generic sense. After that, we reject on empirical grounds the common assimilation of neural computation to either analog or digital computation, concluding that neural computation is sui generis. Analog computation requires continuous (...) signals; digital computation requires strings of digits. But current neuroscientific evidence indicates that typical neural signals, such as spike trains, are graded like continuous signals but are constituted by discrete functional elements (spikes); thus, typical neural signals are neither continuous signals nor strings of digits. It follows that neural computation is sui generis. Finally, we highlight three important consequences of a proper understanding of neural computation for the theory of cognition. First, understanding neural computation requires a specially designed mathematical theory (or theories) rather than the mathematical theories of analog or digital computation. Second, several popular views about neural computation turn out to be incorrect. Third, computational theories of cognition that rely on non-neural notions of computation ought to be replaced or reinterpreted in terms of neural computation. (shrink)

This paper offers an account of what it is for a physical system to be a computing mechanism—a system that performs computations. A computing mechanism is a mechanism whose function is to generate output strings from input strings and (possibly) internal states, in accordance with a general rule that applies to all relevant strings and depends on the input strings and (possibly) internal states for its application. This account is motivated by reasons endogenous to the philosophy of computing, namely, (...) doing justice to the practices of computer scientists and computability theorists. It is also an application of recent literature on mechanisms, because it assimilates computational explanation to mechanistic explanation. The account can be used to individuate computing mechanisms and the functions they compute and to taxonomize computing mechanisms based on their computing power. (shrink)

Quantum field theories are notoriously difficult to understand, physically as well as philosophically. The aim of this paper is to contribute to a better conceptual understanding of gauge quantum field theories, such as quantum chromodynamics, by discussing a famous physical limit, the ’t Hooft limit, in which the theory concerned often simplifies. The idea of the limit is that the number N of colours goes to infinity. The simplifications that can happen in this limit, and that we will consider, are: (...) the theory’s Feynman diagrams can be drawn on a plane without lines intersecting ; and the theory, or a sector of it, becomes integrable, and indeed corresponds to a well-studied system, viz. a spin chain. Planarity is important because it shows how a quantum field theory can exhibit extended, in particular string-like, structures; in some cases, this gives a connection with string theory, and so with its representation of gravity. Previous philosophical literature about how one theory might be emergent from, and-or reduced to, another one has tended to emphasize cases, such as occur in statistical mechanics, where the system before the limit has finitely many degrees of freedom. But here, our quantum field theories, including those on the way to the ’t Hooft limit, will have infinitely many degrees of freedom. Nevertheless, we will show how a recent schema by Butterfield and taxonomy by Norton apply to the quantum field theories we consider; and we will classify three physical properties of our theories in these terms. These properties are planarity and integrability, as in and above; and the behaviour of the beta-function reflecting, for example, asymptotic freedom. Our discussion of these properties, especially the beta-function, will also relate to recent philosophical debate about the propriety of assessing quantum field theories, whose rigorous existence is not yet proven. (shrink)

The purpose of this paper is to show that the Elementary Process Theory (EPT) agrees with the knowledge of the physical world obtained from the successful predictions of Special Relativity (SR). For that matter, a recently developed method is applied: a categorical model of the EPT that incorporates SR is fully specified. Ultimate constituents of the universe of the EPT are modeled as point-particles, gamma-rays, or time-like strings, all represented by integrable hyperreal functions on Minkowski space. This proves that the (...) EPT agrees with SR. -/- Edit: this preprint differs significantly from the published chapter. (shrink)

This paper reviews four significant advances on the feedforward architecture that has dominated discussions of connectionism. The first involves introducing modularity into networks by employing procedures whereby different networks learn to perform different components of a task, and a Gating Network determines which network is best equiped to respond to a given input. The second consists in the use of recurrent inputs whereby information from a previous cycle of processing is made available on later cycles. The third development involves developing (...) compressed representations of strings in which there is no longer an explicit encoding of the components but where information about the structure of the original string can be recovered and so is present functionally. The final advance entails using connectionist learning procedures not just to change weights in networks but to change the patterns used as inputs to the network. These advances significantly increase the usefulness of connectionist networks for modeling human cognitive performance by, among other things, providing tools for explaining the productivity and systematicity of some mental activities, and developing representations that are sensitive to the content they are to represent. (shrink)

This essay explores the use of stringed instruments (and in particular the harpsichord) as models of brain and cognitive function in eighteenth-century French medicine and natural philosophy. These comparisons were founded in part on the anatomical investigations of the latter half of the seventeenth century, which had established both the “fibrous” structure of the white and gray matter of the cerebrum and the vibratory movement the brain underwent in the performance of its functions. Musical instruments—and in particular the harpsichord—helped (...) these philosophers speculate about how the brain worked as the material instrument of sensation and thought: they were machines at once mechanical and affective, grounded in the materiality of their wooden boards and metal strings, yet symbolizing the rational—and immaterial—harmonies of music. (shrink)

Let us start by some general definitions of the concept of complexity. We take a complex system to be one composed by a large number of parts, and whose properties are not fully explained by an understanding of its components parts. Studies of complex systems recognized the importance of “wholeness”, defined as problems of organization (and of regulation), phenomena non resolvable into local events, dynamics interactions in the difference of behaviour of parts when isolated or in higher configuration, etc., in (...) short, systems of various orders (or levels) not understandable by investigation of their respective parts in isolation. In a complex system it is essential to distinguish between ‘global’ and ‘local’ properties. Theoretical physicists in the last two decades have discovered that the collective behaviour of a macro-system, i.e. a system composed of many objects, does not change qualitatively when the behaviour of single components are modified slightly. Conversely, it has been also found that the behaviour of single components does change when the overall behaviour of the system is modified. There are many universal classes which describe the collective behaviour of the system, and each class has its own characteristics; the universal classes do not change when we perturb the system. The most interesting and rewarding work consists in finding these universal classes and in spelling out their properties. This conception has been followed in studies done in the last twenty years on second order phase transitions. The objective, which has been mostly achieved, was to classify all possible types of phase transitions in different universality classes and to compute the parameters that control the behaviour of the system near the transition (or critical or bifurcation) point as a function of the universality class. This point of view is not very different from the one expressed by Thom in the introduction of Structural Stability and Morphogenesis (1975). It differs from Thom’s program because there is no a priori idea of the mathematical framework which should be used. Indeed Thom considers only a restricted class of models (ordinary differential equations in low dimensional spaces) while we do not have any prejudice regarding which models should be accepted. One of the most interesting and surprising results obtained by studying complex systems is the possibility of classifying the configurations of the system taxonomically. It is well-known that a well founded taxonomy is possible only if the objects we want to classify have some unique properties, i.e. species may be introduced in an objective way only if it is impossible to go continuously from one specie to another; in a more mathematical language, we say that objects must have the property of ultrametricity. More precisely, it was discovered that there are conditions under which a class of complex systems may only exist in configurations that have the ultrametricity property and consequently they can be classified in a hierarchical way. Indeed, it has been found that only this ultrametricity property is shared by the near-optimal solutions of many optimization problems of complex functions, i.e. corrugated landscapes in Kauffman’s language. These results are derived from the study of spin glass model, but they have wider implications. It is possible that the kind of structures that arise in these cases is present in many other apparently unrelated problems. Before to go on with our considerations, we have to pick in mind two main complementary ideas about complexity. (i) According to the prevalent and usual point of view, the essence of complex systems lies in the emergence of complex structures from the non-linear interaction of many simple elements that obey simple rules. Typically, these rules consist of 0–1 alternatives selected in response to the input received, as in many prototypes like cellular automata, Boolean networks, spin systems, etc. Quite intricate patterns and structures can occur in such systems. However, what can be also said is that these are toy systems, and the systems occurring in reality rather consist of elements that individually are quite complex themselves. (ii) So, this bring a new aspect that seems essential and indispensable to the emergence and functioning of complex systems, namely the coordination of individual agents or elements that themselves are complex at their own scale of operation. This coordination dramatically reduces the degree of freedom of those participating agents. Even the constituents of molecules, i.e. the atoms, are rather complicated conglomerations of subatomic particles, perhaps ultimately excitations of patterns of superstrings. Genes, the elementary biochemical coding units, are very complex macromolecular strings, as are the metabolic units, the proteins. Neurons, the basic elements of cognitive networks, themselves are cells. In those mentioned and in other complex systems, it is an important feature that the potential complexity of the behaviour of the individual agents gets dramatically simplified through the global interactions within the system. The individual degrees of freedom are drastically reduced, or, in a more formal terminology, the factual space of the system is much smaller than the product of the state space of the individual elements. That is one key aspect. The other one is that on this basis, that is utilizing the coordination between the activities of its members, the system then becomes able to develop and express a coherent structure at a higher level, that is, an emergent behaviour (and emergent properties) that transcends what each element is individually capable of. (shrink)

In this paper, I respond to three critical notices of The Practical Origins of Ideas: Genealogy as Conceptual Reverse-Engineering, written by Cheryl Misak, Alexander Prescott-Couch, and Paul Roth, respectively. After contrasting genealogical conceptual reverse-engineering with conceptual reverse-engineering, I discuss pragmatic genealogy’s relation to history. I argue that it would be a mistake to understand pragmatic genealogy as a fiction (or a model, or an idealization) as opposed to a form of historical explanation. That would be to rely on precisely the (...) stark dichotomy between idealization and history that I propose to call into question. Just as some historical explanations begin with a functional hypothesis arrived at through idealization as abstraction, some pragmatic genealogies embody an abstract form of historiography, stringing together, in a way that is loosely indexed to certain times and places, the most salient needs responsible for giving a concept the contours it now has. I then describe the naturalistic stance that I find expressed in the pragmatic genealogies I consider in the book before examining the evaluative standard at work in those genealogies, defusing the charge that they involve a commitment to a ‘stingy axiology’. (shrink)

continent. 2.2 (2012): 148–151 When things get complex, as they may indeed be getting, the distinction between tools and the things that can be made with them begins to dissolve. The medium is not only also a message, it is an essential counter-valence to our own impulses towards the creation of meaning, beauty and knowledge. The tools we think we are using also use us: They push us around, make us think new things, do new things, even be new things. (...) Language is no different, of course, although in its supremacy and ubiquity, it is even more elusive, difficult to perceive. The very words you are looking at right now are like compact little cryptograms—a written convention, talking back at you in codes. Poetry is language speaking for itself. It is, at its best, where what is being told is coincident with the telling. The words written, or uttered, pop out at us, while in the same moment, constellations of meaning emerge; the components and its composition resonate, vacillate, on the page and in the air. Many of the constraints and styles of poetry we know have developed in order to allow words to express themselves, or show themselves as the mediation of a mental image. Programming languages for computer hardware, no matter how “high level” or abstract they are, are by necessity far less elaborate than traditional forms of writing and speech. But the structure and function of these new languages give them special advantage in clarity: These languages (syntax, sequence) and the results they produce (ideas, ‘executables’) are absolutely inseparable. By design, computing languages are created in order to express specific ideas, creating certain kinds of action or manipulation of other codes (data). In this sense perhaps, software is always, and already, poetic. It is precise description, and pure syntax—the signifier and signified—clearly coincident in the machine. Ishac Bertran ’s code {poems} is an edited book project that exposes the materiality of computer programming languages. Here are presented a small sampling from a compiled book of poetry written by software engineers, artists and other code writers, “exploring the potential of code to communicate at the level of poetry.” ( code-poems.com ) The project solicited for online, public submissions from code-writers in response to the notion of a poem, written in a software language which is semantically valid (i.e.: it compiles ). This solicitation winds up revealing the inner workings, constitutive elements, and styles of both a particular software and its authors. From a large number of submissions, a selection of poems will be printed as a bound volume in the Autumn of 2012. - Jamie Allen __________________________________________________ DAILYGRIND import java.util.Date; public class DailyGrind { public static final void main(String[] args) { boolean its_time_to_go_home = false; boolean away_the_hours = true; while (away_the_hours) { boolean away_the_hours = true; Date now = new Date(); its_time_to_go_home = now.getHours() > 17 && now.getMinutes() > 30; if (its_time_to_go_home) { break; } try { Thread.sleep(60000); } catch (InterruptedException e) { // ignore } } } } Paul Illingworth // Java __________________________________________________ UNHANDLED LOVE class love {}; void main() { throw love(); } Daniel Bezerra // C++ __________________________________________________ TWOFACED public class TwoFaced { public String greet() { return "Hi! So great to see you!"; } private String think() { return "Fucking bitch."; } } Jason Kopylec // Java __________________________________________________ DANCING WITHIN using System; public class PoemCode { private bool dancing_within() { Boolean me = true; while (dancing_within()) { var iables_of_light = ""; try { int elligently_to; object ify_the_world_apart; } catch (Exception s) { int o_the_broken_parts; throw; int o_the_seed_of_life; } Random ashes_of = new Random(); float ing_devices; short age_of; char acter_will_never_let_you = 'b'; } return me; } } Álvaro Matías Wong Díaz // C#  . (shrink)

Barbieri introduced and developed the concept of organic codes. The most basic of them is the genetic code, a set of correspondence rules between otherwise unrelated sequences: strings of nucleotides on the one hand, polypeptidic chains on the other hand. Barbieri noticed that it implies ‘coding by convention’ as arbitrary as the semantic relations a language establishes between words and outer objects. Moreover, the major transitions in life evolution originated in new organic codes similarly involving conventional rules. Independently, dealing with (...) heredity as communication over time and relying on information theory, we asserted that the conservation of genomes over the ages demands that error-correcting codes make them resilient to casual errors. Moreover, the better conservation of very old parts of the genome demands that they result from combining successively established nested codes such that the older an information, the more numerous component codes protect it. Barbieri’s concept of organic code and that of genomic error-correcting code may seem unrelated. We show however that organic codes actually entail error-correcting properties. Error-correcting, in general, results from constraints being imposed on a set of sequences. Mathematical equalities are conveniently used in communication engineering for expressing constraints but error correction only needs that constraints exist. Biological sequences are similarly endowed with error-correcting ability by physical-chemical or linguistic constraints, thus defining ‘soft codes’. These constraints are moreover presumably efficient for correcting errors. Insofar as biological sequences are subjected to constraints, organic codes necessarily involve soft codes, and their successive onset results in the nested structure we hypothesized. Organic codes are generated and maintained by means of molecular ‘semantic feedback loops’. Each of these loops involves genes which code for proteins, the enzymatic action of which controls a function needed for the protein assembly. Taken together, thus, they control the assembly of their own structure as instructed by the genome and, once closed, these loops ensure their own conservation. However, the semantic feedback loops do not prevent the genome lengthening. It increases both the redundancy of the genome and the information quantity it bears, thus improving the genome reliability and the specificity of the enzymes, which enables further evolution. (shrink)

In the field of biosemiotics in our time, Ferdinand de Saussure's theory of semiology has been dismissed for its glottocentric, anthropocentric, and dyadic characteristics and as such unsuitable for the said field. Such accusation is symptomatic of an extremely narrow view of Saussure, which ignores the efforts he made in tackling problems concerning the unification of biology and semiotics . A broader view of Saussure, emerging from the newly-discovered orangery manuscripts along with his thought-provoking course lectures, reveals that his epistemology (...) is actually grounded in evolutionary differences and the concept of uniformitarianism. In order to demonstrate the value of his ideas, this paper proceeds through five sections. To begin with, the understandings and misunderstandings of key terms are summarized while seeking to reconcile arbitrary and relatively arbitrary modes of consciousness within the network of differences that Saussure proposes in his manuscripts. My study points out how such a network blurs disciplinary or systematic boundaries between language and non-verbal systems and how it might serve as a framework for appreciating true analogies between natural sciences and the science of language. The paradox of analogy, torn between the synchronic and diachronic schemes of time, is discussed. This unravels several strings that have made the functioning of analogy into such a delicate point in Saussure's theory of evolution. The concept of état de langue is made comprehensive in relation to appropriations of Darwinian model and Neo-Darwinian ideas. Saussure's model of evolution explicates the phenomenon of symbiogenesis, which is non-linear, non-adaptive, non-restrictive as regards localities, yet claims certain truths about nature and culture. Finally, my study draws attention to the implications of conceptualizing non-linear evolution within and across systems. There are indeed disparities between Saussure's epistemology and that of biosemiotics: nineteenth-century confused epistemology reoccurred within biosemiotics in its early phase. (shrink)

This paper discusses DNA-based stochastic optimizations under the constraint that the search starts from a given point in a search space. Generally speaking, a stochastic optimization method explores a search space and finds out the optimum or a sub-optimum after many cycles of trials and errors. This search process could be implemented efficiently by ``molecular computing'', which processes DNA molecules by the techniques of molecular biology to generate and evaluate a vast number of solution candidates at a time. We assume (...) the exploration starting from a single point, and propose a method to embody DNA-based optimization under this constraint, because this method has a promising application in the research field of protein engineering. In this application, a string of nucleotide bases encodes a protein possessing a specific activity, which could be given as a value of an objective function. Thus, a problem of obtaining a protein with the optimum or a sub-optimum about the desired activity corresponds to a combinatorial problem of obtaining a base sequence giving the optimum or a sub-optimum in the sequence space. Biologists usually modify a base sequence corresponding to a naturally occurring protein into another sequence giving a desired activity. In other words, they explore the space in the proximity of a natural protein as a start point. We first examined if the optimization methods that involve a single start point, such as simulated annealing, Gibbs sampler, and MH algorithms, can be implemented by DNA-based operations. Then, we proposed an application of genetic algorithm, and examined the performance of this application on a model fitness landscape by computer experiments. These experiments gave helpful guidelines in the embodiments of DNA-based stochastic optimization, including a better design of crossover operator. (shrink)

Whether God has a knowledge is a controversial issue both philosophy and theology. Does God have a knowledge? If He has, does He know the particulars? When we assume that God knows particulars, is there any change in God’s essence? In the theistic tradition, it is accepted that God is wholly perfect, omniscience, omnipotent and wholly good. Therefore, it is not possible to say that there is a change in God. Because changing is a kind of imperfection. On God’s knowledge, (...) another controversial issue is whether God knows particulars or not. Most of theist thinkers argued that God is wholly perfect; because of perfectness, He must have perfect attributes. Knowing and goodness are a kind of perfect attributes. Ignoring and evil are a kind of imperfectness. If God is perfect being, He should have the perfect attributes and must know the particulars. For me in this subject, there are some similarities between al-Ghazālī and Maimonides. In this study I took into consideration the idea of al-Ghazālī and Maimonides on this subject. Based on Griffel and Stroumsa’s argument, I tried to show similarity between al-Ghazālī and Maimonides on God’s knowledge. Summary: Whether God has a knowledge is a controversial issue both philosophy and theology. Does God have a knowledge? If He has, does He know the particulars? When we assume that God knows particulars, is there any change in God’s essence? In this study I took into consideration the idea of al-Ghazālī and Maimonides on this subject. Based on Griffel’s and Stroumsa’s arguments, I tried to show similarity between al-Ghazālī and Maimonides on God’s knowledge.In the theistic tradition, it is accepted that God is wholly perfect, omniscience, omnipotent and wholly good. Therefore, it is not possible to say that there is a change in God because changing is a kind of imperfection. On God’s knowledge, another controversial issue is whether God knows particulars or not. Most of theist thinkers argued that God is wholly perfect; because of perfectness, He must have perfect attributes. Knowing and goodness are a kind of perfect attributes. Ignoring and evil are kinds of imperfectness. If God is perfect being, He should have the perfect attributes and must know the particulars. Based on God’s immutability, some thinkers argued that God does not knows particulars. Particulars occurs due to the matter. Matter and its functions are continually changing. Therefore, to know the particulars requires changing in God’s essence. If God is the most perfect being, it is impossible that He is subject to affection. Thus, God does not know the particulars. Other thinkers, like Avicenna, argued that God knows the particulars as a universal way. For example, God knows only humanity and He cannot know Zayd as a particular person. al-Ghazālī criticizes Avicenna’s idea in Tahafut al-Falasifa (The Incoherence of the Philosophers) and argues that God is a perfect being and He should know particulars as a particulars. For al-Ghazālī, God should know everything, and His knowledge is different from our knowledge. In order to explain this matter, he says in Ninety-Nine Names of God;“But this can be understood only through an example. Perhaps you have seen the clock which informs one of the hour of worship. If you have not seen it, then, generally speaking, (it is constructed in this manner). There must be a mechanism in the form of a cylinder which contains a known amount of water. There must also be another hollow mechanism which is placed within the cylinder (but) above the water, and a string which has one of its ends tied to this hollow mechanism. The other end is tied to the part of a small container which is placed above the hollow cylinder. In (this container) there is a ball. Under the ball there is another bowl (placed) in such a manner that if the ball drops will fall into the bowl, and its jingle will be heard. Then the bottom of the cylindrical mechanism must be pierced to a determined extent so that the water can escape through it little by little…. All of this can be determined by a determination of the extent of cause which neither increases nor decreases. It is possible to make the falling of the ball into the bowl a cause of another action and this other action a cause of a third action, and to continue this process indefinitely so that from it are generated remarkable and predetermined movements (actions) of circumscribed extent. The first cause was the falling of the water in a determined quantity…. All of that happens in a determined quantity and to a determined extent which causes the determination of all of it by (adding at this point) the determination of the first movement which is the movement of the water. When you understand that these mechanisms are the principles from which movements must result, and that the movement must be determined if the result is to be regulated, then certainly that which has been determined must proceed from them….Even as the movement of the mechanism, the string, and the ball are not external to the will of the inventor of the mechanism -on the contrary, that is what He willed when He invented the mechanism- so also all the events which occur in the world, both the evil and the good and the beneficial and harmful, are not external to the will of God Most High. Rather (all of) that is the intention of God Most High for the sake of which He has planned its causes.” For Maimonides, as in al-Ghazālī, God is a perfect being and He must have the perfect attributes. Because of knowing is a perfect attribute, He should know everything, and His knowledge is different from human knowledge. In order to explain the difference between God’s knowledge and human knowledge Maimonides gives a parable in The Guide of the Perplexed. “Suppose a thing is produced in accordance with the knowledge of the producer, the producer was then guided by his knowledge in the act of producing the thing. Other people, however, who examine this work and acquire a knowledge of the whole of it, depend for that knowledge on the work itself. An artisan makes a box in which weights move with the running of the water, and thus indicate how many hours have passed of the day and of the night. The whole quantity of the water that is to run out, the different ways in which it runs, every thread that is drawn, and every little ball that descends -all this is fully perceived by him who makes the clock; and his knowledge is not the result of observing the movements as they are actually going on; but, on the contrary, the movements are produced in accordance with his knowledge. But another person who looks at that instrument will receive fresh knowledge at every movement he perceives; the longer he looks on, the more knowledge does he acquire; he will gradually increase his knowledge till he fully understands the machinery…Our knowledge is acquired and increased in proportion to the things known by us. This is not the case with God. His knowledge of things is not derived from the things themselves; if this were the case, there would be change and plurality in His knowledge…” As can be seen from above, when Maimonides is explaining the difference of God’s and human knowledge, he uses the same example what al-Ghazālī used. Even though Maimonides does not mention al-Ghazālī’s name in his works, it could be seen that there are a lot of similarities between al-Ghazālī’s and Maimonides’s ideas. Based on Griffel and Stroumsa’s argument, in this paper, I tried to show that there is a similarity between al-Ghazālī’s and Maimonides’s ideas on God’s knowledge. In my opinion, therefore, in the formation of Maimonides’s thought, as he thanks to Muslim philosophers like al-Farābī, Avicenna and Averroes, he also thanks to al-Ghazālī. (shrink)

Imitation research has been hindered by (1) overly molecular analyses of behaviour that ignore hierarchical structure, and (2) attempts to disqualify observational evidence. Program-level imitation is one of a range of cognitive skills for scheduling efficient novel behaviour, in particular, enabling an individual to purloin the organization of another's behaviour for its own. To do so, the individual must perceive the underlying hierarchical schedule of the fluid action it observes and must understand the local functions of subroutines within the overall (...) goal-directed process. Action-level imitation, copying strings of actions linearly without any such understanding, is less valuable for acquiring complex behaviour and may often have other, social functions. At present, we lack a mechanistic understanding of the abilities underlying program-level imitation that make it possible for the underlying structure of complex actions to be dissected visually and recreated in behaviour. (shrink)

This article focuses on the relevance of computational complexity for cognition. The syntactic items may be expressions that are surface strings. But in general, strings are syntactically ambiguous in that they can be generated in more than one way from atomic expressions and operations. The semantic function must take disambiguated items as arguments. When expressions are ambiguous, expressions cannot be the arguments. Instead, it is common to take the arguments to be terms, whose surface syntax reflects the derivation of (...) the string. The semantic function differs in one other important respect from an arithmetic function, since it maps entities between domains, from a syntactic to an ontic or conceptual domain of meanings. Compositionality helps to explain the rate of success in linguistic communication when the sentence used or the content communicated is new. (shrink)

Harry Collins is a science studies scholar no other description fits without qualification who has contributed enormously to the discussion of tacit knowledge. Collins says that he is providing an account for the ontologically bashful, meaning, presumably, that it does not carry the burdens of Durkheim's notion of the collective consciousness. Polanyi says that 'a wholly explicit knowledge is unthinkable'. Collins wants to translate this into 'strings must be interpreted before they are meaningful'. Somatic limits are the source of the (...) mystery element of tacit knowledge. In fact, machines can be programmed to do the things it involves, although they will do it in a different way. In Social Cartesianism, the individual is not the unit of analysis: the individual merely shares the collectivity's knowledge. Collins point in these contexts is that functional substitutability implies nothing about similarity in underlying causal structure. (shrink)