In applied problems mathematics is used as language or as a metalanguage on which metatheories are built, E.G., Mathematical theory of experiment. The structure of pure mathematics is grammar of the language. As opposed to pure mathematics, In applied problems we must keep in mind what underlies the sign system. Optimality criteria-Axioms of applied mathematics-Prove mutually incompatible, They form a mosaic and not mathematical structures which, According to bourbaki, Make mathematics a unified science. One of the peculiarities of applied mathematical (...) language is a variety of dialects: a problem can be presented in terms of various mathematical notions. Another peculiarity is polysemy: a problem can be presented in the framework of one dialect by a set of various models with equal right to exist. The pragmatic sense of distinction between applied and pure mathematics must lead to specific training in each case. (shrink)

This paper proposes a model for implementation of intrinsic natural language sentence meaning in a physical language understanding system, where 'intrinsic' is understood as 'independent of meaning ascription by system-external observers'. The proposal is that intrinsic meaning can be implemented as a point attractor in the state space of a nonlinear dynamical system with feedback which is generated by temporally sequenced inputs. It is motivated by John Searle's well known (Behavioral and Brain Sciences, 3: 417–57, 1980) critique of the then-standard (...) and currently still influential computational theory of mind (CTM), the essence of which was that CTM representations lack intrinsic meaning because that meaning is dependent on ascription by an observer_._ The proposed dynamical model comprises a collection of interacting artificial neural networks, and constitutes a radical simplification of the principle of compositional phrase structure which is at the heart of the current standard view of sentence semantics because it is computationally interpretable as a finite state machine. (shrink)

A critique of algorithmic rationalisation offers at best some initial reasons and preliminary ideas. Critique is understood as a reflection on validity. It is limited to an “epistemological investigation” of the limits of the calculable or of what appears “knowable” in the mode of the algorithmic. The argumentation aims at the mathematical foundations of computer science and goes back to the so-called “foundational crisis of mathematics” at the beginning of the 20th century with the attempt to formalise concepts such as (...) calculability, decidability and provability. The Gödel theorems and Turing’s halting problem prove to be essential for any critical approach to “algorithmic rationalisation”. Both, however, do not provide unambiguous results, at best they run towards what later became known as “Gödel’s disjunction”. The chosen path here, however, suggests the opposite way, insofar as, on the one hand, the topos of creativity appear constitutive for what can be regarded as cognitive “algorithmic rationalisation” and which encounters systematic difficulties in the evaluation of non-trivial results. On the other hand, the investigations lead to a comparison between the “mediality” of formally generated structures, which have to distinguish between object-and metalanguages, and the “volatile” differentiality of human thought, which calls for syntactically non-simulatable sense structures. (shrink)

An explicit philosophy and meta-philosophy of positivism, empiricism and popperianism is provided. Early popperianism is argued to be essentially a form of empiricism, the deviations from empiricism are traced. In contrast, the meta-philosophy and philosophy of an evolutionary naturalistic realism is developed and it is shown how the maximal conflict of this doctrine with all forms of empiricism at the meta-philosophical level both accounts for the form of its development at the philosophical level and its defense against attack from nonrealist (...) quarters. Following an earlier article on realism of similar theme (Synthese 26 (1974), 409) this paper then further explores the ramifications of a thoroughgoing realist position. (shrink)

We propose category theory, the mathematical theory of structure, as a vehicle for defining ontologies in an unambiguous language with analytical and constructive features. Specifically, we apply categorical logic and model theory, based upon viewing an ontology as a sub-category of a category of theories expressed in a formal logic. In addition to providing mathematical rigor, this approach has several advantages. It allows the incremental analysis of ontologies by basing them in an interconnected hierarchy of theories, with an operation on (...) the hierarchy that expresses the formation of complex theories from simple theories that express first principles. Another operation forms abstractions expressing the shared concepts in an array of theories. The use of categorical model theory makes possible the incremental analysis of possible worlds, or instances, for the theories, and the mapping of instances of a theory to instances of its more abstract parts. We describe the theoretical approach by applying it to the semantics of neural networks. (shrink)

(2013). My Life in Chaos. World Futures: Vol. 69, The Complexity of Life and Lives of Complexity, pp. 248-268.

(No abstract is available for this citation).

This paper is a commentary on the target article by Michael Arbib, “Levels of modeling of mechanisms of visually guided behavior”, in the same issue of the journal, pp. 407–465. -/- I focus on the importance of the inclusion of an ability of a system to entertain, at a given time, multiple instantiations of a given schema (situation template, frame, script, action plan, etc.), and complications introduced into neural/connectionist network systems by such inclusion.

Intermediate constructs are required as bridges between complex behaviors and realistic models of neural circuitry. For cognitive scientists in general, schemas are the appropriate functional units; brain theorists can work with neural layers as units intermediate between structures subserving schemas and small neural circuits.After an account of different levels of analysis, we describe visuomotor coordination in terms of perceptual schemas and motor schemas. The interest of schemas to cognitive science in general is illustrated with the example of perceptual schemas in (...) high-level vision and motor schemas in the control of dextrous hands.Rana computatrix, the computational frog, is introduced to show how one constructs an evolving set of model families to mediate flexible cooperation between theory and experiment. Rana computatrix may be able to do for the study of the organizational principles of neural circuitry what Aplysia has done for the study of subcellular mechanisms of learning. Approach, avoidance, and detour behavior in frogs and toads are analyzed in terms of interacting schemas. Facilitation and prey recognition are implemented as tectal-pretectal interactions, with the tectum modeled by an array of tectal columns. We show how layered neural computation enters into models of stereopsis and how depth schemas may involve the interaction of accommodation and binocular cues in anurans. (shrink)

In attempts to formulate a computational understanding of brain function, one of the fundamental concerns is the data structure by which the brain represents information. For many decades, a conceptual framework has dominated the thinking of both brain modelers and neurobiologists. That framework is referred to here as "classical neural networks." It is well supported by experimental data, although it may be incomplete. A characterization of this framework will be offered in the next section. Difficulties in modeling important functional aspects (...) of the brain on the basis of classical neural networks alone have led to the recognition that another, general mechanism must be invoked to explain brain function. That mechanism I call " binding." Binding by neural signal synchrony had been mentioned several times in the liter ature before it was fully formulated as a general phenomenon. Although experimental evidence for neural syn chrony was soon found, the idea was largely ignored for many years. Only recently has it become a topic of animated discussion. In what follows, I will summarize the nature and the roots of the idea of binding, especially of temporal binding, and will discuss some of the objec tions raised against it. (shrink)

What is Computational Intelligence (CI) and what are its relations with Artificial Intelligence (AI)? A brief survey of the scope of CI journals and books with ``computational intelligence'' in their title shows that at present it is an umbrella for three core technologies (neural, fuzzy and evolutionary), their applications, and selected fashionable pattern recognition methods. At present CI has no comprehensive foundations and is more a bag of tricks than a solid branch of science. The change of focus from methods (...) to challenging problems is advocated, with CI defined as a part of computer and engineering sciences devoted to solution of non-algoritmizable problems. In this view AI is a part of CI focused on problems related to higher cognitive functions, while the rest of the CI community works on problems related to perception and control, or lower cognitive functions. Grand challenges on both sides of this spectrum are addressed. (shrink)

Philosophical questions about minds and computation need to focus squarely on the mathematical theory of Turing machines (TM's). Surrogate TM's such as computers or formal systems lack abilities that make Turing machines promising candidates for possessors of minds. Computers are only universal Turing machines (UTM's)—a conspicuous but unrepresentative subclass of TM. Formal systems are only static TM's, which do not receive inputs from external sources. The theory of TM computation clearly exposes the failings of two prominent critiques, Searle's Chinese room (...) (1980) and arguments from Gödel's Incompleteness theorems (e.g., Lucas, 1961; Penrose, 1989), both of which fall short of addressing the complete TM model. Both UTM-computers and formal systems provide an unsound basis for debate. In particular, their special natures easily foster the misconception that computation entails intrinsically meaningless symbol manipulation. This common view is incorrect with respect to full-fledged TM's, which can process inputs non-formally, i.e., in a subjective and dynamically evolving fashion. To avoid a distorted understanding of the theory of computation, philosophical judgments and discussions should be grounded firmly upon the complete Turing machine model, the proper model for real computers. (shrink)