Computationalism

Robust, concrete and abstract, mathematical computation and inference on the scale now becoming possible should change the discourse about many matters mathematical. These include: what mathematics is, how we know something, how we persuade each other, what suffices as a proof, the infinite, mathematical discovery or invention, and other such issues.

Why are some models, like the harmonic oscillator, the Ising model, a few Hamiltonian equations in quantum mechanics, the poisson equation, or the Lokta-Volterra equations, repeatedly used within and across scientific domains, whereas theories allow for many more modeling possibilities? Some historians and philosophers of science have already proposed plausible explanations. For example, Kuhn and Cartwright point to a tendency toward conservatism in science, and Humphreys emphasizes the importance of the intractability of what he calls “templates.” This paper investigates more (...) systematically the reasons for this remarkable interdisciplinary recurrence. To this aim, the authors describe in more detail the phenomenon they focus on and review competing potentialexplanations. The authors disentangle the various assumptions underlying these explanations based on sensitivity to a computational constraints and assess its relationships with the other analyzed explanatons. (shrink)

Because the label "computing and philosophy" can seem like an ad hoc attempt to tie computing to philosophy, it is important to explain why it is not, what it studies (or does) and how it differs from research in, say, "computing and history," or "computing and biology". The American Association for History and Computing is "dedicated to the reasonable and productive marriage of history and computer technology for teaching, researching and representing history through scholarship and public history" (http://theaahc.org). More pervasive, (...) work in computing and biology enjoys the convenient name of "bioinformatics...the science of using information to understand biology..., a subset of the larger field of computational biology, the application of quantitative analytical techniques in modeling biological systems" (http://oreilly.com/catalog/bioskills/chapter/ ch01.html). The recent venture of the Association for Computing Machinery and the Institute of Electrical and Electronics Engineers to publish the Transactions on Computational Biology and Bioinformatics (TCBB) bears witness to the reach of computing and biology and underscores its objective. TCBB intends to report "archival research results related to the algorithmic, mathematical, statistical, and computational methods that are central in bioinformatics and computational biology; the development and testing of effective computer programs in bioinformatics; the development and optimization of biological databases; and important biological results that are obtained from the use of these methods, programs, and databases" (http://tcbb.acm.org). In the case of "computing and history" and "bioinformatics," each discipline stands in a particular relationship to computers that raises questions unique to itself. But both are devoted to the development of computational tools to aid discovery.. (shrink)

With the rise of the internet and the proliferation of technology to gather and organize data, our era has been defined as "the information age." With the prominence of information as a research concept, there has arisen an increasing appreciation of the intertwined nature of fields such as logic, linguistics, and computer science that answer the questions about information and the ways it can be processed. The many research traditions do not agree about the exact nature of information. By bringing (...) together ideas from diverse perspectives, this book presents the emerging consensus about what a conclusive theory of information should be. The book provides an introduction to the topic, work on the underlying ideas, and technical research that pins down the richer notions of information from a mathematical point of view. The book contains contributions to a general theory of information, while also tackling specific problems from artificial intelligence, formal semantics, cognitive psychology, and the philosophy of mind. There is focus on the dynamics of information flow, and also a consideration of static approaches to information content; both quantitative and qualitative approaches are represented. (shrink)

John Searle dismisses the attempt to understand thought as a form of computation, on the grounds that it is not scientific. Science is concerned with intrinsic properties, i.e. those features which are not observer relative, e.g. science is concerned with mass but not with beauty. Computation, according to Searle, presupposes the property of following an algorithm, but algorithmicity is normative, by reason of appealing to function, and hence not intrinsic. I argue that Searle's critique presupposes the folk notion of function, (...) which is indeed normative. But this folk notion can be replaced by a purely descriptive analogue, thereby showing that algorithmicity can be construed as intrinsic after all. (shrink)

We capture the principal models of computation and specification in the literature by a uniform set of transparent mathematical descriptions which—starting from scratch—provide the conceptual basis for a comparative study.1.

Braitenberg et al.'s proposal, like most previous theories of cerebellar function (see Bower 1997, for review), is fundamentally based on the striking geometric relationship between parallel fibers and Purkinje cells. As in previous models, the current theory assumes that the activation of granule cells results in a of activated Purkinje cells, although it adds the new requirement that the granule cell layer itself have a particular spatial/temporal pattern of activation. I believe there is clear evidence that parallel fibers do not (...) have the type of excitatory effects on Purkinje cells required by this theory. (shrink)

The chapter is concerned with the role of art and design in the history and philosophy of computing, and the role of computing in models of design and art. It offers insights arising from research into a period in the 1960s and 70s, particularly in the UK, when computing became more available to artists and designers, focusing on Bruce Archer and John Lansdown in London. It suggests that models of computing interacted with conceptualisations of art, design and creative activities in (...) important ways. (shrink)

We describe a proof by a computer program of the unsolvability of the halting problem. The halting problem is posed in a constructive, formal language. The computational paradigm formalized is Pure LISP, not Turing machines. The machine was led to the proof by the authors, who suggested certain function definitions and stated certain intermediate lemmas. The machine checked that every suggested definition was admissible and the machine proved the main theorem and every lemma. We believe this is the first instance (...) of a machine checking that a given problem is not solvable by machine. (shrink)

Open peer commentary on the article “Info-computational Constructivism and Cognition” by Gordana Dodig-Crnkovic. Upshot: The main problems with info-computationalism are: (1) Its basic concept of natural computing has neither been defined theoretically or implemented practically. (2. It cannot encompass human concepts of subjective experience and intersubjective meaningful communication, which prevents it from being genuinely transdisciplinary. (3) Philosophically, it does not sufficiently accept the deep ontological differences between various paradigms such as von Foerster’s second- order cybernetics and Maturana and Varela’s theory (...) of autopoiesis, which are both erroneously taken to support info-computationalism. (shrink)

Don’t Bury Your Head in the Sand! • Some say: “AI is dead.” (Or: “AI is dying.”) • This is due to either self-deception or what Turing — the grandfather of computer sci-.

Does what guides a pastry chef stand on par, from the standpoint of contemporary computer science, with what guides a supercomputer? Did Betty Crocker, when telling us how to bake a cake, provide an effective procedure, in the sense of `effective' used in computer science? According to Cleland, the answer in both cases is ``Yes''. One consequence of Cleland's affirmative answer is supposed to be that hypercomputation is, to use her phrase, ``theoretically viable''. Unfortunately, though we applaud Cleland's ``gadfly philosophizing'' (...) (as, in fact, seminal), we believe that unless such a modus operandi is married to formal philosophy, nothing conclusive will be produced (as evidenced by the problems plaguing Cleland's work that we uncover). Herein, we attempt to pull off not the complete marriage for hypercomputation, but perhaps at least the beginning of a courtship that others can subsequently help along. (shrink)