We describe an emerging field, that of nonclassical computability and nonclassical computing machinery. According to the nonclassicist, the set of well-defined computations is not exhausted by the computations that can be carried out by a Turing machine. We provide an overview of the field and a philosophical defence of its foundations.

To compute is to execute an algorithm. More precisely, to say that a device or organ computes is to say that there exists a modelling relationship of a certain kind between it and a formal specification of an algorithm and supporting architecture. The key issue is to delimit the phrase of a certain kind. I call this the problem of distinguishing between standard and nonstandard models of computation. The successful drawing of this distinction guards Turing's 1936 analysis of computation against (...) a difficulty that has persistently been raised against it, and undercuts various objections that have been made to the computational theory of mind. (shrink)

This paper concerns Alan Turing’s ideas about machines, mathematical methods of proof, and intelligence. By the late 1930s, Kurt Gödel and other logicians, including Turing himself, had shown that no finite set of rules could be used to generate all true mathematical statements. Yet according to Turing, there was no upper bound to the number of mathematical truths provable by intelligent human beings, for they could invent new rules and methods of proof. So, the output of a human mathematician, for (...) Turing, was not a computable sequence (i.e., one that could be generated by a Turing machine). Since computers only contained a finite number of instructions (or programs), one might argue, they could not reproduce human intelligence. Turing called this the “mathematical
objection” to his view that machines can think. Logico-mathematical reasons, stemming from his own work, helped to convince Turing that it should be possible to reproduce human intelligence, and eventually compete with it, by developing the appropriate kind of digital computer. He felt it
should be possible to program a computer so that it could learn or discover new rules, overcoming the limitations imposed by the incompleteness and undecidability results in the same way that human
mathematicians presumably do. (shrink)

I analyze Wittgenstein’s criticism of several assumptions that are crucial for a large part of cognitive science. These involve the concepts of computational processes in the brain which cause mental states and processes, the algorithmic processing of information in the brain (neural system), the brain as a machine, psycho physical parallelism, the thinking machine, as well as the confusion of rule following with behavior in accordance with the rule. In my opinion, the theorists of cognitive science have not yet seriously (...) considered Wittgenstein’s criticism so they, quite surprisingly, frequently confuse the question “how does it work?” with “what does it do?” But their most “deleterious” mistake is their confusion of the internal computational (or parallel) processes taking place in the brain (which possibly cause mental states) with socially-based, everyday criteria of recognition and classification of, and knowledge about, the content of mental states. (shrink)

In diesem Essay analysiert der Autor Wittgensteins Kritik an einigen Annahmen, die für einen Großteil der Kognitionswissenschaft von zentraler Bedeutung sind. Diese umfassen die Konzepte von komputationalen Prozessen im Gehirn, die mentale Zustände und Prozesse hervorbringen, die algorythmische Informationsprozessierung im Gehirn , das Gehirn als Maschine, den psychophysischen Parallelismus, die Denkmaschine sowie die Konfusion der Regel, die dem Benehmen folgt im Einklang mit dieser Regel. Nach des Autors Meinung haben die Theoretiker der Kognitionswissenschaft Wittgensteins Kritik noch immer nicht ernsthaft erörtert, (...) so dass sie, was verwundern mag, häufig die Frage „Wie funktioniert das?“ mit der Frage „Was macht das?“ verwechseln. Doch ihr „verhängnisvollster“ Fehler besteht in der Verwechslung interner komputationaler Prozesse, die im Gehirn stattfinden mit sozialbegründeten, alltäglichen Kriterien des Erkennens und der Klassifizierung des Inhalts und des Wissens vom Inhalt mentaler Zustände. (shrink)