In this reply to James H. Fetzer’s “Minds and Machines: Limits to Simulations of Thought and Action”, I argue that computationalism should not be the view that (human) cognition is computation, but that it should be the view that cognition (simpliciter) is computable. It follows that computationalism can be true even if (human) cognition is not the result of computations in the brain. I also argue that, if semiotic systems are systems that interpret signs, then both humans and computers are (...) semiotic systems. Finally, I suggest that minds can be considered as virtual machines implemented in certain semiotic systems, primarily the brain, but also AI computers. In doing so, I take issue with Fetzer’s arguments to the contrary. (shrink)

The nature of modern constructive mathematics, and its applications, actual and potential, to classical and quantum physics, are discussed.

The problem of epistemic opacity in Artificial Intelligence is often characterised as a problem of intransparent algorithms that give rise to intransparent models. However, the degrees of transparency of an AI model should not be taken as an absolute measure of the properties of its algorithms but of the model’s degree of intelligibility to human users. Its epistemically relevant elements are to be specified on various levels above and beyond the computational one. In order to elucidate this claim, I first (...) contrast computer models and their claims to algorithm-based universality with cybernetics-style analogue models and their claims to structural isomorphism between elements of model and target system. While analogue models aim at perceptually or conceptually accessible model-target relations, computer models give rise to a specific kind of underdetermination in these relations that needs to be addressed in specific ways. I then undertake a comparison between two contemporary AI approaches that, although related, distinctly align with the above modelling paradigms and represent distinct strategies towards model intelligibility: Deep Neural Networks and Predictive Processing. I conclude that their respective degrees of epistemic transparency primarily depend on the underlying purposes of modelling, not on their computational properties. (shrink)

According to L.E.J. Brouwer, there is room for non-definable real numbers within the intuitionistic ontology of mental constructions. That room is allegedly provided by freely proceeding choice sequences, i.e., sequences created by repeated free choices of elements by a creating subject in a potentially infinite process. Through an analysis of the constitution of choice sequences, this paper argues against Brouwer’s claim.

Human language has the characteristic of being open and in some cases polysemic. The word “infinite” is used often in common speech and more frequently in literary language, but rarely with its precise meaning. In this way the concepts can be used in a vague way but an argument can still be structured so that the central idea is understood and is shared with to the partners. At the same time no precise definition is given to the concepts used and (...) each partner makes his own reading of the text based on previous experience and cultural background. In a language dictionary the first meaning of “infinite” agrees with the etymology: what has no end. We apply the word infinite most often and incorrectly as a synonym for “very large” or something that we do not perceive its completion. In this context, the infinite mentioned in dictionaries refers to the idea or notion of the “immeasurably large” although this is open to what the individual’s means by “immeasurably great.” Based on this linguistic imprecision, the authors present a non Cantorian theory of the potential and actual infinite. For this we have introduced a new concept: the homogon that is the whole set that does not fall within the definition of sets established by Cantor. (shrink)

In the popular imagination, the relevance of Turing's theoretical ideas to people producing actual machines was significant and appreciated by everybody involved in computing from the moment he published his 1936 paper ‘On Computable Numbers’. Careful historians are aware that this popular conception is deeply misleading. We know from previous work by Campbell-Kelly, Aspray, Akera, Olley, Priestley, Daylight, Mounier-Kuhn, Haigh, and others that several computing pioneers, including Aiken, Eckert, Mauchly, and Zuse, did not depend on Turing's 1936 universal-machine concept. Furthermore, (...) it is not clear whether any substance in von Neumann's celebrated 1945 ‘First Draft Report on the EDVAC’ is influenced in any identifiable way by Turing's work. This raises the questions: When does Turing enter the field? Why did the Association for Computing Machinery honor Turing by associating his name to ACM's most prestigious award, the Turing Award? Previous authors have.. (shrink)