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(1980) Mechanism, mentalism and metamathematics, Dordrecht, Springer.
Proclus spoke for antiquity in branding the infinite as incomprehensible and unknowable, remarking that "the imagination recognizes the infinite by not understanding it." Philosophers long maintained the incomprehensibility of the infinite — according to Descartes, "incomprehensibility is comprised within the. formal concept of the infinite" — though they later tried to explain it by reference to the limitations of the human mind. Hume still spoke for many when he said that "the capacity of the human mind is limited, and can never attain a full and adequate conception of infinity", where by "adequate conception' he meant a clear and distinct image in the mind. Hobbes had already elaborated this thesis as follows: Whatsoever we imagine is fiinite. Therefore there is no idea or conception of anything we call infiinite. No man can have in his mind an image of infinite magnitude, nor conceive infinite swiftness, infinite time, infinite force, or infinite power. When we say anything is infinite, we signify only that we are not able to conceive the ends and bounds of the thing named, having no conception of the thing but of our own inability ([131], p. 36).
Publication details
DOI: 10.1007/978-94-015-7653-6_2
Full citation:
Webb, J. (1980). Mind, number, and the infinite, in Mechanism, mentalism and metamathematics, Dordrecht, Springer, pp. 33-71.