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Article 2435 of comp.ai.philosophy:
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>From: torkel@sics.se (Torkel Franzen)
Newsgroups: sci.philosophy.tech,sci.logic,comp.ai.philosophy
Subject: Re: Penrose on Man vs. Machine
Message-ID: <1991Dec30.114032.7378@sics.se>
Date: 30 Dec 91 11:40:32 GMT
References: <1991Dec23.112144.6884@husc3.harvard.edu>
	<1991Dec30.172852.3305@csc.canterbury.ac.nz>
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Organization: Swedish Institute of Computer Science, Kista
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In-Reply-To: chisnall@cosc.canterbury.ac.nz's message of 30 Dec 91 04:28:51 GMT

In article <1991Dec30.172852.3305@csc.canterbury.ac.nz> chisnall@cosc.
canterbury.ac.nz (The Technicolour Throw-up) writes:

   >But "10^10^10" is an exceedingly compact representation for the number
   >it denotes.  It is a mere 8 ascii characters, and the function "^" can
   >be defined fairly succinctly.  Can your mind grasp, say, the base 10
   >representation of "10^10^10"?

  Claims that our minds, or some particular mind, can or cannot grasp
this or that have long been prominent in philosophy, and perhaps
particularly in the philosophy of mathematics. For example, Berkely
noted in a satirical vein that infinitesimals of various orders were
"clearly conceived and mastered" by the "comprehensive minds" of the
mathematicians; Brouwer claimed that the totality of countable
ordinals "cannot be constructed": others hold that on the contrary
such objects as the powerset of N can be "clearly envisioned without
ambiguities or contradictions". None of these claims really get us
anywhere. That so many discussions of the meaning and justifiability
of mathematics - even among supposed experts - reduce to such earnest
affirmations concerning the results of introspection is one indication
of the difficulty of the subject.


