Just ask yourself how you grasp the notion of infinity. It's not by dividing by zero. It's by using "and then..." There's no obstacle in principle to having a computer reason about the consequences of having an axiom of succession. It doesn't need to have an infinite memory capacity to do so (anymore than you do).
On the general problem of grounding symbols, I think they must be grounded thru interaction with the world and the things symbolized. A computer depends on human beings to interpret and ground the symbols. Only a robot can ground the symbols itself, e.g. a Mars rover grounds they symbols for it's location, for the local terrrain, for the charge in its batteries,... Brent On 07/13/15, Pierz wrote: Here's something that bothers me when I try to think of the brain too much as a computer. How would I teach a computer the notion of infinity? In simple terms, how can I represent infinity in a computer program? All a computer knows about infinity is 'stack overflow' (or simply integer overflow), an inability to continue a calculation due to lack of computational resources. Yet obviously such a state has nothing to do with infinity, and the halting problem shows that no computer can "grasp" the notion of infinity through some algorithmic method. I could program in an infinity symbol and under certain circumstances teach the computer to spew out this symbol, such as when asked to divide by zero, but that's like teaching a monkey to press a button that causes a recording of Hamlet's soliloquy to be played whenever the monkey is asked, "How do you feel about your life?" The understanding of the connection between input and output is all external to the system. I'm curious to know - how could one even in principle write a program that would produce an output that could plausibly be regarded as a representation of infinity, generated by the machine? How, for example, could one get it to "work out" that a number divided by zero gives an infinite or undefined result, without simply programming that response? This is just another variant on the symbol grounding problem of course, but it seems a telling one, because infinity is a mathematical concept, and in its way almost as important as zero. I'm not advancing this exactly as an argument against computationalism, but I am curious to know if anyone has a better answer to it than simply something like "it will emerge at higher levels" or something - which to me just begs the question of how. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
