An article that belongs here, about the relationship between reflexivity and creativity written last year on my other blog. The topic will have to be explored more deeply since this is important for how the proof in Kurt Ammon’s paper (http://arxiv.org/pdf/1302.1155v1.pdf.) works. Note also that Ammon in his paper writes (page 7): “This suggests that formal systems, in particular, Turing programs, cannot refer to themselves, that is, they cannot capture their own existence.” Creative Systems can and it looks like they must. They must be self-referring (reflexive).
The human mind is reflexive and creative. This means that we can (to an extent) look at our own cognitive processes and change them. Reflexivity means we can form descriptions of ourselves and our thinking; creativity means that we can change ourselves and our thinking processes by changing those description and then activating or executing the changed cognitive structure. Therefore, whatever description we form of our own thinking, we can act differently. So if we would describe thought processes in terms of formal theories or algorithms, we would be able to move out of the scope of validity of those descriptions In this way, reflexivity forms the basis of creativity.
In conventional “artificial intelligence”, researchers are trying to describe cognitive processes in terms of what essentially are algorithms or formal theories (these two terms may be used interchangeably). This has not been very successful. They have failed to understand that creativity is at…
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