Self-reference Vs. Self-reproduction

As an answer to the question "are there finite mathematical descriptions that are not effective" posed by Hilbert, Turing provided the halting function as being not effectively computable despite being finitely expressible. This he established by devising the mechanism of Turing Machine, an abstract machine that captured the logic of thought (see Ref 1). In similar lines, von Neumann tried to capture the logic of life through the mechanism of computation, one of his attempts resulting in cellular automata and the self-reproduction theories (see Ref 2).

The primary question is: Self-reference posed a limitation on the logic of thought - can self-reproduction place any such limitation on the logic of life?

Interesting point to be noted here is that researchers study both self-reference and self-reproduction as being applicable to both human-beings as well the machines (see: NASA's Advanced Automation for Space Missions). However, oftentimes it appears that only machines suffer from the self-reference problem while human-beings get along with it fine. Then what about self-reproduction?

In a strict object-oriented sense the term self-reproduction is paradoxical. There is nothing like an object producing "itself". Nevertheless the concept of self-reproduction, at least from the experience of human-beings throughout centuries, is quite clear enough to mean it as the production of similar entity as opposed to "same" entity. This is in contrast to the concept of self-reference, where an object strictly refers to the "same" entity and not a similar entity. Further, if one goes slightly deep in understanding these terms, it could even appear that the whole concept of self-reference is paradoxical too. Details are as below.

A self-reference essentially is a reference (or addressing) mechanism. For it to work, the basic requirement is that one should be able to specify addresses for individual objects. In doing so, any addressing mechanism one thus chooses to use must be able identify each and every object uniquely. One can use any indexing scheme for this purpose (such as those described at Sequence Indexing). And Turing as well Godel have used what is known as Godel numbering mechanism:

Could it be that the concept of self-reference vs. self-replication finally boils down to the mind-body problem?




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