Arguments against the Halting Problem & Cantor’s Diagonalization

The actual is always finite. The infinite only exists as a potential to add more, or increase.

So in the absence of volitional consciousnesses which generate new algorithms, Turing's infinite set of all possible programs becomes finite, and halting problem will become solvable for any finite set of programs.

This throws a new insight into the nature of non-volitional phenomena. In a universe without volitional consciousnesses, it is possible use an inventory of all phenomena to derive a halting predictor, and such a halting predictor will be capable of predicting future of that universe.

This also throws a new insight into the function of volition in the universe. It's function is to maintain the validity of the halting problem. By predicting the future of the all known non-volitional phenomena, it can generate algorithms which makes all known halting predictors useless.

In a society of volitional consciousnesses, aside from the metaphysically given facts of reality, no facts are permanent. So any trend or pattern or algorithm that a sociologist or an economist would discover is temporary and is only valid as long as nobody acts based on it.

This is why a command economy cannot work. There is no way to create a five year plan. Such a plan will make itself inefficient.

All of this points to George Soros's and Karl Popper's idea of reflexivity but premises itself on Objectivism. That explains why George Soros is rich alongside people like Buffet, and Nassim Nicholas Taleb is right about the futility of modeling volitional phenomena.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s