In my last two posts on Computational Theory, I first explained the Church-Turing Thesis which can be summarized as the idea that all (full-featured) computers are equivalent.  I then went on to summarize some Computational Theory principles we can study and research once we assume that the Church-Turing Thesis is true. This research is primarily based around the limits of what a Turing Machine can do or how fast it can perform.

In this post I’m going to explore some of the philosophical ramifications of the Church-Turing Thesis, if it were to actually hold true. And at least so far (with one interesting exception) it has held true. Though in the end, I suspect many readers will feel they need to ultimately reject the Turing Thesis. But even if it does ultimately prove false, the very fact that it holds true in every case we know how to currently devise still makes it an useful scientific principle, for now. Continue reading →