When you do that you are doing nothing more than applying heuristics, preforming limited simulation, looking for repeated states. All of these things are things that may be preformed by algorithmic computation. That we don't have IDEs already doing all of this for us is a reflection of nothing more than the current state of machine learning and the relative computational densities of today's electronic computers and the human brain.
Being able to solve the halting problem for programs generally seen in real life programming does not imply in the slightest that you can solve the halting problem for arbitrary programs. Can you look at arbitrary Turing machine tapes (large enough to eliminate the possibility that you are simulating it without realizing it of course) and non-algorithmically decide if they will terminate? Can you in fact do anything non-algorithmically? That is in essence what you are suggesting, the non-algorithmic nature of the human mind.
You are of course not the first to suggest a non-algorithmic mind. The likes of Roger Penrose have also suggested similar things (see his The Emperor's New Mind and later Shadows of the Mind). His reputation is enough to give me serious pause, and the fact that he does not seem to be a dualist further inclines me to listen to what he has to say.
If you want to delve further into this subject I suggest you check out Penrose's work, then read the criticism of it from his peers. Penrose has mounted the most qualified defence of the non-algorithmic mind of which I am aware, but even so acceptance of his thesis is rather rare in academia. It is not light subject matter but the general consensus among experts in the fields which he touches is that in order to support his thesis he made numerous errors. In absence of their expertise, I must defer to their assessment of Penrose's work.
Being able to solve the halting problem for programs generally seen in real life programming does not imply in the slightest that you can solve the halting problem for arbitrary programs. Can you look at arbitrary Turing machine tapes (large enough to eliminate the possibility that you are simulating it without realizing it of course) and non-algorithmically decide if they will terminate? Can you in fact do anything non-algorithmically? That is in essence what you are suggesting, the non-algorithmic nature of the human mind.
You are of course not the first to suggest a non-algorithmic mind. The likes of Roger Penrose have also suggested similar things (see his The Emperor's New Mind and later Shadows of the Mind). His reputation is enough to give me serious pause, and the fact that he does not seem to be a dualist further inclines me to listen to what he has to say.
If you want to delve further into this subject I suggest you check out Penrose's work, then read the criticism of it from his peers. Penrose has mounted the most qualified defence of the non-algorithmic mind of which I am aware, but even so acceptance of his thesis is rather rare in academia. It is not light subject matter but the general consensus among experts in the fields which he touches is that in order to support his thesis he made numerous errors. In absence of their expertise, I must defer to their assessment of Penrose's work.