Dear Sir,
You say: "Humans are imperfect reasoners". Since no one is perfect - having all the required or desirable elements, qualities, or characteristics; as good as it is possible to be, your statement is correct. But it does not prove that everything about human reasoning is imperfect. If that is so, then your essay itself is imperfect and need not be taken seriously.
You further say: "In particular, humans are imperfect mathematical reasoners". This implies, all of mathematics is wrong. And this begs the question: "What is mathematics"? The validity of a mathematical statement is judged by its logical consistency. When the equations in dynamical systems predict something, innumerable experiments show that it is correct. Do you mean to say, the landing of space crafts on Moon or Mars, which was based on these equations, a hoax? If "They are fallible, with a non-zero probability of making a mistake in any step of their reasoning", then the space crafts cannot land. Because even a slightest mistake would take it miles apart. If "This means that there is a nonzero probability that any conclusion that they come to is mistaken. This is true no matter how convinced they are of that conclusion", then nothing based on mathematical modelling should work. But this is contrary to observation.
If "Since individual mathematicians are imperfect reasoners, the entire community of working mathematicians must also be one big, imperfect reasoner. This implies that there must be nonzero probability of a mistake in every conclusion that mathematicians have ever reached", then all that you teach or the essays or papers you publish, are not worth reading, as they are imperfect. And if something imperfect works, then the definition of your "imperfect" needs to change.
Stochastic refers to a randomly determined process. The word first appeared in English to describe a mathematical object called a stochastic process, but now in mathematics the terms stochastic process and random process are considered interchangeable. In physics as well as in mathematics, there is nothing as random. There is a deeper order behind the seemingly chaotic system. If you could not see that, it is your fault - not that of the system. If one person is blind, it does not mean that the human race is blind.
Your example of "a collection of human brains" is a laughable proposition. It is "a collection of ideas" and not human brains, which are like computer hardware. Without the right software, it can't function. Since as per your principle, your paper is imperfect, I need not read more.
Please do not take it personally,
With regards,
basudeba