Seeing That "French Grand Chef" Remains Relatively Humble, Let Us Continue Educating the Left!

Chán Zhōng Shuō Chán

The reason for continuing to educate the left is that "French Grand Chef" remains relatively humble. Although this person still does not fully understand the proof, at least their attitude is one of discussing the problem. Among all leftists, at least so far, despite still having confused areas, they are the most clear-headed -- not like certain people who can only deny everything, or certain others who haven't even figured out the conditions under which the diagonal method applies and still go around embarrassing themselves.

Since this is a proof by contradiction, all argumentation proceeds from the hypothesis that "all human thoughts can be stored in binary computers," then derives a contradiction, thereby proving the absurdity of this premise. Since we are talking about storing things in a computer, this means these binary numbers can be lined up in order. Whether they are finite or not does not affect the argument, though in practice, these numbers are indeed finite. From your post, I can see you understand this point. Everyone else must understand this first -- otherwise there is no need to read further.

Second, since "all human thoughts can be stored in binary computers," every thought within all human thoughts is encoded into a corresponding binary number. These numbers form a set A. In other words, all binary numbers are divided into two categories: those belonging to set A, and those not belonging to set A. We call those in set A "A-numbers" and those not in set A "B-numbers." You should be able to understand this.

Now, let us examine those binary numbers not belonging to set A -- namely, the B-numbers. These numbers, under this encoding, do not correspond to any human thought; otherwise, by the definition above, they would belong to set A. This point you should also be able to understand, though you might get confused.

Good. Now apply the diagonal method to set A. The binary number corresponding to the diagonal will certainly not belong to set A -- that is, this binary number must be a B-number. However, this binary number corresponds to the following thought: "its Nth digit differs from the Nth digit of the Nth binary number in set A." In other words, this binary number should be an A-number. I trust that after careful study, you will be able to understand this.

From the above analysis, we can find a binary number that is both an A-number and a B-number -- meaning it both belongs to and does not belong to set A. This contradicts the definition of a set. Why does this contradiction arise? Because the initial hypothesis -- "all human thoughts can be stored in binary computers" -- is wrong. By proof by contradiction, we know: "Not all human thoughts can be stored in binary computers." Here, I trust that as long as you are not someone who lets their backside dictate their brain, you should understand clearly.

In short, when the left makes errors, just admit them. You can always gloss it over with a "victory and defeat are the common lot of warriors." There are plenty of knowledgeable people nowadays. If you insist on being stubborn as a duck's beak on such a simple issue, you will only embarrass yourselves before the majority of onlookers -- and that can't be good for your recruitment of lackeys either!