2. The True Method
The editors note mentions Leibniz's early contributions to binary arithmetic, but the text is more about the "computer science" mindset the Leibniz is advocating for.
Leibniz's philosophical optimism and rationalism are some of the most pronounced in the history of philosophy. This text could easily be a founding document for some of the rationalists of our day.
Leibniz tries linking his rationalism to the broader concept of knowledge. The slope is slippery from knowledge, a broader Aristotelean sense, to computation. The obvious critique is that not all knowledge is computable. Putting that aside, it is remarkable how close this gets to a philosophy of computation. Even more, it is the attitude of computer science that is most detailed.
The reason is that mathematics carries its own test with it. For when I am presented with a false theorem, I do not need to examine it or even to know the demonstration, since I shall discover its falsity a posteriori by an easy experiment, which costs nothing but ink and paper, that is, by calculation, which will reveal the error, no matter how small it is. If it were as easy in other matters to verify reasoning by experiments then there would not be such differing opinions. But the trouble is that experiments in physics are difficult and have a high cost, and in metaphysics they are impossible unless God, for our sake, performs a miracle to make remote immaterial things known to us.
One of the beauties of computers is, once you design and program your software, the ability to be certain about your computation. A computer science major just needs their laptop to verify their work, a chemist or physicist needs an entire lab set up.
Leibniz would have been proud of the UIUC mathematicians who pioneered the proof by computer.
But this test is performed only on paper, and consequently on the characters which represent the thing, and not on the thing itself.
Another theme is abstraction. Leibniz paves the way here for relating the act of calculation with representation along with the computability of these representations. When we write software, we are not manipulating the things themselves, but the representations of them as 1s and 0s. This idea is simple but grounds so much of what the fundamentals of computer science are. Furthermore, the idea of trying to represent the real world and compute it is similar to all the patterns we see in AI. One could say a lot of the research in AI and cognitive science is just this, how to understand what humans do when they represent things and how we can formalize it such that we can compute it.
Leibniz touches on another point that has drawn folks to this type of computation-rationalism, the inability of others to objectively verify their beliefs. Rhetoricians and sophists could convince some that their words were true, that their political belief is correct, but never at the level of proof. When one has been burned by this or seen the dangers of it, it is not hard to want to only believe in something if the proof is logically rigorous.
This consideration is fundamental in this matter, and although many very able people, especially in our century, have claimed to give us demonstrations regarding physics, metaphysics, morals, and even in politics, jurisprudence, and medicine, nevertheless either they have been mistaken (because all the steps are slippery and it is difficult not to fall unless guided by some directions), or even if they did hit upon them, they have been unable to make their arguments accepted universally (because there has not yet been a way to examine arguments by some easy tests of which everyone is capable).
Author: Gottfried Wilhelm Leibniz
Original date: 1677