How do you model thought? │ The History of Mathematics with Luc de Brabandère
What are the rules of valid reasoning?
Logic and mathematics are two different concepts.
Find out how Aristotle first came up with the concept of logic - and why you cannot always use his formula to prove your point. Unfortunately.
Philosopher Luc de Branbandère guides us through the history of mathematics, from Egyptians measuring with the Sun to modern algorithms for self-driving cars.
Find out more:
https://en.wikipedia.org/wiki/Mathema...
Who would have thought of using logic? Aristotle, in his pursuit of the first model of thinking. Subscribe to follow the series ‘The History of Maths’ on our YouTube channel now.
There is quite often confusion between the two disciplines: mathematics and logic. You don't know exactly where and when mathematics stops. But logic, it was in Greece and we know who invented it, Aristotle.
Aristotle wanted to create a model of thinking. He wanted to achieve the science of valid reasoning. According to Aristotle, thinking unfolds in three steps. The first step is the concept. I'm thinking about something. I'm thinking about the table. The second step is the proposition, the statement. The table is beautiful. The third step is the reasoning. I like beautiful things. The table is beautiful. Hence, I like the table. And according to Aristotle, the third step was a syllogism. This is amazing. It was a model of thinking. Of course, it didn't work. He studied 256 different possibilities, different combinations of solutions, and he proved only 19 were valid. So, in a way, it's fascinating, but somehow, it's a bit sad, because as Bertrand Russell said, Aristotle’s logic is completely false and the only piece which is not false is useless and that's about the situation. But logic has a starting point with Aristotle.
So, mathematics and logic share a lot of things like rigour in thinking, but there are a lot of differences. In logic for example you don't have numbers, you don't have digits. But the disciplines were similar and lots of people wanted to merge the two disciplines. Leibniz had a dream, he wanted to completely merge mathematics and logic. And when he was disagreeing with somebody, he told the guy let's calculate just as if you can calculate thinking. Today, we know Leibniz's dream will never become a reality. Roughly a hundred years ago, Kurt Gödel a logician from Austria had his famous theorem and he proved that you will never completely merge both mathematics and logic. In other words, he showed that some statements are true, but nobody can prove it.
Join us next time to discover how the French philosopher René Descartes merged geometry with algebra to bring maths into the real world.
Subscribe now to watch our full series of ‘The History of Maths’.
