How do you model thought? │ The History of Mathematics with Luc de Brabandère


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 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 model
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 Russel said, Aristotle 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 day 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. 100
years ago roughly, 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.

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