Philosophy
When it comes to the world of our sensory experience, the idea of "proof" is somewhat misplaced, since there is always the possibility of new evidence contradicting something we previously had every good reason to believe, not to mention the fact it could all be a dream or a simulation in The Matrix!
But in the world of abstract ideas, especially numbers, the kind of reasoning used there does lend itself to proofs because you get to specify exactly what you mean by a certain concept, and then all you have to do is follow a few rules of inference to deduce the logical consequences of your idea.
And we owe a debt of gratitude for the whole idea of theory and proof to the ancient Greeks, people like Pythagoras, Plato and Archimedes. But today we get to learn a little bit about the man who is widely considered the father of geometry, a title appropriate to the scope and importance of his work: he formalized the rules of geometry that mathematicians have relied upon for over two thousand years. That man was Euclid.
QED
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I've been interested in the claim widely made during the last week that by failing to fight the doping allegations against him, Lance Armstrong is implicitly admitting to cheating. There are two questions that are raised here. The first is whether...
- Can You Argue From Ignorance?
There is a standard reasoning error called "argument from ignorance" which is asserting that a lack of proof for something is proof of its falsity. For example, before I was about to teach this fallacy for the first time I came into the room to find the...
- Smartest People You've Never Heard Of (poincare Edition)
I'd been considering an occasional series about fascinating characters from intellectual history that are largely absent from the collective mind and with all of the fuss over the confirmation of the solution of Poincare's conjecture (for a nice...
- Ultimate Dr. Seuss Geek Topic
In The Cat In The Hat Comes Back, the Cat comes returns to visit the brother and sister during the winter-time when they are tasked with shovelling a large amount of snow. The Cat goes into the house and takes a bath, leaving a large ring around the bath...
- "the Light Of Alexandria"...first 1,000 Years Of Science
The Light of Alexandria by James Maynard ISBN-10: 1411653351 ISBN-13: 978-1411653351 SciArt Media writes: This is the history of science, in the first thousand years, from the birth of the world's first two scientists, Thales and Anaximander, until...
Philosophy
How to (and Why) Prove a Mathematical Theory
But in the world of abstract ideas, especially numbers, the kind of reasoning used there does lend itself to proofs because you get to specify exactly what you mean by a certain concept, and then all you have to do is follow a few rules of inference to deduce the logical consequences of your idea.
And we owe a debt of gratitude for the whole idea of theory and proof to the ancient Greeks, people like Pythagoras, Plato and Archimedes. But today we get to learn a little bit about the man who is widely considered the father of geometry, a title appropriate to the scope and importance of his work: he formalized the rules of geometry that mathematicians have relied upon for over two thousand years. That man was Euclid.
QED
- Admitting And Guilt
I've been interested in the claim widely made during the last week that by failing to fight the doping allegations against him, Lance Armstrong is implicitly admitting to cheating. There are two questions that are raised here. The first is whether...
- Can You Argue From Ignorance?
There is a standard reasoning error called "argument from ignorance" which is asserting that a lack of proof for something is proof of its falsity. For example, before I was about to teach this fallacy for the first time I came into the room to find the...
- Smartest People You've Never Heard Of (poincare Edition)
I'd been considering an occasional series about fascinating characters from intellectual history that are largely absent from the collective mind and with all of the fuss over the confirmation of the solution of Poincare's conjecture (for a nice...
- Ultimate Dr. Seuss Geek Topic
In The Cat In The Hat Comes Back, the Cat comes returns to visit the brother and sister during the winter-time when they are tasked with shovelling a large amount of snow. The Cat goes into the house and takes a bath, leaving a large ring around the bath...
- "the Light Of Alexandria"...first 1,000 Years Of Science
The Light of Alexandria by James Maynard ISBN-10: 1411653351 ISBN-13: 978-1411653351 SciArt Media writes: This is the history of science, in the first thousand years, from the birth of the world's first two scientists, Thales and Anaximander, until...