I just stumbled across this delightful quote from Thomas Hobbes: "The use and end of reason is not the finding of the sum and truth of one or a few consequences remote from the first definitions and settled significations of names, but to begin at these, and proceed from one consequence to another. For there can be no certainty of the last conclusion without a certainty of all those affirmations and negations on which it was grounded and inferred... He that takes up conclusions on the trust of authors and doth not fetch them from the first items in every reckoning, which are the significations of names settled by definitions, loses his labour, and does not know anything, but only believeth." www.bartleby.com/34/5/5.html
if we think of unbounded processes that produce a value at each iteration, that's the nearest notion to "infinity" that makes practical sense (computer science and constructivist mathematics would agree with that). but then computing equality between processes in general is impossible so there's a question of practicality of reasoning about such processes mathematically at least in general.
Rewatching some old stuff and this is very fun lecture to watch! The humor is very accurate and on point
I just stumbled across this delightful quote from Thomas Hobbes:
"The use and end of reason is not the finding of the sum and truth of
one or a few consequences remote from the first definitions and settled
significations of names, but to begin at these, and proceed from one
consequence to another. For there can be no certainty of the last
conclusion without a certainty of all those affirmations and negations
on which it was grounded and inferred...
He that takes up conclusions on the trust of authors and doth not fetch
them from the first items in every reckoning, which are the
significations of names settled by definitions, loses his labour, and
does not know anything, but only believeth."
www.bartleby.com/34/5/5.html
Thanks for a lovely quote!
Well, the first 10 minutes at least are completely unconvincing.
Nice ! I do 😅gree
awesome class! thank you so much for that!
This video should have more views
these lectures are amazing but they also slowly make me depressed. you have convinced me that infinite sets don't exist
It should be a happy feeling: that we don't have to repeat this nonsense anymore!
if we think of unbounded processes that produce a value at each iteration, that's the nearest notion to "infinity" that makes practical sense (computer science and constructivist mathematics would agree with that). but then computing equality between processes in general is impossible so there's a question of practicality of reasoning about such processes mathematically at least in general.
Good !