25 May 2021, 10:26 am
25 May 2021, 10:51 am
25 May 2021, 1:53 pm
Fnord wrote:
Gottlob Frege, for example, was a mathematician and philosopher, who worked on set theory and symbolic logic. He was also a mathematical Platonist, which means he believed mathematic propositions must in some way refer to abstract mathematical objects that actually existed in some sense.
If we take his example, and consider that abstract objects might actually exist, we must then empirically prove their existence. However, Bertrand Russell shattered the Platonist myth with his eponymous Paradox, which asks whether or not the set of all sets which do not contain themselves contains itself. If it does then it doesn't, and if it doesn't then it does. A material object cannot exist and not exist at the same time
David Hilbert is a 20th century mathematician, and was famous for examining problems he thought were most pressing to mathematics at the time. Probably most famous was his second problem, which asked for a proof that the axioms of arithmetic are consistent, and Gödel ended up proving that no such proof could be given. Thus, another mathematical proof that abstract objects do not exist in any material sense, because intrinsically inconsistent existence itself contradicts existence of such an object.
Max Stirner was a radical nominalist, believing that nothing exists but the concrete. What he meant by this is that abstract categories and ideas don't properly exist, and shouldn't be considered when deciding on how we live our lives. So, for example, the idea of "religion" is an abstract idea, and can't have any impact on our real immediate lives. Similarly, ideas like Socialism or Communism were abstract and utopian for Stirner, and he thought an individual should never devote his life to abstractions (he would rather colorfully call them "spooks").
Plato should have stuck with washing vegetables.
If we take his example, and consider that abstract objects might actually exist, we must then empirically prove their existence. However, Bertrand Russell shattered the Platonist myth with his eponymous Paradox, which asks whether or not the set of all sets which do not contain themselves contains itself. If it does then it doesn't, and if it doesn't then it does. A material object cannot exist and not exist at the same time
David Hilbert is a 20th century mathematician, and was famous for examining problems he thought were most pressing to mathematics at the time. Probably most famous was his second problem, which asked for a proof that the axioms of arithmetic are consistent, and Gödel ended up proving that no such proof could be given. Thus, another mathematical proof that abstract objects do not exist in any material sense, because intrinsically inconsistent existence itself contradicts existence of such an object.
Max Stirner was a radical nominalist, believing that nothing exists but the concrete. What he meant by this is that abstract categories and ideas don't properly exist, and shouldn't be considered when deciding on how we live our lives. So, for example, the idea of "religion" is an abstract idea, and can't have any impact on our real immediate lives. Similarly, ideas like Socialism or Communism were abstract and utopian for Stirner, and he thought an individual should never devote his life to abstractions (he would rather colorfully call them "spooks").
Plato should have stuck with washing vegetables.
So ... a guy who devoted his life to something called "radical nominalism" said that you "shouldnt devote your life to abstractions"?
That's rich.
25 May 2021, 2:14 pm
naturalplastic wrote:
Fnord wrote:
Gottlob Frege, for example, was a mathematician and philosopher, who worked on set theory and symbolic logic. He was also a mathematical Platonist, which means he believed mathematic propositions must in some way refer to abstract mathematical objects that actually existed in some sense.
If we take his example, and consider that abstract objects might actually exist, we must then empirically prove their existence. However, Bertrand Russell shattered the Platonist myth with his eponymous Paradox, which asks whether or not the set of all sets which do not contain themselves contains itself. If it does then it doesn't, and if it doesn't then it does. A material object cannot exist and not exist at the same time
David Hilbert is a 20th century mathematician, and was famous for examining problems he thought were most pressing to mathematics at the time. Probably most famous was his second problem, which asked for a proof that the axioms of arithmetic are consistent, and Gödel ended up proving that no such proof could be given. Thus, another mathematical proof that abstract objects do not exist in any material sense, because intrinsically inconsistent existence itself contradicts existence of such an object.
Max Stirner was a radical nominalist, believing that nothing exists but the concrete. What he meant by this is that abstract categories and ideas don't properly exist, and shouldn't be considered when deciding on how we live our lives. So, for example, the idea of "religion" is an abstract idea, and can't have any impact on our real immediate lives. Similarly, ideas like Socialism or Communism were abstract and utopian for Stirner, and he thought an individual should never devote his life to abstractions (he would rather colorfully call them "spooks").
Plato should have stuck with washing vegetables.
So ... a guy who devoted his life to something called "radical nominalism" said that you "shouldnt devote your life to abstractions"? That's rich. If we take his example, and consider that abstract objects might actually exist, we must then empirically prove their existence. However, Bertrand Russell shattered the Platonist myth with his eponymous Paradox, which asks whether or not the set of all sets which do not contain themselves contains itself. If it does then it doesn't, and if it doesn't then it does. A material object cannot exist and not exist at the same time
David Hilbert is a 20th century mathematician, and was famous for examining problems he thought were most pressing to mathematics at the time. Probably most famous was his second problem, which asked for a proof that the axioms of arithmetic are consistent, and Gödel ended up proving that no such proof could be given. Thus, another mathematical proof that abstract objects do not exist in any material sense, because intrinsically inconsistent existence itself contradicts existence of such an object.
Max Stirner was a radical nominalist, believing that nothing exists but the concrete. What he meant by this is that abstract categories and ideas don't properly exist, and shouldn't be considered when deciding on how we live our lives. So, for example, the idea of "religion" is an abstract idea, and can't have any impact on our real immediate lives. Similarly, ideas like Socialism or Communism were abstract and utopian for Stirner, and he thought an individual should never devote his life to abstractions (he would rather colorfully call them "spooks").
Plato should have stuck with washing vegetables.
• The First Law of Philosophy: For every philosopher, there exists an equal and opposite philosopher.
• The Second Law of Philosophy: They are both wrong.
It is even more "philosophical" when the two philosophers are the same person; like the "early" Wittgenstein and the "later" Wittgenstein.
29 May 2021, 8:50 pm
29 May 2021, 8:57 pm
