Philosophy Now Forum

1 "reflects" or "directs itself into itself". In doing this a cycle is achieved through reflection which in turn propogates further numbers as extensions of itself. That's just word salad. But one question occurs to me. Are you doing math, metaphysics, or poetry? Perhaps I'm tak...

What about it does not make sense exactly about reflection? You haven't defined it or said what it means. The nearest I can figure is that by reflection you mean that whole numbers come in +/- pairs, so that given 1 we also have -1. The usual terminology is that 1 and -1 are the additive inverses o...

Viveka wrote: ↑Tue Nov 14, 2017 8:36 pm Very interesting!

Glad you find that interesting. The complex n-th roots of 1 form a regular n-gon. That relates ancient geometry to the modern theory of complex numbers.

]I assumed it was public knowledge: https://en.wikipedia.org/wiki/Mathematical_HTML. Regardless of translation that is the meaning. If you said these are your own private ideas and notation and that you have a hard time explaining them to people, that would be believable. Your ideas and notation ar...

1 + 3 = 4 translates really as +1 ≡ +3 ≅ +4 or +1 ≡ (+1≡+1≡+1) ≅ (+1 ≡ +1 ≡ +1 ≡ +1) I'm making an effort to try to relate your ideas to something in standard math that makes sense to me. Now, 1 + 3 = 4 I understand. Can you define your use of the symbols ≡ and ≅? When you say +1 ≡ +3 ≅ +4 what do ...

Through dualities as "rotations" ... You might be interested in the roots of unity . These are the complex n-th roots of 1. As an example, consider the integers mod 4. These are the numbers 0, 1, 2, 3 with addition mod 4, meaning that the addition cycles around. So 2 + 2 = 0, 2 + 3 = 1, a...

dividing infinity is why motion is impossible (at least according to Zeno) He might be right. Perhaps we live in a block universe. Time is an illusion. All the points of spacetime exist "at the same time" in a 4D rectangle whose points are specified by three spatial and one temporal dimen...

Not necessarily, I envisioned this concept of infinity from the perspective of Omar Khayyam's Moving Finger. You mean: “The Moving Finger writes; and, having writ, Moves on: nor all thy Piety nor Wit Shall lure it back to cancel half a Line, Nor all thy Tears wash out a Word of it.” Clearly old Oma...

If I took infinity, traced my finger half way out on it, and cut it equally in half, and added that quantity of 'one' to one of the two sides, would the two sides be equal in size, or would the one with 'one' added be bigger? Both sides would still be the same. As an example, think of the real numb...

With all due respect, going into the modern distinctions between sets and classes and the likes, is irrelevant and misses the point here. I fully agree. I'm hitting the nail with the only hammer I have. I wanted to mention that since I just made a long post along the same admittedly irrelevant line...

@Arising_uk, I want to mention something that might put what follows into context. In grade school they tell us that a set is a "collection of objects." That leads us into error, as shown by Russell's paradox. Rather, a set is a very particular technical gadget in set theory. In fact if yo...

Of course you can disagree. But again, I have to remind you that the conversation I am having on this thread is about ancient logic. And the modern logician's opinion that I was commenting was himself discussing ancient logic in his book I quoted. So all through, the subject matter has been mostly ...

The reference to 1908 is probably a reference to Zermelo's axiomatisation of set theory. All this means that there can be no all-encompassing class/set. I don't agree with this interpretation. Nothing in set theory says that there can't be an all-encompassing collection, or class. It just can't be ...

I know I'm being simple but how can you call 'all sets' a set then? Is that what you mean by a class, all the sets? Oh I see, you're right. I misspoke myself. I should have said, The class of all sets is not a set. Equivalently, there is no set of all sets. When I said, "The set of all sets is...

... Yes that makes perfect sense. A collection that can't be contained in any other collection. In math that's a proper class. Like the set of all sets. ... What is a class then? For myself the 'set of all sets' sounds like it must be a set? Can't be. If the set of all sets is a set, then we can re...