Well you have the mind of a doubter. Won't get you far

showed that to be incorrect — Banno

I dont agree that life and desire work in that "logical" way

Gobbledegook, attempting to make an excuse to not be responsible for one's choices. — Banno

All my choices have been right in my view. How about your's to you?

You get what you desire — Banno

Yes

So that if you get poor outcomes, it's becasue that is what you desire — Banno

There is no such thing as a bad outcome. It all depends on how you take it. Every second is a past but the present remains

Pretty shitty reasoning. — Banno

Then you won't get far. The past doesn't exist

He replied, "No, this life is good. It's this body I am tired of — Questioner

Well I'm not going to argue with that

For example, sometimes we have to accept things in our life that suck — Questioner

Life doesn't suck. As the spirit desires so it has

Or, reading a good book that changes your perspective on life — Questioner

"In the active practical reality of consciousness observation thus finds opened up before it a new field. Psychology contains the collection of laws in virtue of which the mind takes up different attitudes towards the different forms of its reality given and presented to it in a condition of otherness. The mind adopts these various attitudes party in view to receiving these modes of its reality into itself, and conforming to the habits, cutoms, and ways of thinking it thus cones across, as being that wherein mind is reality and as such object to itself..." Hegel, phenomenology of mind

Disregarding what lies beyond our control means separating between what we can and cannot control with a will to control (power)

What does control over life mean?

You never walked to the car knowing you would get there? Usually changes in routine happen gradually

But making plans in life implies we can predict the future with some accuracy

If all is random how do we make decisions by predicting the future? Are you saying we have no control over our lives?

Good OP. Sometimes a beheaded cranium lasts alive for a few seconds. The "seat" of consciousness is the brain, complex matter. A structure like that can be said to have necessary AND random aspects, and I agree the random movements within the brain can be the expression of truly free will. But old Kant was in a bind when said nature was separate from consciousnss, the latter of which sees only appearances. Consciousness is shrouded in ever escaping darkness but to live is be united, to be organism. Sight is the gift that reaches out to expreience beyond it things and other beings. Free will is the core experience of consciousness. Animals may only have partial structures of it

neither believe in the supernatural -- and even if we mean "supernatural" in the sense of "outside of nature" Descartes still believes in nature -- res extensa is just as real as res cogitans, and while God may sit outside of nature and we have knowledge of his existence nature still exists. — Moliere

But nature for Descates is separate from the supernatural and is known psychologically. Logically for him i'm saying all that is is supernatural, although he roams around the objects of extension. I have not finished Being and Nothingness, so I better leave that one alone

Sartre: The meaning of being is different from what either Descartes or Kant are talking about, and Existence precedes essence. — Moliere

With Descartes, existence and essence are the same. For Sartre there is a divide between the two, hence our situation as humans. Maybe everything is supernatural for Descartes, while Sartre keeps it as an illusion out of distance, focusing on material problems

For me the world is as mathematical as geometric imagery. The world is mystical, nah, miraculous in how it is woven together. Maybe mathematics gives you that sense too. Thanks for the conversation!

You continually conflate math with physics and I continually note that this is a category error. — fishfry

I read this same argument in Kant recently. He wants mathematics to come from our intuition of the world yet doesn't believe the second antimony must apply to appearance. The only reason you don't want math to fully apply to reality is because you suspect a problem with infinite divisibility, right? Is not 5 yards minus 3 yards 2 yards? Always, forever? Is not 5 feet minus 3 feet 2 feet? I can get smaller and smaller. There is no reason it should end. You want math to apply to the world when they build bridges but won't go all the way, saying instead there is some invisible indeterminate line across which we can't do math. And you say this without a supporting argument. I don't buy it

I'm not a big fan of matter. How nice it would be to exist without being subject to the vicissitudes of objects - massive, medium size and subatomic - clashing and banging all around you, wantonly careening at you, and roiling inside you without regard for the effect it all has on you. Matter doesn't care at all about me, so why should I respect it? Well, I do respect some of it - nice people, a lovely beach, a perfect avocado, and some jazz records and math books. But most of the rest of it, phooey! One thing for sure, no one ever involved in a head on automobile accident ever said, "Thank the universe for the laws of physics". — TonesInDeepFreeze

An incredible paragraph. You're not just a mathematician

So they're mapping the infinite plane onto a finite disk by projecting it through a sphere — fishfry

Would it be mathematically possible to project an infinite plane unto a "discrete chunk" (to use QM language)? To me this sounds like a contradiction, but "discrete space" seems like a contradiction to me as well. If it's spatial it has parts. Is discrete defined well in mathematics? Again, they use it in QM.

https://m.youtube.com/watch?v=Jl-iyuSw9KM&t=235s&pp=2AHrAZACAcoFCkNjYyBzYWJpbmU%3D

Thanks for your response. The above video is very interesting but it's minute 2 I'm concerned with. This is how i see all geometric objects, and all objects in general actually. It's not as if i recoil in horror before matter itself, but i don't understand why something in mathematics so simple cannot be explained to me as if I were 8. Maybe I'm just neurally divergent. I've teased apart the finite from the infinite in an object, and in putting them together I find them contradictory, as have many philosophers in history, Hegel being one of them. Good day

Engineering claringly uses math as if it applies to reality. You seem to be saying there is nothing contradictory about continuums or that there would only be such only if they were in the real world. So then there is something about physical matter that in its properties is not entirely mathematical as we understand that. That may be true, although I would like to hear reasons why some day. Where do we draw the line when applying math to matter? How do we know we've gone too far?

String theory vs loop quantum gravity. One has little points that are really strings (1 dimension in 0 dimension?) And the other discrete space. The biggest question in physics (quantum gravity) wants to settle the question of the continuum. They don't want to just throw their hands up

the real numbers are defined as the continuum. They can be proven to exist within set theory, but that has no bearing on what's true in the real world. — fishfry

Some things obviously apply to the world. It is often said that there are no perfect shapes in the world. But we can mentally draw a perfect shape WITHIN any object although there it is surrounded by OTHER matter. The shape does exist as a part of another thing

Those are great logicians, great intellectual achievements. And a lot more (not necessarily in chronological order): Predecessors: Boole, De Morgan, Peirce, Cantor, Peano, Dedekind, Frege. Then Lowenheim, Skolem, Whitehead & Russell — TonesInDeepFreeze

It seems to me the foundation of mathematics is the number 1. Even zero is understood as compared to one. Zen masters wrote with one hand while erasing with the other, that is they used concepts to go beyond concepts. If Godel is widely misunderstood, the blame falls on those who explain it because i've seen many contradictory explanations of it (although I get a strong feeling you know what you're talking about). To see reality as one is to understand all duality in a higher sense. Godel might have proven something about human conceptual thinking but I am not sure his theorems are ontological per sé. The concept of strange loop comes to mind. In the philosophy of Zen, there is oneness (1), emptiness(0), and interconnection (web of concepts unsupported by 1, that is they are supported by zero). So the whole scheme of rationality will eat itself, especially with the projectory given by Mr. Godel himself. The final goal of minds within history is not to find an endless task. It would be great if we could base all of mathematics on the Whitehead-Russell argument in Principia Mathematica that 1 plus 1 equala 2. More complex steps from the must simple of ideas

Your picture of all of this is much too woozy — TonesInDeepFreeze

I am sorry if that is true

That makes no sense and is wrong: (1) By definition, a theorem is a statement that has a proof. (2) Incompleteness is not that there are statements that are unprovable "in any way". Rather, incompleteness is that if T is a consistent, formal theory that is sufficient for a certain amount of arithmetic, then there are statements in the language for T that are not provable in T. That does not preclude that statements not provable in T are provable in another theory — TonesInDeepFreeze

But do not Godel's theorems preclude proving everything in mathematics, assuming it's a consistent science, from the ground up. Systems don't exist in isolation. So if you can't prove it in one prove it in the other. And if the second had unprovable assumptions, move to the third? Where does it end? Logicism wanted to prove all of it from self evident logic, from bottom to top. Wasn't that dream shattered by Godel?

Thanks for the book recomendations

Hi. Finding quotes from Cantor on the internet with an apparent reliable source is difficult. There are lots of "quotes" out there but which are actually his? I don't know. Do you accept Wikipedia as a reliable source?
https://en.m.wikipedia.org/wiki/Absolute_infinite

I think the website is, generally, pretty accurate. Maybe you can explain some of the technical parts of it to us. Be that as it may be, it seems unlikely that so msny sources are wrong to claim that Cantor believed Absolute Infinity was divinity and that the mathematics in our minds express a truth about truth itself, truth bring divinity. See the link for some details. I don't have any problem with Cantor. I find his story fascinating and ideas on infinity always amaze me. This has a connection with Godel. As Roger Penrose has argued, the human intellect is non-computational, while Godel's arguments and most mathematics is not. He says basically "where can i look for the non-conputational substrate except in the quantum world". Well that world may be the realm of heaven. We can see it as dark OR light. My point is that what can not be proven in systems may be proven in a higher, err, place or state. Kant divided the mind into understanding and reason (logos). Nous may be a even higher stage when as the faculties work with together without separation ("not two"). Maybe i'm nuts but you can research the Penrose on Godel and Cantor stuff by asking AI where to go to find more information. Let me know what you find if you dig deeper in that mine. I too find it unfitting that there be theorems in mathematics that can never be proven in any way. Can there be a vision of mathematics that sees beyond our structure of systems?

I had no intention of misrepresenting you, but how many times over the years have we debated Zeno? Several for sure. It's not about supertasks. The cylinder simply lies there and the question of what color the top is after we notice it alternates from blue to purple is a basic arithematic geometric question that is so basic i suspect it has no answer. I'd gladly be proven wrong. But it seems the discussion always ends the same way. Is not the clash between string theory and loop quantum gravity largely about this? String theory says there the most basic thing is a zero dimensional string. Which is obviously a contradiction in terms. LQG says there is discrete space, but this suffers the exact same fate. We ARE the very union of finite and infinite, so we can not make sense of Zeno for this reason. So your response about supertasks was just another dodge in another year on a different, to my mind, with Zeno sitting firmly in place. Peaceful

Those are videos that are of the caliber of claiming that Cantor was a nutcase based on the fact that he was in sanitarium.
6h — TonesInDeepFreeze

Ive never seen such a video. And i was supporting Cantor so i dont know what you are talking about. As for seeing beyond mathematics, when i pressed fishfry on Zeno, he said uh oh let's not discuss it. Do you have the same answer?

Would you say that having freedom is dependent on being ignorant about some things? — wonderer1

We are lost because we are free, so say the existentialists

You're serious? You haven't caught on to the fact that such AI bots are so often horribly wrong and fabricate regularly? — TonesInDeepFreeze

No because i hardly ever ever use them. I don't have original sources for quotes by them; I had learned a little about them from internet videos. I've never claimed to have other than secondary sources, but if you search quotes by Cantor on the internet, there are these:

"The fear of infinity is a form of myopia that destroys the possibility of seeing the actual infinite, even though it in its highest form has created and sustains us, and in its secondary transfinite forms occurs all around us and even inhabits our minds."

"A set is a Many that allows itself to be thought of as a One."

Again I don't know if these are in his original writings. I do most of my research from actual books. But I was trying to add something philosophical to the debate

I don't know what relationship you have in mind between the quote of fishfry (refuted by me) and the quote of me, especially since neither references absolute infinity — TonesInDeepFreeze

I thought fishfry was referencing the set of all sets and numbers, and you seemed to wonder how we can go without being able to prove mathematics as a total system. For Cantor google says God is beyond all mathematics (a 0 or a 1?) yet completes all of the theory of numbers and sets. This is very Pythagorean. Only a special infinity can subsume the whole of math

Cantor thought the absolute infinity was God. I don't know if he ever claimed it was the whole story of mathematics.

Don't recall reading whether Gödel had an opinion on the matter. I don't think the concept of absolute infinity was relevant by Gödel's time — fishfry

Well from what I've been reading from secondary sources God is the infinity model for all infinities for Cantor. Godel had his ontological proof too, but i would have to check Chatgpt for more info

"
Cantor believed that God's infinity is the beginning and end of all other infinities, and that God's knowledge makes all infinity finite in some way.

Cantor believed that God put the concept of numbers into the human mind, and that the existence of numbers in God's mind was the basis for their existence in humans

Cantor's views on God were important to his defense of his theory of the transfinite, and he used his conception of God to motivate his conception of infinity in mathematics

Cantor believed that God put the concept of numbers into the human mind, and that the existence of numbers in God's mind was the basis for their existence in humans.

Cantor linked the absolute infinite, which is a number greater than any other quantity, with God"
Google AI

Your principle leads directly to a contradiction. The restriction needed to patch the problem is restricted comprehension, which would already require there to be an infinite set that's a superset of the infinite set you wish to conjure. Without the axiom of infinity, THERE IS NO SET containing all the natural numbers — fishfry

Every arithmetical statement is either true or false. There is a function that determines the truth or falsehood of every arithmetical statement. But, of course, it's not a computable function. The truth or falsehood of every arithmetical statement is determined, but there are arithmetical statements of which we could never find the determination. It's as if those statements and their determinations are "out there floating around" but I can't visualize what it means that they are true or false except that I know there is a function that determines them — TonesInDeepFreeze

Did not Godel and Cantor believe that once one sees Absolute Infinity he knows all (the whole story of mathematics)?

Achilles and the tortoise combine the "fact" (?) of infinite divisibility of space with the arrow paradox. The latter doesn't seem to understand propulsion and inertia but the former has always confused me. I would expect there to be something discrete and yet still space at the bottom of divisibility, but that seems like a contradiction in terms. Discrete can only mean points (it would seem). And sure, you can say that you imagine an infinity of them in a finite space, but you cant really imagine anything infinite. Only reason can understand the infinite, not imagination (it would seem). So how does the principle of infinity unite with the principle of finitude in order to have a geometrical object? To put it philosophically..

The difference between an arithematic infinity and a spacial/geometric one is that in the former the numbers have no spatial size and can thus sum to a finite sum. In the latter there are infinite instantiated steps, hence Zeno.

Most people seem to think Zeno was a minor philosopher. He was actually the first in the West to write a book of philosophy as that is understood in the modern sense. No one before him asked questions about the infinite like that. He was a Newton of his time. To think of infinite division back then was incredible. We still debate this today

Could you calculate the speed in all infinite steps — MoK

The arrow paradox says each is zero, as in time "points". Yet there is still the forward motion of the action, driven by energy

The thing about Zeno's paradoxes is that there is no finite time involved. The time would be divided infinitely just as much as the space or distance. Kant's second antinomy is Zeno's paradox. Maybe Banach-Tarski is too, idn. Everything becomes like infinite balloons stretching without end as they stay in space. Discrete space sounds like the answer for whomever don't like that acid nondual or whatever approach. It's hard to say what a discrete thing would be if it couldn't be divided. The back and forth would end. "Now space does not consist of simple parts, but of spaces. Thus every part of the composite must occupy a space. But the absolutely primary parts of the composite are simple. Thus the simple occupies space. Now since everything real that occupies a space contains within itself a manifold of elements external to one another..." Kant (second antinomy, antithesis).

I still think the mathematics used in physics can already address this question. What about Conformal Cyclic Cosmology (CCC). Penrose explains how the universe goes from the big bang to infinity, how we can used compactification to bring the infinite into the finite, and have a finite beginning after the infinite "forgets" it's infinite (his idea). Relations between that which ends and that which doesn's is the essence of this debate

The books you've recommended sound very interesting. I think Kant was right in saying that mathematics involves time (that is, process, synthesis). To *analyze* one plus one equals two is just to give a verbal description of having one and one. Mathematics is more than that. If i have 1 and see another 1, i have 1 and 1 and i "call that 2". But 1 added! to 1 EQUALS two because there is something in the addition that is synthetic instead of having backwards analysis. I realized this when i was trying to remember how i first used numbers. Mathematics is synthesis and analysis, but it's core meaning is synthesis it seems. I wonder how this relates to logicism

Thanks for the superb reply. The reason i brought up Hawking's "no boundary" thesis is that i was thinking maybe geometry and limits are incomplete by themselves and need the 4 spatial dimensions and 1 time dimension in order to make sense of it. That is, mathematicians assume math can stand on its own, but maybe it can't. However i also now see how the physics can be in trouble where maybe the math isn't. You've explained with the cylinder how the top of it is the limit such that if i metaphorically touch it with my finger i am touching a point limit. However if we bring in time and do the series Zenonian as i proposed (one at a time), and with each new slisce changed the color of the new slice, i can ask "what color" the top of the cylander would be. This causes a problem *because* it is a process and processes aren't used like that in mathematics. But again, Hawking had the thesis from the 80's that 5 dimensions (4 spacial Euclidean ones and 1 temporal one that acts as space and uses "imaginary time" as he says) wherein there is no before of time (as there is no north of the North Pole) express a hologram such that 2 dimensions are projected from the 5 dimensions infinitely far away. I know it's unorthodox, but why can't this been seen purely from it's mathematical side and brought into mathematics itself? Hawking explained away indeterminacy with this idea.The lines here seem rather blurry to me, but i read of mathematics mostly from the historical perspective, although i started working through a discrete mathematics textboom recently.

I will be thinking about your reply and other posts on this thread throughout the day