I've been meaning to ask you: "Descartes great merit here was to have applied geometry to algebra; he was not the first to have applied geometry to geometry... And to Descartes we owe the first systematic classification of curves. After dividing 'geometric curves ' which can be precisely expressed in equations from 'mechanical curves' that cannot, he classified the former into three clases... This new geometry is more than a general theory of quantity: it led to the concept of continuity, from which was developed the theory of function and, in turn, the theory of limits... But he was mistaken in believing that equations of any order could be so resolved." ( Britannica Encyclopedia 1965)

I think applying numbers to geometry is how we apply Godel's numbering to physics

Whether 1+1 creates a new number (Kant) or a set (Frege I think) is a question for phenomenolog psychology, not math. And most of these questions are not useful for modern science.

A process that is active is mental use of the four functions. This can be applied to reality but not perfectly

It's FALSE that motion through a point is the same as resting in a fixed point. There is energy that pushes right through. Imagine an arrow being pushed by the air rushing behind as it pushes forward. What's wrong with this picture (of the arrow)? It's that the motion forward is prior to air rushing behind so we can not saw the air pushes the arrow. The arrow moves through any point with forward velocity so it's never ever at rest

It's the language of a culture

The pre-Socratic ontology said that water was pure simplicity and with fire can make perfect movement. It bowls over into the reality of cars, etc (earth and wind) This was seen within the geometry of atomism and Zeno's thesis

You're approach is typology but you haven't said anything about the system works. (Topology says how you get results)

An object is bounded by points and a finite surface area. This is how continua is defined. The infinity is in the paths within these bounds, because parts, motions, and paths are uncountably infinite with it

He said some wanted an ultimate theory that can understand the world in finite ways with finite equations. He said he changed his mind when he reflected on Godel's theorems and realized that the world gives finite results when there is precision from us, who approach the universe as part of it. So there will always be a dialectic between the infinite and the finite in our dealings with the universe.
I am not allowed to quote that article

Let's let the master speak on that:

http://yclept.ucdavis.edu/course/215c.S17/TEX/GodelAndEndOfPhysics.pdf

All Godel showed in meta-language is that there are infinite things that cannot be prove in math and infinite things that could be proven (from sure foundations). What space IS cannot be precisely said by mathematics. Affirmation of a double negative is what infinity is, which translates to a double positive. The positives are abstract infinity (a single thing, undivided) and abstract finitude (the finite as idea). They merge to form infinite units, composing a single object that swallows itself. It curves back around like on a sphere. We experience objects in their finitude. In thinking abstractly, you have to go back and forth from the infinite as idea and the thought of "the finite" in dealings with uncountable infinity (in the form of points). I think this is how Leibniz understood it, but anyway it certainly is how Hegel understood Leibniz

I don't see how QM indeterminacy can be fitted into mathematics at its foundation

This paradox is fun to think about. Remember though that thinking of perception (like the threshold of hearing a noise) differs for people. SO defining what is out there in discrete terms will not result in the same answer for everyone. I think you are approaching this from a subjective angle for or less, which is how I see it

I've read a lot of your links but I'm not getting the information stuff. Information is "facts in the mind" by definition. A billiard table may be waves and particles but our experience of is as a sculpted particle. You might not see it from the front side, how mind could come from "that". But view.it from the side and then from behind and it is a different story

Why does a segment with a length of finite digits change into a length multiplied by pi (pi×2×r) when the segment is made into a circle? The circumference will have digits going to infinity while as a segment it did not? This must be readily explained in mathematics but I don't remember ever seeing an explanation on it

I apologize for calling your statement stupid. I had just had a fight with someone and your comment annoyed me. It seems you are always debating fishfry or someone about numbers and there relation to Kantian synthesis vs an analytic view. To me that's just a discussion about psychology and mathematics does truly take care to define what addition, subtraction, multiplication, and division are. I have not seen where you have a unique insight into the issue. But on eternal motion, Einstein and countless physicists believed in it. Eternal inflation, the "big bounce" , and all these ideas are just noting more than versions of it. I'm very aware of Aristotle's arguments about an accidental series (one that stands on its own) and an essential series (one with supernatural support). I've discussed this with Thomists who have PhD's. There is no consensus on philosophy on this. I think it's a physics mathematica question and that calling on supernatural support is unnecessary since I can describe it in terms of physics. But this isn't the thread to go into that, since I see no connection between it and continua

Eternal circular motion is fine. What is stupid is what you said about math not defining what addition means

What does it mean to add one unchanging quantitative value signified by '2', to another? Mathematics does not answer this inquiry, — Metaphysician Undercover

Uhhh

Furthermore, the nature of spatial expansion demonstrates that there must points where expansion is centered. — Metaphysician Undercover

I thought you were Aristotilean. You must be aware that Aristotle rejected points (infinitesimals) and instants

the curves are continua. — Ryan O'Connor

Discrete curves?

.

Continua is infinitely pointed. So it has instants all over it. If things move at the top level but fundamentally unmoved in subdivisions an object can't move at all. How I see it, we need to say "the infinite" is on one side and "the finite" is on the other and motion is movement between them

Idn. I've been recently working on this question from the angle of non-Euclidean geometry. I'm trying to understand what space even is

That's just how math is

I don't think you solved Zeno's paradox because you're putting the infinite quantity into philosophically blurry box and focusing just on finite results. Zeno said "the finite" and "the infinite" we're inherently exclusive of each other and so he concluded that idealism was true (a form of idealism wherein there are no 1s and 1s to be added into two)

Continua based constructions are based on an uncountable infinite amount being manipulate to a finite result. That is new. That's exactly what Newton did.

If you have a two foot segment and make it into a circle, suddenly it's pi/r/squared instead of two feet. Hmm. It seems that we must "round to the finite" in everything we do in geometry

Pi is a finite number because it's inbetween 3 and 4. But if the length of a circumference is multiplied by pi than you have a length with space corresponding to each number, so the circle has infinite space within a definite finite limit (like being inbetween 3 and 4). Aristotle never understood this stuff

It seems to me that a philosophy has to start with ideas, beliefs, and arguments before it can develop a further method with which to build a sculpture of thought

Theist say "God won't go to you because you don't go to him" yet this is an implicit admission their arguments aren't full proof. I'm not going to act all goodie and goofy in an attempt to force myself to believe in God. That is just stupid. I know they have no arguments so I stay where I am. I argue with they because they ignorantly say "but this person is your Fathet" and I respond "you don't know my family nor are you my family". Their agenda to make the world better with theism just doesn't work. The best is to have a balance and though I do desire everyone to be atheists im more than happy with the way things are

If I say intellect comes from matter, it's like saying steam comes from water. It's limited to phenomena which we know. When you say that the world is information, you are saying it's less than material and given to us by a higher intellect. My position seems much simpler than yours, if I am understanding you correctly. People seem so concerned that the human idea of universals reflect something real. It seems to me though that each human has his own humanity in a sense, although we can speak of common biology and this common nature in that sense. The first instinct is survival, and the second is the urge to mate. They don't always feel like the most fundamental but when felt strongly they appear as the basic unit of our psychologies. Situations can arise where love seems to trump both desires but the question of free will in those situations might more complex than we realize, and perhaps we love ourselves when we love others

The "principle of least action" is a natural law

What are the laws of the supernatural?

I can't imagine you don't see things in life that make you say "wow that is real". A silver car, a white female leg, a German shepherd, there has to be some thing that makes you pause and think "this is real"

The real is the natural

The supernatural is not something we can investigate so it's ultimate core might be unnatural. Theist want to set a rock in their reasoning to stop the thought that they really can't know what's going on in life. That is why they want to convince agnostics and call agnostics fools. But they can't disprove that the meta-truth of the supernatural is that it is grotesque

What is the probability of God being wicked? The world might be good but then again but God needs to allow the good for a greater evil. If people start thinking of God as just as likely being bad then they are less likely to ascribe strange events to a person instead of to a material cause

Post your thoughts on that thread. I thought that it indicated that proving anything a priori from logic alone is futile, but I may be wrong

"Infinity, the affirmation as the negation of the negation", Hegel

I don't know. I saw an article on Hegel and Heraclitus by an Islamic scholar that was really good. I don't know how they connect their theology to his but there are a lot of moving pieces. I'm finishing up the Encyclopedia brief on Logic today

I'm going to have a busy day, but we can talk more latter. I'm going to finish reading two books im the middle of and try to get a thread up on infinity inside of finite

So saying we are not "ideas" floating out somewhere, that says something about our nature. But maybe it only leads to psychoanalysis

I think I can reason without being in spiritual infinities. A lot of people think that is stupid or impossible, but it makes sense to me

If finite things (infinitesimals) make up finite objects, then the finite stands outside an infinite

Space and time reconcile to eternity and infinity your post said. A materialist view is that it reconciles to what is finite. Seeing objects as the union of pure passivity and activity is what I mean by being. Those are what "things" are in the world. " Stuff" is what people say when speaking of more holistic approaches, putting the universe in another box

Name something that you know with 100 percent certainty