"Zeno’s paradoxes have received some explicit attention from scholars throughout later centuries. Pierre Gassendi in the early 17th century mentioned Zeno’s paradoxes as the reason to claim that the world’s atoms must not be infinitely divisible. Pierre Bayle’s 1696 article on Zeno drew the skeptical conclusion that, for the reasons given by Zeno, the concept of space is contradictory. In the early 19th century, Hegel suggested that Zeno’s paradoxes supported his view that reality is inherently contradictory"
Internet Encyclopedia of Philosophy

Carrying that one step further into calculus using the limit at infinity seems - intuitively - natural and logical — T Clark

When you "imagine" infinite points on a segment you are not really imagining an infinity. I realize that the infinity gets smaller and smaller, but it still never ends and hence should have no finite boundary. Each digit of pi corresponds to a slice of space, so infinite space makes finite object, a contradiction, so says the Eleatics. What is intuitive for me is to say there are discrete steps, but it's impossible to explain that geometrically. Infinity seems necessary as a tool, not as a truth

Representing a continuum as an infinite series of infinitesimals seems like a good model of how the universe works, simple and intuitive — T Clark

It doesn't seem intuitive to me at all that space divides to infinity and yet has a finite limit. To my mind that is a direct contradiction, like a round triangle

I don't see why it would be a problem. For instance, there doesn't seem to be a bound to space or time, making both infinite. Nothing stops working due to that model — noAxioms

https://www.newadvent.org/summa/1007.htm#article3

I tend to agree with Aquinas but not because of the Aristotle stuff. I have a lot of thinking and mulling to do over the idea of "infinity" before i could say more

I concur that the intellect gives happiness, but so does the will. It's interactive. Schopenhauer was so dark in his writings because he placed will over reason and Spinozian philosophy is so bland because there is no will that is truly free in it's freedom, able to choose between options. Part of myself just accepts science as it is taught but there is a strong intuition for something else behind all the spinning atoms and emerging chemicals

How can nature have anything infinite within it?

In our human form understanding and will might be one faculty with two modes. One "soul". But in metaphysical questions of the origin of the world distictions between Will and Intellect can be useful. Will has active power. Intellect is passive, Platonic Ideas

Ye but that's assuming there is no motive power to begin with

Whether will is truly free with or without Reason is a good debate. Which is greater, intellect or will? It seems will is because intellect is completely under the control of will. It's its servant. But can will be without its servant? It seems to me it at least has to have some concepts of its own to function

It's true that the race is a chaotic mix of stops-and-starts, but overall the tortoise moves by infinitesimals, slowly, in what seems like an eternity, to reach a finite distance. Achilles keeps stopping everytime he reaches the tortoise, convinced he is simply faster, and in the end tires-out before even finishing — Nemo2124

For no other reason than that the tortoise starts ahead. But the quicker ability of Achilles must count for something? Ultimately Zeno keeps taking the movement backwards a step when it's constantly going forward. Calculus doesn't solve this

Will was higher than Platonic Forms for Schopenhauer, while Forms and Nous are equal to Will in Hegel's works. Schopenhauer was clearly unfair to Hegel. Hegel had a lot to offer philosophically in terms of Schopenhauer's type of philosophy. Schopenhauer's "Will" was without direction, ultimately free. Hegel says there is Fate founded on Reason. They are both right in a way

The world is Divine Thought- Spinoza
The world is human thought- Kant
The world is Divine Will- Schopenhauer
The world is human will- Nietszche
The world is Divine Thought and Will- Hegel
The world is human thought and will- Heidegger

You have two runners unable to move but Achilles has more force going in him so he wins by force

else to allow for qualitative differences between things. This is why the dualism of matter and form was required — Metaphysician Undercover

The dualism of two less than physical concepts like prime matter and form to get out of the paradoxes of the physical by marrying the fairy concepts together as a substitute for the physical was a mistake for Aristotle. In the hands of latter thinkers it was a disaster.

Ye it's abrigded. I'm gonna try to finish it again. Kant influenced Hegel's whole generation. Everyone was talking about him. By the time of Hegel's death Hegel himself was one of the most famous professors in the world

belief in the unbelievable in order to excuse the inexcusable e.g — 180 Proof

Not always. You won't always have clear cut rational options. Sometimes faith will appear, then go. Normally logic is virtuous, but there are times of higher consciousness wherein another set of laws influence

"Recently Kant has opposed to what has usually been called logic another, namely, a transcendental logic. What has been here called objective logic would correspond in part to what with him is transcendental logic." See para. 81

Absolute Spirit is entirely mystical, hence entirely esoteric

Over here on the left On the right is
is possible experience logic, cogito,
It is potential, it is excitment. and logos
and anticipation

How do we find in these books the nous Anaxagoros?

asserted your idea of what made his philosophy dualistic, but this question only relates conceptions to each other, both of them….matter and noumena….implied as being real things, hence not establishing anything for dualism per se — Mww

I get that. It seems Kant wanted to disprove metaphysics as a science with Newtonian materialism. What do you think?

Neither the matter nor the noumena establish something for dualism? I dont get your point



Wow i had a revelation. If the thing in itself doesnt cause phenomena, because casuality is in phenomena, then the thing in itself is just within the phenomena and is that which we can't psychologically get to. Kants sounds like a materialist then.

Rather confusione

I don't think your quotes from Kant on matter fully establish dualism. Substance is part of the categories and the only thing we know phenomenally is matter. The unknowability of noumena in this life is what makes his philosophy dualistic. Oddly

I think Kant is a dualist because there is the "I think therefore I am" thinking person, and the thing in itself that is unknowable. Kant fails to get rid of the thing in itself. He wants to know more, but can't. Kant can't. Poor Kant

I am reading the thin book with tiny printing "Science of Logic" - it hurts eyes due to the small prints in the pages but makes the book cheap, thin and light. This book has no information on the book — Corvus

Lol i have that copy too. It doesn't even have page numbers

Esoteric does have its place in knowledge. Yes Spirit is mind, body, matter. It is the actuality of all things. You can call it God in fact. It arises in all things and experiences in all things. YOU are your Ego but the true ground is Spirit. It is at the beginning and yet not at the beginning because it is at the end

Would it be the criticism on Kant from Hegel's point of view? — Corvus

Yes. You should know some of Kant before reading Hegel

The Science of Logic is very difficult. I love it but I have yet to finish it lol. And Ive never read a commentary on Hegel so I can't recommend one. You should read the Phenomenology of Mind [Spirit] however. I have not found anything in Hegel that doesn't make sense to me. No contradictions. It does take a lot of reading and also a lot of mental work to start to get what he is saying because he doesn't spell his whole philosophy out right away. Only those willing to run with him will win his prize

Such religious fever happens in all cultures because each religion can't make everyone it touches good. I'm wondering about basic faith as a state in learning though. When mathemticians started doubting parts of Euclid, did that doubt require some kind of intellectual faith in order to go on?

I don't think many writers of this forum would say "give up all reason and follow faith blindly without consideration of custom or common sense!"

So the question is whether faith plays any role in reason, in the life of the mind, and in philosophy

How do you know that it's unjustified? Like I said earlier, you're more certain than I am. The only suffering here is Abraham's inferred psychological suffering which you seem to be extremely concerned with — BitconnectCarlos

Are you saying Isaac deserved the death penalty for a crime/sin? Otherwise he was innocent and surely suffered, as his father suddenly bound him.

In the Book of Hebrews the writer says Abraham thought God would resurrect Isaac. The command was still to murder

"Kant rated dialectic higher- and this is among his greatest merits- for he freed it from the seeming arbitrariness which it possesses from the standpoint of ordinary thought and exhibited it as a necessary function of reason. Because dialectic was held to be merely the art of practising deceptions and producing illusions, the assumpton was made forthwith that it is only a spurious game, the whole of its power resting solely on concealment of the deceit and that its results are obtained only surreptitiously and are a subjective illusion. True, Kant's expositions in the antimonies of pure reason, when closely examined as they will be at length in the course of this work, do not indeed deserve any great praise; but the general idea on which he based his expositions and which he vindicated, is the objectivity of the illusion and the necessity of the contradiction which belongs to the nature of thought determinations: primarily, it is true, with the significance that these determinations are applied by reason to things in themselves; but their nature is precisely what they are in reason and with reference to what is intrinsic or in itself. This result, grasped in its positive aspect, is nothing else but the inner negativity of the determinations as their self-moving soul, the principle of all natural and spiritual life." Science of Logic, Introduction

"In this regard it must be remarked that the assertion that the [Kantian] categories by themselves are empty is certainly correct in the sense that we ought not to rest content with them and the totality which they form (the logical Idea), but to advance to the real domains of Nature and Spirit. This advance, however, should not be interpreted as meaning that the logical Idea comes to receive an alien content that stems from outside it; on the contrary, it is the proper activity of the logical Idea to determine itself further and unfold itself into Nature and Spirit." Paragraph 43, pg 86 in the lesser Logic "The Encyclopaedia Logic", translated by Geraets, Suchting, and Harris, 1991, Hackett Publishing Company, Inc.

The dualism between mind and body is real in Hegel, but at the completion of Spirit all is One, as it always was. Few point this out, but Hegel has matter "sublate" mind as well as mind sublating body. We are one with Spirit so we are in the creating of the world, but not to the denial of us being immediate bodies within Nature. I was gathering some Hegel quotes last night. I will post them latter in the day

Traditional conservatism respects Congress as the supreme law of the land. The executive and judiiciary are there to keep balance. Neither have more power than the other. State soverrenty applies to each state for their own culture and laws. When laws from Congress contradict a local law, the local statute must give way for Federal rights. Or they can go to court. Freedom and union. Now and forever

When you say that principles and mathematical axioms are the transcendental constructs of reason alone, I am not sure what you mean. Those principles, it seems to me, at their most basic are abstracted from reflecting on an analyzing our experiences, and then once established may be elaborated in accordance with the entailments implicit in them, entailments which are discovered progressively by doing (experience) as seems to be the case with mathematics.

So, I don't see reason as a disembodied thing that can stand alone — Janus

Kant seemed to do this 'removal of the mind from it's environment' thing. Reason can twist inward where it can no longer feel truth. This is why The Critique of Judgment is sentimental. He misses certainty that doesn't rely on a spurious infinity

Rosen says it is impossible to understand Hegel without understanding Plato and Aristotle. Do you agree? Why is it the case? — Corvus

Hegel uses terms from Aristotle and Platonism all the time. The "universal" he speaks of often. He turns things around though. In the Science of Logic you have there he says quality comes before quantity, which is the reverse of how Aristotle is usually interpreted. Aristotle seemed to think, in thought, there is first quantity or "matter" and that it is marked and structured by a form, which in turn is derived from a Form which is in the mind of the Prime Mover (or Movers). Simple, right? Hegel's take is influenced by Kant; quality is phenomena. Yes the world is matter. The Left Hegelians were correct! And so were the Right Hegelians after him. They both took part of the paradox and ran with it. Hegel tried to bring contradiction into a non-dual unity where there is no room left for contradiction. The latter becomes paradox, mystery, miracle, and we learn what is truly worth knowing.

This is why i used the term "bi-reality" in the other thread. It's dualism submerged in unity. We create the world (philosophy), and the world thru atoms make us (science). Reconciling this is the goal of Hegel's entire body of work. More on this latter..

He has the 1) unknowable, 2) the knowable by science, 3) those things known by faith without a consulting reason (laws of the heart), 4) and ethical life. None of them relate by causality to another one. "Cause" is only in the scientific realm. Hope and faith are left to stand on their own along with a moral life goal. The unknowable stands as something enticing for the intellect and is described dualistically as noumena and the -thing-in-itself (i have yet to grasp the distinction). But we can never reach it. We are to pretend there is design in beauty even while not allowing the mind to really believe this. All that is just disconnected for me personally. Some people regard him as the greatest philosopher ever

Spiritual, philosophical, mystical.. these are the same thing seen from different angles. Doesn't "phenomena" imply that it is mystical, and doesn't mystical imply miracles (miracles from the spiritual)?

A desire for facts and a desire for truth are not necessarily the same thing. There is something spiritual, which nothing other than that reality is mystical.