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

I dont think that a real number can't be divided infinitely. The area of a circle is pi-r-squared wherein pi represents an aspect of space (the area). Each decimal would be a tiny and tinier slice of space and this goes on forever. So the space represents the number as we visualize it and the the number represents the space. Infinity is in both.

As for Hawking, physical explanations shed light on mathematical concepts just as the reverse is true.

"But nobody in that century or the next could adequately explain what an infinitesimal was. Newton had called them 'evanescent divisible quantities,' whatever that meant. Leibniz called them 'vanishingly small,' but that was just as vague.. Pierre Bayle's 1696 article on Zeno drew the skeptical conclusion that, for the reasons given by Zeno, the concept of space is contradictory."
Internet Encyclopedia of Philosophy

If there are no infinitesimals, than an infinity of zeros can equal anything. Does this mean that 0×infinity=everything? But an argument against infinitesimals and discreteness is that space by definition is that which is divisible. How can there be something in-between space and a point? Where do we even begin with a continuum? (At least Banach-Tarski's paradox makes more sense in this context) Geometric objects seem to be in themselves the opposite of Gabriel's horn. Instead of an infinite surface area for a finite volume we seem to have in the continuum an infinity of space bounded by finite (beginning and end) space

More latter..

If i cut a cake horizontally starting from the halfway point upwards with each slice being half the size of the one immediately below, what would the top of the cake look like? Isn't it indefinite? But you can definitely look at the cake, from all angles, and see that it has definite position in relation to its parts. So how do we reconcile the indefinite with the definite? I think this is what must be asked about the continuum. Hawking would say that four dimensional Euclidean space, with a time dimension that both 1) acts as space, and 2) is described by imaginary numbers, gives an answer to this question. That is to say, the universe as a whole gives the answer to the continuum. But how do imaginary numbers relate to geometry?

So if no real number is an infinitesimal, numbers are then what is relation to geometry. Is 2 then 2 points, or are all numbers a point?

According to Wki both Cauchy (in Cours d'Analyse) and Edwars Nelson also compared infinite points to the numberline. Long before hyperreals i believe. The great writer and philosopher George Berkeley rejected infinitesimals on both mathematical and philosophical grounds

What about imaginary numbers, however? Stephen Hawking, in his attempt at find the wave function of the universe, proposed his (yep) No Boundary Proposal in 1983. I like to apply this "theorem" to consciousness. Hawking uses imaginary numbers to describe time as it goes backwards, behind the Big Bang. How are we to understand mathematically a state not having any boundaries? There is always a "here" and "there" in our experience. That is, except in consciousness wherein we can go deeper and deeper and we find no edge. The "limit" seems to be death, but in our experience we are infinite. Hence we can think about infinities..

Note: if the world is a hologram, then it is proven there is a "thing-in-itself".

The kalam cosmological argument gives a great example of infinities embedded in another. The argument fails in its purpose because eternity, an infinity, contains all steps of infinity. There can be that infinity if there is the eternity. QED?

Just some philosophy and context for this forum

"Thomas Reid's excellent book, Inquiry into the Human Mind... affords us a very thorough conviction of the inadequacy of the senses for producing the objective perception of things, and also of the non-empirical origin of the intuition of space and time. Reid refutes Locke's teaching that perception is a product of the senses. This he does by a thorough and acute demonstration that the collective sensations of the senses do not bear the least resemblance to the world known through perception, and in particular by showing that Locke's five primary qualities (extension, figure, solidity, movement, number) cannot possibly be supplied to us by any sensation of the senses..." The World as Will and Representation, Vol. II, Ch. 2

I have some thoughts on perception that i wanted to post, so here it goes. It seems to me that there has to be a core ability/principle in man that turns raw sensation into perception. If colors are all in the head then an object doesn't "look like" anything. But then our eyes, perhaps the greatest organ, does not know reality. Does it see shape at least? In combination with touch, perhaps. But colors are just as much "there in front of us" as the solidity on which the colors lie. Things wouldn't even be black and white or translucent on there own. "In themselves" no sight could see them. So it seems to me that that there must be a soul in man that sees through the eyes and touches the object of vision in ocular activity. Science says all we see is light and that the objects are images in the brain (the world is in the brain?). George Berkeley was key in the development of this. But when I say soul I
Do not necessarily mean something spiritual. It could be a core principle that is more than spiritual (actually divine) or it could be a material principle (stemming from QM?) which is even more truly material than the world we are trying to know. That there is something unique in man in this way (although unique only as special and foundational, for animals may have it too) can be shown by how children learn language. We all know that if we come across ancient scrolls on which is written a language unlike any we know, we could never translate it. Yet this is the very situation a child is in. If i show a toddler a ball and say "ball", how does the child know that the word ball refers to that object instead of only to its extension, firure, solidity, or number. If i say to him "you jumped", how does he know the word "you" doesn't apply to the jumping? Of course this all happens in a complex context over time, but i still believe everyone would be autistic so to say without a natural core principle uniting our minds to each other. Even if a child is resting on the mother's breast and she says "love" as the child is feeling love, could not the word love mean rather "mother" instead of the act of love itself. Without a place to start we could never have common communication with each other. So I believe and think that we all have bodies that have all kind of natural intelligences in them, and the that mind is a limitless faculty that is designed to know people and the world itself. If we can't know the world, how can we know other people?

Kant quite clearly, after he read Hume, doubted the reality of everything except for his brain. Just as Descartes had done. Kant had logic while Descartes had mathematics. They both seem quite Platonic to me in that they doubted the contingent while holding on to the necessary. Yet Descartes was able to convince himself that a perfect divine Will existed while Kant was unable to prove he was once a baby craddled in his mother's arms. Descartes convinced himself by pure reason that perfect Will could not deceive him, while Kant relied on senses and understanding to hold on to his isolated ego. Descartes didn't seem to have a genuine "relationship" with a deity so maybe he was in the same spot. Descartes's philosophy entails that we can know material things but not all their components (noumena?). For Aristotle form and matter are a union resulting in a substance, but what we perceive is the accidents. The difference between Aristotle and the other two is that the accidents reveal something about the substance. Modern physics seems to disagree in that the space-time/vacuum is unknowable in itself. Night time thoughts..

Hegel on Kant's philosophy:

"The other side, in contrast, is the independence of the thinking that grasps itself, the principle of freedom, which this philosophy has in common with the metaphysics of older tradition; but it empties all the content out of it, and is unable to put anything back into it. Being robbed of all determinations, this thinking, now called 'reason', is set free from all authority. The main effect of Kant's philosophy has been has been that it has revived the consciousness of this absolute inwardness. In that, because of its abstraction, this inwardness cannot develop into anything, and cannot produce by its own mean any determinations, either cognitions or moral laws, it refuses all together to allow something that has the character of outwardness to have full play in it, and to be valid for it. From now on the principle of the independence of reason, of its absolute inward autonomy, has to be regarded as the universal principle of philosophy, and as one of the assumptions of our times." The Lesser Logic

For Hegel, Kant made the world into a lie, something that deceives, and did not allow reason access to the intellect in order that it could circumvent the traps of the understanding. Kant merely gives an inventory of the understanding instead of uniting freedom with thought. Why the understanding is how it is is never explained by Kant. It is truly the outside world provides the "shock" which the unconscious needs into order to become conscious. The non-Ego is as important to Ego as Ego is to itself. Our bodies are, in a sense, non-Ego. We are a part of this world and so Kant thought we could not solve the mystery of existence because we were part of the mystery. Whether he suceeded or not, Hegel's philosophy was an attempt to deduce the essence of existence itself

Eloquent, but it doesn't really address the issue i've raised. I'll let Christopher Hitchens speak for me here:

"I don't believe that it's true that religion is ethical or moral.. Is it moral to believe that your sins, yours and mine ladies and gentleman, brothers and sisters, can be forgiven by the punishment of another person? Is it ethical to believe that? I would submit that the doctrine of vivarious redemption by human sacrifice is utterly immoral. I might if I wished, if i knew any of you, you were my friends, or even if I didn't know you but just loved the idea of you, I could say "look, I'll pay your debts for you. Maybe you'll pay me back some day but for now I can get you out of trouble." I could, if I really loved someone who had been sentenced to prison, if I could find a way of saying "I'd serve your sentence" I'd try and do it. I could do what Sydney Carton does in the Tale of Two Cities, if you like. I'm very unlikely to do this unless you've been incredibly sweet to me, or "I'll take your place on the scaffold". But I can't take away your responsibility. I can't forgive what you did. I can't say you didn't do it. I can't make you washed clean. The name for that in primitive Middle Eastern society was scapegoating. You pile the sins of the tribe on a goat and you drive that goat into the desert to die of thirst and hunger and you think you've taken away the sins of the tribe. A positively immoral doctrine that abolishes the concept of personal responsibility on which all ethics and all morals must depend."

Catholics believe this doctrine, as do evangelicals. Sure there are Christians with different beliefs, but if I make a thread about Islam and 72 virgins, I don't have to mention all the dissenters who still call themselves muslim. There are Christians who believe Christ only covers their sin instead of being propitiation for them, but I don't see how they can explain the "nothing impure shall enter the kingdom of heaven" verse (Rev 21:27). Nevertheless, if you had really been following what I've said here you would know that I was tentitively rejecting atonment theology because of it's incongruence with reason, but was open to how to understand it in a more mystical, feminine sense. Logic is yang, and Christianity is a very feminine religion. I don't want to stand against something as a rationalist who subbornly sticks to his human logic.

Whatever. I've studied theology since i was twelve. Get lost

It implies that the merits can be exchanged between conscious beings even though to be free in a moment is to be in total control of which way to turn, so even God couldn't know what you would do except by vision of the future. So if you are in complete control of sin and repentence it would seem you are in full responsibility for it, so that would rule out atonment. Free will entails "individualism". This is what i've said in this entire thread. Look, if this kind of theology makes Christians feel better about themselves then may they feel their best. I think Christianity was founded by "Paul", whoever that was, and it's insistence on spread the word to the corners of the earth is one of its flaws. Why can't Christians just hope and trust that God will have mercy on them without this convoluted theology about substitution? That's what other religions do. Why do Christians feel they are so bad, that they are unforgivable on their own? Why to they have to put that self-blame on others? Now that is a true Christian mystery

Propitiation to my mind is a denial of free will. To be free is to be the only one making the decision. Ratzinger and Aquinas seem very confused. Do others sin when i sin? No but the merits can be exchanged? Someone cannot act as personhood unless his acts fall on him. Aren't they trying to "have their cake and eat too" by saying mercy and justice were balanced in the cruxifiction? Aren't they denying personhood in humans in line with savage beliefs of old? If we are all "one body" then how can they hold some will be damned? Forever a body divided? How unfitting is that

Thoughts:

With regard to why believe in spirituality, it's important to know that the universe is not necessarily fair. It is just, but that' different. Err, i take that back because I have no idea if the universe also is merciful, and to what extent. It might be in an unfair way. I have a twin brother Matthew and I don't care what he does i would never damn him, and i have a pretty strong commitment to morals. He would be standing there, the murderer of himself, and if i could i would still take him to heaven becausr it is that consciousness that i love. It's not just or fair, but love is the meaning of spirituality

I wonder to what extent we should care about the second truth or the reality beyond our own. There may well be a Paramarthika Satya or ultimate realm beyond the empirical, but what of it? Can a good case be made that we should care about this and to what end — Tom Storm

Only if it brings joy. Those thoughts are pointless if they don't make you happy

Nor Spinozism. My point was that you pick and choose rather randomly what is woowoo and what is not when it comes to the philosophy of physics

You seemed to be objecting to a post because of materialism but Spinoza wasn't a materialist. He thought you and the world were God's mind. Do you have cotempt for Daoism or is that ok as well?

"There is a thing confusedly formed
Born before heaven and earth
Silent and void
It stands alone and does not change
Goes round and does not weary
It is capable of being the mother of the world
I know not its name
So I style it 'the way'"
Lao Tzu as quoted in Primal Myths by Barbara Sproul

When applying philosophy to physics the lines can become blurred

Time can be a very hard thing for people because we only have so much of it. If we want everything to be perfect, we have to accept that for every mistake there can be an equal or greater victory.

shit-"philosophy — 180 Proof

Haven't you espoused Spinoza's philosophy in the past? Just saying

I am under the impression that Kant believed thing in itself or noumena was required for phenomena to appear. Remember, it was Gottlob Schulze who wrote that Kant contradicted himself in saying noumena causes the appearances in us even though causality is a law of phenomena. Schulze's argument is that of a rationalist and i certainly don't buy it

Thanks for the paper. In modern quantum theory they make as fine distinctions as scolastics of old. How many angels can fit in a quark, so to speak. The thing about Many Worlds is that people wonder, regret, and dream of what "could have been" a lot. Humans want it all, however it is that they get it i guess

I get it now: when scientists say the world is not locally real they mean superposition and maybe something like "many worlds" (?), and so non-local would be classical. I hope that's right because it feels right. It's weird how someone can read something and not get the key words but still get something out of it lol.

Anyway- the Nobel Prize in Physics for 2022 was awarded to three scientists for proving the world is not locally real. But is this like saying that noumena is not locally real? We know from experience what the classical is and isn't.. It's pretty interesting how this raises ancient questions but dresses them in modern garb (stylish). Between observer-centric theories and, say, pilot wave theory or objective collapse theory, there is John Wheeler's "participatory universe" theory, which states that the substrate of the quantum combined with the nucleus of the consciousness is what creates the world. It's an interaction between "I" and "not I". It's more of a duality becoming a whole rather than a duality of separation, and this is what guarantees we can have knowledge of the world

Henry P Stapp, an American mathematical physicist, known for his work in quantum mechanics, particularly the development of axiomatic S-matrix theory, the proofs of strong nonlocality properties, and the place of free will in the "orthodox" quantum mechanics of John von Neumann. — Kizzy

I am familar somewhat with Roger Penrose's ideas on the subject. I've never been clear about the distinction between local and non-local however. Are they both referring to aspects of quantum space or, then, what?

Thanks for the support and kind words. I enjoy the discussions on this forum very much and although I don't always know where they are leading, there seems to be a pattern working behind the whole project, and I hope everyone gets a lot of enlightenment from it

Yes a comparison between Kant and Descartes provokes many thoughts. What comes to mind for me is that the argument of the Third Meditation could, or may HAVE been, used by Kant in defense of noumena's existence. The thing-in-itself lives in twilight but it has to be there or else the world is made of plastic. I've never read Critique of Pure Reason in it's entirety. I think I've read 3 fourths of it, having skipped certain parts. The Meditations I've read many times but Hegel is the philosopher I've spent the most time with (maybe I can find where in the Greater Logic he comments on Kant's noumena!)

he never quite let it be known how it does what it does, which, obviously, relates precisely to what it is, or at the very least, to what it is conceived as being. — Mww

Well he did have his Passions of the Mind which tries to work out how the mind works. But that it is a substance, well yes i've read the Meditations and Replies. I would agree with you and Kant that someone can't prove the soul is a substance, but I don't believe it is a substance either apart from biology. Descartes in the Third Meditation argues that a Supreme God exists by insisting that his thoughts were akin to Platonic realities and reality must mirror their substance. Since the thoughts point to a totality of Being, God must exist. The archetypes would be empty and incapable of being thought if they did not indicate what the thoughts were of. What do you think of that argument?

We can research and compare the mental states that arise when I listen to the two styles of music, e.g. notice if my toes tap to the rhythms, check my dopamine levels, brain activity etc. and correlate the results with my reports. That's — jkop

Will they ever be able to say "the firing of this specific number of these neurons in this part of the brain will produce this specific intensity of this emotion"? Sure, some feelings are great and others bad, but a lot of this is subjective. Sometimes i'll feel two different feelings while making a choice and they feel equally strong yet I definitely want one over the other for which reason i have no explanation. Sometimes a bad feeling can feel kind of good, and vice versa. Again, i think it's too subjective to pin down exactly, despite the dream of certain brain scientists.

Since I'm not afraid to put ideas out there as my own, I would say that Absoluteness is nothing and there is nothing more final than nothing. So philosophy is about concepts relating to no thing at all, although it orients the brain to think in interesting and hopefully fruitful ways. Speaking with words such as "God" can have a lot of baggage, nor does the word "soul fair any better (although i am partial to both, especially the latter). The fact that the body is an organic unity is proved by sexual attraction. We notice the parts of the person as aspects of a whole. And the will moves the whole body through space. It's not as if I leave a part of me in another room when I roam the house, right?? There is the physical and the spiritual. Putting them together in non-duality is very difficult. Maybe i can do it someday

Some ideas:

Emergent consciousness is certainly a fact psychologically. We develope in stages thru life. The philosophical aspect is different for me. The self is certainly a substance in that the human body is a substance. The world is real beyond peripheral vision, the body is an organic whole: these are facts. Philosophy is in the Other-realm. Think of something existing in the multiverse. Then think of something existing in no universe, in a different dimension of possibility. That is the moving space of pure philosophy. It is not unknown but it is unknowable. Calling it nothing is the best because it is that, although the word nothing even says to much. In that "place" there is no substance, but just act. It parallels this world of bodies and brains. Where did the universe come from? Try the No Boundary Proposal. Where did the spiritual come from? Nowhere, emerging to be parallel with the bodies of the universe, which started whenever motion started, when matter or energy started to have activity. What causes this? Maybe gravity. So what am I? A body. Who am I? Anatman. Does the brain generate consciousness? Yes. Does the brain generate consciousness? No. Both

Are you saying the self is a substance or not?



You seem to be taking the self in a more than pragmatic self but the the world in simply a pragmatic sense. Could it be that both have more than "meets the eye"?

Very interesting. One can accept the Gospels to an extent while rejecting Paul. Neitszche thought of Jesus as a pacifist, full of love but not willing to defend himself, and therefore an "idiot" and a "decadent" as he said. He was sacrificed though because the love he showed made people uncomfortable with themselves. It wasn't about legal substitution as in "it is finished". He was a man full of divine light. When he said "I am the way, the truth, and the life", the I in that sentence is his union with father divinità. Union with God is the way, truth, and life he meant. "No one comes to the Father except through me" is, i understand, him saying "me" as the illuminened self. Except as you accept the light, so to speak. To be Christian means to feel guilty for something. That's the first requirement.. Someone must suffer and they believe God gives scapegoats out of mercy. It is not about justice, but mercy. Like Jesus with the woman of adultery

Yes because the "act/fact" for Fichte is freedom. Descartes and Kant had a priori structures and innate ideas as the source of consciousness while Fichte had yourself as the source of consciousness. This is how freedom comes about. Freedom is the being responsible for the ones' being(s) and acts. As pointed out, Buddhism seems to imply this same position as well. Schopenhauer kept the Platonic realm as after the will (to act/exist) and it seems this realm is where Descartes and Kant got stuck. I don't think they went as deep as he did

Trying to put Kant, Fitche, Spinoza, Einstein and Schopenhauer together, i recently made this progression of how human consciousness emerges:

1) nothingness > 2) emptiness > 3) imagination > 4) will > 5) personhood > 6) collective unconsciouss > 7) consciousness as intellect

I don't know if i'd swear by it but it feels accurate to me. However, if you think Kant coukd have refuted Fichte, it would be interesting to see how. It's also interesting to ask why Kant didn't do this while alive; maybe he was just getting old

Here is my commentary on the Stanford Encyclopedia's article on Fichte.

First to note, Fichte famously did away with the thing-in-itself early in his career. He wanted to establish a very fact upon which all philosophy could be based. Was this just the cogito?

*The published presentation of the first principles of the Jena Wissenschaftslehre commences with the proposition, “the I posits itself”; more specifically, “the I posits itself as an I.” Since this activity of “self-positing” is taken to be the fundamental feature of I-hood in general, the first principle asserts that “the I posits itself as self-positing.”*

So the I is in some sense prior to itself, hence the strange loop.

*Unfortunately, this starting point is somewhat obscured in Part I of the Foundation of the Entire Wissenschaftslehre by a difficult and somewhat forced attempt on Fichte’s part to connect this starting point to the logical law of identity, as well as by the introduction of two additional “first principles,” corresponding to the logical laws of non-contradiction and sufficient reason...*

I think this is more important that it seems. The I is necessary AS intelligent. The law of identity, non contradiction, and sufficient reason are part of the fabric of the "I posit" as if the I flows logically from it's own nature. The I can only posit an intelligent self that thinks

*"To posit” (setzen) means simply “to be aware of,” “to reflect upon,” or “to be conscious of”; this term does not imply that the I must simply “create” its objects of consciousness.*

Not "simply create" but create in a sense that there is no thing in itself. But the empirical I does not do this. The I of the body is IN the world as born and living

"The principle in question simply states that the essence of I-hood lies in the assertion of ones own self-identity, i.e., that consciousness presupposes self-consciousness (the Kantian “I think,” which must, at least in principle, be able to accompany all our representations). Such immediate self-identify, however, cannot be understood as a psychological “fact,” no matter how privileged, nor as an “action” or “accident” of some previously existing substance or being. To be sure, it is an “action” of the I, but one that is identical with the very existence of the same.*

Fichte was in a pickle. He didn't want to "say" we create the world or ourselves, but he puts himself in between saying we do and we don't in such a carefully balanced act that his philosophy must fall to one side. Everyone seems to agree he was an idealist. The encyclopedia is pointing out his hesitation on this

*In Fichte’s technical terminology, the original unity of self-consciousness is to be understood as both an action and as the product of the same: as a Tathandlung or “fact/act,” a unity that is presupposed by and contained within every fact and every act of empirical consciousness, though it never appears as such therein.

This same “identity in difference” of original self-consciousness might also be described as an “intellectual intuition,” inasmuch as it involves the immediate presence of the I to itself, prior to and independently of any sensory content.*

The difference between the empirical I and the transcendental I!

*To be sure, such an “intellectual intuition” never occurs, as such, within empirical consciousness; instead, it must simply be presupposed (that is, “posited”) in order to explain the possibility of actual consciousness, within which subject and object are always already distinguished. The occurrence of such an original intellectual intuition is itself inferred, not intuited...*

As bodies we are not aware of our source of consciousness directly

*A fundamental corollary of Fichte’s understanding of I-hood (Ichheit) as a kind of fact/act is his denial that the I is originally any sort of “thing” or “substance.” Instead, the I is simply what it posits itself to be, and thus its “being” is, so to speak, a consequence of its self-positing, or rather, is co-terminus with the same*

If it was a substance it could not create itself in any sense whatsoever. It would just "be". As an act which establishes itself, it can "be" prior to itself. Being prior to itself, it can be self conscious by reflecting on the I it is prior to

the idea of “constructing” intelligibility, that intelligibility is something constructed. I find nothing to suggest Kant’s philosophy, or, indeed anyone else’s, is about that, and in particular following from it, this notion of constructing the intelligibility of things. — Mww

This is how Fichte interpreted Kant. Kant's book on the metaphysical foundations of science has him constructing nature from intelligence in link with the noumena. There has to be something "out there" that wasn't phenomenal or spiritual from which intelligence can bounce its intuitions off of. Fichte has us creating ourselves (and probably even the noumena, although he went back and forth on this and probably on purpose) the same way Schopenhauer has it. The "I" posits itself. Why? For the reason that it can. It's a strange loop. (A strange loop has its place outside the world but makes less sense within the world, as does creation from nothing) A human would be responsible even for his birth for Fichte and Schopenhauer, as Buddhism had for so many years before proposed

But it doesn't usually involve the idea of an external force (like a higher power or subconscious mind) making someone do something with "infallible force" while preserving their freedom. Dennett was a strict materialist, i.e. the causal factors he saw were those known to natural science. Nothing at all about "higher powers" in his reckoning, all such ideas being remnants of "folk psychology".

A core idea in compatibilism is that freedom is about acting in accordance with one's desires and rational decisions, even if those desires are in reality determined by prior causes. Dennett and other compatibilists argue that free will is compatible with determinism because what matters is that individuals act according to their own motivations and reasoning, rather than being coerced or forced by external agents. The concept of being "forced" with "infallible force" typically falls outside compatibilist definitions of freedom because it would imply a kind of coercion that most compatibilists would reject. — Wayfarer

I beg to differ. "[T]he causal factors he saw were those known to natural science. Nothing at all about 'higher powers' in his reckoning": I guess you object to the use of the term "higher power" but in relation to Dennett it is just "those known to natural science". I see no different between your description of compatibilism and mine.

For instance, according to Dennett, as long as a person is acting in accordance with their desires and motivations, without coercion or external interference, they are acting freely—even if those desires are themselves determined by prior causes. — Wayfarer

If Dennett is a true compatibilist, he has to believe that the will is actually, genuinely free. That it can act on it's own and is the sole responsibility for it's actions. Spinoza didn't believe in free will, but he thought we act out of desires and motivations. By "without coercion", are you saying what I'm saying?

I think you're missing the background against which the whole idea of atonement makes sense. In ancient Judaism, atonement was achieved through sacrificial rituals, where offerings were made to reconcile the people with God after they had sinned. The idea of the 'scapegoat' comes from these practices—symbolically placing the sins of the community onto a goat and sending it away, taking their guilt with it (Leviticus 16). — Wayfarer

Ah yes, the whole idea of the priesthood is central to this. Jesus as High Priests, himself as sacrifice. But my objection to it is that it seems to be magic. If we are responsible for our own actions, how can something else external to our will affect what level or merit we are at or how we stand before justice? Furthermore, justice is not served to Jesus in this scenario because he has to be killed in order for it to work. And he was innocent they say. So those who did wrong do less than they would have had to and an innocent man gets killed. It doesn't seem rational

The two ideas belong to very different domains of thought—compatibilism in philosophy of mind and determinism, and atonement in religious and moral theology—so it's not clear how they relate to one another. — Wayfarer

Compatibilism is studied in Calvinism and Thomist and is very important in their systems. I think my description of compatibilism was more in line with how they speak of it than what, say, SEP would say.I Also, I related compatibilism to free will in the OP: if Jesus is fully human then he can sin. But he also can't, because he is God. Hence it seems compatibilism is needed in order to save the Incarnation.

Kant said he had to leave reason behind in order to have faith; Kierkegaard said we must crucify reason in order to have faith. Yet when Bergson held up intuition above reason, philosophers quickly retorted that he had to use rationality in order to attack rationality and therefore his position was circular. This is a very difficult subject. I am not a rationalist but the propositions of Christianity appear irrational to me. Many philosophy lovers are in this same position: objecting to to the "unreason" of Christianity while admitting reason only goes so far. Hence the thread

The subject of predication is the object of awareness, so subject and object are the same in that context. The conscious synthetic subject will analyze the object and account for predicates by synthesizing them into a mental picture. Substance and accidents don't refer to anything different anymore than matter and form for the reason that the object is particular (has "thisness"). You said on page 3 that angling was subjective but i think it is objective. You are using a dualism of substance and accidents (or a "quadism?" by using the prior prime matter/form distinction) to say that object of perception is beyond our comprehension. At the right time an object can be known for what it is. Right focus, right concentration are needed for this. Not bare "understanding", but intuitive knowing. Angles are part of the very shape of a thing. Without shape it's not physical anymore