It is common wisdom that the better the economy the better the incumbent president's chances of being re-elected. There are worrisome signs that Trump's trade war with China pose an increasing threat to the health of the economy. In today's NYT:

Chinese direct investment in the U.S. fell to $5.4 billion in 2018 from $46.5 billion in 2016, a drop of 88 percent, according to data from Rhodium Group.

In addition, China is the largest importer of US goods. It is also the largest creditor.

Like it or not the two countries' economies are tied to each other and Trump's attempt to hurt China hurt the US. To be fair, it is not just the trade wars. Concern over security is also a factor. And this has global repercussions that may further hurt the US economy.

Timing is everything. Even if the dire predictions turn out to be true if they are not apparent to the average voter before the election Trump will be ahead of the curve, and if he looses the Democrats will be blamed for the downturn.

The context was that of showing the consequence of the questionable claim that 2 + 2 = 4 exists in a Platonic realm. It was not me stating my own position. — Dfpolis

I do not wish to defend mathematical Platonism, but I think you misrepresent the position. The problem stems, at least in part, from jumping from Aristotle's criticism of Plato's Forms to mathematical platonism.

From the IEP article on Mathematical Platonism:

Formulated succinctly, Frege’s argument for arithmetic-object platonism proceeds as follows:

i. Singular terms referring to natural numbers appear in true simple statements.

ii. It is possible for simple statements with singular terms as components to be true only if the objects to which those singular terms refer exist.

Therefore,

iii. the natural numbers exist.

iv. If the natural numbers exist, they are abstract objects that are independent of all rational activities.

Therefore,

v. the natural numbers are existent abstract objects that are independent of all rational activities, that is, arithmetic-object platonism is true.

Your example of counting fruit is a straw man.

And, yes, abstraction does not create content, it actualizes intelligibility already present in reality. — Dfpolis

This strikes me as a form of Platonism, as if intelligibility is something somehow present in but other than the objects of inquiry.

I am not sure how you distinguish different concepts that were not in prior use from new concepts. Perhaps examples would help. — Dfpolis

Do you mean different concepts that were in prior use? In the briefest terms, the arithmos is always a definite number of definite things,a collection of countable units, whereas in modern math a number, '4' for example, is itself an object. With the move to symbols, 'x' does not signify anything but itself.

This is a wide-ranging topic that goes far beyond the concept of number. The second part of this book review that addresses Klein will give a better sense of what is at issue as it relates to modern philosophy and science: https://ndpr.nd.edu/news/the-origin-of-the-logic-of-symbolic-mathematics-edmund-husserl-and-jacob-klein/

I think we are using "concept" in different senses. I am thinking of <number>, <line>, <irrational number> and so on when I say "concept." You seem to be thinking rules of procedure. — Dfpolis

No, I am speaking here specifically about the concept of number, that is, what a number is.

No, I don't dismiss different conceptual spaces as wrong -- they are just different ways of thinking about the same reality. — Dfpolis

What you said was:

It is an intellible whole that becomes increasingly actualized (actually known) over time. — Dfpolis

Either you think that each of these ways are retained in the development of the intelligibility of the whole or some are modified and rejected.

I see that Fooloso4 has posted already. He quotes Spinoza, "By substance, I mean that which is in itself, and is conceived through itself: in other words, that of which a conception can be formed independently of any other conception."

Our hazard here - maybe just my hazard - lies in accepting something like this from Spinoza as explanation. — tim wood

It is not a question of accepting Spinoza for an explanation of what Hegel means by substance. I introduced Spinoza because of what Hegel goes on to say about God as the one substance. Why does he introduce this here, at this point?

Were Hegel here, I'd say, "Wha-at," and ask him to go through it again. — tim wood

One thing we can do is go through it again and again and again ourselves.

My problem is that I have no idea what it means to have a single unitary conception "formed independently of any other conception. — tim wood

I do not want to get into a discussion of Spinoza but it means that there is only one substance and that it is not derived from or dependent on anything else.

I think Fooloso4 just above has got some of it, but not all. — tim wood

Hence my comment about the tentativeness of what I said. One disadvantage of the way we are proceeding is that we have not read the whole of the preface or the whole of the book.

But at the moment it seems to me Hegel is allowing himself to float a bit, no feet on the ground. — tim wood

One assumption that guides my reading of the philosophers is that when things do not make sense to me the problem is probably with me and not the text. Hegel is certainly not floating. If anything, the density and compactness of what he is saying is likely to sink us. But the sense of not having your feet on the ground is apt. He is talking about the whole from within the whole, there is no ground on which to stand.

Each field of math assumes its principles (its postulates and axioms), but that does not mean that the principles can't be investigated and justified by nonmathematically. I — Dfpolis

You are avoiding the question. Science does not simply "assume its principles". It determines them through observation, hypothesis, testing, theory, modeling, and so on.

mostly via abstraction — Dfpolis

First, someone has to do the abstracting. Second, the properties of say a triangle are not determined by abstraction.

Please read sentences in context. — Dfpolis

You mean this context?

It leaves unexplained how mathematical truths that exist only in the Platonic realm can apply to reality.

In this last point, how can the Platonic relationship 2 + 2 = 4 tell us that if we have two apples and two oranges, we have four pieces of fruit? — Dfpolis

2+2=4 does not exist only in the "Platonic realm", does not need to "apply to reality", and it is meaningless to call it a Platonic relationship. It does not apply to reality because it is counting something real.

I said most of the foundations are the result of abstraction. — Dfpolis

To say what they are the result of is not to say what they are
— Fooloso4

What they are is not my present interest. — Dfpolis

So, in a topic entitled The Foundations of Mathematics, the actual foundations of mathematics is not your present interest.

The concepts that existed before the addition of unknowns, variables, functions and distributions continue in use today. Adding new concepts does not vitiate old concepts. — Dfpolis

It is not simply adding new concepts, it is a matter of different concepts. This does not vitiate old concepts in the sense that they are wrong, but that mathematics no longer operates according to the older concepts. But this is not simply an issue of mathematics but for philosophy.

If you are interested, the following will give you some sense of what is at issue: https://www.unical.it/portale/strutture/dipartimenti_240/dsu/Klein,%20Concept%20of%20Number%20Copy.pdf

Which leads to the question of whose mathematics?
— Fooloso4

Mathematics is not personal property. — Dfpolis

It is a question of assumptions and conceptual framework. As I pointed out, there is no number 0 or 1 in Greek mathematics. You might dismiss this as simply wrong, but in doing so what you miss is the ability to understand a way of looking at the world that is not our own.

17:

I trust that everything I have said in this discussion is taken as tentative, but here it may be necessary to state it. I have worked and re-worked this, each time seeing it somewhat differently. But since, as Hegel says, we cannot see clearly what has not yet completed its development, there may be errors here that will become evident to me as we move forward.

In my view … everything hangs on grasping and expressing the true not just as substance but just as much as subject.

It is instructive to compare this to what Spinoza says about substance.

By substance, I mean that which is in itself, and is conceived through itself: in other words, that of which a conception can be formed independently of any other conception. (Ethics , Part One, Definitions, III)

Hegel continues:

At the same time, it is to be noted that substantiality comprises within itself the universal, or, it comprises not only the immediacy of knowing but also the immediacy of being, or, immediacy for knowing.

The universal is unity of the immediacy, direct and unmediated, of knowing and being, of knowing and for knowing.

However, in part, the opposite view, which itself clings to thinking as thinking, or, which holds fast to universality, is exactly the same simplicity, or, it is itself undifferentiated, unmoved substantiality.

In what sense is this the opposite of the view Hegel presents above as his view? In Hegel’s view the universal is within substance, here thinking is itself undifferentiated, unmoved substantiality, the universal.

But, thirdly, if thinking only unifies the being of substance with itself and grasps immediacy, or intuition grasped as thinking, then there is the issue about whether this intellectual intuition does not then itself relapse into inert simplicity and thereby present actuality itself in a fully non-actual mode.

Intellectual intuition is given in its immediacy to thought by thought. It is inert simplicity because as given it does no work.

In the middle of these distinctions there is what seems to be a non-sequitur:

However much taking God to be the one substance shocked the age in which this was expressed, still that was in part because of an instinctive awareness that in such a view self-consciousness only perishes and is not preserved.

I take this is a direct reference to Spinoza’s God. Hegel thinks it shocked the age not because, as is commonly assumed, threatening the status of God as distinct and separate, but because it threatens the status of man as distinct in his self-consciousness. It is not a non-sequitur because this is precisely what is at issue - the relationship between God, man, thinking, and the whole.

First, sciences do not establish their own principles — Dfpolis

Where do you imagine these principles come from?

I did not claim that Greek math was Platonism — Dfpolis

After a full paragraph on Platonism you said:

Platonic relationship 2 + 2 = 4 — Dfpolis

This is not a "Platonic relationship", it is simple arithmos, the counting of ones or units.

I said most of the foundations are the result of abstraction. — Dfpolis

To say what they are the result of is not to say what they are. The most basic concepts of of Western mathematics underwent a fundamental change with the origin of algebra, that is when numbers were replaced by symbols. Which leads to the question of whose mathematics?

I disagree with much of the quote you gave from Maurer. — Dfpolis

Are you disagreeing with his reading of Aquinas? If so, where do the mistakes lie? Or is it that you are disagreeing with Aquinas?

Once again, the title of your topic is "The Foundations of Mathematics". Those foundations are not in modern mathematical theory or methodology. Greek mathematics is part of that foundation. Greek mathematics is not "Platonism".

To say:

... our mathematical concepts have a foundation in reality. — Dfpolis

Is like saying a building has a foundation in the ground. It says nothing about that foundation.

See Armand Maurer, The Division and Methods of the Sciences — Dfpolis

Instead, it would be more useful to direct the reader to Maurer's "Thomists and Thomas Aquinas On the Foundation of Mathematics", available free online: http://www.u.arizona.edu/~aversa/scholastic/Thomists%20and%20Thomas%20Aquinas%20on%20the%20Foundation%20of%20Mathematics.pdf

From that paper:

There are important consequences of Aquinas's placing the notions of mathematics in the second order of his quaestio disputata instead of the first. Unlike concepts on the first level, those on the second do not properly speaking exist outside the mind. Their proper subject of existence is the mind itself. They are not signs of anything in the external world. Hence mathematical terms cannot properly be predicated of anything real: there is no referent in the external world for a mathematical line, circle, or number. Finally, mathematical notions are not false; but neither are they said to be true, in that they conform to anything outside the mind. Aquinas does not suggest that they might be true in some other sense. (56)

Thank you for your comments. I have no problem with the neoplatonic One Identified as God. — Dfpolis

The title of your topic is The Foundations of Mathematics. The neoplatonic One Identified as God has nothing to do with the foundations of mathematics or anything I said. You have completely ignored the foundation of Greek mathematics which makes your pseudo-problem of counting disappear. 2 + 2 = 4 is not a "Platonic relationship", at least not for Plato or the foundation of Greek mathematics.

In the Greek arithmos a number is always a number of something. A number tells us how many ones or units. This is why Aristotle says that two is the first number. In your example of two apples and two oranges, there is no problem of determining how many as long as we know what the unit of the count is. In this case pieces of fruit. In the same way you determine that there are two apples and two oranges, you determine that there are four pieces of fruit, that is, simply by counting them. Modern number theory and set theory axioms is anachronistic.

With regard to Platonic Forms, what the One itself is remains. But the questions of the One itself and the One and the many do not concern the mathematician.

The classic modern work on this is Jacob Klein's Greek Mathematics and the Origins of Algebra.

16:

In so doing, this formalism asserts that this monotony and abstract universality is the absolute ...

In its formulaic universality it abstracts from every difference, every particularity, and thus renders everything the same. It is not the universal Idea that he objects to but:

... the universal Idea in this form of non-actuality

It calls itself speculative knowledge but:

... what counts as the speculative way of considering things turns out to be the dissolution of the distinct and the determinate, or, instead turns out to be simply the casting of what is distinct and determinate into the abyss of the void, an act lacking all development or having no justification in its own self at all.

As opposed to this:

... whereas in the absolute ...

that is, in the absolute as it is properly understood:

... in the A = A, there is no such “something,” for in the absolute, everything is one.

At first glance it may seem as if the two views are the same, that there is no difference between them, but in unity there is difference, otherwise there is nothing to be unified.

What does it mean for A=A? Traditionally it means identity, but to say that this equals that is to assert some difference. In identity there is difference. Is it then that A=A means this equals this? What then is the function of the equal sign, what does it mean for something to equal itself?

To oppose this one bit of knowledge, namely, that in the absolute everything is the same, to
the knowing which makes distinctions and which has been either fulfilled or is seeking and demanding to be fulfilled – that is, to pass off its absolute as the night in which, as one says, all cows are black – is an utterly vacuous naiveté in cognition.

The opposition here is not between the affirmation and denial that in the absolute everything is the same. Both sides agree on this. The difference is between the knowing which has only this one bit of knowledge and the knowledge which makes distinctions and either has or seeks to fulfilled itself in knowing the same in difference, the one out of many.

' ...this other view instead consists in only a 'monochrome formalism' (para 15 ).

I referred to this earlier, thinking it might have to do with the formalism of Kant.

I would be grateful for some clarity on this, thanks. — Amity

I just looked into this a bit. Hegel says that Kant's Categorical Imperative, his moral formula of universal law, is "empty formalism". It is empty because it has no content just the form. Although we find here the absolute and the universal, I don't think that it is Kant's formalism that is at issue.

So, what is the formalism that Hegel rejects? That "in the absolute everything is one ... in the absolute everything is the same" or, as he mocks it in #7: " to stir it all together into a smooth mélange".

I don't want to derail the topic, so I will only make a few quick comments. I would be glad to discuss the issue elsewhere. While I agree that the Forms can be seen as situated between Parmenides and Heraclitus (there is interestingly enough no dialogue Heraclitus), the setting of the dialogue at the time when Socrates was young suggests that it was not simply in his later years that Plato came to question the Forms as some claim. The Forms are not things known, they are images and despite all the talk of them being what things are the image of, they are themselves images. Further, since Plato makes clear that, contrary to what Neo-Platonists, mystics, and some religious believes hold to be true, anamnesis or recollection is a myth, and as such does not support the Forms but makes their existence even more problematic. They are, in my opinion, and in no way only my own, a gift of philosophical poetry, which does not to diminish their importance and value.

Fooloso4 has taken me to school a bit in "correcting/refining" my contribution above, and in my opinion he did a great job! — tim wood

Thank you Tim. That was most gracious. Perhaps one of these days I will be obliged to return the favor.

The next few paragraphs further develop this. 16 begins:

In so doing, this formalism asserts that this monotony and abstract universality is the absolute ...

I did not think of the intentional breaking of instruments as a "form of expression". But if it is your only instrument then unless or until you get another you can't play. Even if you are playing free jazz you are not free of your instrument.

The wiki article on Naturphilosophie might be helpful, particularly the following:

Schelling's Absolute was left with no other function than that of removing all the differences which give form to thought. The criticisms of Fichte, and more particularly of Hegel (in the Preface to the Phenomenology of Spirit), pointed to a defect in the conception of the Absolute as mere featureless identity.

Re #15, two things I get - infer - from it is that "idea" is itself not static, and thus anyone or anything, any system, that claims to "have" it, is wrong. — tim wood

You are correct in that the idea is not static, it does not follow, however, that anyone or anything, any system, that claims to "have" it, is wrong. Hegel's claim is that he has it.

Your assumption seems to be that since the idea is not static that it does not complete itself. But Hegel claims that it has completed itself, at least to the extent that it understands itself within the whole of itself.

... knowledge conforming itself to what is to be known. — tim wood

What is to be known is itself, that is, it is not simply a matter of knowledge of things but knowledge of knowledge, knowledge of the knower.

I find in this idea an opposition to the Platonic eidos - the perfect form that is the model for the Greek's imperfect reality. — tim wood

That too is correct, but you seem to have missed the point.

When Hegel says:

... having become moments of the whole, again develop themselves anew and give themselves a figuration, but this time in their new element, in the new meaning which itself has come to be.

that does not mean a return to Plato but a dialectical rethinking of not only Plato but of the whole history of philosophy. Although he has not used the term, it is aufheben, both to cancel or negate and preserve. You referred to "aufheben and sublation" on page 4. Sublation is the English translation of aufheben. It is the preserve part that you seem to have overlooked. It is not a matter of leaving the past behind. If we are to understand the ontological status of 'idea' for Hegel we must see that he does not mean what we ordinarily mean when we talk about ideas. On the other hand, he does not mean some transcendent realm of unchanging beings either.*

On the relationship of Hegel to Plato by a quick search I found this: https://www.academia.edu/20121186/Platos_Positive_Dialectic_Hegel_Reads_Platos_Parmenides_Sophist_and_Philebus

I only skimmed parts but it might give you a better sense of what is at issue.


*Of course, it should not be overlooked that Plato himself rejected this. In the dialogue Parmenides, the Forms, as presented by a young Socrates, are shown to be incoherent by Parmenides. The Forms are Plato's poetry, designed to replace the theology of the poets. I have written about this elsewhere on the forum. Plato was, after all, both a master dialectician and rhetorician.

But the extent to which you allow this to happen is determined by you.
— Fooloso4

Not always possible. Think circumcision. — Amity

Point, or should I say tip, taken. But as the sculpturer of yourself you begin with the material you have to work with.

One does not begin with the ability to play freely. So too, one does not begin with the ability to live freely.
— Fooloso4

For sure, we start off with little.
As we grow, a few might still not have the ability or capacity to play music or live freely.
Depending on many factors- physical, geographical, political circumstances. — Amity

While I agree that these things play a role, if two people start off more or less the same, with similar ability or capacity, and have similar physical, geographical, political circumstances they may not both be able to play or live freely. It has to do with what one does with what she is given.

However, a child or someone with limited abilities, knowledge or talent can still sing, dance and jam without constraints of rule following. They are being themselves. — Amity

From the article "What is Free Jazz" from Masterclass https://www.masterclass.com/articles/what-is-free-jazz#what-is-free-jazz

Free jazz stemmed from a basic principle, one that most musicians (and indeed, most artists) are familiar with: learn the rules—then break them.

I might add, learn your instrument and don't break it.

So too with life. To live free one must first learn the rules. In neither case is it simply a matter of doing whatever you want whenever you want.

15:

When it comes to content, at times the other side certainly makes it easy for itself to have a vast breadth of such content at its disposal.

This is a continuation of 14, of the:

... opposition [that] seems to be the principal knot which scientific culture is currently struggling to loosen and which it does not yet properly understand.

The other side refers to those who reproach science. But in doing so they make use of what science has accomplished.

It pulls quite a lot of material into its own domain, which is to be sure what is already familiar and well-ordered, and by principally trafficking in rare items and curiosities, it manages to put on the appearance of being in full possession of what knowing had already finished with but which at the same time had not yet been brought to order.

It treats knowledge as a collection of things known, as a collection of items, and in doing so it does not see the order that science has not yet brought to order, that is, the order of the whole.

It thereby seems to have subjected everything to the absolute Idea, and in turn, the absolute Idea itself therefore both seems to be recognized in everything and to have matured into a wide-ranging science.

The absolute is the unconditioned, that is, what is determined in and of itself. It not to be recognized in everything at this point because there is not yet a science of the whole, which is not wide-ranging but self-contained.

However, if the way it spreads itself out is examined more closely, it turns out not to have come about as a result of one and the same thing giving itself diverse shapes but rather as a result of the shapeless repetition of one and the same thing which is only externally applied to diverse material and which contains only the tedious semblance of diversity.

It is as if it (he is still talking about the reproach to science) lays out the items of knowledge before itself and applies the idea of the absolute to them. It fails to see that it is one and the same thing, namely the absolute idea, giving itself diverse shapes, and instead it repeats one and the same thing, giving to them the idea of the absolute. Rather than finding the absolute idea in them it imposes the idea on them.

... what is demanded is for the shapes to originate their richness and determine their differences from out of themselves ...

A word about the 'idea'. In paragraph 12 Hegel says:

It is the whole which has returned into itself from out of its succession and extension and has come to be the simple concept of itself. The actuality of this simple whole consists in those embodiments which, having become moments of the whole, again develop themselves anew and give themselves a figuration, but this time in their new element, in the new meaning which itself has come to be.

In the history of philosophy the 'idea' at one stage is the 'eidos' of Plato's Forms, that is, the things themselves as they are known in direct immediate intuition. Even as it develops and becomes in Descartes and others something that exists in the mind as an image, it is to be taken up again in its new element in each of its moments. An idea for Hegel is not an image in the mind, something which gives rise to the problem of the relationship between idea and those real things they are ideas of.

[Edited to add the close quote in the second to last paragraph. The next paragraph should not have been enclosed.]

If you don't want Trump reelected, push for a centrist Democrat that will appeal to the working class and will not fit the Republican's caricature. — Relativist

Maybe. One problem with this is that there is some percentage of voters who voted for Obama who voted for Trump because they wanted change. Until they believe the Democratic candidate will bring change they may either stick with Trump or not vote. Another problem is that the center is a moving scale. Since the Tea Party the Republican party moved to the right of Reagan and with Trump even further. So where is the center?

14:

This paragraph ends with a rather surprising statement given what was said above in paragraph 11 about:

... the break of day, which in a flash and at a single stroke brings to view the structure of the new world.

Here he speaks of:

... the boredom and indifference which result from the continual awakening of expectations by promises never fulfilled.

How are these to be reconciled? The answer comes at the beginning of paragraph 14:

At its debut, where science has been brought neither to completeness of detail nor to perfection of form ...

To return to an earlier analogy it is as if one were to look at a baby or toddler or child or youth or teen and on that basis alone judge what it is to be a human being. The potential is there but at each of these stages it has not been actualized and thus cannot even be realized or known.

We must identify the demands on science that he says:

... are just, those demands [that] have not been fulfilled.

They are the demands of those who are critical of science who:

... insists on immediate rationality and divinity

It might help to think of this in relation to the analogy in 12 of the prize at the end of the path, won through struggle and effort.

That prize is:

... the whole which has returned into itself from out of its succession and extension and has come to be the simple concept of itself.

In each of its moments it has not yet completed itself via its return to itself. With its return to itself there is no longer any mediacy. This is the satisfaction of the demand for immediate rationality and divinity, where science has been brought to completeness of detail and to perfection of form.

It’s useless for people to keep condemning Trump’s racism. it’s one of the things that got him there - he gives voice to things that nobody is supposed to say, but that clearly enough people believe to keep him in office. Trump’s racist comments should just be completely ignored; as long as they’re news, you’re just playing his game. — Wayfarer

I agree with the first part of this but not the second. I do not know what the best strategy is to defeat Trump, but I don't think ignoring what he says is the answer. Drawing attention to them may embolden some section of his followers but surely there are others who are upset by them, and, in addition, there are others who are undecided that may be sickened by what is happening and decide that they must vote for someone who opposes him.

The problem is complicated, however, by the fact that the term 'racist' is thrown around indiscriminately. When, for example, Ocasio-Cortez accuses Pelosi of “persistent[ly] singling out ... newly elected women of color” she does damage to the causes she is promoting. Pelosi does not disagree with them because they are women of color, but that is what Ocasio -Cortez makes it about even though she later said that Pelosi is not a racist, thus further muddying the waters.

Here a disagreement - maybe. For anything to be teleological, in a classical sense at least, there has to be a telos - a "finally." That is, something specific that is the final stage. The kitten's telos is to become a cat, and so forth. Hegel had no need to invent a new "science" for this; the Greeks had it long since covered. And if that were what he was trying to accomplish, his contemporaries would have had his number immediately. — tim wood

It is not a question of a new science of teleology, but of the movement of spirit from consciousness to self-consciousness, which is the movement of the whole to self-realization. I am not going to defend that argument now, but I think it will become clearer as we move forward.

Examples of what and where ?
Of revolution ? — Amity

Yes. [Added. Examples of revolutions. I suggested the scientific revolution and the French and American Revolutions.]

Still, I wouldn't describe it as revolutionary. — Amity

Hegel has not given us any examples. The rise of modern science was revolutionary and among other things established the authority of the individual based on reason. The American Revolution, French Revolution.

I think this is important and speaks to my earlier point:

Hegel is not talking just about the development of some intellectual pursuit, philosophy, or even a science of the whole, but of a new world in its incipience. — Fooloso4

Yes, I read that. However, I am wondering how long this took in real life.
How long was 'the winding path' ? — Amity

From the Greeks to Hegel.

The word 'evolution' was in use before Darwin. From the 1660s it meant a growth to maturity and development of an individual living thing. A process. — Amity

It is not always clear what one means when they use the term. For Darwin the process is not predetermined, but for Hegel it is. It is teleological.

I think MU makes a similar point: — Amity

I do not think the leap is an illusion:

11. Spirit has broken with the previous world of its existence and its ways of thinking ... just as with a child, who after a long silent period of nourishment draws his first breath and shatters the gradualness of only quantitative growth ... This gradual process of dissolution, which has not altered the physiognomy of the whole, is interrupted by the break of day, which in a flash and at a single stroke brings to view the structure of the new world.

It is the difference between process and product. The product is not simply the continuation of the linear process that led up to it. It is birth of something new, something revolutionary.

12. ... it is both the prize at the end of a winding path and, equally as much, is the prize won through much struggle and effort.

That is, the prize is the product that one comes at the end of the process and, equally as much, what comes through the through the process of struggle and effort. We do not simply follow along the path we bring about the prize. It is not simply there to be found but brought out through our struggle and effort.

Still, in this context I think that Hegel is mainly trying to contrast the "esoteric" and the "exoteric", stating that only the latter is easily and immediately "graspable": begreiflich. — WerMaat

Right, but what is it that makes it graspable? How is it that what was once esoteric has become exoteric?

By the way, scrolling back to the earlier paragraphs, please note that you have already encountered the noun form of "begreiflich".
The word "Begriff", translated as "concept" in #6, stems from the exactly same root... — WerMaat

See also the following exchanges:

Kaufman notes here that the German word for concept is "Begriff,.. closely related to begreifen (to comprehend),,,
— tim wood

Yes, but this needs to be understood within the whole, that is, it is comprehensive in the double sense of comprehend and inclusive of the subject matter as both subject and object together. See my comments about on #3.
— Fooloso4

The Hegel Glossary from Sebastian Gardner is useful here. Gives different translations and thoughts from Miller, Inwood, Solomon, Geraets et al, Kainz.

Excerpt from CONCEPT ( Begriff)
...
,..When Hegel speaks of the Concept, he sometimes just means concepts in general, but he also uses it to mean, per Solomon, the most adequate conception of the world as a whole...
Solomon...the Concept...has the force of 'our conception of concepts'...may also refer to the process of conceptual change...since for Hegel the identity of concepts is bound up with dialectical movement...
— Sebastian Gardner — Amity

Not initially, if you are the person being sculpted or moulded by someone else. — Amity

But the extent to which you allow this to happen is determined by you.

Usually, there is a form in mind. — Amity

Right, some form or shape or of yourself as you are and as are are to be. But of course this may take shape or change over time.

That might be less deterministic and more like free jazz. — Amity

Right, it is not deterministic but free jazz, despite what it may sound like, requires disciplined practice and the ability to hear and respond. One does not begin with the ability to play freely. So too, one does not begin with the ability to live freely.

Perhaps particularly pertinent to ageing bodies with 'Bits-Falling-Off Syndrome'. — Amity

Or are not where they used to be.

The effects, more evolutionary than revolutionary ? Leading to an exciting new world. — Amity

In #11 he says that the process is interrupted. And in #12 that the beginning of a new spirit is the outcome of a widespread revolution.

Hegel died before the publication of The Origin of Species and so we should not attribute Darwin's vocabulary of evolutionary change to Hegel.

Forget about the double sense, we're talking "understandable" only, "completeness" is not implied in the German Text.( At least not in this sentence.) — WerMaat

Okay, thanks. I think it may be more accurate to say that completeness is not implied in the German term begreiflich, but completeness is certainly central to the text and paragraph: "Only what is completely determinate ...", and this is why prior to this moment it has not been understood or, as both Miller and Pinkard have it "comprehended". Whether they made a connection between comprehend and comprehensive I cannot say. With regard to the root meaning of the term in German you provided I am reminded of the parable of the blind men and the elephant. Each can touch a part but since none can grasp the whole, and so none of them understand or comprehend the object.

It would help us enormously (or not) if somebody had bothered to chisel into stone or baked clay tablets what Jesus had to say. — Bitter Crank

It is not clear if they thought such a thing unnecessary given the belief that the kingdom of God/Heaven is at hand. Apparently some took this to mean personal transformation but others, as Paul preached, as a new beginning, death of the physical body with spirit bodies dwelling on a transformed earth, open only to those who had been saved. At the end of days there is no need to set anything in stone. It was a message intended for the present generation, the last generation, but with each new generation the advent of the end was pushed back until eventually it was placed in some indeterminate future.

One reason Evangelicals are pro-Trump is that they believe he will help usher in the end of days which according to the apocalyptic account of Revelations will not occur without Jerusalem being the capital of Israel.

The USA isn't going to last forever. 5000 years from now we'll just be remembered as a blip at the end of the British Empire.

Enjoy it while it lasts. — frank

This assumes that there will be anyone around to remember. And this is not too far off topic since Trump's indifference to the environment may be an existential threat.

And what does that mean ? How does that answer the question of who we are ?
Is it about working out who the 'Real' you is, or might be - and then some kind of self-realisation or actualization? — Amity

Somewhere Nietzsche uses the analogy of the art of the sculpturer who unlike the painter who adds to a blank canvas, removes all that is extraneous, superfluous, and false.

At each step of becoming who you are it is you who is making that determination. The more skilled the sculpturer the less likely he is to remove what is integral to the work. But perhaps unlike the sculpturer working in marble who cannot replace what has already been removed, we are of a more forgiving material. Or perhaps once something has been removed we must work with what remains.

Echoing Pindar, Nietzsche exhorts us: "Become who you are".

Christians believe that what Jesus had to say is still in effect. — Bitter Crank

And yet we really do not know what Jesus had to say. All we have is what others had to say about what Jesus had to say. Much of Christianity is not about what Jesus had to say or what others had to say about what Jesus had to say, but about what the Gospel authors had to say about what Jesus was and could do for those who believe. And of course all of this in the context of a world that was about to end.

12:

Yet this newness is no more completely actual than is the newborn child, and it is essential to bear this in mind. Its immediacy, or its concept, is the first to come on the scene.

As the oak is in the acorn, the man is in the child, but it its immediacy, that is, at this moment it has not actualized itself.

In the same way, science, the crowning glory of a spiritual world, is not completed in its initial stages. The beginning of a new spirit is the outcome of a widespread revolution in the diversity of forms of cultural formation ...

Just as each stage of gestation is necessary, each moment leading to the new birth of spirit is necessary. And just as each stage in the development of the fetus is itself a revolution (Miller has upheaval) that brings about something that was not present before this stage and adds to the whole of what is developing, each stage of cultural development adds to the diversity of forms that comprise:

... the whole which has returned into itself from out of its succession and extension and has come to be the simple concept of itself.

Returning into itself is to become what from the beginning it is to be. Each stage of this new whole no matter how different it is from earlier stages is not a move away from but within itself, adding to to the completion of itself.

The actuality of this simple whole consists in those embodiments which, having become moments of the whole, again develop themselves anew and give themselves a figuration, but this time in their new element, in the new meaning which itself has come to be.

The moments in the development of spirit do not understand themselves and are not understood by subsequent moment until this moment when it has come to the simple concept of itself. It is in this new element that each of those moments is understood anew as part in the development of the whole.

13:

On the one hand, while the initial appearance of the new world is just the whole enshrouded in its simplicity, or its universal ground, still, on the other hand, the wealth of its bygone existence is in recollection still current for consciousness.

Hegel is not talking just about the development of some intellectual pursuit, philosophy, or even a science of the whole, but of a new world in its incipience. It is not the study of or reflection on the whole but the whole itself. In its simplicity it is not yet revealed itself as what it is to be. At the same time its existence as it was is still present or active in its recollection of itself, that is, its history in the sense of bringing it back to itself in its consciousness of itself.

In that newly appearing shape, consciousness misses both the dispersal and the particularization of content, but it misses even more the development of the form as a result of which the differences are securely determined and are put into the order of their fixed relationships.

Its new shape, the whole enshrouded in simplicity, as the universal ground is no longer what it was in its earlier stages of differentiation and particularization, of fixed relationships. Here we see that Hegel is not completely at odds with those he criticizes.

Without this development, science has no general intelligibility, and it seems to be the esoteric possession of only a few individuals – an esoteric possession, because at first science is only available in its concept, or in what is internal to it, and it is the possession of a few individuals, since its appearance in this not-yet fully unfurled form makes its existence into something wholly singular.

Science appears to be esoteric, that is, shrouded, hidden from view of all but a few who are, so to speak, initiated into its secrets, its specialized language and practices. But it appears this way because it has not yet fully unfurled. It is not something wholly singular but a part of the development of the whole. It is from within this development that science has its general intelligibility.

Only what is completely determinate is at the same time exoteric, comprehensible, and capable of being learned and possessed by everybody. The intelligible form of science is the path offered to everyone and equally available for all.

Up until this point science has not been completely determinate, that is to say, it has not yet completed itself and so cannot be understood. With the completion of its movement it has become comprehensible. Perhaps @WerMaat can comment on whether there is in German this double sense of comprehensive as complete and understandable.

To achieve rational knowledge through our own intellect is the rightful demand of a consciousness which is approaching the status of science. This is so because the understanding is thinking, the pure I as such, and because what is intelligible is what is already familiar and common both to science and to the unscientific consciousness alike, and it is that through which unscientific consciousness is
immediately enabled to enter into science.

What does Hegel mean by "our own intellect"? Is it something uniquely mine or ours? The "pure I" is the thinking I. As such it is the I of thinking. What is intelligible is so to any consciousness whether scientific or unscientific, because the intelligible is what is already familiar to consciousness.

You need to read this in context. God does not need humans to make sacrifice. It has nothing to do with veganism.

Prior to the Flood the eating of meat was prohibited: Genesis 1:29–30, but after the Flood it was permitted: Genesis 9:3

And here was me thinking you a contermacious rebel who would rise to the occasion. And delight. — Amity

There is no doubt I would rise to the occasion and delight, but I simply cannot function without my double entendres.

Constitution. — frank

I'd like to make two points on this. First with regard to Article V of the Constitution which allows for both an amendment process and perhaps more importantly a provision for a constitutional convention:

The Congress, whenever two thirds of both Houses shall deem it necessary, shall propose Amendments to this Constitution, or, on the Application of the Legislatures of two thirds of the several States, shall call a Convention for proposing Amendments, which, in either Case, shall be valid to all Intents and Purposes, as Part of this Constitution, when ratified by the Legislatures of three fourths of the several States, or by Conventions in three fourths thereof, as the one or the other Mode of Ratification may be proposed by the Congress; Provided that no Amendment which may be made prior to the Year One thousand eight hundred and eight shall in any Manner affect the first and fourth Clauses in the Ninth Section of the first Article; and that no State, without its Consent, shall be deprived of its equal Suffrage in the Senate.

The reason why this is so important is that big money interests backed by the Koch Brothers and others are pushing for a Constitutional convention under the guise of a balanced budget amendment. But they are not intent on doing this in the way that amendments have always been passed. If two thirds of the states demand it there must be a Constitutional convention. Once the convention is convened the possibility of radical change to the Constitution is possible.


The second has to do with Jefferson's view. In a letter to James Madison he writes:

The question Whether one generation of men has a right to bind another, seems never to have been started either on this or our side of the water. Yet it is a question of such consequences as not only to merit decision, but place also, among the fundamental principles of every government ...

I set out on this ground, which I suppose to be self evident, ‘that the earth belongs in usufruct to the living’: that the dead have neither powers nor rights over it ...

... no society can make a perpetual constitution, or even a perpetual law. The earth belongs always to the living generation ...

Every constitution then, and every law, naturally expires at the end of 19 years. If it be enforced longer, it is an act of force, and not of right.

https://jeffersonpapers.princeton.edu/selected-documents/thomas-jefferson-james-madison