From arithmetic, geometry and kinematics through mechanics to life.

Steiner’s first lecture of the First Scientific Lecture-Course, the so called, ‘Light course’, given in Stuttgart, on the 23rd December 1919, can be read here and it can be listened to here

He explains how the natural scientists of his day proceeded. They were interested in categorising, looking for causes behind phenomena, and observing phenomena to arrive at the ‘laws’ of nature. Goethe did not proceed in this way. He was not interested in looking for and speculating about unknown causes or categorisation. He looked at nature and observed how it was forever changing and studied this metamorphosis in great detail. He wished to stay within the observable to ask what it could tell him without speculating about any laws or hidden world behind the one observed.

The natural science are forever looking for pointwise forces to explain life. But, according to Steiner, life cannot be explained in this way. Life is formed out of the universal peripheral forces. These forces are not the same as the mechanical pointwise forces which are open to measurement. Steiner explains it thus:

Say you were studying the play of forces in an animal or vegetable embryo or germ-cell; with this method you would never find your way. No doubt it seems an ultimate ideal to the Science of today, to understand even organic phenomena in terms of potentials, of centric forces of some kind. It will be the dawn of a new world-conception in this realm when it is recognized that the thing cannot be done in this way, Phenomena in which Life is working can never be understood in terms of centric forces. Why, in effect, — why not? Diagrammatically, let us here imagine that we are setting out to study transient, living phenomena of Nature in terms of Physics. We look for centres, — to study the potential effects that may go out from such centres. Suppose we find the effect. If I now calculate the potentials, say for the three points a, b and c, I find that a will work thus and thus on A, B and C, or c on A’, B’ and C’; and so on. I should thus get a notion of how the integral effects will be, in a certain sphere, subject to the potentials of such and such centric forces. Yet in this way I could never explain any process involving Life. In effect, the forces that are essential to a living thing have no potential; they are not centric forces. If at a given point d you tried to trace the physical effects due to the influences of a, b and c, you would indeed be referring to the effects to centric forces, and you could do so. But if you want to study the effects of Life you can never do this. For these effects, there are no centres such as a or b or c. Here you will only take the right direction with your thinking when you speak thus: Say that at d there is something alive. I look for the forces to which the life is subject. I shall not find them in a, nor in b, nor in c, nor when I go still farther out. I only find them when as it were I go to the very ends of the world — and, what is more, to the entire circumference at once. Taking my start from d, I should have to go to the outermost ends of the Universe and imagine forces to the working inward from the spherical circumference from all sides, forces which in their interplay unite in d. It is the very opposite of the centric forces with their potentials. How to calculate a potential for what works inward from all sides, from the infinitudes of space? In the attempt, I should have to dismember the forces; one total force would have to be divided into ever smaller portions. Then I should get nearer and nearer the edge of the World: — the force would be completely sundered, and so would all my calculation. Here in effect it is not centric forces; it is cosmic, universal forces that are at work. Here, calculation ceases.

This lecture was given just over a century ago and so the terminology is a bit dated and science has made a vast amount of progress since then, but his points still stand.
The difference between Goethe’s scientific method and the standard methods of natural science is the same difference that separates the practice of Euclidean geometry from that of projective geometry. In the former, lengths and angles are measured and calculated, in the latter there are no measurements as such, it is concerned with the mobility and transformation of form as it is expressed between point and plane.

Goethe takes natural science beyond its self-imposed limits just as projective geometry takes Euclidean geometry beyond its limits.

Feel free to read or listen to the lecture linked to above and comment as you see fit.

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347 thoughts on “From arithmetic, geometry and kinematics through mechanics to life.

  1. Neil Rickert:

    CharlieM: I don’t see what is so misleading about mental activities.

    Neil Rickert: I don’t see what’s so special about them that they deserve a special name.

    You mentioned mental arithmetic. But mental arithmetic is just arithmetic.

    So why do teachers bother to get their pupils to write down the figures when they are given arithmetic problems to solve? Do you think that it takes the same amount of mental effort to solve problems on paper as it does using only the mind without any external props?

    Philosophers refer to beliefs as “mental states”. But I can be said to have a belief even when I am not currently thinking about it. So what is mental about that?

    Nothing until you bring it to mind. Then it becomes mental. After all that is what the word means.

    Using “mental” in descriptions such as these seems to just introduce a new category which is not well defined.

    Unambiguous definitions are for subjects such as mathematics, classical physics and mechanics. When we begin to delve into subjects such as quantum mechanics, the mind, life and such like then hard and fast definitions are seldom possible. But an imprecise definition may be more useful than no definition at all.

    CharlieM: I’m not sure how you can omit ontology if you want to discuss reality.

    Neil Rickert: I have not found ontology to be useful, but I still discuss reality. Where’s the problem?

    When you have any meaningful discussions about reality then you are partaking in ontology like it or not.

    CharlieM: So reality as we understand it bears no relationship to reality in itself?

    Neil Rickert: Or perhaps the expression “reality in itself” is mostly a philosopher’s mistake.

    Perhaps you are correct.

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  2. CharlieM: So why do teachers bother to get their pupils to write down the figures when they are given arithmetic problems to solve?

    The teachers want to see what mistakes the students are making, so that they can help the students learn to avoid those mistakes.

    Nothing until you bring it to mind. Then it becomes mental. After all that is what the word means.

    Having a belief does not require that I bring it to mind. And bringing something to mind does not require that I believe it. It still makes no sense to say that beliefs are mental states.

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  3. Neil Rickert:
    CharlieM: So why do teachers bother to get their pupils to write down the figures when they are given arithmetic problems to solve?

    Neil Rickert: The teachers want to see what mistakes the students are making, so that they can help the students learn to avoid those mistakes.

    And do you think that is the only reason? Do you believe that 11 year old pupils are considered to be capable of carrying out long division by purely mental processes?

    Neil Rickert: … I can be said to have a belief even when I am not currently thinking about it. So what is mental about that?

    Charlie: Nothing until you bring it to mind. Then it becomes mental. After all that is what the word means.

    Neil Rickert: Having a belief does not require that I bring it to mind. And bringing something to mind does not require that I believe it. It still makes no sense to say that beliefs are mental states.

    You’ll need to take that up with those people who say these things. What I would say is that when I think about my beliefs I am performing a mental act.

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  4. CharlieM: When we begin to delve into subjects such as quantum mechanics, the mind, life and such like then hard and fast definitions are seldom possible. But an imprecise definition may be more useful than no definition at all.

    In the spirit of Racker’s “Do not waste clean thinking on dirty enzymes”, I have to disagree. Especially for QM — that’s pathologically wrong.
    Of course, if you like to indulge in equivocation and woolly thinking, then imprecise definitions may have their upside, I guess.

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  5. DNA_Jock:
    CharlieM: When we begin to delve into subjects such as quantum mechanics, the mind, life and such like then hard and fast definitions are seldom possible. But an imprecise definition may be more useful than no definition at all.

    IDNA_Jock: n the spirit of Racker’s “Do not waste clean thinking on dirty enzymes”, I have to disagree. Especially for QM — that’s pathologically wrong.
    Of course, if you like to indulge in equivocation and woolly thinking, then imprecise definitions may have their upside, I guess.

    Go to Wikipedia’s Glossary of mechanical engineering and you will find a straightforward list of terms used. But if you go to Wikipedia’s Glossary of elementary quantum mechanics, they caution the reader: “Different authors may have different definitions for the same term.”

    Definitions begin to get “woolly”.

    You seem to disagree less when it comes to life. Can you be more precise in your definition of “disagreement”? 🙂

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  6. Neil Rickert:
    CharlieM: Do you believe that 11 year old pupils are considered to be capable of carrying out long division by purely mental processes?

    Neil Rickert: Some are, some aren’t.

    Imagine a teacher asking a class of 11 year old pupils (who had been taught how to do long division) to calculate the number 25389 divided by 273. Do you think it would be fair to expect them to arrive at the answer purely by means of mental arithmetic rather than by means of pen and paper? Either way, it’s all just arithmetic. 🙂

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  7. CharlieM: “Different authors may have different definitions for the same term.”

    Definitions begin to get “woolly”.

    Nope. Different authors may use a particular term differently — so what? — that’s just differing use of jargon. They all use precise and explicit definitions. That’s what all the equations are about…

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  8. DNA_Jock:
    CharlieM: “Different authors may have different definitions for the same term.”

    Definitions begin to get “woolly”.

    DNA_Jock: Nope. Different authors may use a particular term differently — so what? — that’s just differing use of jargon. They all use precise and explicit definitions. That’s what all the equations are about…

    True enough. As I said “Unambiguous definitions are for subjects such as mathematics” And equations are mathematical constructions.

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  9. A major difference between a crab and the pebble it sits next to is inner intentionality.

    Kant famously said in his Critique of Judgement
    “Absolutely no human Reason (in fact no finite Reason like ours in quality, however much it may surpass it in degree) can hope to understand the production of even a blade of grass by mere mechanical causes. As regards the possibility of such an object, the teleological connexion of causes and effects is quite indispensable for the Judgement, even for studying it by the clue of experience. For external objects as phenomena an adequate ground related to purposes cannot be met with; this, although it lies in nature, must only be sought in the supersensible substrate of nature, from all possible insight into which we are cut off. Hence it is absolutely impossible for us to produce from nature itself grounds of explanation for purposive combinations; and it is necessary by the constitution of the human cognitive faculties to seek the supreme ground of these purposive combinations in an original Understanding as the cause of the world.”

    Goethe demonstrated to himself and anyone who understands what he achieved that Kant was mistaken about the supersensible being cut off.

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  10. CharlieM: Imagine a teacher asking a class of 11 year old pupils (who had been taught how to do long division) to calculate the number 25389 divided by 273.

    I’m not at all sure what point you think you are making.

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  11. CharlieM: A major difference between a crab and the pebble it sits next to is inner intentionality.

    We ascribe intentionality to the crab but not to the pebble.

    So yes, we see a difference between the crab and the pebble. But throwing the word “intentionality” at it doesn’t really tell us anything.

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  12. Neil Rickert:
    CharlieM: Imagine a teacher asking a class of 11 year old pupils (who had been taught how to do long division) to calculate the number 25389 divided by 273.

    Neil Rickert: I’m not at all sure what point you think you are making.

    I’m pointing out the difference between mental arithmetic and doing arithmetic using external aids.

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  13. Neil Rickert:
    CharlieM: A major difference between a crab and the pebble it sits next to is inner intentionality.

    Neil Rickert: We ascribe intentionality to the crab but not to the pebble.

    So yes, we see a difference between the crab and the pebble. But throwing the word “intentionality” at it doesn’t really tell us anything

    It tell us that Kant had a point. Mechanics explains any movement the pebble makes but it doesn’t explain the movement of the crab.

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  14. CharlieM: It tell us that Kant had a point. Mechanics explains any movement the pebble makes but it doesn’t explain the movement of the crab.

    I’m pretty sure that biologists can give detailed mechanical accounts of the movement of a crab.

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  15. Neil Rickert:
    CharlieM: I’m pointing out the difference between mental arithmetic and doing arithmetic using external aids.

    Neil Rickert: And there isn’t much difference. The external aids are merely aids.

    There is a great deal of difference in the mental effort required.

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  16. Neil Rickert:
    CharlieM: It tell us that Kant had a point. Mechanics explains any movement the pebble makes but it doesn’t explain the movement of the crab.

    Neil Rickert: I’m pretty sure that biologists can give detailed mechanical accounts of the movement of a crab.

    And so am I. I’m also pretty sure that they could give a detailed mechanical account of your finger movements when you type your comments. Do the mechanical movements have anything to do with your intentions? Would your message be different if you dictated it. (I assume you type your comments here. If not just reverse the situation.)

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  17. CharlieM: There is a great deal of difference in the mental effort required.

    Is there a point?

    Somehow, you seem highly enamored of the word “mental”, a word that I don’t find particularly useful. Your inability to explain why you like “mental” only supports my view.

    Do the mechanical movements have anything to do with your intentions?

    I’ll readily grant that “intention” is a more useful word than “mental”. However, you aren’t actually using “intention” very effectively here.

    You manage to leave the impression that you are wanting to appeal to unspecified woo.

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  18. Neil Rickert:
    CharlieM: There is a great deal of difference in the mental effort required.

    Neil Rickert: Is there a point?

    I’m trying to get to the bottom of why you dislike the term “mental act”

    Somehow, you seem highly enamored of the word “mental”, a word that I don’t find particularly useful. Your inability to explain why you like “mental” only supports my view.

    It’s a word that means pertaining to the mind. Have you got something against minds? 🙂

    CharlieM: Do the mechanical movements have anything to do with your intentions?

    Neil Rickert: I’ll readily grant that “intention” is a more useful word than “mental”. However, you aren’t actually using “intention” very effectively here.

    What I mean by ‘intention’ is an inner effort to carry out some action which need not be conscious. Whereas ‘mental’ has more to do with a conscious mind.

    Neil Rickert: You manage to leave the impression that you are wanting to appeal to unspecified woo.

    Maybe it would help if you just discuss what I am actually saying without trying to argue against your own speculations. I take thinking to be a supersensible activity, no woo required.

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  19. CharlieM: Maybe it would help if you just discuss what I am actually saying without trying to argue against your own speculations.

    I discussed what very little you actually said. But you kept coming back to again say very little.

    I take thinking to be a supersensible activity, no woo required.

    Supersensible? That seems to be a term for referring to woo.

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  20. Neil Rickert:
    CharlieM: Maybe it would help if you just discuss what I am actually saying without trying to argue against your own speculations.

    Neil Rickert: I discussed what very little you actually said. But you kept coming back to again say very little.

    I would hope that even a few words can stimulate thinking and further questions.

    CharlieM: I take thinking to be a supersensible activity, no woo required.

    Neil Rickert: Supersensible? That seems to be a term for referring to woo

    And this is a good example of what I said above. Thinking about the word ‘supersensible’. Have you thought much about it? You hear the word and immediately think ‘woo’. But if we consider geometry, many of its terms describe supersensible entities. Points and straight lines are fundamental to geometry but they are never experienced through the senses. Likewise we never perceive photons or quarks. That makes them supersensible entities.

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  21. CharlieM: Thinking about the word ‘supersensible’. Have you thought much about it? You hear the word and immediately think ‘woo’.

    I looked it up.

    Wiktionary: Beyond the range of what is perceptible by the senses; not belonging to the experienceable physical world. Heaven is a supersensible realm.

    Merriam Webster: being above or beyond that which is apparent to the senses : spiritual.

    FreeDictionary: Of, coming from, or relating to forces or beings that exist outside the natural world: extramundane, extrasensory, metaphysical, miraculous …

    To me, those all suggest woo.

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  22. CharlieM: And this is a good example of what I said above. Thinking about the word ‘supersensible’. Have you thought much about it? You hear the word and immediately think ‘woo’. But if we consider geometry, many of its terms describe supersensible entities. Points and straight lines are fundamental to geometry but they are never experienced through the senses. Likewise we never perceive photons or quarks. That makes them supersensible entities.

    Sure, if you want to use the word “supersensible” in your own peculiar way that no one else does. Good luck having a conversation on that basis.

    +1
  23. Kantian Naturalist:
    CharlieM: And this is a good example of what I said above. Thinking about the word ‘supersensible’. Have you thought much about it? You hear the word and immediately think ‘woo’. But if we consider geometry, many of its terms describe supersensible entities. Points and straight lines are fundamental to geometry but they are never experienced through the senses. Likewise we never perceive photons or quarks. That makes them supersensible entities.

    Kantian Naturalist: Sure, if you want to use the word “supersensible” in your own peculiar way that no one else does. Good luck having a conversation on that basis.

    What is peculiar about a word combining super as in above or beyond and sensible as in relating to the senses.

    Dictionaries define it as being out of the range of the senses. Infinity is out of the range of the senses as is a straight line segment as postulated by Euclid. Why shouldn’t these entities be described as supersensible?

    I cannot be held responsible for those who prejudge the meaning of this word.

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  24. Oh. I thought Charlie was using “super” to mean “very very” as in superfine, or super smart. Thus “supersensible” means “very stable genius”, or some such.
    There’s glory for you.

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  25. CharlieM,

    By that line of reasoning, the moons of Jupiter were “supersensible” before the invention of the telescope.

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  26. Neil Rickert: CharlieM: Thinking about the word ‘supersensible’. Have you thought much about it? You hear the word and immediately think ‘woo’.

    Neil Rickert: I looked it up.

    Wiktionary: Beyond the range of what is perceptible by the senses; not belonging to the experienceable physical world. Heaven is a supersensible realm.

    Merriam Webster: being above or beyond that which is apparent to the senses : spiritual.

    FreeDictionary: Of, coming from, or relating to forces or beings that exist outside the natural world: extramundane, extrasensory, metaphysical, miraculous …

    To me, those all suggest woo.

    What about straight lines, big bangs, quarks, Kant’s ‘things in themselves’? These if they exist are all supersensible entities. Do they all suggest woo? Are you capable of thinking that some supersensible ‘entities’ might be ‘woo’ while others are perfectly logical entities. If quarks are physical, can you define ‘physical’, and in what way can it be said that we experience them?

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  27. DNA_Jock:
    Oh. I thought Charlie was using “super” to mean “very very”as in superfine, or super smart. Thus “supersensible” means “very stable genius”, or some such.
    There’s glory for you.

    If you not sure, just ask 🙂

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  28. CharlieM: What about straight lines, big bangs, quarks, Kant’s ‘things in themselves’? These if they exist are all supersensible entities.

    That does not seem right to me. Mostly, those are theoretical entities, and that’s surely different from supersensible entities.

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  29. Kantian Naturalist:
    CharlieM,

    By that line of reasoning, the moons of Jupiter were “supersensible” before the invention of the telescope.

    You make a good point although you are assuming that eagles and the like do not have vision capable of seeing these moons. Or course this wouldn’t invalidate your argument, it would just mean that the first observations would have occurred further back in time. And there are still aspects of these moons that remain supersensible despite the fact that we have the capability to see them with our eyes. Their journey through time from formation to dissolution is beyond sense perception.

    Following the link I gave they use various words such as ‘beyond reach’, ‘beyond the range’, and ‘beyond perception’. Perhaps they should have used ‘beyond the realm’. Can you see the difference between the straight line defined by Euclid and a material heavenly body?

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  30. Neil Rickert:
    CharlieM: What about straight lines, big bangs, quarks, Kant’s ‘things in themselves’? These if they exist are all supersensible entities.

    Neil Rickert: That does not seem right to me. Mostly, those are theoretical entities, and that’s surely different from supersensible entities

    In Faith and Critical Theology, by Richard B Wells writes:
    Wells: “How does the term “supernatural” differ from the term “supersensible”? The term “nature” properly refers to the totality of things and their relationships capable of being experienced by human beings. Human experience is possible only by means of our senses (either directly or with the aid of instrumentation). An object is supersensible if that object is incapable of affecting our senses. For example, the number π (pi) is a transcendental number. It cannot be represented with a finite number of digits and can never be written out in full. It therefore has no sensible representation and, as an object, π is a supersensible object. We say it is the object of an idea, and this is the case for all supersensible objects. Science makes use of ideas of supersensible objects necessarily (for instance, all objects of pure mathematics are supersensible) in order to explain relationships between sensible objects of nature. Without them science could explain nothing. However, in order to make valid scientific use of a supersensible object that object must be capable of being connected to sensible objects in a way that makes a congruent practical and measurable correspondence with sensible objects of nature.

    The supernatural is also and always supersensible but not every supersensible object is a supernatural object”

    CharlieM: This is close to the way I am using the term ‘supersensible’.

    If we are incapable of sense perception of some entities what’s the problem with using the term ‘supersensible’ to describe them? We can see the people around us. They are perceptible to our senses. We understand that they were all conceived and will eventually die (In my case OMagain would prefer it to be sooner rather than later 🙂 ). We cannot perceive these lives but we can use our thinking to understand that these processes will happen. Thinking adds something that the senses doesn’t give us. Observation is the sensible component and thinking is the supersensible component. Apprehension of reality is achieved by the combination of both.

    When you start mixing the supernatural in with the supersensible, then we are getting into the realms of what you call woo.

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  31. CharlieM: In Faith and Critical Theology, by Richard B Wells writes

    You don’t like me using the word “woo”. Yet you cite a book of woo.

    If you want to say that π is supersensible, then you might as well say that Sherlock Holmes is supersensible. Why say that π has no sensible representation, when the symbol “π” is already such a representation. It seems that the author of the cited book is a woo-meister.

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  32. Neil Rickert: You don’t like me using the word “woo”.Yet you cite a book of woo.

    If you want to say that π is supersensible, then you might as well say that Sherlock Holmes is supersensible. Why say that π has no sensible representation, when the symbol “π” is already such a representation.It seems that the author of the cited book is a woo-meister.

    Your main argument against Wells is to throw insults at him. π (pi) is an irrational number which is also transcendental. What do you think transcendental means? It is also the ratio of the diameter of a circle to its circumference. But there are no such physical entity that is circular, there are only approximations. So the circle as defined is a supersensible entity.

    What about Sherlock Holmes? Obviously no such person existed in physical reality. So where did the character exist? In the mind of Arthur Conan Doyle. In other words the product of a creative act of thinking which as I have argued is supersensible.

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  33. CharlieM: Your main argument against Wells is to throw insults at him.

    I have no argument against Wells. I haven’t even read the book. My disagreement was with what you have posted.

    You are using “supersensible” in a way that I do not see as compatible with the dictionary definitions.

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  34. Whatever use there is for the term “supersensible,” there are basic categorical distinctions between mathematical concepts, scientific posits (unobserved entities), regulative ideals, and literary fictions.

    There’s no possibility of a productive conversation when these wildly different things are all put in the same basket.

    +1
  35. Kantian Naturalist:
    Whatever use there is for the term “supersensible,” there are basic categorical distinctions between mathematical concepts, scientific posits (unobserved entities), regulative ideals, and literary fictions.

    There’s no possibility of a productive conversation when these wildly different things are all put in the same basket.

    The intellect sees division and multiplicity and the reason sees the unity in diversity. The unifying basket is the human mind.

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  36. CharlieM: The intellect sees division and multiplicity and the reason sees the unity in diversity. The unifying basket is the human mind.

    Perhaps we have moved from a basket of deplorables to a deplorable basket.

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  37. Neil Rickert: Perhaps we have moved from a basket of deplorables to a deplorable basket.

    And back again. Would Hillary Clinton, had she survived Comey’s shafting, have done a better job than 45? We’ll never know.

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  38. Alan Fox:
    CharlieM: I have argued is supersensible.

    Alan Fox: I suggest there is already a word for this. Try imaginary.

    This is closer than you imagine. Imagination based on fact.

    Henri Bortoft termed the Goethean way ‘exact sensorial imagination’. To get an idea of this look at a plant whose leaves change shape as they progress up the stem. Our visual senses only give us a picture of frozen stages of development. By examining the sequence we can imagine the stages morphing into each other and this gives us a realistic image of the dynamic growth of the plant. It furnishes us with more than the senses can deliver. We use our exact sensorial imagination to further our sense experience. We see the separate parts with our eyes, we see the whole with our minds.

    Craig Holdrege
    “We need to overcome our habit of viewing the world in terms of objects and leave behind the scientific propensity to explain via reification and reductive models”
    “We are presented with a drama of transformation that we can enter into. But we can’t enter into it through observation alone. We need to utilize our faculty of imagination to connect within ourselves what is already connected within the plant. ”

    We use our imagination not to fantasise but to fill in the reality that unifies our sense impressions. And in order to achieve this regarding a particular subject we must gather sense impressions that are as complete and exact as possible. There is no need and no place for speculation about anything lying behind what is observed.

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  39. CharlieM: The intellect sees division and multiplicity and the reason sees the unity in diversity. The unifying basket is the human mind.

    If you attempting to use the distinction between “the intellect” and “the reason” to capture Hegel’s distinction between Verstand and Vernunft, then to some extent, yes — except that Reason or Vernunft establishes the logical interconnections and conceptual interdependence that have been distinguished. If you want to affirm the organic unity of conceptual distinctions, you would need to at least affirm the distinctions themselves to begin with.

    CharlieM: We use our imagination not to fantasise but to fill in the reality that unifies our sense impressions. And in order to achieve this regarding a particular subject we must gather sense impressions that are as complete and exact as possible. There is no need and no place for speculation about anything lying behind what is observed.

    It is a perplexing to me that you cannot see how the contradiction here.

    On the one hand, you say that the senses “fragment” the unity of the object (you give no argument for this claim, though I’ve requested one from you many, many times) and “the imagination” restores this unity.

    On the other hand, you say that the restored unity does not go beyond the senses — it is not (as you say) “speculative”.

    But it is clear that if our experience of the world is mediated by the senses, and we have no capacity to transcend the senses themselves in order to cognize the world, then it is logically impossible for you to know that the unity which is restored by the imagination is the same as the unity of the object independent of how it is perceived.

    In other words, what you want to say is something like this:

    Unity of Object –> Plurality of Sense-Impressions –> Unity of Object

    except that the second “unity of object” is that which is imagined.

    To know that the unified object as imagined is the same as the unified object prior to sense-experience, you would need to be able to transcend the plurality of sense-impressions — which is precisely what you acknowledge cannot be done.

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  40. The excellent video Goethe’s Study of Metamorphosis in Light, Leaf, and Bone by Matthew Segall, gives a good overview of Goethe’s plant and animal morphology, and his experiments with colour. It also informs us about his relationship with the ideas of the likes of Kant and Spinoza.

    There are some nice depictions of developing plants From around this point accompanied by an explanation of what Goethe meant when he said that everything is leaf.

    The ideal triangle relates to physical triangles in the same way that Goethe’s leaf relates to a leaf experienced visually. The ideal triangle is a very dynamic entity assuming all imaginable forms as a unity.

    From here in the video, Goethe’s colour theory is dealt with.

    One thing that I have noticed when I look through a 60 degree prism (equilateral triangle end on) at a white strip of paper on a black background. I see the boundary colours as Goethe also observed. But when I move the prism to the point when these boundary colours meet and green is produced the image I see is shrinking and appears to be thinner than the actual strip of paper. To me this suggests that the green colour is being produced when the image is being compressed, not when it is being spread out. I think this is worth pursuing further.

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  41. CharlieM: The ideal triangle relates to physical triangles in the same way that Goethe’s leaf relates to a leaf experienced visually. The ideal triangle is a very dynamic entity assuming all imaginable forms as a unity.

    I think that encapsulates quite nicely what is completely mistaken about this entire approach: mathematical concepts (e.g. “triangle”) have a different logical structure than empirical concepts (e.g. “leaf”).

    Conflating them is going to lead to either treating empirical concepts as if they were mathematical or mathematical concepts as if they were empirical.

    In the former case, we end up with a Platonism about universals that turns our ability to classify and describe the world into a sheer incomprehensible mystery, epistemically indistinguishable from the skepticism it is intended to refute.

    In the latter case, we end up with a flat-footed empiricism that renders opaque how the entanglement of syntactical structure and semantic content constitutive of rationality generates new forms of cognitive processing, constructs novel affordances and niches, and thus facilitates new forms of world disclosure.

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  42. Kantian Naturalist:
    CharlieM: The intellect sees division and multiplicity and the reason sees the unity in diversity. The unifying basket is the human mind.

    Kantian Naturalist: If you attempting to use the distinction between “the intellect” and “the reason” to capture Hegel’s distinction between Verstand and Vernunft, then to some extent, yes — except that Reason or Vernunft establishes the logical interconnections and conceptual interdependence that have been distinguished. If you want to affirm the organic unity of conceptual distinctions, you would need to at least affirm the distinctions themselves to begin with.

    I am using the distinction as per Kant:
    “According to the German philosopher Immanuel Kant, reason is the power of synthesizing into unity, by means of comprehensive principles, the concepts that are provided by the intellect.”

    The intellect give us separate concepts and by means of reason we unify these concepts.

    CharlieM: We use our imagination not to fantasise but to fill in the reality that unifies our sense impressions. And in order to achieve this regarding a particular subject we must gather sense impressions that are as complete and exact as possible. There is no need and no place for speculation about anything lying behind what is observed.

    Kantian Naturalist: It is a perplexing to me that you cannot see how the contradiction here.

    On the one hand, you say that the senses “fragment” the unity of the object (you give no argument for this claim, though I’ve requested one from you many, many times) and “the imagination” restores this unity.

    Think about someone who has had no interest in birds suddenly decides to take up bird watching as a hobby. He heads down to an estuary to study the birdlife with a friend who is an expert. He sees and hears a wide range of species but has no idea of how they are all related and which birds are responsible for which calls. His friend teaches him the different calls and which birds are making them. She teaches him what the calls signify, how the sexes differ and to watch out for the variety of mating behaviours. Slowly after many outings he begins to recognise the majority of birds and he can even recognise some species by just the hint of a far off call or by the flight characteristics of a bird in the distance.

    Two birds suddenly cross his path and just as quickly disappear out of sight. From this short act of perception he recognises the leading bird as a male blackbird and the pursuing bird as a sparrowhawk. Experience tells him much more than what he witnessed in that instant. He understands the intentions of both birds, the relationship between them and what the favourable outcome would be from the perspective of each bird.

    From his time of ignorance he has advanced so that what was at first for him a confusing mixture of sights and sounds has become a meaningful experience brought about by memories of all that he has learned.

    Kantian Naturalist: On the other hand, you say that the restored unity does not go beyond the senses — it is not (as you say) “speculative”.

    I said “there is no need and no place for speculation about anything lying behind what is observed” I’m sure you’ll agree that observation involves more than just the senses.

    Kantian Naturalist: But it is clear that if our experience of the world is mediated by the senses, and we have no capacity to transcend the senses themselves in order to cognize the world, then it is logically impossible for you to know that the unity which is restored by the imagination is the same as the unity of the object independent of how it is perceived.

    I am not talking about the imagination as in building up a picture in our minds regardless of perception, like a process of imagining a flying spaghetti monster which has no basis in reality. It is as I’ve said a few times, exact sensorial imagination as practiced by Goethe.

    As this author writes
    ” … exact sensorial imagination, involves an almost meditative exercise: with closed eyes, an exact image of the observed object is brought forth inwardly. Without imposing subjective mental constructs or preconceived theories, Goethe’s method extends and deepens our experience of the phenomenon until it reaches an element not given externally to sense-experience. This is the connection of the phenomenon, its relationship to others and ultimately to the universe at large, which is intrinsically lawful and ordered.”

    Even our usual human observation transcends the senses.

    Kantian Naturalist: In other words, what you want to say is something like this:

    Unity of Object –> Plurality of Sense-Impressions –> Unity of Object

    except that the second “unity of object” is that which is imagined.

    To know that the unified object as imagined is the same as the unified object prior to sense-experience, you would need to be able to transcend the plurality of sense-impressions — which is precisely what you acknowledge cannot be done.

    And where do you think I acknowledged that the plurality of sense impressions cannot be transcended?

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  43. Kantian Naturalist:
    CharlieM: The ideal triangle relates to physical triangles in the same way that Goethe’s leaf relates to a leaf experienced visually. The ideal triangle is a very dynamic entity assuming all imaginable forms as a unity.

    Kantian Naturalist: I think that encapsulates quite nicely what is completely mistaken about this entire approach: mathematical concepts (e.g. “triangle”) have a different logical structure than empirical concepts (e.g. “leaf”).

    Conflating them is going to lead to either treating empirical concepts as if they were mathematical or mathematical concepts as if they were empirical.

    In the former case, we end up with a Platonism about universals that turns our ability to classify and describe the world into a sheer incomprehensible mystery, epistemically indistinguishable from the skepticism it is intended to refute.

    In the latter case, we end up with a flat-footed empiricism that renders opaque how the entanglement of syntactical structure and semantic content constitutive of rationality generates new forms of cognitive processing, constructs novel affordances and niches, and thus facilitates new forms of world disclosure.

    I’m not conflating the concepts, I am comparing them. All physical triangles partake of the concept ‘triangle’ in the same way that all physical leafs partake of the concept ‘leaf’

    Obviously there is a great deal of difference between leaves and triangles. The concept ‘leaf’ would be better stated as the idea ‘leaf’. For example a leaf can encapsulate the concept ‘triangle’ but the reverse is not the case. The deltoid leaf is a case in point. The correct concepts give physical entities their reality and there are no physical entities that would consist solely of triangularity. There are always other accompanying concepts that must be applied to them.

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