Questions for Christians and other theists, part 8: the Trinity

One of the strangest doctrines in all of Christianity is the doctrine of the Trinity. This doctrine holds that there are three divine persons — the Father, the Son, and the Holy Ghost — yet only one deity. Each of the three persons is fully God, and not just a part of God. A famous diagram known as the “Shield of the Trinity” compactly summarizes the idea:


The Trinity doesn’t make much sense, and many Christians recognize this. What most of us would call absurd they call a mystery, meaning something that is known to be true through revelation but cannot be demonstrated by mere human reason.

Some questions for the Christians out there:

1. Do you accept the doctrine of the Trinity?
2. Do you recognize the absurdity of it?
3. Do you deal with the absurdity by declaring it a “mystery”?

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309 thoughts on “Questions for Christians and other theists, part 8: the Trinity

  1. keiths:

    Charlie:

    Your equation works fine for physical objects, especially solid objects.

    If you don’t think that 1+1+1=3 applies to liquid and gas, then you don’t understand the meaning of the equation.

    Your equation only becomes practical when the numbers are assigned to specific entities.

    Say they denote sugar lumps, then the equation makes logical sense. What if they apply to mounds of sugar. Take three separate mounds of sugar, add them together and what is the result. You would have one mound of sugar. 1+1+1=1

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  2. keiths:

    Charlie,

    Spirit is unity, matter is multiplicity.

    Then the Trinity doesn’t exist, by your own stipulation.

    I don’t take unity to be simple. I would say that a Bach sonata is a unity, but it is far from simple.

    I am a physical individual and in this sense a unity. And I have previously referred to the body as nerve/sense system, rhythmic system and metabolic limb system. Three systems of equal importance of which I am composed. They are aspects of my unified body.
    three

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  3. Then you should have said “Spirit is unity and multiplicity, and matter is unity and multiplicity.” The latter is obvious, and the former is what you need for the Trinity to exist as a spiritual entity.

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  4. Charlie,

    Regarding “sugar mound math”, you’re overlooking some things. One is that the three mounds won’t necessarily be mashed into one. We could add them together in a way such that, say, five mounds are formed. 1+1+1=5. Will you suggest that we invent a new mathematics for every such scenario?

    Or we can add them in a way that preserves their independent existence. That is, a way in which 1+1+1=3, and there are three mounds on each side of the equals sign.

    Or take your sugar lumps and imagine throwing them in high arcs toward a target. When they hit the surface, they shatter into hundreds of pieces. Will you now invent a new mathematics in which 1+1+1=671?

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  5. Charlie,

    Regarding Euclidean vs projective geometry, my position hasn’t changed. Neither is more dynamic than the other, and neither is more static than the other. You can imagine dynamic scenarios in both, and you can imagine static scenarios in both.

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  6. Charlie,

    The sugar mound analogy has a theological problem as well. In that analogy, three lesser mounds are combined to form a larger mound. The three lesser mounds are each a part of the larger mound.

    The analogy implies that the Father, Son and Holy Spirit are lesser beings that combine to form God. They’re each just a part of God

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  7. keiths:
    Then you should have said “Spirit is unity and multiplicity, and matter is unity and multiplicity.”The latter is obvious, and the former is what you need for the Trinity to exist as a spiritual entity.

    You are right. But on saying that we need to recognise the polarity. Unity is fundamentally spiritual, multiplicity is fundamentally material. Physicists have worked upon material and taken it apart down past the atomic level. But when this limit of the material is approached it is found that there are processes such as entanglement which leads back to unity, which is the spiritual pole.

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  8. keiths:
    Charlie,

    Regarding “sugar mound math”, you’re overlooking some things.One is that the three mounds won’t necessarily be mashed into one.We could add them together in a way such that, say, five mounds are formed.1+1+1=5.Will you suggest that we invent a new mathematics for every such scenario?

    Or we can add them in a way that preserves their independent existence.That is, away in which 1+1+1=3, and there are three mounds on each side of the equals sign.

    Or take your sugar lumps and imagine throwing them in high arcs toward a target.When they hit the surface, they shatter into hundreds of pieces.Will you now invent a new mathematics in which 1+1+1=671?

    We don’t need a new mathematics. We just need to understand what it is that we are equating. Three mounds on the left can produce 671 mounds on the right, but each side’s combined mass will be equal. We can play about with the material and separate it in any way we please but it still remains one substance.

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  9. keiths: Charlie,

    Regarding Euclidean vs projective geometry, my position hasn’t changed. Neither is more dynamic than the other, and neither is more static than the other. You can imagine dynamic scenarios in both, and you can imagine static scenarios in both.

    In the video Euclid’s Elements: A Dynamic Geometry Perspective by Nick Jackiw, he says:

    …one of the things Euclid essentially set out to do in the Elements was to remove time from mathematics… to kill dynamism from geometry…

    This allowed Euclid to ignore paradoxes of movement such as that of Zeno. He had a motive for trying to eliminate dynamism from his geometry.

    It’s true, you can imagine dynamic scenarios in Euclidean geometry, but Euclid would have preferred it if you didn’t.

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  10. keiths:
    Charlie,

    The sugar mound analogy has a theological problem as well.In that analogy, three lesser mounds are combined to form a larger mound.The three lesser mounds are each a part of the larger mound.

    The analogy implies that the Father, Son and Holy Spirit are lesser beings that combine to form God.They’re each just a part of God

    The sugar analogy is concerned with measuring physical substance. We cannot just take physical laws and think they apply to the spirit. The essence of sugar lies not in quantities but in qualities. Whether three mounds or one mound they still have the same essential attributes.

    One physical symbol for Christ is the fish, the vesica pisces. This is an ancient symbol and it is formed during Euclid’s demonstration of the construction of an equilateral triangle (the symbol for the Trinity). A single straight line with two circles inscribed with their centres on its ends and circumferences running through the opposite end. The two further lines of the triangle derived from, begotten of the one single line.

    Much can be discovered about this ancient fish symbol and Darwinians have as much justification for using it as anyone else. They take this basic symbol and make additions in order to symbolise Darwinian evolution. So this could be interpreted as earthly evolution originating from a primal spiritual condition. The physical derived from the spiritual.

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  11. Charlie,

    Spirit is unity, matter is multiplicity.

    since amended to

    Unity is fundamentally spiritual, multiplicity is fundamentally material.

    in order to correct your inadvertent exclusion of the Trinity from the spiritual realm.

    How do you know the former? Which of Steiner’s orifices did it issue from, and why do you trust it?

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  12. Charlie,

    We don’t need a new mathematics.

    Right. You can keep the old math in which 1+1+1=3 and the Trinity is incoherent.

    There’s no reason to replace it.

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  13. Charlie,

    The sugar analogy is concerned with measuring physical substance. We cannot just take physical laws and think they apply to the spirit.

    1) You have no evidence for the spirit;
    2) You have no evidence that if the spirit existed, it would operate under a different mathematics;
    3) You have no evidence that if the spirit existed and operated under a different mathematics, that 1+1+1 would equal 1 in that scheme.

    It’s pure wishful thinking.

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  14. keiths:

    Charlie,

    Spirit is unity, matter is multiplicity.

    since amended to

    Unity is fundamentally spiritual, multiplicity is fundamentally material.

    in order to correct your inadvertent exclusion of the Trinity from the spiritual realm.

    My two statements are not mutually exclusive. There are two poles, the physical and the spiritual. I regard pure thinking as a spiritual activity. But our thinking can be driven from our will and our feelings in which case it becomes fragmented. I have already alluded to the Osiris myth which aligns well with this and with the thinking about the Trinity.

    From the physical pole, each of us has a material body and so we regard ourselves as existing in the form of one individual organism. Each of us is a unity in our physical form.

    How do you know the former? Which of Steiner’s orifices did it issue from, and why do you trust it?

    I believe that spirit is unity through my thinking activity and my researches in striving to gain knowledge. Gaining knowledge is in itself a process of unification.

    If for argument’s sake we assume that we are justified in regarding the human form as consisting of three aspects as I have said, the metabolic/limb system, the rhythmic system and the nerve/sense system, we can then look further into this. The limbs with their joints and mobility are the seat of mechanical activity and movement. The bones are long and radial with respect to the point which is the centre of the earth. Physical forces are dominant.

    The head and central nervous system is predominantly the opposite of the limbs. The brain floats in cerebrospinal fluid shielding it from the full effects of the physical force of gravity. The only joints within the head that are freely mobile are the temporomandibular joints allowing us to move our jaws. The skull tends towards the spherical and is vaulted like the heavenly plane. The head is the seat of thinking which I have already said I believe to be a spiritual force.

    Willing involves physical activity, thinking involves mental activity, and feeling is the connecting link between the two. The following shows where I see the connection between the trinity and the Trinity.

    Thinking, spirit, Father.
    Feeling, soul, Holy Spirit.
    Willing, body, Son.

    You did ask, so thank you for letting me expand on my thoughts 🙂

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  15. keiths:

    Charlie,

    We don’t need a new mathematics.

    Right. You can keep the old math in which 1+1+1=3 and the Trinity is incoherent.

    There’s no reason to replace it.

    Physical objects can be dealt with in this way, but how do you apply mathematics to the spiritual which is taken to be pure being, pure love and wisdom?

    Try this additional analogy:

    Take a photograph and cut it into three pieces. You have three partial images that can be recombined to reform the whole. One image equals three partial images.

    Now take a hologram and break it into three pieces. You now have three whole images in place of the one. One whole image equals three whole images.

    Both of these give different results. Which one would you say was incoherent?

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  16. keiths:

    Charlie,

    The sugar analogy is concerned with measuring physical substance. We cannot just take physical laws and think they apply to the spirit.

    1) You have no evidence for the spirit;

    I regard thinking as a spiritual activity and so for me this is direct evidence.

    2) You have no evidence that if the spirit existed, it would operate under a different mathematics;

    It is a matter of what mathematics can be applied to. There are many areas in which a straight forward mathematical approach is inappropriate.

    3) You have no evidence that if the spirit existed and operated under a different mathematics, that 1+1+1 would equal 1 in that scheme.

    It’s pure wishful thinking.

    It is difficult, but I try to avoid wishful thinking precisely because it isn’t pure. Wishful thinking is thinking that is tainted with feeling. In that situation I would be letting my feelings control my thinking.

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  17. Charlie,

    Take a photograph and cut it into three pieces. You have three partial images that can be recombined to reform the whole. One image equals three partial images.

    Now take a hologram and break it into three pieces. You now have three whole images in place of the one. One whole image equals three whole images.

    No, because each piece carries only the information from a distinct subset of vantage points. It isn’t the whole holographic image. So what you’re getting is just another variation of 1+1+1=3.

    It also doesn’t work theologically as an analogy for the Trinity, because each of the three pieces is less than the single hologram with which you began the exercise. Orthodox trinitarian theology requires that the Father, Son and Holy Spirit each be no greater or less than the God within whom they all “reside”.

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  18. Charlie:

    I regard thinking as a spiritual activity and so for me this is direct evidence.

    And:

    I believe that spirit is unity through my thinking activity and my researches in striving to gain knowledge.

    So thinking is reliable because it is a spiritual activity, and spirit is unity because you think about it. Nicely circular.

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  19. keiths: So thinking is reliable because it is a spiritual activity, and spirit is unity because you think about it. Nicely circular.

    Given CharlieM’s feelings about circles, he probably thinks that “circular reasoning” is a good thing.

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  20. keiths:
    Charlie,

    1) You have no evidence for the spirit;
    2) You have no evidence that if the spirit existed, it would operate under a different mathematics;
    3) You have no evidence that if the spirit existed and operated under a different mathematics, that 1+1+1 would equal 1 in that scheme.

    It’s pure wishful thinking.

    But once freed from the tyranny of evidence, it’s possible to build fabulous superstructures of belief, in mind boggling detail.

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  21. keiths:

    Charlie,

    Take a photograph and cut it into three pieces. You have three partial images that can be recombined to reform the whole. One image equals three partial images.

    Now take a hologram and break it into three pieces. You now have three whole images in place of the one. One whole image equals three whole images.

    No, because each piece carries only the information from a distinct subset of vantage points. It isn’t the whole holographic image. So what you’re getting is just another variation of 1+1+1=3.

    It also doesn’t work theologically as an analogy for the Trinity, because each of the three pieces is less than the single hologram with which you began the exercise. Orthodox trinitarian theology requires that the Father, Son and Holy Spirit each be no greater or less than the God within whom they all “reside”.

    Okay, let me ament the analogy. Replace the image with a vitally important written message that must be transmitted to three separate individuals.

    The message is divided into three and given to each person. They can make no sense of it. But when each piece of the hologram is given all three individuals get the complete message.

    The essential information which can be directly perceived and understood by each subject is transmitted in full; it is complete. The fact that the resolution of the writing is reduced is incidental and trivial.

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  22. keiths:

    Charlie:

    I regard thinking as a spiritual activity and so for me this is direct evidence.

    And:

    I believe that spirit is unity through my thinking activity and my researches in striving to gain knowledge.

    So thinking is reliable because it is a spiritual activity, and spirit is unity because you think about it. Nicely circular.

    I do not say that thinking is reliable. I believe that thinking is fallible.

    My thinking activity is an undeniable fact that I am directly aware of. That is not to say that the contents of my thinking and the way I bring these thought contents into meaningful relationships need be reliable.

    But any errors in my thinking can only be rectified by further thinking on my part. We unify reality through the process of thinking. And this is what I understand by the concept ‘spirit’. It is unified reality. But for me wholeness does not equal simplicity, far from it.

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  23. Kantian Naturalist: Given CharlieM’s feelings about circles, he probably thinks that “circular reasoning” is a good thing.

    It’s quite good, but me absolute favourite is ‘triangular reasoning’. 🙂

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  24. The following passage from The Essential Goethe gives his views on infinity and being.

    A STUDY BASED ON SPINOZA
    (c. 1785)

    The concepts of being and totality are one and the same; when pursuing the concept as far as possible, we say that we are conceiving of the infinite.

    But we cannot think of the infinite, or of total existence.

    We can conceive only of things which are finite or made finite by our mind; i.e., the infinite is conceivable only insofar as we can imagine total existence—but this task lies beyond the power of the finite mind.

    The infinite cannot be said to have parts.

    Although all finite beings exist within the infinite, they are not parts of the infinite; instead, they partake of the infinite.

    We have difficulty believing that something finite might exist through its own nature. Yet everything actually exists through its own nature, although conditions of existence are so linked together that one condition must develop from the other. Thus it seems that one thing is produced by another, but this is not so—instead, one living being gives another cause to be, and compels it to exist in a certain state.

    Therefore being is within everything that exists, and thus also the principle of conformity which guides its existence.

    The process of measuring is a course one, and extremely imperfect when applied to a living object.

    A living thing cannot be measured by something external to itself; if it must be measured. it must provide its own gauge. This gauge, however, is highly spiritual. and cannot be found through the senses. Even in the circle the gauge of the diameter may not be applied to the periphery. There have been attempts to measure the human being mechanically: painters have chosen the head as the best portion to use For a unit of measurement. But this cannot be done without creating tiny, indefinable distortions in the other parts of the body.

    The things we call the parts in every living being are so inseparable from the whole that they may be understood only in and with the whole. As we stated above, a finite living being partakes of infinity, or rather, it has something infinite within itself. We might better say: in a finite living being the concepts of existence and totality elude our understanding; therefore we must say that it is infinite, just as we say that the vast whole containing all beings is infinite.

    The things which enter our consciousness are vast in number, and their relations—to the extent the mind can grasp them—are extraordinarily complex. Minds with the inner power to grow will begin to establish an order so that knowledge becomes easier; they will begin to satisfy themselves by finding coherence and connection.

    Thus all of existence and totality must be made finite in our minds so that it conforms to our nature and our way of thinking and feeling. Only then will we say that we understand something, or enjoy it.

    Being is not something that can be measured.

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  25. CharlieM: It’s quite good, but me absolute favourite is ‘triangular reasoning’.

    Just like circular reasoning but with an obtuse angle to it

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  26. dazz: Just like circular reasoning but with an obtuse angle to it

    Very funny. A cute reply 😉

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  27. Goethe, as quoted by Charlie:

    There have been attempts to measure the human being mechanically: painters have chosen the head as the best portion to use for a unit of measurement. But this cannot be done without creating tiny, indefinable distortions in the other parts of the body.

    Where is the evidence that the choice of a unit of measurement creates “tiny, indefinable distortions” in the rest of the body? It’s a flat assertion. (Also note the weasel words “tiny” and “indefinable”. )

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  28. It appears that St. Johann, like St. Rudolf, is a fan of untethered thinking.

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  29. Charlie,

    But any errors in my thinking can only be rectified by further thinking on my part.

    They can also be worsened through further thinking on your part. The problem is that when thinking is untethered to reality, it can go in either direction, correct or incorrect. Since there are many more ways to be incorrect than correct, untethered thinking will tend toward the incorrect.

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  30. keiths: Goethe, as quoted by Charlie:

    There have been attempts to measure the human being mechanically: painters have chosen the head as the best portion to use for a unit of measurement. But this cannot be done without creating tiny, indefinable distortions in the other parts of the body.

    Where is the evidence that the choice of a unit of measurement creates “tiny, indefinable distortions” in the rest of the body? It’s a flat assertion. (Also note the weasel words “tiny” and “indefinable”. )

    Do you draw or paint? Have you ever done any life drawing? If you have you will understand what Goethe was getting at here.

    You probably know that artists have always tried to standardise human proportions and to set canons. The image below gives an example of this. Now if you were to go to a museum and sketch a statue using the head as a unit of measurement you could probably produce a very accurate representation. Everything remains static, nothing changes.

    Now try the same thing with a living model. They may look as if they are keeping perfectly still but there will be a constant imperceptible shifting of parts relative to each other. The person will be breathing and muscle tensions will be constantly changing. Shoulders will drop as fatigue sets in. You measure out one feature and from there move on to others only to find that when you return to the first feature its relative position has changed slightly which throws the subsequent work off.

    Proportions can be laid out very accurately in still life but with a life model it is much more important to capture the various thrusts within the pose whilst keeping to the basic proportions as accurate as the situation allows.

    You can measure with great accuracy the position of a supporting rod’s attachment on a mechanical structure. Try making the same accurate measurement of the location at which a muscle attaches to a bone.

    A further comment to emphasise the point. A small flaw in the marble of a statue can be accurately measured relative to any other part of the statue. What would be the precise distance between the heart’s tricuspid valve and the base of the sternum?

    Image from here

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  31. keiths:

    Charlie,

    But any errors in my thinking can only be rectified by further thinking on my part.

    They can also be worsened through further thinking on your part. The problem is that when thinking is untethered to reality, it can go in either direction, correct or incorrect. Since there are many more ways to be incorrect than correct, untethered thinking will tend toward the incorrect.

    Of course you are correct that thinking can go either way. But when you say “unteathered to reality” what reality do you mean? Is it the reality of our everyday world of sense experience or the world of whirling, colourless, silent entities that supposedly exists behind the world of our senses?

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  32. I mean things as they actually are.

    (Hence the ‘real’ in ‘reality’.)

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  33. Charlie, quoting Goethe:

    A living thing cannot be measured by something external to itself;

    It happens all the time. In medicine, for instance.

    if it must be measured it must provide its own gauge. This gauge, however, is highly spiritual and cannot be found through the senses.

    Says Goethe, without explaining how he knows this. And for fun, how does one determine this “highly spiritual” gauge?

    Even in the circle the gauge of the diameter may not be applied to the periphery.

    Why not? Presumably he means that you’ll get an irrational number if you use the diameter as a gauge for the circumference. But so what? The measurement isn’t going to be accurate enough for it to make a difference And what’s so important about rational numbers?

    There have been attempts to measure the human being mechanically: painters have chosen the head as the best portion to use for a unit of measurement. But this cannot be done without creating tiny, indefinable distortions in the other parts of the body.

    How does the choice of the head as a measurement unit create “tiny, indefinable distortions” elsewhere in the body? Is this a “spiritual” process?

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  34. CharlieM: A STUDY BASED ON SPINOZA
    (c. 1785)

    The concepts of being and totality are one and the same; when pursuing the concept as far as possible, we say that we are conceiving of the infinite.

    But we cannot think of the infinite, or of total existence.

    We can conceive only of things which are finite or made finite by our mind; i.e., the infinite is conceivable only insofar as we can imagine total existence—but this task lies beyond the power of the finite mind.

    The infinite cannot be said to have parts.

    Although all finite beings exist within the infinite, they are not parts of the infinite; instead, they partake of the infinite.

    We have difficulty believing that something finite might exist through its own nature. Yet everything actually exists through its own nature, although conditions of existence are so linked together that one condition must develop from the other. Thus it seems that one thing is produced by another, but this is not so—instead, one living being gives another cause to be, and compels it to exist in a certain state.

    Therefore being is within everything that exists, and thus also the principle of conformity which guides its existence.

    The process of measuring is a coarse one, and extremely imperfect when applied to a living object.

    A living thing cannot be measured by something external to itself; if it must be measured. it must provide its own gauge. This gauge, however, is highly spiritual and cannot be found through the senses. Even in the circle the gauge of the diameter may not be applied to the periphery. There have been attempts to measure the human being mechanically: painters have chosen the head as the best portion to use For a unit of measurement. But this cannot be done without creating tiny, indefinable distortions in the other parts of the body.

    The things we call the parts in every living being are so inseparable from the whole that they may be understood only in and with the whole. As we stated above, a finite living being partakes of infinity, or rather, it has something infinite within itself. We might better say: in a finite living being the concepts of existence and totality elude our understanding; therefore we must say that it is infinite, just as we say that the vast whole containing all beings is infinite.

    The things which enter our consciousness are vast in number, and their relations—to the extent the mind can grasp them—are extraordinarily complex. Minds with the inner power to grow will begin to establish an order so that knowledge becomes easier; they will begin to satisfy themselves by finding coherence and connection.

    Thus all of existence and totality must be made finite in our minds so that it conforms to our nature and our way of thinking and feeling. Only then will we say that we understand something, or enjoy it.

    For what it’s worth, as a reading of Spinoza, that’s pretty good.

    I’ve been reading Spinoza’s Ethics to pass the time while we’re socially distanced.

    The main thing that I find really striking in this reading of Spinoza is how much he distrusts the imagination — it’s only in the intellect, and especially in mathematics, that we find completely reliable (because necessarily true) knowledge.

    But Spinoza would of course be the first to deny that the Trinity makes any sense — it’s just another superstition of the rabble who lack proper mathematical training!

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  35. keiths: Charlie, quoting Goethe:

    A living thing cannot be measured by something external to itself;

    It happens all the time. In medicine, for instance.

    if it must be measured it must provide its own gauge. This gauge, however, is highly spiritual and cannot be found through the senses.

    Says Goethe, without explaining how he knows this. And for fun, how does one determine this “highly spiritual” gauge?

    Even in the circle the gauge of the diameter may not be applied to the periphery.

    Why not? Presumably he means that you’ll get an irrational number if you use the diameter as a gauge for the circumference. But so what? The measurement isn’t going to be accurate enough for it to make a difference And what’s so important about rational numbers?

    There have been attempts to measure the human being mechanically: painters have chosen the head as the best portion to use for a unit of measurement. But this cannot be done without creating tiny, indefinable distortions in the other parts of the body.

    How does the choice of the head as a measurement unit create “tiny, indefinable distortions” elsewhere in the body? Is this a “spiritual” process?

    I’m sure you agree that in order to criticise somebody’s work and studies we need to have a good understanding of what it is they are trying to say. With Goethe this is made more difficult by the fact that we are reading an English translation of the original German and that his writing are from a couple of centuries ago.

    Nevertheless, if you want to get a better idea of his way of thinking you can find the context of the quotes given above, here

    An organic being is so multifaceted in its exterior, so varied and inexhaustible in its interior, that we cannot find enough points of view nor develop in ourselves enough organs of perception to avoid killing it when we analyze it. I will attempt to apply the idea “Beauty is perfection in combination with freedom” to living organisms. ..

    …Here I allude to the language of gesture which is restrained in well-bred people, and which, I believe, does as much as the language of words to elevate man above the animal.

    To develop the concept of a beautiful human in this manner would require that we take countless matters into consideration; there is clearly much to be done before the exalted concept of freedom can crown human perfection, even in the physical sense.

    Here I must note a further point. We call an animal beutiful when it gives the impression that it could use its limbs at will, but when it really uses them as it chooses, the idea of the beautiful is immediately lost in feelings of the pretty, the pleaant, the easy, the splendid, etc. Thus we see that beauty actually calls for repose together with strength, inaction together with power.

    If the notion of asserting the power of a body or some limb is too closely associated with the being’s physical existence, the spirit of the beautiful seems to take flight immediately; the ancients depicted even their lions in the greatest degree of repose and neutrality in order to draw forth the feeling with which we grasp beauty.

    I would say that we consider a perfectly organised being beautiful if, in beholding it, we can believe it capable of manifold and free use of all its members whenever it wishes. Thus the most intense feeling of beauty is connceted with feelings of trust and hope.

    It seems to me that an essay on the animal and human form viewed in this way might yield agreeable insights and show some interesting relationships.

    In particular, this would elevate the concept of proportion (which we usually try to express through number and measure, as mentioned above) to more spiritual principles, and it is my hope that these spiritual principles, might at last come to agree with the approach used by the great artists whose works have come down to us, and also encompass those beautiful products of nature which appear among us from time to time in living form.

    ***

    Empirical observation and Science.

    Phenomena, which others of us may call facts. are certain and definite by nature, but often uncertain and fluctuating in appearance. The scientific researcher strives to grasp and keep the definite aspect of what he beholds; in each individual case he is careful to note not only how the phenomena appear, but also-how they should appear. There are many empirical fractions which must be discarded if we are to arrive at a pure, constant phenomenon-.—-as I can frequently note, especially in my present field of study? However, the instant I allow myself this, I already establish a type of ideal.

    But there is a great difference between someone like the theorist who turns whole numbers into fractions for the sake of a theory, and someone who sacrifices an empirical fraction for the idea of the pure phenomenon.

    For the observer never sees the pure phenomenon with his own eyes; rather, much depends on his mood, the state of his senses, the light, air, weather, the physical object, how it is handled, and a thousand other circumstances. Hence it is like trying to drink the sea dry if we try to stay with the individual aspect of the phenomenon, observe it, measure it. weigh it, and describe it.

    In my observation of nature and ‘reflection on it l have attempted to remain true to the following method as much as possible, especially in my recent work.

    After observing a certain degree of constancy and consistency in phenomena, I.derive an empirical law from my observation and expect to find it in later phenomena. If the law and the phenomena are in complete agreement, I have succeeded; if they are not in complete agreement, my attention is drawn to the circumstances surrounding each case. and I am forced to find “new conditions for conducting the contradictory experiments in a purer way. But if a case which contradicts my law arises often and under similar circumstance, I realize that I must go further in my research and seek out a higher standpoint.

    Regarding trying to measure the circumference of a circle using the radius you would be correct in assuming that his point is that it cannot be expressed as a simple fraction.

    My view on this is this disconnection between the two is due to the fact that they are an expression of polar opposites. Radii have their origin at the central point whereas the line at the circumference has is an expression of the line at infinity. Radii relate to the point, circumferences relate to the periphery. To inscribe a circle is to produce a trinity, creating form between two infinities.

    Regarding the head as the unit of proportion. A holist might say that the head is actually an expression of the whole,

    The mobile jaw is an expression of the limbs, both are moved through the action of the will.

    The buccal cavity and tongue are an expression of the sexual organs. Through these we can create spiritually and physically respectively. The nose an expression of the lungs, and so on. The whole reflected in the parts.

    Using the head as an aid to physically measure the body does the same as any such analysis, it kills the living form.

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  36. keiths:
    I mean things as they actually are.

    (Hence the ‘real’ in ‘reality’.)

    You mean by circular reasoning we determine that reality is what actually is.

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  37. Kantian Naturalist:

    For what it’s worth, as a reading of Spinoza, that’s pretty good.

    I’ve been reading Spinoza’s Ethics to pass the time while we’re socially distanced.

    The main thing that I find really striking in this reading of Spinoza is how much he distrusts the imagination — it’s only in the intellect, and especially in mathematics, that we find completely reliable (because necessarily true) knowledge.

    But Spinoza would of course be the first to deny that the Trinity makes any sense — it’s just another superstition of the rabble who lack proper mathematical training!

    From here

    Goethe was a Spinozist for his fundamental creed was Spinoza’s ‘deus sive natura’. He once wrote a letter: “Spinoza does not prove the existence or being of God; the existence or being is God. And when others for this label him an Atheum, then I feel tempted to pronounce him Theissimum, or better still, Christianissimum.” And in another portion of this letter: “All effects in nature that we perceive depend upon one another…From the brick that falls from the roof, to the lightning brain-wave,…all these events are interdependent.” We can therefore call Goethe a determinist in the Spinozistic sense of the word.

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  38. Charlie,

    Nevertheless, if you want to get a better idea of his way of thinking you can find the context of the quotes given above, here:

    Sorry, Charlie, but reading Torley-length quotes from Goethe (or Steiner) is just not worth the pain. Could you answer my questions in your own words instead? Or keep the quotes much shorter?

    Charlie:

    Regarding trying to measure the circumference of a circle using the radius you would be correct in assuming that his point is that it cannot be expressed as a simple fraction.

    My view on this is this disconnection between the two is due to the fact that they are an expression of polar opposites. Radii have their origin at the central point whereas the line at the circumference has is an expression of the line at infinity. Radii relate to the point, circumferences relate to the periphery.

    A circle is wholly defined with respect to the center. (Haven’t we had this discussion before?)

    The buccal cavity and tongue are an expression of the sexual organs.

    How do you know this? Is it via “clairvoyant investigation”?

    Using the head as an aid to physically measure the body does the same as any such analysis, it kills the living form.

    And you know this how? And what does it even mean to “kill the living form”?

    We can make these exchanges briefer if you just anticipate this question:

    How do you know this?

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  39. Charlie,

    You mean by circular reasoning we determine that reality is what actually is.

    There’s no circularity, because our knowledge builds incrementally. Learning X does not depend on already knowing X; it depends on some other piece(s) of knowledge.

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  40. keiths:

    Charlie,

    Nevertheless, if you want to get a better idea of his way of thinking you can find the context of the quotes given above, here:

    Sorry, Charlie, but reading Torley-length quotes from Goethe (or Steiner) is just not worth the pain. Could you answer my questions in your own words instead? Or keep the quotes much shorter?

    I do try to add my own comments along with any quote. I leave it up to you whether or not you deem it worthwhile to get some extra information. I don’t wish to compel you or anybody else to do anything.

    Charlie:

    Regarding trying to measure the circumference of a circle using the radius you would be correct in assuming that his point is that it cannot be expressed as a simple fraction.

    My view on this is this disconnection between the two is due to the fact that they are an expression of polar opposites. Radii have their origin at the central point whereas the line at the circumference has is an expression of the line at infinity. Radii relate to the point, circumferences relate to the periphery.

    A circle is wholly defined with respect to the center. (Haven’t we had this discussion before?)

    Yes, coincidentally, we have just completed one full revolution of our journey round the sun since we were discussing this very topic here I will note that we view our distance to the sun in terms of space (radius), but we view our position in orbit in terms of time (circumference).

    Hopefully, just like the solar system we’ve all moved on somewhat in the mean time, even if we are probably on divergent trajectories.

    You are right, a circle is wholly defined with respect to the centre. Euclid defined it thus: “A circle is a plane figure contained by one line such that all the straight lines falling upon it from one point among those lying within the figure equal one another. And the point is called the center of the circle.”

    But there are two sides to a circle , the inside and the outside. By means of the central point the circle is defined, it can be measured. It is restricted within certain limits. In what way is it related to the outside? The outside has no limits, it can be expanded to infinity. It is beyond measurement. Radii are
    segments, they have limits. Circumferences have no beginning or end. They are related to the periphery in the same way that radii are related to points.

    One pole is limited which allows for definition and measurement. The opposite pole has no such restrictions and thus is beyond defining and measuring in this way. Regarding individual people, the body can be quantified by measure, number and weight, the spirit cannot. How do you weigh a thought?

    The buccal cavity and tongue are an expression of the sexual organs.

    How do you know this? Is it via “clairvoyant investigation”?

    The connection has been noted by others. lona Nemesnyik Rashkow posed the riddle, , “Why do men think so much and women talk so much,” and the answer given, “Because men have two heads and women have four lips.” Some Roman art works make the connection more explicit as in the image below.

    Using the head as an aid to physically measure the body does the same as any such analysis, it kills the living form.

    And you know this how? And what does it even mean to “kill the living form”?

    We can make these exchanges briefer if you just anticipate this question:

    How do you know this?

    Living beings are intrinically dynamic. Life drawing necessarily renders a static form which, if the artist were to represent with everything in the correct proportion and nothing more, the result would be a lifeless image. The great masters were able to use light and shadow and the thrust of lines drawn in a way that creates the impression of movement and in this way they bring the work to life.

    I am not interested in the length of the exchanges as long as they give me something to think about.

    Image source

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  41. keiths:

    Charlie,

    You mean by circular reasoning we determine that reality is what actually is.

    There’s no circularity, because our knowledge builds incrementally. Learning X does not depend on already knowing X; it depends on some other piece(s) of knowledge.

    In my opinion to say that reality is what actually is, is the same as saying what actually is is reality. It is circular.

    I was trying to get you to explain what reality meant in your opinion, but you told me nothing new.

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  42. CharlieM: From here

    Goethe was a Spinozist for his fundamental creed was Spinoza’s ‘deus sive natura’. He once wrote a letter: “Spinoza does not prove the existence or being of God;the existence or being is God. And when others for this label him an Atheum, then I feel tempted to pronounce him Theissimum, or better still, Christianissimum.” And in another portion of this letter: “All effects in nature that we perceive depend upon one another…From the brick that falls from the roof, to the lightning brain-wave,…all these events are interdependent.” We can therefore call Goethe a determinist in the Spinozistic sense of the word.

    Perhaps, though it’s a matter of considerable debate as how well Goethe really understood Spinoza. From what I understand, Goethe has a poet’s faith in the power of imagination to construct metaphors that disclose rather than articulate certain truths. Nothing could be more antithetical to Spinoza!

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  43. Kantian Naturalist:

    Goethe was a Spinozist for his fundamental creed was Spinoza’s ‘deus sive natura’. He once wrote a letter: “Spinoza does not prove the existence or being of God;the existence or being is God. And when others for this label him an Atheum, then I feel tempted to pronounce him Theissimum, or better still, Christianissimum.” And in another portion of this letter: “All effects in nature that we perceive depend upon one another…From the brick that falls from the roof, to the lightning brain-wave,…all these events are interdependent.” We can therefore call Goethe a determinist in the Spinozistic sense of the word.

    Perhaps, though it’s a matter of considerable debate as how well Goethe really understood Spinoza. From what I understand, Goethe has a poet’s faith in the power of imagination to construct metaphors that disclose rather than articulate certain truths. Nothing could be more antithetical to Spinoza!

    Goethe believed his archetypes were directly perceived and not metaphors. He would study very thoroughly entities such plants or bone formations in as many states of their development as he possibly could.

    His “exact sensorial imagination” was not to be taken as any type of inner fantasy. It was more akin to using the mind and mental pictures to survey the subject by means of time lapse photography before photography was invented. By this method he could “see” processes in nature that senses alone cannot give us.

    He saw the unity of nature writing:

    She is whole and yet never finished. As she works now, so can she work for ever.

    To every one she appears in a form of his own. She hides herself in a thousand names and terms, and is always the same.

    This view of the wholeness of nature is much more in agreement with the unitary nature of the universe according to Spinoza than it is to, say, the monads of Leibniz with its fragmentation of nature.

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  44. Charlie,

    In my opinion to say that reality is what actually is, is the same as saying what actually is is reality. It is circular.

    The circularity is only apparent. I define reality as “things as they actually are.” I don’t define “things as they actually are” as “reality”. That was your addition.

    Now, it’s true that those things will track each other, but that doesn’t mean that each is defined in terms of the other. And without the bidirectional definitions, there is no circularity.

    To put it differently,

    1) let A and B be our defined terms; and
    2) let B be defined as equal to A; but not A as equal to B.
    3) let c be some condition that qualifies an item to be added to A.

    B will track A, but there is no loop. The causality runs one way:

    condition c -> change to A -> change to B.

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  45. Charlie,

    …I will note that we view our distance to the sun in terms of space (radius), but we view our position in orbit in terms of time (circumference).

    It also works the other way around, with the radius expressed in light-minutes and the arc length in meters.

    You are right, a circle is wholly defined with respect to the centre. Euclid defined it thus: “A circle is a plane figure contained by one line such that all the straight lines falling upon it from one point among those lying within the figure equal one another. And the point is called the center of the circle.”

    But there are two sides to a circle , the inside and the outside. By means of the central point the circle is defined, it can be measured. It is restricted within certain limits. In what way is it related to the outside? The outside has no limits, it can be expanded to infinity. It is beyond measurement.

    The outside does have limits if there is a closed figure surrounding the circle.

    Radii are segments, they have limits. Circumferences have no beginning or end.

    Circumferences are unbounded but they are not infinite.

    They are related to the periphery in the same way that radii are related to points.

    ??

    Regarding individual people, the body can be quantified by measure, number and weight, the spirit cannot. How do you weigh a thought?

    You can’t weigh thoughts, but you can’t weigh heartbeats either. Weighability is not a difference between “the spirit” and the body (even assuming that the spirit exists and is responsible for thought.

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  46. Charllie,

    The buccal cavity and tongue are an expression of the sexual organs.

    The Roman art is nice. Are there other cultures who used that motif? Also, what does it mean to say “is an expression of” in the above context? It sounds like it might be a Steinerism.

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