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Will President Dutarte have to resign? Mathematician Euler offered an equation taken as proof of God

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Leonhard Euler.jpg
Leonhard Euler, 1753/Jakob Emanuel Handmann

Recently, Philippines president Rodrigo Dutarte threatened to resign if anyone could prove that God exists. It turns out that the great mathematician Leonhard Euler (1707–1783) offered a proof of the existence of God.

Today, Euler is considered one of the greatest mathematicians of all time. His interests covered almost all aspects of mathematics, from geometry to calculus to trigonometry to algebra to number theory, as well as optics, astronomy, cartography, mechanics, weights and measures and even the theory of music.

Much of the notation used by mathematicians today – including e, i, f(x), ∑, and the use of a, b and c as constants and x, y and z as unknowns – was either created, popularized or standardized by Euler. His efforts to standardize these and other symbols (including π and the trigonometric functions) helped to internationalize mathematics and to encourage collaboration on problems. More.

Here’s Identity, often taken as a proof of God:

Euler’s identity is an equality found in mathematics that has been compared to a Shakespearean sonnet and described as “the most beautiful equation.” It is a special case of a foundational equation in complex arithmetic called Euler’s Formula, which the late great physicist Richard Feynman called in his lectures “our jewel” and “the most remarkable formula in mathematics.”

In an interview with the BBC, Prof David Percy of the Institute of Mathematics and its Applications said Euler’s Identity was “a real classic and you can do no better than that … It is simple to look at and yet incredibly profound, it comprises the five most important mathematical constants.”

Some of Euler’s other thoughts about God, offered by a friend, cited by Adam Drozdek, “Leonhard Euler as an Apologist,” Theologische Zeitschrift 66 (2010) pp. 62-82:

He wrote in his Examen d’une controverse sur la loi de refraction des rayons, 1753, that

if other arguments for the existence of God make no impression on the spirit of Atheists, just the consideration of the structure of the eye should convince them about the existence of the supremely wise and powerful Being, in comparison with which the highest wisdom of man is reduced to nothing.

He talks about the human eye in his Letters:

Vision «is without a doubt the most wonderful thing which the human spirit could fathom.» The little that we know about the operation of the eye «is more than sufficient to convince us of the Omnipotence and infinite wisdom of the Creator; and its wonders
should enrapture our spirit to more pure adoration of the supreme being. We discover in the structure of eyes perfections which the most intelligentspirit could never thoroughly examine and the most skilful artist could never construct a machine of such a kind» (Letters 41). Although Euler raised the issue of God’s wisdom, indirectly he also addressed the problem of the existence of God: the eye is a witness of a supremely wise creator who only can be God. Euler was convinced that God «has surely followed in his works the simplest route» and thus the eye cannot be reproduced by a simpler device(Letters 43). Today, the intelligent design proponents use the concept of an irreducible complexity which, as it can be seen, would be endorsed by Euler:

“the eye is complex but it cannot be made any simpler since removing but one element from its construction would render the eye unworkable. Therefore, all the elements of the eye must have been put together at the same time to enable the proper execution of its function.” This is the proof of the existence of God from design, which is the first proof used in European philosophy, namely by Socrates, and was a proof frequently used in the age of Euler, frequently under the name of physicotheology.

And the more we know about the eye, the more complex it is.

But President Duarte may have other stuff to read…

President Rodrigo Roa Duterte 2017.jpg
See also: Philippines president claims he’ll resign if anyone can prove God exists. But leaves himself a fine-tuning loophole.

Comments
jerry
What may be convincing for one person may not be convincing for most. Why? That is the point I am making.
I was commenting on an aspect of the point you were making - where you said that there was "no evidence". I was just saying that there is evidence. Some people are convinced by that evidence, others not. But what you're really saying goes beyond that, I understand. You're saying it's not a matter of some evidence but something totally obvious that everybody must accept. Ok.
You should get the movie to look at the skeptics portrayed there.
I've seen movies, read books - I'm very aware of the skeptics. The weight of evidence is overwhelmingly in favor of Lourdes, but that is not the point you're making - I understand. You're looking for 100% - where everyone without exception accepts it.
Someone who should believe does not really believe or else he would have lived his life differently. There is really not enough evidence to make him live his life differently. My friend does not really believe.
The part of your argument that I question is that simple belief or acceptance - even at a factual level, will necessarily result in moral perfection. We can be fully aware, totally convinced and recognize as a fact that a certain thing harms us. But even knowing that, we can still do that certain thing. So, it's not just knowing something (that God exists) but it's having the moral strength to act on the truth that you know. But both things are part of the world God created. Yes, you're right - we do not have 100% obvious information about God's existence. That is for a reason. In my view, it is for the discovery of God which takes a lifetime. We work and struggle and fight through the darkness - God reveals bits of light, hints of His presence. Then we follow those. This builds us in strength and gives us a goal.
In the final frame there are only people being solicitous of each other and asking how they can be kind to them. Obvioulsy false virtue.
Ok, we're in agreement. Because there is ambiguity and we have to search and discover, then we have the chance to show real virtue. We're making actual choices for good, rather than being forced into it.Silver Asiatic
July 20, 2018
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Well, that’s evidence. It may not be convincing enough for you, but it’s a place to look.
You are completely misreading what I am saying. What may be convincing for one person may not be convincing for most. Why? That is the point I am making. It has nothing to do with me or what I believe. I have been to Lourdes and know the story of Bernadette very well. You should get the movie to look at the skeptics portrayed there
You seemed to dismiss Lourdes on an anecdote from a lapsed Catholic.
It illustrates my point perfectly. Someone who should believe does not really believe or else he would have lived his life differently. There is really not enough evidence to make him live his life differently. My friend does not really believe. God could do a lot more to make Himself known but he doesn't. That is my point and I theorize the world would be much different if it wasn't that way. Try to imagine a world where as I said God was as obvious as the sun rising in the east tomorrow. It would not be an interesting world and I believe God made it that way because He knew how people would behave if it was otherwise. I am trying to get some cartoons made that illustrate this. One is a series where people are arguing with each other and cheating others and in the next frame shows an enormous entity which says that you must obey me and be kind to each other or else. In the final frame there are only people being solicitous of each other and asking how they can be kind to them. Obvioulsy false virtue. I have other variations I am working on,jerry
July 20, 2018
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jerry
Yes, there are some things that are apparently miraculous.
Well, that's evidence. It may not be convincing enough for you, but it's a place to look.
Catholics will point to Lourdes and other places for examples.
Yes, true. Catholics point to that and many other places and people where there is evidence. I think it's important to be open to it and investigate. You seemed to dismiss Lourdes on an anecdote from a lapsed Catholic. As you say later, many Christians do not really believe what they profess. But there are many who do believe, and they tell of what they have experienced (like St. Bernadette of Lourdes, for example, among many others).Silver Asiatic
July 20, 2018
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Jerry, Thanks for reading my post, anyway. I think we're just on different wavelengths (and I probably should have included more context initially). It's likely not worth the effort to take this further.daveS
July 19, 2018
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I pointed out that despite these reasons, perhaps it’s logically impossible for God to create a world in which it’s impossible to prove He exists. (For example, the Kalam Cosmological Argument might “work” in every possible world).
I haven't a clue what you are trying to say. Too many negatives. You seem to be making my point. Are you saying the Kalam Cosmological argument routinely convinces most people there is a God. I doubt many would agree with you. Do you personally believe the Kalam Cosmological argument? Do you believe the Kalam Cosmological argument convinces most people? What percentage of the people that belittle Intelligent Design do you think believe in the Kalam Cosmological argument? I did not say that there isn't evidence that there is or is not a God. I said that if the evidence was overwhelmingly certain, a world would ensue that would probably not be desirable from God's point of view. (whatever that is exactly?). We would be automatons. Certainly the Judeo/Christian God could make His presence known in lots of ways that are definitive if He desires it. For example, Christians pray to God constantly but how often are their prayers definitively answered. (Please don't anyone tell me that God answers all prayers in ways we do not know or something to that effect. Assume I am familiar with Christian thought) But there is no evidence that prayer leads to God's intervention. Yes, there are some things that are apparently miraculous. Catholics will point to Lourdes and other places for examples. I have a friend who is a lapsed Catholic who has just visited Lourdes with his wife who has cancer. God could certainly answer prayers in ways that are definitive but He doesn't. Recently a well known writer said he was an atheist because he could not see any evidence that there is a God. My immediate thought was that the evidence is anything but overwhelming to many but that is the way it has to be. But there definitely is evidence, a lot of it. But history is full of so called Christians who acted as if they did not believe.jerry
July 19, 2018
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Axel, we are going beyond UD's remit now. I point here. KFkairosfocus
July 19, 2018
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If I may interject here, KF - would not at least a signifcant part of the mystery that you view as residual, reside (no quasi homophone intended) in the fact that 'personhood' is integral, in our mortal human experience, with a distinct identity of being : the very quintessence of subjectivity. And yet there is the small matter of the true nature of each one of us being in Christ, in his shared Mystical Body. A 'whole mess of persons' adopted into the very life of the Holy Trinity, all sharing the same spirit.... To my mind, KF, virtually by definition, the Holy Trinity is the ultimate paradox and infinite mystery. Understandaby, an atheist might see it as an oxymoron. This has led to the hilarious situation whereby Dawkins gratuitously dreams up what are, in effect, oxymorons (or tantamount to them, in terms of common-sense, such as a blind watchmaker), and with sovereign confidence, classifies them as paradoxes ! And I can't get over the way in which materialists speak of being informed by their intuition concerning truths that are readly accessed by elementary reason ! Though they are materialists, they want a part of 'intutition', 'cos, 'cos Einstein said it was good ; and 'beauty'('elegance') and stuff, too.Axel
July 19, 2018
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KF
with God, somethings are beyond our conception ...
Yes.Silver Asiatic
July 19, 2018
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SA, yes, we normally infer and reason in stages, though sometimes we can reason in parallel too. That does not affect or alter the force of the key conclusions on framework realities. Consider world W with some distinct A as opposed to -- the dichotomy "pipe" character | -- not A ~A: W = {A|~A} A is itself, rooted in the core characteristics that mark its distinctiveness. If we instead had things that are indistinguishable, they would be identical. That's LOI. As | intervenes i/l/o the distinction, no x in W will be A AND ~A. That's LNC. As the dichotomy locks out both-and, and we speak of entities in W, we have that any x in W will be A X-OR ~A, not both or neither. That's LEM, strict form. Such are embedded in rational contemplation, communication (see Paul on distinct sounds in 1 Cor 14) and in the existence of both abstracta and concrete entities. On things not possible of being, a square circle would have core characteristics that cannot both hold, squarish and circular ones. It cannot be in any world, hence why God cannot make one. There literally is not and can never be any such thing. And yes, that is true of God as well as us. There is for some things, no unbridgeable gulch between God and us. After all, he invites, let us reason together -- on certain things. Next, while UD is not a theology thread, I will comment on a point, inferring that likely you are not a native English speaker (not even in the sort of dialects that are common in these parts). The Athanasian creed as rendered in Latin then English (deriving from I believe a Greek original) carefully distinguishes "person" and "being." The triune view of the Godhead is of three persons of one eternal nature, being one being. Not three parts or three beings in a society. The oneness of being is inseparable from the threeness of manifestation as Persons, with role-relationships. There is an element of mystery (we know not how such may be) but there is no contradiction as the threeness and the oneness speak to different aspects. In effect, if you wish a mathematical figure of speech, it is not 1 + 1 + 1 = 3 = 1, but that 1 * 1 * 1 = 1. Where threefold unity has distinction of the ones. A further loose analogy that is mathematical, is that a triangle is one and three at once, in different aspects. This is exploited in the classic shield of faith illustration. Yet another is physical-chemical: at triple-point, water is one chemical substance in three co-existing forms. There is the famed story of Patrick, challenged, picking a shamrock leaf and asking: 3 or 1? If 3, why one stem, if 1 why 3 lobes. Our problem is conceptual, tied to the logic of being and principle of identity. And with God, somethings are beyond our conception but are real. (Sort of reminds me of a few quantum oddities, e.g. the wavicle phenomenon.) (To see this, ponder is it possible to be due north of London, New York and Tokyo while standing at one point? At first, it seems not, but switch to a 3-d frame and we see yes, stand at the North Pole.) KFkairosfocus
July 19, 2018
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jerry
My point is that God would not want a world in which it was obvious He existed. He could certainly create one, but would He want to is the question.
It depends on your theological views, of course. But from a Christian perspective, whether God's existence is obvious or not, would not be the main factor in God's desire to create a world. Again, from a Christian view, God did create a world where His existence was known and was obvious to all intelligent creatures (angels and the first human couple). But knowing that God exists alone is not enough to meet the challenge of why God created intelligent beings. In those cases with angels and men - a test was given. Both knew that God existed, but still, some angels and the first humans failed the test. It's a test of fidelity and moral goodness. So, God did not create rational beings merely so they would discover that He exists. That's only one small step. The fundamental reason why God created was so that intelligent creatures could share His happiness, and be like Him - living with Him, doing (in a small way) what He does. Thinking, creating, loving, family life ... The human mind and innovative imagination is so powerful - we're like little 'gods' (and we sometimes act that way, understandably). So creatures could not only discover God's existence but could learn the highest form of living. Even if we have a high degree of certainty that God exists, it doesn't mean we're going to achieve moral goodness. We can look at a lot of Christians and other believers who have a high level of certainty that God exists - for them it is obvious, but they (I mean, myself) still fail quite often in the challenge of moral living.Silver Asiatic
July 19, 2018
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Jerry, My post was meant to be fairly closely related to yours. You argue that there are reasons to believe that God would not create a world in which one could prove He exists. I pointed out that despite these reasons, perhaps it's logically impossible for God to create a world in which it's impossible to prove He exists. (For example, the Kalam Cosmological Argument might "work" in every possible world). If that is true, then in any world God creates, it will be possible to prove He exists.daveS
July 19, 2018
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KF
SA, the key principles are necessary, framework to any possible world, it is not just HUMAN reasoning, but reasoning.
Well, you seem to be making claims for the mind of God. Human reasoning, a logical process, is sequential. It is time-bound. It moves from premise, through terms to a conclusion. I do not know your understanding of God. In my view, God is timeless. For God, there is no time, no need for sequential logic. So - do you think God's reasoning works like human? You have stated that it's not human reasoning, but just reasoning in general. So, all reasoning requires the limits you state? I have tried to show you that the nature of God is a trinity of three complete, entire, whole, infinite beings - none dependent. These three, each with infinite, fulness - lacking nothing, are actually one. I have shown that this idea is not reducible to human reason or logic. My point here is that God's understanding of His own nature, cannot be constrained by the limits of human reason. The identity of God is not reducible to mathematics or logic. Thus, either God knows Himself poorly, incorrectly and with the same darkness that human reason knows God - or, God's reason is not human reason. I have made this point as clear as I can. I accept that you may disagree. Again, I do not know your understanding of God. I had assumed you took a certain view, but perhaps not.
Once distinct identity obtains, certain things are associated, necessarily so, and any distinct world already has distinct identity. As just one example, God cannot make a square circle.
Again, I explained why this view is not correct. God is three infinite, non-contingent, complete beings. There is no way to resolve this logically or with the law of identity. Either the persons are not distinct, or there are three gods. You cannot resolve the mathematical formula: 1 = 1 therefore 1 = 3. That violates the law of identity.
Not because God is too weak but because such is impossible of being.
I have explained how three absolute infinites, lacking nothing of being, cannot exist at the same time, and moreover cannot be one being. Human reason and logic are not adequate to understand this, and obviously, God's ways are not our ways, God's thoughts are not our thoughts.
Likewise, faith is central not only to the Christian faith but to any worldview and life agenda,<,/blockquote. Yes. I will say that a rejection of the Christ as Logos is a rejection of rationality and reason also.
Silver Asiatic
July 19, 2018
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KF You confused me and Axel there.Silver Asiatic
July 19, 2018
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I haven't followed this thread since I posed the question about God's intentions. I just looked at it again. I asked
Would God create a world where one could prove He exists?
not
Could God create another world?
A completely separate idea and unrelated to the topic of the OP. Immediately it drifted off into an irrelevant question about choice and then mathematics such as the square root of 2 as irrational or not. And the implication that God could not create certain types of worlds. Which if true does not mean that God could not create an infinite number of different worlds. My point is that God would not want a world in which it was obvious He existed. He could certainly create one, but would He want to is the question. Whether the square root of 2 or irrational numbers exists in any world is another question.jerry
July 19, 2018
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Axel, I spoke of the Athanasian creed clip you made, which pivots on logic of being and principle of identity; hence, clips from it. I pointed to the math slide show to document how things that make pretty good sense but are technical and finely balanced can come across as exceedingly abstruse. Next, it is not a prioris as such. Certain things are embedded in the framework for a distinct world to exist, any possible world. One of those is distinct identity and what it instantly brings with it. LOI, LNC, LEM, two-ness thus the naturals etc are examples. Other things -- such as a square circle -- cannot exist in any possible world. As this example shows, impossible of being because some core characteristics contradict others. KFkairosfocus
July 18, 2018
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KF @ 25 : Hi KF. I'm with SA on this re the limit on our understanding; that 'a priori' might only be 'a priori' to our minds, though it seems the ultimate touchstone of reason to us - even though this whole universe seems to be a personal projection from each person's mind. But you soon get incredibly technical, and musing on the difference in the respective scopes of our respective minds, it occurred to me what a wonderful metaphor it provides for the point SA and the Psalmist made about God's thoughts being as far above our thoughts as the heavens are above the earth ! And, alas, not entirely unwontedly, your link took me to a totally incomprehensible world. Thanks for the rely, though. Always good to hear from you and find your less technical posts. @26 : 'PPS: Axel, can I confess a shocking thing? The definition on the whole speaks to me and makes a lot of good sense. What definition are you referring to, KF ? 'BTW, faith and reason and moral responsibilities are inextricably intertwined.' Absolutely !Axel
July 18, 2018
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SA, the key principles are necessary, framework to any possible world, it is not just HUMAN reasoning, but reasoning. Once distinct identity obtains, certain things are associated, necessarily so, and any distinct world already has distinct identity. As just one example, God cannot make a square circle. Not because God is too weak but because such is impossible of being. The form of words can be put together but the substantial thing cannot. Likewise, faith is central not only to the Christian faith but to any worldview and life agenda, that is, we have commitments to finitely remote first plausibles constituting one's faith point. Then, we refer to comparative difficulties to carry out responsibilities to truth, reason and justice etc. KFkairosfocus
July 18, 2018
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KF
The definition on the whole speaks to me and makes a lot of good sense. BTW, faith and reason and moral responsibilities are inextricably intertwined.
Yes, I noted your interest in the Nicene teachings and it is amplified by Athanasius' creed which was directed against a false understanding of the Trinity that was current at the time (and today some Christians have a false idea also). But yes, reason is also a moral virtue - requiring integrity in recognizing and pursuing the truth. Then, we have to conform our mind to the truth, regardless of how difficult it might be to do it. Moral responsibilities make us disposed to faith - gives us strength of soul to accept divine teachings. Yes, faith and reason go together. Reason takes us a long way on the journey, but then we have to make a leap of faith.Silver Asiatic
July 18, 2018
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KF
Axel, I am not sure it is possible to create a world utterly inaccessible to our reason. If a world is possible, it has certain necessary, framework entities that obtain and are a gateway for any reasoning creature.
When we say "possible" we are referring to understanding within human reason. We mean "philosophically possible". When we talk about what God could do, we cannot use human reason as the only standard of judgement. God's "thoughts are not our thoughts". God's mind transcends human reason. Human logic and rationality is consistent with that of the transcendent, but it is not equivalent. "All things are possible with God". What this means is, we cannot assign probabilities to God's thoughts or behaviors. We can learn, philosophically, that nature requires a first cause and that logic gives us good certainty about a necessary being. But we cannot use human reason to evaluate the thoughts and actions and nature of the Trinity. "Who has known the mind of God?"
Distinct identity, thus the core laws of thought, for one; so no, it is inherently impossible to create a distinct world where core logic does not obtain, LOI, LEM, LNC are framework for any world to be possible or actual.
Each person of the Trinity is a distinct whole. Each person is the fullness of God, lacking nothing. The persons are not parts of a whole. Each is a distinct, entire, infinite whole. How can three distinct, infinite, all-powerful, complete beings, form one infinite, all-powerful, complete being? It's a logical contradiction. This knowledge is only known by Faith in statements that are divine revelation. Philosophy could never arrive at this understanding. The point here, is that the Trinity is "possible" - because the Trinity exists, as we know by Faith. However, the Trinity cannot be evaluated by reason and logic - it is a paradox for reason and logic. We can say that belief in the Trinity is consistent with rationality, but only because we have good reason to believe the teaching of Christ. Otherwise, it is impossible to describe how three distinct, complete beings can be one being - not as parts of a whole, but each as whole, and each identified with each other. This just stretches our awareness. Aristotle's teachings give a foundation, in the natural world and reason - showing the logical need for first cause, necessary being. But moving beyond Aristotle, we discover revealed teachings that require Faith. We are taught by Christ - and putting faith in those divine teachings is a virtue. Faith itself is something we do, we accept and embrace the teaching because it comes from an authoritative source.Silver Asiatic
July 18, 2018
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PPPS: Try here: https://sotfom.files.wordpress.com/2015/10/sotfom-3-2015-nopause.pdfkairosfocus
July 18, 2018
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PPS: Axel, can I confess a shocking thing? The definition on the whole speaks to me and makes a lot of good sense. BTW, faith and reason and moral responsibilities are inextricably intertwined.kairosfocus
July 18, 2018
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Axel, I am not sure it is possible to create a world utterly inaccessible to our reason. If a world is possible, it has certain necessary, framework entities that obtain and are a gateway for any reasoning creature. Distinct identity, thus the core laws of thought, for one; so no, it is inherently impossible to create a distinct world where core logic does not obtain, LOI, LEM, LNC are framework for any world to be possible or actual. Distinct identity also carries two-ness with it [A vs ~A] thus numbers and the panoply of core mathematics centred on the counting numbers, so mathematics in its core is also universal and in principle accessible . . . I am very aware of its arduous nature to actually learn. I would further argue, as we also exist as morally governed, intelligent, responsibly and rationally significantly free creatures, that points to a necessary being, framework reality for ANY possible world. Namely, the inherently good creator God (who creates and sustains any actualised world), a necessary and maximally great being, worthy of loyalty and the reasonable, responsible service of doing the good in accord with our evident nature. I suggest, heaven is such an actualised world. KF PS: I spoke to the logic of the triune Godhead, as linked already. The threeness and oneness refer to distinct aspects of being and are thus coherent. BTW, that is highlighted in: "one God in Trinity, and Trinity in Unity; neither confounding the Persons [Latin, essentially, faces], nor dividing the Essence [ = core being]." Much of what follows was an effort to correct many errors of the day, logic of identity and of being can also be abstruse. For example, note: "there is one Father, not three Fathers; one Son, not three Sons; one Holy Ghost, not three Holy Ghosts." This speaks to distinct identity of person which is joined to unity of nature or being, hence also "they are not three eternals; but one eternal. As also there are not three uncreated; nor three infinites, but one uncreated; and one infinite." Yes, this goes beyond mere speculative philosophy, but it is actually coherent obviously though very difficult to understand; reading like a complicated legal definition that seeks to anticipate and block various ways to get it wrong or twist it, which reminds me of not a few things in math etc. And, any worldview will have core, unprovable commitments by faith, which will be difficult to understand and may bristle with difficulties. This is why I speak of faith-points that are subject to comparative difficulties analysis. See here http://nicenesystheol.blogspot.com/2010/11/unit-2-gospel-on-mars-hill-foundations.html#u2_bld_wvukairosfocus
July 18, 2018
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KF The question is with regards to what God could create. He could create a world that is entirely inaccessible to human reason. He could create a world that human intelligence could only perceive as being paradoxical and illogical. I think you are assuming that human reason and rationality are the only possible standards of understanding. God could create a world where what we, today, think is irrational would give a much higher understanding of God. Yes, the Trinity is three distinct persons - they also one being. No diagram can display this. Arms are parts of a whole. The 3 Persons are not parts, subordinate to a whole. Each one is the whole. There is no way that the human mind can fully explain or comprehend the simultaneous unity and yet separateness of the Trinity. In the Christian worldview, the Trinity is fundamental essence and foundation of all reality. The Trinity is an insoluble paradox from the perspective of human intelligence. It may be entirely different for angelic intelligences, for example. The Athanasian Creed, from the same time as the Nicene, supported by the fathers of the Nicene Council, says it:
...we worship one God in Trinity, and Trinity in Unity; neither confounding the Persons, nor dividing the Essence. For there is one Person of the Father; another of the Son; and another of the Holy Ghost. But the Godhead of the Father, of the Son, and of the Holy Ghost, is all one; the Glory equal, the Majesty coeternal. Such as the Father is; such is the Son; and such is the Holy Ghost. The Father uncreated; the Son uncreated; and the Holy Ghost uncreated. The Father unlimited; the Son unlimited; and the Holy Ghost unlimited. The Father eternal; the Son eternal; and the Holy Ghost eternal. And yet they are not three eternals; but one eternal. As also there are not three uncreated; nor three infinites, but one uncreated; and one infinite. So likewise the Father is Almighty; the Son Almighty; and the Holy Ghost Almighty. And yet they are not three Almighties; but one Almighty. So the Father is God; the Son is God; and the Holy Ghost is God. And yet they are not three Gods; but one God. So likewise the Father is Lord; the Son Lord; and the Holy Ghost Lord. And yet not three Lords; but one Lord. For like as we are compelled by the Christian verity; to acknowledge every Person by himself to be God and Lord; So are we forbidden by the catholic religion; to say, There are three Gods, or three Lords. The Father is made of none; neither created, nor begotten. The Son is of the Father alone; not made, nor created; but begotten. The Holy Ghost is of the Father and of the Son; neither made, nor created, nor begotten; but proceeding. So there is one Father, not three Fathers; one Son, not three Sons; one Holy Ghost, not three Holy Ghosts. And in this Trinity none is before, or after another; none is greater, or less than another. But the whole three Persons are coeternal, and coequal. So that in all things, as aforesaid; the Unity in Trinity, and the Trinity in Unity, is to be worshipped. He therefore that will be saved, let him thus think of the Trinity.
There is simply no way to create a purely rational/logical or mathematical description of that belief. It is paradoxical in those terms. It is a statement of Faith, not of philosophy - it transcends reason. Thus, God could create an entire world where logic and mathematics not only do not apply, but would actually give a false understanding entirely.Silver Asiatic
July 17, 2018
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SA, once we have a distinct possible world, LOI obtains . . . and it obtains for abstracta not just concrete entities, also being pivotal to the act of thinking much less communicating. A corollary is that "things" which cannot be distinguished are the same thing. Time is not relevant to core math, esp. sets and numbers. The triune God is understood such that the threeness and oneness refer to distinct aspects of the Godhead -- see the classic shield of the faith diagram that the medievals thought of as the official Arms of God. Being vs non-being is important as the latter does not exist. There are circles and squares but no square circles. There is also but one null set, that set which collects nothing. KFkairosfocus
July 17, 2018
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KF, Thanks for the welcome back. SA, Indeed, perhaps a monist would disagree with my view.daveS
July 17, 2018
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KF I think in a world where there is no concept of time, then those principles do not apply and therefore are not universal. It is the same with the law of identity - it assumes that objects must be discreet and independent of each other. The Christian teaching on the Trinity from the Council of Nicea onwards points to that view. Threeness in oneness. The distinction between being and non-being works from the perspective of human intelligence, but our intelligence does not need to be the universal standard in all possible worlds.Silver Asiatic
July 17, 2018
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DS & SA: I see Math is back on the table, and BTW welcome back DS. SA you used a key term, "imagine a world." You imply the possible worlds context of discourse; sufficiently complete descriptions of possible states of affairs. In that context, domains in Math tend to be abstract logic model worlds. Where I think a pretty good description would be, that Math is the [study of the] logic of structure and quantity. Of course, with non-naive sets and numbers at the heart -- which brings in how von Neumann's construction shows a key bridge, constructing numbers from the null set viewed as 0, etc.. Some models are local, but some aspects of these and some models are universal, being populated by necessary beings. NB's in the end are framework requirements for any world and so will be present in all possible worlds. A capital example is said construction: {} --> 0 {0} --> 1 {0,1} --> 2 . . . {0,1, 2 . . . } --> w This will be framework for any world, and underneath lie first principles of right reason that are similarly framework, starting with LOI, LEM, LNC. Hence my point on Math being the LOGIC of structure and quantity. We also see that mathematics has abstract reality, being. Where, it is impossible to construct a world without these things. So, there is some universality. At the same time other things can vary, e.g. alternative axiom systems that would deny features of one another. However, as a lot of core math facts and structures are historically prior to most axiomatisations, the axiomatisations would not be accepted were they to be demonstrably chaotically illogical, incoherent and counter-factual. It's not just how our brains are wired, it is that reasoned discourse on structure and quantity is possible and partly will be universal. So, I think the answer comes down to partly yes, partly no. KFkairosfocus
July 17, 2018
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Silver Asiatic,
But do we have good grounds to believe that human minds and their methods are the only possible kinds of intellect that could exist? For myself, I don’t think so.
I have to agree here. I also don't have much idea about what other sorts of minds/intellects could exist in this or other worlds. Going back a bit:
Mathematics is a symbolic language which attempts to describe reality as well as describe computational abstractions which exist only in thought. So, it necessarily relies on many assumptions about what reality is, what the human mind is and how things work. These assumptions are givens – they cannot be proven. However, it seems your view is that in any world that God could create, all of these assumptions and givens are necessary.
My view of mathematics is a little different. Mathematics attempts to be agnostic about as much as possible. For just about any assumption or given you identify above, one could also posit that such an assumption or given is false. The particular example that everyone refers to is geometry. Apparently Euclidean geometry works well enough in the physical world for us to use it in designing houses, for example. However, one can also investigate other geometries where the Euclidean parallel postulate fails, and that turns out to be productive in its own right.daveS
July 17, 2018
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daveS
Once again, I can only conjecture, but I don’t believe mathematics could be any different in another world.
Mathematics is a symbolic language which attempts to describe reality as well as describe computational abstractions which exist only in thought. So, it necessarily relies on many assumptions about what reality is, what the human mind is and how things work. These assumptions are givens - they cannot be proven. However, it seems your view is that in any world that God could create, all of these assumptions and givens are necessary. Some examples: The concepts of Time, that objects can be discreet and independent from each other, that infinity is incomprehensible, that paradoxes cannot be resolved ... many more. Mathematics is a means of understanding that conforms to the nature and limits of the human mind. But do we have good grounds to believe that human minds and their methods are the only possible kinds of intellect that could exist? For myself, I don't think so. I'm not talking about evidence that any different kind of mind/intellect could be created by God.Silver Asiatic
July 17, 2018
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Silver Asiatic,
Can you imagine a world that has a different kind of mathematics? Or is our symbolic understanding the only one possible, as you see it?
That's a good question. Once again, I can only conjecture, but I don't believe mathematics could be any different in another world. I should clarify by adding that of course even in this world, people work within distinct axiomatic systems, in which different theorems hold. A person may assume axiom A holds from 8 to noon, and then assume axiom ~A holds from 1 to 5 (obviously one must be careful to keep one's results from the two sessions separate.) However, I believe that if an alien from a different world/universe were allowed to look at this mathematician's notes (translated of course), they would understand---"oh yeah, here you're assuming A, while over here, you assume ~A. I would have come to the same conclusions."daveS
July 17, 2018
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