An interview on God and mathematics

_{Denyse O'Leary

January 17, 2021

Intelligent Design, Mathematics, theism}

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Some of us think mathematics is the best argument for God available. Anyway, here’s Jerry Bowyer’s interview with philosopher Vern Poythress:

The standard modern culture-war revolves around God vs. the mathematical sciences. Take your choice: Faith or physics. Then there are the voices of mutual toleration, which attempt to leave room for science among the faithful and for faith among the scientific. Poythress, though, taps into a different tradition entirely, one which is seldom heard in modern debate: That God and science are neither enemies, nor partners, but rather that God is the necessary foundation for mathematics and therefore of every science which uses it.
The argument is that mathematical laws, in order to be properly relied upon, must have attributes which indicate an origin in God. They are true everywhere (omnipresent), true always (eternal), cannot be defied or defeated (omnipotent), and are rational and have language characteristics (which makes them personal). Omnipresent, omnipotent, eternal, personal… Sounds like God. Math is an expression of the mind of God. Sound strange? It isn’t. Modern natural science was created by people who said that they were trying to “think God’s thoughts after Him.”
Jerry Bowyer, “God In Mathematics” at Forbes

See also: Things exist that are unknowable: A tutorial on Chaitin’s number

Hat tip: Philip Cunningham

Comments

JVL, no, you made several claims, and indeed the norm you just appealed to is another appeal to first duties, that claims should be warranted. Again, truth, right reason, prudence. A further example of the inescapability of the first duties of reason. KFkairosfocus_{January 22, 2021
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ET: YOU made a claim. It is up to YOU to support it. Duh. Really? What claim was that? Kairosfocus is the one who thinks mathematics and morality are linked and I was asking him to elucidate that.JVL_{January 22, 2021
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JVL:
Well, why don’t you show me how math and morality affect each other then?
YOU made a claim. It is up to YOU to support it. Duh.ET_{January 22, 2021
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JVL:
If you’re happy that your position is ambiguous ...
It makes me happy that you think my position is ambiguous. It proves that you don't have a clue and are incapable of follow along.ET_{January 22, 2021
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SA2, As a further exercise in showing the implicit appeals to first duties of reason -- to truth, to right reason [core logic etc], to prudence [so, warrant etc], to sound conscience, to neighbour, to fairness and justice, etc:
>>I’m confused.>> - implicit appeal to principle of distinct identity and correlates, i.e. to right reason >> Is Pi evil? Is the square root of three morally acceptable?>> - same, again - pi and root-3 of course should be justly obtained and reported, which is also duty to truth and prudence as well as right reason - the loaded question begs the main question, that mathematics is a rational activity and so is bound by first duties of reason >> Should calculus repent of its sins?>> - the founders needed to, if you know the quarrel; the locus of responsibility to duty is the reasoners >>And what about the perverse abomination of algebra?>> - I am tempted to suggest that authors of most algebra textbooks need to spend extra time in purgatory for sins against sound education [on Catholic views], but I will be charitable - again, the developers of algebra, its authors, teachers and practitioners are the ones bearing the duties. A page from an Algebra text is inert, it is the rational agent who has sufficient freedom to chose who then finds a duty to choose aright. >>I am beginning to think that mathematics is a moral quagmire.>> - have you sat in a typical faculty lounge recently?
KFkairosfocus_{January 22, 2021
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PS: No, I do not have to be correct, but on this I happen to be so. I have pointed out what should be an uncontroversial readily confirmed observation, which does turn out to have powerful import. Ponder textbooks on logic or on mathematics proof techniques and foundations of math. Such are inert, they have no power to compel attention or motivate diligence. And yet, responsible thinkers and practitioners of the study of the logic of structure and quantity do exert diligence and do feel it important to get things right, logically and factually, with reliable means of verifying that such is so. This is in the end because we find ourselves inescapably under the power of the first duties of reason. When we appeal to one another, this is the implicit premise in our discussion. Even as your attempted objections show again and again.kairosfocus_{January 22, 2021
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JVL, refusal to acknowledge on your part that all rational activities (so, mathematical ones too) inescapably fall under and appeal to first duties of reason does not constitute want of warrant on my part. Nor, does it shift the already shown balance on merits. Let me clip your opening remarks, to again illustrate the point that you are trying to dismiss. This illustrates how even the act of attempted objection cannot escape the appeal/acknowledgement:
No, it’s not. [--> failed appeal to duty to truth and to warrant per principles of right reason (so, to duty to prudence as well as to right reason)] You have not shown [--> failed appeal to duties of warrant (so, prudence) and right reason] how the practice of mathematics is a moral endeavour except to assert it [--> failed appeal to warrant (so, prudence) and first duties of reason, claim of question begging i.e. appeal to right reason, when the warrant is in precisely the inescapability] because of rationality and ‘right reason’. [--> strawman fallacy, ducking the issue of inescapability, a failed appeal to right reason] You can’t come up with any other argument than that [--> strawman fallacy again] and you keep repeating the same thing over and over and over again [--> strawman fallacy again, also projection of question-begging . . . unacknowledged appeals by you to known duty of warrant [so, duty to prudence], thus duty to right reason and duty to truth].
See the point? Your objections are utterly unable to set the first duties of reason aside and having set such aside, achieve traction as arguments. You yet again illustrate that arguments and reasoning are inescapably governed by first duties of reason. Thus, instead, you need to acknowledge the inescapability and what that brings out. I have pointed out that even in attempting to object, dismiss, deny or sidestep, the objector is forced to appeal to the first duties of reason. That sort of inescapability is precisely the mark of a self-evident first truth. If you insist on repeating a false claim of want of warrant -- which appeals to duties to truth, to right reason and to prudence in the form of warrant -- then I cannot but point out the same reason why these fail. And from step one it has been pointed out that the issue is inescapability so inescapable first truth which is self evident. Refusal to acknowledge simply shows that you are unwilling to accept what you cannot escape. As I just showed again. On self-evidence, the immediate absurdity of unavoidably appealing to what you would deny should be clear. Mathematics is a rational activity. All -- all -- rational activities inescapably appeal to first duties of reason. So, mathematical activities appeal to first duties of reason. Especially, to truth, to right reason [core logic] and to prudence [to warrant]. The fact that liars can figure shows the moral choice involved in mathematically grounded acts and the duty of just weights and measures surely is a manifestation of duty to fairnes and justice, applicable to core structures and quantities themselves. I remind of a classic sub-case, Epictetus on logic:
DISCOURSES CHAPTER XXV How is logic necessary? When someone in [Epictetus'] audience said, Convince me that logic is necessary, he answered: Do you wish me to demonstrate this to you?—Yes.—Well, then, must I use a demonstrative argument?—And when the questioner had agreed to that, Epictetus asked him. How, then, will you know if I impose upon you?—As the man had no answer to give, Epictetus said: Do you see how you yourself admit that all this instruction is necessary, if, without it, you cannot so much as know whether it is necessary or not? [Notice, inescapable, thus self evidently true and antecedent to the inferential reasoning that provides deductive proofs and frameworks, including axiomatic systems and propositional calculus etc. Cf J. C. Wright]
KFkairosfocus_{January 22, 2021
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Kairosfocus: Strawman. No, it's not. You have not shown how the practice of mathematics is a moral endeavour except to assert it because of rationality and 'right reason'. You can't come up with any other argument than that and you keep repeating the same thing over and over and over again. We all agree that 'doing' mathematics takes thought and a rational, logical frame of mind. But that does not lead to any kind of moral stance or statement because mathematics has nothing to do with that. As you said: figures don't lie but liars can figure which just point out that the moral issues have nothing to do with the mathematics. Anyway, since you clearly think you HAVE to be correct and everyone else is wrong I'll stop talking about it. But I would like to point out that this is another case of you being elitist in your opinion, i.e. you won't even consider someone else's point of view because you're right and they're wrong according to you by definition.JVL_{January 22, 2021
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SA2, as you full well know, the thinking and reasoning that studies the logic of structure and quantity -- mathematics -- is an exercise in rationality. Rationality inevitably, inescapably involves first duties. Duties to truth, to right reason and to prudence (so, to warrant) are particularly relevant in this case. Do not omit due weights and measures as directly connected. There is a saying of notorious relevance in statistics and accounting, that figures don't lie but liars can figure. KFkairosfocus_{January 21, 2021
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I’m confused. Is Pi evil? Is the square root of three morally acceptable? Should calculus repent of its sins? And what about the perverse abomination of algebra? I am beginning to think that mathematics is a moral quagmire. :)Steve Alten2_{January 21, 2021
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JVL, I pick up for now: >>Mathematics is a rational activity, of course.>> Therefore, inescapably, it is governed by first duties of reason. As already explained. >>But it does not ground morals>> Strawman. >> which are not universal or invariant.>> First duties of reason are self-evident, inescapable and antecedent to argument. They are universal and invariant. >> They change, mathematics does not.>> Again, false. And the reason Mathematical core realities do not change is that they are framework to all possible worlds. Once reasoning creatures exist, the first duties of reason obtain. KFkairosfocus_{January 21, 2021
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Viola Lee: Re 72: what a non-answer. Why oh why do I try to have such conversations! The funny thing is: no one here who supports his views understands his answers either! They just agree because they should. It's all just magic and hand-waving. But it must be true because someone who also believes in God says it's so.JVL_{January 21, 2021
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Re 72: what a non-answer. Why oh why do I try to have such conversations! :-(Viola Lee_{January 21, 2021
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Kairosfocus: Observe my comment: mathematics, insofar as it is a study, is a rational practice. Rationality, through and through, inescapably, is governed by first duties of reason as even your objections manifest. That is, rationality — including mathematical rationality — is morally governed. Mathematics is a rational activity, of course. But it does not ground morals which are not universal or invariant. They change, mathematics does not. Disregard for such would reduce any rational endeavour to chaos, deception, manipulation. Mathematics, not excepted. The case of lying with statistics and that of creative accounting should at least help us to see how. Only people who are unaware of the subtleties of statistic get taken in by half-truths and shading. Statistics, in and of themselves, don't lie if they are mathematically correct. People lie, math does not. That is not trying to twist things to fit my particular worldview — yet another rather sharpish accusation without good warrant — it is pointing out that to be free to be rational, including on mathematics, we must be free by nature. Such freedom of course brings with it the issue of morally freighted choice so too duty. Especially, first duties of reason. Mathematics isn't true or false depending on your morality or cause or warrant or any such thing. You are trying too hard to bend everything to your world view and it's not working. And there is a bigger issue, most easily seen with mathematics: truth is truth. You can't bend it to your stance. Gravity works no matter what your creed or view. The Laws of Thermodynamics are true regardless of how you vote or your moral standard. Quantum Mechanics works and is not dependent on your theology. None of those things care about your interpretation or your agendas. If you want to believe in an ultimate supreme loving being that's fine with me. But trying to bend scientific and mathematical truths to be in support of your desires is not valid. It denigrates the science and your faith. Why can't you just accept that you believe because it's part of your personal experience and leave science and mathematics out of the discussion? God does not exist because e^(I*pi) = -1. And I find it hard to believe that God designed mathematics so that that particular identity would come up so some people would then say: wow, clearly someone designed that. You cherry pick one particularly lovely mathematical truth and claim the whole system was designed. What about Zorn's lemma? What about the Prime Number Theorem? What about the Mean Value Theorem? What about Zeno's Paradox? Or the Goldbach Conjecture? Or Fermat's Last Theorem? Or The Four Colour Problem? Or the Fundamental Theorem of Arithmetic? Do they all point to some benevolent and loving God who somehow managed to design a system of mathematics which most people don't understand and many dread learning to prove he exists? Really? Rainbows are lovely. Eclipses are sublime. Euler's identity is beautiful. But most of the world and science and math is dirty, messy, complicated and hard to understand. Just like you would expect if there was no direction and no purpose. Most scientists and mathematicians do what they do because they try really, really hard to find that unifying principle, that underlying structure, that simple summation which explains some seemingly chaotic situation. And those are hard to find because the systems are NOT designed to be discernible. They are what they are. They don't care about us. If we disappeared they would continue to be true. Other things stem from pondering, what sort of source can adequately explain a world in which there are creatures with enough rational freedom to do mathematics. Given where freedom points: the power of choice and the resulting is-ought gap. How about an environment where being able to do basic calculations and mathematical estimates gives a survival advantage? morality governs mathematics because mathematics is a rational activity. Nope. Maths is not related to morality at all. Get over it. The most hated and dangerous dictator can be morally bankrupt but if they have a valid mathematical proof then it stands.JVL_{January 21, 2021
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JVL, morality governs mathematics because mathematics is a rational activity. The first duties of reason govern rational behaviour. Duties to truth, right reason and to prudence expressed in sound warrant are particularly manifest. The academic crime of plagiarism is about stealing. And much more. KFkairosfocus_{January 21, 2021
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VL, The topic then on the table had enough polarised loading all to itself. Unfortunately, as I said in 1976 as a 15 year old 5th former, I smell a Reichstag burning. Again. 45+ years later that homeland has not recovered, I am an exile for cause and many are still in denial. Younger generations seem to be hardly aware of what a popular PM did in Parliament that June, and where it led, both over the next four years and ever since. I hope you appreciate some of why I am concerned when I see much the same dynamics playing out in the leading maritime power that stabilises the world. As for divorce, it is far afield from Mathematics, but I suppose News will allow me to indulge a bit of natural law reasoning, through a Dominical example. Where, natural law is about core matters coeval with our humanity and as such will have universal jurisdiction. You can set up things under colour of law contrary to such, but they will only lead to needless chaos:
Matt 19:19 Now when Jesus had finished these sayings, he went away from Galilee and entered the region of Judea beyond the Jordan. 2 And large crowds followed him, and he healed them there. 3 And Pharisees came up to him and tested him [--> hoping to discredit] by asking, “Is it lawful to divorce one's wife for any cause?” [--> a current debate, with she burns my dinner as a test example] 4 He answered, “Have you not read that he who created them from the beginning made them male and female, [--> coeval with humanity in two complementary sexes] 5 and said, ‘Therefore a man shall leave his father and his mother and hold fast to his wife, and the two shall become one flesh’?[--> unity, respecting naturally evident creation order] 6 So they are no longer two but one flesh. What therefore God has joined together, let not man separate.” [--> Mal 2:16, I hate divorce.] 7 They said to him, “Why then did Moses command [--> note, word choice, for clever casuistry] one to give a certificate of divorce and to send her away?” 8 He said to them, “Because of your hardness of heart [--> moral government diagnosis, defective conscience, but noting that there are compromises to be made with society at a given stage, with amelioration, but this is nowhere near a good option. Many other cases are parallel down to today] Moses allowed you [--> notice word focus] to divorce your wives [--> and provided for some protection, e.g. a duly made certificate, likely after some hearing] , but from the beginning it was not so. 9 And I say to you: whoever divorces his wife, except for sexual immorality, and marries another, commits adultery.”[a] [--> not in letter of law sense but moral sense, the changing for a newer shinier trophy model game is objected to. So much for the mid-life itch] 10 The disciples said to him, “If such is the case of a man with his wife, it is better not to marry.” [--> they too were tainted] 11 But he said to them, “Not everyone can receive this saying, but only those to whom it is given. [--> he acknowledges that virtue goes beyond what can be written in civil law]
More can be raised but the basic outline is clear enough. Neighbour love, fairness and justice informed by the nature of marriage lead to a policy that has to reckon with where society is, so ameliorative regulation of evils looking to their minimisation is there. But an evil is an evil. Coming back to Mathematics and its connexion to logic of being and possible worlds, let me clip from my OP on first duties, bearing in mind the paper I linked to in my response to JVL:
The case of Mathematics is central. Mathematics, being best understood as [The study of] the logic of structure and quantity, where certain core intelligible mathematical facts are framework to any possible world (= a sufficiently complete chain of propositions describing a possible state of affairs), and lead to a programme of analysis and elaboration of logic-model worlds that may then apply to relevant situations of interest. For example, per von Neumann: {} –> 0 {0} –> 1 {0,1} –> 2 . . . . {0,1,2 . . .) –> w, omega From reflecting on the principle of distinct identity, we see that for a world W to be distinct from some arbitrarily close neighbour W’, we have some A in W that is not in W’, so W = {A|~A} and also W = {A|W’}, thence, we see the partition | is empty, manifesting nullity. A is a simple and ~A = W’ is a complex, unity. With distinct unities, we find duality, and already we see that von Neumann’s framework applies to any distinct world. It is truly universal, i.e. we find the natural counting numbers, N as an abstract structure necessarily present in and framework to any possible world. From N, we can define additive inverses so for n in N, -n is such that n + (-n) = 0, i.e. we have that vector set where elements have both size and direction in an abstract space, the integers Z. Taking ratios, we have the rationals, Q. Reals bring in transfinite converging sums of rationals without repeating cycles when displayed in place value form, R. From that we go in a second orthogonal spatial direction, to C, using the j* rotating operator: j*x for all x in R defines the imaginary axis by anticlockwise rotation through one right angle and j*j* x is – x so we see j is sqrt – 1. Beyond we define the hyperreals R* on the reals R being mileposted by N. H = 1/h, where h is smaller than 1/n for any finite n in N, where for any k in N the von Neumann succession continues k+1, k+2 etc, i.e. we cannot exhaust N stepwise. From this h is an infinitesimal hyperreal near 0; H is a transfinite integer hyperreal and we see a connected domain from zero and N,Z,Q,R to the hyper-domain R* such that any r in R may be surrounded by an infinitesimally altered cloud of form r + h, *r*, in effect vector shifting and adding the cloud *0* to r. (This allows us to use Robinson’s tamed infinitesimals and Model Theory etc to view Calculus as an extension of algebra.) Notice, we have nowhere specified a particular individual world, this holds for any distinct world, for all possible worlds. It is reality-universal and possibility-universal. That is, a core domain of numbers, associated relationships and operations is a body of abstracta framework for any possible world, physical or imaginary. Hence, immediately, some of the universal power of both mathematics and logic. Hence too, we can recognise a category of beings, necessary, world framework entities; abstracta that constrain what is possible, by laying out constraints on possible being.
I believe that should make the basic point on math clear enough. Other things stem from pondering, what sort of source can adequately explain a world in which there are creatures with enough rational freedom to do mathematics. Given where freedom points: the power of choice and the resulting is-ought gap. KFkairosfocus_{January 21, 2021
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ET: I have. That you cannot understand it is on you. If you're happy that your position is ambiguous I guess I can live with that. How does JVL know that mathematics doesn’t have nothing to do with morality? "doesn't have nothing" . . . Well, why don't you show me how math and morality affect each other then?JVL_{January 21, 2021
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JVL, Let's pick up:
Kairosfocus: That is, rationality — including mathematical rationality — is morally governed. [JVL:] That is not correct [--> appeal to duty to truth, right reason and warrant, so to prudence]. Mathematics has nothing to do with morality [--> appeal to truth etc].
I highlighted the way in which your objections themselves show how the first duties of reason are inescapable. Observe my comment: mathematics, insofar as it is a study, is a rational practice. Rationality, through and through, inescapably, is governed by first duties of reason as even your objections manifest. That is, rationality — including mathematical rationality — is morally governed. Disregard for such would reduce any rational endeavour to chaos, deception, manipulation. Mathematics, not excepted. The case of lying with statistics and that of creative accounting should at least help us to see how. As to a core of mathematics being part of the framework of any possible world, I explored that here, which you have been referred to previously. It turns out to be key to the universality, general applicability and analytical power of mathematics. Further to this, despite your sharp dismissiveness rationality requires freedom, e.g. the power to freely choose to accept a logical chain and to judge when a conclusion is or is not warranted. Otherwise, we are locked into some deep level of programming, organisation of computational substrates and/or chance. This would utterly undermine credibility of reasoning claims and knowledge claims. Perhaps, you may recall Haldane:
"It seems to me immensely unlikely that mind is a mere by-product of matter. For if my mental processes are determined wholly by the motions of atoms in my brain I have no reason to suppose that my beliefs are true. They may be sound chemically, but that does not make them sound logically. And hence I have no reason for supposing my brain to be composed of atoms. In order to escape from this necessity of sawing away the branch on which I am sitting, so to speak, I am compelled to believe that mind is not wholly conditioned by matter.” ["When I am dead," in Possible Worlds: And Other Essays [1927], Chatto and Windus: London, 1932, reprint, p.209. Cf. here on (and esp here) on the self-refutation by self-falsifying self referential incoherence and on linked amorality.]
That is not trying to twist things to fit my particular worldview -- yet another rather sharpish accusation without good warrant -- it is pointing out that to be free to be rational, including on mathematics, we must be free by nature. Such freedom of course brings with it the issue of morally freighted choice so too duty. Especially, first duties of reason. Which, as was just pointed out, even in objecting, you were unable to escape. And more, but I think this is enough for a reasonable evaluation on merits in a blog context. KFkairosfocus_{January 21, 2021
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We've been over all that, and I bet I've read more or less the same a couple dozen times. However, you gaveled discussing an example (divorce is what was suggested) of this theory put to use as off-topic in the thread. But your philosophical thesis doesn't address the central question: can two people fully committed to the duties of right reason reach different conclusions on a moral issue (for instance, whether it is OK for two people to get divorced because they don't want to be married to each other any more) without one position being right and all the other positions wrong? What say you to that general question? Do all moral issues, taking a full implementation of the duties of right reason into account, have a right position, and all others wrong?Viola Lee_{January 21, 2021
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VL, it is not a jump, the reference to Hume's so-called guillotine argument on reasoning is-is then suddenly OUGHT . . . shows the issue of coherence and the only locus of that bridge. Only if is and ought are fused at root is there coherence. Where, the issue is that freedom, a requisite of reason [as opposed to blind computation] inevitably leads to the gap between is and ought. Once that is on the table, it implies mathematics as a rational activity is morally governed. The worldview level options for a reality root capable of sustaining morally governed rationality then point to characterising the root: an IS that is necessary (so, eternal), capable of being source-sustainer of worlds [root], inherently good in itself which also entails utterly wise as a major component of effective goodness -- no demiurges doing a half-baked job need apply. Such goodness is also inherently rational and in key parts intelligible to us. More can be said but I do not want to try writing a thesis bit by bit. KFkairosfocus_{January 21, 2021
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How does JVL know that mathematics doesn't have nothing to do with morality?ET_{January 21, 2021
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JVL:
Why don’t you state clearly, succinctly and unambiguously what your position is then?
I have. That you cannot understand it is on you.ET_{January 21, 2021
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Kairosfocus: That is, rationality — including mathematical rationality — is morally governed. That is not correct. Mathematics has nothing to do with morality. Insofar as we address the substance of logic, structure and quantity tied to being and to possible worlds, a core of mathematics is framework to any world that is possible of existence. Mathematics is not an indication of possible worlds. Mathematics tells you, based on the models you pick, how possible worlds might interact or behave but it doesn't give you them. That core is about necessary (and so, eternal) being. Further to the moral government of mathematical reason and other foci for reason through first duties, those are moral premises, oughts. Hume long ago showed that is and ought only can find unification in the root of reality, and so we face the is-ought gap as an issue of world coherence. The only serious candidates to fill such a bill must be utterly wise and inherently good, on pain of euthyphro type incoherence. Math has nothing to do with morality and your doubling and tripling down on the idea that it does just makes you look like someone exhibiting motivated reasoning. Math has nothing to do with theology. I note too, that computational substrates are inherently about mechanical necessity or chance, they are incapable of grounding responsible rational freedom; a requisite of mathematics and other domains of reason. That's all just rubbish. Math has nothing to do with freedom or any human considerations. You need to stop trying to twist everything to your world view. We can sketch the outline, necessary, eternal being capable of being source-sustainer of worlds, inherently good and utterly wise. A familiar figure looms. Nothing to do with mathematics. No thing.JVL_{January 21, 2021
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ET: No, I am not saying that. Clearly you have an inability to think. Why don't you state clearly, succinctly and unambiguously what your position is then?JVL_{January 21, 2021
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KF, I have repeatedly acknowledged our duties to reason. As I have said, though, I don't accept your jump from there is "utterly wise" and especially an "inherently good" being. You say further to our duties to reason there are moral premises, but I don't see that as necessarily true. I can tell you that it is not necessary for you to respond, as I have read thousands of (mostly repetitive) words from you on this subject. I just want to register a dissent from your worldview.Viola Lee_{January 21, 2021
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VL & JVL, mathematics, insofar as it is a study, is a rational practice. Rationality, through and through, inescapably, is governed by first duties of reason as even your objections manifest. That is, rationality -- including mathematical rationality -- is morally governed. Insofar as we address the substance of logic, structure and quantity tied to being and to possible worlds, a core of mathematics is framework to any world that is possible of existence. That core is about necessary (and so, eternal) being. Further to the moral government of mathematical reason and other foci for reason through first duties, those are moral premises, oughts. Hume long ago showed that is and ought only can find unification in the root of reality, and so we face the is-ought gap as an issue of world coherence. The only serious candidates to fill such a bill must be utterly wise and inherently good, on pain of euthyphro type incoherence. I note too, that computational substrates are inherently about mechanical necessity or chance, they are incapable of grounding responsible rational freedom; a requisite of mathematics and other domains of reason. We can sketch the outline, necessary, eternal being capable of being source-sustainer of worlds, inherently good and utterly wise. A familiar figure looms. KFkairosfocus_{January 21, 2021
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JVL:
So, you’re on the side that says mathematics is invented as opposed to those that think mathematics is discovered.
No, I am not saying that. Clearly you have an inability to think.ET_{January 21, 2021
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Mike1962, There are rules in the Platonic realm. Perhaps they are all ways of expressing the same thing. Mathematics, geometry, logic, language. Those rules govern "what can be imagined, or located, in the platonic realm, such as forms and relationships (meaning, the relationship of one thing to another.) It is like a unified algorithm that cascades into the potential for every possible thing. In my other threads I argue that this is where we actually exist; in the Platonic realm, or mental reality. Our "physical world" existence is a manifest, internal experience, the translation of Platonic values and forms into what we call "reality." We all still have access to every possible thing, but unfortunately, via external-world theory and conditioning, our access to that essential nature of our existence, and so our capacity to interact fully with it, has been marginalized.William J Murray_{January 21, 2021
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Yes, but then you have to know where the power series comes from. I like building them from polynomials using the idea of having the derivatives of the polynomials match the derivatives of the function in question, but then of course you have to know why the derivatives of sine, cosine, and e are what they are! What is neat is how it all flows backwards to more fundamental ideas. This is relevant to the thread where there is a video of five guys discussing whether math is discovered or invented. One of them (or perhaps it is Wigner) points out that the development of math depends on us creating new and fruitful concepts so we can build past what has come before.Viola Lee_{January 21, 2021
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WJM: That argument applies to anything that is possible. If it is possible, it exists. Do you mean to equate the latter with the "Platonic realm?" It seems to my intuition that anything possible has at least the same "Platonic" reality as anything that can be expressed with mathematics. And that consciousness "explores" that "space." (For humans, while living, that is, while "incarnated", consciousness is limited to, and informed by, brain states, but not so before incarnation (attachment to brain) and after death/detachment.) Is this what you were trying to express on the other threads?mike1962_{January 21, 2021
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