Is the Galton Board evidence for intelligent design of the universe?

_{Denyse O'Leary

January 16, 2023

Intelligent Design, Physics}

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Ken Francis writes: “Proof that God placed order out of chaos in the universe. Each ball has a 50-50 chance of bouncing right or left off of each peg as it traverses the board, but every time the result is a bell curve. More proof of Intelligent Design.”

The comments are interesting.

Hat tip: Ken Francis, co-author with Theodore Dalrymple of The Terror of Existence: From Ecclesiastes to Theatre of the Absurd

Comments

VL@100, very well said. And as far as I can see the same applies to his is-ought gap argument. He insists that the only way to ground ought is if the “is” is derived from his mysterious root of reality. He further insists that the only alternative is might and manipulation make right. Completely ignoring things like cooperation, logic, desire, goals, etc, none of which need be linked to his root of reality.Ford Prefect_{January 19, 2023
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I will continue to respond a bit for the sake, perhaps, of some new participants who haven’t been around the block with KF on this subject before. KF makes his usual dismissive and condescending response when he writes, “Ahem, do you not see that you just appealed to my known duty to truth, right reason, warrant and wider prudence, with hints of to sound conscience, thus neighbour and justice?” No, KF, I don’t “see” that: I understand what you are saying and disagree with you about it. One can believe that human beings have the ability to reason and seek truth without believing that they have a “duty” to reason that flows from the root of reality, just as one can believe humans have a moral nature without believing they are “governed” by a morality that flows from the root of reality. It’s a cheap out to dismiss arguments against your philosophy by dismissing the possibility that reason flows from other sources than the root of reality. That makes it impossible to have your philosophy challenged because you automatically declare victory and refuse to address those challenges. My claim is that the only arguments that you provide for there being moral duties flowing from the root of reality are arguments from consequences: your mistaken belief that only by your position can one escape nihilism. Address the issues: don’t shoo me away by condescendingly saying, “Hey, you’re using reason, so you must agree with me about “duties” and the root of reality. See 44 and 95 and 97 for more.Viola Lee_{January 19, 2023
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VL:
I object to the “governed” part of KF’s need, as to him it inserts his conclusion into the need: that there needs to be a basis for morality at the root level to “govern” us.
Ahem, do you not see that you just appealed to my known duty to truth, right reason, warrant and wider prudence, with hints of to sound conscience, thus neighbour and justice? My point is and has been that Cicero and his antecedents saw something profound, and that it is of branch on which we sit character, objectors are hope;essly caught in self referentiality. PM1:
Hume’s argument does not say that we can’t have a causal explanation for the evolution of norm-governed behavior amongst large-brained social animals. In other words, one can “bridge” the “gap” between “is” and “ought” by way of science — his point is only that one cannot do so by way of logic alone.
Scientism, anyone? The problem is, accidental collocations of atoms without due end have no obligations, no responsible rational freedom, so no ought. You have proposed no is adequate to ground ought. At most you are at the level of the delusion that gets us to cooperate better. Wide open for nihilistic dismissal. KF And of course, you too are sitting on the same branch with VL, the undersigned and the rest of us.kairosfocus_{January 19, 2023
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PM1, possible worlds discussions were conceived before Kripke et al [think Leibniz, or even Anselm or Aristotle et al, but more to the point those who conceived world systems/views or just wrote novels, fantasies, fairy stories and other fictional genres -- before we get to things like the Euclidean axiomatisation and its cousins, or scientific theories]. Yes, my view is that such schemes are ancient, we are dealing with formalisations not proper origins. Then, of course, these latterday worthies were inhabitants of a going concern, credibly contingent cosmos, which has come down to our own day. In case you think my approach a strange and dubiously idiosyncratic one, ponder: https://plato.stanford.edu/entries/possible-worlds/ Which, begins:
Anne is working at her desk. While she is directly aware only of her immediate situation — her being seated in front of her computer, the music playing in the background, the sound of her husband's voice on the phone in the next room, and so on — she is quite certain that this situation is only part of a series of increasingly more inclusive, albeit less immediate, situations: the situation in her house as a whole, the one in her neighborhood, the city she lives in, the state, the North American continent, the Earth, the solar system, the galaxy, and so on. On the face of it, anyway, it seems quite reasonable to believe that this series has a limit, that is, that there is a maximally inclusive situation encompassing all others: things, as a whole or, more succinctly, the actual world. Most of us also believe that things, as a whole, needn't have been just as they are. Rather, things might have been different in countless ways, both trivial and profound. History, from the very beginning, could have unfolded quite other than it did in fact: the matter constituting a distant star might never have organized well enough to give light; species that survived might just as well have died off; battles won might have been lost; children born might never have been conceived and children never conceived might otherwise have been born. In any case, no matter how things had gone they would still have been part of a single, maximally inclusive, all-encompassing situation, a single world. Intuitively, then, the actual world of which Anne's immediate situation is a part is only one among many possible worlds . . .
Now of course SEP goes on:
Although ‘possible world’ has been part of the philosophical lexicon at least since Leibniz, the notion became firmly entrenched in contemporary philosophy with the development of possible world semantics for the languages of propositional and first-order modal logic. In addition to the usual sentence operators of classical logic such as ‘and’ (‘?’), ‘or’ (‘?’), ‘not’ (‘¬’), ‘if...then’ (‘?’), and, in the first-order case, the quantifiers ‘all’ (‘?’) and ‘some’ (‘?’), these languages contain operators intended to represent the modal adverbs ‘necessarily’ (‘?’) and ‘possibly’ (‘?’). Although a prominent aspect of logic in both Aristotle's work and the work of many medieval philosophers, modal logic was largely ignored from the modern period to the mid-20th century . . . . Specifically, in possible world semantics, the modal operators are interpreted as quantifiers over possible worlds, as expressed informally in the following two general principles: Nec A sentence of the form ?Necessarily, ?? (????) is true if and only if ? is true in every possible world.[3] Poss A sentence of the form ?Possibly, ?? (????) is true if and only if ? is true in some possible world. Given this, the failures of the classical substitutivity principles can be traced to the fact that modal operators, so interpreted, introduce contexts that require subtler notions of meaning for sentences and their component parts than are provided in classical logic
Where, a PW can be taken as a way this or another world is, may be etc. This opens up using PWs to include the sorts of entities already pointed to. Thence, a candidate c is impossible of being IFF there is no W in which it would be actual were W actualised. Possible beings exist in at least one W, and necessary ones in every W. Contingent ones are in at least one PW but not all. Going back to sets, because of the paradoxes of naive set theory, modern set theories sought to construct a hierarchy of sets not vulnerable to such. Thus we come to things like the von Neumann construction of N and the like, from {} --> 0. From which, we go, N, so ZQRCR* etc. Modern ZFC set theory is not as colourful as it used to be in the naive days, but it is more reliable. In this context, I think you will see why I suggest ZFC is a particular axiomatisation that sets up a logic-model world, not the root of such world-describing, modelling, simulating and building. The rest follows directly. KFkairosfocus_{January 19, 2023
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KF writes, "We need adequate causal ground for a world with morally governed creatures, us." I object to the "governed" part of KF's need, as to him it inserts his conclusion into the need: that there needs to be a basis for morality at the root level to "govern" us. Humans are moral creatures (more broadly, they are normative creatures), but the grounding of that moral nature is in the complexities of our biological, cultural, social, psychological, cognitive nature, which includes our rational abilities. But ultimately we make moral choices: we take lots of things into consideration, and we are subject to lots of forces and influences, but ultimately we govern ourself. This is a very long way from any "need' for the root of reality to have anything to do this.Viola Lee_{January 19, 2023
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@93
no one has asserted that worldviews are deductive conclusions. What has been on the table is grand explanatory inferences and comparative difficulties. We need adequate causal ground for a world with morally governed creatures, us.
I completely agree with all of that.
That requires bridging is-ought, where post Hume that can only credibly be done at necessary being reality root level.
and that is where I get off the bus. You're claiming that we ought to response to Hume by positing ought-ness at the level of fundamental reality. As I've argued before, I don't think that makes sense. All Hume is saying is that there's no deductively valid argument that has only descriptive statements in the premises and a prescriptive statement in the conclusion. (To put the same point in terms of symbolic logic, one cannot introduce a deontic logic operator in the conclusion if there are no deontic operators in the premises.) Hume's argument does not say that we can't have a causal explanation for the evolution of norm-governed behavior amongst large-brained social animals. In other words, one can "bridge" the "gap" between "is" and "ought" by way of science -- his point is only that one cannot do so by way of logic alone.PyrrhoManiac1_{January 19, 2023
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KF writes, "Your alternative is _________ and it is able to ground and bridge IS-OUGHT as _________, As I said above, "There is no bridge across the is-ought gap. “Is” is about reality. “Ought” is about judgments people make about how to behave. There is always a gap that is filled in by individual choice." Your belief that there must be such a bridge at the root of reality is a faith-based belief, but as I have repeatedly said, the only arguments for such that you seem to offer is one of consequences: that if such does not exist and is not believed in, then nihilism follows. That is not an valid argument for your assertion.Viola Lee_{January 19, 2023
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@92
PM1, again, to discuss sets and collections, there first has to be a we, in a world. This is branch on which we sit territory; a we BTW who need to be responsibly, rationally, significantly free. We then proceed to describe our world and find a set of propositions, then realise that other worlds are possible, other actual or conceivable states of affairs for this or other worlds. This is before we debate semantics or realise that such descriptions are or translate to sufficient systems of propositions to specify how a world is or might be.
OK, if I'm understanding you correctly, then nothing in the passage just quoted above requires anything in possible world semantics or set theory. If that's what you're saying, I'm completely fine with that. I'd happily take what's quoted above as a starting point for any philosophical reflection. Given my background and training, I'd call that "transcendental reflection", which I'd describe as a systematic inquiry into the cognitive capacities and incapacities, the actualization of which is disclosed in the kinds of experiences we manifestly take ourselves to have (including our experience of ourselves as norm-governed beings). Disclosure of the experiences in which these capacities and incapacities are reliably manifested, and description of those capacities and incapacities based on second-order reflection on those experiences, is not wholly separable from the ontological question of what the world must be like such that (1) beings such as ourselves can be amongst its beings and (2) it is possible for beings with our cognitive capacities and incapacities can (as it were) "mesh" with empirically detectable regularities and irregularities grounded in the world's causal and modal structures.
In discussing a distinct possible world W we find that distinct identity etc are present. These are prior to axiomatisation of set theory, e.g. ZFC, and to the relevant sets NZQRCR* etc. That elucidation starts from being.
I'm just baffled at the idea that it is possible to talk about possible worlds prior to set theory, since possible world semantics relies on set theory. This was how Kripke and Lewis more or less defined the metaphysics of possible worlds: the use of set theory to make explicit the ontological commitments of modal discourse. The idea of talking about possible worlds without relying on set theory doesn't make sense to me. But, if I'm understanding the first part correctly, then you don't really need any logic or mathematics at all -- just transcendental reflection (as I call it) is sufficient to clarify the starting-point of philosophizing.PyrrhoManiac1_{January 19, 2023
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VL, no one has asserted that worldviews are deductive conclusions. What has been on the table is grand explanatory inferences and comparative difficulties. We need adequate causal ground for a world with morally governed creatures, us. That requires bridging is-ought, where post Hume that can only credibly be done at necessary being reality root level. That adequacy requirement points to a bill of requisites: inherent goodness and utter wisdom (we are not dealing with a demiurge). The "candidate to beat" is the inherently good, utterly wise creator God, a necessary and maximally great being. Your alternative is _________ and it is able to ground and bridge IS-OUGHT as _________, also it is better on comparative difficulties due to ________ . KF PS, as God is clearly a serious candidate NB, God as characterised is either impossible of being [incoherent core characteristics] or is actual.kairosfocus_{January 19, 2023
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PM1, again, to discuss sets and collections, there first has to be a we, in a world. This is branch on which we sit territory; a we BTW who need to be responsibly, rationally, significantly free. We then proceed to describe our world and find a set of propositions, then realise that other worlds are possible, other actual or conceivable states of affairs for this or other worlds. This is before we debate semantics or realise that such descriptions are or translate to sufficient systems of propositions to specify how a world is or might be. In discussing a distinct possible world W we find that distinct identity etc are present. These are prior to axiomatisation of set theory, e.g. ZFC, and to the relevant sets NZQRCR* etc. That elucidation starts from being. As was already sufficiently shown. KF PS: I address this here:
the cardinality of mathematically possible worlds must be smaller than the cardinality of logically possible worlds. It cannot be the case that elementary mathematics is true of all logically possible worlds, precisely because we can conceive of logically possible worlds in which the axioms of elementary mathematics cannot hold
Nope, so soon as a distinct PW, W is identified, dichotomy is present, as was already discussed. So, we see 2, 1, 0. By von Neumann, thence N, necessarily. What you are trying to suggest is worlds in which 2ness does not exist as a property, or one ness [a world . . . ] or 0 [empty of content] etc. On the contrary, as was shown long since, once N, ZQRCR*. So the difference of cardinality you suggest is an error.kairosfocus_{January 19, 2023
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PM clearly lays out some interesting issues, and then asks, "It would nevertheless also be a question as to whether “because it was willed as such by a transcendent personal God” is an intellectually satisfying answer to any or all of those questions." I'd say no. My point (way back when Ford asked about the "ethical" in "ethical theism") is that all. these interesting and messy questions about the relationship between logic, math, and the root of reality do not imply or logically lead to a belief that the root of reality has a personal concern about human beings, or any other attributes of being "personal" in respect to the world.Viola Lee_{January 19, 2023
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@88
PM1, actually, as just outlined, we are dealing with ontology and thus foundations of math. This is prior to set theory. When we discuss, a world is already implied for us to exist and be discussing, branch on which we sit. PW discussion is about this and other ways things might be, described as sets of assertions, propositions. Again, antecedent to proper revised set theory, the naive forms ran into paradoxes. So, we start from getting to N then extending NZQRCR* etc. The rest follows
First of all, possible worlds is not prior to set theory: what we are discussing in possible world semantics is sets of worlds. Possible world semantics just is the use of set theory to make explicit the ontological commitments of modal discourse. (It's been a while since I've read David Lewis, but I'm pretty sure this is how he develops his version of extensional possible world semantics.) Secondly, there's still a difference between what is true about sets of worlds and what is true of any particular world. My point is that the cardinality of mathematically possible worlds must be smaller than the cardinality of logically possible worlds. It cannot be the case that elementary mathematics is true of all logically possible worlds, precisely because we can conceive of logically possible worlds in which the axioms of elementary mathematics cannot hold.PyrrhoManiac1_{January 19, 2023
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@85
KF argues that reality is such that any possible world is in accord with logic and math. Is anyone contesting his claim? It seems to me that there is only some disagreement about details.
I'm not contesting the claim about logic, only about mathematics (even "core mathematics"). I have no complaints about the idea that logic constrains the set of all possible worlds. The question is, what follows from this?
Suppose we move on and ask: what explains the fact that any possible world is in accord with logic and math? KF suggests that the ‘root of reality’ must have put logic and math into reality and that this fact tells us something about the nature of the root of reality. Is anyone contesting those claims? I am asking because that seems to be the bigger issue here.
One would need to consider whether possible worlds really exist in some sense or if all talk about possible worlds is just a way of articulating modal discourse about how the actual world could be. (This is sometimes construed as a debate between modal realism and modal actualism.) I guess I'm just puzzled as to how this debate relates to whether God exists. Even if modal realism is true (which seems bonkers to me, but whatever), it wouldn't show that God exists, and even if modal actualism is true (which is my personal inclination), it wouldn't show that God doesn't exist. Put otherwise, even if modal actualism were true, and possible worlds is just a convenient device for representing our modal commitments about how the actual world could be, one might still feel the urge to ask such questions as: (1) Why is it the case that this universe has the requisite spatio-temporal structure for beings such as ourselves to conceive of both Euclidean and non-Euclidean geometries? (2) Why is it the case that this universe has the requisite spatio-temporal structure for beings such as ourselves to empirically determine that the actual geometry of the universe is roughly non-Euclidean (in the presence of mass)? (3) Why it is the case that this universe has the requisite spatio-temporal structure for beings such as ourselves to construct mathematical tools such as set theory and category theory? (4) Why it is the case that this universe has the requisite spatio-temporal structure for beings such as ourselves to sense, imagine, and think of empirically detectable objects as countable, such that arithmetic operations can be applied to empirically detectable objects? It would nevertheless also be a question as to whether "because it was willed as such by a transcendent personal God" is an intellectually satisfying answer to any or all of those questions.PyrrhoManiac1_{January 19, 2023
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PM1, actually, as just outlined, we are dealing with ontology and thus foundations of math. This is prior to set theory. When we discuss, a world is already implied for us to exist and be discussing, branch on which we sit. PW discussion is about this and other ways things might be, described as sets of assertions, propositions. Again, antecedent to proper revised set theory, the naive forms ran into paradoxes. So, we start from getting to N then extending NZQRCR* etc. The rest follows. KFkairosfocus_{January 19, 2023
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Origenes, once you have a distinct possible [much less actual!] world, the law of distinct identity is already present. It carries with it its close corollaries, excluded middle and non contradiction. These are already clearly fabric to any possible world and so are necessary entities constitutive of any given world. Branch on which we all sit. Next, there is a fourth principle that in some forms is quite controversial, sufficient reason. I short circuit the vexed debates . . . this one is so powerful it triggers hot objections . . . by using a weak, inquiry form: for any A that is, may be or is impossible of being we may freely ask why, and hope to find a reasonable answer. This cannot be successfully objected to, it is a declaration of freedom of inquiry. It also leads us to see that some things are impossible of being [IoB] in any possible world [PW], similar to a Euclidean plane square circle. That is because, core proposed characteristics are irreconcilably contradictory. Where, to get all strict, picky and fussy, consider that plane to be a disguised form of the complex plane C. Next, some things are possible and some are actual. Of these, some are in at least one PW but not all, these are contingent beings, CB. Others, are in every possible world, necessary beings, NB. If you doubt, try to imagine a particular world W where twoness does not exist, or begins, or ceases. Of course just from W is distinct from a near neighbour W', so W = {W'|A}, A some distinguishing attribute, 2 is already present in the existence or possible existence of W. NB's are framework for any PW, so they are always there. NB's are of course aspects of the root world already discussed W0. They always existed, cannot cease, are thus . . . eternal. The atheists are getting hot under the collar and sending out VT quake swarms, magma on the move heading for the surface. Never mind, we are just looking at what is now logic of being. Nope, not religion [the favourite dismissive rhetorical eruption], strictly, the branch of metaphysics termed ontology. We also see, that contingent beings, like fires, are caused. This can be elaborated but simply consider a fire and its requisites, as Copi did in his famous introductory text. Obviously, what begins to exist and/or depends on something else to continue and/or can cease from existing and/or is composite (made from prior parts) is contingent and caused. Necessary beings are not caused but from W0, may be causes. Or, like 2, may be logical constraints on possible being. No, not everything has or needs a cause. We are far enough along that we can modify my fav Austrian Prof, a certain HN (loved the dashikis!), and define math:
MATHEMATICS: [the study of] the logic of structure and quantity, i.e. an extension of a key aspect of logic of being to a foundational intellectual discipline
In that context, necessarily, any PW has logic and a certain core of math embedded in it as NB fabric to its existence, including NZQRCR* etc, the etc being royal, i.e. expandable into a realm. That's my answer to Wigner's wonder on the seemingly magical power of math. There is a universal core of math that is utterly pervasive, an aspect of requisites of being. However, not all of math is like that. We set up abstract logic model worlds, LMW's, at top level, axiomatic systems, at other levels mere models or even programmed abstract machines such as Turing machines. Euclidean geometry is an axiomatic system and it was discovered ~ 200 years ago that its 5th postulate is limited in scope, i.e. there are non Euclidean geometries. We can go to C to get an abstract result as needed in any world, but we can also define curvilinear systems etc and in our own world navigation, perspective etc already go beyond Euclid. As to creating that NB structure, no, it is already embedded in W0, we discover that core we do not invent it, and it is fabric to W0. Classically, on theism, these are eternal contemplations of God. On other proposed schemes they are part of the fabric of what is and always was. I argue separately that schemes that try to dismiss God are causally inadequate for us as responsible, rational, significantly free creatures. Also, they cannot find a way to have God impossible of being. Attempts to sever God from goodness and moral perfection are similarly wanting in cogency. Those asides are there as there seems to be endless debate on such and need for clarity. The quincunx, then is as I noted in 11:
the Quincunx shows by striking demonstration the depth to which logic of structure and quantity pervades our world and points onward to the utter, eerie universality of core mathematics in any possible world as a necessary being structure; the very same issue Eugene Wigner highlighted. The world is so mathematically pervaded, indeed possible being is so mathematically pervaded that it is manifestly akin to mind rather than to utterly non rational chaos; indeed, in many cases, randomness reveals an underlying ordered structure, as this very case demonstrates. Onward, lieth statistical thermodynamics, via the classic case of 500 or 1,000 coins and their distribution, thence the threshold search space challenge at the core of ID, how to get to FSCO/I expressive bit patterns by the blind chance and mechanical necessity the Galton Board illustrates. That context is remarkable, not trivial and readily dismissible.
KFkairosfocus_{January 19, 2023
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@53
PM1, not all of mathematics, just the core. Once there is a distinct possible world W, marked apart from W’ a near neighbour, instantly 0,1,2 obtain thence NZQRCR*, etc. This is a general result on an abstract order for any PW descriptive set, it matters not if your world is “a world that was a sheer homogeneous plenum,” say P, once that is distinguishable from any neighbour that is not quite the same, there is an attribute in the set for P that is not in P’ say P’ is just shy of complete homogeneity or something like that, which makes your description mean P is pure homog, an attribute not in P’.
This is all fine, but let's take stock of what this shows: if we're doing possible world theory, then we're using the tools of set theory to describe sets of possible worlds. So it's just an presupposition of doing set theory that we can distinguish between elements in those sets: there are no sets if we can't distinguish between elements (in this case, worlds). My point was only that using the elementary mathematics of set theory to describe possible worlds doesn't show that mathematics must be true of every possible world. One of the basic truths of set theory is that sets can have different cardinality, and my point was that the set of mathematically possible worlds must have a smaller cardinality than the set of logically possible worlds. This is because the only constraint on logically possible worlds is that they cannot violate the axioms of non-classical logics. (This is because the set of all classically logically possible world has a smaller cardinality than the set of all non-classically logically possible worlds, since classical logic has more restrictive axioms than non-classical logics.) But the constraints on mathematically possible worlds are more restrictive than the constraints on logically possible worlds, because in addition to logical axioms, there are additional axioms -- the axioms of geometry and the axioms of number theory. It's an intuitive result of possible world theory that as one adds axioms, the cardinality of the set of possible worlds decreases, since there will always be possible worlds in which the axioms do not hold. For this reason, I believe it is mistaken to say
Core mathematics is part of the fabric of any distinct possible world, giving it universal power.
precisely because one can conceive of logically possible worlds in which the axioms of geometry and number theory cannot be used. A sheer homogeneous plenum is a logically possible world in which it is impossible to do geometry, since one could not differentiate between points, lines, planes. A world of zero dimensionality would be a world in which only points are mathematically possible. A world that had no spatio-temporal structure at all would be a world in which no mathematics could be done. Yet all these worlds are thinkable without contradiction, hence they are classically logically possible.PyrrhoManiac1_{January 19, 2023
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VL @, JVL @, KF@ KF argues that reality is such that any possible world is in accord with logic and math. Is anyone contesting his claim? It seems to me that there is only some disagreement about details. Suppose we move on and ask: what explains the fact that any possible world is in accord with logic and math? KF suggests that the ‘root of reality’ must have put logic and math into reality and that this fact tells us something about the nature of the root of reality. Is anyone contesting those claims? I am asking because that seems to be the bigger issue here.Origenes_{January 19, 2023
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PPS, you may wonder on universality. Lengths of lines are real values, as are angles at vertices, and of course trig function values, logs etc are reals, typically irrationals and it is suspected most of the time strictly transcendentals. But in curvilinear spaces world lines are curves so what does the angle of intersection mean, between curves, or the length of a curve? Clearly, we are dealing with close approximations to straight lines and planes etc (though surveyors beyond a certain scope do deal with curvature), and this points to what lurks, infinitesimal increments in the lines that are straight and do intersect at an angle. Curve lengths are in effect integrals of such increments, and more, that is, R* is relevant.kairosfocus_{January 19, 2023
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VL, we are talking of the axiomatisation of geometry, that there are alternative axiomatisations that yield diverse results; as was stated and exemplified. Go through C and you will see all you need for geometry work, Trig functions and trig, likewise through power series. I note, Cartesian coords, are C in disguise in effect: j*x --> y. Extensions to 3-d space have similar vector approaches, try ijk, hinted at by the physicist's j just now. The exponential function and its inverse are likewise. My point is not that the Euclidean world is not useful and relevant but that its framework per classical axiomatisation is not present in every possible world automatically. We know this directly through the creation of alternative worlds where the 5th postulate does not hold. The universal core I have pointed out, NZQRCR* etc, does hold in any possible world giving it universal power. We already know in a relativistic world that on the grand scale our spacetime domain is non euclidean, also making non euclidean geometry relevant. Though, navigation on the Earth's surface gives cases also. Notice, two finitely separated lines of longitude intersect the equator locally at right angles but intersect at a non zero angle at the N pole, thus we see the triangle analogue in the surface of the Earth having the angle sum exceeding 180 degrees, something evident from the days of Eratosthenes. Likewise, projective geometry, including perspective is non Euclidean, parallel lines analogues converge at a vanishing point; this is the geometry of vision, manifest to us since our ancestors could reflect on vision. I gather pygmies from Central Africa taken out on the plains misunderstood remote animals as nearby bugs. I note that other examples have been set to one side for the moment but these also show the same pattern. The universal core I am speaking of is particular to the issue of being manifest in any possible world, each PW being a sufficient set of propositions feasible of instantiation, here as an abstract model framework. For related example, standard non naive set theory and fuzzy sets are both useful in diverse contexts but each is obviously a diverse axiomatisation, as are different algebraic logics. KF PS, Notice how differing geometries with differing axiomatisations are practically relevant to us in diverse contexts.kairosfocus_{January 18, 2023
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KF. Is trigonometry part of core mathematics? Exponents and logarithms? If the geometry of surfaces is not core, then would all math in coordinate systems, such as the graphs of functions not be core? Can you explain what criteria is being used to answer the above questions.Viola Lee_{January 18, 2023
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VL, by for example citing Euclidean vs non Euclidean geometry I gave a well known clarifying case. That should be enough spelling out. KFkairosfocus_{January 18, 2023
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VL, my operative word was analogue, e.g. the ellipsoidal case has the angles greater than 180 degrees for the analogue of a triangle and in other frames less than, it is the Euclidean case that has 180. So, yes, common school geometry is not part of the universal core as discussed though it is relevant to us. KFkairosfocus_{January 18, 2023
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Kairosfocus @
as a matter of design inference, there is no equating of W0 with the immediate designers of cell based life on earth.
Again, I agree. And I would add that I also don't see a metaphysical necessity of equating the two.
As an initial abstraction, personality is not attributed to the root world W0. That may be built up later on evidence but that is not where this starts.
Understood. I note again that evidence derived from this universe relates to the designer(s) of this universe who may be ontologically distinct from the W0.Origenes_{January 18, 2023
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re 70. So geometry is not core mathematics? And you writes, "VL, the parallel postulate and the angle sum of a triangle analogue are decisively different." Different from what? Different from each other? The sum of the angles in a triangle is a direct consequence of which parallel postulate you are adopting. Explain, please.Viola Lee_{January 18, 2023
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re 70. So geometry is not core mathematics? And you writes, "VL, the parallel postulate and the angle sum of a triangle analogue are decisively different." Different than what? Different than each other? The sum of the angles in a triangle is a direct consequence of which parallel postulate you are adopting.Viola Lee_{January 18, 2023
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Origenes, as a matter of design inference, there is no equating of W0 with the immediate designers of cell based life on earth. As an initial abstraction, personality is not attributed to the root world W0. That may be built up later on evidence but that is not where this starts. KFkairosfocus_{January 18, 2023
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JVL, where did you ever get a suggestion that I connected the axiomatic systems in question to earth life? KFkairosfocus_{January 18, 2023
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Kairosfocus @71
I am saying, absent a necessary being reality root there would be just utter non being, no worlds of any sort at all, where world here enfolds a whole universe that might be or is, from a list of possible propositions to a computer simulation to a mathematical domain to our world 90 bn ly across or more.
I agree with you that something fundamental must exist.
Utter non being has no causal powers and were such the case, that would always and only be the case, there would be no reality whatsoever, no time, no entities, no propositions, no minds, no matter, no spaces of any dimension, no locations, utter non being.
Good and solid argument. Again, we both hold that something fundamental must exist.
As a world is, something always was of adequate causal capacity for our world to be and us in it. Responsible, rational, significantly free creatures. So, the issue is, of what character is that reality root, W0 as I tagged it.
I think we both agree that the cause of this world is an excessively intelligent being. A few notes: 1. The cause of this world and the W0 (reality root/something fundamental that must exist) are not necessarily the same thing. It is conceivable that the intelligent being that caused our world sprang from the W0. Given that, it is conceivable that the W0 is a nonconscious being that is not directly involved in creating our world. 2. As an aside, it is conceivable that the intelligent being that caused our world went through a learning process and acquired his incredible powers over time.Origenes_{January 18, 2023
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Kairosfocus: such variable cases are often set up as axiomatic systems where on changing certain axioms one gets a different frame that may be equally valid. The classic case in point is Euclidean geometry and its famous fifth postulate where across C19, there emerged various non Euclidean Geometries. I would think that standard and fuzzy sets are another case. The development of various non standard logic systems insofar as they are expressed as special algebras would count. But, but, but, why are those systems dependent on Earth life? You said something and we are just asking you to justify your statement. AND haven't humans already shown their ability to consider and deal with those cases? How can you show that those cases could not be understood by another .. . realm? Domain? For such, one can construct an abstract, logic model world in which there are local results that do not extend to all possible frameworks or possible worlds; that is the border that seems relevant. Okay, spell that out please. No supposition or guessing, show us how that would work. The relevant general core is not like that, and the frame involving NZQRCR* would be my primary case in point. I think, in part, that is because its root is simple distinct identity thence N via say von Neumann’s construction, where onward classes of numbers [where from Z on up we are dealing with vectors] rooted in N, follow by logic and general demonstration, e.g. Z inserts that n’ + n = 0, n in N, Q uses p/q, both being in Z, R extends to limits of infinite chains of summed rationals [think, decimal representation and place value], C is two orthogonal real lines with rotations, R* is about infinitesimal and transfinite extensions to R that are now established in non standard analysis.k Just spouting off a lot of mathy sounding verbiage doesn't help you. You've made some specific claims or assertions, we'd just like you to support them. Please. Give us some specific examples of areas of mathematics that might be 'regional'ly dependent or admit you can't. You make lots and lots of vague statements when what we'd like you to do is state some specific, clear mathematical regions or areas which you think might be different in a different domain. Just do that. Please. the parallel postulate and the angle sum of a triangle analogue are decisively different. They define flat, ellipsoidal [including spherical] and hyperboloidal spaces. So, this postulate is not consistent for all possible worlds. That marks a clear distinction, But, guess what, human mathematicians have learned to deal with those cases because we can accommodate different axioms.. So those cases can both be considered true in the human derived system. Why wouldn't aliens or others come to the same conclusions? So, AGAIN, what is considered true in the math realm that you think would not be considered true or essential in a different realm.JVL_{January 18, 2023
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VL, I also note that world schemes that do not have as core the good, holy, morally perfect God are not cases of ethical monotheism. They are other types of worldview, such as a dualism, a monism, a polytheism, a henotheism, a physicalism etc. KFkairosfocus_{January 18, 2023
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