Amen mordant.
He took the Model T Ford of ancient Christianity and updated it to a Tesla powered by modal logic.
But, under all the superficial changes and high-falutin’ language… both are still cars.
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And with the principles of logic, which Gödel’s argument has been widely criticised for not doing, by making unevidenced assumption in his premises that amount to question begging. Our newly departed friend never honestly addressed that, merely making subjective claims using esoteric terms, that amounted to little more than handwaving. I am also dubious that he fully understood the difference between subjective and objective, as he seemed often to imply this was some sort of binary condition, rather than a scale from entirely subjective claims to objective facts, but then this acknowledgment would require he understand that objective evidence is what causes that difference, and he was determined to ignore that fact. So he may have been being deliberately and dishonestly obtuse, I guess we will never know.
You mean Gödel can’t just make them up based on unevidenced religious beliefs? Funny how this fact seemed to bead up and roll off our friend.
Which was pretty much all he offered against criticisms of Gödel’s argument, and yes I agree, his responses added no value to the debate, just doggedly refusing to acknowledge the criticisms existed.
This is also probably true, either delusional, or devoid of integrity, either way nothing anyone said was ever going to engage him in honest debate.
As @Get_off_my_lawn said, that acknowledgment would have destroyed his favourite (and NB only argument presented) for any deity. Once you acknowledge the axioms must reflect objective fact and reality to have any meaning, Gödel’s proof fails, it can only work if you accept a priori without any supporting evidence the very things he is arguing for, that a deity is possible and must have certain “necessary” properties.
More like he pimped an old model T to look like a Tesla, but underneath the rusting useless model T remained.
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Or to put it another way, “if you can’t dazzle them with facts, baffle them with bullshit”.
We might take another look at these so called axioms? Being an uneducated dullard who is bound to get it wrong I will go first, and then you can all let me know where I erred.
Axiom 1: If φ is a positive property, and if it is necessarily true (true in all possible worlds) that every object with property φ also has property ψ, then ψ is also a positive property.
Why would it follow that if something has a positive property, and if it necessarily always has another specific property, that the second property must be positive?
Axiom 2: The negation of a property φ is positive if, and only if, φ is not positive.
This seems almost trivially true.
Theorem 1: If a property φ is positive, then it is possible that there exists an object
x that has this property (in at least one possible world, there exists an object x that has this property).
Since the author does not define what he means by “positive property”, the possibility of its existence seems like pure speculation. Why does it follow that an a property imagined as positive must exist? So if I decide invisibility is a positive property then it is possible an object x has this property, and thus x exists? I must be making a hash of this surely?
Definition 1: An object x is God-like if, and only if, x has all positive properties.
This then amounts to begging the question, as it makes a completely unevidenced assumption about the very thing the author is arguing for. NB positive properties remains undefined.
Axiom 3: The property of being God-like is itself a positive property.
Another unevidenced assumption about the thing being argued for, and again no amount of fancy philosophical phrases will convince this is not begging the question.
Theorem 2: It is possible that there exists a God-like object x (in at least one possible world, there exists a God-like object x.
Only if we ignore him defining a deity’s existence as being itself a positive property, and positive property still remains undefined.
Definition 2: A property φ is an essential property of an object x if, x has property
φ, and every property ψ of x necessarily (in all possible worlds) and generally (for all objects) follows from φ.
The first part seems plausible, but a property of mine is being sarcastic, I am not sure this property is essential though, the second assertion again seems like little more than speculation, it’s a little woolly and slung together for me, but I am not an expert in modal logic, sorry…a student implying they are an expert…in modal logic.
Axiom 4: If a property φ is positive, then it is necessarily positive (positive in all possible worlds).
Again pure speculation, and not least because he has yet to accurately define what he means by a positive property, either way, how many “worlds” were in his test group here, oh that’s right modal logic doesn’t need any empirical verification.
Theorem 3: If x is God-like, then being God-like is an essential property of x.
This to me seems like another rather trivial tautology? If x is mermaid-like, then being mermaid-like is an essential property of x.
Definition 3: An object x “exists necessarily” if each of its essential properties φ applies, in each possible world, to some object y.
Lost me there, the author has yet to define property φ in any meaningful way, now I see the word essential appear, the last part I will freely admit is beyond my reason to understand, how he gets from a woolly undefined phrase - to essential - let alone in all possible worlds, are we assuming that logic applies in every possible world, since we are imagining properties, I can imagine a method X that is superior to logic, I can imagine a world where only the best method applies, and this method makes logic redundant.
Axiom 5: “Necessary existence” is a positive property.
Plucked out of thin air again, and again no attempt to accurately define what a positive property is.
Theorem 4: It is necessarily true (true in all possible worlds) that a God-like object exists.
I am underwhelmed of course, but perhaps someone can explain as gently as possibly why my dull intellect is left lukewarm by this?
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This is IMO the central problem. Not only is “positive property” undefined, “positive” is an inherently subjective and contextual adjective. Since a thing can be positive from the perspective of observer A and negative from the perspective of observer B and neutral for C and so on, it is logically impossible to define his God (or god, or Absolute or whatever).
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Yes, that was pointed out repeatedly to bsengstock20, but I cannot remember having seen him address it at all, at least not in any meaningful manner. If he did, I missed it. Did anyone else notice him addressing the positive property objection?
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Yes, that’s right mordant.
I’ve presented several examples from different cultures of what they would consider to be positive moral actions. Actions which we find immoral and extremely negative. Which demonstrates that any notion of positive morality is contextual to the time, place and culture in question. Which further indicates that there are no absolute positive or negative moral values in human life.
That there are no absolutes of any kind in REAL human life and these concepts only exist as abstract things in the minds of philosophers and metaphysicians with too much time on their hands.
There being no absolutes to be found in human experience, how then can Gödel’s absolutes be in any way connected to or related to human life? The simple answer is that they can’t. They remain as immaterial and intangible abstract concepts of the mind that have no real, physical and concrete existence at all. No physical examples. No concrete correlates. Nothing real at all.
Would bsengstock20 get around this by claiming that the mind is the true reality? Perhaps. But if he did so I’d ask him to jump in my time machine and stand below ground zero in Hiroshima.
What’s that? You don’t want to go, bsengstock20? Why not? Isn’t your mind the true reality? Or are you worried that the true reality of physical existence (aka Little Boy) will snuff you and your mind out in an instant?
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Calling something an axiom is safe, axioms don’t have to make sense, and they don’t have to reflect reality. I’m not aware of any requirement for a statement to be labelled an axiom they are just definitions. It is strange that they have some sentences labelled as axioms and some labelled as definitions, imo. But when you call something a theorem, that means the statement has been formally proved. You can make up axioms all day long, but you don’t get to make up theorems.
And that’s the crux of the matter. You can develop and prove the most beautiful theorems in logic and mathematics that serve you all sorts of mind-boggling results and conclusions that don’t need to have anything at all to do with physical reality[1], and don’t serve (as far as we know now) other purposes than to just reflect mathematics for mathematics’s own sake. If, however, you want the output of your theorem to reflect objective reality, your axioms and your input also have to adequately reflect objective reality. Otherwise it’s shit in, shit out, reality-wise. And in that context, data is king.
The Banach-Tarski paradox springs to mind ↩︎
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Perhaps in some technical philosophical sense, but I have always regarded something that’s considered axiomatic as a time-tested truth – something that works every time but it’s an axiom rather than a fact because we can’t prove it. For example, an axiom in geometry is that a straight line can connect any two points. I suppose we can’t prove that someplace in the universe a straight line does not connect two points, hence it’s axiomatic – but I doubt that anyone here as ever experienced it not being true or can conceive of a scenario where it wouldn’t be true, at least in the Euclidean system.
The practice of just asserting something and then claiming it’s an axiom is not how axioms work. it has to be a base assumption that actually plays out in reality. The definition of “axiom” is “a statement or proposition which is regarded as being established, accepted, or self-evidently true" which means it is something we have experience with. The problem with bsengstock20’s assertions is that they are not “established” or “accepted” and they certainly aren’t “self evidently true”. In fact he needs a specialist grammar to even describe them.
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Nope, he just altered the phrase to describe the claim, like he was Googling for philosophical terms in some niche philosophical tome on modal logic.
Axiom 3: The property of being God-like is itself a positive property.
Like that…
And this…
Axiom 5: “Necessary existence” is a positive property.
So does everything that exist, exist necessarily, and if not why not?
“Many philosophers have called the axioms into question. The first layer of criticism is simply that there are no arguments presented that give reasons why the axioms are true. A second layer is that these particular axioms lead to unwelcome conclusions.
This line of thought was argued by Jordan Howard Sobel, showing that if the axioms are accepted, they lead to a “modal collapse” where every statement that is true is necessarily true, i.e. the sets of necessary, of contingent, and of possible truths all coincide (provided there are accessible worlds at all).”
“There are, however, many more criticisms, most of them focusing on the question of whether these axioms must be rejected to avoid odd conclusions. The broader criticism is that even if the axioms cannot be shown to be false, that does not mean that they are true. Hilbert’s famous remark about interchangeability of the primitives’ names applies to those in Gödel’s ontological axioms (“positive”, “god-like”, “essence”). According to André Fuhrmann (2005) it remains to show that the dazzling notion prescribed by traditions and often believed to be essentially mysterious satisfies Gödel’s axioms. This is not a mathematical, but a theological task. It is this task which decides which religion’s god has been proven to exist.”
I mentioned bsengestock20 that even if the argument were sound, it gets you no closer to Jesus, than Yahweh, or Allah, or pretty much any other deity, he went straight to semantics and subjective definitions of what he called God and what I labelled a deity, and pointed out I’d seen no objective difference between deities. He dismissed my objection and said there were objective differences, but when I asked him for one he couldn’t provide any, and word salad peppered with subjective claims was all I got.
Anyway….Here is the proof in it’s original formal form:
Outside of my mediocre ability I’m afraid, but others can have some fun with it.
Axioms determine the rules for the game; they are not required to reflect reality. Ideally they shouldn’t be controversial but sometimes it can’t be avoided. Consider the axiom of choice in set theory:
It tells us that given a collection of (non-empty) sets, we can select one element from each set to create a new set; EVEN IF THERE ARE AN INFINITE NUMBER OF SETS IN THE COLLECTION.
You don’t have to accept that axiom. If you do, it leads to one group of logical conclusions; if you reject it, it leads to a different group of logical conclusions.
You don’t have to agree to the rules of a game, you can reject them and play a different game. But if you want your game to model reality; a good starting point would be to have your axioms reflect reality.
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Oh for sure. My noggin was once chock-a-block full of all sorts of axioms that didn’t reflect reality, so much as my idealistic preferences about how things “should” be in a world that was fair and just (to and for me, at any rate). It was my own form of bsengstock20’s monomania. And it wasn’t all religious, either. Some of it was just standard-issue youthful naiveté and wishful thinking.
So these days I want my “game” to model reality. There are a lot of beautiful ideas that don’t help you deal in reality. They might help you construct fantasy worlds, which can be useful if you’re a writer or actor or something of that nature. It might even help a mathematician or scientist explore ideas, hopefully ideas that lead to discoveries about actual reality. I can see how alternate or imaginary models could be used to bypass habitual thought patterns or provide legitimate relief from the burdens of everyday existence. But at some point, rubber has to meet the road or it is just so much virtual fapping.
Simple bias, which is what Gödel and bsengestock20 are using. Biased assumptions that violate a basic principle of informal logic, as clever as the formal argument may be (I can’t comment), when translated into an informal argument, even an uneducated dumbo like me can see some of the assumptions in the premises amount to begging the question.
As I said earlier no amount of word salad and esoteric philosophical terms will change that fact, or address it. Since no one here (I think) is arguing that the conclusions of the proof can’t be correct if the premises are true, only that the premises are dubious, since they are as much in need of supporting argument as the conclusion.
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Exactly. And this is the very point I have been trying to drive home with bsengstock20, and which he ignored. I suspect he deep down knows that this is an argument to be taken seriously. And I also suspect that’s why he chooses to ignore it, as it would undermine his whole line of inquiry.
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And this is why bsengstock20 is, deep down, holding to the same mindset as any religious person.
They have a strong emotional dislike of the way reality presents itself to them and so they reject it as it really is and, using leaps of faith, claim that it is not the true face of reality. They claim that there is a better, higher, greater and more emotionally satisfying reality. The usual pathways they use to actualise this better reality in their minds are ancient religious texts. But even if you replace these texts with modal logic and metaphysics, the mindf**k still works.
And the deep-seated emotional cause of it is still the same.
Which might go some way Goml, to explaining why bsengstock20 could never bring himself to address our criticisms of his choice of axioms. Just as a devout Christian or Muslim can never openly admit that the Bible or the Quran contradict themselves and are contradicted by physical evidence. It means too much to them to face up to the cold, hard reality.
So, for all his claims and posturing about ultimate reason and ultimate rationality bsengstock20 was reacting emotionally to our questions and challenges. It’s even possible that we saw some kind of emotional defence mechanism at work in his replies. The closer we got to bringing him to some kind of crisis point, the more esoteric and obscure became his language. As if he were reinforcing the security of what he loved by throwing up new walls of impenetrably arcane verbiage.
I’m basing this line of argument on something that slipped past his defences, btw. Three days ago this went between us…
Very well… I’ll try to strip the term of esotericism…
See that?
It’s a dual admission that his replies are couched in esoteric terms AND that he can make the effort to strip all of that away and reply in plainer language if he chooses to. So, he’s known what he was doing all along. I rest my case.
Thank you,
Walter.
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Or pretend reality has an untestable undetectable magic deity in it. The real irony is that if you’re going to do that, why bother with logic at all. If magic trumps objective empiricism, why are they bothered about logic.
The irony has been (for me anyway) that reality isn’t all that cold and hard if you just accept it rather than fight it. Fighting reality can be pretty cold and hard, too. Leaky rationalizations can be pretty hard and cold. Illusions can put up quite the death struggle if you insist on being attached to them.
It’s human nature to be possessed of beautiful dreams but in the end they just amount to avoidance of what IS and prevent you from seeing what beauty and symmetry actually EXIST.