Author Topic: Searching for GOD...  (Read 3879059 times)

bluehillside Retd.

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Re: Searching for GOD...
« Reply #51100 on: June 24, 2024, 01:27:33 PM »
NS,

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Sort of, and yet billions accept this. You are in a world where logic is not always accepted, indeed, I know no people who work just to logic. Nor how you could

Yes I know, but – billions accepting something as true or not – the only way I know of to test whether or not any belief is well-founded is to examine logically its justifying arguments. That when those arguments thus fail the same billions carry on believing the claim nonetheless is a different matter.     
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Re: Searching for GOD...
« Reply #51101 on: June 24, 2024, 01:54:16 PM »
NS,

Yes I know, but – billions accepting something as true or not – the only way I know of to test whether or not any belief is well-founded is to examine logically its justifying arguments. That when those arguments thus fail the same billions carry on believing the claim nonetheless is a different matter.   
And if you want to argue against a straw man, off you go. If you examine the idea of thinking you are right because of logical arguments, then by the problem of no free will, you can't.



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Re: Searching for GOD...
« Reply #51102 on: June 24, 2024, 02:17:32 PM »
NS,

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And if you want to argue against a straw man, off you go. If you examine the idea of thinking you are right because of logical arguments, then by the problem of no free will, you can't.

Your were the one leaning toward the argumentum ad populum, not me and what does "If you examine the idea of thinking you are right because of logical arguments, then by the problem of no free will, you can't." mean?

 
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Re: Searching for GOD...
« Reply #51103 on: June 24, 2024, 02:23:00 PM »
NS,

Your were the one leaning toward the argumentum ad populum, not me and what does "If you examine the idea of thinking you are right because of logical arguments, then by the problem of no free will, you can't." mean?
At no point did I suggest that because billions of people thought something that it was right.

As to free will position, you don't believe in free will so what you believe is never going to be rational. It's just what you believe.

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Re: Searching for GOD...
« Reply #51104 on: June 24, 2024, 02:35:28 PM »
NS,

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At no point did I suggest that because billions of people thought something that it was right.

Then what point were you attempting: "Billions of people believe things for wrong reasons"? Well yes, but so what?

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As to free will position, you don't believe in free will so what you believe is never going to be rational. It's just what you believe.

What are you even trying to say here? Person A says: "If you run across the MI ten times without looking you'll likely be fine because I've put a lucky spell on you"; person B says: "You likely won't because there are no good reasons to believe in lucky spells, and moreover we can test your thesis with experiments".

Who's right, and what's that got to do with free will?

   
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Re: Searching for GOD...
« Reply #51105 on: June 24, 2024, 02:48:54 PM »
I was attempting to deal with the factor about what people believe. Seems to me important about how you deal with stuff. Rather than lying about what people say.

As to free will, your basic inability to understand choice that you portray, if you don't believe in free will, is hard to explain to someone who misses basic logic.

But let's start, if you don't believe in free will, how can tell people off for believing in free will?
« Last Edit: June 24, 2024, 02:53:08 PM by Nearly Sane »

bluehillside Retd.

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Re: Searching for GOD...
« Reply #51106 on: June 24, 2024, 03:06:18 PM »
NS,

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I wax attempting to deal with the factor about what people believe. Seems to me important about how you deal with stuff.

How was the platitude that billions of people believe things for wrong reasons dealing with something?

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As to free will, your basic inability to understand choice that you portray, if you don't believe in free will, is hard to explain to someone who misses basic logic.

What “inability” would that be?

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But let's start, if you don't believe in free will, how can tell people off for believing in free will?

And speaking of straw men…

…I don’t “tell off” anyone for anything. I merely identify why “true” free will as, say, AB asserts it to be is logically incoherent. I also though argue that at an everyday level we treat will as "free" for practical purposes – the legal system being just one example. You could not for example succeed with the defence, “yes I bumped off granny, but I’m innocent because I had no true free will in the matter”.

We’ve been to this rodeo before – your critique is that absent “true” free will discussion of right and wrong is meaningless; mine is that at a practical level of abstraction it’s anything but, which is why societies function without also claiming absolutes.       
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Re: Searching for GOD...
« Reply #51107 on: June 24, 2024, 03:12:26 PM »
NS,

How was the platitude that billions of people believe things for wrong reasons dealing with something?

What “inability” would that be?

And speaking of straw men…

…I don’t “tell off” anyone for anything. I merely identify why “true” free will as, say, AB asserts it to be is logically incoherent. I also though argue that at an everyday level we treat will as "free" for practical purposes – the legal system being just one example. You could not for example succeed with the defence, “yes I bumped off granny, but I’m innocent because I had no true free will in the matter”.

We’ve been to this rodeo before – your critique is that absent “true” free will discussion of right and wrong is meaningless; mine is that at a practical level of abstraction it’s anything but, which is why societies function without also claiming absolutes.     
'true' as opposed to anything that makes sense? Your inability to explain choice as something you can condemn at the same time as pushing the idea that there is no free will is laughably contradictory.

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Re: Searching for GOD...
« Reply #51108 on: June 24, 2024, 03:55:09 PM »
NS,

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'true' as opposed to anything that makes sense?

No, "true" as in epistemically absolute, unfettered, not determined by prior events, done by magic souls etc rather than just functionally useful - essential in fact. 
 
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Your inability to explain choice as something you can condemn at the same time as pushing the idea that there is no free will is laughably contradictory.

No it isn't. Does your inability to explain in absolute terms why you think Turner's The Fighting Temeraire is great art and the poster of the girl scratching her backside on the tennis court isn't invalidate your opinions about those things? Why not?

You seem lost in a world of thinking that, unless truth claims can be justified in absolute terms, they're all equally in/valid. They're not though - there's a perfectly reasonable level of abstraction about what's true/not true beneath the absolute that we all rely on in order to function. If you don't believe me, try Person A's claim about crossing the M1 ten times without looking and then tell me whether or not his claim was true (assuming there's enough left of you to do that).       
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Re: Searching for GOD...
« Reply #51109 on: June 24, 2024, 04:30:02 PM »
NS,

No, "true" as in epistemically absolute, unfettered, not determined by prior events, done by magic souls etc rather than just functionally useful - essential in fact. 
 
No it isn't. Does your inability to explain in absolute terms why you think Turner's The Fighting Temeraire is great art and the poster of the girl scratching her backside on the tennis court isn't invalidate your opinions about those things? Why not?

You seem lost in a world of thinking that, unless truth claims can be justified in absolute terms, they're all equally in/valid. They're not though - there's a perfectly reasonable level of abstraction about what's true/not true beneath the absolute that we al in order to function. If you don't believe me, try Person A's claim about crossing the M1 ten times without looking and then tell me whether or not his claim was true (assuming there's enough left of you to do that).       
Oh it's perfectly reasonable to claim truth when you assert it. Silly me, why should i ever doubt you,?

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Re: Searching for GOD...
« Reply #51110 on: June 24, 2024, 07:50:42 PM »
NS,

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Oh it's perfectly reasonable to claim truth when you assert it. Silly me, why should i ever doubt you,?

As there’s no rhetorical path to this from what I actually said, and as you’ve just ignored the arguments I did make should I take it that you’ve now abandoned the attempt at an argument of your own?

And no, it’s not because I just assert it at all – it’s because reason and evidence justify it. To take the crossing the M1 example you ignored – it’s more likely true that you’ll make it if you look first and that you’ll won’t make it if you don’t look. Why? Because if you look you have a better chance of timing to your run to dodge the traffic. Moreover, if I were to try the experiment with real volunteers and then compare the bodies/survivors that would confirm the truth statement.

That’s why can we can say with reasonable confidence that the statement “looking before crossing the road has a better survival rate than not looking” is true. Notice here that this has fuck all to do with free will, and moreover that “true” does not require epistemic certainty – all true/false statement are probabilistic in character (including this one), but they still provide perfectly useful and workable approximations of “true” and “false” nonetheless. 

Not sure why this is hard for you to address, but there it is anyway.           
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jeremyp

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Re: Searching for GOD...
« Reply #51111 on: June 25, 2024, 10:13:14 AM »
all true/false statement are probabilistic in character (including this one), but they still provide perfectly useful and workable approximations of “true” and “false” nonetheless. 

I would argue that all truth/false statements about the real World are probabilistic in nature, especially as they ultimately rely on inductive arguments.

Anything that is purely deductive such as mathematics is absolute. For example, the statement "assuming Euclid's axioms of geometry are true, then the angles of a triangle add up to 180 degrees". There's nothing probabilistic about that. What I find interesting is that it is information free. It doesn't tell us anything, it merely reframes a question. i.e. from "do the angles of a triangle add up to 180 degrees?" to "do Euclid's axioms hold?"

I also don't get NS's free will angle. A chain of reasoning is right or wrong whether it was arrived at by a deterministic process or some sort of magic (I too believe that the classic concept of free will is logically incoherent).
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bluehillside Retd.

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Re: Searching for GOD...
« Reply #51112 on: June 25, 2024, 10:37:53 AM »
jeremyp,

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I would argue that all truth/false statements about the real World are probabilistic in nature, especially as they ultimately rely on inductive arguments.

No argument here!

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Anything that is purely deductive such as mathematics is absolute. For example, the statement "assuming Euclid's axioms of geometry are true, then the angles of a triangle add up to 180 degrees". There's nothing probabilistic about that. What I find interesting is that it is information free. It doesn't tell us anything, it merely reframes a question. i.e. from "do the angles of a triangle add up to 180 degrees?" to "do Euclid's axioms hold?"

Here we part company though. At some point all beliefs rest on axioms – statements that have to be accepted as true, but nonetheless may not be. Axioms though could still be wrong – how then on the basis of the tiny sliver of information we have about the universe can we claim to be “absolute” about anything? Like you I can’t conceive of a circumstance in which the internal angles of a triangle won’t add up to 180 degrees, but I can’t eliminate entirely either the possibility at least that, for example, I’m not just an algorithm programmed to think that way.

As ever, Shakespeare put it best: “There are more things in heaven and earth, Horatio,/Than are dreamt of in your philosophy.”     

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I also don't get NS's free will angle. A chain of reasoning is right or wrong whether it was arrived at by a deterministic process or some sort of magic (I too believe that the classic concept of free will is logically incoherent).

Me neither.
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Stranger

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Re: Searching for GOD...
« Reply #51113 on: June 25, 2024, 11:02:58 AM »
Like you I can’t conceive of a circumstance in which the internal angles of a triangle won’t add up to 180 degrees, but I can’t eliminate entirely either the possibility at least that, for example, I’m not just an algorithm programmed to think that way.

Try drawing a triangle on the surface of a sphere...    ;)

Actually, since we are in a gravitational field, Euclidean geometry is only an approximation. The geometry of space-time is variable. The space-like part is only Euclidean in 'flat' space-time.

What's perhaps closer to absolute proofs are in number theory, which is about the natural numbers, ℕ = {0, 1, 2, 3,...}. We can say for certain, for example, that there is no largest prime number.
« Last Edit: June 25, 2024, 11:06:11 AM by Stranger »
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jeremyp

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Re: Searching for GOD...
« Reply #51114 on: June 25, 2024, 11:06:42 AM »

Here we part company though. At some point all beliefs rest on axioms – statements that have to be accepted as true, but nonetheless may not be. Axioms though could still be wrong – how then on the basis of the tiny sliver of information we have about the universe can we claim to be “absolute” about anything?
Because, in mathematics, you simply assume a set of axioms are true and see where it takes you. This is why I say that mathematical statements are information free. The statement "if the axioms of plane geometry are true then the angles of a triangle add up to 180 degrees" is guaranteed 100% true. I can show you a deductive line of reasoning that takes you from the premise to the conclusion.

However, if you want to ask the question "do the angles of this triangle I have just drawn on a piece of paper add up to 180 degrees?" and I give you the proof, all I've done is reframe the question as "are Euclid's geometry axioms true?" I haven't answered it. You need to do measurements either of the triangle or the axioms and, of course, these are always probabilistic.

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bluehillside Retd.

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Re: Searching for GOD...
« Reply #51115 on: June 25, 2024, 11:36:43 AM »
Stranger,

Quote
Try drawing a triangle on the surface of a sphere...     

Actually, since we are in a gravitational field, Euclidean geometry is only an approximation. The geometry of space-time is variable. The space-like part is only Euclidean in 'flat' space-time.

What's perhaps closer to absolute proofs are in number theory, which is about the natural numbers, ℕ = {0, 1, 2, 3,...}. We can say for certain, for example, that there is no largest prime number.

But still we can’t claim to be “absolute” about anything for the reasons I set out. We can have a qualified “absolute” at best: “X is absolutely true but only inasmuch as human minds are capable of understanding such matters”, but that’s all. 



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Because, in mathematics, you simply assume a set of axioms are true and see where it takes you.

Yes, but assumptions can be wrong – and so therefore can the conclusions they lead to be wrong.

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This is why I say that mathematical statements are information free. The statement "if the axioms of plane geometry are true then the angles of a triangle add up to 180 degrees" is guaranteed 100% true. I can show you a deductive line of reasoning that takes you from the premise to the conclusion.

But mathematical statements exist within a context that may or may not be true. That context is that 2+2 actually = 4, which assumes that you’re not a SIMS-style algorithm programmed to think that 2+2=4 when a reality of which we’re oblivious says otherwise.     

The statement “if the axioms of plane geometry are true then the angles of a triangle add up to 180 degrees” still doesn’t get you to the internal angles of a triangle adding up to 180 degrees being an absolute truth therefore. It’s “absolutely” true only within the confines of its own conditions and of our ability to understand such things, but it's not necessarily universally true too.     

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However, if you want to ask the question "do the angles of this triangle I have just drawn on a piece of paper add up to 180 degrees?" and I give you the proof, all I've done is reframe the question as "are Euclid's geometry axioms true?" I haven't answered it. You need to do measurements either of the triangle or the axioms and, of course, these are always probabilistic.

And, axiomatically (!), probabilistic statements can’t be absolute. 
« Last Edit: June 26, 2024, 10:51:59 AM by bluehillside Retd. »
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jeremyp

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Re: Searching for GOD...
« Reply #51116 on: June 25, 2024, 12:45:44 PM »
jeremyp,

But still we can’t claim to be “absolute” about anything for the reasons I set out. We can have a qualified “absolute” at best: “X is absolutely true but only inasmuch as human minds are capable of understanding such matters”, but that’s all. 



Yes, but assumptions can be wrong – and so therefore can the conclusions they lead to be wrong.

But mathematical statements exist within a context that may or may not be true. That context is that 2+2 actually = 4, which assumes that you’re not a SIMS-style algorithm programmed to think that 2+2=4 when a reality of which we’re oblivious says otherwise.     

The statement “if the axioms of plane geometry are true then the angles of a triangle add up to 180 degrees” still doesn’t get you to the internal angles of a triangle adding up to 180 degrees being an absolute truth therefore. It’s “absolutely” true only within the confines of its own conditions and of our ability to understand such things, but it's not necessarily universally true too.     

And, axiomatically (!), probabilistic statements can’t be absolute.

No. You are still not getting it. Mathematics doesn't deal with he real world - it deals with imagined worlds in which certain conditions are just assumed to be true. The statement "the internal angles of a triangle add up to 180 degrees under Euclidean plane geometry is absolutely true. There is no doubt. The probabilistic part comes when you want to use mathematics as a tool to describe the real world. Then you do have to ask "are the axioms true in the real world?". You also have to ask if the mathematical operations you are employing are legitimate in the real world. For example, you may choose to model relative speeds from different viewpoints by adding and subtracting speeds, but Einstein told us that normal addition doesn't quite work.

It's nonsensical to say (in the context of pure mathematics) "is this axiom true"? You just define it as true. By calling it an axiom, you are saying "this statement just is true".
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Re: Searching for GOD...
« Reply #51117 on: June 25, 2024, 01:20:39 PM »
But still we can’t claim to be “absolute” about anything for the reasons I set out. We can have a qualified “absolute” at best: “X is absolutely true but only inasmuch as human minds are capable of understanding such matters”, but that’s all.

Since the system is entirely human-made, the idea that we don't understand it is somewhat bizarre. The logic that goes from the axioms to the conclusion is absolutely true because it is pure logic. Unless you reject logic itself, we have an absolute proof.

Yes, but assumptions can be wrong – and so therefore can the conclusions they lead to be wrong.

But mathematical statements exist within a context that may or may not be true. That context is that 2+2 actually = 4, which assumes that you’re not a SIMS-style algorithm programmed to think that 2+2=4 when a reality of which we’re oblivious says otherwise.

This is potentially more interesting. In fact, 2 + 2 = 4 is true by definition. It's truth comes simply from the way we've defined '2', '4', '+', and '='. We've just labelled quantities and the process of addition. Take the quantity of rocks we call 'two', put two more next to them, a process we call 'addition', and you've now got the quantity we call 'four'.

In fact, mathematics goes back and defines the numbers in terms of set theory, so as to make it more formal. My signature (the axiom of infinity from set theory) can be considered as a construction of the natural numbers from nothing but the empty set, but I digress.

What's interesting is that, unlike geometry, we can't fully axiomatise all the true theorems of arithmetic (Gödel's incompleteness theorems).

The statement “if the axioms of plane geometry are true then the angles of a triangle add up to 180 degrees” still doesn’t get you to the internal angles of a triangle adding up to 180 degrees being an absolute truth therefore. It’s “absolutely” true only within the confines of its own conditions and of our ability to understand such things, but it's not necessarily universally true too.

We actually know that Euclidean geometry is a special case, that doesn't, in general, apply to the real world. However, the proof is still absolutely correct.
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bluehillside Retd.

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Re: Searching for GOD...
« Reply #51118 on: June 25, 2024, 01:33:20 PM »
jeremyp,

Quote
No. You are still not getting it. Mathematics doesn't deal with he real world - it deals with imagined worlds in which certain conditions are just assumed to be true. The statement "the internal angles of a triangle add up to 180 degrees under Euclidean plane geometry is absolutely true. There is no doubt. The probabilistic part comes when you want to use mathematics as a tool to describe the real world. Then you do have to ask "are the axioms true in the real world?". You also have to ask if the mathematical operations you are employing are legitimate in the real world. For example, you may choose to model relative speeds from different viewpoints by adding and subtracting speeds, but Einstein told us that normal addition doesn't quite work.

I think I am getting it though. Yes I know that mathematics deals in “imagined worlds”, but still its conclusions are only as reliable as the axioms on which it rests. It gives you “absolute” truths only inasmuch as its axioms are true, which may or may not be the case. This is a highly bounded and delineated (and likely circular too) definition of “absolute” and not necessarily therefore a universal one, which I took to be your original position re “absolute” status.

“Knowledge” isn’t stuff lying about the place – it’s a description of human understanding, with all the risks of bias, mistake, misplaced certainty etc that necessarily entails. To Fred the goldfish, “the universe” is your auntie Mabel’s front parlour – and for all I know Fred is “absolutely” sure about that because that’s the limit of his ability to capture his reality. We’re just Freds with shoes though, and so we’re as limited by our biology as Fred is by his. That’s all I’m saying really.     
 
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It's nonsensical to say (in the context of pure mathematics) "is this axiom true"? You just define it as true. By calling it an axiom, you are saying "this statement just is true".

Yes, and that’s all you can say about it axioms though – which was rather my point. On what basis therefore can we claim “absolute” truths when we will always hit the impenetrable bedrock of those axioms?   
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Re: Searching for GOD...
« Reply #51119 on: June 26, 2024, 09:22:34 AM »
But they are equally as mutually exclusive as each other.
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I look forward to your justification for this
We obviously recoil at the idea of something being both square and circular, but you expect us to just blithely accept 'fully human and fully divine' without blinking an eye.
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I understand perfectly why I recoil at something being both square and circular. I don't understand why you find the same justification covers recoiling at something being both human and divine
and As you say, that's not a 'physical' rule, so God's magical nature to redefine reality to suit doesn't count, it's a logical exclusion. Being divine precludes the limitations that make humanity humanity, you cannot be divine and yet be human, it makes no sense, even if you accept the premise of 'divinity' in the first place.

No, it's an argument that's flawed at pretty much every stage, from the presumption that not all things can be contingent because reasons, through to 'therefore the non-contingent things must be my preferred intelligent uncreated creator which I totally didn't come in to the argument to try to demonstrate at all look at that, how did that happen?'

How does infinite regress disapply reason? Everything we see has a cause. Each of those causes has, so far as we can tell, a cause. Disapplying reason is suddenly deciding, in the absence of any justification, that that sequence has to stop somewhere.
 
By 'unexplained network of contingency' I presume you're talking about the possibility of a cyclic nature to reality? That's just a particular iteration of the infinite regress above. That you don't understand the reason, perhaps, doesn't mean that it's not there.

God willing, obviously.

O.
Cycle of nature occurring in what context?
How does a two dimensional line know it's a circle?

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Re: Searching for GOD...
« Reply #51120 on: June 26, 2024, 09:57:44 AM »
Cycle of nature occurring in what context?

Any. It's not being proposed as a fully fleshed-out theory, it's being noted as a possibility that undermines the assertion that there 'must' be a start point.

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How does a two dimensional line know it's a circle?

Neuroproprioception? That fails to even start to address any of the issues raised.

O.
Universes are forever, not just for creation...

New Atheism - because, apparently, there's a use-by date on unanswered questions.

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bluehillside Retd.

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Re: Searching for GOD...
« Reply #51121 on: June 26, 2024, 10:49:02 AM »
Hi Stranger,

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Since the system is entirely human-made, the idea that we don't understand it is somewhat bizarre. The logic that goes from the axioms to the conclusion is absolutely true because it is pure logic. Unless you reject logic itself, we have an absolute proof.

My point wasn’t about the specifics of any given example; it was a contextual point about claiming “absolute” truth about anything. To be justifiably absolutely certain of something you’d also have to be omniscient, and thereby to be able to rule out any possibility at all of being wrong no matter how inconceivable such a possibility might be. In other words, simply to say, “I can’t imagine how I could be wrong, therefore I’m certainly right” is just a restatement of the argument from incredulity.

I have no problem at all with qualified certainty – “inasmuch as I am capable of understanding truth, X is certainly true” for example – but unqualified certainty seems to me to be overreaching.

One characteristic of paradigm shifts through history by the way is how certain people were about their beliefs before they were overturned – a pre-Copernican astronomer would have been “absolutely” certain that the sun orbited the Earth for example (after all, he actually saw it rise and set every day with his own eyes right?), which makes me chary about claiming “absolute” truth about anything.   

Quote
This is potentially more interesting. In fact, 2 + 2 = 4 is true by definition. It's truth comes simply from the way we've defined '2', '4', '+', and '='. We've just labelled quantities and the process of addition. Take the quantity of rocks we call 'two', put two more next to them, a process we call 'addition', and you've now got the quantity we call 'four'.

In fact, mathematics goes back and defines the numbers in terms of set theory, so as to make it more formal. My signature (the axiom of infinity from set theory) can be considered as a construction of the natural numbers from nothing but the empty set, but I digress.

What's interesting is that, unlike geometry, we can't fully axiomatise all the true theorems of arithmetic (Gödel's incompleteness theorems).

Fascinating stuff, and I defer unhesitatingly to your mathematical wizardry. I still though am stuck on claims of “absolute”, “certain” etc without a method to eliminate even the possibility of being wrong – ie, omniscience.   
« Last Edit: June 26, 2024, 10:53:54 AM by bluehillside Retd. »
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Re: Searching for GOD...
« Reply #51122 on: June 26, 2024, 12:10:31 PM »
Since the system is entirely human-made, the idea that we don't understand it is somewhat bizarre. The logic that goes from the axioms to the conclusion is absolutely true because it is pure logic. Unless you reject logic itself, we have an absolute proof.

Your concept of "pure logic" is entirely derived from perceived premisses.  You need to verify whether certain premisses are entirely valid before you can claim absolute proof.

For example your rejection of the concept of human free will is entirely dependent on the premiss of everything existing and conforming to the time dimension perceived within our material universe.  You ignore the possibility that this universe came into existence from a source outside the time dimension, and that this source would have the power to allow us to override the perceived restrictions of time in order to facilitate the consciously driven freedom we all enjoy.
The truth will set you free  - John 8:32
Truth is not an abstraction, but a person - Edith Stein
Free will, though it makes evil possible, is also the only thing that makes possible any love or goodness or joy worth having. - CS Lewis
Joy is the Gigantic Secret of Christians - GK Chesterton

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Re: Searching for GOD...
« Reply #51123 on: June 26, 2024, 12:19:16 PM »
Fascinating stuff, and I defer unhesitatingly to your mathematical wizardry. I still though am stuck on claims of “absolute”, “certain” etc without a method to eliminate even the possibility of being wrong – ie, omniscience.

I think the point is that if we are dealing with abstractions that we effectively invent, there isn't the uncertainty we necessarily have with the real world. Clearly the natural numbers I mentioned before,  ℕ = {0, 1, 2, 3,...}, have a connection to the real world but they remain abstract and well defined logical concepts. The same goes for the basic operations; addition and multiplication. If we're restricting ourselves to ℕ, then division and subtraction are restricted but also well defined.

Once you are in such an abstract space, we don't have the sort of problems with soundness that we have with the real world, because everything we're dealing with is abstract and well defined. You can also do proofs in ways that are not possible in reality, like rigorous induction.

Often proofs are surprisingly simple. For example, we can say with certainty that every natural umber greater than 1 can be factored into a unique product of prime numbers and that there is no largest prime. The certainty is because it's really rather, simple, basic logic and the entities we are dealing with are well defined and abstract.

What's really fascinating is that this opens up a system so rich and complex, that it cannot be reduced to a complete set of axioms (unlike geometry).
x(∅ ∈ x ∧ ∀y(yxy ∪ {y} ∈ x))

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Re: Searching for GOD...
« Reply #51124 on: June 26, 2024, 12:28:33 PM »
Your concept of "pure logic" is entirely derived from perceived premisses.

  The process of logic is different to premises.

You need to verify whether certain premisses are entirely valid before you can claim absolute proof.

In the context, we are dealing with an abstract formal system. The premises (axioms) are true by definition.

For example your rejection of the concept of human free will is entirely dependent on the premiss of everything existing and conforming to the time dimension perceived within our material universe.

No. It is based on the fact that minds in general, and choices in particular, require time.

You ignore the possibility that this universe came into existence from a source outside the time dimension...

"Coming into existence" also requires time.

...and that this source would have the power to allow us to override the perceived restrictions of time in order to facilitate the consciously driven freedom we all enjoy.

Nonsensical for all the reasons given before and above.    ::)

I see you still haven't been arsed to learn anything about logic and critical thinking....
x(∅ ∈ x ∧ ∀y(yxy ∪ {y} ∈ x))