If small changes have big consequences then it adds a huge amount of uncertainty into all science.
I don't know about "all science", but deterministic nonlinear systems (such as the atmosphere), at any rate.
Because nobody is factoring in the impact of a butterfly into the weather models.
Again, if you look at the scientific record you will see how many different systems are affected by chaos theory. Because natural systems are really complicated.
There are ways to incorporate chaos theory into physics, when you do that to models of natural systems it just adds a huge amount of uncertainty. Because conceptually it means that a factor that nobody has thought of could have a massive impact on the result.
The multitude of variables and interacting factors involved, and their complexity and dynamism, make tick-borne transmission systems beyond (current) human comprehension. That is, perhaps, the main reason for our inability to precisely predict new epidemics of vector-borne diseases in general.
How many axioms does it take to change a lightbulb? (1 dud + 1 working = 2). 379 pages worth.
Got ten thousand hours?
@Martin54 it's Greek to me. And a gentle reminder, I don't have 10k hours to give it or even 100. Or to wade through and decide whether comments amount to thoughtful attempts to work through a thought in a group, or well-developed conclusions based on real knowledge in fields I abandoned at the entry level.
Digits fluttering waste my time. I wonder, if the scientific record has gone platinum yet.
I am more impressed with Russell's willingness, determination and frequent ability to take on skull cracking ideas and systems of thought, even when he didn't always entirely succeed.
Even with Russell on occassion I wonder if we see evidence that reader reception as an essential element of human thinking?
The butterfly effect is really a thought experiment in the philosophy of science, bringing into question whether something as small as a butterfly could influence a tornado. Probably not, but how could we possibly know?
The butterfly effect isn't really a thought experiment - as the wikipedia page explains, it's a poetic description of a chaotic system, in which a small perturbation can have big consequences. The butterfly effect is demonstrable, in the movement of a double pendulum in the example shown in the wikipedia page.
Lorenz originally used a metaphorical sea gull, but was persuaded to change it to a butterfly.
I.e. @pease, no real world effect at all. It's complete BS.
A 1g butterfly generates 0.01 N in 0.1s.
A tornado generates a billion times as much force over 1,000s, so 100,000 times as much in 0.1s. Hmmmm. Who'd have thought a hundred thousand butterflies could do so much damage in a tenth of a second! And if one of them fluttered differently no tornado! Or ten times worse and in the other direction. Well ten using Lorenz' number:
Lorenz' '61 numerical computer model (a million calculation per second at best, more likely about 10,000 order of magnitude (OOM), using transistors, and 1,000 kB OOM of memory, generated completely different weather scenarios from a 'full' precision 0.506127 value compared with a rounded value of 0.506. A difference of 0.000127! Whatever that number is. Butterfly wingbeats? So that butterfly's wing beat is in the ball park!!! Now that computing is a trillion times more powerful, I wonder what the numbers say?
Anyway to summarise my thoughts, I’m essentialist on mathematics, existentialist on human perceptions of reality.
That looks like good news. If 'Essentialism is the view that objects have a set of attributes that are necessary to their identity.' then mathematical objects would seem to have that. It even seems to apply to humans and their essentialist or existentialist perceptions of existential reality.
@kendel, you don't need even a 100 hours, not 1. It's all irrelevant to belief in essence. And aye, Russell was impressive, his protégé Wittgenstein alone shows that.
Ok what’s a better word? The axioms have created a system of mathematics that works. Doesn’t that say something about the axiom?
Kurt Gödel's Incompleteness Theorems are widely regarded to have ended the search for a complete axiomatic system for mathematics. However he distinguished between truth and proof. Just because an axiomatic system has its limitations in providing mathematical proofs, this doesn't mean that mathematics doesn't contain necessary truths. Gödel remained a Platonist regarding mathematical entities until his death.
Distinguishing between truth (called semantics) and proof (called syntax) is common if not universal in modern set theory.
@MPaul:Well that may be but I don’t understand it.” @Martin 54:What may be? That I might understand it?.
Well Mr Sealion ..I am not tempted to engage further.
That's not my surname Mr Soup-Tureen (I see you and raise you). Might one enquire of its provenance?
@KOF: I don’t think one really needs the named person in this scenario to be deluded, just a bunch of other people to put into him their own ideas of what he was about.
Yep, the assumption I make is that Jesus did and said what the gospels state he did and on that basis, CS Lewis is on the money for mine.
A natural assumption. I wonder when Lewis' 1942 formulation of the fallacious trilemma, first published a hundred years before in 1846, will age out?
Even the appalling William Lane Craig agrees.
That so much weight, "the most important argument in Christian apologetics". is still put upon it shows how desperate apologists are.
Only Lane Craig's unnatural Kalaam cosmological argument comes close.
Or did you mean Lewis' bet in some other regard? Did he put his mouth where his money is in actually non-fallacious reasoning based on your assumption?
The butterfly effect isn't really a thought experiment - as the wikipedia page explains, it's a poetic description of a chaotic system, in which a small perturbation can have big consequences. The butterfly effect is demonstrable, in the movement of a double pendulum in the example shown in the wikipedia page.
Lorenz originally used a metaphorical sea gull, but was persuaded to change it to a butterfly.
I.e. @pease, no real world effect at all. It's complete BS.
A 1g butterfly generates 0.01 N in 0.1s.
A tornado generates a billion times as much force over 1,000s, so 100,000 times as much in 0.1s. Hmmmm. Who'd have thought a hundred thousand butterflies could do so much damage in a tenth of a second! And if one of them fluttered differently no tornado! Or ten times worse and in the other direction. Well ten using Lorenz' number:
Lorenz' '61 numerical computer model (a million calculation per second at best, more likely about 10,000 order of magnitude (OOM), using transistors, and 1,000 kB OOM of memory, generated completely different weather scenarios from a 'full' precision 0.506127 value compared with a rounded value of 0.506. A difference of 0.000127! Whatever that number is. Butterfly wingbeats? So that butterfly's wing beat is in the ball park!!! Now that computing is a trillion times more powerful, I wonder what the numbers say?
Thanks - I thought you'd like it.
It led me to wonder if these forums were themselves a chaotic system - whether the choice of a particular word over synonyms in an opening post would, a few pages later, lead to different disagreements between different people.
I am not a robustly independent mathematical Platonist as I can't point to the number one let alone any operation on it in nature. I can point to (a set of) one Biro in my desk, but is it a set of one in itself? Or is that just a referent? And a set of one biro, one pot of chewing gum (unused), one set... of electronic scales, one ruler, one phone. Does that make five? As in beans?
From the Stanford link above,
Robust Independence.
Mathematical objects are metaphysically on a par with ordinary physical objects.
I'm sure they are. What is metaphysics on a par with? The butterfly effect?
If we use lightweight semantic (truth) values,
assumptions can now be stated neutrally as the claim that mathematical singular terms have abstract semantic values
if some lightweight account of semantic values is defensible, we can accept object realism and Counterfactual Independence without committing ourselves to a more robust form of platonism
mathematical objects are ontologically dependent or derivative in a way that distinguishes them from independently existing physical objects... “qualified realism”
So, I'm a mathematical lightweight...
And yes @pease, chaos is in play here. But no handwaving. Is that the essence?
@MPaul:Well that may be but I don’t understand it.” @Martin 54:What may be? That I might understand it?.
Well Mr Sealion ..I am not tempted to engage further.
That's not my surname Mr Soup-Tureen (I see you and raise you). Might one enquire of its provenance?
@KOF: I don’t think one really needs the named person in this scenario to be deluded, just a bunch of other people to put into him their own ideas of what he was about.
Yep, the assumption I make is that Jesus did and said what the gospels state he did and on that basis, CS Lewis is on the money for mine.
A natural assumption. I wonder when Lewis' 1942 formulation of the fallacious trilemma, first published a hundred years before in 1846, will age out?
Even the appalling William Lane Craig agrees.
That so much weight, "the most important argument in Christian apologetics". is still put upon it shows how desperate apologists are.
Only Lane Craig's unnatural Kalaam cosmological argument comes close.
Or did you mean Lewis' bet in some other regard? Did he put his mouth where his money is in actually non-fallacious reasoning based on your assumption?
First, not everyone agrees that it’s fallacious. There is no reason to assume that it will “age out.” Apologists don’t have to be “desperate,” even if you think they/we are wrong about this – if they are wrong, people can be wrong honestly with no desperation at all. The other cosmological argument doesn’t at all seen “unnatural” to me. Is it really necessary to be rude about all of this rather than simply disagree?
@MPaul:Well that may be but I don’t understand it.” @Martin 54:What may be? That I might understand it?.
Well Mr Sealion ..I am not tempted to engage further.
@KOF: I don’t think one really needs the named person in this scenario to be deluded, just a bunch of other people to put into him their own ideas of what he was about.
Yep, the assumption I make is that Jesus did and said what the gospels state he did and on that basis, CS Lewis is on the money for mine.
Well @MPaul. Now that Sealioning (which I had encountered before in my dotage, I just hadn't joined up the dots), I most disappointedly invite you to justify that in Hell. All welcome.
@MPaul:Well that may be but I don’t understand it.” @Martin 54:What may be? That I might understand it?.
Well Mr Sealion ..I am not tempted to engage further.
That's not my surname Mr Soup-Tureen (I see you and raise you). Might one enquire of its provenance?
@KOF: I don’t think one really needs the named person in this scenario to be deluded, just a bunch of other people to put into him their own ideas of what he was about.
Yep, the assumption I make is that Jesus did and said what the gospels state he did and on that basis, CS Lewis is on the money for mine.
A natural assumption. I wonder when Lewis' 1942 formulation of the fallacious trilemma, first published a hundred years before in 1846, will age out?
Even the appalling William Lane Craig agrees.
That so much weight, "the most important argument in Christian apologetics". is still put upon it shows how desperate apologists are.
Only Lane Craig's unnatural Kalaam cosmological argument comes close.
Or did you mean Lewis' bet in some other regard? Did he put his mouth where his money is in actually non-fallacious reasoning based on your assumption?
First, not everyone agrees that it’s fallacious. There is no reason to assume that it will “age out.” Apologists don’t have to be “desperate,” even if you think they/we are wrong about this – if they are wrong, people can be wrong honestly with no desperation at all. The other cosmological argument doesn’t at all seen “unnatural” to me. Is it really necessary to be rude about all of this rather than simply disagree?
First, I know but those who don't can't explain why. I agree it won't age out, as it's been going for at least 180 years. And I'm sure, as always, that you are absolutely right and not all apologists are desperate, especially not in your and @MPaul's cases for two here. That has always been obvious to me. You are both utterly sincere and manifest no desperation whatsoever.
Therefore I apologize for my careless unintendedly universal use 'it shows how desperate apologists are'.
Nonetheless I, like William Lane Craig, find Lewis' trilemma utterly inadequate semantically, just as I find Craig's Kalam apologetic, which ignores the elephant in the room of eternity.
First, I know but those who don't can't explain why.
No. You believe you know, and others can't explain why to your own personal satisfaction. This business of saying you "know" things in discussion/debate is really, really unhelpful. I've said this again and again now, in multiple threads. It's aggressive and counterproductive to any kind of discussion, on any topic, in which two or more people disagree. Could you kindly stop it?
Therefore I apologize for my careless unintendedly universal use 'it shows how desperate apologists are'.
Lorenz' '61 numerical computer model (a million calculation per second at best, more likely about 10,000 order of magnitude (OOM), using transistors, and 1,000 kB OOM of memory, generated completely different weather scenarios from a 'full' precision 0.506127 value compared with a rounded value of 0.506. A difference of 0.000127! Whatever that number is. Butterfly wingbeats? So that butterfly's wing beat is in the ball park!!! Now that computing is a trillion times more powerful, I wonder what the numbers say?
Opinion about the numbers apparently continues to be divided, as referenced by a couple of articles mentioned on the recent debates section of the wikipedia page:
The first kind of butterfly effect, known as SDIC (Sensitive Dependence on Initial Conditions), is widely recognized and demonstrated through idealized chaotic models. However, opinions differ regarding the second kind of butterfly effect, specifically the impact of a butterfly flapping its wings on tornado formation, as indicated in two 2024 articles.
The Butterfly Effect: Can a Butterfly in Brazil Really Cause a Tornado in Texas?
"The length scale where dissipation dominates in the atmosphere is about 0.1 to 10 millimeters" so the flap of a butterfly's wings would dissipate nearly immediately and not be capable of causing a tornado - but they don't say how large the wings need to be to cause one.
The real butterfly effect and maggoty apples
"Even though the Navier–Stokes equations are deterministic, it seems that you cannot make predictions beyond a fixed time horizon, no matter how small the initial uncertainty."
First, I know but those who don't can't explain why.
No. You believe you know, and others can't explain why to your own personal satisfaction. This business of saying you "know" things in discussion/debate is really, really unhelpful. I've said this again and again now, in multiple threads. It's aggressive and counterproductive to any kind of discussion, on any topic, in which two or more people disagree. Could you kindly stop it?
Therefore I apologize for my careless unintendedly universal use 'it shows how desperate apologists are'.
Accepted, and thank you.
What, I believe that I know that, first, not everyone agrees that Lewis' trilemma is fallacious? I can't know that not everyone agrees that Lewis' trilemma is fallacious? But you said it. And it's coherent. So by every reasonable definition of knowing, I know that not everyone agrees that Lewis' trilemma is fallacious. I believe it as a coherent justified true belief, i.e. knowledge, despite not having interviewed everyone who has an opinion on it. So no, I don't, can't reasonably, rationally accept your negation of my knowledge.
And I can't disagree with you over the perfectly reasonable, reasoned falsity of Lewis' trilemma, the falsity of which a noted Christian philosopher agrees with discursively, as you just gainsay it, merely assert the negative, fine.
You're welcome.
@pease, aye, the chain of causality disappears, attenuates in noise.
The Butterfly Effect: Can a Butterfly in Brazil Really Cause a Tornado in Texas?
"The length scale where dissipation dominates in the atmosphere is about 0.1 to 10 millimeters" so the flap of a butterfly's wings would dissipate nearly immediately and not be capable of causing a tornado - but they don't say how large the wings need to be to cause one.
But I thought that the whole idea of the Butterfly Effect was that something minuscule could affect something that would affect something else (and so on) and *eventually* lead to a hurricane, because of Chaos Theory.
First, I know but those who don't can't explain why.
No. You believe you know, and others can't explain why to your own personal satisfaction. This business of saying you "know" things in discussion/debate is really, really unhelpful. I've said this again and again now, in multiple threads. It's aggressive and counterproductive to any kind of discussion, on any topic, in which two or more people disagree. Could you kindly stop it?
Therefore I apologize for my careless unintendedly universal use 'it shows how desperate apologists are'.
Accepted, and thank you.
What, I believe that I know that, first, not everyone agrees that Lewis' trilemma is fallacious? I can't know that not everyone agrees that Lewis' trilemma is fallacious? But you said it. And it's coherent. So by every reasonable definition of knowing, I know that not everyone agrees that Lewis' trilemma is fallacious. I believe it as a coherent justified true belief, i.e. knowledge, despite not having interviewed everyone who has an opinion on it. So no, I don't, can't reasonably, rationally accept your negation of my knowledge.
And I can't disagree with you over the perfectly reasonable, reasoned falsity of Lewis' trilemma, the falsity of which a noted Christian philosopher agrees with discursively, as you just gainsay it, merely assert the negative, fine.
Again, with emphasis emphasized:
This business of saying you "know" things in discussion/debate is really, really unhelpful. I've said this again and again now, in multiple threads. It's aggressive and counterproductive to any kind of discussion, on any topic, in which two or more people disagree. Could you kindly stop it?
Any topic. Not just this one, or theology, or philosophy, or pizza, or Daria. It’s aggressive and rude and basically stops discussion. Please stop it.
The Butterfly Effect: Can a Butterfly in Brazil Really Cause a Tornado in Texas?
"The length scale where dissipation dominates in the atmosphere is about 0.1 to 10 millimeters" so the flap of a butterfly's wings would dissipate nearly immediately and not be capable of causing a tornado - but they don't say how large the wings need to be to cause one.
But I thought that the whole idea of the Butterfly Effect was that something minuscule could affect something that would affect something else (and so on) and *eventually* lead to a hurricane, because of Chaos Theory.
Well possibly. It is just taken to mean that there is something small in a system that may not be well understood but could have big impacts on the overall effects.
When we talk about chaos in natural systems, it means that there is much more variability (or potential variability) within them. Most/much of the time this might make no difference, but the point is that it isn't possible to take account of these factors. And we've seen studies where there are chaotic results, presumably due to factors that science cannot account for.
The Butterfly Effect: Can a Butterfly in Brazil Really Cause a Tornado in Texas?
"The length scale where dissipation dominates in the atmosphere is about 0.1 to 10 millimeters" so the flap of a butterfly's wings would dissipate nearly immediately and not be capable of causing a tornado - but they don't say how large the wings need to be to cause one.
But I thought that the whole idea of the Butterfly Effect was that something minuscule could affect something that would affect something else (and so on) and *eventually* lead to a hurricane, because of Chaos Theory.
Well possibly. It is just taken to mean that there is something small in a system that may not be well understood but could have big impacts on the overall effects.
When we talk about chaos in natural systems, it means that there is much more variability (or potential variability) within them. Most/much of the time this might make no difference, but the point is that it isn't possible to take account of these factors. And we've seen studies where there are chaotic results, presumably due to factors that science cannot account for.
First, I know but those who don't can't explain why.
No. You believe you know, and others can't explain why to your own personal satisfaction. This business of saying you "know" things in discussion/debate is really, really unhelpful. I've said this again and again now, in multiple threads. It's aggressive and counterproductive to any kind of discussion, on any topic, in which two or more people disagree. Could you kindly stop it?
Therefore I apologize for my careless unintendedly universal use 'it shows how desperate apologists are'.
Accepted, and thank you.
What, I believe that I know that, first, not everyone agrees that Lewis' trilemma is fallacious? I can't know that not everyone agrees that Lewis' trilemma is fallacious? But you said it. And it's coherent. So by every reasonable definition of knowing, I know that not everyone agrees that Lewis' trilemma is fallacious. I believe it as a coherent justified true belief, i.e. knowledge, despite not having interviewed everyone who has an opinion on it. So no, I don't, can't reasonably, rationally accept your negation of my knowledge.
And I can't disagree with you over the perfectly reasonable, reasoned falsity of Lewis' trilemma, the falsity of which a noted Christian philosopher agrees with discursively, as you just gainsay it, merely assert the negative, fine.
Again, with emphasis emphasized:
This business of saying you "know" things in discussion/debate is really, really unhelpful. I've said this again and again now, in multiple threads. It's aggressive and counterproductive to any kind of discussion, on any topic, in which two or more people disagree. Could you kindly stop it?
Any topic. Not just this one, or theology, or philosophy, or pizza, or Daria. It’s aggressive and rude and basically stops discussion. Please stop it.
Don't worry @ChastMastr. I will never interact with you again directly here, unless you invite it, and even then.
First, I know but those who don't can't explain why.
No. You believe you know, and others can't explain why to your own personal satisfaction. This business of saying you "know" things in discussion/debate is really, really unhelpful. I've said this again and again now, in multiple threads. It's aggressive and counterproductive to any kind of discussion, on any topic, in which two or more people disagree. Could you kindly stop it?
Therefore I apologize for my careless unintendedly universal use 'it shows how desperate apologists are'.
Accepted, and thank you.
What, I believe that I know that, first, not everyone agrees that Lewis' trilemma is fallacious? I can't know that not everyone agrees that Lewis' trilemma is fallacious? But you said it. And it's coherent. So by every reasonable definition of knowing, I know that not everyone agrees that Lewis' trilemma is fallacious. I believe it as a coherent justified true belief, i.e. knowledge, despite not having interviewed everyone who has an opinion on it. So no, I don't, can't reasonably, rationally accept your negation of my knowledge.
And I can't disagree with you over the perfectly reasonable, reasoned falsity of Lewis' trilemma, the falsity of which a noted Christian philosopher agrees with discursively, as you just gainsay it, merely assert the negative, fine.
Again, with emphasis emphasized:
This business of saying you "know" things in discussion/debate is really, really unhelpful. I've said this again and again now, in multiple threads. It's aggressive and counterproductive to any kind of discussion, on any topic, in which two or more people disagree. Could you kindly stop it?
Any topic. Not just this one, or theology, or philosophy, or pizza, or Daria. It’s aggressive and rude and basically stops discussion. Please stop it.
Don't worry @ChastMastr. I will never interact with you again directly here, unless you invite it, and even then.
@Martin54 ... Similar past exchanges haven't ended well for either party. I for one am not keen to see a repeat.
Please remind yourself of the extra guidelines you're working to, particularly this:
The extended ground rules will now include all other aspects of your interactions with other Shipmates. This includes statements where you appear to know something for certain and then don't appear to engage constructively with others when they ask for how you reach your conclusions, or have differing views.
Just to be completely clear: this is not you "losing a life".
@Martin54 ... Similar past exchanges haven't ended well for either party. I for one am not keen to see a repeat.
Please remind yourself of the extra guidelines you're working to, particularly this:
The extended ground rules will now include all other aspects of your interactions with other Shipmates. This includes statements where you appear to know something for certain and then don't appear to engage constructively with others when they ask for how you reach your conclusions, or have differing views.
Just to be completely clear: this is not you "losing a life".
[/friendly shipmate comment]
Just a note— I’ve taken my further comments on Martin’s posting style to the Hell thread, rather than clutter up this one further.
@Martin54 ... Similar past exchanges haven't ended well for either party. I for one am not keen to see a repeat.
Please remind yourself of the extra guidelines you're working to, particularly this:
The extended ground rules will now include all other aspects of your interactions with other Shipmates. This includes statements where you appear to know something for certain and then don't appear to engage constructively with others when they ask for how you reach your conclusions, or have differing views.
Just to be completely clear: this is not you "losing a life".
[/friendly shipmate comment]
Thank you @Nenya. I always try and engage constructively with others when they ask for how I reach my conclusions, but I do see the subtlety in engaging constructively with others when they have differing views, hence my withdrawing from any purely negating views, where how how I reach my conclusions isn't asked.
The Butterfly Effect: Can a Butterfly in Brazil Really Cause a Tornado in Texas?
"The length scale where dissipation dominates in the atmosphere is about 0.1 to 10 millimeters" so the flap of a butterfly's wings would dissipate nearly immediately and not be capable of causing a tornado - but they don't say how large the wings need to be to cause one.
But I thought that the whole idea of the Butterfly Effect was that something minuscule could affect something that would affect something else (and so on) and *eventually* lead to a hurricane, because of Chaos Theory.
That's my understanding too. Not that the butterfly directly causes the tornado, but that it forms part of the chain of causation that ultimately results in the tornado* - and if it hadn't flapped its wings at that time then the chain of causality would have been radically different to the extent that the tornado didn't happen.
The Butterfly Effect: Can a Butterfly in Brazil Really Cause a Tornado in Texas?
"The length scale where dissipation dominates in the atmosphere is about 0.1 to 10 millimeters" so the flap of a butterfly's wings would dissipate nearly immediately and not be capable of causing a tornado - but they don't say how large the wings need to be to cause one.
But I thought that the whole idea of the Butterfly Effect was that something minuscule could affect something that would affect something else (and so on) and *eventually* lead to a hurricane, because of Chaos Theory.
That's my understanding too. Not that the butterfly directly causes the tornado, but that it forms part of the chain of causation that ultimately results in the tornado* - and if it hadn't flapped its wings at that time then the chain of causality would have been radically different to the extent that the tornado didn't happen.
@pease' quote about length scale shows that the chain of causation sinks to noise in millimetres. As it must for the other billions of butterflies' flutters.
Mathematically, I have nearly no mass.
However there are some interesting things here, I think I can say something brief about in hopes that a mathematical heavyweight can say more and better.
I feel there must be a branch of mathematics that studies axioms.
From this discussion, it seems there is, must be. And that that branch would subdivide into various branches of mathematics. Perhaps the axioms are normally handled only within the branch of mathematics to which they apply, though. That would be a shame, because I think it would add to the confusion that mathematics (like "Science") is like a single chemical compound.
I too am a mathematical Platonist - the proof that no axiomatic system can be complete is phrased in terms that presuppose that mathematical truths exist - but I think mathematical entities are a lot more complicated than just collections of true propositions.
Yes, and that bolded statement describes much of the recent parts of this discussion, although the individual entities are brushed over with the single word "mathematics." @Martin54 gets at a few of them below:
I am not a robustly independent mathematical Platonist as I can't point to the number one let alone any operation on it in nature. I can point to (a set of) one Biro in my desk, but is it a set of one in itself? Or is that just a referent? And a set of one biro, one pot of chewing gum (unused), one set... of electronic scales, one ruler, one phone. Does that make five? As in beans?
The concept of the thing, and the language we use to describe the concept or thing, are not the same as the thing itself. I used to count the busses with my youngest going into and out of preschool. She was learning not only the words and order of the ordinal numbers but also the correspondence between the thing that was a bus that we could name ("bus") and count. There was no intrinsic oneness or twoness, or firstness or secondness to the first or second busses that we counted. And later, different busses might be there that we count first and second.
There was no intrinsic oneness or twoness, neither Einheit or Zweiheit. Or "busness" rather than "Autobusheit".
The words were different from the concepts, which were different from the buses themselves. And there could be no realistic, permanent agreement on the order any particular bus would be counted on any particular day, as some had not yet returned to the lot. Although that we called a bus a bus is by cultural agreement.
We haven't even gotten to doing anything with those numbers or busses.
So, yes. There's a lot more to math than a single, simple thing. I don't know if platonism in one area is transferable to another.
As far as I understand the term mathematical Platonism, which to be clear I had never heard before this thread despite spending time with mathematicians, it involves believing that mathematical concepts and truths exist out there somewhere and that humans discover new things about it.
Platonism because it operates in a similar way to platonic forms.
So it isn't about language and notation and whatnot. That there actually is something intrinsic about twoness and everything else.
Other philosophical views about mathematics exist, but for me, I'm inclined to believe it is Platonic, to the extent that I'm inclined to think of it in the kind of way some of you talk about God.
I feel there must be a branch of mathematics that studies axioms.
That would be a branch of philosophy, called epistemology. Mathematics doesn't study mathematics. Or to put it another way, metamathematics is not a branch of mathematics, it is a branch of philosophy.
I feel there must be a branch of mathematics that studies axioms.
That would be a branch of philosophy, called epistemology. Mathematics doesn't study mathematics. Or to put it another way, metamathematics is not a branch of mathematics, it is a branch of philosophy.
I think you’ll appreciate this song by Tom Lehrer—not “New Math,” but another one!
I feel there must be a branch of mathematics that studies axioms.
That would be a branch of philosophy, called epistemology. Mathematics doesn't study mathematics. Or to put it another way, metamathematics is not a branch of mathematics, it is a branch of philosophy.
Actually I since looked it up and the branch of mathematics that studies axioms and the general structure of axiomatic systems is called algebra, or abstract algebra to distinguish it from elementary algebra.
(From a mathematical standpoint how we know which axiomatic systems apply to the real world isn't an interesting question. That's for physicists to work out.)
There is quite a lot of material on the foundations of mathematics. I could, but won't, list the few works on my shelves, and the extensive bibliographies in those books.
But "Introduction to the Foundations of Mathematics" by Wilder might be a start.
I feel there must be a branch of mathematics that studies axioms.
From this discussion, it seems there is, must be. And that that branch would subdivide into various branches of mathematics. Perhaps the axioms are normally handled only within the branch of mathematics to which they apply, though. That would be a shame, because I think it would add to the confusion that mathematics (like "Science") is like a single chemical compound.
As the wikipedia page points out, the definition of "axiom" varies:
The precise definition varies across fields of study. In classic philosophy, an axiom is a statement that is so evident or well-established, that it is accepted without controversy or question. In modern logic, an axiom is a premise or starting point for reasoning.
In mathematics, an axiom may be a "logical axiom" or a "non-logical axiom". Logical axioms are taken to be true within the system of logic they define and are often shown in symbolic form (e.g., (A and B) implies A), while non-logical axioms are substantive assertions about the elements of the domain of a specific mathematical theory, for example a + 0 = a in integer arithmetic.
Putting it another way, the frame of reference matters.
Comments
Again, if you look at the scientific record you will see how many different systems are affected by chaos theory. Because natural systems are really complicated.
There are ways to incorporate chaos theory into physics, when you do that to models of natural systems it just adds a huge amount of uncertainty. Because conceptually it means that a factor that nobody has thought of could have a massive impact on the result.
Climate change, biodiversity, ticks and tick-borne diseases: The butterfly effect https://www.sciencedirect.com/science/article/pii/S2213224415300067
@Martin54 it's Greek to me. And a gentle reminder, I don't have 10k hours to give it or even 100. Or to wade through and decide whether comments amount to thoughtful attempts to work through a thought in a group, or well-developed conclusions based on real knowledge in fields I abandoned at the entry level.
Digits fluttering waste my time. I wonder, if the scientific record has gone platinum yet.
I am more impressed with Russell's willingness, determination and frequent ability to take on skull cracking ideas and systems of thought, even when he didn't always entirely succeed.
Even with Russell on occassion I wonder if we see evidence that reader reception as an essential element of human thinking?
I.e. @pease, no real world effect at all. It's complete BS.
A 1g butterfly generates 0.01 N in 0.1s.
A tornado generates a billion times as much force over 1,000s, so 100,000 times as much in 0.1s. Hmmmm. Who'd have thought a hundred thousand butterflies could do so much damage in a tenth of a second! And if one of them fluttered differently no tornado! Or ten times worse and in the other direction. Well ten using Lorenz' number:
Lorenz' '61 numerical computer model (a million calculation per second at best, more likely about 10,000 order of magnitude (OOM), using transistors, and 1,000 kB OOM of memory, generated completely different weather scenarios from a 'full' precision 0.506127 value compared with a rounded value of 0.506. A difference of 0.000127! Whatever that number is. Butterfly wingbeats? So that butterfly's wing beat is in the ball park!!! Now that computing is a trillion times more powerful, I wonder what the numbers say?
That looks like good news. If 'Essentialism is the view that objects have a set of attributes that are necessary to their identity.' then mathematical objects would seem to have that. It even seems to apply to humans and their essentialist or existentialist perceptions of existential reality.
@kendel, you don't need even a 100 hours, not 1. It's all irrelevant to belief in essence. And aye, Russell was impressive, his protégé Wittgenstein alone shows that.
"well-chosen"
Distinguishing between truth (called semantics) and proof (called syntax) is common if not universal in modern set theory.
A natural assumption. I wonder when Lewis' 1942 formulation of the fallacious trilemma, first published a hundred years before in 1846, will age out?
Even the appalling William Lane Craig agrees.
That so much weight, "the most important argument in Christian apologetics". is still put upon it shows how desperate apologists are.
Only Lane Craig's unnatural Kalaam cosmological argument comes close.
Or did you mean Lewis' bet in some other regard? Did he put his mouth where his money is in actually non-fallacious reasoning based on your assumption?
It led me to wonder if these forums were themselves a chaotic system - whether the choice of a particular word over synonyms in an opening post would, a few pages later, lead to different disagreements between different people.
From the Stanford link above,
I'm sure they are. What is metaphysics on a par with? The butterfly effect?
If we use lightweight semantic (truth) values,
So, I'm a mathematical lightweight...
And yes @pease, chaos is in play here. But no handwaving. Is that the essence?
@KoF, @Martin54, this is getting unduly personal. Take it to hell or stop the name calling please.
Hostly beret off
la vie en rouge, Purgatory host
I think we failed to include here @MPaul
Doublethink, Admin
First, not everyone agrees that it’s fallacious. There is no reason to assume that it will “age out.” Apologists don’t have to be “desperate,” even if you think they/we are wrong about this – if they are wrong, people can be wrong honestly with no desperation at all. The other cosmological argument doesn’t at all seen “unnatural” to me. Is it really necessary to be rude about all of this rather than simply disagree?
Well @MPaul. Now that Sealioning (which I had encountered before in my dotage, I just hadn't joined up the dots), I most disappointedly invite you to justify that in Hell. All welcome.
First, I know but those who don't can't explain why. I agree it won't age out, as it's been going for at least 180 years. And I'm sure, as always, that you are absolutely right and not all apologists are desperate, especially not in your and @MPaul's cases for two here. That has always been obvious to me. You are both utterly sincere and manifest no desperation whatsoever.
Therefore I apologize for my careless unintendedly universal use 'it shows how desperate apologists are'.
Nonetheless I, like William Lane Craig, find Lewis' trilemma utterly inadequate semantically, just as I find Craig's Kalam apologetic, which ignores the elephant in the room of eternity.
No. You believe you know, and others can't explain why to your own personal satisfaction. This business of saying you "know" things in discussion/debate is really, really unhelpful. I've said this again and again now, in multiple threads. It's aggressive and counterproductive to any kind of discussion, on any topic, in which two or more people disagree. Could you kindly stop it?
Accepted, and thank you.
"The length scale where dissipation dominates in the atmosphere is about 0.1 to 10 millimeters" so the flap of a butterfly's wings would dissipate nearly immediately and not be capable of causing a tornado - but they don't say how large the wings need to be to cause one.
The real butterfly effect and maggoty apples
"Even though the Navier–Stokes equations are deterministic, it seems that you cannot make predictions beyond a fixed time horizon, no matter how small the initial uncertainty."
Ah - chaotic essentialism - why stop at science?
A tiny tiny amount can mess up an ecosystem.
So how do you model that?
What, I believe that I know that, first, not everyone agrees that Lewis' trilemma is fallacious? I can't know that not everyone agrees that Lewis' trilemma is fallacious? But you said it. And it's coherent. So by every reasonable definition of knowing, I know that not everyone agrees that Lewis' trilemma is fallacious. I believe it as a coherent justified true belief, i.e. knowledge, despite not having interviewed everyone who has an opinion on it. So no, I don't, can't reasonably, rationally accept your negation of my knowledge.
And I can't disagree with you over the perfectly reasonable, reasoned falsity of Lewis' trilemma, the falsity of which a noted Christian philosopher agrees with discursively, as you just gainsay it, merely assert the negative, fine.
You're welcome.
@pease, aye, the chain of causality disappears, attenuates in noise.
So … Mothra, then?
https://youtu.be/g5qMaTgb4cg?si=HaZEt7Tpx-Tb21u7
But I thought that the whole idea of the Butterfly Effect was that something minuscule could affect something that would affect something else (and so on) and *eventually* lead to a hurricane, because of Chaos Theory.
Again, with emphasis emphasized:
This business of saying you "know" things in discussion/debate is really, really unhelpful. I've said this again and again now, in multiple threads. It's aggressive and counterproductive to any kind of discussion, on any topic, in which two or more people disagree. Could you kindly stop it?
Any topic. Not just this one, or theology, or philosophy, or pizza, or Daria. It’s aggressive and rude and basically stops discussion. Please stop it.
Well possibly. It is just taken to mean that there is something small in a system that may not be well understood but could have big impacts on the overall effects.
When we talk about chaos in natural systems, it means that there is much more variability (or potential variability) within them. Most/much of the time this might make no difference, but the point is that it isn't possible to take account of these factors. And we've seen studies where there are chaotic results, presumably due to factors that science cannot account for.
That makes sense.
Don't worry @ChastMastr. I will never interact with you again directly here, unless you invite it, and even then.
I’m not asking for that. Please see above.
@Martin54 ... Similar past exchanges haven't ended well for either party. I for one am not keen to see a repeat.
Please remind yourself of the extra guidelines you're working to, particularly this:
Just to be completely clear: this is not you "losing a life".
[/friendly shipmate comment]
Just a note— I’ve taken my further comments on Martin’s posting style to the Hell thread, rather than clutter up this one further.
Thank you @Nenya. I always try and engage constructively with others when they ask for how I reach my conclusions, but I do see the subtlety in engaging constructively with others when they have differing views, hence my withdrawing from any purely negating views, where how how I reach my conclusions isn't asked.
That's my understanding too. Not that the butterfly directly causes the tornado, but that it forms part of the chain of causation that ultimately results in the tornado* - and if it hadn't flapped its wings at that time then the chain of causality would have been radically different to the extent that the tornado didn't happen.
.
*= A bit like how you could demolish the Empire State Building simply by knocking over a domino that's 5mm high.
@pease' quote about length scale shows that the chain of causation sinks to noise in millimetres. As it must for the other billions of butterflies' flutters.
However there are some interesting things here, I think I can say something brief about in hopes that a mathematical heavyweight can say more and better. From this discussion, it seems there is, must be. And that that branch would subdivide into various branches of mathematics. Perhaps the axioms are normally handled only within the branch of mathematics to which they apply, though. That would be a shame, because I think it would add to the confusion that mathematics (like "Science") is like a single chemical compound. Yes, and that bolded statement describes much of the recent parts of this discussion, although the individual entities are brushed over with the single word "mathematics." @Martin54 gets at a few of them below: The concept of the thing, and the language we use to describe the concept or thing, are not the same as the thing itself. I used to count the busses with my youngest going into and out of preschool. She was learning not only the words and order of the ordinal numbers but also the correspondence between the thing that was a bus that we could name ("bus") and count. There was no intrinsic oneness or twoness, or firstness or secondness to the first or second busses that we counted. And later, different busses might be there that we count first and second.
There was no intrinsic oneness or twoness, neither Einheit or Zweiheit. Or "busness" rather than "Autobusheit".
The words were different from the concepts, which were different from the buses themselves. And there could be no realistic, permanent agreement on the order any particular bus would be counted on any particular day, as some had not yet returned to the lot. Although that we called a bus a bus is by cultural agreement.
We haven't even gotten to doing anything with those numbers or busses.
So, yes. There's a lot more to math than a single, simple thing. I don't know if platonism in one area is transferable to another.
Platonism because it operates in a similar way to platonic forms.
So it isn't about language and notation and whatnot. That there actually is something intrinsic about twoness and everything else.
Other philosophical views about mathematics exist, but for me, I'm inclined to believe it is Platonic, to the extent that I'm inclined to think of it in the kind of way some of you talk about God.
That would be a branch of philosophy, called epistemology. Mathematics doesn't study mathematics. Or to put it another way, metamathematics is not a branch of mathematics, it is a branch of philosophy.
I think you’ll appreciate this song by Tom Lehrer—not “New Math,” but another one!
https://youtu.be/2VZbWJIndlQ?si=x0eMt02wlAx1oEJe
(From a mathematical standpoint how we know which axiomatic systems apply to the real world isn't an interesting question. That's for physicists to work out.)
But "Introduction to the Foundations of Mathematics" by Wilder might be a start.