Debarra

Jasnah and maths

36 posts in this topic

1 minute ago, Oltux72 said:

But aren't we picking the assumptions because they fit (or you would say create) a model that works?

Historically speaking people calculated orbits, described electromagnetism mathematically or did calculus before they did a rigorous definition of the underlying assumptions, didn't they?

The example I am thinking of that illustrates my point is pretty mathy and much less physics-y. Yes, of course, in that situation you describe, you're doing an application problem and so you want it to apply to observations. But hey in pure math land, we don't need anything to apply to anything (though eventually results could be useful potentially)! Maybe some real observation can motivate things though.

The example that crystallized this for me in grad school was the idea of uniform convergence. The problem comes when you have an infinite sequence of functions. How do you define what the limit of that sequence of functions is? The most natural way to define it--which is to just do the limit at each point--has some serious problems. So the way it goes is, "hmmm... The normal way we would define this limit doesn't have the property we want. So what condition do I need to write so that the limit of this sequence does have the properties we want?" (For the math people, the properties we want are that if every function in the sequence is differentiable, we want the limit to also be differentiable. Pointwise convergence doesn't do that, actually.) So what happens is people create this notion of "uniform convergence" that is a bit of a different way to talk about what it means to be a limit of a sequence of functions. If the sequence converges in that way, then ta-da! The limit of the sequence has what we want.

You could argue that the notion of uniform convergence always existed in the abstract, but to me, it really seems like a very practical thing that humans created. Our first instinct didn't work, so we created a new condition that if the sequence has that, then we get the stuff we want in the end. I am not a professional mathematician, so that means as my profession goes, I'm not creating new math as a job. But, my master's committee chair (who was a brilliant old man who was sharp all the time, and really, truly knew math, how it worked, and how to teach it) very persuasively argued that this is a thing that humans are creating, when we are actually performing math and producing new results. Really, I am just repeating his argument and probably explaining it more poorly :) Separate from the philosophical matter at hand, this seems like a far more practical way to talk about how math is actually done. If you're a Ph.D. student in pure math, your thesis is literally to create a new mathematical result that no one has ever done (that we know of, of course). It's an act of creation. It is logic incarnate, and is dang cool that humans have created such elaborate, crazy things. To me, it is genuinely incredible that humans have been able to create very real truth, that once we have proven that theorem, it doesn't matter if we all die. It is true forever!

Again, applied math is quite different, where the goal is to create a mathematical model to deal with the data at hand. But hey, if we are talking about fundamental mathematics and if math is created or discovered, we have to talk about this from the pure math perspective. Get that "observation" and "data" out of here! 

Anyway, I don't know if this very long digression is actually answering the question at hand, but I hope this was interesting to read even if you disagree! 

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15 minutes ago, Chaos said:

The example that crystallized this for me in grad school was the idea of uniform convergence. The problem comes when you have an infinite sequence of functions. How do you define what the limit of that sequence of functions is? The most natural way to define it--which is to just do the limit at each point--has some serious problems. So the way it goes is, "hmmm... The normal way we would define this limit doesn't have the property we want. So what condition do I need to write so that the limit of this sequence does have the properties we want?" (For the math people, the properties we want are that if every function in the sequence is differentiable, we want the limit to also be differentiable. Pointwise convergence doesn't do that, actually.) So what happens is people create this notion of "uniform convergence" that is a bit of a different way to talk about what it means to be a limit of a sequence of functions. If the sequence converges in that way, then ta-da! The limit of the sequence has what we want.

OK, now I am a bit confused. You are talking about definitions, right? As far as I understood it, a definition cannot be right or wrong. At worst you can have one that contradicts itself, thence there can be no example of meeting that definition, but even so it is not, strictly speaking wrong. Did I get that correctly so far?
I would say the pure math in the sense relevant to this post is when you prove properties arising from your definitions.
Hence whenever you use a definition in a proof you strictly speaking limit the proof to the cases the definition applies, don't you?

The big question seems to be whether the properties always exist or whether the properties are consequences of something. Definitions are basically fiction. They exist as information, but they are not in that sense real, while they are real in another sense.

15 minutes ago, Chaos said:

You could argue that the notion of uniform convergence always existed in the abstract, but to me, it really seems like a very practical thing that humans created. Our first instinct didn't work, so we created a new condition that if the sequence has that, then we get the stuff we want in the end. I am not a professional mathematician, so that means as my profession goes, I'm not creating new math as a job. But, my master's committee chair (who was a brilliant old man who was sharp all the time, and really, truly knew math, how it worked, and how to teach it) very persuasively argued that this is a thing that humans are creating, when we are actually performing math and producing new results. Really, I am just repeating his argument and probably explaining it more poorly :) Separate from the philosophical matter at hand, this seems like a far more practical way to talk about how math is actually done. If you're a Ph.D. student in pure math, your thesis is literally to create a new mathematical result that no one has ever done (that we know of, of course). It's an act of creation. It is logic incarnate, and is dang cool that humans have created such elaborate, crazy things. To me, it is genuinely incredible that humans have been able to create very real truth, that once we have proven that theorem, it doesn't matter if we all die. It is true forever!

Well, if I put my strictly formalist hat on, I would have to say that it is true as long as the axioms are true.

15 minutes ago, Chaos said:

Again, applied math is quite different, where the goal is to create a mathematical model to deal with the data at hand. But hey, if we are talking about fundamental mathematics and if math is created or discovered, we have to talk about this from the pure math perspective. Get that "observation" and "data" out of here! 

Anyway, I don't know if this very long digression is actually answering the question at hand, but I hope this was interesting to read even if you disagree! 

It is interesting. The problem is that I am confused to whether it is relevant. And possibly Jasnah was misleading in that example.
If you had a bag of marbles and you took one out, you have reduced the maximum number of times you can get another whole marble out without refilling. That is the implication of Jasnah's statement, as far as I can tell. But is that mathematics or an experimental result?
Can you come up with a consistent arithmetic where that is not the case? In fact I am not sure we are not arguing about semantics here because we are failing to clearly distinguish between truth and consistency.

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4 hours ago, Oltux72 said:

The big question seems to be whether the properties always exist or whether the properties are consequences of something. Definitions are basically fiction. They exist as information, but they are not in that sense real, while they are real in another sense.

That is why, (and hopefully I am not putting words in anyone's mouth) Chaos said math is about the "how", not the "why". Math and science explains how a baseball travels from the pitcher' hand to the catcher's glove. When it is asked what created math or what is math a consequence of, that posits the assumption that math needs one, and that is what then opens up the argument to what is a "source" that math could derive from. At least that is my understanding. Not saying that to reargue any prior points. 

edit: just in case, the how and the why is what I believe Chaos is saying. Not the part that asks what causes math. 

edit2: just in case of the just in case. By saying what created math, that implies there was a point where math did not function as it does. That it did not function at all. That something had to put the function into place. But math is explaining the how of the thing. To understand how something works. It is not telling the thing how it should work. Basically even if we erased the written math, and the individuals who know the concepts, the thing still functions the way it functions. Maybe that helps? 

Edited by Pathfinder
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From what I have seen so far, I think here would be a good place to mention that the idea we associate with "cause" is actually four separate ideas.  Aristotle came up with a set of definitions for each of them, available at https://en.wikipedia.org/wiki/Four_causes.

In summary, the "cause" can be any of what the thing is supposed to be, what the thing is made out of, what the thing is supposed to do, or what it is that resulted in the thing existing.  For example, the causes of a table are the idea of what a table is (flat surface supported by legs, should be strong enough to put things on), the wood that a table is made out of, holding things (why else would one make a table?), or the carpenter who made the table out of wood.  All four of these can be a cause to the table.  Conflating the various ideas of cause can often lead to confusion, leading to something like the Fallacy of Four Terms (https://en.wikipedia.org/wiki/Fallacy_of_four_terms).  As an example of this confusion, I give the following:

Rock is produced by geological events, such as the cooling of magma or the compression of sand.

Rock is a popular type of music.

Geological events can produce popular music.

This claim is obviously wrong, and for the obvious reason that "Rock" means two different things here.  Many of the earlier posts on this thread have fallen into the same trap, because we are not used to something as fundamental as a cause having multiple answers.  The results, as seen, can be as bewildering and upsetting as if I had turned to my friend to talk about the train that just went past, only for him to insist that there was no train, only a pair of sheep.  Suddenly, even the obvious is disputed.

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This doesn't directly relate to math (it does, just not directly), but it does directly relate to the scene in the OP. I think a very important thing to be cognizant of when discussing Jasnah's belief system is that while her conclusions do follow from her premises, they're not the only way one could go given those premises. Before we get to math, let's first exemplify with a more (in my opinion) straightforward example, from this quote:

Quote

'Well I simply claim that morality and human will are independent of him too.'

So, let's talk morality. Just like Jasnah, I am an atheist utilitarian. Importantly though, my atheism has nothing to do with my utilitarianism. I was a utilitarian even when I WAS religious. I wasn't a divine command theorist, I was a religious utilitarian. This is an unironic position one can hold in ethics, and was held at certain times by *religious* theologians and philosophers. What it basically boils down to is considering the Euthyphro dilemma ("Do the gods love good action because it is good, or is good action good because it is loved by the gods?" ) and fully biting the bullet that yes, it IS the former. That yes, something is moral independently of God (in other words, that God is not the truthmaker for moral propositions). But that doesn't mean God isn't great.

Here's why God is still great (from the religious utilitarian viewpoint). Even if the truthmaker for whether an action or a moral prescription is moral is its consequences, rather than God, there is only one being without epistemic limits. And that's God. God is the only being who has all the information, all the context, and perfect future sight to follow the butterfly effect down the road. God is the only omniscient, so even if we could determine/discover/deduce moral codes independently of Him, we can't ever do it as well as He can. So, instrumentally speaking, as long as we assume that God IS benevolent, it is still the right thing to obey God's Commands, to do what God says is good, because whether or not he is strictly speaking the source of morality, he is still uniquely qualified to issue Commands, qua omniscience. Ergo, God is still great.

Here's how this forays into math. Even if math *transcends* God, even if math has the same theorems and axioms and all that good jazz in all possible worlds, and as such could not have been otherwise in the actual world, no matter how God designed the actual world (basically, that math is empirically unbound), God is still great, because he is the repository of all mathematical knowledge, we can't do as well orbetter than taking His word when it comes to mathematical truths irrespective of Him being the truthmaker there or not. So God is still "mathematically great".

For an interesting read, here is a paper published by a Christian philosopher defending the idea that logic transcends God. (Yes, I know that logic is not the same thing as math, we've had quite a bit of development in philosophy of math since Frege, and that in many ways the position that logic transcends God is "easier to defend" than the position that math transcends God, but it's still, I feel, a topical read.)

https://www.tandfonline.com/doi/pdf/10.1080/15665399.2003.10819775

TL;DR: While I do think that Jasnah's atheism informs/influences her perspective on the relationship between abstract truths and divinity, her perspective on the relationship between abstract truths and divinity is NOT reliant on or conducive to atheism.

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On 1/15/2022 at 11:23 PM, CryoZenith said:

This doesn't directly relate to math (it does, just not directly), but it does directly relate to the scene in the OP. I think a very important thing to be cognizant of when discussing Jasnah's belief system is that while her conclusions do follow from her premises, they're not the only way one could go given those premises. Before we get to math, let's first exemplify with a more (in my opinion) straightforward example, from this quote:

So, let's talk morality. Just like Jasnah, I am an atheist utilitarian. Importantly though, my atheism has nothing to do with my utilitarianism. I was a utilitarian even when I WAS religious. I wasn't a divine command theorist, I was a religious utilitarian. This is an unironic position one can hold in ethics, and was held at certain times by *religious* theologians and philosophers. What it basically boils down to is considering the Euthyphro dilemma ("Do the gods love good action because it is good, or is good action good because it is loved by the gods?" ) and fully biting the bullet that yes, it IS the former. That yes, something is moral independently of God (in other words, that God is not the truthmaker for moral propositions). But that doesn't mean God isn't great.

Here's why God is still great (from the religious utilitarian viewpoint). Even if the truthmaker for whether an action or a moral prescription is moral is its consequences, rather than God, there is only one being without epistemic limits. And that's God. God is the only being who has all the information, all the context, and perfect future sight to follow the butterfly effect down the road. God is the only omniscient, so even if we could determine/discover/deduce moral codes independently of Him, we can't ever do it as well as He can. So, instrumentally speaking, as long as we assume that God IS benevolent, it is still the right thing to obey God's Commands, to do what God says is good, because whether or not he is strictly speaking the source of morality, he is still uniquely qualified to issue Commands, qua omniscience. Ergo, God is still great.

Here's how this forays into math. Even if math *transcends* God, even if math has the same theorems and axioms and all that good jazz in all possible worlds, and as such could not have been otherwise in the actual world, no matter how God designed the actual world (basically, that math is empirically unbound), God is still great, because he is the repository of all mathematical knowledge, we can't do as well or better than taking His word when it comes to mathematical truths irrespective of Him being the truthmaker there or not. So God is still "mathematically great".

For an interesting read, here is a paper published by a Christian philosopher defending the idea that logic transcends God. (Yes, I know that logic is not the same thing as math, we've had quite a bit of development in philosophy of math since Frege, and that in many ways the position that logic transcends God is "easier to defend" than the position that math transcends God, but it's still, I feel, a topical read.)

https://www.tandfonline.com/doi/pdf/10.1080/15665399.2003.10819775

TL;DR: While I do think that Jasnah's atheism informs/influences her perspective on the relationship between abstract truths and divinity, her perspective on the relationship between abstract truths and divinity is NOT reliant on or conducive to atheism.

I guess where I keep getting confused regarding this thread, is I thought the purpose of it was to better understand where Jasnah (as an atheist and utilitarian) is coming from and what are her arguments. Taravangian was the one that replied that if a deity was not the source of/force of which they depended on (math, morality, and human will), then that deity served no purpose. Taravangian was the one that felt that if that was the case (math, morality, and human will existing separate from a deity), then the deity's purpose of existing ceased. Jasnah replied based on that reasoning, it would indeed in that light, remove the necessity of a deity.

Now for a religious utilitarian as the one you used in your example, it would make perfect sense to start on the premise that there does in fact exist an entity with perfect knowledge. Then building on that premise, everything that follows is perfectly reasonable. But it still depends on the premise of an entity that can in fact be all knowing for it to be reasonable to follow such an entity over one's own judgement. Thereby, as you said, it would be reasonable to hold such a being's opinion in high regard and follow its tenets. (Though also as you said, we would also have to assume such a being has to be benevolent (i.e. in order to rely on information from an all knowing entity, we must know that said entity is not trying to trick us and lie to us), which in various philosophical discourses, just like all philosophies, is up for debate)

So I return to what I thought was the point, which was how would Jasnah (the atheist utilitarian) approach it. And since the question has now slid from Taravangian's metric of what makes a deity's existence of worth, to now that of the supreme advisor, the question would then lead to for an atheist, what proofs are there that an all knowing being could exist? And if such being could exist, what proofs are there that such a being could be trusted? But since me explaining the reasoning behind those questions can be seen as attacking various religions, I will leave it there. 

Ultimately the reason I thought this was about understanding the view and the arguments, over trying to dispute the view and arguments is because there will always be a response from either side to either side. And I say there will always be, because if there was in fact an argument that covered all bases, and completely resolved the question, then there wouldn't be any discussion anymore. Because there would be a resolution. A finality if you will. 

Edited by Pathfinder
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My take wasn't meant to dispute/defend such or such view, but rather to lay out the skeleton of mindspace that contextualizes the quote, philosophically speaking. I think it is important to be aware that Jasnah's beliefs are both reasonable as well as unnecessary (and I'm using necessity in the modal logic sense) given her priors, and that one can disagree with Taravangian's position without having Jasnah's position (because for many people, creator of physical reality + supreme adviser is good enough to worship. most people, both presently as well as historically, don't have "creator of transcendent truths" as a prerequisite for worship. Certainly not most Vorins, which is the context in the book). I felt the need to give this clarification because some of the messages in the thread either outright said or implied something along the lines of "of course Jasnah believes X, since she believes Y" which doesn't obtain. I did some epistemic hygiene basically.

As a funny side tangent, to respond to your third paragraph, as an atheist I find it very easy to imagine how you can convince me God exists (or has a chance to exist). Maybe not easy to accomplish, but easy to imagine (Here's an example. If our physicists successfully create an artificial pocket universe, that will significantly increase my prior that our universe might've been deliberately Created as well.) I can also easily imagine how you can convince me God is either omniscient, or, at the very least, has epistemic limits beyond our wildest dreams. (Just have a person who claims to be divinely inspired guess, with perfect accuracy, on the numbers produced by a random number generator based on atmospheric noise or lava lamp imaging, such as random.org). But I have a very hard time thinking about how a God could prove omnibenevolence/trustworthiness. I guess that's where faith comes in, right?

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33 minutes ago, CryoZenith said:

My take wasn't meant to dispute/defend such or such view, but rather to lay out the skeleton of mindspace that contextualizes the quote, philosophically speaking. I think it is important to be aware that Jasnah's beliefs are both reasonable as well as unnecessary (and I'm using necessity in the modal logic sense) given her priors, and that one can disagree with Taravangian's position without having Jasnah's position (because for many people, creator of physical reality + supreme adviser is good enough to worship. most people, both presently as well as historically, don't have "creator of transcendent truths" as a prerequisite for worship. Certainly not most Vorins, which is the context in the book). I felt the need to give this clarification because some of the messages in the thread either outright said or implied something along the lines of "of course Jasnah believes X, since she believes Y" which doesn't obtain. I did some epistemic hygiene basically.

So it was asked of Brandon what would Jasnah need to be presented with for her to say god exists, and Brandon replied the omnipotent/omniscient god. I have included the WoB below:

 

Robert W

Does Jasnah still consider herself to be atheist and what would she have to see in order to change her view?

Brandon Sanderson

Jasnah would stop being atheist if she got definitive proof of an omniscient and caring and omnipotent God. She does not, and I kind of agree with her, consider the Shards to be Gods (capital G). In her realm these are beings that, you know, everything is Invested, they're Invested more. Atheist means she does not believe that there is, in these terms, an omnipotent God. It doesn't necessarily have to mean loving, I might have said that. She means that there is no omnipotent, capital G God. She doesn't think one exists. She would need to have irrefutable proof that they do or that they did and then she would believe. It doesn't mean she would worship, but it does mean she would believe.

YouTube Livestream 32 (June 3, 2021)

 

Quote

As a funny side tangent, to respond to your third paragraph, as an atheist I find it very easy to imagine how you can convince me God exists (or has a chance to exist). Maybe not easy to accomplish, but easy to imagine (Here's an example. If our physicists successfully create an artificial pocket universe, that will significantly increase my prior that our universe might've been deliberately Created as well.) I can also easily imagine how you can convince me God is either omniscient, or, at the very least, has epistemic limits beyond our wildest dreams. (Just have a person who claims to be divinely inspired guess, with perfect accuracy, on the numbers produced by a random number generator based on atmospheric noise or lava lamp imaging, such as random.org). But I have a very hard time thinking about how a God could prove omnibenevolence/trustworthiness. I guess that's where faith comes in, right?

It was never my intent to imply an atheist could never be convinced to believe in god, just a theist could never be convinced god does not exist. I think both are perfectly plausible and possible. However, as I said, I thought the point was to understand Jasnah's reasoning for stating math existed outside of a supreme being. As Jasnah is an atheist, I assumed that when explaining, one should take the perspective of an atheist thereby to explain the rationale. As I said, anyone can be convinced in either direction. That is why the overall topic of Jasnah and Taravangian's discussion is an ongoing discussion. Because if there was a conclusive argument that answered all issues for everyone, there wouldn't be a discussion to be had. So there will always be a person that would like to reply to the last reply and go "oh but wait, there is this". 

Edited by Pathfinder
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Yeah, I'm aware of that WoB. You're right that it is useful to bring it up in the conversation. It says something meaningful about not just Jasnah's descriptive view of the world (in other words, her projection of the territory), but also Jasnah's conceptual categorization of the world (in other words, her map proper).

Because someone could totally be like "Yes, if you define omnipotence to include the ability to defy/modify transcendent truths, then nobody is omnipotent, not even God." without being an atheist. Arguably Taravangian does that when he says "Perhaps" in the quote. Her atheism is not just a feature of what she thinks is the case, but also a feature of how she conceptualizes what is the case (as, again, someone could be 100% in agreement with her about what is the case without considering themselves an atheist). So part of it is a Wittgensteinian language game.

Edited by CryoZenith
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19 minutes ago, CryoZenith said:

Yeah, I'm aware of that WoB. You're right that it is useful to bring it up in the conversation. It says something meaningful about not just Jasnah's descriptive view of the world (in other words, her projection of the territory), but also Jasnah's conceptual categorization of the world (in other words, her map proper).

Because someone could totally be like "Yes, if you define omnipotence to include the ability to defy/modify transcendent truths, then nobody is omnipotent, not even God." without being an atheist. Arguably Taravangian does that when he says "Perhaps" in the quote. Her atheism is not just a feature of what she thinks is the case, but also a feature of how she conceptualizes what is the case (as, again, someone could be 100% in agreement with her about what is the case without considering themselves an atheist). So part of it is a Wittgensteinian language game.

Oh totally, though in discussing topics, the context of the discussion/situation also comes into play to inform on the context of the user. So although as you said, a religious individual could explain the conflicts of omnipotence and omniscience with full faculty and knowledge, as well as an atheist could agree with the existence of faith and god (for instance Steven Hawking elaborating on his theories of a finite universe, and that a person that believes can enter the theory with the premise of such, and it reasonably self conclude as well as a person that does not believe enter the theory with the premise of such, and it reasonably self conclude). Anyone can bark like a dog, not just a dog, and not all dogs bark or at least bark in the classically same way, but when one considers a sound a dog makes, based on the context they would think in terms of a dog barking. So although atheists as individuals can think all sorts of ways, and hold all sorts of complex and conflicting thoughts, when we are presented with the discussion as we have been, with the arguments presented, and the one presenting and being presented to is an atheist, and has made this view clear on multiple occasions in various contexts, one can (when requested) going on the context and content, present and explain concepts based on that context and content. Or at least that was my rationale and attempt lol.

But forgive me in advance if this has turned into a roundabout way of talking past each other lol. 

Edited by Pathfinder
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