I think this just fundamentally misplaces what "math" is. It's not some mystical object we've found, like the alien artifact that allowed humans FTL travel in Mass Effect or something. It's a...
I think this just fundamentally misplaces what "math" is. It's not some mystical object we've found, like the alien artifact that allowed humans FTL travel in Mass Effect or something. It's a tool, that humans invented. Humans have great need of predicting the future of our physical world, so much of the tools we developed in this area are geared towards modeling physics.
That is, the fact that "math" and the world fit each other like a glove is an indication of intelligent design - but not of the physical world, but rather of math!
It's like asking why the chainsaw is so unreasonably effective at cutting down trees.
There's all kinds of mathematical constructs that are not particularly useful in modeling most of the physical world. Take a riemann sphere or the extended real number line - these notably define division by zero, and are thus the resulting system isn't even a ring anymore, let alone a field. If you were to try and use them for physics, it would not turn out very well. The real numbers works well for physics because we very, very carefully designed it to.
Or take a galois field - which is useful in cryptography. In GF(7), if Susan had 3 apples and Bob had 6 apples, how many apples do they have? Well, 2, of course! Wait a minute. Not fitting like a glove anymore, now that we're using the wrong tool for the wrong job!
That's a bit of an amusing anecdote, considering chainsaws were originally developed to aid in child birth. But your point still stands, and it's why I rankled at this article. Math is simply a...
It's like asking why the chainsaw is so unreasonably effective at cutting down trees.
I often find apologetics deeply frustrating in the way of misunderstanding, misattributing, and cherry picking your way toward your foregone conclusion. But, as a side note, holy hell that...
I often find apologetics deeply frustrating in the way of misunderstanding, misattributing, and cherry picking your way toward your foregone conclusion.
But, as a side note, holy hell that chainsaw thing is horrific. That's fascinating and also a thing I would be happy to un-learn.
The problem are the cases where we developed math that initially had no applicability to the natural sciences. We have regularly found, completely after the fact, that different mathematical...
Math is simply a way that humanity developed to explain events and the world around us. It's a tool like any other.
The problem are the cases where we developed math that initially had no applicability to the natural sciences. We have regularly found, completely after the fact, that different mathematical concepts have this unreasonable applicability well after the concepts were already developed. That is to say, the math couldn't have been developed for its applications, as the application was discovered afterward.
That’s not a problem though? The world appears to act according to consistent rules. We have developed math to explore those rules as a model of the world. Why should it be a surprise that the...
That’s not a problem though? The world appears to act according to consistent rules. We have developed math to explore those rules as a model of the world. Why should it be a surprise that the implications of our explorations of the model of the world have analogues in the actual world?
I think it is precisely the world's organization around specific rules that is the crux of the argument. I'm not sure that these rules are "consistent", but that mathematics is unreasonably...
That’s not a problem though? The world appears to act according to consistent rules.
I think it is precisely the world's organization around specific rules that is the crux of the argument. I'm not sure that these rules are "consistent", but that mathematics is unreasonably applicable in domain-specific ways.
Maybe an argument by analogy will help. Consider a globe of the earth: it is a tool to figure out how to get from point a to point b without getting eaten by dragons on the way. It later becomes...
Maybe an argument by analogy will help. Consider a globe of the earth: it is a tool to figure out how to get from point a to point b without getting eaten by dragons on the way. It later becomes instrumental in understanding geology, and continental drift. Is it “unreasonably effective” at a purpose outside of what it was designed for? Or is it a natural consequence of exploring a good model?
Well, math starts with a set of axioms, unprovable truths, as the basis of the logic system. Then, using these fundamental choices, you build layers of proofs for results. One simple axiom is that...
Well, math starts with a set of axioms, unprovable truths, as the basis of the logic system. Then, using these fundamental choices, you build layers of proofs for results. One simple axiom is that there exists an empty set.
We can choose different axioms to get different results, or the same results differently. We've happened to generally settle on a common set precisely because they create a system that fits the real world rather well.
But there are choices, like the axiom of choice, that have strange and weird results which don't fit the real world as we understand it particularly well. It's a bit of an open question to figure out what weird things on math are just weird things, and what might have some meaning when used in physical models.
A good example of this is the history of solving depressed cubics (look up the old school math duels like with Tartaglia), and the creation of the imaginary number i to be a placeholder for the square root of negative 1. This allowed for the solving of all cubics, but centuries later we started seeing maths in physics that required i. Eventually it showed up in quantum wave equations, which really unsettled folks.
So I'm not particularly shocked that we keep finding odd things in math that apply to the real world, because we've chosen our axioms to help us in that.
This is all from memory on my phone so please forgive any little errors of memory.
That’s my point precisely. Math models reality. It is therefore not surprising or “unreasonably effective” that when we make inferences from the model, that we find their analogues in reality.
That’s my point precisely. Math models reality. It is therefore not surprising or “unreasonably effective” that when we make inferences from the model, that we find their analogues in reality.
I don't know much about math, but I know there are many ways to think of mathematics in addition to the one you stipulated. So I did a little search for some links that might provide a broader...
I think this just fundamentally misplaces what "math" is. It's not some mystical object we've found, like the alien artifact that allowed humans FTL travel in Mass Effect or something. It's a tool, that humans invented.
I don't know much about math, but I know there are many ways to think of mathematics in addition to the one you stipulated. So I did a little search for some links that might provide a broader context.
Thank you for your reply! If I'm being fair to the argument, I don't think Dr. Craig is taking a stance on what mathematics is, which I imagine would be an interesting, but completely separate...
Thank you for your reply!
I think this just fundamentally misplaces what "math" is.
If I'm being fair to the argument, I don't think Dr. Craig is taking a stance on what mathematics is, which I imagine would be an interesting, but completely separate discussion.
That is, the fact that "math" and the world fit each other like a glove is an indication of intelligent design - but not of the physical world, but rather of math!
I think the argument hinges on the mathematics that are not created for application to the natural world. Not all mathematics is applied. This math that is initially developed by an aesthetic impulse (or to do mathematical problem solving) is later discovered to have unreasonably accurate applications in the natural sciences. The math is developed completely a priori to its application, which makes its applicability otherwise happily unexpected.
These examples are all borne of survivorship bias, however. We expand upon mathematical models that are most useful for our purposes, and we abandon mathematical models that are less useful. This...
This math that is initially developed by an aesthetic impulse (or to do mathematical problem solving) is later discovered to have unreasonably accurate applications in the natural sciences. The math is developed completely a priori to its application, which makes its applicability otherwise happily unexpected.
These examples are all borne of survivorship bias, however. We expand upon mathematical models that are most useful for our purposes, and we abandon mathematical models that are less useful. This works in the same as any tool humans have created: we invented wheels for children's toys, and then later discovered that wheels are also useful for a huge array of other purposes: transporting goods, spinning wool into yarn, devising clocks to measure time, converting the flow of rivers into usable power, etc.
Yet there are tons of other things that were invented for children's toys that turned out to not be nearly as useful as wheels. Likewise, it is common to develop mathematical models that have only very limited use — or are just plain bad. Humans do it all the time, but it's easy to not notice because bad math doesn't make headlines.
It is also worth pointing out that a model can be useful without being accurate, and vice versa. You don't see this so much in the sciences (where the goal is to simulate natural processes as accurately as possible), but it is common in other industries. For example, consider mathematical models used in video games to render scenes. In most cases, these models mimic the appearance of light and shadows, but they do not accurately simulate photons because that would require way too much computation power. These algorithms were invented whole cloth and offer no meaningful insight into natural process — yet they have been developed to a very high degree, and become ever more impressive year after year, because they are very handy to a lucrative industry.
Hypothetically, a scientist or engineer might have a look at one of these video game algorithms and find some way to refine it and apply it to their own work (for all I know, this has already happened a few times), but this does not make these models any less manmade. After all, the GPU is a wholly manmade tool developed for the video game industry, but it has turned out to also be extremely useful to the sciences.
He is implicitly taking the stance that it is something that is, rather than something that is created, however. In that regard, the article doesn't actually have any examples of that. His main...
He is implicitly taking the stance that it is something that is, rather than something that is created, however.
I think the argument hinges on the mathematics that are not created for application to the natural world.
In that regard, the article doesn't actually have any examples of that. His main example is the prediction of the Higgs Boson, which did not require any particularly esoteric mathematical models. In fact, the main issue with the Higgs Boson was that there's LOTS of times where our mathematical models predict something we haven't observed... and the models are just wrong, actually.
Like I have described, there's plenty of esoteric models which are not useful and have never been useful to modeling physical items. The fact that occasionally some are pulled out of obscurity is a mix of 1) confirmation bias, most people have little reason to even learn about all the weird models that aren't ever useful 2) the fact that humans can never truly make something disconnected from the world, since our minds are developed with an intuition to the world we inhabit 3) the fact that many are just small deviations from mainstream models, and in many cases our models for the physical world are just slightly off from reality.
The Higgs boson is particularly interesting because it's the last major prediction we've made that we've experimentally verified, and completed the Standard Model. There's been a lot of math...
The Higgs boson is particularly interesting because it's the last major prediction we've made that we've experimentally verified, and completed the Standard Model. There's been a lot of math developed since, and I daresay most of it doesn't represent reality at all, even if it's very advanced.
I found this article very frustrating to read. It is structured as a series of questions answered by non-theists and theists, but the author doesn't seem to have put much thought into the...
I found this article very frustrating to read. It is structured as a series of questions answered by non-theists and theists, but the author doesn't seem to have put much thought into the non-theistic answers. In order to write a piece like this in good faith, you have to really deeply engage with people representing the other side of your argument, otherwise it comes across as a series of strawmen.
How is it, for example, that a mathematical theorist like Peter Higgs can sit down at his desk and, by pouring over mathematical equations, predict the existence of a fundamental particle which 30 years later, after investing millions of dollars and thousands of man hours, experimentalists are finally able to detect?
He's still alive, why not go ask him? Or at least ask some physicists and mathematicians familiar with the field. The author is a philosopher, so I understand why they exclusively reference other philosophers, but since this is framed as a persuasive essay ("Theism provides the best answer to this question"), I don't think it's acceptable to misrepresent the non-theism side.
For the non-theistic realist, the fact that physical reality behaves in line with the dictates of acausal mathematical entities existing beyond space and time is, in the words of philosopher of mathematics Mary Leng, “a happy coincidence.”
This is not a mainstream view. I've never heard any mathematician or physicist say anything like this, and I find it hard to believe this is a common view even among mathematical philosophers. I think the author would benefit from asking actual working mathematicians who consider themselves mathematical realists whether they believe that the applicability of math to reality is a coincidence.
Later on, in the anti-realism section:
Balaguer admits that he has no explanation why, on anti-realism, mathematics is applicable to the physical world or why it is indispensable in empirical science.
I'm sorry to hear that Balaguer had trouble answering this question. Did you look for any other philosophers or mathematicians who might have had an answer? No, you just immediately moved on to your own theistic view? That seems a little uncharitable.
In order to convince someone, you need to attempt to understand their point of view. When you wildly misrepresent that view, as I believe this essay has done, you can't expect anyone who disagrees with you to take you seriously. I don't know who the intended audience of this is, but as a persuasive essay it is not effective.
A lot of good points. If I may expand a bit on the points you made, I don't think this argument was written in good faith, nor was it written to substantially evaluate different points of view....
A lot of good points. If I may expand a bit on the points you made, I don't think this argument was written in good faith, nor was it written to substantially evaluate different points of view. But this is not necessarily a "mistake" on the author's part. I think it's likely that, consciously or subconsciously, this argument was written to convince some people on the fence, but more than that, it was written with motivated reasoning to affirm the views of the author and the already-convinced reader. It's basically an in-group validation of already existing beliefs.
This doesn't necessarily mean it's wrong, and I do think it's wrong for a variety of reasons, but it explains why it misinterprets the conflicting opinion. Because that's an easy way to achieve such validation.
For background, I grew up in a conservative Christian environment and although I would not identify as Christian anymore, I am still a Follower of the Way of Jesus (the distinction being a topic...
It's basically an in-group validation of already existing beliefs.
For background, I grew up in a conservative Christian environment and although I would not identify as Christian anymore, I am still a Follower of the Way of Jesus (the distinction being a topic for another day).
I can't begin to count the number of books/videos/etc we were exposed to as children and teenagers that bent over backwards to explain why the Bible was not only right, but literally true. One that comes to mind was a book about "white holes" (as opposed to black holes) that tried to account for the apparent age of the universe. It was a very thin book with no math in it. As far as I can remember, there were none that ever presented a compelling (to me) case to reconcile science or math with that particular brand of faith. But they were held up s important, even scholarly ideas in the community.
Since you can't prove a negative, I won't say there aren't any books that make compelling theistic arguments and fairly represent the other side, but I believe @daywalker that you have hit the nail on the head with your analysis of this article and that it applies to the genre in general.
My own experience was being steeped in that culture, having certain things being presented as truth, and not having alternatives presented at all (or presented dismissively with weak strawmen). One of the consequences of that was that I didn't really have the vocabulary or framework to object to that treatment. I can imagine writing something like this as a teenager, and know now that it was probably about as far as I could go toward questioning things, because even trying to engage with the non-believers point of view at all or to read or study anything about it would have been pretty radical.
Back then, I knew something was not adding up, but was made to feel that it was something about me because it was unthinkable and sinful to question the "Truth". I would not learn how varied the ideas about what the Bible means, even among Christians until much later. It took me a long time to even realize how deeply I had internalized l that guilt, and I am still dealing with the effects decades later.
So that is all to say, I don't think we need to cut these authors any slack on picking apart their arguments. If they want to engage in the domain of logic/math/rhetoric, IMO they should follow the rules of those domains, or else stick to theological debate. But I think we can have some empathy and compassion for people steeped in this culture and realize that they may be acting in good faith (so to speak) but are buried so far into a specific set of norms that they can't function much differently than this.
To be clear, I'm just offering my viewpoint in the context of my agreement with @daywalker, not meaning to say anything about how they or anyone else are approaching the author or the posted article.
I went to a private religious high school and there was quite a bit of teaching about Jesus as a historical figure. The premise was that there are historical records that Jesus existed, so we...
I went to a private religious high school and there was quite a bit of teaching about Jesus as a historical figure. The premise was that there are historical records that Jesus existed, so we should believe the other claims about him that are in the Bible, including the supernatural ones. If we believe historians about the life of Abraham Lincoln or King Henry VIII, why don't we believe the writers of the Bible?
Of course this is a ridiculous argument but when you are a kid you believe adults who are in positions of authority, and it creates unquestioned beliefs that can last a lifetime. Then you write papers about how mathematics proves God or that creationism is scientific.
I think this is why religious leaders talk so much about indoctrination. They know that it is pretty much the only reason they have followers and they don't want some other group doing the same thing with "liberal" ideas.
The funny thing is, as someone who also went to a private Christian high school, none of this Bible shit prevented me from leaving the church because the thing that sparked my "fall" from...
The funny thing is, as someone who also went to a private Christian high school, none of this Bible shit prevented me from leaving the church because the thing that sparked my "fall" from Christianity had nothing to do with doubting the Bible. I didn't come to abandon the young Earth creationism I'd been raised in until well after I had mostly abandoned the faith. I've only come to be interested in other historical discrepancies between the Bible and what we understand of history way later.
The thing that did break me out was an inability to reconcile the cruelty of our beliefs about homosexuality with my empathy for my irl gay friend. The load-bearing joint there was the belief that it was a choice... but when my best friend, who'd been indoctrinated in the same way as I, confessed to me that he was gay despite trying with all his might not to be? I couldn't continue to believe being gay was an active act of defiance in the face of such evidence, and without that piece I couldn't handle the cruelty inherent in creating gay people only to condemn them. I remember telling my mom (who remains steadfastly religious to this day) that even if it were true and God was real, I couldn't worship a God who would do something like that.
Of course I'm sure the vast majority of people from the Christian community I grew up in believe I "fell away" because of secular influence when I went to college. That's the usual myth. But I was VERY resistant to secular influence. I read all the Answers in Genesis books. When we went to Washington D.C. in 8th grade my best friend (the same one who would later come out as gay to me) and I planned to go to the National History Museum and argue with "the evolutionists" (thank god that never materialized, I don't think I could handle the retrospective embarrassment on that one). I completely bought into it all -- until I was confronted with someone I cared about and believed whose existence meant God was either unfathomably cruel or what I'd been taught wasn't true.
I once joked to my therapist that I stopped being a Christian because I cared more about my friends than Jesus. And that's sort of true. But I think more fundamentally, indoctrination is just fundamentally weak to empathy.
It's funny how we landed at the same conclusion from different ends. I started out by questioning why the Hindu gods were fake and ours wasn't, and never got a satisfactory answer. I was told I...
It's funny how we landed at the same conclusion from different ends. I started out by questioning why the Hindu gods were fake and ours wasn't, and never got a satisfactory answer. I was told I had to had faith, but I reckoned Hindu Raistlin was also being told to have faith, and one of us was definitely wrong.
And if they were wrong about that, they must be wrong about gay people too. So, in my very homophobic society, I landed at empathy for the LBGTQ+ almost by accident.
Regarding homosexuality being a choice: I used to listen to Dennis Prager on the radio quite a bit. A recurring theme for him was that gay marriage should not be allowed because being gay is a...
Regarding homosexuality being a choice: I used to listen to Dennis Prager on the radio quite a bit. A recurring theme for him was that gay marriage should not be allowed because being gay is a choice. And his proof for it being a choice is that societies that accept open homosexuality have more of it.
This has got to be one of the most ridiculous arguments of all time. Is he so stupid that he didn't realize that when you persecute and shun something fewer people admit to it? Or is he just a liar?
Well, now we know he is just a liar because of Prager U and it's misrepresentation of every topic that it covers.
By the way, he's yet another conservative who is very concerned that gay marriage harms the institution of marriage but he has multiple ex wives.
Oh yeah there's tons of BS like that from conservative grifters like him. But the true believers eat it up because the "it's a choice" tenet is absolutely foundational to the story they tell...
Oh yeah there's tons of BS like that from conservative grifters like him. But the true believers eat it up because the "it's a choice" tenet is absolutely foundational to the story they tell themselves about what they believe.
I think there are some leaders who cynically manipulate and indoctrinate their flock. Especially when you see significant divergence between the leader's behavior and their own actions. But I've...
I think this is why religious leaders talk so much about indoctrination. They know that it is pretty much the only reason they have followers and they don't want some other group doing the same thing with "liberal" ideas.
I think there are some leaders who cynically manipulate and indoctrinate their flock. Especially when you see significant divergence between the leader's behavior and their own actions.
But I've known a lot of leaders, especially in small churches where most of the congregation is involved in leadership (the men, anyway, but that is a whole different tirade). And they seemed sincere in their belief and in their conviction that their teaching and work were morally right. I have trouble believing that they were all cynically manipulating the group. I think it's much more likely that they are themselves victims of that indoctrination.
It took me almost 15 years and the forced time when we physically stopped going to church in the pandemic shutdown to face the fact that my values no longer aligned with many of the ways I was raised. During those years, I had a lot of physical symptoms of stress that would manifest when I was in the church environment, and I couldn't even admit to myself that was what it was about.
If it was so hard for me when my connection to the church was pretty small (someone once accurately characterized me as "the one who comes in after the greeting and sits in the back"), how much harder for someone who has devoted their life to it?
I am scared of the Christian nationalist movement in the US and what it might mean if they successfully gain power. I know there are people leveraging and weaponizing the movement to build a power base.
But when I deal with individuals, I try to remember that they can be sincere in their faith and that we are all to some extent a product of our raising. I have been lucky to have a lot of support in making the moves I needed to unwind things, but with a different spouse and s different family (like many families I grew up with), I can easily see how there could have been tremendous pressure to just bury those feelings and conform.
Like water poured into a container, most of us eventually turn into – or remain – whoever we surround ourselves with. We can choose our tribe, but we cannot change that our tribe is our destiny.
~ Stefan Molyneux
Most if not all arguments are constructed to persuade the receiver of a conclusion that the author already holds to be true or false. If not for this emotional motivation, it would be very...
Most if not all arguments are constructed to persuade the receiver of a conclusion that the author already holds to be true or false. If not for this emotional motivation, it would be very difficult to produce compelling arguments. That is a given in philosophical discourse, of which this article is an example.
Unlike most things on the internet, WLC writes in a formalized way, so he doesn't have a lot of soft language to conceal his intentions. It's not a pleasant reading, but I wouldn't say it lacks "good faith". In fact, it may have it in excess.
Many modern apologetics do not seek to prove the existence of God. Arguments like this one seek to increase the credence in theism, even if just by a small amount, by showing that some state of...
this argument was written to convince some people on the fence, but more than that, it was written with motivated reasoning to affirm the views of the author and the already-convinced reader. It's basically an in-group validation of already existing beliefs.
Many modern apologetics do not seek to prove the existence of God. Arguments like this one seek to increase the credence in theism, even if just by a small amount, by showing that some state of affairs is otherwise more expected on theism than on naturalism.
Specifically, the author doesn't actually think that these arguments work on their own. They give "intellectual permission" for the would-be theist to pursue theism when inclined due to other factors (religious experience, witness of the Holy Spirit, etc.)
Yeah, I disagree on this take. It's written very obviously in bad faith misinterpretation and unwillingness to engage properly with conflicting opinions, and it doesn't understand science or...
Yeah, I disagree on this take. It's written very obviously in bad faith misinterpretation and unwillingness to engage properly with conflicting opinions, and it doesn't understand science or nature other than some surface level take. Meanwhile, there are so much misinterpretations and "gotcha" takes.
Constant atheist polemics can be utterly exhausting, and can rob these discussions of the joy they may otherwise bring. Not everyone you disagree with operates in bad faith, and I think we should...
It's written very obviously in bad faith misinterpretation
Constant atheist polemics can be utterly exhausting, and can rob these discussions of the joy they may otherwise bring. Not everyone you disagree with operates in bad faith, and I think we should assume good faith until otherwise. This is coming from someone who isn't even a theist.
unwillingness to engage properly with conflicting opinions
He debated this subject fairly exhaustively with atheist philosopher Dr. Graham Oppy. He's willing to engage with conflicting opinions with anyone who will give him the time of day. Really these atheistic polemics are quite off-putting.
I don't think you're trying to understand why I think it's bad faith, and insinuating that I'm being unreasonably polemical, or saying that I only think this argument is bad faith because it...
I don't think you're trying to understand why I think it's bad faith, and insinuating that I'm being unreasonably polemical, or saying that I only think this argument is bad faith because it challenges my opinion leaves a bad taste in my mouth. Good luck on your topic, and hopefully it's more productive than this conversation, but I lost my interest in ours.
I'm sorry but calling daywalker's replies to you "atheist polemics" is an incredibly insulting and disrespectful way to respond here. Their comments criticizing WLC have not remotely approached...
Constant atheist polemics can be utterly exhausting, and can rob these discussions of the joy they may otherwise bring. Not everyone you disagree with operates in bad faith, and I think we should assume good faith until otherwise.
I'm sorry but calling daywalker's replies to you "atheist polemics" is an incredibly insulting and disrespectful way to respond here. Their comments criticizing WLC have not remotely approached "polemics" and don't even mention atheism in their comments. Criticizing WLC and believing he's arguing in bad faith in the polite manner daywalker has is perfectly reasonable discussion here om tildes, especially given that daywalker's comment is in response to WLC not engaging with or misrepresenting the fields he's using for his arguments here.
If you cannot be exposed to people criticizing your position, without accusing someone of writing "atheist polemics" when they do so, perhaps you shouldn't post or engage with Christian/theistic apologetics on Tildes. It's far from conducive to good discussion. You certainly shouldn't be lecturing others about taking others' arguments in good faith while simultaneously doing this.
His specific claims were that the article was "very obviously" made in bad faith and that it is unwilling to engage with dissenting opinions. This is polemicism. I think the argument is very...
His specific claims were that the article was "very obviously" made in bad faith and that it is unwilling to engage with dissenting opinions.
This is polemicism. I think the argument is very interesting, and I'm not even a theist. To dismiss it outright as being made in bad faith may play well rhetorically, but isn't the sort of conversation I'm interested in having. I'm interested in talking about the merits of the argument, not defending some Christian apologist from ad hominems when I'm not even a Christian myself.
I am a theist and I don't find the argument in the article convincing (nor imo is it particularly novel among theistic arguments). Furthermore, I'm an ex-evangelical and know from that background...
I am a theist and I don't find the argument in the article convincing (nor imo is it particularly novel among theistic arguments). Furthermore, I'm an ex-evangelical and know from that background that WLC does indeed have a huge audience of devout Christians who engage with his arguments primarily to validate their already firmly set beliefs (I used to do this myself with WLC's own work!). Believing that he is operating in bad faith, again based on evidence that he is not engaging with the science and mathematics he bases his arguments on particularly thoroughly, and saying so in a very concise and polite manner on a Tildes topic is neither polemicism or an ad hominem.
No one is asking you to defend Craig from accusations of bad faith. You're free to disagree with that assessment. But you're shutting down discussion of the topic with accusations of polemicism rather than just leaving that thread be and engaging with the parts of the discussion that you want to engage in. Let other people discuss WLC's place in the philosophical discourse and whether they believe he's operating in good or bad faith if you don't want to do it. You not wanting to do it doesn't make them "polemics" or "ad hominem"
It doesn't really matter if you think the attack on WLC's character or motivations has merit or not; either way this is still the realm of polemics. And attacking the motivations of an opponent...
It doesn't really matter if you think the attack on WLC's character or motivations has merit or not; either way this is still the realm of polemics. And attacking the motivations of an opponent rather than the merits of their argument is literally textbook ad hominem.
But you're shutting down discussion of the topic with accusations of polemicism rather than just leaving that thread be and engaging with the parts of the discussion that you want to engage in.
Accusing proponents of an argument of acting in bad faith is precisely what shuts down conversations like these.
To me this reads like a more abstract version of the argument that the eye is too complex to have evolved naturally and work as well as it does, ergo it must have been created artificially. An...
To me this reads like a more abstract version of the argument that the eye is too complex to have evolved naturally and work as well as it does, ergo it must have been created artificially.
An inability to adequately explain some natural phenomena is only evidence of our own limited understanding, not evidence for the existence of anything specific like a god.
Ditto. The concept is appropriately named the God of the gaps. Especially from a scientific standpoint, it's very unproductive to bring in deities in an attempt to fill the gaps in our knowledge.
Ditto. The concept is appropriately named the God of the gaps. Especially from a scientific standpoint, it's very unproductive to bring in deities in an attempt to fill the gaps in our knowledge.
This is precisely it — it’s a rework of intelligent design. It’s a bit like watching a conspiracy theorist hastily rationalizing as facts contradict their deeply held beliefs about the moon...
This is precisely it — it’s a rework of intelligent design. It’s a bit like watching a conspiracy theorist hastily rationalizing as facts contradict their deeply held beliefs about the moon landing or JFK .
Oh, all the arguments for intelligent design are actually clearly disproven by science and mathematics under close examination? My god, this means the intelligent design goes even deeper. Even mathematics itself must have been intelligently designed!
I don't think his arguments here are very good, but I don't think it's really possible to disprove something like intelligent design. That's part of why it doesn't really belong in a scientific...
I don't think his arguments here are very good, but I don't think it's really possible to disprove something like intelligent design. That's part of why it doesn't really belong in a scientific context at all - it's completely unfalsifiable. Imo that's why any arguments for its existence that aren't strictly philosophical tend to fall flat as well (in addition to those who try to "prove" intelligent design through math or science generally not being particularly well-versed in those fields, as we see here with WLC).
There's a lot to be said on the topic, and I'm not interested in expressing my feelings and thoughts on most of them, because these discussions are a bit old for me personally. But I'm just going...
There's a lot to be said on the topic, and I'm not interested in expressing my feelings and thoughts on most of them, because these discussions are a bit old for me personally. But I'm just going to say that, it's amusing a little when people use the "elegance" and "beauty" of the universe or one of its properties as an argument.
Nobody can tell me the standard model is anything elegant or beautiful. It's ugly as hell, but it works. A similar point goes for genetics. A lot of the genetic code is unoptimized or utter shit, but evolution is diverse, so it's there. So these discussions always remind me of this comic. I'm sure there must be an xkcd comic making the same joke.
Edit: I guess I should elaborate that I don't think there isn't beauty in nature. Leaving aside the subjective nature of beauty here, I'm trying to say that the ugly side of nature (and science) doesn't get emphasized much. There's a lot of mundanity and ugliness in natural phenomena and science, but you don't hear about them or see them if you don't get into science on a deeper level.
I feel it is also worth noting here that, as they say, beauty is in the eye of the beholder. The beauty we see in the universe is a reflection of the evolutionary forces that shaped us, not an...
I feel it is also worth noting here that, as they say, beauty is in the eye of the beholder. The beauty we see in the universe is a reflection of the evolutionary forces that shaped us, not an inherent quality of the universe.
A rolling landscape with greenery and water is, perhaps, attractive to us because our ancestors who were drawn to such places found it easier to meet their needs. A cloudless night sky bedecked with stars is, perhaps, attractive to use because our ancestors who made a study of it could navigate and judge the passage of seasons. Rhythmic sounds and repeating patterns are, perhaps, attractive to us because they are usually markers of life, which our ancestors would have been foolish to stray far from.
Meanwhile, to a dog, poop and rotting carcasses are beautiful; the human perspective is not definitive. Our ideals toward elegance probably say more about our long history as tool makers than they say about what is good or true.
I want to point out that the Standard Model is so ugly that we've spent the last 50 years trying to supersede it. We've spectacularly failed. The Standard Model and Einstein's theories of...
I want to point out that the Standard Model is so ugly that we've spent the last 50 years trying to supersede it. We've spectacularly failed. The Standard Model and Einstein's theories of relativity are incredibly successful and predictive, and remain the gold standard for anything we do. String theory, less so.
I was going to post this at the top level, but since we got into beauty and elegance, I think I will post it here. I don't personally find the topic of the article compelling. I didn't even know...
I was going to post this at the top level, but since we got into beauty and elegance, I think I will post it here.
I don't personally find the topic of the article compelling. I didn't even know about the realism/anti-realism split, and it seems pretty abstract to me.
One thing I have always found compelling regarding a sense of order in the universe is the pattern that complex things emerge from simple things.
For example, 200 odd elements make up ... everything. Somehow mountains and water and farts and Gorilla glass are all possible from those atoms. I mean, it could just be lucky, or maybe this is a shit universe and the really good universes have a million types of atoms. But there is strange beauty in it.
Since you mentioned genetics, I don't disagree that our DNA is a mess, but the fact that all that mess, nuance, and variety is possible by coding just with four base pairs is quite something. Protein folding is another case -- just a handful of amino acids make up all the varied proteins that make our bodies and catalyze their biological processes. I know that proteins are manufactured by coding off of nucleotide sequences, so in some sense these two examples are related, but the way that protein folding (and therefore function) is emergent from the protein sequences feels like its own kind of amazing thing.
All that said, this is just something I enjoy about our universe. Whether anyone wants to take it as proof of a design or a designer, much less the work of a particular deity, is a matter of faith. If I have it, I can see its effects everywhere I look. If I don't, I won't. Which is why I think attempts to prove or argue that God exists like this article does are ultimately a fruitless exercise.
The more I think about it, the more I think that this kind of exercise is rooted in a believer struggling with doubt. Faith is by definition belief in something unproven (and perhaps unprovable). Certainty would be much more comforting, much less work, much less worry. But if it's unprovable, then that quiet voice of doubt will always be there. I think everyone believes in something, so maybe that common struggle can be a basis for understanding and kindness between us.
Edit to add: I just realized this is my second comment under one of @daywalker's comments. Not intentional, but your thoughts must be striking a vibe with me today.
My problem with this argument is that it seems like God is superfluous. The question we seek to answer is, why is the universe so structured? Why isn't it a chaotic place incapable of supporting...
My problem with this argument is that it seems like God is superfluous.
The question we seek to answer is, why is the universe so structured? Why isn't it a chaotic place incapable of supporting life? I don't know of a formal way to quantify or do statistics on the set of "every logically possible universe", but it seems intuitively true that the vast majority of that set would be less structured, less mathematically elegant (according to human notions of elegance) and probably incapable of supporting life as we know it. A more thorough examination of the question would have to substantiate that intuition, but let's grant it for the sake of argument.
So you say, because God made it so. But my issue is: in this set of possible universes, aren't there many universes with creator-gods that chose to make a chaotic universe? I don't see any reason, a priori, to assume that a creator-god couldn't do so. If we seek to use this to establish the existence of some kind of god, before we get onto specific theology, we can't assume the properties of God according to our beliefs while we're in the process of establishing that something like a god must exist. So we can't be sure that "God creates a highly mathematically structured and elegant universe" is any more likely than "God creates total chaos". In fact, if the intuitions about most possible godless universes are right, I don't see why the same doesn't apply to most godly universes as well.
But if that's the case, then why do we need God at all? If a universe with a god that creates mathematical elegance is as unlikely as a universe without a god at all that happens to be mathematically elegant, what exactly does God explain? The "why" is left unanswered.
The issue in general with these sorts of arguments is that they seek to establish the existence of a generic creator-god as a starting point to further expand into theology, but secretly smuggle in assumptions based on a particular theology to start with. It's a form of circular reasoning.
On your last point, I notice these arguments never end with a pantheon. Like, obviously there's a god for the strong nuclear force, which is entirely separate from the electromagnetic god. No,...
On your last point, I notice these arguments never end with a pantheon. Like, obviously there's a god for the strong nuclear force, which is entirely separate from the electromagnetic god. No, they end with whatever god the writer currently believes in. More to the point, they end with the theological and cosmological structure their society raised them with. Happy coincidence indeed!
This is a really good objection. Craig takes as a matter of definition that God has certain attributes (that Craig establishes separately), but I think even taking that, your objection stands. It...
This is a really good objection. Craig takes as a matter of definition that God has certain attributes (that Craig establishes separately), but I think even taking that, your objection stands. It seems that the kind of theism that this argument supports is one where God cares about bringing into being a world that is intelligible by human beings, or perhaps its design itself cries out for some sort of explanation (though I want to avoid design arguments here.)
Craig often uses probabilistic arguments, none of which will likely establish God for someone independently, but together raise the credence of theism or lower the credence of naturalism, potentially to a degree that one's mind may be changed. The Kalam, for instance, raises the credence in not just any creator-god, but a specific kind of creator-god (i.e., timeless, spaceless, personal.) When you use an argument like the one for math with other arguments, it seeks to raise the credence of a specific kind of theism.
All of that said, I think the objection specifically to this argument still stands.
While I don't agree with the conclusion of the article, I don't think it is badly done insofar as explanations of the unexplainable go. Of course as a mathematician I already knew that I was...
While I don't agree with the conclusion of the article, I don't think it is badly done insofar as explanations of the unexplainable go.
Of course as a mathematician I already knew that I was closer to God's light than the other sciences. 😉 However, I do think a few notes are in order. First, while mathematics may provide many of the tools used in physics, I think the physicists deserve some credit in creating the standard model, and Peter Higgs is a physicist. The standard model is more than just a patch work of mathematical shovels; it was the creation of a conceptualization of the universe's mechanics.
That math fits the universe is because we've chosen axioms that help math do so. It's possible that our universe had others rules in the moments before, during, and after the big bang, and this is the rules that settled out from the annealing of our universe. Had those rules prevailed, our math and our physics would have been built differently.
When I said that the argument was attempting to explain the unexplainable, I'm thinking of things like the primordial synthesis of hydrogen, whose origins we may never unlock because it happened before the big bang. Or perhaps we will. But there is so much room for faith for those that choose it, even with our understanding of physics, that marshalling math to the defense of God seems almost silly to me.
That said, I don't mean to ridicule the argument or the author. Indeed, math is beautiful, and its applications wondrous. If one wants to find God's fingerprints in it, well, there are worse places. I mean, the equation for the dilation of time is just a reshuffling of the Pythagorean theorem. Simple math shovel, paired with deep insights.
That is a fair and reasonable take. I like how you understand that this is a philosophy article, so the role of mathematics in the argument does not necessarily require the correction you would...
That is a fair and reasonable take.
I like how you understand that this is a philosophy article, so the role of mathematics in the argument does not necessarily require the correction you would expect from an article within the field of mathematics. That kind of nuance is rare to find online.
Although WLC is a respected philosopher, he is also a (literal) preacher. So you gotta read it with the understanding that his articles sometimes have two goals, and those goals are not necessarily in support of each other.
Why does there need to be a reason why? If the universe could have been any which way, and how it ended up was "breathtakingly" complex, why is that a problem? That was one of the possibilities,...
Well and good, but what remains wanting on naturalistic anti-realism is an explanation why the physical world exhibits so complex and stunning a mathematical structure in the first place. Perhaps the universe had to have some mathematical structure--though couldn’t the world have been a structureless chaos?--still, that structure might have been describable by elementary arithmetic.
Why does there need to be a reason why? If the universe could have been any which way, and how it ended up was "breathtakingly" complex, why is that a problem? That was one of the possibilities, and it's what we got. Maybe I just don't get philosophy but the arguments against naturalistic anti-realism seem especially weak.
I think if we do concede that it is "breathtakingly" ordered according to mathematical principles, the question would be whether this outcome is more expected under naturalism or theism. Dr. Craig...
Why does there need to be a reason why? If the universe could have been any which way, and how it ended up was "breathtakingly" complex, why is that a problem?
I think if we do concede that it is "breathtakingly" ordered according to mathematical principles, the question would be whether this outcome is more expected under naturalism or theism. Dr. Craig would likely say that it is more expected under theism, and I think there is some intuitive force to this. Depending on your metaphysics, of all the possible worlds that could've obtained, most wouldn't abide by the principles of mathematics, and the fact that mathematics keeps being applicable across domains in our world is unexpected. This doesn't "prove" theism by any stretch, but makes an argument that seeks to potentially raise the credence of theism at least a little.
I'm not so sure I can concede it's extraordinarily complex. We have a sample size of one; there's no way to know if our universe's complexity is at, above, or below the norm. There's no reason to...
I'm not so sure I can concede it's extraordinarily complex. We have a sample size of one; there's no way to know if our universe's complexity is at, above, or below the norm. There's no reason to believe universes fall on a bell curve, either. We can't make any assumptions about how things ought to be, because we only have one to go off.
I would say every single possible universe c would have its own mathematics. Whether the speed of light is faster or slower, mass has negative or positive values, etc. What universes are you...
I would say every single possible universe c would have its own mathematics. Whether the speed of light is faster or slower, mass has negative or positive values, etc.
What universes are you envisioning that wouldn't have their own math?
What would that mean? What would a universe that “doesn’t abide by the principles of mathematics” be? The axioms we choose for the real numbers are designed by humans. If the universe worked...
Depending on your metaphysics, of all the possible worlds that could've obtained, most wouldn't abide by the principles of mathematics
What would that mean? What would a universe that “doesn’t abide by the principles of mathematics” be? The axioms we choose for the real numbers are designed by humans. If the universe worked differently, you may need to choose different number systems. That’s fine.
Our existing universe is already pretty obnoxious. Quantum mechanics is extremely unintuitive, and extremely obnoxious to model. Non-determinism is not fun.
Why would whatever other universe that could exist not be describable by sufficiently complex logical models as this one can clumsily be?
Inconsistency can be made into consistency, just as the non-determinism of quantum mechanics is. We straight up cannot with absolute certainty predict how a quantum interaction goes - we can only...
Inconsistency can be made into consistency, just as the non-determinism of quantum mechanics is. We straight up cannot with absolute certainty predict how a quantum interaction goes - we can only model it probabilistically, and from there the tools of statistical physics enables useful, but not pin-point certain, predictions.
I don't see how this universe could not be modeled. In every interaction is it just uniformly random what happens? Well, that's a clusterfuck, but it can be modeled nonetheless. Just saying it's intelligible is just vacuously circular.
That's a good point. We've now landed at the idea that particles can be in a superposition of states, non locality, outcomes being inherently random, and knowledge of position and velocity being...
That's a good point. We've now landed at the idea that particles can be in a superposition of states, non locality, outcomes being inherently random, and knowledge of position and velocity being fundamentally contradictory. None of this black arts stuff means we can't model it. We can model it quite well. And if it looks like a weird foamy impossible mess? Shut up and calculate.
Two questions to that line of thought. Why wouldn't other possible worlds abide by mathematics? How can we possibly know that? Why is it unexpected that mathematics keeps finding application, and...
Depending on your metaphysics, of all the possible worlds that could've obtained, most wouldn't abide by the principles of mathematics, and the fact that mathematics keeps being applicable across domains in our world is unexpected.
Two questions to that line of thought.
Why wouldn't other possible worlds abide by mathematics? How can we possibly know that?
Why is it unexpected that mathematics keeps finding application, and why is that a problem?
When people first came up with viagra, they didn't expect it to become the world's premiere drug for sexual dysfunction in men. They came up with it as a drug to treat cardiovascular problems. The fact that it just happened to "help" some folks with sexual problems was a happy side-effect. It was an unexpected application, but it could have been predicted based on what the drug does (dilate blood vessels).
William Lane Craig is the one living American philosopher who seriously and effectively defends the cosmological argument and the existence of God, but that doesn't mean that every single one of...
William Lane Craig is the one living American philosopher who seriously and effectively defends the cosmological argument and the existence of God, but that doesn't mean that every single one of his articles is a defense of those very broad and disputed claims. Reading him can be frustrating because what he seeks to demonstrate is often of little consequence to most readers.
That is his conclusion:
Thus, the theist—whether he be a realist or an anti-realist about mathematical objects—has the explanatory resources to account for the mathematical structure of the physical world and, hence, for the otherwise unreasonable effectiveness of mathematics—resources which the naturalist lacks.
Which actually makes up for a cogent argument with a reasonable conclusion. Particularly if you understand that the mentions of mathematics are only meant to embody and exemplify a greater discussion on the nature of things.
I sometimes imagine WLC nervously trying to fit in with his largely atheistic analytic colleagues, covering his tracks by being overly explicit, logical, predictable, and referential (which is just another way to say "boring"). You would expect more passion and spark from a true believer, but maybe he is just not that inventive to begin with.
On a personal note.
Yes, I believe in God. But, to me, trying to prove God's existence is as silly as trying to prove its inexistence. You can show that the idea of God is unreasonable, unlikely, stupid, and silly (strong atheism can be deconstructed in a similar fashion). I do not believe we can currently demonstrate it is impossible.
Unlike William Lane Craig, I am neither a preacher nor a philosopher. I am also not an Evangelical. I was raised Catholic, now I'm a spiritualist. This means that my views on the whole idea of preaching and proselytizing are very different than his.
I don't believe religion should indiscriminately spread and persuade the masses, much to the contrary. To me, religion and spirituality should always be a personal choice by a free-thinking adult. I would be very careful not to lead anyone into religion through forceful rhetoric.
That is, ultimately, what I find most disappointing in William Lane Craig's work.
Understood as theological discourse, I don't believe he lacks consistency or intellectual rigor. But, to me, this very carnal (and very Evangelical) notion that whatever it is that we believe must be reflected in a very literal manner onto the things that make up the material world is poor and narrow-minded. This shoddy motivation permeates his writing, and once I see it I cannot ignore it. He uses the words of a philosopher and employs concepts from mathematics and physics, but, in the end, he is a preacher more than anything. And I don't like preachers.
I'm sorry, I guess I don't understand. It's not unreasonable that math works. I can write 2 + 2 = 3, and the fact that that fails isn't proof that math is unreliable. It's proof that I'm wrong....
I'm sorry, I guess I don't understand. It's not unreasonable that math works. I can write 2 + 2 = 3, and the fact that that fails isn't proof that math is unreliable. It's proof that I'm wrong.
Saying that it's a happy coincidence that math and the universe conform is like saying it's a happy coincidence that things that are correct are correct. The math that doesn't conform to reality is discarded, the one that does is kept. Eventually you can predict things because you have a bunch of equations that are correct and that you've verified as being correct.
Maybe I'm misunderstanding the core argument here, but math being correct is what I would expect in any universe that has rules.
I think the question posed sort of biases the argument in favor of the theistic side. The writer poses questions about why math happens to work out, and when an answer is available presses the...
I think the question posed sort of biases the argument in favor of the theistic side.
The writer poses questions about why math happens to work out, and when an answer is available presses the scope further. In general the argument is that the fact that the universe obeys these patterns and rules that can be elegantly explained is itself evidence of intelligent design. But at one point the argument goes to saying that the insane complexity of how certain phenomenon work is evidence that math can't just be us projecting the simplest explanation onto complex phenomenon. This is all argued from the question of "why", and that's always going to tilt the argument in favor of the side which can give the easy answer of "because an intelligent mind decided it should be that way".
But you could just as easily ask the inverse question of why not and shift the argument toward the naturalist side. If you ask the question "why does the Earth's orbit have a period of 365 and a quarter days?" That's really easy for the naturalist to answer. The Earth isn't a conscious entity which chose to have that orbit length, so every answer makes as much sense as any other answer. But the theist has to figure out some rationale for why a God would have thought that an extra 1/4 of a day is important to some divine plan. So in that kind of question it would seem the naturalist has the more advantageous position.
The author makes strong assumptions about mathematical modeling that I (PhD in physics) disagree with. For example, he writes: (Emphasis added.) I am not sure why the author suggests the models...
The author makes strong assumptions about mathematical modeling that I (PhD in physics) disagree with. For example, he writes:
the fact that physical reality behaves in line with the dictates of acausal mathematical entities existing beyond space and time is, in the words of philosopher of mathematics Mary Leng, “a happy coincidence.”
(Emphasis added.) I am not sure why the author suggests the models are acausal. The entire purpose of mathematical models is to predict effects from causes. Or does the author mean to suggest that triangles are acausal? But then the adjective doesn't seem to fit; nobody would describe a sheep as "acausal".
The author uses this anecdote in an attempt to convince us that the coupling of mathematics and physics should feel unnatural. However, I would point out that the alternative -- i.e., that the universe should be completely divorced from mathematics -- is nearly inconceivable. Thus I do not find his appeal to intuition particularly convincing.
I could continue in this manner, but rather than repeat the comments others have made, I will suggest an alternative hypothesis.
The "unreasonable effectiveness" of mathematics might just be the unsurprising consequence of the universe being, in fact, a mathematical object. Perhaps the concept is a bit unintuitive, but I find this to be a more parsimonious explanation than "God dunnit".
I think the point he's making there is that if Mathematical Platonism is true, that is, if mathematical entities actually exist in some world of forms beyond time and space, then we shouldn't...
I am not sure why the author suggests the models are acausal. The entire purpose of mathematical models is to predict effects from causes. Or does the author mean to suggest that triangles are acausal?
I think the point he's making there is that if Mathematical Platonism is true, that is, if mathematical entities actually exist in some world of forms beyond time and space, then we shouldn't expect these forms to have a causal relationship with objects in the physical world. If the Platonic ideal of a triangle actually exists, it doesn't follow that this ideal has some sort of causal power within spacetime.
Regarding your last paragraph, I was wondering what you think mathematics is ontologically?
I'm rather sympathetic to Tegmark's philosophy. It's essentially Platonism without separating the mathematical world from the physical world. Tegmark argues that mathematical objects actually do...
I'm rather sympathetic to Tegmark's philosophy. It's essentially Platonism without separating the mathematical world from the physical world. Tegmark argues that mathematical objects actually do exist, and that our universe is one of those objects. Other mathematical worlds would exist but be inaccessible to us (in the same sense that two homework problems can exist in separate "worlds").
To give some motivation for the philosophy (not exactly arguments, more like intuition):
the universality of logic: for instance, consider the proposition "A and not A". In logic, this proposition always evaluates to false. I do not think that in other universes this proposition could ever evaluate to anything differently. That is, logic appears to have a sort of universal truth that transcends any sort of physical medium. If you assume something like logicism, then those other mathematical objects must be out there, somewhere.
the universality of Turing machines: if we keep abstracting away what is a permissible Turing machine (a computer, a human being with some paper and pencils, or maybe just a bunch of rocks), then at some point we must wonder where the thing we're simulating actually is. For instance, if you believe that simulated consciousness is conscious, then what's stopping you from simulating consciousness by rearranging rocks in the sand? And where would that consciousness be? In the rocks? In the mover? Or somewhere else entirely separate?
A relatively new argument for the existence of God based on the applicability of mathematics to the natural world. Considering that most arguments and theodicies that exist are hundreds if not...
A relatively new argument for the existence of God based on the applicability of mathematics to the natural world. Considering that most arguments and theodicies that exist are hundreds if not thousands of years old, this addition may be refreshing to those looking for new arguments to support or to deconstruct.
It's based on this paper [PDF] that's short enough to warrant being read in its entirety
If you genuinely want to advocate for more compassionate conversation, I feel it may be of interest to know that, to me, your comment severely misses the mark. To me, this reads more as veiled...
If you genuinely want to advocate for more compassionate conversation, I feel it may be of interest to know that, to me, your comment severely misses the mark.
To me, this reads more as veiled insults with belittling ("sciency people"), blaming ("tend to get angry"), victim complex ("Christian theology," not just theology in general), and blame shifting ("everyone [...] exercise emotional caution", as a command to others), finished off with a winky face as to indicate that a reader will get your thinly veiled meaning.
There is no need to apologize to me. I am not personally offended, nor do I feel I was the target of your comment. I have not contributed anything in the debate on the actual topic in the post and...
There is no need to apologize to me. I am not personally offended, nor do I feel I was the target of your comment. I have not contributed anything in the debate on the actual topic in the post and have no intention of doing so - in part because I know how heated these debates can be.
I only told you what your comment meant to me. You can choose to disregard my opinion and nothing more will come from that. My reply wasn't critiquing religion or science or anyone's stance on either. It observed that, if what you wished to communicate was genuinely for people to be kind with their comments and not let their emotions run wild, then for me at least the comment had the completely opposite effect.
You don't need to write "completely defensibly", "in accordance with everyone's feelings", or "like a lawyer", but genuinely, please, ask yourself if your reply here espouses the emotional caution you were yourself arguing for.
Can you expand upon what it is you find intense and forceful? I have tried to communicate the low stakes (examples below), but from your reply it seems clear to me that that is not how you have...
Can you expand upon what it is you find intense and forceful? I have tried to communicate the low stakes (examples below), but from your reply it seems clear to me that that is not how you have understood my responses.
I feel it may be of interest ...
To me, this reads more as ...
There is no need to apologize to me
I am not personally offended
I only told you what your comment meant to me
You can choose to disregard my opinion and nothing more will come from that
I mean those things. I am communicating my perspective, because I assume the same situation would arise with other people and that the message you intended to convey would be lost.
What do you mean by whether this is about you or not? Communication is never solely dependent on one person. To me, you seem to be taking away something completely different from my replies than what I am attempting to communicate. This is very much in parallel with your comment I originally replied to. I could be defensive and say that you are putting words in my mouth, or I could try to clarify so we can have clear communication. I try to choose the latter.
To expand on this, you say that you don't appreciate having your language scrutinized like that "with adversarial intent", but this to me seems as if you have the causality reversed. I didn't scrutinize your language to come to the conclusion that I found your original comment hostile. Rather, I read your comment and found it hostile, then introspected as to why I felt that way so that I could provide constructive feedback.
Would you have preferred I replied only with "This is a very hostile phrasing"?
Would you prefer not knowing that your intent did not survive in the communication?
You also seem to completely misunderstand why I replied to you, even though I tried putting it in clear terms.
I said you do not need to apologize to me, and I meant it. Any bad feelings I had about it subsided before I wrote the message. I did not write it in affect, I wrote it after consideration, in a desire to inform and assist. I practiced one part of what I would call emotional caution - not engaging solely with my first emotional reaction to the comment. What remains is that, whether you think so or not, whether you care or not, I am confident that your original comment is not communicating what you say you want it to, to a not insignificant portion of people.
This doesn't feel to be at all about me. I apologize for using language which caused you unfavorable thoughts, but it really feels that you are putting words in my mouth and sentiments in my heart here.
It is about both of us, and it is about all the other people who may read your comments. It is about what you want to convey, and what people understand from what you say. It is communication.
I am not putting sentiment in your heart, I am reading sentiment in your words. I am not saying that you have ill intent or bad faith, and I certainly have no intent of insinuating either of those. I am saying that the way it is phrased in your original comment, your intent is likely to get miscommunicated and lost.
I read your bio, and I would like to highlight this:
When interpreting my sentences, please keep in mind that I'm most likely in a context that is very different than yours.
This is exactly what I tried to assist with. I am not putting words in your mouth. I am not saying that the intent I received from the message is what you tried to convey or you believe in. I am only informing about how your message came across, because 1) I am certain I am not the only one for which that holds true and 2) I think the intent you say you had is worthwhile to argue for.
There are examples of folks immediately jumping to ad hominems to attack the character and motivations of those they disagree with in this thread. I don't know if I will be posting this sort of...
Additionally, I should emphasize that atheism on Tildes is a majority stance, and, if I seem a bit inflamed is because I speak from a minority position that is often barraged and overwhelmed with ridicule in environments like this.
There are examples of folks immediately jumping to ad hominems to attack the character and motivations of those they disagree with in this thread.
I don't know if I will be posting this sort of content on Tildes moving forward. I'm open to suggestions for places that are better suited to discussing the merits and problems of various philosophical or religious beliefs in a more nuanced way.
I'm an agnostic, ex-Christian that went through an angry atheist phase, but really have gotten bored of intense atheist polemics dominating any discussion of theology or philosophy. Often these...
I'm an agnostic, ex-Christian that went through an angry atheist phase, but really have gotten bored of intense atheist polemics dominating any discussion of theology or philosophy. Often these polemics are based in religious trauma, which makes them hard to reason with.
The Tildes crowd is far better than many other places, but I fundamentally agree about it being it's own topic.
I think this just fundamentally misplaces what "math" is. It's not some mystical object we've found, like the alien artifact that allowed humans FTL travel in Mass Effect or something. It's a tool, that humans invented. Humans have great need of predicting the future of our physical world, so much of the tools we developed in this area are geared towards modeling physics.
That is, the fact that "math" and the world fit each other like a glove is an indication of intelligent design - but not of the physical world, but rather of math!
It's like asking why the chainsaw is so unreasonably effective at cutting down trees.
There's all kinds of mathematical constructs that are not particularly useful in modeling most of the physical world. Take a riemann sphere or the extended real number line - these notably define division by zero, and are thus the resulting system isn't even a ring anymore, let alone a field. If you were to try and use them for physics, it would not turn out very well. The real numbers works well for physics because we very, very carefully designed it to.
Or take a galois field - which is useful in cryptography. In GF(7), if Susan had 3 apples and Bob had 6 apples, how many apples do they have? Well, 2, of course! Wait a minute. Not fitting like a glove anymore, now that we're using the wrong tool for the wrong job!
That's a bit of an amusing anecdote, considering chainsaws were originally developed to aid in child birth. But your point still stands, and it's why I rankled at this article.
Math is simply a way that humanity developed to explain events and the world around us. It's a tool like any other.
I often find apologetics deeply frustrating in the way of misunderstanding, misattributing, and cherry picking your way toward your foregone conclusion.
But, as a side note, holy hell that chainsaw thing is horrific. That's fascinating and also a thing I would be happy to un-learn.
The problem are the cases where we developed math that initially had no applicability to the natural sciences. We have regularly found, completely after the fact, that different mathematical concepts have this unreasonable applicability well after the concepts were already developed. That is to say, the math couldn't have been developed for its applications, as the application was discovered afterward.
That’s not a problem though? The world appears to act according to consistent rules. We have developed math to explore those rules as a model of the world. Why should it be a surprise that the implications of our explorations of the model of the world have analogues in the actual world?
I think it is precisely the world's organization around specific rules that is the crux of the argument. I'm not sure that these rules are "consistent", but that mathematics is unreasonably applicable in domain-specific ways.
Maybe an argument by analogy will help. Consider a globe of the earth: it is a tool to figure out how to get from point a to point b without getting eaten by dragons on the way. It later becomes instrumental in understanding geology, and continental drift. Is it “unreasonably effective” at a purpose outside of what it was designed for? Or is it a natural consequence of exploring a good model?
Why is it unreasonable that a tool can find application outside of its original, intended use?
Well, math starts with a set of axioms, unprovable truths, as the basis of the logic system. Then, using these fundamental choices, you build layers of proofs for results. One simple axiom is that there exists an empty set.
We can choose different axioms to get different results, or the same results differently. We've happened to generally settle on a common set precisely because they create a system that fits the real world rather well.
But there are choices, like the axiom of choice, that have strange and weird results which don't fit the real world as we understand it particularly well. It's a bit of an open question to figure out what weird things on math are just weird things, and what might have some meaning when used in physical models.
A good example of this is the history of solving depressed cubics (look up the old school math duels like with Tartaglia), and the creation of the imaginary number i to be a placeholder for the square root of negative 1. This allowed for the solving of all cubics, but centuries later we started seeing maths in physics that required i. Eventually it showed up in quantum wave equations, which really unsettled folks.
So I'm not particularly shocked that we keep finding odd things in math that apply to the real world, because we've chosen our axioms to help us in that.
This is all from memory on my phone so please forgive any little errors of memory.
Have a great night!
That’s my point precisely. Math models reality. It is therefore not surprising or “unreasonably effective” that when we make inferences from the model, that we find their analogues in reality.
Well, once again - just because a tool was developed to do one thing, doesn't mean it cannot ALSO be applied to others.
Take chainsaws, for example!
I don't know much about math, but I know there are many ways to think of mathematics in addition to the one you stipulated. So I did a little search for some links that might provide a broader context.
The discovered/invented debate is absolutely not a settled philosophical question, FWIW. Here's a decent Reddit thread on it.
Thank you for your reply!
If I'm being fair to the argument, I don't think Dr. Craig is taking a stance on what mathematics is, which I imagine would be an interesting, but completely separate discussion.
I think the argument hinges on the mathematics that are not created for application to the natural world. Not all mathematics is applied. This math that is initially developed by an aesthetic impulse (or to do mathematical problem solving) is later discovered to have unreasonably accurate applications in the natural sciences. The math is developed completely a priori to its application, which makes its applicability otherwise happily unexpected.
These examples are all borne of survivorship bias, however. We expand upon mathematical models that are most useful for our purposes, and we abandon mathematical models that are less useful. This works in the same as any tool humans have created: we invented wheels for children's toys, and then later discovered that wheels are also useful for a huge array of other purposes: transporting goods, spinning wool into yarn, devising clocks to measure time, converting the flow of rivers into usable power, etc.
Yet there are tons of other things that were invented for children's toys that turned out to not be nearly as useful as wheels. Likewise, it is common to develop mathematical models that have only very limited use — or are just plain bad. Humans do it all the time, but it's easy to not notice because bad math doesn't make headlines.
It is also worth pointing out that a model can be useful without being accurate, and vice versa. You don't see this so much in the sciences (where the goal is to simulate natural processes as accurately as possible), but it is common in other industries. For example, consider mathematical models used in video games to render scenes. In most cases, these models mimic the appearance of light and shadows, but they do not accurately simulate photons because that would require way too much computation power. These algorithms were invented whole cloth and offer no meaningful insight into natural process — yet they have been developed to a very high degree, and become ever more impressive year after year, because they are very handy to a lucrative industry.
Hypothetically, a scientist or engineer might have a look at one of these video game algorithms and find some way to refine it and apply it to their own work (for all I know, this has already happened a few times), but this does not make these models any less manmade. After all, the GPU is a wholly manmade tool developed for the video game industry, but it has turned out to also be extremely useful to the sciences.
He is implicitly taking the stance that it is something that is, rather than something that is created, however.
In that regard, the article doesn't actually have any examples of that. His main example is the prediction of the Higgs Boson, which did not require any particularly esoteric mathematical models. In fact, the main issue with the Higgs Boson was that there's LOTS of times where our mathematical models predict something we haven't observed... and the models are just wrong, actually.
Like I have described, there's plenty of esoteric models which are not useful and have never been useful to modeling physical items. The fact that occasionally some are pulled out of obscurity is a mix of 1) confirmation bias, most people have little reason to even learn about all the weird models that aren't ever useful 2) the fact that humans can never truly make something disconnected from the world, since our minds are developed with an intuition to the world we inhabit 3) the fact that many are just small deviations from mainstream models, and in many cases our models for the physical world are just slightly off from reality.
The Higgs boson is particularly interesting because it's the last major prediction we've made that we've experimentally verified, and completed the Standard Model. There's been a lot of math developed since, and I daresay most of it doesn't represent reality at all, even if it's very advanced.
I found this article very frustrating to read. It is structured as a series of questions answered by non-theists and theists, but the author doesn't seem to have put much thought into the non-theistic answers. In order to write a piece like this in good faith, you have to really deeply engage with people representing the other side of your argument, otherwise it comes across as a series of strawmen.
He's still alive, why not go ask him? Or at least ask some physicists and mathematicians familiar with the field. The author is a philosopher, so I understand why they exclusively reference other philosophers, but since this is framed as a persuasive essay ("Theism provides the best answer to this question"), I don't think it's acceptable to misrepresent the non-theism side.
This is not a mainstream view. I've never heard any mathematician or physicist say anything like this, and I find it hard to believe this is a common view even among mathematical philosophers. I think the author would benefit from asking actual working mathematicians who consider themselves mathematical realists whether they believe that the applicability of math to reality is a coincidence.
Later on, in the anti-realism section:
I'm sorry to hear that Balaguer had trouble answering this question. Did you look for any other philosophers or mathematicians who might have had an answer? No, you just immediately moved on to your own theistic view? That seems a little uncharitable.
In order to convince someone, you need to attempt to understand their point of view. When you wildly misrepresent that view, as I believe this essay has done, you can't expect anyone who disagrees with you to take you seriously. I don't know who the intended audience of this is, but as a persuasive essay it is not effective.
A lot of good points. If I may expand a bit on the points you made, I don't think this argument was written in good faith, nor was it written to substantially evaluate different points of view. But this is not necessarily a "mistake" on the author's part. I think it's likely that, consciously or subconsciously, this argument was written to convince some people on the fence, but more than that, it was written with motivated reasoning to affirm the views of the author and the already-convinced reader. It's basically an in-group validation of already existing beliefs.
This doesn't necessarily mean it's wrong, and I do think it's wrong for a variety of reasons, but it explains why it misinterprets the conflicting opinion. Because that's an easy way to achieve such validation.
For background, I grew up in a conservative Christian environment and although I would not identify as Christian anymore, I am still a Follower of the Way of Jesus (the distinction being a topic for another day).
I can't begin to count the number of books/videos/etc we were exposed to as children and teenagers that bent over backwards to explain why the Bible was not only right, but literally true. One that comes to mind was a book about "white holes" (as opposed to black holes) that tried to account for the apparent age of the universe. It was a very thin book with no math in it. As far as I can remember, there were none that ever presented a compelling (to me) case to reconcile science or math with that particular brand of faith. But they were held up s important, even scholarly ideas in the community.
Since you can't prove a negative, I won't say there aren't any books that make compelling theistic arguments and fairly represent the other side, but I believe @daywalker that you have hit the nail on the head with your analysis of this article and that it applies to the genre in general.
My own experience was being steeped in that culture, having certain things being presented as truth, and not having alternatives presented at all (or presented dismissively with weak strawmen). One of the consequences of that was that I didn't really have the vocabulary or framework to object to that treatment. I can imagine writing something like this as a teenager, and know now that it was probably about as far as I could go toward questioning things, because even trying to engage with the non-believers point of view at all or to read or study anything about it would have been pretty radical.
Back then, I knew something was not adding up, but was made to feel that it was something about me because it was unthinkable and sinful to question the "Truth". I would not learn how varied the ideas about what the Bible means, even among Christians until much later. It took me a long time to even realize how deeply I had internalized l that guilt, and I am still dealing with the effects decades later.
So that is all to say, I don't think we need to cut these authors any slack on picking apart their arguments. If they want to engage in the domain of logic/math/rhetoric, IMO they should follow the rules of those domains, or else stick to theological debate. But I think we can have some empathy and compassion for people steeped in this culture and realize that they may be acting in good faith (so to speak) but are buried so far into a specific set of norms that they can't function much differently than this.
To be clear, I'm just offering my viewpoint in the context of my agreement with @daywalker, not meaning to say anything about how they or anyone else are approaching the author or the posted article.
I went to a private religious high school and there was quite a bit of teaching about Jesus as a historical figure. The premise was that there are historical records that Jesus existed, so we should believe the other claims about him that are in the Bible, including the supernatural ones. If we believe historians about the life of Abraham Lincoln or King Henry VIII, why don't we believe the writers of the Bible?
Of course this is a ridiculous argument but when you are a kid you believe adults who are in positions of authority, and it creates unquestioned beliefs that can last a lifetime. Then you write papers about how mathematics proves God or that creationism is scientific.
I think this is why religious leaders talk so much about indoctrination. They know that it is pretty much the only reason they have followers and they don't want some other group doing the same thing with "liberal" ideas.
The funny thing is, as someone who also went to a private Christian high school, none of this Bible shit prevented me from leaving the church because the thing that sparked my "fall" from Christianity had nothing to do with doubting the Bible. I didn't come to abandon the young Earth creationism I'd been raised in until well after I had mostly abandoned the faith. I've only come to be interested in other historical discrepancies between the Bible and what we understand of history way later.
The thing that did break me out was an inability to reconcile the cruelty of our beliefs about homosexuality with my empathy for my irl gay friend. The load-bearing joint there was the belief that it was a choice... but when my best friend, who'd been indoctrinated in the same way as I, confessed to me that he was gay despite trying with all his might not to be? I couldn't continue to believe being gay was an active act of defiance in the face of such evidence, and without that piece I couldn't handle the cruelty inherent in creating gay people only to condemn them. I remember telling my mom (who remains steadfastly religious to this day) that even if it were true and God was real, I couldn't worship a God who would do something like that.
Of course I'm sure the vast majority of people from the Christian community I grew up in believe I "fell away" because of secular influence when I went to college. That's the usual myth. But I was VERY resistant to secular influence. I read all the Answers in Genesis books. When we went to Washington D.C. in 8th grade my best friend (the same one who would later come out as gay to me) and I planned to go to the National History Museum and argue with "the evolutionists" (thank god that never materialized, I don't think I could handle the retrospective embarrassment on that one). I completely bought into it all -- until I was confronted with someone I cared about and believed whose existence meant God was either unfathomably cruel or what I'd been taught wasn't true.
I once joked to my therapist that I stopped being a Christian because I cared more about my friends than Jesus. And that's sort of true. But I think more fundamentally, indoctrination is just fundamentally weak to empathy.
It's funny how we landed at the same conclusion from different ends. I started out by questioning why the Hindu gods were fake and ours wasn't, and never got a satisfactory answer. I was told I had to had faith, but I reckoned Hindu Raistlin was also being told to have faith, and one of us was definitely wrong.
And if they were wrong about that, they must be wrong about gay people too. So, in my very homophobic society, I landed at empathy for the LBGTQ+ almost by accident.
Regarding homosexuality being a choice: I used to listen to Dennis Prager on the radio quite a bit. A recurring theme for him was that gay marriage should not be allowed because being gay is a choice. And his proof for it being a choice is that societies that accept open homosexuality have more of it.
This has got to be one of the most ridiculous arguments of all time. Is he so stupid that he didn't realize that when you persecute and shun something fewer people admit to it? Or is he just a liar?
Well, now we know he is just a liar because of Prager U and it's misrepresentation of every topic that it covers.
By the way, he's yet another conservative who is very concerned that gay marriage harms the institution of marriage but he has multiple ex wives.
Oh yeah there's tons of BS like that from conservative grifters like him. But the true believers eat it up because the "it's a choice" tenet is absolutely foundational to the story they tell themselves about what they believe.
I think there are some leaders who cynically manipulate and indoctrinate their flock. Especially when you see significant divergence between the leader's behavior and their own actions.
But I've known a lot of leaders, especially in small churches where most of the congregation is involved in leadership (the men, anyway, but that is a whole different tirade). And they seemed sincere in their belief and in their conviction that their teaching and work were morally right. I have trouble believing that they were all cynically manipulating the group. I think it's much more likely that they are themselves victims of that indoctrination.
It took me almost 15 years and the forced time when we physically stopped going to church in the pandemic shutdown to face the fact that my values no longer aligned with many of the ways I was raised. During those years, I had a lot of physical symptoms of stress that would manifest when I was in the church environment, and I couldn't even admit to myself that was what it was about.
If it was so hard for me when my connection to the church was pretty small (someone once accurately characterized me as "the one who comes in after the greeting and sits in the back"), how much harder for someone who has devoted their life to it?
I am scared of the Christian nationalist movement in the US and what it might mean if they successfully gain power. I know there are people leveraging and weaponizing the movement to build a power base.
But when I deal with individuals, I try to remember that they can be sincere in their faith and that we are all to some extent a product of our raising. I have been lucky to have a lot of support in making the moves I needed to unwind things, but with a different spouse and s different family (like many families I grew up with), I can easily see how there could have been tremendous pressure to just bury those feelings and conform.
Most if not all arguments are constructed to persuade the receiver of a conclusion that the author already holds to be true or false. If not for this emotional motivation, it would be very difficult to produce compelling arguments. That is a given in philosophical discourse, of which this article is an example.
Unlike most things on the internet, WLC writes in a formalized way, so he doesn't have a lot of soft language to conceal his intentions. It's not a pleasant reading, but I wouldn't say it lacks "good faith". In fact, it may have it in excess.
Many modern apologetics do not seek to prove the existence of God. Arguments like this one seek to increase the credence in theism, even if just by a small amount, by showing that some state of affairs is otherwise more expected on theism than on naturalism.
Specifically, the author doesn't actually think that these arguments work on their own. They give "intellectual permission" for the would-be theist to pursue theism when inclined due to other factors (religious experience, witness of the Holy Spirit, etc.)
Yeah, I disagree on this take. It's written very obviously in bad faith misinterpretation and unwillingness to engage properly with conflicting opinions, and it doesn't understand science or nature other than some surface level take. Meanwhile, there are so much misinterpretations and "gotcha" takes.
Constant atheist polemics can be utterly exhausting, and can rob these discussions of the joy they may otherwise bring. Not everyone you disagree with operates in bad faith, and I think we should assume good faith until otherwise. This is coming from someone who isn't even a theist.
He debated this subject fairly exhaustively with atheist philosopher Dr. Graham Oppy. He's willing to engage with conflicting opinions with anyone who will give him the time of day. Really these atheistic polemics are quite off-putting.
I don't think you're trying to understand why I think it's bad faith, and insinuating that I'm being unreasonably polemical, or saying that I only think this argument is bad faith because it challenges my opinion leaves a bad taste in my mouth. Good luck on your topic, and hopefully it's more productive than this conversation, but I lost my interest in ours.
I'm sorry but calling daywalker's replies to you "atheist polemics" is an incredibly insulting and disrespectful way to respond here. Their comments criticizing WLC have not remotely approached "polemics" and don't even mention atheism in their comments. Criticizing WLC and believing he's arguing in bad faith in the polite manner daywalker has is perfectly reasonable discussion here om tildes, especially given that daywalker's comment is in response to WLC not engaging with or misrepresenting the fields he's using for his arguments here.
If you cannot be exposed to people criticizing your position, without accusing someone of writing "atheist polemics" when they do so, perhaps you shouldn't post or engage with Christian/theistic apologetics on Tildes. It's far from conducive to good discussion. You certainly shouldn't be lecturing others about taking others' arguments in good faith while simultaneously doing this.
His specific claims were that the article was "very obviously" made in bad faith and that it is unwilling to engage with dissenting opinions.
This is polemicism. I think the argument is very interesting, and I'm not even a theist. To dismiss it outright as being made in bad faith may play well rhetorically, but isn't the sort of conversation I'm interested in having. I'm interested in talking about the merits of the argument, not defending some Christian apologist from ad hominems when I'm not even a Christian myself.
I am a theist and I don't find the argument in the article convincing (nor imo is it particularly novel among theistic arguments). Furthermore, I'm an ex-evangelical and know from that background that WLC does indeed have a huge audience of devout Christians who engage with his arguments primarily to validate their already firmly set beliefs (I used to do this myself with WLC's own work!). Believing that he is operating in bad faith, again based on evidence that he is not engaging with the science and mathematics he bases his arguments on particularly thoroughly, and saying so in a very concise and polite manner on a Tildes topic is neither polemicism or an ad hominem.
No one is asking you to defend Craig from accusations of bad faith. You're free to disagree with that assessment. But you're shutting down discussion of the topic with accusations of polemicism rather than just leaving that thread be and engaging with the parts of the discussion that you want to engage in. Let other people discuss WLC's place in the philosophical discourse and whether they believe he's operating in good or bad faith if you don't want to do it. You not wanting to do it doesn't make them "polemics" or "ad hominem"
It doesn't really matter if you think the attack on WLC's character or motivations has merit or not; either way this is still the realm of polemics. And attacking the motivations of an opponent rather than the merits of their argument is literally textbook ad hominem.
Accusing proponents of an argument of acting in bad faith is precisely what shuts down conversations like these.
To me this reads like a more abstract version of the argument that the eye is too complex to have evolved naturally and work as well as it does, ergo it must have been created artificially.
An inability to adequately explain some natural phenomena is only evidence of our own limited understanding, not evidence for the existence of anything specific like a god.
Ditto. The concept is appropriately named the God of the gaps. Especially from a scientific standpoint, it's very unproductive to bring in deities in an attempt to fill the gaps in our knowledge.
This is precisely it — it’s a rework of intelligent design. It’s a bit like watching a conspiracy theorist hastily rationalizing as facts contradict their deeply held beliefs about the moon landing or JFK .
Oh, all the arguments for intelligent design are actually clearly disproven by science and mathematics under close examination? My god, this means the intelligent design goes even deeper. Even mathematics itself must have been intelligently designed!
I don't think his arguments here are very good, but I don't think it's really possible to disprove something like intelligent design. That's part of why it doesn't really belong in a scientific context at all - it's completely unfalsifiable. Imo that's why any arguments for its existence that aren't strictly philosophical tend to fall flat as well (in addition to those who try to "prove" intelligent design through math or science generally not being particularly well-versed in those fields, as we see here with WLC).
There's a lot to be said on the topic, and I'm not interested in expressing my feelings and thoughts on most of them, because these discussions are a bit old for me personally. But I'm just going to say that, it's amusing a little when people use the "elegance" and "beauty" of the universe or one of its properties as an argument.
Nobody can tell me the standard model is anything elegant or beautiful. It's ugly as hell, but it works. A similar point goes for genetics. A lot of the genetic code is unoptimized or utter shit, but evolution is diverse, so it's there. So these discussions always remind me of this comic. I'm sure there must be an xkcd comic making the same joke.
Edit: I guess I should elaborate that I don't think there isn't beauty in nature. Leaving aside the subjective nature of beauty here, I'm trying to say that the ugly side of nature (and science) doesn't get emphasized much. There's a lot of mundanity and ugliness in natural phenomena and science, but you don't hear about them or see them if you don't get into science on a deeper level.
I feel it is also worth noting here that, as they say, beauty is in the eye of the beholder. The beauty we see in the universe is a reflection of the evolutionary forces that shaped us, not an inherent quality of the universe.
A rolling landscape with greenery and water is, perhaps, attractive to us because our ancestors who were drawn to such places found it easier to meet their needs. A cloudless night sky bedecked with stars is, perhaps, attractive to use because our ancestors who made a study of it could navigate and judge the passage of seasons. Rhythmic sounds and repeating patterns are, perhaps, attractive to us because they are usually markers of life, which our ancestors would have been foolish to stray far from.
Meanwhile, to a dog, poop and rotting carcasses are beautiful; the human perspective is not definitive. Our ideals toward elegance probably say more about our long history as tool makers than they say about what is good or true.
I want to point out that the Standard Model is so ugly that we've spent the last 50 years trying to supersede it. We've spectacularly failed. The Standard Model and Einstein's theories of relativity are incredibly successful and predictive, and remain the gold standard for anything we do. String theory, less so.
I was going to post this at the top level, but since we got into beauty and elegance, I think I will post it here.
I don't personally find the topic of the article compelling. I didn't even know about the realism/anti-realism split, and it seems pretty abstract to me.
One thing I have always found compelling regarding a sense of order in the universe is the pattern that complex things emerge from simple things.
For example, 200 odd elements make up ... everything. Somehow mountains and water and farts and Gorilla glass are all possible from those atoms. I mean, it could just be lucky, or maybe this is a shit universe and the really good universes have a million types of atoms. But there is strange beauty in it.
Since you mentioned genetics, I don't disagree that our DNA is a mess, but the fact that all that mess, nuance, and variety is possible by coding just with four base pairs is quite something. Protein folding is another case -- just a handful of amino acids make up all the varied proteins that make our bodies and catalyze their biological processes. I know that proteins are manufactured by coding off of nucleotide sequences, so in some sense these two examples are related, but the way that protein folding (and therefore function) is emergent from the protein sequences feels like its own kind of amazing thing.
All that said, this is just something I enjoy about our universe. Whether anyone wants to take it as proof of a design or a designer, much less the work of a particular deity, is a matter of faith. If I have it, I can see its effects everywhere I look. If I don't, I won't. Which is why I think attempts to prove or argue that God exists like this article does are ultimately a fruitless exercise.
The more I think about it, the more I think that this kind of exercise is rooted in a believer struggling with doubt. Faith is by definition belief in something unproven (and perhaps unprovable). Certainty would be much more comforting, much less work, much less worry. But if it's unprovable, then that quiet voice of doubt will always be there. I think everyone believes in something, so maybe that common struggle can be a basis for understanding and kindness between us.
Edit to add: I just realized this is my second comment under one of @daywalker's comments. Not intentional, but your thoughts must be striking a vibe with me today.
My problem with this argument is that it seems like God is superfluous.
The question we seek to answer is, why is the universe so structured? Why isn't it a chaotic place incapable of supporting life? I don't know of a formal way to quantify or do statistics on the set of "every logically possible universe", but it seems intuitively true that the vast majority of that set would be less structured, less mathematically elegant (according to human notions of elegance) and probably incapable of supporting life as we know it. A more thorough examination of the question would have to substantiate that intuition, but let's grant it for the sake of argument.
So you say, because God made it so. But my issue is: in this set of possible universes, aren't there many universes with creator-gods that chose to make a chaotic universe? I don't see any reason, a priori, to assume that a creator-god couldn't do so. If we seek to use this to establish the existence of some kind of god, before we get onto specific theology, we can't assume the properties of God according to our beliefs while we're in the process of establishing that something like a god must exist. So we can't be sure that "God creates a highly mathematically structured and elegant universe" is any more likely than "God creates total chaos". In fact, if the intuitions about most possible godless universes are right, I don't see why the same doesn't apply to most godly universes as well.
But if that's the case, then why do we need God at all? If a universe with a god that creates mathematical elegance is as unlikely as a universe without a god at all that happens to be mathematically elegant, what exactly does God explain? The "why" is left unanswered.
The issue in general with these sorts of arguments is that they seek to establish the existence of a generic creator-god as a starting point to further expand into theology, but secretly smuggle in assumptions based on a particular theology to start with. It's a form of circular reasoning.
On your last point, I notice these arguments never end with a pantheon. Like, obviously there's a god for the strong nuclear force, which is entirely separate from the electromagnetic god. No, they end with whatever god the writer currently believes in. More to the point, they end with the theological and cosmological structure their society raised them with. Happy coincidence indeed!
This is a really good objection. Craig takes as a matter of definition that God has certain attributes (that Craig establishes separately), but I think even taking that, your objection stands. It seems that the kind of theism that this argument supports is one where God cares about bringing into being a world that is intelligible by human beings, or perhaps its design itself cries out for some sort of explanation (though I want to avoid design arguments here.)
Craig often uses probabilistic arguments, none of which will likely establish God for someone independently, but together raise the credence of theism or lower the credence of naturalism, potentially to a degree that one's mind may be changed. The Kalam, for instance, raises the credence in not just any creator-god, but a specific kind of creator-god (i.e., timeless, spaceless, personal.) When you use an argument like the one for math with other arguments, it seeks to raise the credence of a specific kind of theism.
All of that said, I think the objection specifically to this argument still stands.
While I don't agree with the conclusion of the article, I don't think it is badly done insofar as explanations of the unexplainable go.
Of course as a mathematician I already knew that I was closer to God's light than the other sciences. 😉 However, I do think a few notes are in order. First, while mathematics may provide many of the tools used in physics, I think the physicists deserve some credit in creating the standard model, and Peter Higgs is a physicist. The standard model is more than just a patch work of mathematical shovels; it was the creation of a conceptualization of the universe's mechanics.
That math fits the universe is because we've chosen axioms that help math do so. It's possible that our universe had others rules in the moments before, during, and after the big bang, and this is the rules that settled out from the annealing of our universe. Had those rules prevailed, our math and our physics would have been built differently.
When I said that the argument was attempting to explain the unexplainable, I'm thinking of things like the primordial synthesis of hydrogen, whose origins we may never unlock because it happened before the big bang. Or perhaps we will. But there is so much room for faith for those that choose it, even with our understanding of physics, that marshalling math to the defense of God seems almost silly to me.
That said, I don't mean to ridicule the argument or the author. Indeed, math is beautiful, and its applications wondrous. If one wants to find God's fingerprints in it, well, there are worse places. I mean, the equation for the dilation of time is just a reshuffling of the Pythagorean theorem. Simple math shovel, paired with deep insights.
Have a great night!
That is a fair and reasonable take.
I like how you understand that this is a philosophy article, so the role of mathematics in the argument does not necessarily require the correction you would expect from an article within the field of mathematics. That kind of nuance is rare to find online.
Although WLC is a respected philosopher, he is also a (literal) preacher. So you gotta read it with the understanding that his articles sometimes have two goals, and those goals are not necessarily in support of each other.
Why does there need to be a reason why? If the universe could have been any which way, and how it ended up was "breathtakingly" complex, why is that a problem? That was one of the possibilities, and it's what we got. Maybe I just don't get philosophy but the arguments against naturalistic anti-realism seem especially weak.
I think if we do concede that it is "breathtakingly" ordered according to mathematical principles, the question would be whether this outcome is more expected under naturalism or theism. Dr. Craig would likely say that it is more expected under theism, and I think there is some intuitive force to this. Depending on your metaphysics, of all the possible worlds that could've obtained, most wouldn't abide by the principles of mathematics, and the fact that mathematics keeps being applicable across domains in our world is unexpected. This doesn't "prove" theism by any stretch, but makes an argument that seeks to potentially raise the credence of theism at least a little.
I'm not so sure I can concede it's extraordinarily complex. We have a sample size of one; there's no way to know if our universe's complexity is at, above, or below the norm. There's no reason to believe universes fall on a bell curve, either. We can't make any assumptions about how things ought to be, because we only have one to go off.
Probably the best objection imo. We really don't have a means of assessing the probability of different types of universes forming.
I would say every single possible universe c would have its own mathematics. Whether the speed of light is faster or slower, mass has negative or positive values, etc.
What universes are you envisioning that wouldn't have their own math?
What would that mean? What would a universe that “doesn’t abide by the principles of mathematics” be? The axioms we choose for the real numbers are designed by humans. If the universe worked differently, you may need to choose different number systems. That’s fine.
Our existing universe is already pretty obnoxious. Quantum mechanics is extremely unintuitive, and extremely obnoxious to model. Non-determinism is not fun.
Why would whatever other universe that could exist not be describable by sufficiently complex logical models as this one can clumsily be?
It wouldn't behave in ways that are consistent or even intelligible. I think the argument goes that most would be completely incomprehensible.
Inconsistency can be made into consistency, just as the non-determinism of quantum mechanics is. We straight up cannot with absolute certainty predict how a quantum interaction goes - we can only model it probabilistically, and from there the tools of statistical physics enables useful, but not pin-point certain, predictions.
I don't see how this universe could not be modeled. In every interaction is it just uniformly random what happens? Well, that's a clusterfuck, but it can be modeled nonetheless. Just saying it's intelligible is just vacuously circular.
That's a good point. We've now landed at the idea that particles can be in a superposition of states, non locality, outcomes being inherently random, and knowledge of position and velocity being fundamentally contradictory. None of this black arts stuff means we can't model it. We can model it quite well. And if it looks like a weird foamy impossible mess? Shut up and calculate.
Two questions to that line of thought.
When people first came up with viagra, they didn't expect it to become the world's premiere drug for sexual dysfunction in men. They came up with it as a drug to treat cardiovascular problems. The fact that it just happened to "help" some folks with sexual problems was a happy side-effect. It was an unexpected application, but it could have been predicted based on what the drug does (dilate blood vessels).
William Lane Craig is the one living American philosopher who seriously and effectively defends the cosmological argument and the existence of God, but that doesn't mean that every single one of his articles is a defense of those very broad and disputed claims. Reading him can be frustrating because what he seeks to demonstrate is often of little consequence to most readers.
That is his conclusion:
Which actually makes up for a cogent argument with a reasonable conclusion. Particularly if you understand that the mentions of mathematics are only meant to embody and exemplify a greater discussion on the nature of things.
I sometimes imagine WLC nervously trying to fit in with his largely atheistic analytic colleagues, covering his tracks by being overly explicit, logical, predictable, and referential (which is just another way to say "boring"). You would expect more passion and spark from a true believer, but maybe he is just not that inventive to begin with.
On a personal note.
Yes, I believe in God. But, to me, trying to prove God's existence is as silly as trying to prove its inexistence. You can show that the idea of God is unreasonable, unlikely, stupid, and silly (strong atheism can be deconstructed in a similar fashion). I do not believe we can currently demonstrate it is impossible.
Unlike William Lane Craig, I am neither a preacher nor a philosopher. I am also not an Evangelical. I was raised Catholic, now I'm a spiritualist. This means that my views on the whole idea of preaching and proselytizing are very different than his.
I don't believe religion should indiscriminately spread and persuade the masses, much to the contrary. To me, religion and spirituality should always be a personal choice by a free-thinking adult. I would be very careful not to lead anyone into religion through forceful rhetoric.
That is, ultimately, what I find most disappointing in William Lane Craig's work.
Understood as theological discourse, I don't believe he lacks consistency or intellectual rigor. But, to me, this very carnal (and very Evangelical) notion that whatever it is that we believe must be reflected in a very literal manner onto the things that make up the material world is poor and narrow-minded. This shoddy motivation permeates his writing, and once I see it I cannot ignore it. He uses the words of a philosopher and employs concepts from mathematics and physics, but, in the end, he is a preacher more than anything. And I don't like preachers.
I'm sorry, I guess I don't understand. It's not unreasonable that math works. I can write 2 + 2 = 3, and the fact that that fails isn't proof that math is unreliable. It's proof that I'm wrong.
Saying that it's a happy coincidence that math and the universe conform is like saying it's a happy coincidence that things that are correct are correct. The math that doesn't conform to reality is discarded, the one that does is kept. Eventually you can predict things because you have a bunch of equations that are correct and that you've verified as being correct.
Maybe I'm misunderstanding the core argument here, but math being correct is what I would expect in any universe that has rules.
I think the question posed sort of biases the argument in favor of the theistic side.
The writer poses questions about why math happens to work out, and when an answer is available presses the scope further. In general the argument is that the fact that the universe obeys these patterns and rules that can be elegantly explained is itself evidence of intelligent design. But at one point the argument goes to saying that the insane complexity of how certain phenomenon work is evidence that math can't just be us projecting the simplest explanation onto complex phenomenon. This is all argued from the question of "why", and that's always going to tilt the argument in favor of the side which can give the easy answer of "because an intelligent mind decided it should be that way".
But you could just as easily ask the inverse question of why not and shift the argument toward the naturalist side. If you ask the question "why does the Earth's orbit have a period of 365 and a quarter days?" That's really easy for the naturalist to answer. The Earth isn't a conscious entity which chose to have that orbit length, so every answer makes as much sense as any other answer. But the theist has to figure out some rationale for why a God would have thought that an extra 1/4 of a day is important to some divine plan. So in that kind of question it would seem the naturalist has the more advantageous position.
The author makes strong assumptions about mathematical modeling that I (PhD in physics) disagree with. For example, he writes:
(Emphasis added.) I am not sure why the author suggests the models are acausal. The entire purpose of mathematical models is to predict effects from causes. Or does the author mean to suggest that triangles are acausal? But then the adjective doesn't seem to fit; nobody would describe a sheep as "acausal".
The author uses this anecdote in an attempt to convince us that the coupling of mathematics and physics should feel unnatural. However, I would point out that the alternative -- i.e., that the universe should be completely divorced from mathematics -- is nearly inconceivable. Thus I do not find his appeal to intuition particularly convincing.
I could continue in this manner, but rather than repeat the comments others have made, I will suggest an alternative hypothesis.
The "unreasonable effectiveness" of mathematics might just be the unsurprising consequence of the universe being, in fact, a mathematical object. Perhaps the concept is a bit unintuitive, but I find this to be a more parsimonious explanation than "God dunnit".
I think the point he's making there is that if Mathematical Platonism is true, that is, if mathematical entities actually exist in some world of forms beyond time and space, then we shouldn't expect these forms to have a causal relationship with objects in the physical world. If the Platonic ideal of a triangle actually exists, it doesn't follow that this ideal has some sort of causal power within spacetime.
Regarding your last paragraph, I was wondering what you think mathematics is ontologically?
I'm rather sympathetic to Tegmark's philosophy. It's essentially Platonism without separating the mathematical world from the physical world. Tegmark argues that mathematical objects actually do exist, and that our universe is one of those objects. Other mathematical worlds would exist but be inaccessible to us (in the same sense that two homework problems can exist in separate "worlds").
To give some motivation for the philosophy (not exactly arguments, more like intuition):
A relatively new argument for the existence of God based on the applicability of mathematics to the natural world. Considering that most arguments and theodicies that exist are hundreds if not thousands of years old, this addition may be refreshing to those looking for new arguments to support or to deconstruct.
It's based on this paper [PDF] that's short enough to warrant being read in its entirety
If you genuinely want to advocate for more compassionate conversation, I feel it may be of interest to know that, to me, your comment severely misses the mark.
To me, this reads more as veiled insults with belittling ("sciency people"), blaming ("tend to get angry"), victim complex ("Christian theology," not just theology in general), and blame shifting ("everyone [...] exercise emotional caution", as a command to others), finished off with a winky face as to indicate that a reader will get your thinly veiled meaning.
I assume that this isn't your intent.
There is no need to apologize to me. I am not personally offended, nor do I feel I was the target of your comment. I have not contributed anything in the debate on the actual topic in the post and have no intention of doing so - in part because I know how heated these debates can be.
I only told you what your comment meant to me. You can choose to disregard my opinion and nothing more will come from that. My reply wasn't critiquing religion or science or anyone's stance on either. It observed that, if what you wished to communicate was genuinely for people to be kind with their comments and not let their emotions run wild, then for me at least the comment had the completely opposite effect.
You don't need to write "completely defensibly", "in accordance with everyone's feelings", or "like a lawyer", but genuinely, please, ask yourself if your reply here espouses the emotional caution you were yourself arguing for.
Can you expand upon what it is you find intense and forceful? I have tried to communicate the low stakes (examples below), but from your reply it seems clear to me that that is not how you have understood my responses.
I mean those things. I am communicating my perspective, because I assume the same situation would arise with other people and that the message you intended to convey would be lost.
What do you mean by whether this is about you or not? Communication is never solely dependent on one person. To me, you seem to be taking away something completely different from my replies than what I am attempting to communicate. This is very much in parallel with your comment I originally replied to. I could be defensive and say that you are putting words in my mouth, or I could try to clarify so we can have clear communication. I try to choose the latter.
To expand on this, you say that you don't appreciate having your language scrutinized like that "with adversarial intent", but this to me seems as if you have the causality reversed. I didn't scrutinize your language to come to the conclusion that I found your original comment hostile. Rather, I read your comment and found it hostile, then introspected as to why I felt that way so that I could provide constructive feedback.
Would you have preferred I replied only with "This is a very hostile phrasing"?
Would you prefer not knowing that your intent did not survive in the communication?
You also seem to completely misunderstand why I replied to you, even though I tried putting it in clear terms.
I said you do not need to apologize to me, and I meant it. Any bad feelings I had about it subsided before I wrote the message. I did not write it in affect, I wrote it after consideration, in a desire to inform and assist. I practiced one part of what I would call emotional caution - not engaging solely with my first emotional reaction to the comment. What remains is that, whether you think so or not, whether you care or not, I am confident that your original comment is not communicating what you say you want it to, to a not insignificant portion of people.
It is about both of us, and it is about all the other people who may read your comments. It is about what you want to convey, and what people understand from what you say. It is communication.
I am not putting sentiment in your heart, I am reading sentiment in your words. I am not saying that you have ill intent or bad faith, and I certainly have no intent of insinuating either of those. I am saying that the way it is phrased in your original comment, your intent is likely to get miscommunicated and lost.
I read your bio, and I would like to highlight this:
This is exactly what I tried to assist with. I am not putting words in your mouth. I am not saying that the intent I received from the message is what you tried to convey or you believe in. I am only informing about how your message came across, because 1) I am certain I am not the only one for which that holds true and 2) I think the intent you say you had is worthwhile to argue for.
As you wish. I sincerely disagree with you on multiple things you say here, but I have no ill intent. I wish you well.
There are examples of folks immediately jumping to ad hominems to attack the character and motivations of those they disagree with in this thread.
I don't know if I will be posting this sort of content on Tildes moving forward. I'm open to suggestions for places that are better suited to discussing the merits and problems of various philosophical or religious beliefs in a more nuanced way.
I'm an agnostic, ex-Christian that went through an angry atheist phase, but really have gotten bored of intense atheist polemics dominating any discussion of theology or philosophy. Often these polemics are based in religious trauma, which makes them hard to reason with.
The Tildes crowd is far better than many other places, but I fundamentally agree about it being it's own topic.