Author here. My goal is to eventually turn this series into a book whose target audience is young people growing up in households where science is either not valued or actively denigrated, the kids who end up becoming flat earthers and young-earth creationists. Constructive criticism is welcome.
It's pretty rare for a child growing up in an anti-science household to be convinced to change their worldview by abstract philosophy, not least because they won't have access to those sorts of books.
It's quite common for a child growing up in an anti-science household to be convinced to change their views on science by devout Christians writing about evolution, dinosaurs, astronomy and so on. Fundamentalist parents are often quite surprisingly happy for their children to read those kinds of books because they are written from the perspective of the in-group. There's a reason that Life of Fred is popular.
If you want to write a book about the theory of science and what truth is, go ahead, but you aren't going to make much of an impact on that particular target audience.
I was just such a person. I was taught that being a YEC meant that we were the only ones who earnestly sought after the truth. The world was blind, and by rejecting a corrupted authority and assessing the world on their own we were more likely to arrive at the truth.
In college, I successfully took apart the arguments of the peers who tried to dissuade me from my beliefs. They weren't good arguments; they had no idea why what they believed was true, but I did. This reinforced my views more than anything.
But, this earnest searching for the truth also led me to take philosophy of science and religion courses at my university, and that was the first time that I actually learned the mechanics of what went into the scientific method, and particularly why that method tends to achieve its goal of arriving at the truth. My entire primary and secondary education had never contained an discussion of this, nor had anyone I'd ever spoken to known it.
I also came across the talk.origins pages (https://www.talkorigins.org/faqs/faq-welcome.html), which contained the first full exposition I'd seen of not just the theory of evolution, but also the tremendous host of failed falsification opportunities that support it. I was pulled into a more correct view of the world kicking and screaming, by the same forces that had kept me away from it for my entire life.
I can't speak to how common my experiences are, but I'm endlessly grateful to those who didn't presume that there wasn't anyone like me out there. Admittedly I do have a stick up my butt about this, since it's a refrain I hear often. But I suspect that many of the flat-earthers out there are budding scientists in disguise, poorly served by their environment, and waiting to be freed.
I don't disagree, but FWIW, I've spent quite a bit of time studying theology, and Christian apologetics and YEC in particular. I actually ran a Bible study in conjunction with a local church for about four years. So I may have a little bit more leverage than you think.
To reduce math to models of objective reality, you need to say what a model is.
To get Banach-Tarski you need to either accept Formalism - it is just a formal game whose concepts like uncountable sets do not "really" exist, or you need to accept that Platonic reality with uncountable things in it. If you try to model math in a way that can actually be rooted in objective reality, then you wind up with some form of Constructivism. And now Banach-Tarski goes away.
Well, it is an empirical question whether or not matter is continuous and infinitely divisible, or discrete. Our best theories tentatively suggest that matter is discrete (though it is hard to say how much confidence to put in that, or how we could really know either way).
Saying that Richard Nixon either did or did not eat eggs for breakfast at a certain date is a bit naive. There are many possible physical occurrences where the material reality will fail to neatly fall into whatever definitions you have of Richard Nixon, eat, breakfast and eggs. Reality itself is pretty cut and dry, till you start to take many worlds seriously, but the mapping of human concepts to physical phenomenon is very very slippery. Would you take it as a given that for some universal wave function, there is a mathematical predicate, formed from your Unicode, that corresponds to “a human is in the room”? It is plausible but unproven and seems like quite a big assumption to incorporate into your world view.
Yes, natural language is very problematic, and those problems extend even to what are normally considered very cut-and-dried propositions like "The sun rises in the east" or "The earth is round" or even "one plus one equals two." If you have a better example to suggest, I'm all ears.
FWIW, I take many-worlds very seriously. You might find this interesting:
Get technical proof reading, lots of technical proof reading.
I'm no expert in anything and I can see so many flawed or incomplete or inappropriate arguments. This might be okay for an interesting coffee table book but not for anything serious. I'll list a few examples of where my shallow understanding differs.
My biggest beef is "I've already tipped my hand and told you that (my hypothesis is that) mathematics is the study of possible models of objective reality." This is where I stopped reading altogether. That's not what most of mathematics is, such as those areas you listed. They are largely axiomatic systems of logic. That they correspond to such a degree with our experience of the 'real' world is the shocker.
Another one is the Banach-Tarski "paradox", the paradoxical part isn't that there's two from one. We can do this with only the real number line between 0 and 0.5 and fill the line from 0 to 1. That this defies our experience of the world isn't surprising as we don't deal interactively with uncountable infinities of any degree.
A final example is Church numerals--they encode numbers, just the numbers with no associated nouns. Something that might not make sense in our world but does in lambda calculus.
> the paradoxical part isn't that there's two from one
What do you think the paradoxical part is then?
> We can do this with only the real number line
Actually you don't even need the reals. You can do the same trick with just the rationals. Half of aleph-zero is still aleph-zero.
> Church numerals--they encode numbers, just the numbers with no associated nouns.
That's debatable. I would say that a Church numeral's noun is an action (actions are nouns), specifically, function application.
[UPDATE]
> My biggest beef is "I've already tipped my hand and told you that (my hypothesis is that) mathematics is the study of possible models of objective reality."
I guess I didn't make it sufficiently clear that I'm not claiming this is an accepted consensus, this is a hypothesis that I am advancing and prepared to defend. Maybe I should be more explicit about that.
> They are largely axiomatic systems of logic.
I don't deny that. But not all axiomatic systems of logic are mathematically interesting. Chess, for example, can be axiomatized, but it's not particularly interesting from a mathematical point of view. You're not going to win a Fields medal for finding interesting chess puzzles.
> That they correspond to such a degree with our experience of the 'real' world is the shocker.
Yes, exactly. That is one of the facts that supports my position.
I've spent decades studying YEC and Christian apologetics. I even ran a Bible study for four years, and I was on the YouTube YEC debate circuit for a while. I don't know if that counts as "talking to my users" but I'm not going in to this cold.
In fact, the reason I wrote this installment in the series is because I know that apologists often cite the (alleged) "purity" of mathematical truth as evidence for the existence of God and I wanted to nip that argument in the bud.
But Gandalf absolutely exists in objective reality. it's a very real fantasy figure. there exists posters, figurines, drawings, the word "Gandalf" printed millions of time in tens of thousands if not hundreds of thousands of printed physical copies of LOTR
That essay was written earlier, so it's not part of the series, but that's the answer. Yes, Gandalf exists in objective reality, but as a fictional character, not as a wizard. So "Gandalf was a wizard" is false if it is taken to mean that Gandalf was an actual wizard in the real world.
The power of science is to find evidence to the best explanations, not to get people to believe something.
If the learner does not or cannot connect explanations to his lived world, the method is irrelevant as it is dogma. To copy dogma is robotic.
All of us routinely depend on systems we can't explain, nor is there any point to trying to explain everything.
What's valuable is that the systems can be explained by their maintainers and adventurers, and that systems of explanation are federated to permit those who wants to know to participate constructively.
As to pedagogy, society has an interest in public education, to ensure that wide sectors do not become organized around bullshit. As we all largely depend on systems no individual can be expected to completely understand, hygiene of knowledge is important because knowledge is scarce relative to the total societal system, demanding conservation.
Due to scale and complexity of society, narrowly localized and unmediated communities of knowledge may work as cults. The balance is achieved through federation and sharing of responsibilities which ensure that explanations are locally relevant.
The service space of the community determines the natural scope of knowledge.
A decent society will encourage exploration and contribution to the larger commons, and accept dissent as a rigorous part of collaboration and maintenance of the commons.
The greatest immediate hazard of AI is the replacement of the commonwealth of knowledge with proprietary, mediated and transduced explanatory templates which even the maintainers of services follow but do not understand, leading to a breakdown in the social fabric of knowledge and the submission of people to the status of robots. This might lead to society tearing apart b in a way that destroys the largesse which every wealthy person unconsciously presumes as his entitlement.
"Do not make machines in the likeness of the human mind."
> What's valuable is that the systems can be explained by their maintainers and adventurers, and that systems of explanation are federated to permit those who wants to know to participate constructively.
Yes, I agree. But I think it's also important that the ability to recognize people who actually understand the systems, to distinguish actual experts from skilled charlatans, be much more widely distributed than it currently is.
Sounds like you would like to help people activate their BS detectors. You would need to show them easy to detect examples and then break it down. With each iteration getting more and more abstract in the BS cataloged.
> I can't show you "green" unless I show you a green thing. Adjectives have to be bound to nouns to be exhibited, but that doesn't mean that "green" does not exist in objective reality. It does, it's just not a thing.
I disagree. Green is quite literally a figment of our imagination. It has some shared properties (e.g. humans can perceive green better than red or blue) but to say it "exists in objective reality" implies that it’s not subjective. But it is; there’s no way to know whether how I see green is how green looks to you. All that we can say is that we can distinguish green from other colors at similar rates.
I don’t think this is a small quibble. It’s the fundamental problem of trying to pin down philosophy too precisely. https://paulgraham.com/philosophy.html
> "Much to the surprise of the builders of the first digital computers," Rod Brooks wrote, "programs written for them usually did not work." [6] Something similar happened when people first started trying to talk about abstractions. Much to their surprise, they didn't arrive at answers they agreed upon. In fact, they rarely seemed to arrive at answers at all.
> They were in effect arguing about artifacts induced by sampling at too low a resolution.
> The test of utility I propose is whether we cause people who read what we've written to do anything differently afterward. Knowing we have to give definite (if implicit) advice will keep us from straying beyond the resolution of the words we're using.
And to your point, we can even say we do know for certain that some people have different color experience than us, given that there are colorblind individuals.
I wouldn't say we can't ever know how someone elses' green looks to us, I think that's an empirical question that's tied up in structure and function of consciousness, where better theories or advances brain to machine (or, who knows, brain to brain) interfaces may produce inroads.
>but to say it "exists in objective reality" implies that it’s not subjective.
Props to you for your careful phrasing here, as you've phrased this in a way that accounts for things being both in objective reality but also nevertheless subjective. I think that's very important, but I think it has a slightly different upshot.
That it's subjective means it's not necessarily a property out there in the world since it's tied to our subjectivity, but the flip side is, subjectivity itself is built out of the same stuff that builds the objective world and the greenness of subjectivity, so it could be objectively in there, so to speak. (E.g. specific color experiences might consistently show up the same way in brains, or we can come up with robust definitions that tie color to something objective that's in the spirit of normal usage of color terms even while accounting for individual variation).
I would just say it's something contingent on better future understanding and we have to be careful about declarations that imply some kind of ultimate unknowability-in-principle.
You and the GP have both missed the point. The reason green is part of objective reality has nothing to do with human's subjective experience (except insofar as it leads us to attach a label to this particular phenomenon). I can predict with very high accuracy what things other humans will identify as "green", and I can even build a machine that will do this as well. That fact is hard to account for if "Green is quite literally a figment of our imagination." It isn't. Green screens would still work and green detectors would still work even if there were no humans. The green-ness of green things isn't contingent on human perception any more than the roundness of round things is.
>But it is; there’s no way to know whether how I see green is how green looks to you.
The consciousness conversation comes up pretty often here. I kinda disagree with the idea that there's no way to communicate experience directly. Yea, at present there is no way to know that we have the same experience of green. But imagine in the future we were able to analyze/probe the computation of the brain and had more advanced biological engineering. Would we still not be able to determine experimentally what constitutes the sensation of green (and, as a result, be able to manipulate it)? Why not? It seems more like a practical/current problem rather than a theoretical one.
I think it is a claim, not an argument, really (one I do happen to agree with); essentially that if we had good enough neuroscience we could find the sensation of green in the cells, signals, or whatever.
There’s something in those cells and signals that is having the first-person perspective of being me, which is experiencing the sensation of green. I believe that the matter is all there is, so it must be in there somewhere. But for example if it is in the carbon, I wonder why we haven’t found it when we look very hard at pencil lead? I mean, that’s getting way ahead of ourselves, we don’t really know how to characterize it at all other than by this one very odd thing that it seems to do.
How do you account for the fact that I can predict with overwhelming accuracy what things other people will identify as "green", and that I can even build a machine that will do the same thing?
The trouble with those concepts is that there’s no way to measure them precisely. This tends to be at odds with the scientific method, though people try to sidestep them.
E.g. the noun definition of green is
> a color intermediate in the spectrum between yellow and blue, an effect of light with a wavelength between 500 and 570 nanometers; found in nature as the color of most grasses and leaves while growing, of some fruits while ripening, and of the sea.
This is different than saying that quarks exist, and that protons are formed from two up quarks and one down quark. These are truths of nature, whereas your examples are of human nature. It’s hard to even say whether a statement about them is true or not, let alone that those things exist.
Readit News
It's quite common for a child growing up in an anti-science household to be convinced to change their views on science by devout Christians writing about evolution, dinosaurs, astronomy and so on. Fundamentalist parents are often quite surprisingly happy for their children to read those kinds of books because they are written from the perspective of the in-group. There's a reason that Life of Fred is popular.
If you want to write a book about the theory of science and what truth is, go ahead, but you aren't going to make much of an impact on that particular target audience.
In college, I successfully took apart the arguments of the peers who tried to dissuade me from my beliefs. They weren't good arguments; they had no idea why what they believed was true, but I did. This reinforced my views more than anything.
But, this earnest searching for the truth also led me to take philosophy of science and religion courses at my university, and that was the first time that I actually learned the mechanics of what went into the scientific method, and particularly why that method tends to achieve its goal of arriving at the truth. My entire primary and secondary education had never contained an discussion of this, nor had anyone I'd ever spoken to known it.
I also came across the talk.origins pages (https://www.talkorigins.org/faqs/faq-welcome.html), which contained the first full exposition I'd seen of not just the theory of evolution, but also the tremendous host of failed falsification opportunities that support it. I was pulled into a more correct view of the world kicking and screaming, by the same forces that had kept me away from it for my entire life.
I can't speak to how common my experiences are, but I'm endlessly grateful to those who didn't presume that there wasn't anyone like me out there. Admittedly I do have a stick up my butt about this, since it's a refrain I hear often. But I suspect that many of the flat-earthers out there are budding scientists in disguise, poorly served by their environment, and waiting to be freed.
To get Banach-Tarski you need to either accept Formalism - it is just a formal game whose concepts like uncountable sets do not "really" exist, or you need to accept that Platonic reality with uncountable things in it. If you try to model math in a way that can actually be rooted in objective reality, then you wind up with some form of Constructivism. And now Banach-Tarski goes away.
I did. See the paragraph that starts, "A model is any physical system whose behavior correlates in some way with another physical system."
> If you try to model math in a way that can actually be rooted in objective reality...
It's pretty clear you didn't actually read all the way to the end.
FWIW, I take many-worlds very seriously. You might find this interesting:
https://blog.rongarret.info/2019/07/the-trouble-with-many-wo...
I'm no expert in anything and I can see so many flawed or incomplete or inappropriate arguments. This might be okay for an interesting coffee table book but not for anything serious. I'll list a few examples of where my shallow understanding differs.
My biggest beef is "I've already tipped my hand and told you that (my hypothesis is that) mathematics is the study of possible models of objective reality." This is where I stopped reading altogether. That's not what most of mathematics is, such as those areas you listed. They are largely axiomatic systems of logic. That they correspond to such a degree with our experience of the 'real' world is the shocker.
Another one is the Banach-Tarski "paradox", the paradoxical part isn't that there's two from one. We can do this with only the real number line between 0 and 0.5 and fill the line from 0 to 1. That this defies our experience of the world isn't surprising as we don't deal interactively with uncountable infinities of any degree.
A final example is Church numerals--they encode numbers, just the numbers with no associated nouns. Something that might not make sense in our world but does in lambda calculus.
What do you think the paradoxical part is then?
> We can do this with only the real number line
Actually you don't even need the reals. You can do the same trick with just the rationals. Half of aleph-zero is still aleph-zero.
> Church numerals--they encode numbers, just the numbers with no associated nouns.
That's debatable. I would say that a Church numeral's noun is an action (actions are nouns), specifically, function application.
[UPDATE]
> My biggest beef is "I've already tipped my hand and told you that (my hypothesis is that) mathematics is the study of possible models of objective reality."
I guess I didn't make it sufficiently clear that I'm not claiming this is an accepted consensus, this is a hypothesis that I am advancing and prepared to defend. Maybe I should be more explicit about that.
> They are largely axiomatic systems of logic.
I don't deny that. But not all axiomatic systems of logic are mathematically interesting. Chess, for example, can be axiomatized, but it's not particularly interesting from a mathematical point of view. You're not going to win a Fields medal for finding interesting chess puzzles.
> That they correspond to such a degree with our experience of the 'real' world is the shocker.
Yes, exactly. That is one of the facts that supports my position.
In fact, the reason I wrote this installment in the series is because I know that apologists often cite the (alleged) "purity" of mathematical truth as evidence for the existence of God and I wanted to nip that argument in the bud.
I address that here:
https://blog.rongarret.info/2015/02/31-flavors-of-ontology.h...
That essay was written earlier, so it's not part of the series, but that's the answer. Yes, Gandalf exists in objective reality, but as a fictional character, not as a wizard. So "Gandalf was a wizard" is false if it is taken to mean that Gandalf was an actual wizard in the real world.
If the learner does not or cannot connect explanations to his lived world, the method is irrelevant as it is dogma. To copy dogma is robotic.
All of us routinely depend on systems we can't explain, nor is there any point to trying to explain everything.
What's valuable is that the systems can be explained by their maintainers and adventurers, and that systems of explanation are federated to permit those who wants to know to participate constructively.
As to pedagogy, society has an interest in public education, to ensure that wide sectors do not become organized around bullshit. As we all largely depend on systems no individual can be expected to completely understand, hygiene of knowledge is important because knowledge is scarce relative to the total societal system, demanding conservation.
Due to scale and complexity of society, narrowly localized and unmediated communities of knowledge may work as cults. The balance is achieved through federation and sharing of responsibilities which ensure that explanations are locally relevant.
The service space of the community determines the natural scope of knowledge.
A decent society will encourage exploration and contribution to the larger commons, and accept dissent as a rigorous part of collaboration and maintenance of the commons.
The greatest immediate hazard of AI is the replacement of the commonwealth of knowledge with proprietary, mediated and transduced explanatory templates which even the maintainers of services follow but do not understand, leading to a breakdown in the social fabric of knowledge and the submission of people to the status of robots. This might lead to society tearing apart b in a way that destroys the largesse which every wealthy person unconsciously presumes as his entitlement.
"Do not make machines in the likeness of the human mind."
Yes, I agree. But I think it's also important that the ability to recognize people who actually understand the systems, to distinguish actual experts from skilled charlatans, be much more widely distributed than it currently is.
I disagree. Green is quite literally a figment of our imagination. It has some shared properties (e.g. humans can perceive green better than red or blue) but to say it "exists in objective reality" implies that it’s not subjective. But it is; there’s no way to know whether how I see green is how green looks to you. All that we can say is that we can distinguish green from other colors at similar rates.
I don’t think this is a small quibble. It’s the fundamental problem of trying to pin down philosophy too precisely. https://paulgraham.com/philosophy.html
> "Much to the surprise of the builders of the first digital computers," Rod Brooks wrote, "programs written for them usually did not work." [6] Something similar happened when people first started trying to talk about abstractions. Much to their surprise, they didn't arrive at answers they agreed upon. In fact, they rarely seemed to arrive at answers at all.
> They were in effect arguing about artifacts induced by sampling at too low a resolution.
> The test of utility I propose is whether we cause people who read what we've written to do anything differently afterward. Knowing we have to give definite (if implicit) advice will keep us from straying beyond the resolution of the words we're using.
I wouldn't say we can't ever know how someone elses' green looks to us, I think that's an empirical question that's tied up in structure and function of consciousness, where better theories or advances brain to machine (or, who knows, brain to brain) interfaces may produce inroads.
>but to say it "exists in objective reality" implies that it’s not subjective.
Props to you for your careful phrasing here, as you've phrased this in a way that accounts for things being both in objective reality but also nevertheless subjective. I think that's very important, but I think it has a slightly different upshot.
That it's subjective means it's not necessarily a property out there in the world since it's tied to our subjectivity, but the flip side is, subjectivity itself is built out of the same stuff that builds the objective world and the greenness of subjectivity, so it could be objectively in there, so to speak. (E.g. specific color experiences might consistently show up the same way in brains, or we can come up with robust definitions that tie color to something objective that's in the spirit of normal usage of color terms even while accounting for individual variation).
I would just say it's something contingent on better future understanding and we have to be careful about declarations that imply some kind of ultimate unknowability-in-principle.
The consciousness conversation comes up pretty often here. I kinda disagree with the idea that there's no way to communicate experience directly. Yea, at present there is no way to know that we have the same experience of green. But imagine in the future we were able to analyze/probe the computation of the brain and had more advanced biological engineering. Would we still not be able to determine experimentally what constitutes the sensation of green (and, as a result, be able to manipulate it)? Why not? It seems more like a practical/current problem rather than a theoretical one.
There’s something in those cells and signals that is having the first-person perspective of being me, which is experiencing the sensation of green. I believe that the matter is all there is, so it must be in there somewhere. But for example if it is in the carbon, I wonder why we haven’t found it when we look very hard at pencil lead? I mean, that’s getting way ahead of ourselves, we don’t really know how to characterize it at all other than by this one very odd thing that it seems to do.
How do you account for this then?
https://www.studiobinder.com/blog/what-is-a-green-screen-vid...
How do you account for the fact that I can predict with overwhelming accuracy what things other people will identify as "green", and that I can even build a machine that will do the same thing?
"Green" as in Plato's form, an external perfect entity surpassing out physical word, probably doesn't exist.
"Green" as in a specific frequency of electromagnetic spectrum we choose to label thusly, exists
all the way out to measurement i.e. measured data i.e. inputs.
> Green is quite literally a figment of our imagination
All words are made up, so in that sense "figments of imagination." Green is a shared concept. Like cold. Or love. Or justice.
And to address the author, just like those other non-concrete things, green is literally a noun.
Well, it can be, if you say something like, "I ate some greens." But most of the time it's an adjective, as in, "The pine trees were tall and green."
"the truth" is conceptually an adjective. to treat it as a noun is to get into philosophically tight spaces.
E.g. the noun definition of green is
> a color intermediate in the spectrum between yellow and blue, an effect of light with a wavelength between 500 and 570 nanometers; found in nature as the color of most grasses and leaves while growing, of some fruits while ripening, and of the sea.
This is different than saying that quarks exist, and that protons are formed from two up quarks and one down quark. These are truths of nature, whereas your examples are of human nature. It’s hard to even say whether a statement about them is true or not, let alone that those things exist.