That attitude is the weapon of suppression. Yes, it's true that life isn't fair. But it's also true that people have agency and can make material improvements to their own quality of life through smart decisions and dedication. Of course most of us won't start the next Google, but that doesn't mean dreams and hope are bad in general.
We have no evidence that people have meanginful agency, or even agency at all. It is an assumption that to start with requires that the universe is not largely or entirely deterministic beyond what we can measure, but even in the case of some "hidden variable" that provides agency (try to even define it in a way that doesn't make it either deterministic, random, or a combination that implies no actual control) we have plenty of evidence that events outside our control ("life isn't fair") means that the vast majority of people, while they may make decisions - with or without agency - that will make material improvements - still are not able to get anywhere near a position that makes it meaningful in this context.
Dreams and hopes are great - I believe we have zero actual agency, but that doesn't mean I lie in bed despairing, because not doing the work and trying will still have negative effects whether I have agency over that decision or not.
But the point is that dreams and hopes are also often used to play up the idea that "anyone" can achieve something everyone clearly can't, and so for most people, their most ambitious dreams will never be reached, and so a better gamble for most people would be to work for a society that improves everyones odds at reaching at least some of them.
If you think you have no agency why do anything at all?
You could choose to stop doing anything.
Or you could decide that your partial knowledge(unrealised futures) gives you agency.
It's a matter of metacognition. Being able to compute possible futures gives you artificial agency at some level. At a meta level even if that compute can be deterministic at a higher level, but you should not care.
It's a nested universes system just like in type theory. The meta of the meta. Agency is only defined within a single universe at a time.
> If you think you have no agency why do anything at all?
I addressed that in my comment, but let me address it again since it's the most frequent objection to this:
> You could choose to stop doing anything.
In the mechanical sense that an "IF ... THEN ... ELSE" statement makes the program "choose" which branch to take, you're right, yes I could.
But then I'd also suffer the consequences.
As I pointed out, if I were to life down in despair and not go to work, I won't keep getting paid just because I didn't have agency over the "choice" of whether to lie down and sulk or get up and go to work.
But for "agency" to have any meaning, we can't interpret choice that way. If we don't have agency, then while I may have an artificial "choice", that "choice" can't change the outcome.
In that case every "choice" I make is just as deterministic as that IF ... THEN ... ELSE: The branch taken depends on the state of the system.
> Or you could decide that your partial knowledge(untealised futures) gives you agency.
>
> It's a matter of metacognition. Being able to compute possible futures gives you artificial agency at some level. At a meta level even that compute ca be deterministic but you should not care.
What you are describing is compatibilism: The school of thought on "free will" that effectively says that free will is real, but is also an illusion.
Personally I think that is basically brushing the issue under the carpet, though I also think it is the only definition of free will that is logically consistent.
I do agree with the point that you mostly should not care:
You need to mostly act as if every "choice" you make does matter, because whether or not you have control over it, if you do lie down in despair, your paychecks will stop arriving.
Cause and effect does not care whether or not you have agency.
Where I take issue with compatibilism is because there are considerable differences in how you should "choose" to act if you consider agency to be "artificial" or an illusion (compatibilism) or not exist at all (for this purpose these are pretty much equivalent) vs. if you consider it to be real.
E.g. we blame and reward people or otherwise treat people differently based on their perceived agency all the time, and a lot of that treatment is a lot harder to morally justify if you don't believe in actual agency. Real harm happens to people because we assume they have agency. If that agency isn't real, it doesn't matter if we have an illusion of it - in that case a lot of that harm is immoral.
To tie it back to the thread: Whether agency is not real at all, or just significantly constrained by circumstance, it changes the considerations in what we should expect ourselves and others to be able to overcome.
E.g. it makes no logical sense to feel bad about past choices, because they couldn't have gone differently (you can still feel bad about the effects, and commit to "choosing" differently in the future). You also then shouldn't feel bad if you haven't achieved what you wanted to if you believe the context you live within either have total control over the actions you take, or "just" a significant degree of influence over it.
And so we're back to my original argument that for most people, acting as-if they have agency by "choosing" to bet on making the surrounding conditions more amenable to good outcomes is a better bet than thinking they have agency or enough agency to achieve a different outcome.
But again: The fact that I believe we have no agency, does not mean I won't try to do things that will get me better outcomes. I just don't assume I could act any other way in a given instance than I end up acting in that given instance, any more than a movie will change if you rewind it and press play again.
I think we agree. The subtelty is that, it is about closed and open systems.
Your partial knowledge makes things a locally open system.
You are processing new data and then acting accordingly.
That's dynamic agency. The better you can get knowledge, the better you can influence the next step.
That realization happens at the meta level and gives you agency in your actual universe.
Even though at the meta-meta level, that realization itself can be deterministic.
Not to be confused with someone who would be external to the system and could watch your life as if it was a video tape, being omniscient.
They would not have agency in your system as they can't interact with you and for them everything is predetermined, and they could compute the next state of the system from the past state.
You can't but the system is impredicative enough that by recognizing this, by self-consciousness, the system effects itself toward its own favored state.
And in fact, the more knowledge you have, the less agency. Because the fewer choices.
The meta level person doesn't just observe how the video. It observes the fact that people realize they are characters in a video and how that realization affects the choices they make. Given the initial conditions.
Should you have regrets in life? You had the choice of knowing more and be more able so it makes sense. Could things have happened differently given that they did and obviously you wanted back then for them to be different and wish they had been? Or did it happen because the conditions were set to happen?
Basically the question is whether we control our odds?
Doing anything is controlling some odds so I'd say yes. Requires increased self consciousness. Being able to imagine what is not there. Animals seem to have that capacity. Especially humans.
We can make sure that certain things don't happen by virtue of our own existence. This is our agency.
Are we biased by construction toward the best odds of we can recognize them? Yes. Are their really things with the exact same odds in the system? Wouldn't that block us? Probably. But the system is already made in a way that it wouldn't happen by virtue of having (at least local) asymmetries. In practice we wouldn't be blocked. Someone perfectly symmetrical in a system that also is, would perhaps. But there might not be any two same most desired odds then so no. Unlikely.
So again, this is basically the compatibilist stance. To me, it rings hollow because it glosses over whether you actually made a decision in a way that is qualtitively different from how a clock "chooses" to move the minute hand one minute further.
And so I would answer to your question about regrets that I don't believe you had that choice. That you couldn't have chosen differently given the same inputs and state. Your "choice" followed the preceding state with the same predictability as a well functioning clock.
Interesting thought exercise, let me try something:
Only if we can predict everything ourselves do we not have a choice.
But since we don't know what we don't know and that may occur at any moment (black swan), we can only act given probabilities.
Then what we control is our level of appetite for risk of an undesired outcome.
That risk is not data that we can reliably measure and assert.
So it creates randomness/stochasticity in the system.
That's why I was speaking of open vs closed system.
Randomness provides agency.
That randomness is subjective. You may well still be predictable for an omniscient person. But that person would not have any agency.
You do as long as your choice does not rely upon knowledge.
I guess that's why the human society is weird in a sense. People act from belief they have no certitude about.
A clock does not do that, there is no metacognitive process to influence an action toward a yet unrealised future. Seems incomparable?
But yes, other than that, there is not real accurate way to deny compatibilism I'm afraid.
In fact, true agency is the attempt to eliminate choice.
It is like being in a Labyrinth where the walls are moving.
The clock sits in the labyrinth and gets crushed by a moving wall.
An agentic person detects the movements and recalibrates.
Honestly I don't disagree with anything you wrote, I don't think. It is worth remembering that if we were born in someone else's shoes, with their genes and their environment, we would literally be them and would act as they act. In that way, yes, agency is an illusion. Remembering this can help us to have empathy for others, potentially even those with whom we vehemently disagree.
But, as you said, we still all make decisions every day, and those decisions do affect our lives. So by acting as if we have agency, we can still have a positive impact, both on ourselves and others.
The attitude that we should all have access to more freedoms and that inequality has reached extreme levels is suppression? Then sign me up to be suppressed.
I am not saying we should be defeatist! I making the argument that it does not, and morally should not, have to be so that we all have to toil when we have such a wealth of technology.
How we go about changing this, I do not know, but everyone just playing along nicely in hope of one day being the one who strikes gold seems not to be working!
“Life isn’t fair, suck it up and get good!” is another form of suppression/delusion. Well, if life isn’t it fair, let us at least try to counteract that with cooperation. It seems to me that we have all the tools and technologies we need to make it a lot better.
This framing I'm on board with. The original comment took it too far for me, and even if not intended as defeatist I think could encourage that response. I'm all for people working not only to better their own conditions, but society as a whole.
This is very true but the path to that seems to require a weird optimization where it is concentrated among a few before being being widespread.
Technologic improvements should help. Help decouple time and money.
And when does this start being for everyone? We have had agricultural machines for ages, but I still have to pay an ever increasing part of my salary (and hence time here on earth) not to starve.
Because of asymmetry. Some people are more inclined toward certain things than others.
People who are excellent at math are much more likely to be able to advance AI for instance.
The goal of physical systems being to remain at rest/(humans included ;) the gradient of resources lean toward these people so that they can improve the technology allowing everyone to be able to conserve their energy (be lazy in a sense).
This seems to me to be the same as saying that mathematicians do not care about the meaning of their theorems. That they are only playing a game. They care about consistency only because inconsistency means one can cheat in their game.
I know TFA says that the purpose of foundations is to find a happy home (frame) for the mathematicians intuition. But choosing foundation has real implications on the mathematics. You can have a foundation where every total function on the real numbers is continuous. Or one where Banach–Tarski is just false. So, unless they are just playing a game, the mathematicians should care!
I'd say that I care deeply about the meaning behind theorems, but just find results which swing widely based on foundational quirks to be less interesting from an aesthetic standpoint. I see the most interesting structures as the ones that are preserved across different reasonable foundations. This is speaking as someone who was trained as a pure mathematician, moved on to other things, but tries to keep up with pure math as a hobby.
Yes, but most mathematicians do not seem to make this distinction between sturdy and flimsy truths. Which puzzles me. Are they unaware? If so, would they care if educated? Or do they fully commit to classical logic and the axiom of choice if pushed? I can see it go either way, depending on the psychology of the individual mathematician.
I don't think they usually make the distinction in a formal sense, but I think most are aware. The space of explorable mathematics is vastly larger than what the community of mathematicians is capable of collectively thinking about, so a lot of aesthetic judgment goes into deciding what is and what isn't interesting to work on. Mathematicians differ in their tastes too. A sense of sturdiness vs flimsiness is something that might inform this aesthetic judgment, but isn't really something most mathematicians would make part of the mathematics. Often, ones interest isn't the result itself, but some proof technique that brings some sense of insight and understanding, and exploring that often doesn't make much contact with foundational matters.
No one not working on foundations has any problem with axiom of choice. It has weird implications but so what? Banach Tarski just means physical shapes aren't arbitrarily subdividable.
My 2 cents is they do justify it by the interest of the consequences, as Tychonoff or Nullstellensatz. I wouldn't call that faith: Best practices is to state Tychonoff as "AC implies Tychonoff" and that last is logically valid. Sometimes the "AC implies..." is missing, buried in the proof or used unawaredly or predates ZFC, and is a bad thing. But very ofen one now see asterisks on theorems needing it.
AC makes things much easier as it allows to play God powers. Negating AC is not significantly different from constructing mathematics that avoids AC (no assumption about validity of AC). And that makes things way harder with longer proofs and only in sub-cases of classical theorems.
Simply assuming the negation of AC is boring, as negations often are. But there are stronger statements, implying the negation of AC which might be as useful. I think for instance one could assume all subsets of the plane to be measurable. Seems convenient to me.
Same with law of the excluded middle. Tossing it out we can assume all functions are computable and all total functions in the real are continuous. Seems nice and convenient too!
Newton and Gauss and Euler did just fine without such solid foundations. If you get a PhD, very likely even a undergraduate degree in mathematics you cover this stuff, then (unless you choose foundations as your field) you go about doing statistics, or algebra (the higher kind), or analysis knowing you're working on solid fundamentals. It would be crazy if every time you proved something in one of those fields you had to state which derivation of real number you were using. And I guarantee at least 90% of PhD mathematicians could do so if they really needed to.
We are not talking about having to return to foundational axioms in every argument! Just that what axioms one chooses has an impact on which arguments are valid, and thus in turn what truths there are.
The foundations have real implications on very little of the mathematics. Say I'm working in differential equations in vector spaces. I really do not care whether the axiom of choice is true or false. I'm not building up my functions of multiple real parameters out of sets.
You say you have a foundation where that is in fact what I am doing? Great, if that floats your boat. I don't care. That's several layers of abstraction away from what I'm doing. I pretty much only care about stuff at my layer, and maybe one layer above or below.
Very little of mathematics, like analysis? I am sure the analyst will care about all functions on the reals suddenly turning continuous. (Or rather losing the discontinuous ones)
Or what of commutative algebra and their beloved existence of maximal ideals!
you're kind of coming at this backwards. it's not that someone doing analysis doesn't care about whether all functions on reals is continuous, it's that if you hand them a foundation where that's true, they'll disagree with whether your foundation is correctly modeling functions/real numbers.
Having a PhD in mathematics myself, I have been surrounded by such and had this discussion a few times. Some even like the ideas suggested!
I would say the most common counter argument is cultural: Classical mathematics is the norm in the field, hence one must use it to participate in research in this field.
But that seems to me a rather intellectually unsatisfying argument, if one cares about the meaning of the work.
It is nicer to state theorems that hold for all vector spaces, so mathematicians like to invoke AoC. However, in any applications that are practically relevant, you can obtain a basis without invoking AoC.
To be fair, in some fields I've seen arguments between "a widget should be defined as ABC" vs. "a widget should be defined as XYZ", to the point that I wonder how they're able to read papers about widgets at all. (If I had to guess, likely by focusing on the 'happy path' where the relevant properties hold, filling in arguments according to their favored viewpoint, and tacitly cutting out edge cases where the definitions differ.)
So if many mathematicians can go without fixed definitions, then they can certainly go without fixed foundations, and try to 'fix everything up' if something ever goes wrong.
In my experience those debates are usually between experts who deeply understand the difference between ABC and XYZ widgets (the example I'm thinking of in my head is whether manifolds should be paracompact). The decision between the two is usually an aesthetic one. For example, certain theorems might be streamlined if you use the ABC definition instead of the XYZ one, at the cost of generality.
But the key is that proponents of both definitions can convert freely between the two in their understandings.
> But choosing foundation has real implications on the mathematics. You can have a foundation where every total function on the real numbers is continuous. Or one where Banach–Tarski is just false.
I mean, mathematicians do care about the part of the foundations that affect what they do! Classical vs constructive matters, yes. But material vs structural is not something most mathematicians think about. (They don't think about classical vs constructive either, but that's because they don't really know about constructive and it's not what they're trying to do, rather than because it's irrelevant to them like material vs structural.)
Try to be charitable. Remember, research mathematicians aren't HN commenters. They're forced to live within their intellectual limitations, however narrow those may be.
I still get that feeling sometimes, even after 25 years with computers at home. But it is so dependent on what I do. I get this feeling when I create stuff on my own terms, like making a game or a website. I also get this feeling when discovering other people’s personal creations online.
The idea of Church numerals is quite similar to induction. An induction proof extends a method of treating the zero case and the successor case, to a treatment of all naturals. Or one can see it as defining the naturals as the numbers reachable by this process. The leap to Church numerals is not too big from this.
Indeed! This morning I needed a service to port forward ssh from my server to a firewalled machine, to access stuff while I work from a mountain cabin over the next few days. ChatGPT gave me a nice nix config snippet, and it just worked! Auto reconnecting and everything.
I would of course have thrown up a port forward manually today, and maybe even spent the time to add a service later, but now it was fixed once and “forever” in two minutes!
Not only. There is an inherent aliasing effect with this method which is very apparent when the light is close to the wall.
I implemented a similar algorithm myself, and had the same issue. I did find a solution without that particular aliasing, but with its own tradeoffs. So, I guess I should write it up some time as a blog post.
