Which is to say that space isn't measurably continuous, — noAxioms

I take it you are talking about physical space, not mathematical space?

Physics: There are no solids. — noAxioms

But there are 3-dimensional figures in physics, aren't there? It's the solidity that's the problem, isn't it?

The set of points on say a circle is an uncountable set — noAxioms

That's a surprise to me. One can measure or calculate the length of a circumference, can't one? Or is uncountability a consequence of the irrationality of "pi"?

As has been stated so many times, by performing all the steps, which happens in finite time no problem. — noAxioms

Just checking - by "step" do you mean stage of the series? If I am travelling at a steady speed, I will complete more and more steps in a given period of time, and that number (of steps) will approach (but not reach) infinity. Can that really work?

The cutting up of the path into infinite steps was already a mathematical exercise. — noAxioms

So is the cutting up of the path into standard units. It's just a question of choosing the appropriate mathematical calculation for the task at hand.

The causal history, however, is what makes it necessary to experience the frog as a frog and not as a hopping constellation of colored shapes. — jkop

I think the point goes deeper than that. We can experience a constellation of coloured shapes as a frog, but only as a picture of a frog. My past experience acting in the world no doubt contributes to that. But to seriously fool me as a real frog, it would have to respond to my attempts to catch it (by hopping out of reach). Can I be fooled into thinking I am attempting to catch it? I would have to have all the sensory inputs, including the proprioceptive inputs that tell me where my body is and what it is doing. But if that was all controlled by the simulation machinery, I would not feel that I was doing it - my "body" would not be my own. The inputs would have to respond to my outputs - the signals that would, in real life, control my body. That is, inputs from the machinery would never be enough. I would have to be in control of my "body". The machinery has to respond to me - it has to become my body.

Yet many people seem to believe that the whole universe, or at least our experienced part of the universe, is or could be a simulation. — jkop

"Universe" is a bit slippery here. If it means "everything that exists", we have to take into account that a simulation cannot be everything that exists, because it must be a simulation of something and that something must be real - an alternate reality. We are used to the idea that there can be alternate worlds in the same universe nowadays, but the idea of alternate universes presupposes that there can be no communication of any kind from one to another.

If the universe is simulated or in part simulated, it doesn't make it any less real, — Barkon

The idea of "real" is also slippery here - or better, it's meaning is contextual. A simulation of a battle isn't a real battle, but it is a real simulation, and it is a simulation of real (or possibly real) events. I think you are proposing that a whole universe might be simulated by a process that would be controlled in order to serve some purpose. But if everything is included, not only is there no reality to be simulated, but also there is nowhere for the creators (or their hardware) to be. So I don't quite understand what you are getting at here.

If a simulation exists, then there must exist at least one more thing (or set of things) which is constitutive for the simulation, e.g. a brain, a computer, their materials and properties and surrounding conditions of satisfaction. Therefore, everything cannot be a simulation. — jkop

I like that argument a lot. :smile:

Furthermore, if the simulation (e.g an emergent property within a network of electrical circuits) is about something (e.g. our world at the level of humans and mid sized objects), then we have at least three things to consider: the simulation (emerging from electric circuits), what causes it (a brain and computers etc), and what it is about (a part of our world). So, not only is it impossible for everything to be a simulation, the simulation is just one thing among many other things in our world. — jkop

"Three things" might prove to be contentious, depending on how you define "thing". But the conclusion seems to me to be sound.

A frog is not just a constellation of coloured shapes that hop around for no apparent reason. Simulations, pictures, or descriptions of frogs are syntactically disjoint and detachable in a way that real frogs are not. Real frogs are continuous, recalcitrant, and seamlessly connected to other creatures and environments, which in turn are connected to chemistry, physics, astrophysics, cosmology or everything. Our ability to identify frogs, as frogs, has a causal history that arguably amounts to everything, and a simulation cannot be everything. — jkop

You are, rightly, thinking of me as a passive spectator in the simulation. You have left out a really important point. We are embodied and active in the world. So the frog is not just a "constellation of coloured shapes" (and sounds, smells, touches and even tastes), but also something that we interact with (as the frog interacts with us). For me, it's the interaction that distinguishes the real frog from the dream. True, I can imagine an illusory frog that I don't interact with, but only because I sometimes interact with the things that I perceive.

'highly improbable.' — jasonm

That's very generous.

If this world is simulated, the "real" world must be very like this one - as in the "Matrix". But then, it if the real world is very like this one, does it include all the evidence that this world is simulated. In other words, will the inhabitants of the real world believe that they are living in a simulation. So the real world is also a simulation.....

But how do we know that this world is a simulation if we have no access to the real world and cannot compare one with the other?

I cannot distinguish the idea that this world is simulated from a fantasy or, better, a nightmare.

If you agree, I'm happy, because that's the only point I'm making. I've never written more just say less. My only point is that in the lamp and these other problems, we're not defining the state at the limit. Therefore the choice of state is pretty much arbitrary. If we thought about it that way it might be more clear. — fishfry

:smile:

If I can walk from one end of the grocery aisle to the other, I don't see why you can't get down the staircase, infinitely many steps or not. — fishfry

But I did walk through infinitely many inverse powers of two lengths at the grocery store. I did sum an infinite series in finite time. — fishfry

I find this very confusing. I take your point about abstraction. But I find that abstraction can create confusion, because it persuades us to focus on similarities and neglect differences. My reaction here is to pay attention to the difference between these kinds of infinite series. It's not meant to contradict the abstraction.

It's a thought experiment. There are no infinite staircases. — fishfry

Exactly. So it isn't about physics. But it isn't about mathematics either. So it seems to me an exercise in imagination, and that provides a magic wand.

Aha. You'd have to ask those who care so much. I think they only show that underspecified problems can have arbitrary answers. But others see deeper meanings. — fishfry

Deep? or Deepity? (RIP Dennett)

How do dimensionless points form lines and planes and solids? — fishfry

Yes. Euclid (or Euclidean geometry at least) starts from a foundation - axioms and definitions. But they are an extension of our common sense processes of measuring things. (You can understand more accurate and less accurate measurements.) Extend this without limit - Hey Presto! dimensionless points! That is, to understand what a point is, you have to start from lines and planes and solids and our practice of measuring them and establishing locations. I find that quite satisfying. Start with the practical world, generate a mathematics, take it back to the practical world. (Yes, I do think that actual practice in the real world is more fundamental than logic.)
Once you define geometrical points in that context, there is no difficulty about passing or crossing an infinite number of points. (But the converging series does not consist of points, but of lengths, which are components.)

So there's something interesting going on. — fishfry

My supervisor used to say that when he got really excited, which was not often.

I believe Churchill also said that the greatest argument against democracy is a five minute conversation with the average voter. — fishfry

Yes, he did say that. He was also right about that, as well.
People are making a mistake when they think that voters need to decide on specific measures. That way, madness lies. The classic reference for this is the expedition to Sicily by Athens in 415–413 BCE. See Wikipedia - Sicilian Expedition. A better model is the Spartan one (which was a democracy, of sorts, despite rumours to the contrary); that is about consent, not decision. Which is the other point people don't seem to understand. The vote is, or should be, about legitimizing the regime, and all that requires is acquiescence, not decision. A majority vote with a choice is a way of palliating the opposition - much better than repressing it. But then, it does require that the opposition accepts defeat; when that breaks down, the system is in serious danger. (Trump!) The Government needs to secure approval of the election arrangements from the opposition - too many of them neglect that.

That's very interesting! I wouldn't mind government subsidies if they're fairly distributed among the college and non-college individuals. — fishfry

H'm. It's true that there is government support for both groups, but many people feel that there is less support for sub-degree programmes and complain about that - with justification in my view. Others complain the employers should pay for these programmes, as the primary beneficiaries - and they do pay for, and are involved in the delivery of, many of them by providing work experience.

I am no fan of Churchill, but I tend to agree with the statement (probably falsely attributed to him and loosely paraphrased) "Democratic capitalism is the worst of all possible systems, apart from all the others". — Janus

Churchill does quote it, but doesn't take credit for it. Also, there are various forms of it. See Quote Investigator.

We have no disagreement then. People should pay off their own loans that they knowingly agreed to pay. — fishfry

I thought I had already said that I don't have a problem with that. When I said that politics is a messy business, best not really be conducted in public, I was also accepting that it was a bribe to voters. All democracies do that - it's an inevitable outcome of the system. Non-democratic governments do it as well. Politicians have to keep their supporters sweet. I'm not even saying it is right, or all right, just that it always happens.

Welders don't have student loans. — fishfry

Each country has its own system. In the UK, the "trades" like welding and pipefitting, do get government support - and this is a "right-wing" government. See Skills for careers. Some people regard this as a blatant subsidy for employers, who should be paying. But there are complications.
Higher-level professions depend on degree-level courses, and these get student loans. But these are repaid on a sliding scale, dependent on you income. (Effectively, it's an additional income tax). The Government assumes that 35% to 40% of the total will never be repaid. There's your forgiveness, but sanctioned by Parliament.
Re-training is more of a problem.

they (potential parents) will somehow, in blind anticipation, be innately inclined to sufficiently understand and appropriately nurture their children’s naturally developing minds and needs. — FrankGSterleJr

Yes. The idea that we all know how to bring up children, just because we have been through it ourselves, or because of "instinct" is arrogant beyond belief.

We can, however, educate young people for this most important job ever, even those who plan to remain childless, through mandatory high-school child-development science curriculum. — FrankGSterleJr

On the other hand, anyone who is can be confident that their study and research has revealed to them the correct way to do that is also arrogant beyond belief.

The only thing that's certain is that no-one knows for sure. It's wiser to muddle through with a great deal of humility and with as much restraint as possible.

The greatest error of all is to think of bringing up children as like making a cake. It is an interaction, in which the child is a partner, not a passive subject.

But the State's function is anti-social in both origin and function. — NOS4A2

I don't know what you have in mind when you say that. I don't see how state can exist without society, or society without the state. They are interdependent.
It's nice to think of a society that works by co-operation and not compulsion. But I don't see how that is possible. At the same time, compulsion can only get so far. So a society based only on compulsion won't get far.

Now you're speaking my language. Thomas Paine wrote that writers tend to confound Society and Government, as if the two were one and the same, so I appreciate your distinction. — NOS4A2

I don't know much about the detail of what he said. But Government does like to think of itself as above the fray. In some ways, it is, but in other ways it is just one part of it. Whether its use of physical force gives it a special role or not depends on whether the force is used to keep the peace or to squash opposition. There is also the awkward point that the people who are the Government are also members of Society and so liable to see society from a point of view within it.
So although the two are not just one and the same, they are not two clearly distinct entities.

I suspect also that he thought that the "common man" was a special group, with special rights. That makes him just another spokesman for an interest group. (I'm getting at the idea that the majority can become tyrannical just as easily as any other sub-group in a society).

Exactly. Capitalism and socialism - Tweedledum and Tweedledee.

So we have only two things to fear - the state and everyone else.

Why don’t we just organize, find some like minded people, and implement our philosophy by living it and doing it? — NOS4A2

Excellent. But you should think it through. It is not capitalism or socialism as long as everyone is a volunteer and so can leave when they want to. When that stops - and it always does - Society begins.

In one it could be you; in the other it couldn't. — NOS4A2

There's always a group of people in control, who exclude most of us. In either state, in theory, I could join the group that's in control. But then I would have to serve them.

The only thing that differs between them is who they believe should control capital. — NOS4A2

..... but what they all have in common is that it isn't us.

But yes, I think any system modelled on the republican state relegates us to the status of serfs. — NOS4A2

What other state, other than anarchism, wouldn't relegate us to serfdom?

I don't know that anyone would disagree with you. It is always a question of how to achieve such a goal. — Leontiskos

I agree - no-one would disagree - until it comes to the question of what children need. Then, we're all over the place.

That is precisely where the socialism comes in, and it quickly resembles serfdom. — NOS4A2

.... and do you really think that capitalism doesn't resemble serfdom?

But one cannot use armchair philosophy to determine the smallest unit of space/time/movement. — Michael

Given the logical paradoxes that continuous space and time entail, I think that discrete spacetime is not just a physical fact but a necessity. — Michael

I don't think you can have it both ways.

And the passage of time that we would measure as being 60 seconds occurs even when we don't measure it. — Michael

I'm not quite sure what you are saying. Do you think that the passage of time occurs when we can't measure it? Analogously (if that's a word), if we can't measure the location or momentum of an object, it doesn't have them? Does that mean that it doesn't exist?
There are two philosophies that I can think of that would justify those views. One of them is Logical Positivism, which was developed precisely to justify both Quantum Mechanics and General Relativity. The other is Bishop Berkeley's idealism. Which do you hold?

There are physical theories that treat spacetime as discrete. They are not supported to the extent that General Relativity is, but given that quantum mechanics and General Relativity are known to be incompatible, it would seem that at least one of them is false, and my money is on General Relativity being false. — Michael

That means you think it is possible that space-time is continuous at the quantum level. Interesting. But I suppose it fits with your acceptance of continuous space-time in mathematics.
The empirical evidence for your position is the empirical fact that we can't measure very small units of time or space. I'm not sure that constitutes convincing empirical one way or the other. Or have I got something wrong?

Given the logical paradoxes that continuous space and time entail, I think that discrete spacetime is not just a physical fact but a necessity. — Michael

Which ones do you have in mind? You mentioned the problems with a converging series. But that's a mathematical problem, not an empirical one. How does empirically non-continuous space and time solve those issues?

Even if you are determinist and do not agree with free will causation, quantum mechanics clearly demonstrates that your statement is false. — Metaphysician Undercover

I hope you don't mind my saying that your choice of free will as an example was perhaps ill-advised. It's far too contentious to work. Quantum mechanics is a much better choice. But there is the problem that there are many interpretations of it, so it is not clear that it proves what you think it proves.

In the future, if physics ever figures out how to work with physically instantiated infinities, supertasks might be possible. Way too soon to know. — fishfry

I think you are both mistaken to rely on physics to define what one wants to get at in this context. Physics is not only limited by the current state of knowledge, but also by its exclusion of much that one would normally take to be both physical and real. Somewhere near the heart of this is that there is no clear concept that will catch what we might mean by "whatever exists that is not mathematics" or by "whatever applied mathematics is applied to".

Jeez that's kind of creepy ... true, I suppose. Death is the least upper bound of the open set of life. — fishfry

I'm sorry. I didn't mean to gross you out. Perhaps if you think of death as a least upper bound, you'll be able to think of it differently. It is, after all, an everyday and commonplace event - even if, in polite society, we don't like to mention it.

I just mentioned that I could argue it either way. — fishfry

Yes. I was just drawing out the implications. You might disagree.

The sequence is endless, and there's an extra point that's defined to be strictly greater than all the others. We can't get to the limit by successors, but we can get there by a limiting process. — fishfry

Yes. In the context of the Achilles problem that's fine and I understand that you are treating that and the natural numbers as parallel. It's not clear to me that it really works. It makes sense to say that "1" limits "1/2, 1/4, ..." But I'm not at all sure that it makes sense to say that <omega> limits the sequence of natural numbers. "+1" adds to the previous value. "<divide by 2>" reduces from the previous value. The parallel is not complete. There are differences as well as similarities.

How can it be out of reach? I went to the supermarket today. I walked from one end of the aisle to the other. I reached the end. I did indeed evidently sum a convergent infinite series. — fishfry

Did you "get to the limit by successors" or "get there by a limiting process"? I don't think so. You are just not applying that frame to your trip.

I think some of Zeno's other paradoxes are more interesting. When you shoot an arrow, it's motionless in an instant. How does it know where to go next, and at what speed? I think that's a more interesting puzzle. Where are velocity and momentum "recorded?" How does the arrow know what to do next? — fishfry

I've met other mathematicians who agree that Achilles is not interesting. But I'm fascinated that you think the arrow is interesting. I don't. Starting is a boundary condition and so not part of the temporal sequence, any more than the boundary of my garden is a patch of land. End of problem.

But this may be interesting in the context of what we are talking about. A geometrical point does not occupy any space. It is dimensionless. One could say it is infinitely small. But it is obvious that there is no problem about passing an infinite number of them. It is a question of how you think about them. This is not quite the same as Zeno's problem, but it is close.

That is a perfectly sensible answer to the question, "What is the state at the limit?" It's perfectly sensible because the conditions of the problem don't specify the value at the limit. And since the lamp is not physical, it can turn into anything we like at the limit. It's no different than Cinderella's coach, which is a coach at 1/2 second before midnight, 1/4 second before midnight, and so on, and turns into a coach at midnight. — fishfry

I agree with that.
Perhaps then, these problems are not mathematical and not physical, but imaginary - a thought experiment. (The Cinderella example shows that we can easily imagine physically impossible events) That suggests what you seem to be saying - that there are no rules. (Which is why I posited another infinite staircase going up). But if there are no rules, what is the experiment meant to show? The only restriction I can think of is that it needs to be logically self-consistent - and the infinite staircase is certainly that. I guess the weak spot in the supertask is the application of a time limit. However, I also want to say that I cannot imagine an endless staircase, only one that has not ended yet - once I've imagined that, I can wave my hand and say, that is actually an infinite staircase.

Why shouldn't I take out $100,000 US in loans to study underwater basket weaving, if I'm reasonably sure some future administration is going to transfer my loans to the taxpayers? — fishfry

I'm sorry about this rant, but I don't know how else to respond.

It depends on your philosophy of education. The thinking behind all education is a mess; the thinking behind higher education is even more of a mess; and the thinking about adult education is practically non-existent. You can think about in terms of vocational (career) benefits and non-vocational ("for fun") programmes and a combination of private benefits (for the student) and public benefits (for society in general). There's also an issue about benefits to employers, but these are rarely thought about in their own right.

Underwater basket weaving looks like a bad career choice, but possibly a good choice for fun. Either way, the student should pay. Some programmes, like IT skills (and mathematical ones) lead to extremely profitable careers in the finance industry; again, the student should pay. But if there's a serious shortage of welders, such that various industries cannot find the workers they need, there's good reason why employers, and/or the state, might want to pay. Then there are programmes like social work and nursing, which require specialized professional training, but don't pay well. Isn't there a good case for state support? What abaout high-level professional careers which could be financed by students, but where that is impractical because of their high costs whether in infrastructure or time required; again, public subsidy makes sense. Another category is risky careers, like acting or archaeology or philosophy; again, there's a case for public subsidy, not only to ensure a supply for the labour market, but because the existence of those careers is a public good.

If you thought that was a mess, consider the non-vocational subjects, or those subjects which can be studied for vocational reasons and can also be studied for fun. The catch here is that all the specific vocational careers presuppose some level of basic, general skills and knowledge, which enables people to function in society in general, both within and without their vocations; these skills are also the basis of good citizenship. These include reading, writing, and arithmetic, but also extend (In the UK) to Science, Technology, Engineering and Mathematics (practice needs theory, after all) and to various skills under the heading of good citizenship - philosophy, literature and history and the arts. Those last four are often regarded as purely for fun, so I don't claim that the idea that they are not just for fun is uncontentious. Perhaps the most effective argument for them is that democracy cannot function properly without them. J.S. Mill recognized this, but it seems now to be ignored, which is a pity. Mind you, the idea that an understanding of the humanities was essential for a decent society took a very serious knock in WW2. But it is far from dead.

Underwater basket weaving? Probably not. Philosophy? Fine Art? There's at least a case to think about, isn't there?

PS. I forgot to explain how students should pay when they need to. Through the tax system. If their career choice pays off, they will pay increased taxes, so the public purse will benefit and their debt "repaid" - or, if you prefer, the public investment in their career pays off. Where their career does not pay off in that way, the public (and employers) will benefit from an increased supply of highly qualified labour. Where their career is not directly developed by their qualification, it will have been helped by the "transferable skills" developed in their programme and by the improved contribution they can make by their contribution to social and political life.
In other words, payment through the tax system is perfectly well justified by the multiple benefits provided by higher education. Nobody has a problem with that way of paying for schools. Why would higher education be any different?

"Classical" liberalism, which is more like conservatism today. Although conservatism is pretty muddled, what are they really for? — fishfry

That process - what was liberal and new, becomes old hat, and conservative. That what's happened to feminism, etc. The agenda has moved on. It's very disappointing to those of us who thought the problems were solved. But there are unsolved and unconsidered issues and big gaps in even the basic rights that one thought had been established.

There's no rehabilitation going on. There's a revolving door of people committing violent crimes, being put back on the street, and re-offending. — fishfry

If that's so, there is a problem.

Some of the people on that "side" are victims, I imagine they don't even have an inner monologue so they can't even filter what information is fed to them. — Lionino

That's perfectly possible. But if you want them to develop one, it's as well not to tell them about it. Shouting about it just breeds resentment and resistance.

I don't see why not. The whole point of the puzzle is to sum 1/2 + 1/4 + ... = 1, and then to ask what is the final state. — fishfry

The sequence is endless, and there's an extra point that's defined to be strictly greater than all the others. We can't get to the limit by successors, but we can get there by a limiting process. — fishfry

OK. I remembered WIttgenstein's oracular remark that death is not a part of life. My concern that the limit is not generated by the defining formula isn't the problem I thought it might be.

I've convinced myself both ways. On the one hand we can't physically count all the natural numbers, because there aren't enough atoms in the observable universe. We're finite creatures.
On the other hand, supertasks are possible, because I can walk a mile, meaning I walked 1/2 a mile, 1/4 mile, dot dot dot. — fishfry

I don't really believe in "possible" without qualification. There's logically possible, (is mathematically possible the same or something different? Does is apply here?), physically possible, and a range of others, such as legally possible. So what kind of possibility is a supertask?

A lamp that cycles in arbitrarily small amounts of time is not physical. A staircase that we occupy for arbitrarily small intervals of time is not physical. So trying to use physical reasoning is counterproductive and confusing. That's my objection to all these kinds of puzzles. People say there's a conflict between the math and the physics ... but as i see it, there's no physics either. — fishfry

So your reply is that it is neither. It suggests a combination of physical and mathematical rules which is incoherent but generates an illusion. That's why

It may "lead" somewhere but there's no law that constrains the final state. It may be discontinuous, like Cinderella's coach that's a coach at 1/2, 1/4, 1/8, ... seconds before midnight, then becomes a coach at midnight. That's why it's perfectly possible that the lamp becomes a pumpkin after 1 second. — fishfry

But then you say

On the other hand, supertasks are possible, because I can walk a mile, meaning I walked 1/2 a mile, 1/4 mile, dot dot dot

Obviously, as each stage gets smaller, I will complete it more quickly. But still, it will take some period of time, and the final step looks out of reach. That looks like a combination of physical and mathematical rules.
It isn't a real problem because I can analyze the task in a different way. I can complete the first yard, the second yard.... When I have completed 1760 yards, I have completed the task. But the supertasks seem not to permit that kind of analysis. Is that the issue?

We were on the right track - UK, Australia, NZ, Canada, most of Europe and even the US - for a large portion of the 20th century. (Chastened by the depression, governments curbed big capital and invested in the population at large) Then, starting about 1980, the political pendulum was pushed hard to the right. Now, the far left is where the moderate right (remember them?) was in 1976. Now, we're heading toward fascism at a fair clip. — Vera Mont

I won't disagree with any of that. The obvious questions are when the pendulum will start to move the other way and how much damage will be done before that finally happens. Oh, and whether it is just a pendulum but more of a spiral - upwards. I happy to answer the first with "eventually". The others require "Don't know"

Reform is an uphill battle. — Vera Mont

Well, yes. Obviously a downhill battle would be better, but I'll settle for that.

Thanks for the clips. Very instructive.

The practicality is not yet upon us. I don't think reform is feasible. — Vera Mont

You are not alone. I also think the prospects are very very gloomy. I have the impression that many people all round the world have a sense of impending doom. I wish I could be more optimistic.

House-of-cards economies like the one we're living in periodically collapse. — Vera Mont

Yes. Any economic/social system is vulnerable to catastrophic events. But life goes on. People pick themselves up and work out what they will do next. That's not a facile optimism. It would be much, much better to avoid the disaster in the first place, but it isn't always possible.
Your analysis of where we are is quite familiar, but doesn't help much. Capitalism has been in crisis practically ever since it was invented. It is extremely resilient and adaptable, which is both a curse and a blessing. The obvious alternative is Socialism, which is as polymorphous as capitalism. It seems to be more effective as way of modifying capitalism than as a system in its own right. We seem to be working out how to blend the two, and that seems to me to be the right way to go

In the DEI departments of university administrations I imagine. — fishfry

Not so. I don't know what data is available to you, but perhaps you should look around. All I'm saying is that you cannot assume that every vocational programme provides marketable qualifications nor that every non-vocational programme does not. It's up to the market to decide what it wants.
Equally, it is up to students to decide what they want, even if they make choices that you think are unwise. It's not as if we can predict and provide what the economy wants.

Point being that pipefitters shouldn't be shouldering the cost of the loans forgiven for social justice majors. — fishfry

Well, if the cost is funded by general taxation, the contribution will depend on their income. That doesn't seem unreasonable - unless you think that people should not study social justice. But I think it is a good thing that as many people as possible should understand what social justice is.

Right. The "liberals" used to be for the working classes. Now the liberals support the elite against the working classes. Bit of a puzzler. — fishfry

It's complicated. In the UK, liberals in the 19th century were, by and large, members of the elite. They were never particularly enthusiastic about supporting the working classes. They were much more interested in free trade, political issues like voting rights and moral/social issues like divorce, gay rights &c. (Conservatives supported protection and social conservatism). The working classes, by and large, had to fight their own battles, which they did through the Trade Unions.
But I'm sure the alignments were different in the USA.

Violent criminals are being put back on the street to re-offend. That's not fair to the victims. Violent criminals belong behind bars. — fishfry

People can't re-offend if they're locked up. — fishfry

You can't imprison violent criminals forever, unless you can prove them criminally insane. Sooner or later, they have to hit the streets again. That's why rehabilitation is so important.

Perhaps I just spend to much time following NYC politics. They're having a problem with soft-on-crime politicians leading to a great decrease in public safety. — fishfry

Nothing wrong with that, so long as you are open to new ideas occasionally.
I don't know the details, but my instinct is to suggest that if the rehabilitation programmes in NYC aren't working, find a better programme, don't give up on the attempt. Money spent on effective programmes to keep people out of prison is a good investment. Back that up by improving detection and arrest, which is by far the most effective deterrent. Tossing people out of prison into the general population will not work and putting them back in prison later on is very expensive, not only in running the prisons, but also in the damage inflicted on families and children.

I didn't think I was. I meant to describe political positions. I'm quite aware of the magnanimous billionnaires who use their money for culture and charity, as well as larcenous beggars. — Vera Mont

I'm sorry if I took you the wrong way.

No. I have trouble dealing with the concept of wealth in any distribution. I'd rather think in terms of resource allocation and sharing. — Vera Mont

I don't understand this. Money represents resources. So the distribution of money is allocation of resources. Sharing is more complicated, but the family is partly about sharing resources, isn't it? Perhaps you are just talking about an attitude? Or do you have in mind a reform of property laws?

I believe everyone should have enough food, shelter, security and leisure, a chance to contribute to their community and be recognized for their effort, access to education and the freedom to fulfill their potential.
I believe nobody should have more of anything than they can use and enjoy in one lifetime.
I believe no child should start life materially better off than others of its cohort, and those who start life with a handicap should be offered all available support by the community, as should any adult who falls ill, is injured or grows feeble.
I believe we should not take from the Earth more than we collectively need, and dispose of our waste in a productive manner.
I realize it's a pipe-dream. — Vera Mont

I don't have a problem with pipe-dreams. I understand your objection to inherited wealth. But I'll spare you any flat-footed objections about practicalities.

Who makes these systems? Is power and authority not a trait of the "winning faction" of any competitive environment? — Benj96

Our only hope is substantial and persistent political pressure. What else is there? How else would you ensure "constructive and healthy competition", given that the people in power have substantial political support?
The history of the 19th and early 20th century gives ground for hope.

Oh, please don't fall into the 'both are as bad as each other' fallacy. — Vera Mont

I'll tell you what - I'll promise not to fall into that fallcy if you'll promise not to fall into mine. OK?
Here's my side of the bargain.

But neither side seems willing to acknowledge that and work with it, so I'm not optimistic. — Ludwig V

describes the present socio-political situation; I am not making a moral judgement.
The fallacy I'm asking you to avoid is the fallacy of stereotyping groups of people. Deal?
I think we agree that the present situation is seriously wrong. So, a question. Do you know what the right distribution of wealth across our society should be?

At the present level of disparity compromise is impossible; the "sides" far too unequal to negotiate. — Vera Mont

So what is your recommendation. Surely not civil war?

This is the bit the right wingers don't get: it's cheaper for society to assure everyone a reasonable life than to protect the wealth of a few. — Vera Mont

True.

Where the gap between the richest and poorest is an immense chasm, many are disenfranchised, marginalized and driven to despair. — Vera Mont

Tell me about it. It isn't an easy problem to shift the views of the rich and (therefore) powerful. It doesn't help that there is no objective criterion for what the right distribution would be. I think it comes down to a deal - not a formal deal, but a state of affairs that most people are prepared to acquiesce in. But neither side seems willing to acknowledge that and work with it, so I'm not optimistic. I cling to hope because I remember Bismarck. That story tells you that you are just as likely to get a solution from a right-winger as from a left-winger.

Police forces in many countries are increasingly militarized, insulated and alienated from the community they're meant to protect; in many communities, the citizenry and the police are locked in a cold war that occasionally erupts in gunfire. — Vera Mont

Oh, I know that. But if the difference was implemented, most of those problems would go away. Very few people actually want chaos or a "cold war that occasionally erupts in gunfire". They want order without repression.

That's right. So the students majoring in unmarketable majors are subsidized by people who skipped school and went into the trades. — fishfry

H'm. In principle, that is a valid complaint. But, back when I was involved, something like 60% of vacancies for graduates (i.e. those requiring a BA degree or higher) did not specify the subject. That may have changed. But you might be surprised at where Eng. Lit. and Fine Arts graduates end up.
I'm not sure how education for professions and trades differs now; there's a lot of emphasis on training all the way up to BA level and higher. Many Universities are re-casting their non-vocational qualifications as vocational and there's effort going in to tracking what level of job graduates actually get. I've heard anecdotes that some vocational programmes don't do very well. It's complicated. I suspect that the identity of the awarding institution is more important than the subject. Whether it is question of reputation, prestige or snobbery depends on how polite I'm feeling.

It's just that the college grads vote for Democrats and the tradesmen vote for Republicans, so the Democratic administration forgives billions in student loans -- illegally, as the Supreme Court has already ruled -- in an election year. — fishfry

Oh, I wondered why that business about the student loans was happening now. Not pretty, but then, one has to please one's voters.

The Democratic party use to be the party of the tradesmen and no longer is. When did the left abandon the workers, and why? I gather the Labour party in the UK has undergone a similar transition, is that right? — fishfry

It has happened gradually over two or three decades. I hesitate to get too detailed. It's mainly about social liberalism/conservativism - abortion, gay rights &c. Curiously, the Conservative party now seems to be at least as socially liberal as the Labour party, if not more so. There is certainly an issue in the Labour party that the liberal metropolitan elite now vote for Labour and this often clashes with the conservative social values of many "working class" people (not a politically correct classification any more.)
Originally the Labour party was explicitly a party for the working class - it was founded by the Trade Union movement. The Conservative Party tended also to have foundations in the "higher" parts of the class system; but now it's more about economics - free market vs state intervention (not Socialism as such). It does seem that many people in what used to be the working class who might well have voted Labour in the past now vote Conservative. This is all not very reliable. I'm not an expert.

Compassion for criminals is anti-compassion for their victims. — fishfry

I don't see why it has to be. Except, of course, that a victim may be more vengeful than the system is. But I don't see that as a question of compassion or not. Support for victims (in the UK at least) has been pathetic, but is now improving (but not nearly perfect).

I think the first duty of civic authorities is to provide for civic order. — fishfry

Of course that's true. Part of the argument is that sympathetic ("humane") treatment of criminals and addicts gets better results in preventing recidivism - and a huge proportion of crime is recidivism. There's empirical evidence for that.
Another part is that more severe sentences are not effective in preventing crime. Effective detection and police work is much more effective. It makes sense. 20 years in jail is not much of a deterrent if you aren't going to get caught. But if you know you won't get away with, you know also that you won't benefit much, whatever the penalty. (Some crimes are not deterred even by the high likelihood of getting caught, but those are unlikely to be deterred by severe penalties.) I know, I know, justice demands.... That, in my book, is not about justice; it is about revenge. Prevention is more important than revenge.

The page itself isn't all that enlightening, but it does at least show that the ordinal numbers really are a thing in math, I'm not just making it all up. — fishfry

Yes. I got enough from it to realize a) that ω is one of a class of numbers and b) that it comes after the natural numbers (so doesn't pretend to be generated by "+1")

This business about actions is what confuses people. — fishfry

Certainly. That's what needs to be clarified, at least in my book. There's a temptation to think that actions must, so to speak, occur in the real world, or at least in time. But that's not true of mathematical and logical operations. Even more complicated, I realized that we continually use spatial and temporal terms as metaphors or at least in extended senses:-

By the way, ω is the "point at infinity" after the natural numbers — fishfry

What does "after" mean here?

If you want to think about the sequence 1/2, 3/4, 7/8, ... "never ending," that's fine. Yet we can still toss the entire sequence into a set, and then we can toss in the number 1. That's how sets work — fishfry

Yes, but it seems to me that this is not literally true, because numbers aren't objects and a set isn't a basket. (I'm not looking for some sort of reductionist verificationism or empiricism here.)

Just think about {1/2, 3/4, 7/8, ..., 1}. It's the exact same set, with respect to what we care about, namely the property of being an infinite sequence followed by one extra term that occurs after the sequence. — fishfry

In that respect, yes. But I can't help thinking about the ways in which they are different.

That's a confusing way to think about it. It "ends" in the sense that we can conceptualize all of the natural numbers, along with one extra thing after the natural numbers. — fishfry

Yes. But it doesn't end in the sense that we can't count from any given natural number up to the end of the sequence.

And two, calculus classes are not designed to teach people how to think about limits in the more general ways that mathematicians sometimes do. — fishfry

I try not to mention this in public, but the fact is that I never took a calculus class, nor was I ever taught to think about limits or infinity in the ways that mathematicians sometimes do. I did a little formal loic in my first year undergraduate programme. Perhaps that's an advantage.

And as I keep explaining, the issue with supertasks has nothing to do with mathematics. Using mathematics to try to prove that supertasks are possible is a fallacy. — Michael

Fair enough. That coincides with my intuition that supertasks are not possible. But given that they are not physically possible either, can I conclude that they are not possible at all?

Put those together with quasi-physical entities like physics-defying lamps, and you have a recipe for confusion. — fishfry

I have the impression that you don't think that they are mathematically possible either. (I admit I may be confused.) So does that mean you don't think that supertasks are possible?

Health care policy's hard, I agree. I've only heard anecdotal evidence about NHS. — fishfry

Well, be careful. Most anecdotes have an agenda behind them - not that statistics don't. You wouldn't believe the impression I get from the anecdotes I hear about the US "system". I just don't believe that it can be as bad as that.

Government doesn't have any money that it doesn't take from someone else. Or borrow and print, that's a nice game that has to end at some point too. — fishfry

The issue behind the student loan question is the question how far state-funded free education should go. If you want a level playing field in careers, everyone who can benefit should get higher education - and that means that almost everybody should be entitled to have a go. At the same time, if people benefit financially, there is a good case for saying that some of that benefit should go back to whoever funded it. Ironically, in the UK, the financial benefit from higher education is rapidly shrinking and, some say, has disappeared, mainly because it has been extended so widely. The proportion of student loans that is actually repaid is astonishingly low. (I can't remember the actual figures.)

Nobody has any money they don't take from someone else. We all give something in exchange. But even Government has to provide something in exchange. Sure taxes are compulsory, but is food and housing voluntary? They are certainly not classified as discretionary spending by economists.

Electronic money seems to be on the way, and that is going to making the arbitrary printing of money look like a tea party, if the existing private systems are anything to go by.

Perhaps it's a matter of pendulum swinging and patience. — fishfry

Yes, it probably is. That's one of the few things that my mother told me that I have found to be true.

I agree. We need a balance between trying to homogenize society, and old-fashioned notions of merit. — fishfry

II would prioritize effectiveness in the job (in the widest sense) above everything else. If that's what you mean by merit, then I agree.

I can't think of any totally unregulated capitalist systems. — Janus

Well, yes. A market can only exist in a legal framework, which is a form of regulation. I'm only referring, n short-hand to the movement at the end of the 19th century to palliate (welfare) or control (additional regulation) some of the anti-social consequences of capitalism.

On the other hand, communist systems, insofar as they are anti-democratic (which most seem to be and to have been) exercise far more control over their citizens. — Janus

Far more overt control, yes. Capitalism is subtler. I prefer the second, of course.

In the modern world it is money which effectively rules, and governments are, to a large extent, bought. The CCP on the other hand controls the money because it effectively owns the business it seems. — Janus

So either the people who control the money or the people who are members of the CCP are in charge. It doesn't look like a particularly exciting choice. Who looks after your interests and mine?

A badly organized society creates many malcontents and disrupters; a well organized one tends to give rise to very little crime and abuse. — Vera Mont

H'm - tempting
Dictatorships are quite good at creating an organized society, but at a high cost. Democracies (and free markets) seem to be chaotic, but the social costs are lower.
The critical factor is the extent to which the organization has consent, and has enough flexibility to give space to minority and unpopular interests.
The difference between a police force and an army is that the police must have the consent of those being policed and must be an integral part of the community, while an army needs neither.

It makes no sense to claim that my endless recitation can end, or that when it does end it doesn't end on one of the items being recited – let alone that it can end in finite time. — Michael

The natural numbers do not end, yet they have a successor in the ordinal numbers, namely ω. This is an established mathematical fact. — fishfry

I've watched this debate for a long time - though I don't claim to have understood all of it. But I think those two quotes show that you are talking past each other.

I didn't like ω at all, when it was first mentioned. I'm still nowhere near understanding it. But the question whether a mathematical symbol like ω is real and a number is simply whether it can be used in calculations. That's why we now accept that 1 and 0 are numbers and calculus and non-Euclidean geometries. ω can be used in calculations. So that's that. See the Wikipedia article on this for more details.

But it is also perfectly true that a recitation of the natural numbers cannot end. As I said earlier, it is remarkable that we can prove it. Yet we cannot distinguish between a sequence of actions that has not yet ended from one that is endless by following the steps of the sequence. So we are already in strange territory.

In the way I'm describing this, you may think that the difference is between the abstract world (domain) of mathematics and another world, which might be called physical, though I don't think that is right. I'm very puzzled about what is going on here, but I'm pretty sure that it is more about how one thinks about the world than any multiverse.

Under a capitalist system, apart from whatever welfare state is in play, people end up getting whatever their capacities enable them to. Under most communist regimes, people simply get what they are given by the powers that be. — Janus

Interesting. Under capitalism, you think that people get things from an entirely passive system, and under communism, the system dishes things out to people who are entirely passive. That's far too simple. The systems are far more alike than you seem to think. Under communism, people manipulated the system as much as they could to get what they wanted, and under capitalism, the system exercises its power as much as it can. Though it is true that each system does to present itself in the way you outline.

You may be thinking that I'm saying that the two are as bad as each other. I'm not saying that. I'm saying that it's not a black and white issue. I would not choose to live under a communist system as we knew them. But I would not choose to live under a pure capitalist system, as in the 19th century, either. We live under a modified capitalist system and that seems to me a reasonable way to go - at least, I don't know of a better. But that doesn't mean it cannot be improved.

By the way, you recognize that any welfare system modifies capitalism and that is true, and those systems are very important in making it possible for many more people to live in a more civilized way than pure capitalism can. But the various regulatory systems that West has introduced are also critically important to making capitalism liveable.

I would think that many people interested in politics do follow New York City politics. But if you don't, that's cool. Not sure you are qualified to comment on the social justice approach to crime, though. It's failing in New York City in a very obvious way. — fishfry

So is it possible that a different version of the social justice approach might be more effective? Is it possible that other places may be implementing it in a better way?

But isn't that the same question asked now, when allocating resources and remunerations under capitalist organization? Somebody always seems willing to decide who is worthy of what. — Vera Mont

The trick is, to find something that is objective, or at least rational, or at least acceptable to those who are rejected. As things are, the first two are achieved to some extent, but the last is often suspected of being primarily acceptable only to those in power. Hence all the business with equality of outcomes.

Who decides what the needs of each are? Perhaps the same question could be asked of abilities. — Janus

Good question. The short answer is, public discussion followed by a political deal - not because it is right, but because it is practical. A consensus would be a good basis, but one would probably have to settle for a majority view that is acquiesced in by those who don't agree. But I think with reasonable good will, one could make an initial deal and go from there.

Everybody needs food, shelter and security. But when you get down to details, it gets difficult. One question is what level of needs is appropriate - the level of bare survival or the level required to function as a member of society. Is health care part of the package or not?
Level of ability is not too hard, but very difficult if you are trying to assess what level someone is capable of achieving, rather than what level they are at. Enthusiasm or commitment is, in practice, part of the package as well.

I did say that. Everything but money - because joy also has a dollar value. Just watch the ads if you don't believe me. — Vera Mont

Sorry, I didn't think I was contradicting you. Just expressing the point differently.

We cannot describe the tortoise's position as a simple limit to Achilles' position, because the tortoise is already moving at a constant velocity, and no matter how fast Achilles accelerates he cannot catch up to the tortoise. This is the problem of acceleration, which demonstrates the fundamental incompatibility between distinct rest frames. Einstein attempted to bridge this incompatibility by stipulating the speed of light as the limit, (therefore absolute rest frame) in his special theory of relativity. — Metaphysician Undercover

I do agree with you that people seem not to understand the meaning of limit in this context. Many of them seem to think that calculus solves the problem, though it clearly doesn't.
As to special relativity, I'm not going to argue with you. Most people neglect acceleration, on the grounds that including it won't make any material difference. Does Einstein's theory tell us when Achilles will overtake the tortoise? I thought that both started at the same time, and therefore in the same rest frame. When Achilles overtakes the tortoise, won't they both be in the same rest frame?
Neglecting acceleration, let's say Achilles gives the tortoise a head start of 100 units of length and that Achilles runs at 11 units per second and the tortoise at 1 unit per second. So, at time t seconds after the tortoise is at 100 units from the start, the tortoise will be at 100 + t units from the start, and Achilles at 11t units. These will be the same - 110 units - at time t = 10 seconds.

There are similar paradoxes that don't involve two moving elements:-

Suppose Atalanta wishes to walk to the end of a path. Before she can get there, she must get halfway there. Before she can get halfway there, she must get a quarter of the way there. Before traveling a quarter, she must travel one-eighth; before an eighth, one-sixteenth; and so on. — Wikipedia

It's not. Modern Olympic games are business. Huge government contracts to build new arenas, huge financial losses for the public sector - but, hey, some jillionnaire will buy the arena cheap, plaster his name all over it and charge exorbitant ticket prices to the people who paid for the building of it. As for the athletes, if they survive with body and mind intact, their best hope is to sell their name to a corporation. — Vera Mont

I'm so sorry. There's a small typo in what I said. It should have read:-

That (i.e., the acclaim and reputation tends to result in financial opportunities. was certainly true in ancient Greece and I would be surprised if it wasn't true of modern Olympics as well. — Ludwig V

Though you are also quite right to observe that there are also financial opportunities in creating and running the opportunities to acquire acclaim and success. Not to mention in training and looking after the competitors.

In a society that monetizes everything, and sucks the joy out of everything but money, yes. — Vera Mont

There's a valid complaint here, because our society does tend to suck the joy out of everything. But I'm not sure it is money that is the problem. The thing is, money represents resources. It isn't possible to set up or compete in sport without any resources. Ditto art and pure science. Or raising a family.
It would be better to say that the tendency to measure the value of everything by reference to money that sucks the joy out of everything, because that measure misses the point. Money isn't worth anything for in its own right. Its value is what you can buy or do with it.

Games and sports don't always carry 'lucrative' prizes. The winner used to be content with the acclaim of his peers, a reputation for accomplishment in some specialized area, perhaps increased social status.
Material rewards turn games into business, to the detriment of both the players and the standard of fair play. — Vera Mont

The complication is that the acclaim and reputation tends to result in financial opportunities. That was certainly true in ancient Greece and I would be suprised if it wasn't true of modern Olympics as well. I don't think one can draw a clear line.

A healthy society can have universal healthcare and universal income so long as we are happy consuming healthy competitions so we don't create unhealthy ones out of a desperate need for purpose and flexing our competitive prowess. — Benj96

That sounds good. Not easy, though. There are always free riders and malcontents.

We must subvert our tendency to compete so that we do not do so in a directly oppressive manner to society and human rights. — Benj96

There is always a problem about excessive competition. There are usually systems in place to control it and they are at least reasonably successful.

As Margaret Thatcher once noted, "The problem with socialism is that you eventually run out of other people's money." — fishfry

The problem with Margaret Thatcher is that she thought that a dumb quip is a substitute for serious thinking. But then, she was a politician. She also believed that there is no such thing as society.

when I say that a lot of people these days are advocating for equality of outcome rather than equality of opportunity — fishfry

I agree that equality of outcome is not a reliable index of equality of opportunity and that people often talk, lazily, as if they were. But if equality of opportunity does not result in changes to outcomes, then it is meaningless. The only question is, how much change is it reasonable to expect? If 50% of the population is female and only eight of UK's top 100 companies are headed by women (Guardian Oct. 2021), don't you think it is reasonable to ask why? I agree that it doesn't follow that unfair discrimination is at work, but it must be at least a possibility. No?

Many issues with long wait times at NIH in Great Britain. — fishfry

There are always issues with the NHS in the UK. But that's not about universal health care or not. It's about what can be afforded, what priority it has. Difficult decisions, indeed, but anyone with sense knows they must be made. That's why we have the national institute of clinical excellence. It is not perfect, but it is an attempt to make rational decisions; other systems do not even attempt to do that.
Of course, when my life, or my child's life, is at stake, I will put the system under as much pressure as I can to try everything. And to repeat, it's not about charity or robbing the rich. It's about insurance.

Given that ad infinitum means "without end" — Michael

Yes, it does. But there is a small but significant mistranslation there. I have no problem with saying that "infinite" means "endless", but "ad" does not mean "without". It means "to".
So there are two different ways of thinking about infinity embedded here. One thinks of infinity as a destination, which, paradoxically, cannot, by definition, be reached. The other doesn't, but rather denies that there is a destination. At first sight, one wants to say that the second is correct.
But how do we know that the operation "+1" generates a sequence without end? In one way, it doesn't seem absurd to think that it might be done. After all, given that "+1" can be defined, the result of every step is determined (fixed) - the whole sequence is always already there, for us to inspect. But that seems a mistake; we can't survey the whole sequence and notice that there is no end.
Well, there is the proof that there can be no largest (natural) number. We can prove lots of other things, as well. We don't have to survey the whole sequence to do any of that. It really is magical, and yet inescapably logical. (Poetry? Perhaps. But this is about how we think about things, so it is also philosophy.)

So it seems that we are locked into two incompatible ways of thinking about infinity. One as if it were a sequence which stretches away for ever. The other as a succession of operations which can be continued for ever. (Two metaphors - one of space, one of time.) I'm not suggesting it needs to be resolved, just that we are subject to confusion and need to think carefully, but also recognize that our normal ways of thinking here will need to be adapted and changed.

Well I can walk a mile, and I first walked the first half mile, and so forth, so it's a matter of everyday observation that supertasks exist. That would be an argument for supertasks. Zeno really is a puzzler. I don't think the riddle's really been solved. — fishfry

Quite so. That's why these puzzles are not simply mathematical and why I can't just walk away from them.

The process carries on, unlimited, despite the fact that the mathematician can determine that lowest total amount of time which it is impossible for the process to surpass. — Metaphysician Undercover

Yes, quite so. But it follows that applying the calculus to Achilles doesn't demonstrate that Achilles will overtake the tortoise. I think that only ordinary arithmetic can do that.

Then rather than recite the natural numbers I recite the digits 0 - 9 on repeat ad infinitum.
It makes no sense to claim that I can finish repeating the digits ad infinitum, or that when I do I don't finish on one of those digits.
This is an issue of logic and nothing to do with what is physically possible. — Michael

Does it make any sense to claim that you can repeat the digits ad infinitum? All you can do is repeat the digits again and perhaps promise or resolve to repeat them again after that.

The truths of mathematics and logic are timelessly true, aren't they? There is no change in that world. We frame them in the present tense, but it is, grammatically speaking, the timeless present, not the present that is preceded by the past and followed by the future. We speak of logical operations, but what does that mean? Their results are always already fixed - determinate. So when we carry them out - nothing in logic changes.