I find no error in this. — tim wood

There is no error, hence the apparent paradox.

Here is another take I just thought of. We can define two functionals, one that gives some measure of the distance between the points of the stair functions and the diagonal (e.g. the average distance), and the other that gives the length of those functions. The shape functional steadily converges to zero, but the length functional does not.

Nice.

he number of "stairs" tells something similar how polygons start resembling a circle: — ssu

The difference is that in the case of polygons approximating a circle, with each successive step the error decreases (don't ask me for a proof - it's pretty messy, from what I remember), whereas in the case of the staircase the error stays the same throughout.

People define free-will in different ways. And so they argue about different things. But it really goes back to the concept of "you". You like others, will say you have a body, you have a brain, you have... maybe a spirit or soul... two arms and two legs. Who is "you"? The idea of there being a "you" and the continuation of self is intertwined with all definitions of free-will. — Malice

Nature as in, our exact state. — Malice

Our nature is not identical with our physical state. I am not making some dualistic statement here - I am just agreeing with what you said earlier that I quoted here. What constitutes "you" or "your nature" isn't simply reducible to your physical body (or else your personal identity would be extremely volatile). It is a somewhat vague notion rooted more in psychology and culture than in physics - you know, like "free will."

The solution to deal with its demoralizing power. ‘Solution’ sounds confusing, I’ll change that — Rystiya

What does "its" refer to here? You never say.

What do you even mean by "being moral"? — Pfhorrest

Making right moral decisions. What is right is, of course, the very subject of morality.

The criteria for the success of what? A moral science, or generally any system of morality? The criteria for success of those things is to provide a means of answering questions about morality. When someone wonders what is moral, how do they figure it out? When two people disagree about what is moral, how do they resolve those difference? Answering how to do that, how to figure out those answers to questions about morality, is the criteria for the success of a system of morality. — Pfhorrest

So any procedure for answering moral questions will do, as long as it is comprehensive? No other criteria of success are required?

That you think I'm even trying to do that shows you haven't understood a word that I've said so far. — Pfhorrest

If by that you mean that I haven't read your articles on morality, then no, I haven't. That wasn't the subject of this thread.

I predict you'd respond here "aha! So you're starting with a system of morality already, your 'ought' premises, just like I said!" But no, no more than the physical sciences start with some set of unquestionable "is" premises. — Pfhorrest

That sort of Cartesian scheme that you outline doesn't remotely resemble the way science is done. But even if your approach was better at aping science, that still wouldn't make it any better than a cargo cult, because you still aren't thinking about why you do what you do. Why should morality resemble science?

It's certainly incompatible with materialism. A mathematical ontology isn't compatible with there being stuff, so I don't see how it's physical. But I guess if we're allowed to redefine the meaning of "physical" to be whatever is consistent with physical models. — Marchesk

There is nothing to redefine here, because there aren't any commonly established definitions for physicalism or materialism. All these arguments over this or that being compatible with physicalism/materialism is pure wankery, in my opinion. Argue substance, not isms. (Same goes for realism, of course. Crispin Wright famously wrote that "a philosopher who asserts that she is a realist about theoretical science, for example, or ethics, has probably, for most philosophical audiences, accomplished little more than to clear her throat.")

It seems that it's hard to say whether we have free will or not. — Rystiya

It's hard to say what free will is. It's hard to even get people to think seriously about the question: they would rather argue endlessly about "free will" than think about the question that ought to be addressed before anything else.

The solution is simple — Rystiya

The solution to what?

Because while you busy yourself with procedural details of how to reduce morality to a utilitarian optimization, you don't ask what any of that has to do with being moral. What are the criteria of success (other than aping the superficial trappings of science)? How do you jump the is-ought gap?

Thanks, I got it when I thought about it again. I got into a habit of thinking of numbers as abstract objects that just satisfy certain requirements, like Peano axioms, whose representation and internal structure need not concern us. I lost track of the obvious idea that a number can also be thought of as a collection with that many distinct objects - a cardinal*. When you mentioned von Neumann construction, I thought about Zermelo's construction with its Russian doll structure - that wouldn't work so well. I guess that's one of the advantages of the von Neumann model, right?

* Heh, now that I think about it, that was exactly how numbers were introduced to us in preschool, using little sacks with different amounts of marbles :)

Being correct and being clear is not the same thing. I took ten or so different courses of mathematics in college. It's been a long time and I have forgotten much of it, but I still understand basic combinatorics, thank you very much.

"Methodically" is the key word here. Yes, you have a method, but that's not enough to qualify as "science." If you don't understand why you do what you do, then your method is no more scientific than astrology or divination.

This wasn't very helpful.

It's still not clear to me how the use of this set theoretic representation explains "the number of functions from 2 into 2 is 4". Whatever representation you use, you still have one number (in this case, one set) in the domain and one number (one set) in the codomain. I mean, I can see (after your explanation) what he is doing, but I am not even sure how to formulate that correctly without specifically referring to the internal structure of a von Neumann ordinal.

The number of functions from 2 into 2 is 4. — GrandMinnow

I don't understand.

$\biggl(2\biggr) \rightarrow \biggl(2\biggr)$

How is this four functions?

(FWIW in calculus texts the exponential function is usually defined generically as a power series.)

All we need for an "ethical science" is that kind of broad agreement. — Pfhorrest

Why do we need an "ethical science"? You never stop to ask yourself this question. This is cargo cult.

2^0 = 1

The number of functions from 0 into 2 is 1. — GrandMinnow

x^y = the cardinality of {f | f is a function & domain(f) = y & range(f) is a subset of x}. — GrandMinnow

OK, but by the same token 2^2 = 1, because the number of functions from 2 into 2 is 1. What am I missing?

x^y may be defined as the number of functions from y into x. — GrandMinnow

What do you mean by that?

Somehow I'm not surprised. — Artemis

Yeah. And I didn't even read any of the religion, gender, race or politics stuff, which is what usually gets people into hot water.

I'm wondering if everybody perceives themselves as all alone with nobody of the same "general color" as them, or if everybody else feels like they're in good company with like-minded people who just have "shades of disagreement". — Pfhorrest

That's an odd wish, from my point of view, to have a camp of people that agree with you on everything. But you strike me as an opinionated fellow, with a definite position on everything, so I can kind of see how you would expect all water to flow to the same level. I like to think of myself as too much of a chameleon to be the same color with anyone (though I am probably deluding myself).

I think it may be related to the Uncanny Valley effect: someone sufficiently different is just an Other, but someone who's a lot like us but slightly off is just... sick somehow, disgusting. — Pfhorrest

Intraspecific competition is the most vicious.

It is impossible to do science without agreement on foundational things like empiricism and realism and some form of rationalism (as in rejecting appeals to intuition, authority, etc). Those practicing scientists may not have all made explicit their philosophical assumptions, but the work they did as a community had to take them for granted; those who continued to dispute those principles did not become part of the scientific community, but instead became its opponents, disputing its results on what scientists consider fallacious philosophical grounds. Because those scientists had at least an implicit philosophical framework in common. — Pfhorrest

You are conflating actual practice with its philosophical interpretations. Science is done the way it is done not because scientists have come to an agreement about its philosophical foundations (even the philosophical community is far from such an agreement), but because science is a fairly distinctive enterprise and there is a particular way in which it is practiced, which scientists learn in the course of their training. This is not to say that science is a game with arbitrary rules institutionalized by tradition. I believe that modern science is a product of cultural evolution, the seed of which is just our instinctive way of understanding our environment, one which we practice on an everyday basis. Moreover, the weightiest normative criteria in science - closeness of fit and parsimony - are objective to an extent that few other activities can boast (which partly explains the trust that we put in science). It is because science is constrained between its determinate natural origins and its semi-determinate goals that we think we can retrofit it with determinate philosophical foundations.

Which leads us to the contrast case: morality. On the one hand, morality, like science, has deep evolutionary, cultural, social and psychological roots, which makes it fairly determinate and eminently suitable as an object of study. But the other, normative end does not hold up, because of course morality is itself normative. This immediately short-circuits any question about what ought to be moral - what ought to be moral is what is moral, duh!

There is a clear trend of moral thinking moving toward a more “scientific” methodology based on common experience and critical reasoning, we just haven’t fully developed a consensus on how exactly those principles all fit together yet. — Pfhorrest

Yeah, this is just cargo cult science, I am afraid. There is a science for everything nowadays (or rather since the Enlightenment), so there must be a science of morality! Never mind that it makes no sense - to be intellectually respectable it gotta look like science.

That can't be right. Death is a symptom. If you are asymptomatic, you don't die any more than you cough or have a temperature. And if you are asymptomatic, in most cases you don't get tested. — unenlightened

That's what I said. Death rate is estimated on the basis of confirmed infections. Adding a hypothetical number of untested and asymptomatic cases doesn't change anything if what you want to know is how dangerous and disruptive the epidemic will be, or what your chances of falling ill are, or what your chances of dying will be if you develop symptoms.

That is why the quarantined ship makes a good statistical sample - everyone was tested. — unenlightened

Yes, I mentioned that too. When the entire population or subpopulation is tested regardless of symptoms, that is where the true fatality rate becomes relevant. But such testing is done in a small minority of cases.

Bottom line is that statistics should be used with care.

You should get together with @Sam26, another OBE "expert."

You like reasoning and argument, don't you? Here's some reasoning and argument.

https://slate.com/technology/2020/03/coronavirus-mortality-rate-lower-than-we-think.html?fbclid=IwAR2Di6GSNzwF8WJ4RDVmkLjwJr7x8sY5Bnwq-UJY_Uv3WmUu4EmjHP3XRZU — unenlightened

There are reasonable points here, but the article is too focused on massaging the fatality rate. Yes, if you include asymptomatic cases, the fatality rate will go down. But the hypothetical asymptomatic cases that were not counted for fatality rate were also not counted for infection rate, so the net result is zero. All you've shown is that in addition to cases with pronounced symptoms, having fatality rate f, there are also X asymptomatic cases.

Now, if people were tested regardless of their symptoms, then knowing the true fatality rate would be relevant. This is the case with those who are quarantined and tested because of their previous contact with an infected person. But for most people testing is still confined to those with pronounced symptoms.

Why do those ones deserve an exception?

The physical sciences we have today began as a branch of philosophy, "natural philosophy", that pretty much solved its foundational questions and then went on to do the business of applying them. — Pfhorrest

Science didn't wait around for its foundational questions to be solved before it could get off the ground - if it did, it would have been waiting to this day. Historical nomenclature aside, what we today recognize as science came together haphazardly as a living practice, rather than as a systematic application of a fully developed philosophical program. If anything, metaphysics and epistemology have for the most part been playing catch-up to science, taking its practice and its findings as a subject of study.

There is no reason to think that moral philosophy cannot do the same thing, solve those foundational questions, and go on to start doing ethical sciences by applying those. — Pfhorrest

Well, since in truth nothing in history has followed this path, then there is nothing for moral philosophy to imitate here.

Are there something else in our mind makes us know that divine commands are moral? If we have it, we don’t need divine commands, as our hearts know what to do. — Rystiya

No, you don't second-guess God, that's not how divine command works. All you need to know is that you must accept God's authority. This is where your role as a moral agent ends and God's begins.

No, it's a meta-ethical question. Just like the foundations of the physical sciences are found in answers to meta-physical questions (broadly, including epistemology in there). — Pfhorrest

The relationship of science and philosophy is a complex one. Philosophy can and does take science as an object of study, just like anything else, but its prescriptive role is very limited. I personally believe that there can be some fruitful cross-pollination between science and philosophy, but it would be the height of hubris to think that science is principally guided by philosophical doctrines, other than the ones that emerged organically in the course of its own development.

The situation with ethics is different though. You can think up metaphysical interpretations and epistemological models, you can package ethics into systems - all as part of the descriptive program of philosophy. But philosophy has no prescriptive role to play with respect to ethics, because at the end of the day, the question that ethics is answering is what one ought to do. Ought questions cannot be decided by anything other than moral judgement. They are like the universal acid: any philosophy that you throw at them will be cut through to the foundation by this stubborn ought: Why ought this be so?

If ideological spam is acceptable here, then responding to it with ideological trolling is fair game.

Do the criteria of success for a system of science themselves belong in the science category? Must you have a scientific judgment before you can judge a system of science?

No. Same with ethics. — Pfhorrest

You are right about science, of course, but wrong about ethics. Whether ethical principles are right or wrong is an ethical question - a redundant one, of course, which was my point. You can evaluate ethical systems by other criteria, but the most important criterion for ethical principles is their moral truth - and that judgement cannot be subordinated to philosophy or science or anything that is not ethics.

Bringing people out of existence through horrible disease is not part of the antinatalist agenda, sorry. Certainly being brought into existence exposes people all around the world to this though. — schopenhauer1

Which is why you should welcome the culling that I propose. I promise, it will be quick - not like dying from pneumonia. Or just kill yourself already and stop spamming the forum.

Say something or be silent. — schopenhauer1

I say we should start the virus containment program by culling antinatalists. OK, it's not the most effective means to combat the epidemic, but it's something. And best of all, it will be easily the most welcome virus-containment measure of all. Since antinatalists' maxim is that living perpetuates suffering, they will all be in favor of their own extinction - not to mention everyone else around them. It's pure win!

He is suggesting that the majority of Atheists are angry. — 3017amen

Well, O'Reilly is a professional bullshitter, so what he says is on him (and why are you watching this garbage anyway?) But if you really think that "the majority of atheists is angry," then you know nothing. Atheists are as heterogeneous a group as the population as a whole, and being angry is certainly not a distinctive trait of theirs. (Citing Einstein as an authority on this issue is clueless or disingenuous - he wasn't an authority on sociology of psychology, and he's been dead for more than half a century.)

And by what standard, pray tell, do you judge the reliability of your system of morality? — SophistiCat

Short answer: Same way I judge the reliability of science.

Long answer is about 80,000 words if you care to read it. You could start here for just the objectivity part or the last section of this for a general overview. — Pfhorrest

Yes, I understand that you have some pet utilitarian system, but this doesn't really answer the question. If my system of morality prescribes maximizing the amount of Chinese fortune cookies in the world, the reliability of this system qua moral system will not be judged by its own criteria of success, i.e. by the amount of Chinese fortune cookies.

This was a trick question, of course. The criteria of success for a system of ethics themselves belong in the ethical category. You have to have ethical judgment before you can judge a system of ethics. But if you already have ethical judgment, then what need is for a system?

Do not have children. Over and out. But I'll be back shortly. — schopenhauer1

Enough with the spamming.

Near as I can tell, you mean something like 'coordinate time' when using the phrase 'relativistic time'. — noAxioms

Time is an integral part of relativistic spacetime. If you need a specific measurement of time, you can use proper time in conjunction with a specific timelike worldline, or a coordinate time in conjunction with a specific reference frame - doesn't matter, since they are all mutually convertible.

Can there be time without clocks? — noAxioms

I mean "clocks" in a general sense, as any observable regular physical process, such as an oscillation.

Up to a point, yes. However, by its nature, secular morality allows for challenge. — Txastopher

The flexibility and openness to change of secular moral systems can vary as much as the flexibility of and openness of religious systems (which vary a good deal). But ultimately systems are only as open and as flexible as their users.

Even if every person where to think exactly the same about morality that wouldn't make morality objective. It's an objective fact that all people think the same in that case, but it's still something people think... so it doesn't get anymore 'subjective' than that. Words have meanings.

Morality is something we create, like language is, we do not observe or find morality or language like we find objective facts about the world. And so it doesn't make a whole lot of sense to use terms like true or correct or whatever equivalent. — ChatteringMonkey

Well, morality is what people think in the same way in which electric charge, say, is what particles have. Morality (and language) is no more and no less subjective than facts about the world - it is a fact about the world. I think this subjective/objective dichotomy isn't helpful at all.

So yeah, what philosophers have been trying to do in ethics over the ages, seems pure hubris to me, and doomed to fail. — ChatteringMonkey

Right on. I generally agree with what you say, except it seems like you overestimate the degree to which morality is a social contract. First of all, we need to distinguish social mores and individual moral character. The genesis of social moral codes can plausibly be analyzed that way, but there are probably other contributing causes. And when it comes to personal morality, its development will vary greatly case by case.

Certainty is still the quality lacking in secular morals. — Txastopher

Nah, there's no lack of moral certainty among secularists; you need to look a bit more into history and generally get out and meet more people. Being certain that you are right is more related to character than anything else.

Here's one right here:

A secular system of morality as reliable as the physical sciences is possible. — Pfhorrest

And by what standard, pray tell, do you judge the reliability of your system of morality?

Actually, you never really defined what you mean by 'relativistic time'. You say physical time is that which clocks measure. I think physics would say that a clock measures proper time, a frame independent property of any timelike worldline. — noAxioms

Sure. But as you note later, proper time can be well-defined even in the absence of anything to mark its passage, and that is where I see a problem. You could have a relativistic spacetime with nothing else, and formally it would still have time of every description. But would it be physically meaningful?

Of course, here we run into the more general question of the nature of the physical law. Are laws ontologically prior to things and events that are subject to them? Do they describe potentialities (like what would happen if that empty spacetime did have something in it to demonstrate its relativistic properties)? Or do laws serve only to connect the dots, describe the regularities in our observations? In the latter case - and only in the latter case - it would be unjustified to talk about time in the absence of anything that is time-like. I think I lean towards the Humean regularity view.

One might object that clock time, as instantiated by physical clocks (regular processes), is a naive concept and that relativistic time is more fundamental. But clocks are epistemically prior to our concept of time. The reason we came up with the theory of relativity in the first place was to give a better account of clock-based time (among other things). Without clocks what is the point of relativity?

An empty, flat spacetime with a positive cosmological constant is an interesting case. Formally, there is a temporal process (expansion of spacetime), but with nothing clock-like to register the passage of time, does it still make sense to talk about time? Does it even make sense to model it with a Lorentzian manifold and Einstein's field equations?

No.

The article states: "In fact, unless inflation went on for a truly infinite amount of time, or the Universe was born infinitely large, the Universe ought to be finite in extent." I admit I was only addressing the first possibility, but the second possibility remains just an assumption. — Relativist

As is the alternative. It is widely understood that the universe (or at least the inflationary "pocket" that we occupy, if we go with the still somewhat speculative eternal inflation hypothesis) was either always finite or always infinite. Neither option is granted the default status by cosmologists (your epistemological arguments notwithstanding). The question is decided by the weight of evidence, or lacking that, by considerations of simplicity; these two epistemological criteria constitute the foundation of scientific epistemology. As far as the former, there have been some publications that claimed that a closed (finite) spacetime topology fits some of the observational evidence better than the flat topology of the standard FLRW model, but their conclusions have not yet gained widespread acceptance. As for simplicity, here the flat semi-Euclidean spacetime wins over the more structurally complex closed topologies.

The first article showed that, according to accepted physics, spatial extension can only be infinite if there is an infinite past - that's why I focused on past time. — Relativist

If you mean this article, then it doesn't say that, and it would be pretty incredible if it did, because the best established cosmological model to date implies an infinitely extended universe without the assumption of an infinite past. Note that the article spends considerable time talking about inflation, which is less well established than standard Big Bang cosmology, but inflation doesn't imply what you claim either.

This does not apply to my claim. Sure, it's coherent - his statement entails no logical contradiction, but it circularly assumes the infinity exists, and it is that assumption that I challenge. — Relativist

There is no circularity, because the refutation does not seek to establish the positive claim and makes no assumptions of its own. It only shows that the anti-infinitist argument doesn't work - the specific argument that you were making originally involving "completeness." (Morriston makes a similar case in Must the Past have a Beginning?)

As for your first order/second order abstractions, that's something completely different. I won't go further than just to say that I am not buying your epistemological construction.