So we know that faith healing works, to an extent, and it is supposed to be the foundation of medicine that it works better than faith. But the supposition is faith, and disentangling that faith from 'real' medical benefits is only possible if you question that faith. — unenlightened

That is what clinical testing is supposed to tease out, no? Which is also how we know about the placebo effect in the first place.

Look, first you say that the placebo effect is interesting because it evidences brain's (and thus mind's) control over the body. Then you say that the brain's total control over the body is a "scientific fact" and "not up for debate." You can't have it both ways. If the placebo effect evidences brain's control over the body, then (also according to you) this doesn't tell us anything we don't already know for a fact. What makes your argument even worse is that the placebo effect is just about the weakest manifestation of the brain's effect on the rest of the body that we know about.

BTW, I am not a medical man, but does anyone else think that "Everything the body does has it's origin in the brain?" That is news to me.

This is scientific fact and as far as I know not up for debate. — Tzeentch

Lawyers have a saying: "If you have the law on your side, pound the law. If you have the facts on your side, pound the facts. If you have neither on your side, pound the table."

The facts in question do not support your position, so you resort to pounding the table. You think it's graceful?

The fact that the brain has such a large influence on the body lends credibility to the claim that the brain is master over the body. — Tzeentch

Are we talking about the same thing here? The placebo effect suggests that the mind has slightly more influence over the body than most of us had credited it with, although this extra influence manifests itself in rather obscure and capricious ways. "The brain is master of the body?" Please...

Most such sayings are neither true nor false. They require some (or a lot of) unpacking before we can make an informed judgment. And much will then depend on what meaning (if any!) was packed into them.

Take this one, for instance, from fdrake's "academic" pile:

Moral responsibility is undermined by determinism. — fdrake

Quite a lot of thoughtful and nuanced arguments have been offered in defense of this position, so it can't simply be dismissed as a settled matter. While I mostly disagree, I do believe that there is some truth to it - but much more needs to be said for there to be a meaningful debate over it.

Here is an example of a different kind:

Nothing comes from nothing.

This is something that is usually taken as unquestionably true. And yet, when you ask to unpack its meaning, people are either stumped by the request, or else it turns out that the adage is not fit to do the work for which it was brought up.

I don't really understand why the placebo effect is regularly trotted out in the context of the philosophy of mind. What is it that calls for a philosophical explanation here? That mind and body interact should not be a surprise to anyone. Can you do something at will, e.g. move your hand? Well, there you go. The placebo effect is interesting in that your mental attitudes have effects that we do not usually expect them to have. But then most of us know very little about how the mind works, so the fact that something does not meet our expectations in this context is not particularly significant. What is it specifically about the placebo effect that philosophy of mind ought to address? Does it vindicate or go against some philosophical theory?

What, pray tell, is the alternative to adapting? — Bitter Crank

What makes you think there must be some happy alternative? If you are told that you've got an untreatable cancer, you will, of course, have to "adapt" to that fact, but that doesn't take away the fact that you've got cancer.

Fucked in the way climate science forecasts. I am not going to paraphrase it here for you - go read about it if you really want to know (or fuck off if you are here to troll).

How do you have so much time to read? — ProbablyTrue

Heh, you'll be surprised how much you can get through if you set aside just an hour of undistracted reading a day. — StreetlightX

Good reading skills must help too. I too set aside some reading time, usually more than one hour per day, but there is no way I could get through an average-sized book in a week, especially a philosophy book.

(I read mostly fiction though. Currently finishing Javier Marías's A Heart So White in English translation. It is a fairly slim book, as novels go, but it still took me a couple of weeks.)

You are simply reprising the original argument of the OP, which I've already addressed in my first response.

The reason why market forces won't help us avert the catastrophe is simple: the time scale of climate changes is much longer than any business cycle, or for that matter senior executives' expected tenure on their current jobs. So there simply is no economic incentive for anyone to do anything right now, and if we don't do anything right now we'll miss the last window of opportunity. So yeah, we are fucked.

This story is a fake. First, the vote happened over a year ago. Second, the article, and especially the scandalous title, misrepresents the content of the resolution. It was directed broadly against the death penalty:

1. Urges all States to protect the rights of persons facing the death penalty and other affected persons by complying with their international obligations, including the rights to equality and non-discrimination;
2. Calls upon States that have not yet acceded to or ratified the Second Optional Protocol to the International Covenant on Civil and Political Rights aiming at the abolition of the death penalty to consider doing so;
3. Calls upon States that have not yet abolished the death penalty to ensure that it is not applied on the basis of discriminatory laws or as a result of discriminatory or arbitrary application of the law;
4. Calls upon States to ensure that all accused persons, in particular poor and economically vulnerable persons, can exercise their rights related to equal access to justice, to ensure adequate, qualified and effective legal representation at every stage of civil and criminal proceedings in capital punishment cases through effective legal aid, and to ensure that those facing the death penalty can exercise their right to seek pardon or commutation of their death sentence;
5. Urges States that have not yet abolished the death penalty to ensure that the death penalty is not applied against persons with mental or intellectual disabilities and persons below 18 years of age at the time of the commission of the crime, as well as pregnant women;
6. Also urges States that have not yet abolished the death penalty to ensure that it is not imposed as a sanction for specific forms of conduct such as apostasy, blasphemy, adultery and consensual same-sex relations;
7. Calls upon States to comply with their obligations under article 36 of the Vienna Convention on Consular Relations, and to inform foreign nationals of their right to contact the relevant consular post;
8. Also calls upon States to undertake further studies to identify the underlying factors that contribute to the substantial racial and ethnic bias in the application of the death penalty, where they exist, with a view to developing effective strategies aimed at eliminating such discriminatory practices;
9. Calls upon States that have not yet abolished the death penalty to make available relevant information, disaggregated by gender, age, nationality and other applicable criteria, with regard to their use of the death penalty, inter alia, the charges, number of persons sentenced to death, the number of persons on death row, the number of executions carried out and the number of death sentences reversed, commuted on appeal or in which amnesty or pardon has been granted, as well as information on any scheduled execution, which can contribute to possible informed and transparent national and international debates, including on the obligations of States with regard to the use of the death penalty;
10. Requests the Secretary-General to dedicate the 2019 supplement to his quinquennial report on capital punishment to the consequences arising at various stages of the imposition and application of the death penalty on the enjoyment of the human rights of persons facing the death penalty and other affected persons, paying specific attention to the impact of the resumption of the use of the death penalty on human rights, and to present it to the Human Rights Council at its forty-second session;
11. Decides that the upcoming biennial high-level panel discussion to be held at the fortieth session of the Human Rights Council will address the human rights violations related to the use of the death penalty, in particular with respect to the rights to non-discrimination and equality;
12. Requests the Office of the United Nations High Commissioner for Human Rights to organize the high-level panel discussion and to liaise with States, relevant United Nations bodies, agencies, treaty bodies, special procedures and regional human rights mechanisms, as well as with parliamentarians, civil society, including non-governmental organizations, and national human rights institutions with a view to ensuring their participation in the panel discussion;
13. Also requests the Office of the High Commissioner to prepare a summary report on the panel discussion and to submit it to the Human Rights Council at its forty-second session;
14. Decides to continue its consideration of this issue in accordance with its programme of work. — UN resolution, 22 September 2017

That said, I fully support the resolution and can't see any good reason for the US to oppose it. The resolution does not require states to abolish the death penalty; it only urges them to "consider doing so."

You need to remember that most science is about spherical cows in a vacuum. If you are modeling the Solar system in Newtonian mechanics (or even in relativistic mechanics) you'll probably treat the Sun and the planets as point masses. FLRW cosmology (which is where the Big Bang theory comes from) treats the entire universe as a fluid. Obviously, you would be crazy to take either of these ontologies too literally; you would be even more crazy to commit to both of these, as well as all the other ontologies of the many scientific models at the same time.

It seems that science in general makes no commitment to what really exists. Science deals in models, which only need to be good enough for the job. And if point masses or ideal fluids or spherical cows do the job in a given context, so much the better.

Now, what about epistemology? Does science have anything to say about ways of acquiring knowledge, and whether or not we are justified in believing something? The scientific method, in its general outlines, is basically an empiricist epistemology. If we are talking about science in general, rather than specific theories and discoveries, then we are mostly talking about epistemology. And the epistemological discussion doesn't stop at the general principles; it can get very specific, very detailed, and sometimes even very controversial (take, for instance, arguments over the use of different statistical methods in cladistics).

Quantum mechanics seems to make claims of the form (and please further my insight if I’m wrong) “if some particular measurement is taken, there is some particular probability that the value measured will be...” — Bearden

This can be read either as an operationalization of the theory, which you can similarly do with classical mechanics or any other theory, or a particular philosophical interpretation of the theory (as in the following quote from Heisenberg). While individual scientists and philosophers of science will have different takes on metaphysics and ontology, I don't think they can be generalized to anything very specific, if we are talking about science in general.

You keep using this word "intelligent." What do you think it means? At one point you say "organized/intelligent." So does "intelligent" simply mean organized, orderly, patterned, non-random? If so, then "an intelligent [organized, orderly, patterned, non-random] external force" shouldn't be a problem in our world, where, science tells us, external forces tend to be quite organized, orderly, patterned and non-random.

OK, I think I understand. The way you tell it, you seem to think that bodies are driven entirely by their internal processes. And yet you have also mentioned external forces - doesn't that begin to answer your question?

Let's imagine a setup with a potential field and a particle that interacts with that field (e.g. think of a rock falling from a height). Assume that the particle has no parts; it still responds to that field and does something (maybe not anything very interesting, but hey, it's just one particle). Does this solve the problem?

Well, what I am trying to understand is why you are framing the problem in mereological terms. You say that "without component parts, it is hard to imagine how..." So would it be easier to imagine with component parts?

I am not even doing the Socratic thing here, I am genuinely not understanding your thought process.

I am not sure why you think that "irreducible particles" in particular present a difficulty with respect to interaction and complex behavior. How do you think compound bodies manage it? What is it about irreducible particles that should prevent them from interacting and behaving?

If you look at my article, "Mind or Randomness in Evolution" (https://www.academia.edu/27797943/Mind_or_Randomness_in_Evolution) — Dfpolis

Thank you. Having looked over your article, I have no further interest in this conversation.

The way a Wager-like argument is commonly used (again, it is arguable whether Pascal himself meant it that way), the argument seeks to sidestep the burden of justifying its ontological claim; the cost/benefit analysis, as stated in the argument, is supposed to be doing all the heavy lifting. That is the main selling point of the argument. But we have concluded, at least for your version, that the burden of providing a convincing argument for the existence of God cannot be avoided.

1.The beauty of the universe is improbable under atheism
2.The beauty of the universe is not improbable under theism.
3.If we have two hypotheses and some evidence is not improbable under the first hypothesis but is improbable under the second, then that evidence counts as evidence for the first hypothesis.
4.Therefore, the beauty in the universe counts as evidence for God’s existence (1,2,3 Modus Ponens) — Empedocles

Others have developed an objection along the lines that our sense of beauty is not independent of the universe's constitution, so it is no coincidence that we see beauty in the universe.

In addition, there are more general considerations that also apply to the original fine-tuning argument, which have to do with the nature of the inference - your premise 3.

Atheism places no constraints on the physical universe - in other words, atheism is completely uninformative with regards to its constitution. Therefore, under the assumption of atheism, the probability of any given feature of the universe is either inscrutable or infinitesimal (depending on who you talk to). This goes for the laws of nature, fundamental constants, initial conditions, and anything else, including beauty. But the flip side of this is that evidence of the universe's constitution is uninformative with respect to atheism. Evidence can only count for or against a hypothesis when there is some structural relationship between the two, but not otherwise.

How about the God hypothesis - is there any relationship between it and beauty? Well, I suppose there is, but that's just because you say so. Your God hypothesis is fashioned in such a way as to make beauty likely - it is ad hoc in this way. Ad hoc hypotheses have the annoying property that they automatically raise the likelihood of whatever evidence they were fine-tuned for. For example, looking out of the window and seeing a car with a particular license number passing along the road is a very unlikely event, assuming that there is no particular reason for a car with that number being there at that moment. But if, for example, you hypothesize that God intended you to see that number at that particular moment, then the event is pretty much inevitable! Does this mean that your observation of the license plate favors God (and disfavors atheism)? Of course not. Ad hoc hypotheses, depending on who you talk to, are either inadmissible, or else they pay a high penalty in credibility that cancels out any boost they can get from evidence.

I was telling what happened, not boasting. — Dfpolis

If you say so :roll:

Any system that exhibits any regularity has "telos" in this sense, but so what? Any connection to intelligence is far from obvious. — SophistiCat

I am glad that we agree. But, if biological systems do tend toward determinant ends — Dfpolis

As do all systems (the concept of a system already implies some degree of orderliness). If telos characterizes everything in existence, simply in virtue of the definition that you give it, then it is a vacuous concept. Your analysis of teleology is wholly inadequate, or rather it is wholly absent. Once again, I recommend that you actually read something on the subject - you may learn something interesting, even if you don't agree with all of it. It's much more fun than railing against imaginary "naturalists," at least as far as I am concerned.

The point in question was special pleading by naturalists on the principle of sufficient reason. My position, stated by Freud in The Psychopathology of Everyday Life, is that if you allow any exception to the principle, you undermine the whole structure of science. — Dfpolis

It occurred after no one could rebut my argument for the existence of God in a manner consistent with the foundations of science. — Dfpolis

That's just as I said: your ideas about science and the PSR are idiosyncratic, and I expect that you will find few allies, regardless of their position on naturalism. And when you add boasts like this, you, frankly, sound like a crank. If you want to make a persuasive case, you don't want to explicitly hinge it on extreme foundational positions that few are likely to accept as an unconditional ultimatum.

It depends on what you mean by "supernatural and theological explanations." — Dfpolis

I mean the kind of explanations that hinge on the existence of a powerful and largely inscrutable personal agent.

It is clear from physics, chemistry and biology that many systems have a potential to a determinate end. That is all it means to have a telos — Dfpolis

I strongly suspect it is because they see telloi as strong evidence of intelligence — Dfpolis

That is far too general to be of much use. Any system that exhibits any regularity has "telos" in this sense, but so what? Any connection to intelligence is far from obvious.

I think you're right. Maybe if I qualified premise 1 to say something like, "If the stakes of a belief are high and credible, then you should take arguments regarding that belief seriously" then it might work? I think it's pretty intuitive that stakes play an important role in how highly we prioritize something (e.g. I am more nervous for a piano recital than a practice session, I run faster if I'm being chased by a bear, I work harder when my boss is around, etc...), so I'm hesitant to throw that idea out. — Empedocles

Yes, making the threat credible would help, but that means that the claim no longer justifies itself, which is what constitutes the principal appeal of popular invocations of Pascal's Wager; you still have to all the usual epistemological work of justifying the credibility of your claim.

At most, high stakes can serve as a lever, a force multiplier: If you present a convincing case for your claim, then I would be obliged to take it seriously and act on it. Which is what the original Pascal's Wager seeks to do, in my opinion.

I am sorry for offending you. — Dfpolis

That's ok, I wasn't really offended, and looking back, my sharp tone was unnecessary.

It was based on my experience of discussions with naturalists. Some have even rejected the foundations of science in order to maintain their faith positions. — Dfpolis

Given that your ideas of what constitutes foundations of science are rather idiosyncratic, I suspect that what you interpret as patent irrationality in the service of "maintaining faith positions" is simply a case of disagreement over those matters.

Anyway, I am not surprised at the hostile reception from self-professed naturalists who engage with you in Youtube comments. Teleology, rightly or wrongly, is commonly associated with intelligent agency, making it a poor fit for anything that doesn't have to do with human psychology, except in the context of supernatural and theological explanations. I myself am not entirely sold, not so much on teleology, as on the importance of the controversy. Some of it is merely semantic. And some, like teleology vs. teleonomy, just doesn't present high enough stakes in my mind. But that is probably because I view the issue in the epistemological plane, more than in the ontological one, and in epistemology I favor pluralism. So it's no big deal for me to accept teleological-sounding modes of explanation where they make sense.

Have I made some specific error of biological fact, or ignored some obvious rejoinder? If so, I welcome your correction. — Dfpolis

Your mistake is to charge in like a culture warrior, thinking that naturalists would necessarily be on the opposite side of the barricades, whereas much of the conversation about teleology appears to be secular. Why would a naturalist have an issue with a complex systems analysis of teleology, for example?

By not engaging, you confirm me in my position that we are discussing a faith position, not a rational conclusion. — Dfpolis

My point was that if you want to engage those whom you want to convince, you don't want to open the discussion by poisoning the well with such an obnoxious and unfair accusation. Unfair because, your famous biologist brother notwithstanding, you don't appear to be familiar with secular thought on this subject.

Your response is... to double down on the obnoxiousness. So yes, I would rather engage with Ruth Millican, or Mark Bedau, or Pierre-Normand for that matter.

What I am suggesting is that the selection process is teleological in the very same sense in which the organism's physiological and behavioral activities are teleological (or structured by means/end relationships), and for the very same reason. An organism, for instance, engages in some sort of behavior in order to quench its thirst. If it tends to succeed, thanks to some heritable feature of its physiology or anatomy, then this feature tends to be positively selected. And the reason why descendants thereafter exhibit this feature, and have the ability to engage in the behavior that such structures enables, is precisely because they subserve the end that was being actively pursued by the ancestor: namely, quenching its thirst. I conclude that the process of evolution through natural selection does have a telos, but that telos isn't external to the life form of the evolving organism; it is rather internal to it. The main engine of evolution is the organism's already existing struggle to flourish and survive (in very specific ways) in its day to day existence. — Pierre-Normand

I think you get biological teleology wrong. The way you describe it, teleology arises from individual organisms' striving to achieve a goal, much like Lamarck thought that when a giraffe reaches for higher branches its neck grows progressively longer with each generation (he even hypothesized a causal mechanism for this: a "nervous fluid"). We know that this is not how evolution works (for the most part). Fitness does not increase as a direct response to organisms' strivings and desires. As you say, the internal teleology of evolution is in the process itself, not in some agent's mental attitude. The process of evolution by natural selection molds successive populations to better fit their environment, and that works just as well on a moth's passive mimicry as on a giraffe's active feeding. It works even on unconscious, inanimate things that are similarly subject to natural selection!

I think the key to the controversy over biological teleology is in what Bedau called "mentalism:" psychologizing teleology, thinking of teleology only as a pattern of thought. Proponents of the concept of biological teleology argue that there is a more general pattern that manifests itself in other, non-psychological domains, and that both evolutionary adaptation and organismal functions are valid examples of this pattern.

Meanwhile, biology students are taught to eschew talk of biological ends. — Dfpolis

I don't know about that. I was never a biology student (and neither were you, AFAIK), so I don't know what students are taught; but teleology in biology is a controversial but well-explored topic. I wonder whether you are actually familiar with any of that discussion.

Philosophical naturalists reject finality, not because doing so is rational, but because it threatens their faith position — Dfpolis

Oh boy. You know, when you write something as obnoxious as that, one is discouraged from reading further.

In the context of this topic (purported normativity of logic), "logic" is not just any abstract system of inference. You could throw together any number of such systems; obviously, they couldn't all be normative. (Normative for what?) The "logic" under consideration is what underlies ordinary deduction. Sometimes people talk of the FOPL in this context, but I think that FOPL can only serve as a proxy. What is (purportedly) normative is an unformalized intuitive rationality, which can be brought out with simple, uncontroversial examples of deduction. Formal logic, such as the modern-day FOPL, aims to capture this intuitive rationality.

Logic does not just set out how we ought speak, but how we can speak. It shows us what sorts of speaking are wrong. — Banno

You think you are saying something different, but you are not. You just understand "normative" in a narrow ethical sense.

Good question. I have never had a clear idea of what people mean by normative, and looking up definitions doesn't seem to help. — andrewk

I would define a normative belief as one that directly justifies and urges or inhibits action or conduct. It says "You should do this," "This is the right way" or "That is the wrong way." A normative principle is a generalization of such beliefs. When I say "directly" I mean that the normative belief does not acquire its normative status in virtue of something else. It doesn't tell you that you should do this or that for reasons, because if there are other reasons, then they are in turn the source of normativity. Normative beliefs are where reasons bottom out.

The condition that a normative principle applies not just to oneself, but to everyone is a contingent, non-essential property of normative principles, I think. Normative principles are often, but not always universal. Moral relativists typically believe that the force of moral principles is limited to a particular culture or community. Jews believe that their religious strictures apply only to Jews (there are a few Biblical prescriptions applicable to gentiles as well, known as Noahide laws). Personal obligations and vows have force only for one particular person.

I realize that all this is somewhat vague and squishy, and will fray and crumble at the edges when subjected to scrutiny, as analytical philosophers especially like to do. But that just means that the concept of normativity is not simple, clean and sharp-edged, which is to be expected for a concept whose nature is psychosocial.

One can raise the stakes of any proposition, simply by appending to it a stake-raising clause. For any proposition A there is a proposition A* = A & C, where C = (costly consequences for not believing A). So the consequence of your position is that you have to take seriously infinitely many propositions, not just those concerning the existence of god and his proper worship.

You could object that A* is spurious, but your argument does not say anything about the content and the quality of the propositions that you say should be taken seriously; the only reason you give for taking them seriously C.

Try to mount an argument that we ought to use logic if we wish to arrive at true beliefs, without using logic. — andrewk

Isn't that what the normative principle amounts to (or something similar)? It's precisely because mounting an argument without the use of logic is impossible by definition that such guiding principles cannot be anything other than normative.

It's mind-boggling that despite a consensus opinion of the expert community, no remotely credible scientific and engineering justification, no independently verified demonstrations, and no apparent interest from the industry, which would stand to profit enormously if LENR was viable, there are still people eager to uncritically swallow this bullshit year after year after year. "Coming to market soon!" (And we've been hearing this song for how long? From Rossi alone - since 2011 at least.)

Fascinating factoid: In a single hour, the amount of power from the sun that strikes the Earth is more than the entire world consumes in an year — Hanover

But in order to make use of all that energy you would have to cover the entire surface of the earth with perfectly efficient solar panels, which then perfectly efficiently deliver that energy to end consumers. So, all things considered, that doesn't actually seem like that much usable energy.

In The Norton Dome and the Nineteenth Century Foundations of Determinism, 2014 (PDF) Marij van Strien takes a look at how 19th century mathematicians and physicists confronted instances of indeterminism in classical mechanics*. She notes that the fact that differential equations of motion sometimes lacked unique solutions was known pretty much for as long as differential equations were studied, since the beginning of the 19th century. Notably, in 1870s Joseph Boussinesq studied a parameterized dome setup, of which what is now known as the Norton's Dome is a special case. Although Boussinesq did not solve the equations of motion for the dome, he studied their properties, and noting the emergence of singularities for some combinations of parameters he concluded that the equations must lack a unique solution in those instances (this can also be seen by noting that the apex of the dome does not satisfy the Lipschitz condition in those configurations - see above.)

* A less technical work by the same author is Vital Instability: Life and Free Will in Physics and Physiology, 1860–1880, 2015 (PDF).

Van Strien writes that "nineteenth century determinism was primarily taken to be a presupposition of theories in physics." Boussinesq was something of an exception in that he took the nonunique solutions that he and others discovered seriously. (He acknowledged that his dome was not a realistic example, taking it more as a proof-of-concept; rather, he thought that actual indeterminism would be found in some hypothetical force fields produced by interactions between atoms, which he showed to be mathematically similar to the dome equations.) Boussinesq believed that such branching solutions of mechanical equations provided a way out of Laplacian determinism, giving the opportunity for life forces and individual free will to do their own thing.

But by and large, Van Strien says, such mathematical anomalies were not taken as indications of something real: in cases where solutions to equations of motion were nonunique, one just needed to pick the physical solution and discard the unphysical ones. This is probably why these earlier discoveries did not make much of an impression at the time and have since been partly forgotten, so that Norton's paper, when it came out, caused a bit of a scandal.

From my own modest experience, such attitudes towards mathematical models still prevail, at least in traditional scientific education and practice. It is not uncommon for a model or a mathematical technique to produce an unphysical artefact, such as multiple solutions where a single solution is expected, a negative quantity where only positive quantities make sense, forces in an empty space in addition to forces in a medium, etc. Scientists and engineers mostly treat their models pragmatically, as useful tools; they don't necessarily think of them as a perfect match to the structure of the Universe. It is only when a model is regarded as fundamental that some begin to take the math really seriously - all of it, not just the pragmatically relevant parts. So that if the model turns out to be mathematically indeterministic, even in an infinitesimal and empirically inaccessible portion of its domain, this is thought to have important metaphysical implications.

Interpretations of quantum mechanics are another example of such mathematical "fundamentalism". Proponents of the Everett "many worlds" interpretation, such as cosmologist Sean Carroll, say (approvingly) that all their preferred interpretation does is "take the math seriously." Indeed, the "worlds" of the MWI are a straightforward interpretation of the branching of the quantum wavefunction. (Full disclosure: I myself am sympathetic to the MWI, to the extent to which I can understand it.)

Are "fundametalists" right? Can a really good theory give us warrant to take all of its implications seriously?

"Nuclear fusion is always 30 years away," as they say. This indeed has been the case for the last half-century if not more.

LENR is just a rebranding of cold fusion. It is largely the province of cooks and scammers.

And then, of course, as SophistiCat astutely concluded (and I didn't concluded at the time) the ideal case might be inderminate because of the different ways in which the limiting case of a perfectly rigid body could be approached. — Pierre-Normand

Thanks, but I cannot take credit for what I didn't actually say :) The rigid beam case is indeterminate in the sense that multiple solutions are consistent with the given conditions. I did think that there may be a way to approach a different solution (with non-zero lateral forces) by an alternative path of idealization, perhaps by varying something other than elasticity. My intuition was primed by the 0/0 analogy, in which a parallel strategy of approaching the limit from some unproblematic starting point would clearly be fallacious. But I couldn't think of anything at the moment, so I didn't mention it.

I think I have such an example now though.



Suppose that a pair of lateral forces of equal magnitude but opposite directions were applied to the beam. This would make no difference to the original rigid beam/wall system: the forces would balance each other, thus ensuring equilibrium, and everything else would be the same, since the forces wouldn't produce any strains in the beam; the forces would thus be merely imaginary, since they wouldn't make any physical difference. However, if we were to approach the rigid limit by starting from a finite elasticity coefficient and then taking it to to infinity, there would be a finite lateral force acting on the walls all the way to the limit.

Korolev actually does a similar limiting analysis of the dome itself, showing that for any finite elasticity (assuming a perfectly elastic material of the dome) there is a unique solution for a mass at the apex: the mass remains stationary; but when the elasticity coefficient is taken to infinity, i.e. the dome becomes perfectly rigid, the situation changes catastrophically and all of a sudden there is no longer a unique solution.

In the case of the beam in Norton's paper, in order to definitely answer the question we need to find the state of stress inside the beam, which for normal bodies is fixed by boundary conditions. The problem with infinite stiffness is that constitutive equations are singular, and therefore, formally at least, the same boundary conditions are consistent with any number of stress distributions in the beam. This happens for the same reason that division by zero is undefined: any solution fits. In the simple uniaxial case, the strain is related to the stress by the equation $\epsilon = \frac{1}{E}\sigma$. When E is infinite and 1/E is zero, the strain is zero and any stress is a valid solution to the equation. Boundary conditions in an extended rigid body will fix (some of the) stresses at the boundary, but not anywhere else. Or so it would seem.

However, what meaning do stresses have in an infinitely stiff body? Because there can be no displacements, there is no action. Stresses are meaningless. Suppose that instead of perfectly rigid and stationary supports, the rigid beam in Norton's paper was suspended between elastic walls. Whereas in the original problem the entire system, including the supports, was infinitely stiff and admitted no displacements, now elastic walls would experience the action of the forces exerted by the ends of the beam. Displacements would occur, energy would be expended, work would be done. The problem becomes physical, and physics requires energy conservation, which immediately yields the solution to the problem.

So I wouldn't worry too much about these singular limits; just as in the case of the division by zero, no solution makes more sense than any other, they are all meaningless.

In Determinism: what we have learned and what we still don't know (2005) John Earman "survey[ s] the implications of the theories of modern physics for the doctrine of determinism" (see also Earman 2007 and 2008 for a more technical analysis). When it comes to Newtonian mechanics he gives several indeterministic scenarios that are permitted under the theory, including the Norton's dome of the OP. Another well-known example is that of the "space invaders":

Certain configurations of as few as 5 gravitating, non-colliding point particles can lead to one particle accelerating without bound, acquiring an infinite speed in finite time. The time-reverse of this scenario implies that a particle can just appear out of nowhere, its appearance not entailed by a preceding state of the world, thus violating determinism.

A number of such determinism-violating scenarios for Newtonian particles have been discovered, though most of them involve infinite speeds, infinitely deep gravitational wells of point masses, contrived force fields, and other physically contentious premises.

Norton's scenario is interesting in that it presents an intuitively plausible setup that does not involve the sort of singularities, infinities or supertasks that would be relatively easy to dismiss as unphysical. has already homed in on one suspect feature of the setup, which is the non-smooth, non-analytic shape of the surface and the displacement path of the ball. Alexandre Korolev in Indeterminism, Asymptotic Reasoning, and Time Irreversibility in Classical Physics (2006) identifies a weaker geometric constraint than that of smoothness or analyticity, which is Lipschitz continuity:

A function $f$ is called Lipschitz continuous if there exists a positive real constant $K$ such that, for all real $x_1$ and $x_2$, $|f(x_1) - f(x_2)| \le K |x_1 - x_2|$. A Lipschitz-continuous function is continuous, but not necessarily smooth. Intuitively, the Lipschitz condition puts a finite limit on the function's rate of change.

Korolev shows that violations of Lipschitz continuity lead to branching solutions not only in the case of the Norton's dome, but in other scenarios as well, and in the same spirit as Andrew above, he proposes that Lipschitz condition should be considered a constitutive feature of classical mechanics in order to avoid, as he puts it, "physically impossible solutions that have no serious metaphysical import."

Ironically, as Samuel Fletcher notes in What Counts as a Newtonian System? The View from Norton’s Dome (2011), Korolev's own example of non-Lipschitz velocities in fluid dynamics is instrumental to productive research in turbulence modeling, "one whose practitioners would be loathe to abandon on account of Norton’s dome."

It seems to me that Earman oversells his point when he writes that "the fault modes of determinism in classical physics are so numerous and various as to make determinism in this context seem rather surprising." I like Fletcher's philosophical analysis, whose major point is that there is no uniquely correct formulation of classical mechanics, and that different formulations are "appropriate and useful for different purposes:"

As soon as one specifies which class of mathematical models one refers to by “classical mechanics,” one can unambiguously formulate and perhaps answer the question of determinism as a precise mathematical statement. But, I emphasize, there is no a priori reason to choose a sole one among these. In practice, the choice of a particular formulation of classical mechanics will depend largely on pragmatic factors like what one is trying to do with the theory. — Fletcher

Yes indeed. They are abrogating their moral duty to the letter of the law. Which makes them less human, allegedly. — unenlightened

Not exercising a quintessentially human faculty in the context of performing a specific task does not make you "less than human," in and of itself - it all depends on context. Following printed instructions while assembling an IKEA table won't land you in Nuremberg. What is morally suspect is abrogating moral duty when exercising moral duty is called for (and yes, that can happen in a legal context as well).