Far more important to human life is how we value, or disvalue the things of sense, how we find beauty or indifference in them, how we love or hate them, or disregard them. — Janus

I don't like "more important" or "highest". Everyday mundane reality is important, not "low".

We all know them, by virtue of being human, but their truth cannot be demonstrated in any determinable way as the truth of the fact of the world of the senses can. As I understand it it is that that Wittgenstein is getting at. — Janus

You seem to be trying to say that our values cannot be described in the way that facts can and hence are not true or false and cannot be known, and yet we know them and they are true. I think that's what Wittgenstein was trying to face up to. It certainly seems to follow from the Tractatus that nothing can be said about values. Yet here you are, trying to say something about values and it is not obvious that what you are saying is nonsense or non-sense. I think he was so focused on a certain use of language that he wasn't able to recognize other uses as having a validity of their own.
But there are some other things that seem to belong here. One of the things that he was getting at is that the relationship between language and the world cannot be stated, only shown, just as the relationship between a picture and what it represents cannot be pictured. (I'm not sure about whether logic in general is among the things that cannot be said.)

One must conclude a danger of some sort first before the chemicals come into play. — noAxioms

But there is a conceptual link between danger and fear that makes it hard to understand what recognizing a danger could be if one didn't fear it.

Another word for determinism, and determinism is not hand waving. It's simply a valid philosophical view. — noAxioms

I hope I'm free to disagree with you?

Yes, that part is hand waving. It assumes that the hard problem isn't hard, or rather, that there isn't a hard problem. The hard problem, as stated, is also hand waving, and will by definition never be solved, regardless of the progress of science and the success of a simulation such as Bostrom describes. — noAxioms

So we agree on something.

Simulated cognition influenced by simulated chemistry. — noAxioms

And that adds up to genuine emotion?

And you can’t posit or define or conceive of half without reference to half of some other defined, conceived thing, and that thing must be a whole unit. — Fire Ologist

Yes, but once you have defined your half, you can treat it as a unit and define a half of a half... and repeat indefinitely. What limits that process?

Infinity applies to numbers. Numbers aren’t physical things, like stairs. — Fire Ologist

That's certainly where are problems are. But you need to state this carefully. For example, there are no infinite natural numbers and while numbers are not physical things like stars, they do apply to physical things. The tricky point is that the idea of infinity is embedded in the number system, not some accidental additional property.

There is no infinity apart from the mind that conceives it. There are things apart from the mind that conceives of the unit. — Fire Ologist

Infinity is certainly not a concept and not a physical entity - I doubt that it should be called an entity at all. I would love to know what things apart from the mind "conceive of the unit".

That's not the case. "Object" is not implied. You are simply saying that whatever it is that the two names refer to, it is one and the same. — Metaphysician Undercover

Ostensive definition can only work if you know, or can work out from the context, what kind of thing (category) is being defined. When you gesture at a red car and say this is red, you will misunderstand if you take red to mean a car or a wheel or a heavy object.

Again, this is not true. When you say Ringo Starr is Richard Starkey, all you are saying is that these two names have the same referent. It is only upon analysis, if one seeks to determine whether it is true or not, or something like that, that one would determine that the two names both refer to a person. — Metaphysician Undercover

It's not enough to know that the two names have the same referent. You need to know, in Wittgenstein's phrase, where the referent "is stationed in the language".

My point is that once we've entered the realm of speculative fantasy, where do we stop? — fishfry

I think that there some rules that apply in fiction (imaginary stories), because the story needs to have plausibility. But I don't know how to work out what they are. Coleridge, I think it was, said that there needs to be a "suspension of disbelief" for any fiction to work. The reader/audience needs to co-operate and not ask awkward questions. But there are limits. There needs to be some realism for the story to be recognizable at all.

s has a greatest number in its domain, and the last value for s is x. — TonesInDeepFreeze

I don't quite see why x is the last value, nor why you think that defining the set in that way gets round the point that w is not derived from the criterion from which all the other numbers in that set are derived.

Your question was why does this analysis of ethics and religion "end up in the same place." — Constance

I looked at your post again, and now I see better what you - and @Astrophel - are talking about. I got distracted by the question of freedom.

Another way to put this is to refer to earlier on in the Tractatus when he says the point of the book is to draw a limit to the expressions of thought. What lies on the other side of language is nonsense, and what is on the other side of language? Metaphysics. — Astrophel

Yes, that's exactly his argument. What is not clear is whether he thought of that as debunking metaphysics or legitimizing it (in some form)? (Throwing away the ladder once one has climbed up it.) I can't see that he might have intended to allow (or would have allowed), if he had known about it) a project like Husserl's or Heidegger's - both of whom abjured metaphysics (as traditionally understood.)

But a very real and palpable metaphysics in the burned finger, the falling in love, the heartbreak, the joy, the despair, and so forth. These and the value that is pervasive in our existence, from vague interest to thrill and excitement, literally constitute ethical possibility. — Astrophel

I'm all for giving a central place in philosophy to human life. But classifying that as metaphysics is a bit of a stretch don't you think?[/quote]

I want say that if ethics were just as coercive (meaning one really has no choice to accept constructions in symbolic logic) and absolute (though logic itself is understood in language, and language cannot be said to be apodictic; I mean, when we ask what language is, we don't get truth tables and theorems. We get history and evolving meanings) as logic, then everything would change. — Constance

It certainly would. Ethics as we know it would not exist. It would reduce to determinism.

Plainly put, our ethics, so familiar and complicated, would be grounded in Being itself. In Being, this qualitative play of good and bad that is our existence is risen to a new order of significance, one traditionally reserved for religion. — Constance

That depends on what you mean by "grounded". You seem to be attributing some sort of coercive force to Being and that is the nightmare of a world without ethics or even value.

I'm not qualified to provide specific examples, but I'm pretty sure in my readings I have come across a notable amount of "instances" in Philosophical "calculations" where God must be assumed for the "equation" to resolve a metaphysical or even Ethical question. Correct me if I'm wrong. — ENOAH

You are probably reading philosophers who have an religious agenda.

It's natural for humans to think they are worth more than other animals, just as other animals care only, or at least predominately, for their own. — Janus

Yes. I don't see that as a problem. We put our families first - not to do so is morally questionable - and we often do so to our own cost. "Putting first" in not simply "prioritizing over everything else". In any case, enlightened self-interest would prompt us to recognize that our well-being depends on the well-being of everything in our environments.

I find all of that list to be part of cognitive content, but with chemical influences as well. — noAxioms

Code which is influenced by chemistry. Good luck with that.

Give it particles and forces and such, and off you go. It would need an insane amount of power and memory, but a relatively trivial code base. — noAxioms

That's just a version of Laplace's demon. Hand-waving.

But Bostrom adds a lot more to the software requirement because it needs to know which molecules comprise a set of particles that is designated as a human, and it needs to glean intent from that human so that it can change the physics of some systems when necessary. Now the software is a million times more complicated, but the extra code is worth it for the optimization it buys. — noAxioms

That's just a lot of hand-waving.

I'm sorry to be so abrupt. But I've tried to follow the detailed arguments to no avail.

Are we anything other than extraordinarily complex wind up toys? — Patterner

I hope you are not winding me up with that question. I certainly am extraordinarily complex, but I am also certainly not a toy. Partly, its a question of attitude. We have a physical existence, so, in a way, the answer has to be yes. In fact regarding the body as a complex mechanism is very useful. (Medicine, for example.) More to the point, when that mechanism fails, we die. Yet that mechanism allows us to laugh and sing and fall in love, as well as destroying the planet and each other. Reconciling those two facts is, for me, the only game in town, or out of it. Notice that I have not answered your question which has presuppositions that require definition or at least explanation.

And I really don't think Laplace was trying to convince us that such a demon is likely, or possible. He was just saying, in a universe where everything is deterministic, anything at any point in the future would be, in theory, calculable. — Patterner

Yes, that's right. But that form of determinism does not amount to anything that could threaten freedom. There's a difference between being able to determine which horse will win the race, in the sense of being able to predict the result of the race and being able to determine which horse will win the race by fixing the race. Laplace's demon can do the first, but not the second.

Ah, Searle said that, which makes sense. Of course Searle isn't going to accept a naturalist premise, but his unwillingness to set aside his opinion about it prevents his rendering any proper critique. — noAxioms

I don't think a proper critique requires the critic to set aside their opinion. But it does require a willingness to engage with the opposition. I think he has an extreme form of a regrettable, but not uncommon, tendency to adopt a premiss (axiom, "truism") which presupposes his conclusion. But to be fair Derrida, in their famous debate, does not exactly go overboard to understand Austin, but I thought that he did at least try to do so.

I need to correct myself. I found an entry on Google Books:-

With special emphasis on vision Searle explains how the raw phenomenology of perception sets the content and the conditions of satisfaction of experience. ...... He next justifies the claim that perceptual experiences have presentational intentionality and shows how this justifies the direct realism of his account. — GoogleBooks on Searle's Theory of

For my money, this doesn't amount to direct realism. Note the references to "raw phenomenology" and "presentational intentionality". But I can see why one might pigeon-hole him under that heading. But I'm quoting the summary, not Searle himself. Perhaps there's a distortion in that.

For purposes of this discussion, I've been using the two terms interchangeably. — noAxioms

Yes. Only a naive person like myself would want to differentiate the two. But I had in mind the much-abused ordinary experience that was so popular in Oxford at a certain point; it seemed better to call it naturalism.

If this world is part of a simulation, it is definitely going to have to simulate chemical/hormonal influences on our experience. Far more than that even. — noAxioms

Yes. The question is How much more? Emotions (as opposed to moods) have a cognitive content, and that wouldn't be a problem. But they also involve desire and value. That is extremely problematic. It seems to me that software commands can simulate emotion, but having an emotion (desire, value) is a very different kettle of fish.

I believe that what is attempted with the law of identity is to express an unqualified sense of "same". You seem to think it fails. Why? — Metaphysician Undercover

If I say that Hesperus is Phosphorus, I am saying that they are the same object (heavenly body). If I say that Ringo Starr is Richard Starkey, I am saying that Ringo Starr is the same person as Richard Starkey.
If I say that Venus is Venus, I say nothing at all. But even then, it makes a big difference whether you are talking in a context in which Venus is a goddess or a planet.

The distance between your eyes is a whole. — Fire Ologist

I suppose you can. But then I can define as a whole anything I like. A spoonful of sugar. A rainbow. Six inches of two-by-four. The distance between my front door and the shop on the corner. What counts as a part is defined in relation to that. But each part is a whole in its own right. The leg of a chair. The branch of a tree. The handle of a door. Half of a penny. It's just a convenient trick of language.

Mind

You need to grab that finite whole thing first from the physical world to then posit the concept of half of that whole. The half wasn’t grabbed from the physical world. — Fire Ologist

"Grabbed" from the physical world is a completely inappropriate metaphor. Nothing is grabbed. Something was defined. In any case, if the whole thing was "grabbed from the physical world", it follows that both halves of it were "grabbed". If they weren't, nothing was "grabbed".

The simple solution is simply to say that motion isn’t continuous. Discrete motion at some scale is a metaphysical necessity. — Michael

The simple solution is to recognize the difference between an analysis and a dissection. A dissection physically separates an object into separate parts (and the parts then become wholes in their own right). An analysis has no physical impact on the object at all. One can analyse a distance into metres, centimetres, millimietrs or yards, feet and inches or any other units you like. You can analyse it into any fractions you like. All at the same time. The object doesn't change.

If I ask you what the minimum unit of space is, I can analyse that distance into fractions, however small it it is. Whether I can physically divide an object into those fractions is another question.

I was not expecting that response. I don't know what to say. So I'm absolutely delighted!

Intellectuals are lost if there is nothing to say. — Constance

That's why their chatter is endless.

Truth is, I don't know where to begin.
I had in mind looking at Heidegger's project and perhaps comparing it with Wittgenstein's (or Kant's or Husserl's or ...)
Or perhaps looking more carefully as Cavell's idea that the roots of philosophy go deeper than its problems.
Or something else.

What if ethics were as apodictic, that is certain, as logic? I will simply hand this question to you to see what you think. — Constance

I don't think that I really understand how to follow up your question.
We could start by asking whether logic is as apodictic as it is thought to be.

Rather, you are given the sequence; and given the limit; and you can apply a formal definition to see that 0 is indeed the limit of the sequence. It's conceptually sort of the other way 'round from thinking that the limit is the result of some logical process applied to the sequence. — fishfry

I take the point. I may not have stated it accurately enough, but the crucial thing, it seemed to me, is to realize that the limit is part of the definition from the start - not, as I think you're saying, something that is worked out from the sequence itself.

I believe that what is attempted with the law of identity is to express an unqualified sense of "same". You seem to think it fails. Why? — Metaphysician Undercover

If I say that Hesperus is Phosphorus, I am saying that they are the same object.

“The infinite” or “infinity” as a noun, is best used for dramatic effect. It’s not a thing, like a noun is best employed. “Infinitely” as an adverb, sets out some activity that, by definition, cannot conclude. Thereby banishing all finitude, which marks conclusion, such as a step, or a series of steps, or a noun. — Fire Ologist

You are right, Language is a great trap here. I would like to use "endless" or "endlessly" and even "endlessness" instead. That would make it more difficult to talk about conclusions. But we are lumbered with a world which uses "infinity". Natural language allows this, but has no guard rails to prevent us from talking nonsense.

But the infinite finds no home, no place in the physical world, — Fire Ologist

The difficulty here is that it is possible to defined an infinite series in a finite frame, which leads people to think of apply the abstract idea to the physical world. Sometimes that works, as in physics, so we can't just say that such ideas have no place in the physical world.

But you never find the infinite. There need be no infinitely small fraction. — Fire Ologist

Yes, we do. We don't find them by failing to count them, but through various arguments. The proofs that π or sqrt(2) or that there is no largest natural number are all well established. So is the possibility of a convergent series.

There is no such thing as a half step. — Fire Ologist

True, if you are thinking of a staircase. But nobody would contest that. But if you think of the distance between my eyes, you can certainly divide that by 1/2 or 1/4 or...

He (sc. Searle) associates it (sc. "secret sauce") with life. Something about living things. — fishfry

But that's an issue that goes back millennia. A century ago, there was "elan vital" or "Life Force". Before that, it was the "mind", the "soul". Aristotle's "psyche",
Searle's mystery component can be seen in his Chinese Room. It is (from what you tell me and my memories) just a gesture towards something in the future.

I could think about it a lot, without ever figuring out what you were trying to tell me here!
I thought I was agreeing with you, that emotions are an argument against computationalism. But perhaps I misunderstood. — fishfry

I'm sorry. It was lazy of me to do that.
One point about it was indeed that the physical basis of the emotions is clearly not just a matter of processing information. The focus on the brain, together with the computer analogy, misleads us. Even the knowledge that we already have should prevent us from thinking that there is necessarily any simple correlation between mental and physical phenomena. People equate fear and anger with the circulation of specific hormones. But that is, surely, clearly not the sort of thing that our computers can do. It is one phenomenon in among others that are associated with the emotions. The brain, presumably, is involved in triggering the release and the whole of the rest of the body is affected. Compare the call of "action stations" in a ship or perhaps the fire alarm in a building. Everything is affected. There's no way of picking out the specifics, except by the general description "ready for action" or "falling in love".
Computers of the kind we are familiar with do not (so far as I can see) have any capacity to be afraid or fall in love, to value one outcome over another and one of the reasons for that, it seems to me, is that the way they "think" has no conceptual space for those things. (Though I'm sure that some people will respond to the challenge by developing simulations.)
I'm going to stop there. There's not much I'm sure of beyond this point, except that philosophers don't seem to be able to grapple sensibly with what's going on here.

Emotions are another good example, thanks for that. They're squirts of hormones in the limbic system or some such. Nobody understands how it works. It doesn't seem very computer-like to me. — fishfry

No, they are not just hormones. The causes of the hormones in the brain and the effects of the hormones in the body, together with their psychological counterparts are all part of the package. Think about it.

The lamp is either on or off at t1. The fact that it makes no sense for it to be on and no sense for it to be off if the button has been pushed an infinite number of times before that is proof that it makes no sense for the button to have been pushed an infinite number of times. — Michael

Exactly. The contradiction follows from the fact that no final state is defined.

That completion is just as arbitrary as any other. But it has one supreme virtue: 0 happens to be the limit of the sequence. So that's why I call it natural. — fishfry

I understand that. What seems important to me is that the convergent series is the result of a calculation which involves 0 and 1, while "0,1, 0, 1, ..." doesn't involve any calculation at all. You could also have a series "a, b, a, b, ..." or "fish, chips, fish, chips, ..." The calculation involves numbers, but "0, 1, 0, 1, ..." only involves numerals.

It makes no sense to answer this question with "a plate of spaghetti" or "1/2". — Michael

I think you'll find that's because it makes no sense to answer the question.

In other words, it also makes no sense to answer the question with "on" or "off".

I understand why those answers seem more natural, but that's an illusion.

But this is just a hypothesis based on "Let us suppose for a moment that these predictions are correct." — SpaceDweller

You are quite right. Enthusiasts are fascinated by the speculative possibilities and so forget the provisos. It's really quite annoying.

Is naturalism = physicalism? Or is there a further distinction? — fishfry

That's not exactly wrong. But let analytic philosophers loose on an -ism and in a few years you'll have dozens of them. In the first half of the last century, there wasn't a concept of computability, so that issue is undetermined.

The term “naturalism” has no very precise meaning in contemporary philosophy. Its current usage derives from debates in America in the first half of the last century. The self-proclaimed “naturalists” from that period included John Dewey, Ernest Nagel, Sidney Hook and Roy Wood Sellars. These philosophers aimed to ally philosophy more closely with science. They urged that reality is exhausted by nature, containing nothing “supernatural”, and that the scientific method should be used to investigate all areas of reality, including the “human spirit” — Stanford EP - Naturalism

In philosophy, naturalism is the idea that only natural laws and forces (as opposed to supernatural ones) operate in the universe.[1] In its primary sense,[2] it is also known as ontological naturalism, metaphysical naturalism, pure naturalism, philosophical naturalism and antisupernaturalism. — Wikipedia - Naturalism

I believe in that same lecture (or perhaps a different one) he did NOT advocate dualism. He advocated what I call "secret sauce," my phrase, not Searle's. That is, consciousness is physical, but not computational. That's the point I've been making to noAxioms. — fishfry

I'm clearly out of date. Apologies to Searle. However, I'm not much reassured. If Searle is positing consciousness as an unknown something-or-other in addition to what is currently recognized as physical, he is positing a consciousness of the gaps, which is at least close to dualism.
The mistake is to start with "Consciousness is....". We know what consciousness is; we don't know how to explain the physical basis of consciousness - yet. But it is clear that there are many disparate phenomena involved and it is possible that consciousness will not map neatly onto the physical world. (Consider the many complicated physical phenomena that are involved in the emotions, for example).

Mind-body problem is only relevant to dualism, and sim theory isn't dualism, so the there's no problem. I think the term is 'interactionism', how the dual aspects interact with each other. — noAxioms

I apologize. I should have referred more generally to "philosophical theories of the mind". Bostrom clearly has one, though he proceeds as if it was certainly correct. A serious error, in my book.

How does my decision to point a gun at the baddie cause Lara Croft to raise her arm? There has to be a causal connection between my decision and her arm, and there is. But under sim theory, there isn't two separate things that need to interact, so the problem doesn't arise. — noAxioms

If there is a causal connection between my decision to point a gun and Lara Croft raising her arm, there are two things that interact. That's what causality means. Whether you are dualist, monist, physicalist, idealist, epiphenomenonalist or panpsychist.

But there's no need for there to be any logical relation between the sequence itself, and the arbitrarily-defined terminal state. — fishfry

So, the terminal state not being defined does not prevent me defining one arbitrarily?
Isn't it the case that there is a requirement - that the terminal state not be defined by the function.

There is no last term in any infinite sequence. There may (or may not) be a limit. Big difference. — fishfry

Yes. The exact status of 1 or 0 in these cases is more complicated than I realized.

Even if you insist that the terminal state must be either 0 or 1, there is no logical way to prefer one over the other. — fishfry

So can you help me to describe the role of 1 in defining the series 1/2, 1/4, ... when the limit state is 0? (Or indeed when it's the other way round?)

Ah the mind-body problem. I saw a video of Searle giving a lecture. He raised his right arm and said, "I think to myself, I'll raise my right arm. And my right arm goes up. How does that happen?" — fishfry

How could the mind-body problem not be relevant if people are positing that sims might be people (and sometimes asserting that at least some people are sims?)
Yes. Sometimes I find his tendency to present dualism as common sense ridiculous and sometimes annoying. It reminds me of Bishop Berkeley and his wilful refusal to recognize that he is contradicting common sense.
But the rhetoric of that sentence is genius. A mystery created from a commonplace.

But I do object to the "best they could do at the time" argument that video games are getting better, therefore in the future they'll be indistinguishable from reality. — fishfry

I do so agree. That argument is pure hand-waving. Completely acceptable in a (conventional) fiction, where we aren't expected to ask questions.

Nevermind, I looked it up. It's "the philosophical belief that everything arises from natural properties and causes, and supernatural or spiritual explanations are excluded or discounted." — fishfry

"Naturalism" is used much more widely than that. I've been classified as a naturalist because I reject dualism.

If my reality is nothing but a "simulation," then I'm not real. There is only the simulation. Meaning that I'm not a simulation, I'm an instantiation. — fishfry

Better put than I managed.

The code here is effectively the same as a recursive function. — Michael

Not quite. The code specifies a process which must take time. The function does not.

I'm arguing that supertasks are metaphysically impossible. He's arguing that supertasks are metaphysically possible. — Michael

Thank you. I must have got confused.

Don't follow. The limit of 0, 1, 0, 1, ... can not be 1. Nor can it be 0. It's a sequence that has no limit. — fishfry

I'm sorry. I was talking about the convergent series. Didn't check

I do not think Michael and I are making the same point. — fishfry

Perhaps not. But if the last term in the series is not defined, contradictions are likely to follow from the attempt to identify it. Equally, if something gives rise to a contradiction, the definition will be faulty. So, if you are right, I need to ask why it matters.

I'd agree except that the law of identity was first, set theory came along after. — Metaphysician Undercover

Temporal priority is not logical priority.
Whether a proposition is obvious (self-evident) or (self-evidently) absurd are subjective.

Well, if the law of identity is an obvious self-evident tautology, then it appears like there must be something wrong with set theory if it's in contradiction with what is obvious. — Metaphysician Undercover

There are plenty of ways to formulate that law without using the word "same". In any case, "same" in that context just means "same object", so it isn't absolute. moreover, If you drive my car, you don't drive it at the same time.

The thing is that everything about it is not the same, only those named qualities are the same, and that's why it's incorrect to say that it is "the same" in that unqualified sense. — Metaphysician Undercover

There is no unqualified sense of "same".

Not everything about the two is necessarily the same, only the stipulated required qualities. — Metaphysician Undercover

We agree!

So it is incorrect to say that the two sets are the same, in the unqualified sense, — Metaphysician Undercover

There is no unqualified sense of "same".

He (sc. Aristotle) claimed that the law of identity was necessary to battle against sophists who could logically demonstrate absurdities. — Metaphysician Undercover

I'm sure that Aristotle would not object to my regarding that as not a logical argument.

That's precisely why supertasks are impossible. — Michael

My point is that I think that the disagreement between you and @fishfry is about different ways to make the same point.

There's nothing wrong with defining, or performing, a recursive function. There is a problem with claiming that it is possible to have completed a recursive function. — Michael

Quite so. Wittgenstein made much of the endlessness of infinity and asked how it was possible. You may know what his answer is. If you don't, it is easy to look it up. (It would be far too long to try to outline it in this context and you likely know anyway.
My question is, how do we know that it is not possible to complete a recursive function (in the sense of writing or speaking each step that the function defines)? BTW, I don't think there is any particular problem about defining such a function, though you could argue that it is the result of misapplying an operation that is perfectly harmless in other contexts, like √2 or a self-referential pronoun like "I" or "this".

For example, proving that √2 is irrational doesn't rest on trying and failing to write it down, but on showing that the assumption that √2 is rational leads to a contradiction - reductio ad absurdum.
In the case of infinity the argument rests on mathematical induction. I understand that not everyone is happy with that argument but it seems OK to me. A recursive function is defined, but in such a way that its end is not defined.
So even if a sequence cannot be completed empirically, so to speak, there are ways of proving that it is endless with attempting the impossible refutation of writing down each step.

The terminal state isn't just undefined; any proposed terminal state is inconsistent. The lamp cannot be either on or off after two minutes even though it must be either on or off after two minutes. This is a contradiction, therefore it is impossible to have pushed the button an infinite number of times. — Michael

The contradiction is the result of the fact that there is no criterion set for the final step in your process - i.e., the end state is undefined.

You have not defined the terminal state. So why do you think there should be a sensible answer for what it is? — fishfry

Surely, the contradiction is the result of the lack of any definition of the terminal state. If the terminal state could be a plate of spaghetti, why couldn't be a lamp that is neither on nor off?

I really cannot see what you two are arguing about. Why does the difference matter?

You can define the terminal state to be on, off, or a plate of spaghetti and be consistent with the rules of the game. It's not a real light bulb, it's not driven by a real circuit. — fishfry

The plate of spaghetti is a great dramatic way of making the point that there is no definition. But the series is defined on the basis that its limit is 1. You can't derive 1/2 from a plate of spaghetti.

Conclusion: set theory is in violation of the law of identity. I've explained to you why this is the case. Do you agree with me? — Metaphysician Undercover

It seems pretty clear that "same" does not have the same (!) meaning in the context of set theory that it has in the context of the law of identity. How could it? The definition that applies in the context of the law of identity is inapplicable to the context of set theory, and vice versa. So why don't you conclude that the use in the context of the law of identity violates the use in the context of set theory? It seems to be an arbitrary choice.
The meaning of "same" depends on its context. There are many other concepts of which that is true.

But this is the real hard question. Being in a prison implies one is not free, so the question then is, what is the nature of freedom? — Constance

So freedom is always there as it is our nature, our existence, to stand in this openness of possibilities, but this is forgotten. — Constance

Yes, freedom is about possibilities. Prison means that certain possibilities are denied. All of that is true if I am in prison. But what freedom means in that context is perfectly clear, both in respect of the possibilities that are denied to me and in respect of the possibilities that are open to me. Your question implies that something is not clear. For me, the question of the nature of freedom seems to be posed in a vacuum, without context. Some would call this the quest for absolute freedom, but trip up because without context there is neither freedom nor constraint.

Just going along, day by day, is a bit like being a thing, for a thing doesn't have choices. — Constance

It can be a bit like being a thing, but it is also being free. It depends how you look at it. Either way, it is where we live.

Pain is OF the world, not of our laws that deal with pain. Pain is this primordiality, a givenness of our existence, and will not be spoken. — Constance

It certainly is a given. I'm not sure what you mean by speaking of pain. We can certainly talk about it, and we do - especially when we are suffering from it.

so the question then is, what is the nature of freedom? — Constance

That's (one version of) the question that philosophers ask. But they don't think through what that question means and so end up is quagmire.

And you likely know that Heidegger, Sartre, Kierkegaard, and so on, including Kant and his rationalism, all have something to say about freedom. — Constance

Quite so. But I'm intrigued that you go through a huge process and end up in the same place that I'm in. Pain is part of life. So what is at stake here?

Forgive me - what the "GS"?

I'm sorry if I confused things. I'm happy to take answers from anyone who is moved to provide one.

One need not think of specifically the physical realm as a closed system, one can instead imagine (physical realm plus mind realm) as a combined closed system. And an LD that's fully aware of what's going on in all the relevant realms of the combined closed systems is still conceivable. — flannel jesus

All I was saying is that it makes no difference whether one thinks of the universe as a closed system or as a combined closed system. It is just one way of thinking about the universe. It may be useful, but is it true? What is the evidence one way or the other?

It's Laplace's premise. It's not mine. I don't believe it to be the case. — Patterner

That's fair enough. I'm just trying to say that it isn't an empirical idea - no amount of empirical evidence will confirm it, or refute it.

There's nothing wrong with defining, or performing, a recursive function. There is a problem with claiming that it is possible to have completed a recursive function. — Michael

Quite so.

Can you prove that it is impossible to complete a given recursive function?

For reference:-

We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes. — Laplace

It's just a day-dream.
You can summarize this as "If determinism is true, it would be possible to predict everything". Not very exciting, is it?

One need not think of specifically the physical realm as a closed system, one can instead imagine (physical realm plus mind realm) as a combined closed system. And an LD that's fully aware of what's going on in all the relevant realms of the combined closed systems is still conceivable. — flannel jesus

"IF the universe is a closed system.." we can make all sorts of deductions and predictions. But is it? What's your evidence?

Determinism rules all things, and LD has the perception and intellect to figure everything out. — Patterner

"IF determinism rules all things..." but does it? What's your evidence? Laplace is perfectly clear that "we may regard the present state of the universe..." He doesn't pretend that this is any more than a possible way of looking at things.
Similiarly, he says clearly " An intellect which at a certain moment would know all forces ... and all positions of all items..., if this intellect were also vast enough...". He doesn't even suggest that this is possible. (Interesting that he doesn't mention that God would be such an intellect.)

I answer Yes to both. Why not? That's the premise. — Patterner

You need to establish the premises in order to assert the conclusion.
Still, consider your answers:-
1 If LD cannot figure some things out, what follows? Does it follow that determinism is false? Yes.
The catch is that you have to wait until LD has figured everything out before you know whether there are some things it cannot figure out, and even longer before you know that it has not just made a mistake.
2 If LD can predict everything accurately for the next n years where n is any number you like. Does it follow that determinism is true? Yes
No, it does not follow that determinism is true, even if you can predict for any finite number of years ahead. Even if the universe is finite and time will run out, and LD predicts that, it will not follow that it got things right because it's calculations were correct.

No, the mathematical operation of division cannot be applied to an infinite number of times, for the reason explained above. — Metaphysician Undercover

Recursion occurs when the definition of a concept or process depends on a simpler or previous version of itself. Recursion is used in a variety of disciplines ranging from linguistics to logic. The most common application of recursion is in mathematics and computer science, where a function being defined is applied within its own definition. — Wikipeida

I know it is only Wikipedia, but I'm sure that more authoritative references could be found.

What is wrong with that?

LD is also aware of where every particle in the universe outside of our solar system is, which way each is going, and can calculate which will interact with our SS, and when. Even if two hunks of rock a thousand light-years away that are not heading this way are going to collide, and some debris from that collision will then head this way. — Patterner

Nonetheless, it is treating the universe as a closed system.

We seem to be unable to communicate. — noAxioms

Oh, I don't think it's as bad as that.

But there very much is storms and rain in the world simulated. It wouldn't be a weather simulation without such things. — noAxioms

No, there are only simulated storms and rain in the simulated world.

The point of the simulations would be lost if real people capable in their own right of acting and reacting in their world.
That sentence lacks a verb, and you lost me. ....
Your wording in the verb-less sentence suggests that simulated people would perhaps need to exert some sort of free will over the physics of the simulation. That model isn't compatible with Bostrom's view. — noAxioms

I'm sorry. I'm afraid I can't re-construct what that sentence was supposed to be. But your version of it is what I was trying to say. I can believe that it is not compatible with Bostrom's view. The question is whether Bostrom's view is coherent.

Once you suppose that the simulations are conscious

I don't think anybody is supposing that. See the above. — noAxioms

Similarly, a simulation of a conscious being would not make a computer conscious, but that doesn't mean that simulated person is not conscious. Bostrom suggests that is exactly what's going on. — noAxioms

So Bostrom does suggest that the simulations of people "inside" the (non-conscious) computer are conscious.

I am not an avatar in a video game, for the usual Cartesian reason. There's a "me" in here having subjective experiences. — fishfry

I'm agree with fishfry here, but adding that if the "me" in here is having subjective experience, then I must be able to interact with the presented illusory environment, that is, I can cause things to happen in the environment and get appropriate feed-back from the environment. But that would make me a real person, not a simulation (though I might be a clone.)

Yes, a simulated person would behave differently than 'their originals', which I put in quotes because there are no originals in the scenario in question, — noAxioms

There's an ambiguity here. There could be simulations of people that are like fictional people. Their originals would be people in general, not people in particular (though an ancestral simulation suggests that they would need to be people in particular - if they aren't, then what makes it an "ancestral" simulation.)

So one is always already IN some historical framework (this for Heidegger was the essential ontology for dasein), bound to a particular finitude. — Astrophel

There are two issues with this. First, the framework that I have learnt is not bounded, in the sense that it has infinite possiblities within it. Second, it is not a fixed framework, but is subject to change and development - Derrida is acutely aware of this, isn't he? So I ask the question, what tells us that we are "bound" to a particular framework? Awareness of history, perhaps, and/or awareness of change. Perhaps we should think of our historical framework as a starting-point, rather than a prison.

But it is a very sticky matter simply because one has to bite this absurd bullet that says as I acknowledge my cat on the sofa, it is somehow existentially remote from possible understanding. There is this impossible distance between me and the cat that says I know, but I really don't know in the deeper ontology. This distance is about language and the world. — Astrophel

I can, and do, acknowledge my cat on the sofa and acknowledge also that I do not know - am not aware of - everything that the cat is. Some things may be beyond any possibility of knowing, such as knowing (i.e. experiencing) the lived world of the cat (because I could not be the cat without ceasing to be me, a human being). There is surely, no harm, in admitting my limitations while at the same time acknowledging the cat is "really" there, and on the sofa.

I'm not sure that there are not some typos in this - I certainly can't construe it:-

the pain from this broken knee cap is does not issue from a construction of beliefs about pain, and the prohibition against bringing this into the world some from the pain itself, not as the pain is construed, interpreted. Pain qua pain makes sense even though the language that speaks it cannot speak the world, so to speak. — Astrophel

But, yes, the world resists us and obtrudes on us - however much we may try to control it or ignore it. That's how reality becomes real for us as we exist in our framework - and, of course, how our framework has to stretch and adapt to accommodate it. The limitations we posited at the beginning do not exist.

I believe this is saying that LD knows everything about everything IF everything about everything is deterministic. That, I believe, is the point of Laplace's thought experiment.
But if all of reality is not deterministic, LD's calculations would not be able to figure everything out. — Patterner

If you think of some restricted problem, such as the movements of the planets in our solar system, this seems to work. But it treats the solar system as a closed system and restricts the predictions that are made about it. Laplace is generalizing from that to everything. That's not a defined system and it posits a range of predictions restricted to those that physics can make or a final and complete physics of the future. Don't you think that is a rather generous assumption?

Even if you swallow that assumption, consider:-
1 If LD cannot figure some things out, what follows? Does it follow that determinism is false? No.
2 If LD can predict everything accurately for the next nyears where n is any number you like. Does it follow that determinism is true? No.

Laplace's demon proves nothing.

Worse than that, if LD can accurately predict some things, does it follow that they happened because of LD's prediction? No.

Laplace's demon is irrelevant.

By most definitions of 'reality', yes, a simulated world would be a reality of its own, but it being called a simulation is an explicit admission of it being dependent on the deeper reality running the simulation, just like saying 'God created the universe' makes the explicit relation of the universe being dependent on the god. — noAxioms

The meaning of "dependent" is context-dependent. The dependence of a simulation on its deeper reality is quite different from the dependence of a created object on it creator. If one thinks of some entity having created a universe, the implication is that the creation exists in its own right. Insofar as a simulation is a reality of its own in the way that a story is a reality of its own, it will not exist in its own right and remains under the control of the story-teller, even though it may have an internal logic that is not the same as the logic of reality.

I'm a sim fishfry and there's a "real" entity fishfry who's being simulated, but who isn't really there. — fishfry

..... unless you think of fishfry as an avatar. On the other hand, if I am a simulation that is not aware of the fact, I must be able to act and react in my world. In that case, I am not a simulation of anything.

Bostrom suggests a sim of ancestral history, which means that random new people get born, and these people do not in any way correspond to actual people that might have existed in the history of the GS. — noAxioms

I can think of models of the weather system that are used to predict the weather. They can be called simulations. They remain quite distinct from the actual weather. There are neither storms, nor rain, nor sunshine inside the computer. Yet the point of the exercise is that it remain as close as possible to what actually happens/-ed. (I can't imagine what the point of ancestral simulations would be, if not that.)
Once you suppose that the simulations are conscious (perhaps per impossibile), those people are not simulations. They might be clones (even if they are not clones in the classical sense). But they would be actual people, perfectly capable of behaving differently from their "originals".

The history being simulated is quite different than the one that actually happened way in the past history of the GS world, although the initial state of the simulation presumably had similarities to some actual past state of the GS history. — noAxioms

The point of the simulations would be lost if real people capable in their own right of acting and reacting in their world. It wouldn't even be a way of running an alternative history. Or is there some other point at stake here, that I've failed to grasp?

I can't respond to all of this. I'll just pick out some remarks for comment. I'll try to respect their context.

Phenomenology asks the right questions. — Astrophel

How do you know they are the right questions?

Also, he never read phenomenology beyond Kierkegaard. — Astrophel

I expect that's true. On another thread recently, someone remarked that he never read Aristotle; from the context, it seemed natural to infer that this was a deficiency. I thought it remarkable that someone would think that any philosopher who had not read Aristotle was deficient in some way.

Wittgenstein was not aligned with the positivism that so emphatically rejected metaphysics. He was different. A great admirer of Kierkegaard, he insisted that meaningful talk had no place in metaphysics because it would offend the most important part of our existence. He writes in Value and Culture: Divinity is what I call the Good. And would go no further — Astrophel

Yes, his position was much more nuanced than many of his contemporaries. But he had very little, if anything, to say about it. We are left with the business about speech and silence, which is a blank sheet of paper on which we can write more or less what we wish to - and people do.

Heidegger, the greatest philosopher of the 20th century, perhaps ever. — Astrophel

He's certainly an impressive figure. But those accolades come and go. They said that about Russell at one time, and Wittgenstein. I'm not good at hero-worship.

Yes, as I said. One cannot doubt the apodicticity, but one can doubt the way language takes up the world. — Astrophel

I'm not sure about apodicticity, so if you don't mind, I'll just talk about certainty.
That doubt is unresolvable, because it frames the issue in the wrong way. In the first place, as Wittgenstein argues (mostly in the early period) just as one cannot draw a picture of a picture, one cannot expect to explain in language what the relationship is between language and the world. As he would say, it "shows itself", just as a picture (once we have learned to interpret it) shows what it is a picture of.
But the big mistake is to think that the problem is about the relationship between language (as given, and our starting-point) and the world. Language arose in the world, from the world, to be of use in living in the world. Hence the only question is about the relationship between the world (as given, and our starting-point) and language, just as we assess a picture by comparing it to the world and not the world by comparing it to a picture.

Mostly, as I pointed out, it is framed in language and analyticity itself is a language construction, and so one would have first to establish that language itself is apodictically certain. — Astrophel

Language is a construction, in a sense, yes - in the sense that a game is a construction. Actually, it is a set of rules (or several sets of rules). There was not law-giver who laid them down - they evolved in the interchange of our social lives in the world - the useful rules stayed, the useless ones disappeared without trace. What makes those rules certain is that we keep them - nothing else. (Actually, we don't keep them - we mess with them all the time, as Derrida realized, but set that aside for the moment) In itself, however, language is neither true not false. It is the means by which we assert and ascertain what it true and what is false. The certainty that Descartes was after was to be found or lost in the use of language, not in language.

Thus should not the true object of an inaugural inquiry be the Being of the ego rather than the ego itself, or more precisely, the Being in and by which the ego can rise to existence and acquire its own Being? — Astrophel

I'm not not particular about where I find good philosophical ideas and I'm quite pragmatic about which school or tradition the ideas originate from. Heidegger and the others have some good ideas from time to time. But I think I can detect eyewash as well. Unless I think of it as a sort of (not very good) poetry.

In any case, it is far too late for an inaugural enquiry. The horse has left the stable and is busy ploughing the fields etc. We arrive or are thrown into a world that includes language and we gradually learn to participate. There are no beginnings or foundations to be found apart from that.

What I've explained though, is that infinite divisibility is really incoherent due to self-contradiction. So the supertask is not even logically possible. It just appears to be, when not subjected to critical analysis. — Metaphysician Undercover

.... and when one analyses it, it is a confused mixture of physical possibility and logical possibility, each of which are coherent on their own.

It's only the contradictory notion, that a finite thing can be divided an infinite number of times, which produces the paradox. — Metaphysician Undercover

A finite thing certainly cannot be divided an infinite number of times, if by "divided" you mean "physically divided", subject to clarification of what you mean by a finite thing.
At the same time, it is possible to divide it into halves, quarters, etc. (how many fractions are there?) and into feet, inches, etc. and into metres, etc, and according to an indefinite number of other units of measurement. To physically divide in one of those ways excludes dividing it in any other way, so you can't divide it by all those things at the same time. But those possibilities do all exist, all at the same time.
On the other hand, the number 2 is finite, in one sense. Yet it cannot be physically divided at all (because it is an abstract thing), yet it can be divided by a familiar mathematical operation, and that operation can be applied to it an infinite number of times. (No, I'm not talking about space or time.)

From past experience I understand that fishfry is very slow to accept the reality that some principles employed by mathematicians are incoherent. — Metaphysician Undercover

I wonder if that's because the principles that you are applying to mathematics do not apply to mathematics? For example, numbers are abstract objects; they do not exist in space and time. Geometry is not about physical objects, but about ideal objects, which do not exist in space and time. Abstract entities that do not exist in space or time are not subject to the restrictions you wish to impose on space and time - obviously. You may or may not regard such entities as not true (or not real) objects, but that's neither here nor there.

I agree. Michael keeps saying supertasks are metaphysically impossible, and I think they're metaphysically possible. — fishfry

Now I'm confused. I thought you didn't know what "metaphysics" means - or what metaphysics is.

No. I'm saying that there's no natural way to define the terminal state. There are lots of ways to defined it. I define it as a plate of spaghetti. — fishfry

I'm puzzled now about "natural". If the terminal state of the lamp is not defined, there is no way to define it - natural or otherwise. Or, possibly better, any arbitrary state will do. Hence the plate of spaghetti.

the lamp problem, which only defines the state of the lamp at the points of the sequence, and not at the limit; — fishfry

Yes, of course - and since it is not defined, Michael can derive a contradiction - two equally possible or impossible states.

"Complete" is not an applicable mathematical term. Unless you want to say that sqrt(2) completes the sequence 1, 1.4, 1.41, 1.414, ... That's an acceptable usage. But it doesn't mean there is any kind of magic jump at the end. It just means the terms of the sequence are arbitrarily close to the limit. — fishfry

H'm. I would be quite happy with that acceptable usage. But it suggests that 1,1.4,1.41, 1.414... is incomplete, and we are back with the temptation to think that series can somehow be completed. It's probably better to stick with "not applicable".

Under the thought process experiment of "adding the next term" at successively halved time intervals, I'd say it completes in finite time. But that confuses people because we're conflating math and physics. — fishfry

I think that's the heart of the problem. My only hesitation is that the lamp is imaginary, so it sits on an ill-defined boundary between the two. I'm very suspicious of the idea that anything anyone can imagine is (logically) possible. Twin Earth is a good example. But there's a raft of others.

possible worlds exist as concrete entities in logical space, — fishfry

I don't know what to say. Ryle would go on about category mistakes. In poetry (or politics) people sometimes talk of a "tin ear". That's exactly what this is - a rhetorical gesture that confuses "concrete" with "well defined" and with - well - concrete. It's protesting too much. There must be some repressed doubt going on there.

Well it all went over my head when I took a MOOC on the subject. — fishfry

You are lucky. It will spare you a world of grief and confusion. Modal logic can look after itself.

The nested interval construction can be explicitly written down. I perhaps am not sharing your vision here. — fishfry

The system is telling me that you mentioned me in the context of this comment in the thread on the Fall of Man paradox, but I can't find any mention of me. But the system is doing some weird things anyway, so I'm not going to worry about it. I do regret not having been aware of the thread sooner. I thought it had something to do with theology.

I can't contribute to the discussion you are involved in there, but this quotation:

I concur that this narrative couldn't unfold in our physical reality, but your argument doesn’t address the core of the paradox. The inclusion of God and the Garden of Eden in the story was specifically to lift us beyond our finite limitations. — keystone

does make me think that the same problem, of the interface between mathematics and empirical reality, is at the heart of this paradox as well.