I'm really glad people are interested, but I will remind you that there is an email address set up for questions and potential solutions because I sent this to a couple of forums and fifty philosophy departments, so trying to keep up with communication in every avenue is going to be difficult — Dan
I think we can make an even stronger statement: the only way that the usual probability rules (normalizability, additivity) can be satisfied on an infinite sample space is if all but a finite number of simple outcomes have probability zero. — SophistiCat
I can try to give you an example of "an algorithm that gives all integers (without limit) SOME probability of happening" if you like. — flannel jesus
This algorithm is theoretically capable of randomly producing ANY of the infinite sequence of integers, but it preferentially chooses lower numbers. — flannel jesus
I just had a train of thought I thought might be vaguely interesting:
1. With an infinite number of options, not all options can have equal probability. — flannel jesus
I have a metaphysical probability question:
Suppose there are an infinite number of parallel Earths. Alice uses a teleporter to teleport to a random Earth. Bob tries to follow Alice, but he has to guess which Earth she teleported to. What are Bob's chances of getting it right? Is there any way for a teleporter machine to randomly select an Earth out of an infinite number of them in a finite amount of time, or is there always going to be, practically speaking, only a finite amount of Earths for Alice to teleport to because of the limitations of the machine? — RogueAI
What if I cheat and say the teleporter pokes a hole into the universe and the universe somehow, through a mysterious process, randomly picks an Earth out of an infinitely large ensemble for Alice to teleport to? Are Bob's chances of teleporting to Alice's world zero? — RogueAI
In fact, this means that is some kind of hidden collusion between these candidates. — Linkey
This is explained by the fact that the 1% of richest people control the mass media and are motivated to keep this situation as long as possible. — Linkey
The middle-class female does not need any resources from a male — Tarskian
There isn't a problem with specialist terms. But "cogent and useful" is both cogent and useful as a definition of "make sense". I would rather not have to try to find another definition. "Cogent and useful" can mean different things in different contexts. — Ludwig V
In the background, I understand, there are people who have doubts about the validity of mathematical induction — Ludwig V
In the supertasks article, they mention a “hotel with a countably infinite number of rooms”. Right there, at the premise, what does “countably infinite” point to? That’s nonsense. That’s a square circle. We don’t get out of the gate. The infinite is by definition uncountable — Fire Ologist
When I first saw the phrase "countably infinite", I thought that was absurd, and I still think it is an unfortunately ambiguous description of what it means. I would put it this way - any (finite) part of the infinite set can be counted, even though the whole of the set cannot be counted in one go. — Ludwig V
This isn't the result of word games. The observations that underlie solipsism are not a matter of semantics. We observe that we do not experience anything that isn't Sensory Data. — Treatid
But if I didn’t think of the sickness of the situation and recognize all of the apparatus and planning that had to be in place to put me here, and I just played along, that doesn’t make me a hero or murderer for pulling the lever. It makes me quick at math under some pressure. It demonstrates the immorality of telling someone to make that choice in that fabricated situation. It doesn’t make me any better or worse if I made a choice that someone else would have made differently. — Fire Ologist
Yes, I hate the trolley problem. It's one of those things that gives philosophy a bad name. It's nothing like any person will ever have to face in the real world. — T Clark
I’m using Thomson’s lamp to show that continuous motion entails contradictions. — Michael
The problem is that if motion is continuous and if the sensors are set up as stated — Michael
Continuous motion suffers from the same problem. We can imagine sensors at each successive half way point that when passed turn a lamp on or off. Is the lamp on or off when we finish our run? — Michael
The simple solution is to say that motion isn’t continuous. Discrete motion at some scale is a metaphysical necessity. — Michael
Swoooooooning. — AmadeusD
Beloved Little Spot
Do you know where I like to linger
In the cool of an evening?
In the quiet valley there spins
A little mill,
And there is a little brook beside it,
With trees standing all around it.
I often sit there for hours on end,
Looking around and daydreaming.
Even the little flowers in the grass
Begin to speak,
And the little blue one says:
Look at how my little head is hanging!
The little rose with a thorny kiss
Has pricked me:
Ah, it has made me so sad
That my heart has broken.
There approaches a small white spider,
saying: Be content;
Some day you will die,
For that is the way it is here on this earth;
Better that your heart breaks
From the kiss of a rose,
Than that you never know love
And die loveless. — Friederike Robert, tr. Emily Ezust
Knowledge, then, is multifaceted. Since to agree, to accept and to devote have different truth conditions - or none at all, like a devotion. One can say one knows in different senses. Knowledge isn't one kind of thing, and an item of knowledge need not be a statement. And knowing as conviction may not be itemizable at all. — fdrake
Yes, there are different kinds of knowing. There is 'knowing how', there is the knowing of familiarity and there is 'knowing that'. I think the salient question in this thread concerns only 'knowing that' or propositional knowing, because the other two categories do not necessarily involve belief. — Janus
Rules are always common to many different cases. To find out, if a singular case applies to a rule, judgement is necessary. There is no way to find this out by exerting another rule, as this results in an infinite regress. So my argument to support the provocative title of this discussion is: AI is indeed intelligent in that it is able to find patterns in huge amounts of data but there is no way AI could reach to judgements like we humans can. — Pez
A physical entity is part of the P-Region if and only if it is essential to M. This facet is what rules out multiple realizability. If a physical entity can be removed from the system and it doesn't affect M then by definition it in not included in the P-Region. We are now in a situation where P cannot vary unless M also varies (P is in fact defined in terms of M so that this is the case). — Count Timothy von Icarus
Ha, not to go back on my OP, but I am now thinking that B-Minimal Properties do not rule out multiple realizability in an important sense. — Count Timothy von Icarus
If you are defining superveniance with B-minimal properties or P Regions this is not the case. Any change in P, the (relevant) brush strokes (or their properties) would, by definition, be a change in the experience/aesthetic qualities of the painting. Multiple realizability is sacrificed by using these methods to define superveniance. — Count Timothy von Icarus
By limited I mean restricted in size. Think of spacetime for example. If spacetime is restricted in size then we can reach its edges by moving in straight lines (of course if spacetime is not a closed manifold). The problem is what is beyond the edges. It cannot be nothing since nothing does not have any geometry and occupies no room. So, whatever is the beyond edges of spacetime is something. Therefore, what I said follows. — MoK
For whatever bounds it, that thing must itself be bounded likewise; and to this bounding thing there must be a bound again, and so on for ever and ever throughout all immensity. Suppose, however, for a moment, all existing space to be bounded, and that a man runs forward to the uttermost borders, and stands upon the last verge of things, and then hurls forward a winged javelin,— suppose you that the dart, when hurled by the vivid force, shall take its way to the point the darter aimed at, or that something will take its stand in the path of its flight, and arrest it? For one or other of these things must happen. There is a dilemma here that you never can escape from.
To show this let's assume that the whole is limited, let's call the whole W1. This means that W1 is bounded by something else, let's call this B1. — MoK
Sorry if you misunderstood my post, but I really meant that my definition has the same meaning as Wikipedia 's definition. — Ypan1944
A property A is called supervenient over a (subvenient) property B if a change in B has direct consequences for A. — Ypan1944
A set of properties A supervenes upon another set B just in case no two things can differ with respect to A-properties without also differing with respect to their B-properties. — SEP
In the case of consciousness: this is certainly emergent and my remark that some parts of the brain are crucial for consciousness indicates that there is at least some form of supervenience. — Ypan1944
To argue that our consciousness is highly emergent you must show that the features of our consciousness are supervenient over the underlying complex structure of neurons. This would mean that any damage to the brain has consequences for consciousness. — Ypan1944
Sorry, but look at Wikipedia for this definition:
"In philosophy, supervenience refers to a relation between sets of properties or sets of facts. X is said to supervene on Y if and only if some difference in Y is necessary for any difference in X to be possible."
This has nothing to do with your "downward causation" conception — Ypan1944
A property A is called supervenient over a (subvenient) property B if a change in B has direct consequences for A. — Ypan1944
To argue that our consciousness is highly emergent you must show that the features of our consciousness are supervenient over the underlying complex structure of neurons. This would mean that any damage to the brain has consequences for consciousness. — Ypan1944
A set of properties A supervenes upon another set B just in case no two things can differ with respect to A-properties without also differing with respect to their B-properties. In slogan form, “there cannot be an A-difference without a B-difference”. — SEP
Yes, but this is the man-made (artificial) case that I excluded. The determinist's claim is not a claim which limits itself to artificial realities. There is no formal model to justify the determinist's claim, which is a claim about all of reality. — Leontiskos
Okay, fair enough. Since our approach to the act of understanding may be different, I may be begging the question here. I would want to say that an intellect which understands something transcends that thing through its act of understanding. So if I understand a Roomba vacuum in its entirety then I have, at least in some way, transcended it. I have contained it in a way that it has not contained me. A concrete example of this would be the case where I am able to predict its movements whereas it is not able to predict my movements.
From there I want to say that 1) to assert that something is deterministic is to imply exhaustive (in-principle) comprehension or standing-over or encompassment; 2) to assert that all existing things are deterministic entails asserting that I myself am deterministic; 3) to assert that I am deterministic involves applying (1) to myself; but 4) I cannot pretend to comprehend or stand over or encompass myself, for it is impossible for something to stand over itself or encompass itself.
The weak premise here is surely (1). Someone will say, "I am not claiming exhaustive comprehension, but only a probabilistic opinion." To be naively concise, my point is not that the act itself is an act of comprehensive understanding, but rather that the supposition or hunch or opinion contains within itself a failure to recognize the boundary of (4). "I have a hunch that I myself am fully explainable in terms of deterministic principles," involves the idea that a theory which came from minds itself fully explains minds. But that can't be. Just as a mind cannot comprehend itself, neither can a theory produced by a mind comprehensively explain minds. Whatever else we want to say determinism is, it is surely also a theory.
So feel free to have a go at (1), but do give me some insight into your own views in the process. — Leontiskos
This is a different argument. I don't want to stretch this post too long, but I want to say something about it. Would you be willing to grant that it appears that the act of understanding is neither necessitated nor inevitable? Or does it simply appear to you that an act which is accepted to be necessitated, like two billiard balls colliding, and an act of understanding, like Pythagoras' act of understanding the Pythagorean theorem, equally possess the quality of "necessitated"? It seems that we usually take necessitation to preclude knowledge, e.g., "He's just parroting the definition of the Pythagorean theorem to pass the quiz. He doesn't really understand it." (Although this example doesn't utilize strict causal necessitation, it does utilize instrumental or consequence necessitation, i.e. <It is necessary to recite this theorem in order to pass the quiz, therefore I will recite the theorem>.) — Leontiskos
A scientist who calls an arbitrary system deterministic—such as a Roomba vacuum—is not thereby a determinist. Determinism is a philosophical theory about the entirety of existence, not some subset of it — Leontiskos
So apparently determinism is an absolute truth about the world and not a limited truth about certain parts of the world. — Leontiskos
Echoing my elaboration post, what justification is required to claim that a system is deterministic? Exhaustive predictability is the strongest form of justification, is it not? At least when it comes to systems which are not man-made (artificial)? And at the very least, everything in the system must at least plausibly be in-principle predictable. It's not at all clear to me that the thesis of determinism can be separated from a claim of in-principle predictability, and if this is correct then where in-principle predictability is incoherent, determinism fails. — Leontiskos
I would want to say that no intellect which understands determinism could be deterministic. If such an intellect claims that it itself is deterministic, then either it does not understand what determinism means (and is therefore equivocating), or else it does understand what determinism means and is drawing a non-sequitur. To understand what determinism means is at the same time to place oneself outside of the deterministic paradigm. As I said in my follow-up, the theorizer can never be accounted for by his theory (at least in the way the determinist supposes he could be). — Leontiskos
My guess is that this rests on my conviction that true knowledge—which is different than Plato's "true opinion"—cannot be necessitated. — Leontiskos
But determinism is a "final and absolute truth about the world," and even the minimal definition, provided in your very first post, is committed to in-principle predictability. — Leontiskos
The distinction does save the logical coherence of determinism in the short term, but at what price? Does it rise above the level of an ad hoc response to the paradox of predictability? Is the determinist doing more than merely defending their theory by saying, "Oh, well in that case we stipulate that our observer is not part of the universe"? — Leontiskos
↪andrewk rightly makes the claim that the demon must be "causally isolated from [our universe]." But is it really coherent to envisage a being who is outside of the causal universe in this manner? — Leontiskos
↪T Clark suggests that determinism without in-principle predictability is a meaningless idea. Whether or not that is right, such a form of determinism is a great deal more meaningless and toothless than the sort of determinism which brings along with it the intuitive consequence of in-principle predictability. — Leontiskos