Cardinality is the generalization that allows that the concept of "ammount of elements" can be made to include infinite Sets as well.
It basically got established to say f.e. infinity of N is smaller then infinity of R ect.

What do you think "trans"-finite means?

I just don't see how you can equate the process of counting with the claim that there will be an end to the counting or not.
I also don't understand what your answer means

Are you saying the Natural numbers are
A) not countable
B) not infinite

Are you aware that this is your own position that basically no one holds? — CaZaNOx


Yes the countable numbers are countable. — tim wood

It seems that you view the Natural numbers as countable(correct me if I am wrong)
So, are you contesting the notion that the natural Numbers are infinite? If yes are you aware that no one else (I know of) holds this position?

I just don't see how you can equate the process of counting with the claim that there will be an end to the counting or not. — CaZaNOx

Imagine you have beads, a lot of beads. You start counting them. For so long as you are counting them, the number that you have counted is finite. When you finish counting them, the number you have will be finite. Might be a really big number, but finite.

Are you suggesting the beads you have are in principle uncountable? That is not just a lot of beads; rather that is something about the beads themselves that makes them uncountable. Inasmuch as we're referring to the universe, I hold the universe to be a large collection of things - like beads. That is, countable. If countable, finite. The issues on this topic so far are elementary with respect to the topic, which I understand to be about the mathematical concept of infinity. None of this is up for debate or question. It's all just a matter of correct understanding, of information.

Thank you for your thoughtful post. Perhaps, we can incorporate a few of these concepts from physics into understanding mental experience. The putative grasp of mind these days is commonly and sort of unreasonably constrained by classical physics. The nature of consciousness just isn't very clear and to think of it as an epiphenomenon of the brain same as bile secreted by the liver is falling short of explaining its "ethereal" quality. Sensory information is supposed to be transduced in the brain, and what is seen not what's "out there" but re-presented in the brain. This isn't intuitively satisfying...not wrong, but an incomplete grok. In some way, what is seen is really out there where it seems to be and not solely a representation in the brain. Something obvious like this isn't handled very well by classical physics. It's as though our eyes project images as well as receive them, don't ask me how (the information is both out there and in the brain at once, as it were). It's not a one-way conveyance of information, otherwise objects could not be out in the world where they saliently are by sight. Most will say the mind is not something which goes past sensed data...which again, really doesn't satisfy in completing the cryptic information of mind. Something of the mind does extend over the horizon, saying how so, is what I'm wondering here. Proponents of materialist monism, in attempting to shuttle all back to classical physics, tends to not ask questions that are good, honest ones to be asked. There is in all probability, information which includes consciousness and mind, we as yet know little of.

Someone will mention how it takes time for signals to travel from light reflected from an object to the retina, and so on. If the mind and body are out of communication, as the mind-body paradox is extant, we can't say for sure whether or not matter and mind obey the same spacetime. It may take time for signals to travel in a physical environoment, while from the perspective of idealist monism (or that all is mind "stuff"), maybe it doesn't work that way. Spacetime itself, even for a physicalist, is seen as one thing. To the physical monist, then, perhaps spacetime is a little spooky. The mind could be a little closer to mere spacetime, or on a different frequency than matter.

Thank you for this post, it is very lucid and helpful. Your style of writing is better than some popular science books in print! Keep up the good work! :up:

In Einstein's theories, as you approach the speed of light, distance contracts. — petrichor

On Youtube are a number of videos by Fermilab in which are covered a lot of interesting topics including several on relativity. The idea is that (your) distance contracts as measured by someone in motion relative to you. To you, in your system, no contraction. It's all not-so-simple and requires attention to how relativistic ideas are expressed. The casual - intuitive - idea can be suggestive and descriptive, but often is also completely wrong.

The idea is that (your) distance contracts as measured by someone in motion relative to you. To you, in your system, no contraction. — tim wood

I believe you are mistaken.

If Bob in a ship is moving relative to me at close to the speed of light, his ship will be length-contracted. At the speed of light, his length would be zero (I realize he has mass and can't reach that speed). But consider that from Bob's perspective, in his frame, it is as if the distance being crossed is moving relative to him. It is therefore similarly contracted. In the galaxy's frame, his length is contracted. In his frame, the galaxy is contracted.

video

So, if it makes sense to talk about what is happening from the perspective of a photon, since it is massless and travels at the speed of light, the distance contracts to zero.

Also, a curious thing about photons is that we never observe them in travel. We only register when one is absorbed. We think we see light as it travels, but we don't. When we see a light beam, our retinas are absorbing photons arriving from such things as dust particles on the air from which they were reflected (absorbed and emitted). You can't see light's travel "from the side". A laser beam through a completely empty space, with no dust, gas, or any such thing, would be invisible.

So photons are never observed crossing space from some other frame of reference. What does this mean? I don't know. Combined with the length contraction from the photon's perspective, it suggests to me that photons perhaps don't cross space at all. We don't observe them travelling across space. And from their perspective, the distance is always zero. From a QM perspective, when unobserved, there are also uncertainties.

Maybe they aren't even travelling particles, but rather just packets of energy being transferred directly from one electron to another. This is pure speculation on my part. But it may have something to do with light not needing a medium like aether to travel through.

A laser beam through a completely empty space, with no dust, gas, or any such thing, would be invisible. — petrichor

hmm, but wouldn't that mean that stars are invisible from a spaceship? what dust is there in outer space to de/reflect the sun's or other stars light?

If Bob in a ship is moving relative to me at close to the speed of light, his ship will be length-contracted. — petrichor

As you measure it. But Bob will think he's at rest and that you're length contracted. If, for example, you were correct, the length of Bob's yardstick as measured by Bob (moving East to West) would vary depending on if he were measuring in the E-W direction or in the N-S direction. (And Bob would then be able to measure his velocity simply by twirling a stick.)

In Bob's reference frame, he measures his yardstick at a "true" yard (true for him). Alice measures Bob's yardstick as length contracted in the direction of Bob's motion. Alice measure's her own yardstick as a true yard. They both in their own reference frames measure their own yardsticks at a true yard. But each measures the other's as contracted.

hmm, but wouldn't that mean that stars are invisible from a spaceship? what dust is there in outer space to de/reflect the sun's or other stars light? — TheArchitectOfTheGods

You can see stars because photons are being emitted by them and then absorbed by electrons in your eye. The photon's "path", if such a thing makes sense, is directly between the star and your eye, directly toward you. Nowhere are you watching a photon fly, from the side, as for example you might watch a ball fly from the side. When you watch a ball fly, you can see it from the side as it travels because photons are leaving the ball and being absorbed in your retina. All the photons you have ever detected have come toward you.

As you measure it. — tim wood

Yes. That's in full agreement with what I said. Maybe I could have been more clear. Here is what I said:

If Bob in a ship is moving relative to me at close to the speed of light, his ship will be length-contracted. — petrichor

I should perhaps have been more explicit. In my frame of reference (implied by "relative to me"), Bob and his ship are length-contracted.

But Bob will think he's at rest and that you're length contracted. — tim wood

Yes! I never said otherwise! In fact this is just the point I made to begin with!

From Bob's perspective, in his frame of reference, he is not length-contracted. But to him, I am! That also means that if he is travelling from Alpha Centauri to Earth, in his frame, from his perspective, that distance between Alpha Centauri and Earth is length-contracted, just like my body is. If he were to be able to travel at the speed of light, that distance would contract to zero.

If, for example, you were correct, the length of Bob's yardstick as measured by Bob (moving East to West) would vary depending on if he were measuring in the E-W direction or in the N-S direction. (And Bob would then be able to measure his velocity simply by twirling a stick.) — tim wood

You are apparently reading me saying something that I am not saying. I never said that in Bob's frame, his ruler, his body, or his ship are contracted. They are not. Everything at rest relative to Bob, which would include his ruler, his ship, and his own body, all appear normal. I never said otherwise. What I was pointing out is that the distance between his origin and his destination is contracted in his frame as he moves relative to it. For Bob, Bob is not contracted. For Bob, Bob's journey is shortened.

They both in their own reference frames measure their own yardsticks at a true yard. But each measures the other's as contracted. — tim wood

You think you are disagreeing with me but you aren't. :smile: I am either not expressing myself clearly or you are not reading me carefully. We agree. Yes.

But if you are having trouble with the idea that Bob's journey is shortened (I am not clear on whether you disagree with this or not), consider the following. If Bob is flying from Alpha Centauri toward Alice on Earth in a ship and Alice is holding a ruler such that it is aligned with the direction of Bob's travel, in Bob's frame, from Bob's perspective, the ruler will be shortened, yes? But what about the remaining distance between Bob and that same ruler? That too is contracted just like the ruler. There is no difference. The length of the ruler is just atoms arranged in space. The distance between Alpha Centauri and Earth is just like the distance between an atom on one end of that ruler and an atom on the other end.

For the moving object, in its own frame, from its own perspective, all distances traversed (moving relative to it) parallel to its direction of travel are shortened.

So, to return to the point I was making initially, from a photon's perspective, in the photon's frame of reference, since it is "traveling" at the very speed of light, the distance between its source and its destination is contracted to zero.

The nature of consciousness just isn't very clear and to think of it as an epiphenomenon of the brain same as bile secreted by the liver is falling short... — Anthony

The nature of consciousness certainly isn't clear. And epiphenomenalism is a position with fatal defects.

I feel confident in saying that nobody understands consciousness. That includes scientists, materialist philosophers, idealist philosophers, dualists, spiritualists, Buddhists, Hindus, Protestants, New Agers, neuroscientists, psychologists, cognitive scientists, AI researchers, Daniel Dennett, Deepak Chopra, and all the rest! Nobody has a friggin clue. Consciousness as such hasn't even begun to be understood. And the fact that it isn't understood by materialists doesn't make spiritualists correct. The converse is also true. The truth is, we just don't know. Some people have a pretty good grasp on why consciousness is a problem. Those who don't take the "hard problem" seriously, I think, are experiencing a failure of insight. But those who think the hard problem is solved by spiritual stuff are also experiencing a similar failure. The existence of the hard problem doesn't clearly favor any of the usual available positions. It is often presented as a threat to materialism and presumably then a weapon that can be used by spiritualists, but it isn't. An immortal soul made of pure light or some such doesn't help us understand it either. It is just as hard to see why that would involve subjective experience as it is to see why a special arrangement of atoms would (not much different in fundamental substance than light anyway).

It's as though our eyes project images as well as receive them, don't ask me how (the information is both out there and in the brain at once, as it were). — Anthony

I don't agree.

In some way, what is seen is really out there where it seems to be and not solely a representation in the brain. — Anthony

When you see a distant star, the very star itself is in your mind? Or what? Your mind goes out and wraps around the star? If you are imagining something like that, I don't quite agree.

But consider what I said about photons. Perhaps, when you see light from a distant star, an electron in that star is maybe making a transaction with an electron in your retina. Maybe, to get what you seem to want here, you don't have to imagine that your mind somehow leaps out of your eyes to go touch a star. Maybe, instead, the star is just touching your eye and you haven't gone anywhere.

Disclaimer: I understand QM poorly and am likely to make mistakes. But if I understand correctly, in QM, any two particles that interact become entangled. And entanglement seems to mean that the two particles cannot really be understood properly as distinct things. They need to be treated together. So, in a moment of conscious experience, it might be that it isn't only your brain state that comprises it, as if there is some magical membrane around your brain that designates it as a separate entity, but also all those things influencing the state of the brain. Maybe it is the whole causal complex.

Maybe all of the "external" objects that you see are in some sense part of the "mental state". Let me explain. There are interactions and causal relationships between neurons in your brain, right? Nobody argues with that. And your mental state is often thought to be made up of these interactions somehow, as being in some sense the very complex of interactions itself. But why draw a line at the skull? There are also interactions and causal relationships that are involved in a mental state that are happening between the brain and the world. Somewhere in your brain, a chemical messenger is traveling from one side of a synaptic cleft to another, causing some effect. Elsewhere, something electrical is happening, perhaps mediated by virtual photons. Why is this any different than a photon coming from an electron in a flower, entering your eye, striking your retina, firing a neuron, generating a signal, and so on? That electron in the flower might be as much a part of the overall mental state as any neuron. So one neuron is receiving a signal from an upstream neuron. But that neuron might be connected to a retinal cone cell, which is receiving a signal from an electron in a flower. Is there some magical reason that one signal reception is part of the mental state while the other isn't?

And maybe each different mental state is a different complex of interaction between particles, which might be understood as an entangled system. A mental state could then be thought to span galaxies, since it might include parts of your brain and also parts of stars in distant galaxies.

But that doesn't require that anything exits your eye when you see a flower. For the flower itself to be part of your mental state doesn't require anything in addition to standard physics. And it doesn't require the causal influence to become bidirectional.

I feel confident in saying that nobody understands consciousness. That includes scientists, materialist philosophers, idealist philosophers, dualists, spiritualists, Buddhists, Hindus, Protestants, New Agers, neuroscientists, psychologists, cognitive scientists, AI researchers, Daniel Dennett, Deepak Chopra, and all the rest! Nobody has a friggin clue. — petrichor

I would modify this statement by saying that if nobody understands consciousness then they don't understand materialism, physicalism and empiricism either. Because each is completely dependent and co-implied by the other. And I would assert that philsophers like Heicegger, Derrida and Merleau-Ponty have a better understanding of consciousness that realists, objectivists and physicalists do of empiricism.

As Evan Thompson puts it:

"Many philosophers have argued that there seems to be a gap between the
objective, naturalistic facts of the world and the subjective facts of conscious experience.
The hard problem is the conceptual and metaphysical problem of how to bridge
this apparent gap. There are many critical things that can be said about the hard problem
(see Thompson&Varela, forthcoming), but what I wish to point out here is that it
depends for its very formulation on the premise that the embodied mind as a natural
entity exists ‘out there’ independently of how we configure or constitute it as an
object of knowledge through our reciprocal empathic understanding of one other as
experiencing subjects. One way of formulating the hard problem is to ask: if we had a
complete, canonical, objective, physicalist account of the natural world, including all
the physical facts of the brain and the organism, would it conceptually or logically
entail the subjective facts of consciousness?

If this account would not entail these
facts, then consciousness must be an additional, non-natural property of the world.
One problem with this whole way of setting up the issue, however, is that it presupposes
we can make sense of the very notion of a single, canonical, physicalist description
of the world, which is highly doubtful, and that in arriving (or at any rate
approaching) such a description, we are attaining a viewpoint that does not in any way
presuppose our own cognition and lived experience. In other words, the hard problem
seems to depend for its very formulation on the philosophical position known as
transcendental or metaphysical realism. From the phenomenological perspective
explored here, however — but also from the perspective of pragmatism à la Charles
Saunders Peirce, William James, and John Dewey, as well as its contemporary inheritors
such as Hilary Putnam (1999) — this transcendental or metaphysical realist
position is the paradigm of a nonsensical or incoherent metaphysical viewpoint, for
(among other problems) it fails to acknowledge its own reflexive dependence on the
intersubjectivity and reciprocal empathy of the human life-world.

Another way to make this point, one which is phenomenological, but also resonates
with William James’s thought (see Taylor, 1996), is to assert the primacy of the
personalistic perspective over the naturalistic perspective. By this I mean that our
relating to the world, including when we do science, always takes place within a
matrix whose fundamental structure is I-You-It (this is reflected in linguistic communication:
I am speaking to You about It) (Patocka, 1998, pp. 9–10). The hard problem
gives epistemological and ontological precedence to the impersonal, seeing it as the
foundation, but this puts an excessive emphasis on the third-person in the primordial
structure of I–You–It in human understanding. What this extreme emphasis fails to
take into account is that the mind as a scientific object has to be constituted as such
from the personalistic perspective in the empathic co-determination of self and other.
The upshot of this line of thought with respect to the hard problem is that this problem
should not be made the foundational problem for consciousness studies. The
problem cannot be ‘How do we go from mind-independent nature to subjectivity and
consciousness?’ because, to use the language of yet another philosophical tradition,
that of Madhyamika Buddhism (Wallace, this volume), natural objects and properties
are not intrinsically identifiable (svalaksana); they are identifiable only in relation to
the ‘conceptual imputations’ of intersubjective experience."

That is a thought-provoking post. Yes. I don't fully understand what Evan Thompson is saying as I am not familiar with his work and the context of what you quoted, but I think I get the gist of it.

I would modify this statement by saying that if nobody understands consciousness then they don't understand materialism, physicalism and empiricism either. — Joshs

I agree. I don't think that anyone understands matter, time, or space, or even the deep underpinnings of mathematics any more than they understand consciousness. We don't even understand very well what it means to understand!

I am not sure the world is fully intelligible. I think we can relate some features of the world to others and say that such and such is like such and such, but to really get under it all and understand it deeply, understand it in a way that makes all of its features obvious why they should be there and have the qualities they do, is probably beyond what we are capable of. I think that to some extent, we can work out many of the structural relationships in the world. But I don't think we can go much deeper. In the same way that Chalmers points out that there are easy problems of cognition and whatnot that really deal with structural features of the brain, perceptual processes, and so on, I think there are easy problems of physics and also a hard problem. Maybe the hard problem of consciousness and the hard problem of physics are in fact the same hard problem.

Probably, if we were to understand deeply what matter is, we'd also deeply understand what consciousness is. But at present, we understand neither. And people who think that reducing one to the other and announcing all the problems solved are superficial thinkers.

But people that assume that non-conscious matter comes along first, that there is a third-person world out there with no mind-like qualities, and that only when certain parts of that world come to be arranged in a very, very special manner, POOF!, consciousness arises, and then go on to ask not IF this happens, but only HOW, are already hopelessly lost. It isn't hard to see why there is trouble trying to figure out how the brain produces the mind, as it probably doesn't. And that's where most of our academics are at the moment. We might improve our situation if academia can relax its anti-religion, anti-mystical knee-jerking for a moment and begin to question whether the brain produces the mind in the first place. And no, for you materialists, I am not even remotely suggesting some kind of soul-stuff in relation to the brain or anything that would allow me, as an individual, to survive my death.

But even if we come to a place where we look at the world in a way more along the lines of what Evan Thompson is suggesting, hard problems will remain. It still won't be obvious why there should be experientiality at all. Similarly, it still won't be obvious why there is anything at all rather than nothing. It still won't be obvious why there is time or any of it. These are probably different ways of talking about the same problem.

The problem is, to understand is to stand under. And you can't stand under yourself.

Where there are things standing in clear relation, we can make maps, note differences and similarities, and that's about it.

After all, what do our brains do but make associations? Neurons that fire together wire together. So impressions that activate the brain in ways similar to other impressions get associated, get connected, such that one might trigger the other. Such and such is like such and such. Materialists are just saying that everything is reducible to something like rocks that they've tossed, something familiar that is part of our primitive environment, something we incorrectly think we understand, something that seems obviously comprehensible, part of monkey's world. Spiritualists are saying it is all really like the invisible, ethereal, vaporous air that seems to leave a person when they die. Both views are obviously deeply flawed.

What is matter then? Little rocks. What are the little rocks made of? Little rocks. What is the deep nature of rocks? Rock-likeness. :roll: What is a gas?Little rocks bouncing off one another. What is light? Little massless rocks being thrown. What is space? Little rocks holding hands. (Yes, there are new particle/network theories of spacetime).

You can't understand rocks in terms of rocks. And that's the problem, isn't it? We are always stuck trying to understand one part of our experience in terms of other parts of it. It is like words in the dictionary ultimately being defined in a circular or oppositional or interdependent way.

How do you do this relating of one thing to another with experience itself or with the world itself? What in your experience do you compare experience with? How do you do this with the conditions for the possibility of making comparisons? How do you understand understanding?

Notice that any answer to a "What is X?" question is usually somehow saying that X is like Y and maybe unlike Z. And X, Y, and Z are all things in the world of our experience.

I find it curious that philosophers of mind have decided to talk about subjective experience by saying that it is the "something it is like-ness" of being some conscious being in the world. There is something it is like to be a bat. How does that really clarify anything? What is it like to be conscious?

Maybe some of these things are just what they are and can't be understood in terms of anything. Maybe we reach the end of the line. Maybe, in experiencing the flow of time, in its immediate qualities, we grasp all that there is to grasp, and trying to relate it to a river or something gets us further away from the direct experience of it and further from understanding what it is. Maybe you can't get deeper than that.

After reading your post and responding, I later listened to a talk by Evan Thompson while doing some yard work: link

Very interesting! I was rather impressed. I think I did actually come across him some years ago in my wanderings through podcast and video space.

I felt that he gives quite a good overview of the landscape. And he articulates it all very well. He understands a lot of the problems. I don't feel though, at least in what I heard, that he solves any of the deep problems. When he got around to criticizing panpsychism and talking about the combination problem, I don't feel like what he seems to present as a solution goes any distance toward actually providing any really satisfying answers on the matter. I've never found any argument that really puts my mind at ease with respect to the combination problem. Most people seem to wave their hands here, including me.

He seems to understand all the issues better than most, though.

Thompson makes some use of Merleau-Ponty, but I think relies more on Husserl, who believes that there is such a thing as a pre-reflective consciousness. Meleau-Ponty's view is more novel. He argues that there is no such thing as pre-reflective consciousness. That is, awareness, the self, the 'I' , the ego, in order to be itself, reaches out to the world, and what comes back to the self IS the self. In other words, consciousness is radically inter-subjective, composed within its very core as interaffection between inside and outside. He compares this to one hand touching the other.


"If my left hand is touching my right hand, and if I should suddenly wish to apprehend with my right hand the work of my left hand as it touches, this reflection of the body upon itself always miscarries
at the last moment: the moment I feel my left hand with my right hand, I correspondingly cease touching my right hand with my left hand. But this last-minute failure does not drain all truth
from that presentiment I had of being able to touch myself touching: my body does not perceive, but it is as if it were built around the perception that dawns through it; through its whole internal arrangement, its sensory-motor circuits, the return ways that control and release movements, it is, as it were, prepared for a self-perception, even though it is never itself that is perceived nor itself that perceives."(Merleau-Ponty, the Visible and the Invisible)

"Consciousness is removed from being, and from its own being, and at the same time
united with them, by the thickness of the world. The true cogito is not the intimate communing of thought with the thought of that thought: they meet only on passing through the world. The consciousness of the world is not based on self-consciousness: they are strictly contemporary.
There is a world for me because I am not unaware of myself; and I am not concealed from myself because I have a world. This pre-conscious possession of the world remains to be analysed in the pre-reflective cogito."(Phenomenology of Consciousness)

"..the identity of the thing with itself, that sort of established position of its own, of rest in itself, that plenitude and that positivity that we have recognized in it already exceed the experience, are already a second interpretation of the experience...we arrive at the thing-object, at the In Itself, at the thing identical with itself, only by imposing upon experience an abstract dilemma which experience ignores(p.162)." Merleau-Ponty

Maybe some of these things are just what they are and can't be understood in terms of anything. Maybe we reach the end of the line. Maybe, in experiencing the flow of time, in its immediate qualities, we grasp all that there is to grasp, and trying to relate it to a river or something gets us further away from the direct experience of it and further from understanding what it is. Maybe you can't get deeper than that. — petrichor

I agree, it is immediate existence that is of primary importance. And only the subject relates directly to existence. The direct relation is negated when it is rendered objectively - as a speculative explanation of what it is to exist in subjectivity. The more proof that is collected for determining the objective truth of subjectivity, the further one is led from the truth of subjective existence, which is simply existing as subject.