Hi! Interesting concept. I would like to challenge two of your assumptions.

1. Thought machines reading the state of the relevant physical world. Here, the assumption that a physical world exists is not unassailable.
2. Thought machines would need an infinite number of points to connect to the physical world. Receptors, sensing points.This I challenge as well. There need not to be so many points. A few indicative and strategically connected points are enough, and the thought machines could interpolate for needed reality the "empty space" between the points, if needed. By "empty space" I meant space not sensed, space void of receptor or sensing points. And in fact that is what I think is happening in reality.

I would like to challenge your conclusion as well.

You say that the infinite-point sensing apparatus of thought machines are only possible by the help of supernatural forces. This is not a valid conclusion, as the infinite-number of sensing points between the conscious of the thought-machine and reality is perfectly possible without an intervening supernatural element.

We move in a perceived world of finites, but in fact our world comprises many infinites; and each infinite is capable of sustaining itself without any supernatural element's aid. Therefore I reject your conclusion that a supernatural force must necessarily exist because and only because there is an infinite number of access points between the thought machine and reality.

"For example, we could divide a chess square into ten pieces, a.k.a. ten different sensors, each measuring whether its fraction of the square is completely occupied by a chess piece. The length could be the same as before, but the width is divided by 10 (or vice versa if moving the other way). Then when the first tenth is occupied, one state is triggered, and when the second tenth is occupied, another state is triggered. However, we still run into the problem of what to do about intermediate fractions of the ten subdivisions."

This discrete model you gave describes thought better than the continuous model and shouldn't be dismissed. Let's take vision. The human eye is only capable of perceiving a limited number of frames in a given time. So the information our brain gets is finite. (Even if the world is not)

My other problem with your argument is that you say in order to code an infinite amount of information we need a subspace with infinite volume. This contradicts your assumption that a chessboard has infinite states. Edit: There can be sensors with continuous states that encode every information about the chessboard.

The hard problem of consciousness is the question how physical events can give rise to the phenomenal experience of consciousness. This problem may be akin to wondering which part of a banknote constitutes its monetary value. We investigate every atom of the note and nowhere do we find its value. So we conclude that the value arises not from anything physical about the note, but from something outside. Possibly God? Either Him, or the Bank of England. But then we can go through the same process with the Bank of England and we still won't find the monetary value of our note. Finally it will occur to us that perhaps our search is not entirely coherent.

I'm having a little trouble following, so my apologies if I'm missing your point. The problem is not the number of inputs per se. There could be an few, such as the limited number that the human eye could process, or a reading of everything in the universe. It's how an input could register change. If the input takes up area/volume, how does it handle cases where it is only partially filled? In section VII I argue the sensor must be completely filled to fulfill all we expect of a sensor. If a point/plane/lower dimensional object, how can it have relevance in the space being measured due to it's area/volume of 0?

Hi, thanks for reading! Some replies...

1) Admittedly, the potential paradox is strongest when considering physical cases, and the physical is not a 100% assumption that we can make. However, even if reality is more idealistic, I tend to think that we need both something that measures (our hands/eyes, brain, or whatever represents "us") and something that is measured (the stimuli allowing us to form a thought, whether atom/photons in a physical location or something more mental). I find it hard to escape something resembling a physical "space", where the stimuli can exist independently when we aren't interacting with them, and which we can then measure. Thought needs to change for a reason. Perhaps we jump around between, say, Platonic forms, but I'm trying to stay away from solipsism, and a physical background allows for other minds to exist in the same sphere of reality I might be in.

2) The problem is not so much having an infinity of points or space to overcome, à la Zeno, but what is a point doing affecting our reality? Whether it is an infinity or just one or two points, if we abscribe properties to these points, but they have a volume of 0, can they really be said to affect 3D objects? Going back to the light switch example from the paper, how could we tell if the point had properties in reality or not? If it is really the adjacent areas that have the properties, then let's not abscribe them to the points, but to the area/volume in the dimension we are measuring.

I don't want to leave an impression of just finding a potential problem and getting out through deus ex machina. I just think there are issues reconciling our experience in a system without some higher thought at the most fundamental metaphysical level. The properties of the one underlying this thought are another question.

Without delving too deeply into what qualia are, if we accept that we had "thoughts", or whatever we call the phenomenal properties, in the past, and have different "thoughts" now, how could such a situation come about? What is constant that represents a human whose "thoughts" are different, and what changes and is being measured to allow for different "thoughts"? I would think the paradox still applies.

I don't have access to the paper, but from the abstract, the conclusion seems to establish not merely God's existence but a rather strong version of divine illuminationism. What do you mean by suggesting that God is the explanation for thought? Is he responsible for the thoughts I'm having right now? Is he implanting the thoughts that I think? That doesn't sound like God but something else, perhaps something more sinister, owing to the damage such an idea does to man's freedom. On the other hand, maybe you mean that God is the ground of there being thought at all, not that he creates the individual thoughts we think. If so, then I think the abstract's wording is a bit misleading.

Hi ,

You should be able to just click on the "Download from archive" button on the PhilPapers page. If that doesn't work I can post another link.

Regarding your concerns, it's too late to change the abstract, but I think the abstract shows we need something like God in our conception of reality, and we can't escape it by just assuming, say, a physicalist ontology. I want though to leave open the question of how thought emanates from my proposed base level. I think it depends on potential theories about free will, divine causation and omniscience, the problem of other minds, etc. I do believe my paper works well if we assume there is no free will, but that doesn't stop us from throwing other elements into the mix to get to our preferred outcomes. A theologian or philosopher will need to do this anyway to demarcate God's powers, how he might "know" what we are thinking or doing, and how we as individual units come into this world and experience the arrow of time. My theory is just one potential puzzle piece.

My struggling with English makes it harder to express my thoughts. So again. My problems with your claim are that
1) Senses don't perceive every bit of information about the world. It is possible that our perception is finite.
2) Even if our perception is infinite that doesn't mean the sensors must have infinite volume (as your model shows: what if we have a sensor totally similar to the chess board).

No worries. Let's see if I can address your concerns. The paper addresses it in more depth, but here goes...

Say a sensor covers a chessboard square. In one sense we don't need all the information the square could convey. We could just need, say, whether a chess piece is present on the square in our thought mapping, but not need how much the piece weighs, or its color. We would take this limited information and map it to all possible thoughts. If there are 2^64 permutations of a 8x8 chessboard having filled or not filled squares, there are 2^64 possible thoughts. In this sense our perception is finite, and the outcome is finite. Such a system could work, as long as we can address how the sensors work, but the problem is in the sensors themselves, and how they could register just whether a piece was present. There could even be infinite possible sensors, and infinite combinations, but it is the nature of the sensors that is the problem.

Hopefully we agree that infinite sensors with each having volume is unreasonable (any overlapping sensors should be split into separate sensors). To make the system reasonable, we need to either have a finite number of sensors with volume, or infinite point-sized sensors. I believe each of these two options has problems.

From your objections, you might be thinking that a finite number of sensors with volume is possible. However, I don't think we can just say that the chessboard squares are continuous sensors, so that they could register if they are 80% filled, or 60% filled or 42.3346734591% filled. This is how it looks from the top down as we examine how it might work. But for something fundamental, to avoid the infinite regress, it needs to be built from the bottom up. We must assume that the sensors, at the lowest level, are always on, always giving a state valid throughout and completely encompassing their space, and not relying on subsensors to tell what percentage of its space is actually filled. With continuous sensors, we push the question of what is happening in a given space down another level, to cover the various places on the continuum, but at some point we can't do that anymore.

I don't know if your model is merely mathematical or physical.

If it is mathematical then fractal-like objects like an infinite "regress" of chess boards can exist so I don't see a contradiction.

If it is physical then on a very small scale the universe is nothing like an euclidean space. Particles can act as waves. The world is much more homogeneous than we would think by observing the macro world. Basically everything is a form of energy and I think that your problem can be explained by using wave functions and probability theory.

If it is something inbetween then we need axioms about those sensors. And I am sure that a lot of people will disagree with those axioms.

I think in your classification it's a physical theory. There are always points, fractals, or any other construct we might devise that overlays a space, but we need to build from the bottom up.

The ultimate reality can be anything, whether waves or 3D objects. Sensors can be in any dimension and the thing they measure be in any dimension. The sensors just have to be in the same dimensions as the thing they measure. The thing being measured (let's say the waves) can move about as needed, through pseudorandom, random, or probabilistic methods, through any topology we give the universe. The sensors though are constant with respect to the waves, so that when the waves change, the sensors can register the change.

Let us have an example where a wave moves one way, however we would define movement, that means I think thought X. A wave moves another way, and now I think thought Y. What is constant, so that I can say it is I who thought X and Y, and not me thinking X and you thinking Y? It's not the wave itself, for if that was all that it took, the substance of the wave never changed, so how can it register change? If we care about the position, we need something outside of the wave, and that would be the sensors measuring the wave. Perhaps the sensors somehow move too in a way, as our brain follows our bodies around, but they need to be constant in relation to the wave, and external to the wave.

There are always theories where we can say stuff just happens. For example, it's always possible that the current thought I am thinking right now is the only one that has ever existed, with the past a figment of my imagination. There is no change, and thus no paradox. But that road, by denying our past, leads to the abandonment of the scientific method and any role for a system that makes sense through reason. I'm not saying you mean to go down this path, but let's put it out there to be clear, and not have the waves or any other hypothesized physics performing a role like this.

I don't really understand your arguments and I think this is getting a little messy. My philosophy is that we can only argue within the frames of a formal logical system and I don't really see if you have one behind your arguments.

I would argue that the arguments are there, but it's hard to clarify if you just throw up your hands in exasperation. There is a formal logic behind it, but there are some assumptions to start with, and many of the ways people might get out of the arguments are reducible to the assumptions. I think they are reasonable assumptions, but perhaps you disagree. Is there a point giving the most trouble?

Every bit of information in the universe can be stored in a tiny sphere. So every (continuous) state of the chessboard can theoretically be stored in an object with finite volume. This shows that either
1. You have implicit assumptions about sensors or
2. You dont know what you are talking about.

I dont know what you mean by building from the bottom up either.

There is infinite information in a finite space. There are an infinte number of ways to divide a centimeter, a milimeter, a tiny sphere, a cube, etc. However, let's be clear about your counterexample. What do you mean by stored? What is doing the storing? How is this thing storing staying constant in one sense, so we can say it is an object that is storing, yet measuring change?

By storing information I mean there is a one-to-one correspondence between the states of the chess board and the states of the sensor.

The easiest example for this is when the sensor is another chess board.

Do you envision then that the second chessboard has a third chessboard for one of its sensors, which has a fourth chessboard, then a fifth chessboard, in an infinite regress? Do you disagree that at some point we can't do this anymore and must stop?

No, I dont see why a second chessboard is needed.

Lehet. Lehetseges. Elkepzelheto.

Pontosabban, milyen pontokat lat? Pontosan latja a pontokat, vagy esetleg pontatlanul? Szemuveggel jobban? A pontok mind egyszinuek, es a kozbulso ter szinezett, vagy maguknak a pontoknak van szine?

Pontosan.

You say the easiest example is when the sensor is another chessboard, so that sensor is what I meant by the second chessboard. If the sensor is not a chessboard, how do you envision the sensor working?

I dont envision the sensor working. Im just saying that theoretically it is possible to store all information on the chessboard in a finite body hence your argument that says an infinite volume is needed is wrong. Unless you have other axioms about the sensors.

The only possible explanation is something outside, argued to be God. — ThroughAGlassDarkly

Is it the only explanation because it is your idea, or because you couldn‘t find an other one?

It seems you are taking back your proposal of how storage works, so we are now back to what do you mean by stored, and what is doing the storing?

I don't like the word storing, because I think of it more as reading a physical system state and mapping to a thought. Don't be confused by the infinity of potential physical states in a finite space. Instead, how can these states be interpreted and mapped? Let's take a tiny sphere, square, or some other space and call it a thought machine, with input a physical state and output to a thought. How do we read the physical input?

We need to break the space into smaller units so we can register difference in the space. These are the sensors, which have the properties of measuring physical space, and their sum readings output a thought. Subdivisions of the space, and the subdivisions having properties contributing to the whole, can't be avoided if the object having the thoughts is the same. Why fire a thought at one point, based on one physical state, or why fire another, based on another state?

We need to avoid the infinite regress, so these sensors don't have their own sensors, and are the smallest unit by which the thought machine can interpret space. From these indivisible units of space, however many there are, we can then build our thought machine. This is what I mean when I say from the "bottom up". Start with the sensors and then figure out the machine. Don't take the space the thought machine operates in and keep subdividing (from the "top down") to accommodate any state you wish.

For what I think is frequently missed is that the thought machine has its own properties independent of what is actually in a physical space. First, its sensors don't follow around the objects being measured. We don't redraw the sensors as the chess piece moves, for example. If the chess piece's sensor was in the same place relative to the chess piece, how would it register change?

Also, the machine is always firing and always measuring a state, independent of what is physically there. Take a square in space divided into two equal halves, and that same square also divided into three equal thirds. Let's say enough matter moves into the square so that half is filled. Sensors measuring matter for the halves would work, but the ones for the thirds would not, as we have to account for at least one sensor for one third needing knowledge of smaller intervals. We can't switch the sensors for the third back on if we later have enough matter for a 1/3 or 2/3 of the square, as that means the sensors for the halves would not work. We need to pick one fractional division of the square and stick with it.

Thus, in short, two axioms about sensors are:
1) They are the lowest interval by which a thought machine can measure and interpret distance. They can't process any states that require knowledge of smaller intervals.
2) They always give a reading, and their properties are independent of the item being measured.

It is a logical argument based on certain assumptions and one potential property of God. You are free to disagree. Just make sure your alternative solution makes more sense.

The only possible explanation is something outside, argued to be God. — ThroughAGlassDarkly

I‘m just simply not sure, if that something has to be outside, thats all. : )

Thus, in short, two axioms about sensors are:
1) They are the lowest interval by which a thought machine can measure and interpret distance. They can't process any states that require knowledge of smaller intervals.
2) They always give a reading, and their properties are independent of the item being measured.

I don't understand this but formulating the problem is the first step to understanding. I dont know what these concepts mean (a thought machine is like a Turing machine maybe?) .

I can only repeat my previous thought. Only mathematical or physical theories are worth arguing about. If this is a mathematical model then you must be able to express your argument in terms of sets and the membership relation. If your model is a physical one then it uses the classical model hence it does not describe our observed reality.

Fair enough : ). If there is too much baggage with "outside", we could always define the universe as encompassing everything there is, which can include God. I'm not giving a deus ex machina, but explaining how a potential property of God might help.

It's been awhile since I've done automata / language theory, but I guess it could like a Turing machine in that it takes the "input tape" of physical reality, instaneously performs any calculations needed, and stops at a thought (assuming it always stops). I like to think of it as a movie projector though, taking film as physical input and transforming into an image at a particular instant. Or perhaps a piano, in that whatever keys are pressed, it transforms into one sound, with the sound dependent on the exact keys pressed.

I still think it's a physical theory, and that it's not bound to classical physics, although I do use classical examples because they are easy to understand. Even what we know now might change in the future, if we ever get a unified theory combining our quantum / relativistic / string models. Even then, we may not know everything, and some stimuli from a parallel universe might upend our model yet again. Better to work out through reason what is fundamental.

Without delving into the full literature of the mind/body problem, we have both physical and mental properties, and I think something like a thought machine is a good way to link physical and mental properties, while letting us experience continuity of thoughts. Whatever is physical can be matter, energy, waves, quantum fluctuations, or whatever. The challenge is how to interpret the input.