A human body can be described by the state of all its fundamental particles.
I am not sure the state of a human body is fully defined by the state of its fundamental particles, but I used this to mean all of its physical properties.
The key issue is that continuous variation in underlying physical parameters does not entail continuous variation in the properties that emerge from them.
For my argument to work, it is enough for pain intensity to be quantitatively comparable for infinitesimally different physical parameters. The pain intensity does not have to be a continuous function of the physical parameters. I actually suspect physical parameters can only vary discretely, in agreement with quantum mechanics. So I believe both physical parameters and pain intensity vary in infinitesimally small jumps.
When you heat a ferromagnet continuously, nothing dramatic happens for a while. Then, at a specific critical temperature (the Curie temperature), ferromagnetism doesnāt just decrease, but it vanishes entirely. The property ābeing able to attract ironā is not something that fades smoothly to zero. It disappears at a sharp threshold, even though the underlying control parameter (temperature) was varied continuously.
This is not true. I wonder whether Claude hallucinated it. Spontaneous magnetisation (M) just below the Curie temperature is proportional to (āCurie temperatureāāātemperatureā)^āexponent (0.34 for iron)ā. So spontaneous magnetisation smoothly goes to 0 as the temperature approaches the Curie temperature. In any case, spontaneous magnetisation would be comparable across any 2 temperatures even if it abrupty dropped to 0 near the Curie temperature. The spontaneous magnetisation for a temperature at least as high as the Curie temperature is 0 times that for a temperature below it.
For example, steam can do mechanical work via expansion (it drives turbines); liquid water cannot.
The mechanism via which steam does mechanical work is fundamentally the same as that through which liquid water does mechanical work in hydropower. In both cases, molecules of water collide with turbines, and make them spin. For the case of steam, water vapour molecules are accelerated by temperature. For the case of hydropower, liquid water molecules are accelerate by gravity. In any case, the mechanical work done by steam and liquid water is quantitatively comparable.
The density of water also varies smoothly as it boils. It increases linearly with the vapour quality, which is the mass of water vapour as a fraction of all the mass. For a vapour quality of 0, there is saturated liquid water, and the density matches that of liquid water at the boiling point. For a vapour quality of 1, there is saturated water vapour, and the density matches that of water vapour at the boiling point.
In the example above, an infinitesimal change in a physical property (temperature) leads to an abrupt change in another physical property (density), but the underlying physical state does not change infinitesimally (at the boiling point, an infinitesimal change in vapour quality results in an infinitesimal change in density). In any case, a physical property varying abrupty for an infinitesimal change in the underlying physical state would not undermine my argument. The physical property in one state would have to be quantitatively incomparable with that on another state. The density of water at different states is quantitatively comparable.
Liquid water has surface tension (it forms droplets, menisci, capillary action); steam doesnāt.
Surface tension is technically not a property of liquid water or water vapour. It is a property of liquidāair interfaces, and it varies smoothly with temperature. The surface tension for the interface between liquid water and water vapour is different than that between liquid water and other gases.
Topological transformations
Are you practically arguing that some pain intensities are not quantitatively comparable, even if their underlying physical states only differ infinitesimally, because there are mathematical functions which are not continuous? I do not understand why the space of possible mathematical functions would provide any meaningful empirical evidence about pain intensities.
I think the burden of proof is on showing that pain intensity actually behaves like temperature
My core point is that infinitesimal changes in physical reality do not make pain intensities quantitatively incomrable. Physical reality is infinitesimally changing all the time, and personally experienced pain intensities seem very much quantitatively comparable. So I would say the burden of proof is on showing this is not the case.
I hope this helps clarify where Iām at!
Likewise. Thanks for the opportunity to clarify my position.
Nice response, thanks a lot! :) I might share some more thoughts soon (e.g., maybe the assumption that pain is a one-dimensional quantity could be doing some additional heavy lifting here; and I guess others have discussed problems with aggregationism, which may still apply even if all pains are comparable in the sense that you mean).
Hi Alfredo. Thanks for sharing your thoughts.
I am not sure the state of a human body is fully defined by the state of its fundamental particles, but I used this to mean all of its physical properties.
For my argument to work, it is enough for pain intensity to be quantitatively comparable for infinitesimally different physical parameters. The pain intensity does not have to be a continuous function of the physical parameters. I actually suspect physical parameters can only vary discretely, in agreement with quantum mechanics. So I believe both physical parameters and pain intensity vary in infinitesimally small jumps.
This is not true. I wonder whether Claude hallucinated it. Spontaneous magnetisation (M) just below the Curie temperature is proportional to (āCurie temperatureāāātemperatureā)^āexponent (0.34 for iron)ā. So spontaneous magnetisation smoothly goes to 0 as the temperature approaches the Curie temperature. In any case, spontaneous magnetisation would be comparable across any 2 temperatures even if it abrupty dropped to 0 near the Curie temperature. The spontaneous magnetisation for a temperature at least as high as the Curie temperature is 0 times that for a temperature below it.
The mechanism via which steam does mechanical work is fundamentally the same as that through which liquid water does mechanical work in hydropower. In both cases, molecules of water collide with turbines, and make them spin. For the case of steam, water vapour molecules are accelerated by temperature. For the case of hydropower, liquid water molecules are accelerate by gravity. In any case, the mechanical work done by steam and liquid water is quantitatively comparable.
The density of water also varies smoothly as it boils. It increases linearly with the vapour quality, which is the mass of water vapour as a fraction of all the mass. For a vapour quality of 0, there is saturated liquid water, and the density matches that of liquid water at the boiling point. For a vapour quality of 1, there is saturated water vapour, and the density matches that of water vapour at the boiling point.
In the example above, an infinitesimal change in a physical property (temperature) leads to an abrupt change in another physical property (density), but the underlying physical state does not change infinitesimally (at the boiling point, an infinitesimal change in vapour quality results in an infinitesimal change in density). In any case, a physical property varying abrupty for an infinitesimal change in the underlying physical state would not undermine my argument. The physical property in one state would have to be quantitatively incomparable with that on another state. The density of water at different states is quantitatively comparable.
Surface tension is technically not a property of liquid water or water vapour. It is a property of liquidāair interfaces, and it varies smoothly with temperature. The surface tension for the interface between liquid water and water vapour is different than that between liquid water and other gases.
Are you practically arguing that some pain intensities are not quantitatively comparable, even if their underlying physical states only differ infinitesimally, because there are mathematical functions which are not continuous? I do not understand why the space of possible mathematical functions would provide any meaningful empirical evidence about pain intensities.
My core point is that infinitesimal changes in physical reality do not make pain intensities quantitatively incomrable. Physical reality is infinitesimally changing all the time, and personally experienced pain intensities seem very much quantitatively comparable. So I would say the burden of proof is on showing this is not the case.
Likewise. Thanks for the opportunity to clarify my position.
Nice response, thanks a lot! :) I might share some more thoughts soon (e.g., maybe the assumption that pain is a one-dimensional quantity could be doing some additional heavy lifting here; and I guess others have discussed problems with aggregationism, which may still apply even if all pains are comparable in the sense that you mean).