Thank you, those were thought-provoking questions. They really helped me dive deeper into this topic, as I’ve been wanting to do. Here is my elaboration on this:
Do you think pain A having a higher intensity than B implies that averting an infinitesimal duration of pain A with an infinitesimal probability is better than averting an astronomically long time of pain B with certainty?
I believe this thought experiment fails to test our core question which is “Should moral prioritization be determined by the aggregation of suffering (intensity × duration/number of individuals), or does the intensity of pain possess an inherent lexical priority that outweighs duration or population size regardless of their scale?”.
The reason it fails is its reliance on the false assumption that intensity and duration are independent variables. In biological systems, these two variables are deeply coupled. A stimulus that causes moderate discomfort over 3 seconds can escalate into profound agony if sustained for a minute. Conversely, an ‘extreme’ stimulus experienced for a mere 0.0001 seconds may fail to even trigger a affective state at all.
To truly test the lexical priority of intensity, we must use a thought experiment that isolates the intensity from the ‘compounding effect’ of time. To do this I suggest a reincarnation model: Let’s say you must choose between an infinite number of lifetimes where a speck of dust irritates your eye for 1 minute, versus a single 1 minute lifetime of extreme agony. Which one would you prefer? The mathematical disutility of the former is technically infinite. Yet, I would choose that option without a second thought and the calculation would carry no weight.
The claim that mathematical dominance constitutes an inherent “better” or “worse” is actually an example of begging the question. By assuming that a larger sum of utility automatically translates into a moral obligation, one presupposes the very value judgment they claim to derive. Numerical superiority is the moral victory only within the framework of total utilitarianism and if one operates within a different ethical framework, these mathematical results may carry no moral weight at all. To bridge the gap between the “is” of mathematical aggregation and the “ought” of moral action, a separate, qualitative value judgment is required.
This distinction is clearly illustrated by the analogy of heat capacity versus temperature. A massive iceberg possesses a far greater total heat capacity than a single cup of boiling water due to the sheer volume of its molecules. However, it does not follow that the iceberg is “superior” unless one has already decided that total heat capacity (aggregate sum) is the metric that matters. If your moral compass is calibrated to temperature (intensity), the iceberg’s mass is irrelevant; no amount of ice can ever surpass the boiling water’s temperature.
But how can I justify that”temperature” is what matters rather than “heat capacity”? I believe that to establish a grounded ethical code, we must align our moral framework with the actual preferences of the subjects in whom valence is embodied. I also believe that if we do so, we will find that our moral imperative is not the maximization of a mathematical aggregate, but the maximization of what truly carries weight for the experiencing subjects themselves.
For the subject, while low-level experiences are inherently tradable by their very nature (functioning as manageable costs for a rational agent) high-intensity states aren’t just ‘more’ of the same unit of pain; they represent a different kind of reality that demands absolute priority over any trade. (more on this later) This shift marks a morally significant qualitative change that aggregation inherently ignores.
I always felt that the true strength of utilitarianism lies in its commitment to grounding moral value in the most objective reality of the universe: the experienced valence of sentient beings. However, by prioritizing the “mathematical aggregate” over the nature of the experience, I believe that total utilitarianism drifts into a state of theoretical hallucination, detached from the very subjects it claims to represent.
If the ith pain intensity starts at T_(i − 1), and ends at T_i, what would change so much from temperature T_i_before = T_i − 0.001 ºC to T_i_after = T_i + 0.001 ºC that makes you prioritise averting pain at T_i_after infinitely more than pain at T_i_before?
Consider the engineering analogues: a bridge rated for exactly 10,000 tons does not merely become “slightly more strained” when the 10,001st ton is added; it undergoes a catastrophic structural collapse. Similarly, an electrical circuit rated for 15 amps will heat up intensely at 14.99 amps, but at 15.01 amps, the fuse blows and the circuitry melts.
Biological systems similarly operate through this ‘all-or-nothing’ dynamic. Take protein denaturation as an example: a protein can withstand thermal stress and keep its function until it hits a specific temperature. However, even a tiny increase as little as 0.001 °C past this tipping point causes its internal bonds to snap at the same time. This results in a sudden, irreversible loss of activity, much like an egg white irreversibly turning solid after a certain point. Likewise, in toxicology, a body can manage a certain amount of poison, but once a specific dose is reached, the body’s natural defenses are suddenly defeated. At this stage, the system is no longer just struggling more; it is undergoing a collapse, which is why preventing that final tiny increase is more critical than any increase before it.
Coming back to your question: on a physiological level, we can ground the radical shift between Ti_before and Ti_after at the 44 °C threshold (the scientifically proven point where the activation energy peak for TRPV1 receptors is reached). At Ti_before, the thermal energy is high but remains below the critical barrier; the nociceptors are under severe stress, yet the ion channels stay closed.
At Ti_after, however, the system crosses the precise energetic tipping point where these receptors snap open simultaneously. This causes a sudden, massive influx of ions and the signal sent to the brain changes completely. It stops being a manageable warning that says, ‘It is getting very hot,’ and becomes a definitive alarm screaming, ‘Tissue is being destroyed.’
So, the microscopic gap between these two temperatures represents the exact moment heat alarm receptors are triggered, causing the system to send not just a signal of a small increase in warmth, but an emergency alarm of actual tissue damage.
From an evolutionary perspective, it would be counter-intuitive for the nervous system to function as a linear thermometer. Instead, it is optimized to prioritize a hierarchy of survival-critical thresholds. Consequently, it is much more biologically grounded to suggest that conscious experience operates through discrete qualitative phases, where each phase represents a distinct functional mode with corresponding affective experiences hardwired to trigger specific behavioral responses.
Consider someone holding their hand in hot water for 1 min. If you think there are only 5 pain intensities, what would be the range of temperature for each pain intensity?
By modelling pain as a hierarchical control system designed by evolution to force a specific behavioral response (specifically to signal how much agency, mental energy, and priority the brain must allocate to a threat), I would propose a taxonomy along these lines:
Level 1: Ignorable (40°C – 43°C)
Biological Response: Low-level nociception filtered by the thalamus; does not interrupt primary behavioral goals or internal maintenance.
Affective Experience: The mind acknowledges it but grants no priority; attention might remain elsewhere.
Tradability Status: Easily traded for even the smallest reward (e.g., “I’ll keep my hand here just to see what happens”).
Level 2: Manageable (44°C – 47°C)
Biological Response: The brain uses adrenaline to handle the heat, managing the situation while calculating the cost.
Affective Experience: Annoying and sharp. It takes effort to keep the hand submerged, but it does not hijack your thoughts. The “Self” remains an active agent.
Tradability Status: If you expect a reward you would be okay to endure this.
Level 3: Dominant (47°C – 50°C)
Biological Response: Inflammatory response begins. Forced reprioritization occurs as the organism is signaled to stop to prevent permanent tissue loss.
Affective Experience: Significant distress. You are likely sweating. Your brain is screaming that this is a “crisis” and the world is split between the task and the pain.
Tradability Status: A heavy burden. You would only keep your hand in only if the incentive is exceptionally valuable or the objective is critical for survival.
Level 4: Invasive (50°C – 53°C)
Biological Response: This temperature causes second-degree burns quickly. Total limbic system hijack occurs, and the body will likely trigger an involuntary withdrawal reflex.
Affective Experience: Extreme desperation. Future and past vanish; there is only the agonizing “Now.” The “Self” is a prisoner fighting the pain.
Tradability Status: Agency is barely holding on; rational calculations become nearly impossible due to the systemic emergency.
Level 5: Annihilating (>53°C)
Biological Response: Hardware failure. Cognitive fragmentation occur as biological limits are exceeded (e.g., rapid protein denaturation).
Affective Experience: The subject is erased. No “decision” can be made because the “Self” that makes decisions has been replaced by raw, overwhelming signals.
Tradability Status: As the intensity has achieved absolute priority, any other consideration is impossible.
I believe, the most morally significant element of this taxonomy lies in the ‘Tradability Status’ assigned to each phase as it tracks the gradual dissolution of an agent’s capacity to engage in value exchange. At lower levels, pain is merely a “cost” that a rational subject might willingly pay to secure a greater “utility.” However, as we move through the phases, we witness a profound shift: pain ceases to be a negotiable variable and instead becomes a priority that overrides all other possible values.
Do you believe empirical studies of people’s preferences would find a few temperatures (4 if you believe in 5 pain intensities) with this property, where people would prefer averting any time in pain at temperature T_i_after over an arbitrarily long time in pain at temperature T_i_before?
Like I mentioned, while individuals demonstrate a willingness to trade intensity for duration at lower levels of pain, for instance, accepting 43∘C water for a longer duration over 44∘C for a shorter one, this linear trade-off curve fractures sharply as it approaches the threshold of systemic breakdown. As intensity increases, our willingness to trade it for duration diminishes.
However, I want to take a step further than suggesting a logarithmic preference curve. I contend that if we strip away all confounding factors, intensity possesses a lexical superiority over duration in our preferences. Here’s what I mean:
Let’s analyze why someone might prioritize ending a long-duration mild pain (like mild chronic pain) by undergoing a short-duration intense pain (like a painful invasive surgery). I claim that this choice is not driven by the total number of seconds endured. Instead, the persistent nature of chronic pain degrades the system’s integrity in a way that fundamentally alters the intensity of the total experience.
Consider these factors;
1-) As I stated earlier, duration is not just a multiplier; it is a catalyst for a qualitative shift. ( In the context of my Five-Phase Model, after a certain threshold, a prolonged Level 3 experience does not simply “add up” to a large Level 3 sum, it undergoes a functional priority shift, effectively transforming into a Level 4 state for example.)
2-) There is a profound opportunity cost of utility. Persistence of pain acts as a “utility block,” preventing the subject from accessing or enjoying positive states throughout the entire duration. (Furthermore, the realization that this obstacle is enduring creates a secondary layer of profound psychological disutility, distinct from the sensory pain itself.)
Therefore, I believe that the “value” we assign to duration is actually a value judgment about the quality of the state the subject is forced to inhabit, rather than a preference for a smaller numerical sum.
This perspective suggests that in a perfectly isolated system (where the “self” is reset and no systemic degradation carries over) the accumulation of duration might never alter the preference for intensity. If we strip away the biological “wear and tear” and the psychological erosion that typically accompanies time, we are left with a pure hierarchy of states. To test this claim, consider the reincarnation thought experiment I provided at the beginning of this comment.
I think you meant 44 ºC instead of 43 ºC. Level 2 starts at 44 ºC.
1-) As I stated earlier, duration is not just a multiplier; it is a catalyst for a qualitative shift. ( In the context of my Five-Phase Model, after a certain threshold, a prolonged Level 3 experience does not simply “add up” to a large Level 3 sum, it undergoes a functional priority shift, effectively transforming into a Level 4 state for example.)
It makes sense the maximum level of pain increases with duration, but I do not think this solves the core issue. There will still be very small changes in temperature or duration leading to a change in the level of pain. Consider the function f(T = “temperature of the water”, t = “time with a hand under water”) which outputs the highest level of pain (1 to 5). Below is an illustration from Gemini. It assumes the temperature ranges you provided apply to a duration of 1 min, and the level of pain increases with duration as you mentioned. The specific shape of the boundaries between pain level is not important. What matters is that boundaries exist. Imagine 45 ºC for 3 min separates the levels of pain 2 and 3, as it is roughly the case below. Would you prever averting i) 45 ºC for 3 min 0.1 s (maximum pain level of 3) for 1 person with probability 10^-100 over ii) 45 ºC for 2 min 59.9 s (maximum pain level of 2) for the 8 billion people on Earth with certainty? i) corresponds to 1.80*10^-98 s (= (3*60 + 0.1)*1*10^-100) of level 3 pain in expectation, and ii) to 1.44*10^12 s (= (2*60 + 59.9)*8*10^9*1) of level 2 pain in expectation. I understand you would prefer averting i) because you prioritise averting level 3 pain infinitely (lexically) more than averting level 2 pain. I do not understand this. People would not distinguish between 45 ºC for 3 min 0.1 s (maximum pain level of 3), and 45 ºC for 2 min 59.9 s (maximum pain level of 2).
I think you meant 44 ºC instead of 43 ºC. Level 2 starts at 44 ºC.
Yes, thank you!
People would not distinguish between 45 ºC for 3 min 0.1 s (maximum pain level of 3), and 45 ºC for 2 min 59.9 s (maximum pain level of 2).
Actually, this comes down to how we define the boundaries. If the difference is truly imperceptible, it remains within the same region where numerical comparisons are perfectly valid. However, my claim is based on a discontinuous graph. Just as water undergoes a qualitative jump at 100 °C and turns into steam, I believe consciousness undergoes a phase transition at specific thresholds which creates a qualitative leap in the nature of pain.
I am not entirely certain, but maybe we might also consider the following hypothesis: This qualitative shift in experience morally corresponds to the tradability status of the experience itself. At lower levels of intensity, the exchange value remains high; however, as we ascend the levels, this value drops logarithmically (an approach that would also align closely with my model). This means that averting even a minute amount of a higher-level pain requires sacrificing an exponentially larger quantity of a lower-level one. But at a certain critical threshold (the point of systemic collapse where the subject entirely loses its rationality) this tradability factor effectively hits zero. In such a model, while Level 3 and Level 4 pain might possess vastly different coefficients due to the hidden tradability factor, they remain theoretically comparable. However, once we reach Level 5, we encounter a state of incomparability.
Actually, this comes down to how we define the boundaries. If the difference is truly imperceptible, it remains within the same region where numerical comparisons are perfectly valid.
Do you think there is a temperature T, and duration t for which the pain of T for t + 0.1 s is infinitely (lexically) worse than pain of T for t − 0.1 s?
However, my claim is based on a discontinuous graph. Just as water undergoes a qualitative jump at 100 °C and turns into steam, I believe consciousness undergoes a phase transition at specific thresholds which creates a qualitative leap in the nature of pain.
What do you mean by “qualitative leap”? A large, but finite increase in pain intensity for a small increase in temperature or duration? If so, it would still be the case that a sufficiently long time in pain of level i would be worse than any given time in pain of level i + 1, as argued in Bentham’s Bulldog’s post.
I am not entirely certain, but maybe we might also consider the following hypothesis: This qualitative shift in experience morally corresponds to the tradability status of the experience itself.
This is how I would think about it. I do not know if there are large increases in pain intensity for small increases in temperature or duration. However, I agree pain intensity increases superlinearly with temperature for some ranges of temperature. Note the above goes very much against prioritising higher levels of pain infinitely (lexically) more.
But at a certain critical threshold (the point of systemic collapse where the subject entirely loses its rationality) this tradability factor effectively hits zero. In such a model, while Level 3 and Level 4 pain might possess vastly different coefficients due to the hidden tradability factor, they remain theoretically comparable. However, once we reach Level 5, we encounter a state of incomparability.
Imagine 53 ºC for 1 min separates the levels of pain 4 and 5, as it is roughly the case in the graph above (which assumes the temperature ranges you mentioned apply to a duration of 1 min). Would you prever averting i) 53 ºC for 60.1 s (maximum pain level of 5) for 1 person with probability 10^-100 over ii) 53 ºC for 59.9 s (maximum pain level of 4) for the 8 billion people on Earth with certainty? i) corresponds to 6.01*10^-99 s (= 60.1*1*10^-100) of level 4 pain in expectation, and ii) to 4.79*10^11 s (= 59.9*8*10^9*1) of level 5 pain in expectation. I understand you would prefer averting i) because you prioritise averting level 5 pain infinitely (lexically) more than averting level 4 pain. I do not understand this. People would not distinguish between 53 ºC for 60.1 s (maximum pain level of 5), and 53 ºC for 59.9 s (maximum pain level of 4).
People would not distinguish between 53 ºC for 60.1 s (maximum pain level of 5), and 53 ºC for 59.9 s (maximum pain level of 4).
If the pain is imperceptible, how can we call it ‘MORE’ pain? Pain is a subjective experience; if the subject cannot feel the difference, then in what sense is it more?
What do you mean by “qualitative leap”? A large, but finite increase in pain intensity for a small increase in temperature or duration?
If there is a qualitative leap, it means there is a fundamental difference in the experience. Different brain circuits are fired; the brain classifies the situation with a different prioritization.
With a little annoyance, you might be so tired that you don’t even bother to scratch your nose to get rid of it. With manageable pain, you can still enjoy other things, like enjoying music even with a headache. If the pain is dominant, you are truly occupied by it, but you wouldn’t want to kill yourself. But with invasive pain, you would give everything, even your life, just to make it stop.
This isn’t just a higher magnitude of the ‘I’m too tired to scratch my nose’ response. It is completely something else. In none of these examples is it a case of the same neurons simply firing more; completely different circuits are fired in entirely different ways.
If so, it would still be the case that a sufficiently long time in pain of level i would be worse than any given time in pain of level i + 1, as argued in Bentham’s Bulldog’s post.
In that case, it becomes a qualitatively different experience.
Would you prever averting i) 53 ºC for 60.1 s (maximum pain level of 5) for 1 person with probability 10^-100 over ii) 53 ºC for 59.9 s (maximum pain level of 4) for the 8 billion people on Earth with certainty?
Pain perception doesn’t work like a slider. We are not thermometers :)) Think about your experiences, do you experience pain like, “Yeah it became 2 iotas higher, yeah now it became 6 iotas higher”? No… It is distinct different codes to inform different responses.
You feel it like: “Hmm it’s a bit annoying, but anyway.” “Hmm it’s bad, it would be good to get rid of this.” “Oh it is serious, I REALLY WANT TO stop this.” “Oh it’s absolute hell, I can’t think of anything else than stopping this exactly this moment.”
I would prefer infinite people to experience the “Hmm it’s a bit annoying” response rather than one person to feel “Oh it’s absolute hell.” There are different considerations when making real-world decisions, but in a vacuum, I would even prefer the “Oh it’s serious” response infinite times than the “Oh it’s absolute hell, I can’t think of anything else” response. (As I would choose infinite reincarnations with a broken leg for 3 months rather than one reincarnation of 30 min of being eaten alive).
Between 10x absolute hell and 11x absolute hell, I would choose the second because it’s comparing apples to apples, but otherwise, it’s comparing oranges to apples. If the difference is imperceptible, it is still an apple or an orange. Actually, in my model, level 5 is unnecessary as it is evolutionarily the same response as level 4, so I’ll probably remove it from my updated model.
If reincarnation were real, would you prefer infinite lifetimes with dust specks irritating you for 10 minutes, or just one lifetime of 10 min extreme unbearable hell? The former is infinity times larger than the second.
People would not distinguish between 53 ºC for 60.1 s (maximum pain level of 5), and 53 ºC for 59.9 s (maximum pain level of 4).
I should have been clearer. I meant “people would barely distinguish”. In any case, my point is that you seem to believe pain of level 5 is infinitely worse than pain of level 4 despite people barely or not distinguishing between experiences with pain of level 4 and 5 if they are sufficiently close to the temperature-duration curve separating a highest level of pain of 4 and 5.
Would you prever averting i) 53 ºC for 60.1 s (maximum pain level of 5) for 1 person with probability 10^-100 over ii) 53 ºC for 59.9 s (maximum pain level of 4) for the 8 billion people on Earth with certainty?
You did not answer this? If it helps, you could imagine that it was a real situation, and that by default ii) all people on Earth would have one hand under water at 53 ºC with certainty for 59.9 s, but that you could prevent this, and instead have i) just one person have their hand under water at 53 ºC with probablity 10^-100 for 60.1 s. It seems obvious to me i) is way better. However, if you think level 5 pain is infinitely worse than level 4 pain, you would pick ii).
Actually, in my model, level 5 is unnecessary as it is evolutionarily the same response as level 4, so I’ll probably remove it from my updated model.
The number of levels of pain, and temperture is not important to the situation I described above. As long as you believe some pains are infinitely worse than others, it is possible to come up with a situation like the above where you would pick ii) all people on Earth having one hand under water at temperature T with certainty for 59.9 s (maximum level of pain of k) over i) just one person having their hand under water at temperature T with probablity 10^-100 for 60.1 s (maximum level of pain of k + 1).
I am only discussing temperature and duration, but my argument generalises to any number of dimensions affecting the maximum level of pain. If this depends on N variables, there will be a N-dimensional space with boundaries separating experiences with maximum level of pain k and k + 1. So, for a boundary which contains experiences with duration 60 s, people prioritising pains of level k + 1 infinitely more than pains of level k would pick ii) all people on Earth being subject to a painful stimulus with certainty for 59.9 s (maximum level of pain of k) over i) just one person being subject to the same painful stimulus with probablity 10^-100 for 60.1 s (maximum level of pain of k + 1).
If reincarnation were real, would you prefer infinite lifetimes with dust specks irritating you for 10 minutes, or just one lifetime of 10 min extreme unbearable hell? The former is infinity times larger than the second.
I do not know whether literal dust specks would be sufficiently bad to make my welfare negative. However, I would prefer 10 min of extreme unbearable hell over an infinite time with slighly negative welfare.
You did not answer this? If it helps, you could imagine that it was a real situation, and that by default ii) all people on Earth would have one hand under water at 53 ºC with certainty for 59.9 s, but that you could prevent this, and instead have i) just one person have their hand under water at 53 ºC with probablity 10^-100 for 60.1 s. It seems obvious to me i) is way better. However, if you think level 5 pain is infinitely worse than level 4 pain, you would pick ii).
Still thinking about it.
I do not know whether literal dust specks would be sufficiently bad to make my welfare negative. However, I would prefer 10 min of extreme unbearable hell over an infinite time with slighly negative welfare.
Okay, let’s change it then. What would be bad enough, a mild headache? Let’s go with that. Would you prefer infinite lifetimes with a mild headache for 10 minutes, or just one lifetime of 10 min extreme unbearable hell? The disutility of the former is infinitely greater than that of the latter. Actually, even if you replace those 10 minutes with 10^10000000000 years of uninterrupted extreme torture, the disutility of the former is still infinitely greater. Which one would you choose in that case?
Or lets’say you have to choose between these two worlds:
World A: a Rayo’s number of people experience extreme suffering but also an infinite number of people live barely above neutral (defined as 1/Rayo’s number above neutral) World B: a world where a Rayo’s number of people experience extreme hedonia without any suffering whatsoever.
The utility of the former is infinitely greater than that of the latter. Which one would you go for?
I would go with world A. I think world B is worse than, for example, a world with 1 M times as many people as B, and welfare per person just 0.0001 % lower. Repeating a similar comparison sufficiently many times, I conclude that world B is worse than a world C with way way more people than B, and welfare per person just above 0. I also believe world C is worse than a world D with 10 billion more people than C, all of whom experiencing super high welfare except for 1 person with welfare just below 0 (for example, −10^-100 times the welfare of a random human). So I conclude world B is worse than a world D with lots and lots of people with barely positive lives, 10^10 − 1 people with super high welfare w, and 1 person with welfare just below 0. I think 10^10 − 1 people with welfare w is worse than 10^11 people with welfare 0.0001 % lower than w. Repeating this, I determine that 10^10 − 1 people with welfare w is worse than lots and lots of people with barely positive welfare. So I conclude that world B is worse than a world E with lots and lots of people with barely positive lives, and 1 person with welfare just below 0. Based on a similar reasoning, world B is worse than a world F with lots and lots of people with welfare just above 0, and lots of people with welfare just below 0. For the reasons I have mentioned in the thread, I think sufficiently many people with welfare just below 0 is worse than a given number of people with very negative welfare. So I conclude world B is worse than world A with infinitely many people with welfare just above 0, and a large number of people with very negative welfare.
My conclusion that A is better than B may seem counterintuitive. However, I strongly endorse all the steps that lead me to conclude A is better than B. So I also endorse this conclusion. It is also counterintuitive that the mass of sufficiently many grains of sand could be larger than the mass of a mountain. However, I strongly endorse that grains of sand have mass, and therefore I am forced to endorse the conclusion that sufficiently many grains could have a greater mass than a mountain.
Thank you, those were thought-provoking questions. They really helped me dive deeper into this topic, as I’ve been wanting to do. Here is my elaboration on this:
I believe this thought experiment fails to test our core question which is “Should moral prioritization be determined by the aggregation of suffering (intensity × duration/number of individuals), or does the intensity of pain possess an inherent lexical priority that outweighs duration or population size regardless of their scale?”.
The reason it fails is its reliance on the false assumption that intensity and duration are independent variables. In biological systems, these two variables are deeply coupled. A stimulus that causes moderate discomfort over 3 seconds can escalate into profound agony if sustained for a minute. Conversely, an ‘extreme’ stimulus experienced for a mere 0.0001 seconds may fail to even trigger a affective state at all.
To truly test the lexical priority of intensity, we must use a thought experiment that isolates the intensity from the ‘compounding effect’ of time. To do this I suggest a reincarnation model: Let’s say you must choose between an infinite number of lifetimes where a speck of dust irritates your eye for 1 minute, versus a single 1 minute lifetime of extreme agony. Which one would you prefer? The mathematical disutility of the former is technically infinite. Yet, I would choose that option without a second thought and the calculation would carry no weight.
The claim that mathematical dominance constitutes an inherent “better” or “worse” is actually an example of begging the question. By assuming that a larger sum of utility automatically translates into a moral obligation, one presupposes the very value judgment they claim to derive. Numerical superiority is the moral victory only within the framework of total utilitarianism and if one operates within a different ethical framework, these mathematical results may carry no moral weight at all. To bridge the gap between the “is” of mathematical aggregation and the “ought” of moral action, a separate, qualitative value judgment is required.
This distinction is clearly illustrated by the analogy of heat capacity versus temperature. A massive iceberg possesses a far greater total heat capacity than a single cup of boiling water due to the sheer volume of its molecules. However, it does not follow that the iceberg is “superior” unless one has already decided that total heat capacity (aggregate sum) is the metric that matters. If your moral compass is calibrated to temperature (intensity), the iceberg’s mass is irrelevant; no amount of ice can ever surpass the boiling water’s temperature.
But how can I justify that”temperature” is what matters rather than “heat capacity”? I believe that to establish a grounded ethical code, we must align our moral framework with the actual preferences of the subjects in whom valence is embodied. I also believe that if we do so, we will find that our moral imperative is not the maximization of a mathematical aggregate, but the maximization of what truly carries weight for the experiencing subjects themselves.
For the subject, while low-level experiences are inherently tradable by their very nature (functioning as manageable costs for a rational agent) high-intensity states aren’t just ‘more’ of the same unit of pain; they represent a different kind of reality that demands absolute priority over any trade. (more on this later) This shift marks a morally significant qualitative change that aggregation inherently ignores.
I always felt that the true strength of utilitarianism lies in its commitment to grounding moral value in the most objective reality of the universe: the experienced valence of sentient beings. However, by prioritizing the “mathematical aggregate” over the nature of the experience, I believe that total utilitarianism drifts into a state of theoretical hallucination, detached from the very subjects it claims to represent.
Consider the engineering analogues: a bridge rated for exactly 10,000 tons does not merely become “slightly more strained” when the 10,001st ton is added; it undergoes a catastrophic structural collapse. Similarly, an electrical circuit rated for 15 amps will heat up intensely at 14.99 amps, but at 15.01 amps, the fuse blows and the circuitry melts.
Biological systems similarly operate through this ‘all-or-nothing’ dynamic. Take protein denaturation as an example: a protein can withstand thermal stress and keep its function until it hits a specific temperature. However, even a tiny increase as little as 0.001 °C past this tipping point causes its internal bonds to snap at the same time. This results in a sudden, irreversible loss of activity, much like an egg white irreversibly turning solid after a certain point. Likewise, in toxicology, a body can manage a certain amount of poison, but once a specific dose is reached, the body’s natural defenses are suddenly defeated. At this stage, the system is no longer just struggling more; it is undergoing a collapse, which is why preventing that final tiny increase is more critical than any increase before it.
Coming back to your question: on a physiological level, we can ground the radical shift between Ti_before and Ti_after at the 44 °C threshold (the scientifically proven point where the activation energy peak for TRPV1 receptors is reached). At Ti_before, the thermal energy is high but remains below the critical barrier; the nociceptors are under severe stress, yet the ion channels stay closed.
At Ti_after, however, the system crosses the precise energetic tipping point where these receptors snap open simultaneously. This causes a sudden, massive influx of ions and the signal sent to the brain changes completely. It stops being a manageable warning that says, ‘It is getting very hot,’ and becomes a definitive alarm screaming, ‘Tissue is being destroyed.’
So, the microscopic gap between these two temperatures represents the exact moment heat alarm receptors are triggered, causing the system to send not just a signal of a small increase in warmth, but an emergency alarm of actual tissue damage.
From an evolutionary perspective, it would be counter-intuitive for the nervous system to function as a linear thermometer. Instead, it is optimized to prioritize a hierarchy of survival-critical thresholds. Consequently, it is much more biologically grounded to suggest that conscious experience operates through discrete qualitative phases, where each phase represents a distinct functional mode with corresponding affective experiences hardwired to trigger specific behavioral responses.
By modelling pain as a hierarchical control system designed by evolution to force a specific behavioral response (specifically to signal how much agency, mental energy, and priority the brain must allocate to a threat), I would propose a taxonomy along these lines:
Level 1: Ignorable (40°C – 43°C)
Biological Response: Low-level nociception filtered by the thalamus; does not interrupt primary behavioral goals or internal maintenance.
Affective Experience: The mind acknowledges it but grants no priority; attention might remain elsewhere.
Tradability Status: Easily traded for even the smallest reward (e.g., “I’ll keep my hand here just to see what happens”).
Level 2: Manageable (44°C – 47°C)
Biological Response: The brain uses adrenaline to handle the heat, managing the situation while calculating the cost.
Affective Experience: Annoying and sharp. It takes effort to keep the hand submerged, but it does not hijack your thoughts. The “Self” remains an active agent.
Tradability Status: If you expect a reward you would be okay to endure this.
Level 3: Dominant (47°C – 50°C)
Biological Response: Inflammatory response begins. Forced reprioritization occurs as the organism is signaled to stop to prevent permanent tissue loss.
Affective Experience: Significant distress. You are likely sweating. Your brain is screaming that this is a “crisis” and the world is split between the task and the pain.
Tradability Status: A heavy burden. You would only keep your hand in only if the incentive is exceptionally valuable or the objective is critical for survival.
Level 4: Invasive (50°C – 53°C)
Biological Response: This temperature causes second-degree burns quickly. Total limbic system hijack occurs, and the body will likely trigger an involuntary withdrawal reflex.
Affective Experience: Extreme desperation. Future and past vanish; there is only the agonizing “Now.” The “Self” is a prisoner fighting the pain.
Tradability Status: Agency is barely holding on; rational calculations become nearly impossible due to the systemic emergency.
Level 5: Annihilating (>53°C)
Biological Response: Hardware failure. Cognitive fragmentation occur as biological limits are exceeded (e.g., rapid protein denaturation).
Affective Experience: The subject is erased. No “decision” can be made because the “Self” that makes decisions has been replaced by raw, overwhelming signals.
Tradability Status: As the intensity has achieved absolute priority, any other consideration is impossible.
I believe, the most morally significant element of this taxonomy lies in the ‘Tradability Status’ assigned to each phase as it tracks the gradual dissolution of an agent’s capacity to engage in value exchange. At lower levels, pain is merely a “cost” that a rational subject might willingly pay to secure a greater “utility.” However, as we move through the phases, we witness a profound shift: pain ceases to be a negotiable variable and instead becomes a priority that overrides all other possible values.
Like I mentioned, while individuals demonstrate a willingness to trade intensity for duration at lower levels of pain, for instance, accepting 43∘C water for a longer duration over 44∘C for a shorter one, this linear trade-off curve fractures sharply as it approaches the threshold of systemic breakdown. As intensity increases, our willingness to trade it for duration diminishes.
However, I want to take a step further than suggesting a logarithmic preference curve. I contend that if we strip away all confounding factors, intensity possesses a lexical superiority over duration in our preferences. Here’s what I mean:
Let’s analyze why someone might prioritize ending a long-duration mild pain (like mild chronic pain) by undergoing a short-duration intense pain (like a painful invasive surgery). I claim that this choice is not driven by the total number of seconds endured. Instead, the persistent nature of chronic pain degrades the system’s integrity in a way that fundamentally alters the intensity of the total experience.
Consider these factors;
1-) As I stated earlier, duration is not just a multiplier; it is a catalyst for a qualitative shift. ( In the context of my Five-Phase Model, after a certain threshold, a prolonged Level 3 experience does not simply “add up” to a large Level 3 sum, it undergoes a functional priority shift, effectively transforming into a Level 4 state for example.)
2-) There is a profound opportunity cost of utility. Persistence of pain acts as a “utility block,” preventing the subject from accessing or enjoying positive states throughout the entire duration. (Furthermore, the realization that this obstacle is enduring creates a secondary layer of profound psychological disutility, distinct from the sensory pain itself.)
Therefore, I believe that the “value” we assign to duration is actually a value judgment about the quality of the state the subject is forced to inhabit, rather than a preference for a smaller numerical sum.
This perspective suggests that in a perfectly isolated system (where the “self” is reset and no systemic degradation carries over) the accumulation of duration might never alter the preference for intensity. If we strip away the biological “wear and tear” and the psychological erosion that typically accompanies time, we are left with a pure hierarchy of states. To test this claim, consider the reincarnation thought experiment I provided at the beginning of this comment.
I think you meant 44 ºC instead of 43 ºC. Level 2 starts at 44 ºC.
It makes sense the maximum level of pain increases with duration, but I do not think this solves the core issue. There will still be very small changes in temperature or duration leading to a change in the level of pain. Consider the function f(T = “temperature of the water”, t = “time with a hand under water”) which outputs the highest level of pain (1 to 5). Below is an illustration from Gemini. It assumes the temperature ranges you provided apply to a duration of 1 min, and the level of pain increases with duration as you mentioned. The specific shape of the boundaries between pain level is not important. What matters is that boundaries exist. Imagine 45 ºC for 3 min separates the levels of pain 2 and 3, as it is roughly the case below. Would you prever averting i) 45 ºC for 3 min 0.1 s (maximum pain level of 3) for 1 person with probability 10^-100 over ii) 45 ºC for 2 min 59.9 s (maximum pain level of 2) for the 8 billion people on Earth with certainty? i) corresponds to 1.80*10^-98 s (= (3*60 + 0.1)*1*10^-100) of level 3 pain in expectation, and ii) to 1.44*10^12 s (= (2*60 + 59.9)*8*10^9*1) of level 2 pain in expectation. I understand you would prefer averting i) because you prioritise averting level 3 pain infinitely (lexically) more than averting level 2 pain. I do not understand this. People would not distinguish between 45 ºC for 3 min 0.1 s (maximum pain level of 3), and 45 ºC for 2 min 59.9 s (maximum pain level of 2).
Yes, thank you!
Actually, this comes down to how we define the boundaries. If the difference is truly imperceptible, it remains within the same region where numerical comparisons are perfectly valid. However, my claim is based on a discontinuous graph. Just as water undergoes a qualitative jump at 100 °C and turns into steam, I believe consciousness undergoes a phase transition at specific thresholds which creates a qualitative leap in the nature of pain.
I am not entirely certain, but maybe we might also consider the following hypothesis: This qualitative shift in experience morally corresponds to the tradability status of the experience itself. At lower levels of intensity, the exchange value remains high; however, as we ascend the levels, this value drops logarithmically (an approach that would also align closely with my model). This means that averting even a minute amount of a higher-level pain requires sacrificing an exponentially larger quantity of a lower-level one. But at a certain critical threshold (the point of systemic collapse where the subject entirely loses its rationality) this tradability factor effectively hits zero. In such a model, while Level 3 and Level 4 pain might possess vastly different coefficients due to the hidden tradability factor, they remain theoretically comparable. However, once we reach Level 5, we encounter a state of incomparability.
Do you think there is a temperature T, and duration t for which the pain of T for t + 0.1 s is infinitely (lexically) worse than pain of T for t − 0.1 s?
What do you mean by “qualitative leap”? A large, but finite increase in pain intensity for a small increase in temperature or duration? If so, it would still be the case that a sufficiently long time in pain of level i would be worse than any given time in pain of level i + 1, as argued in Bentham’s Bulldog’s post.
This is how I would think about it. I do not know if there are large increases in pain intensity for small increases in temperature or duration. However, I agree pain intensity increases superlinearly with temperature for some ranges of temperature. Note the above goes very much against prioritising higher levels of pain infinitely (lexically) more.
Imagine 53 ºC for 1 min separates the levels of pain 4 and 5, as it is roughly the case in the graph above (which assumes the temperature ranges you mentioned apply to a duration of 1 min). Would you prever averting i) 53 ºC for 60.1 s (maximum pain level of 5) for 1 person with probability 10^-100 over ii) 53 ºC for 59.9 s (maximum pain level of 4) for the 8 billion people on Earth with certainty? i) corresponds to 6.01*10^-99 s (= 60.1*1*10^-100) of level 4 pain in expectation, and ii) to 4.79*10^11 s (= 59.9*8*10^9*1) of level 5 pain in expectation. I understand you would prefer averting i) because you prioritise averting level 5 pain infinitely (lexically) more than averting level 4 pain. I do not understand this. People would not distinguish between 53 ºC for 60.1 s (maximum pain level of 5), and 53 ºC for 59.9 s (maximum pain level of 4).
If the pain is imperceptible, how can we call it ‘MORE’ pain? Pain is a subjective experience; if the subject cannot feel the difference, then in what sense is it more?
If there is a qualitative leap, it means there is a fundamental difference in the experience. Different brain circuits are fired; the brain classifies the situation with a different prioritization.
With a little annoyance, you might be so tired that you don’t even bother to scratch your nose to get rid of it. With manageable pain, you can still enjoy other things, like enjoying music even with a headache. If the pain is dominant, you are truly occupied by it, but you wouldn’t want to kill yourself. But with invasive pain, you would give everything, even your life, just to make it stop.
This isn’t just a higher magnitude of the ‘I’m too tired to scratch my nose’ response. It is completely something else. In none of these examples is it a case of the same neurons simply firing more; completely different circuits are fired in entirely different ways.
In that case, it becomes a qualitatively different experience.
Pain perception doesn’t work like a slider. We are not thermometers :)) Think about your experiences, do you experience pain like, “Yeah it became 2 iotas higher, yeah now it became 6 iotas higher”? No… It is distinct different codes to inform different responses.
You feel it like: “Hmm it’s a bit annoying, but anyway.” “Hmm it’s bad, it would be good to get rid of this.” “Oh it is serious, I REALLY WANT TO stop this.” “Oh it’s absolute hell, I can’t think of anything else than stopping this exactly this moment.”
I would prefer infinite people to experience the “Hmm it’s a bit annoying” response rather than one person to feel “Oh it’s absolute hell.” There are different considerations when making real-world decisions, but in a vacuum, I would even prefer the “Oh it’s serious” response infinite times than the “Oh it’s absolute hell, I can’t think of anything else” response. (As I would choose infinite reincarnations with a broken leg for 3 months rather than one reincarnation of 30 min of being eaten alive).
Between 10x absolute hell and 11x absolute hell, I would choose the second because it’s comparing apples to apples, but otherwise, it’s comparing oranges to apples. If the difference is imperceptible, it is still an apple or an orange. Actually, in my model, level 5 is unnecessary as it is evolutionarily the same response as level 4, so I’ll probably remove it from my updated model.
If reincarnation were real, would you prefer infinite lifetimes with dust specks irritating you for 10 minutes, or just one lifetime of 10 min extreme unbearable hell? The former is infinity times larger than the second.
I should have been clearer. I meant “people would barely distinguish”. In any case, my point is that you seem to believe pain of level 5 is infinitely worse than pain of level 4 despite people barely or not distinguishing between experiences with pain of level 4 and 5 if they are sufficiently close to the temperature-duration curve separating a highest level of pain of 4 and 5.
You did not answer this? If it helps, you could imagine that it was a real situation, and that by default ii) all people on Earth would have one hand under water at 53 ºC with certainty for 59.9 s, but that you could prevent this, and instead have i) just one person have their hand under water at 53 ºC with probablity 10^-100 for 60.1 s. It seems obvious to me i) is way better. However, if you think level 5 pain is infinitely worse than level 4 pain, you would pick ii).
The number of levels of pain, and temperture is not important to the situation I described above. As long as you believe some pains are infinitely worse than others, it is possible to come up with a situation like the above where you would pick ii) all people on Earth having one hand under water at temperature T with certainty for 59.9 s (maximum level of pain of k) over i) just one person having their hand under water at temperature T with probablity 10^-100 for 60.1 s (maximum level of pain of k + 1).
I am only discussing temperature and duration, but my argument generalises to any number of dimensions affecting the maximum level of pain. If this depends on N variables, there will be a N-dimensional space with boundaries separating experiences with maximum level of pain k and k + 1. So, for a boundary which contains experiences with duration 60 s, people prioritising pains of level k + 1 infinitely more than pains of level k would pick ii) all people on Earth being subject to a painful stimulus with certainty for 59.9 s (maximum level of pain of k) over i) just one person being subject to the same painful stimulus with probablity 10^-100 for 60.1 s (maximum level of pain of k + 1).
I do not know whether literal dust specks would be sufficiently bad to make my welfare negative. However, I would prefer 10 min of extreme unbearable hell over an infinite time with slighly negative welfare.
Still thinking about it.
Okay, let’s change it then. What would be bad enough, a mild headache? Let’s go with that. Would you prefer infinite lifetimes with a mild headache for 10 minutes, or just one lifetime of 10 min extreme unbearable hell? The disutility of the former is infinitely greater than that of the latter. Actually, even if you replace those 10 minutes with 10^10000000000 years of uninterrupted extreme torture, the disutility of the former is still infinitely greater. Which one would you choose in that case?
Or lets’say you have to choose between these two worlds:
World A: a Rayo’s number of people experience extreme suffering but also an infinite number of people live barely above neutral (defined as 1/Rayo’s number above neutral)
World B: a world where a Rayo’s number of people experience extreme hedonia without any suffering whatsoever.
The utility of the former is infinitely greater than that of the latter. Which one would you go for?
I would go with world A. I think world B is worse than, for example, a world with 1 M times as many people as B, and welfare per person just 0.0001 % lower. Repeating a similar comparison sufficiently many times, I conclude that world B is worse than a world C with way way more people than B, and welfare per person just above 0. I also believe world C is worse than a world D with 10 billion more people than C, all of whom experiencing super high welfare except for 1 person with welfare just below 0 (for example, −10^-100 times the welfare of a random human). So I conclude world B is worse than a world D with lots and lots of people with barely positive lives, 10^10 − 1 people with super high welfare w, and 1 person with welfare just below 0. I think 10^10 − 1 people with welfare w is worse than 10^11 people with welfare 0.0001 % lower than w. Repeating this, I determine that 10^10 − 1 people with welfare w is worse than lots and lots of people with barely positive welfare. So I conclude that world B is worse than a world E with lots and lots of people with barely positive lives, and 1 person with welfare just below 0. Based on a similar reasoning, world B is worse than a world F with lots and lots of people with welfare just above 0, and lots of people with welfare just below 0. For the reasons I have mentioned in the thread, I think sufficiently many people with welfare just below 0 is worse than a given number of people with very negative welfare. So I conclude world B is worse than world A with infinitely many people with welfare just above 0, and a large number of people with very negative welfare.
My conclusion that A is better than B may seem counterintuitive. However, I strongly endorse all the steps that lead me to conclude A is better than B. So I also endorse this conclusion. It is also counterintuitive that the mass of sufficiently many grains of sand could be larger than the mass of a mountain. However, I strongly endorse that grains of sand have mass, and therefore I am forced to endorse the conclusion that sufficiently many grains could have a greater mass than a mountain.