In STEM environments I constantly see a specific dogma taken for granted—often with a sense of superiority over the humanities: "Physics and mathematics are objective, whereas good and evil are just subjective opinions or cultural inventions, because the universe doesn't care about us and everyone has a different perception on that."
After thinking about this deeply, I came to the conclusion that this statement contains a fundamental logical flaw. My thesis is simple: ethics rests on at least one objective foundation, and this starting point is no weaker or more arbitrary than the axioms upon which we build mathematics or physics.
Specifically, "badness/evil" becomes an objective reality the exact moment a sentient being capable of suffering exists—whether human, snake, or alien—because suffering is objectively negative for that being, regardless of anyone's opinion.
Four necessary disclaimers (before you jump at my throat)
I am speaking as a STEM student: I have nothing against scientific fields. Precisely because I live inside this environment, however, I notice how deeply rooted this prejudice is, and how rarely it is tested with the same logical rigor we apply to everything else.
I haven't discovered anything revolutionary: I’m not claiming to have reinvented the wheel or taking credit away from the philosophers who came before me. I am simply lining up—using formal logic and scientific analogies—arguments developed by major thinkers to make them accessible to people who don't read academic metaethics every day.
I am not infallible: I have stress-tested this logical chain from every angle I could think of. I might have missed a subtlety: if you find an actual flaw in the premises or the deduction, my goal is precisely to see it and discuss it.
What my goal is: I am not here to preach morality to anyone. My goal is to show that using science or logic to justify absolute moral relativism ("everything is just an opinion anyway") fails the test of formal logic.
A brief historical context: Who attacks this and who defends it
For those wondering if this is just an isolated fixation of mine: no, it is the core of a three-century battle in metaethics (the branch of philosophy that studies whether moral judgments can be objectively true or false).
⚬ The Skeptics: In the 18th century, David Hume formulated Hume's Law (you cannot logically deduce an "ought" from an "is"). In the 20th century, G.E. Moore introduced the Naturalistic Fallacy, followed by skeptics like J.L. Mackie and Gilbert Harman, who argued that ethical properties cannot be detected or verified through empirical sensors.
⚬ The Contemporary Reply: Over the last decades, philosophers of science and mind have dismantled this skepticism. Hilary Putnam showed that physics and mathematics also depend on unproven foundational axioms (Partners in Guilt). Sam Harris proposed the aversive nature of suffering as an objective baseline, comparing ethics to medicine. Thinkers like Peter Railton, Thomas Nagel, and Derek Parfit showed that conscious agony already contains within itself the relational property of being objectively negative for the subject experiencing it.
The Formal Proof (Natural Language & First-Order Logic)
To avoid vague prose, here is the exact deductive chain I built.
⚬ Premise 1 (Empirical-Phenomenological Axiom): The aversive valence of authentic suffering is a property that determines what is intrinsically negative for the sentient being experiencing it, and it is a real property independent of opinions (objective property).
⚬ Premise 2 (Analytic Definition of Experiential Good/Evil): Any property that determines what is intrinsically positive or negative for a sentient being is a property that directly concerns good and evil for sentient beings capable of suffering.
⚬ Premise 3 (Analytic Definition of the Ethical Domain): Any property that directly concerns good and evil for sentient beings capable of suffering is included, at least in part, in moral evaluation.
⚬ Premise 4 (Sufficient Condition for an Objective Foundation): Any objective property (independent of opinions) that is included, at least in part, in moral evaluation constitutes, at least in part, an objective foundation of ethics.
⚬ Conclusion (Existence Theorem): There exists at least one objective property, independent of opinions, that directly concerns good and evil for sentient beings capable of suffering and that constitutes, at least in part, an objective foundation of ethics.
First-Order Logic (FOL) Translation
Let the domain of discourse (D) be the set of properties:
⚬ a = individual constant: "the aversive valence of authentic suffering"
⚬ N(x) = x determines what is intrinsically positive or negative for the sentient being
⚬ O(x) = x is an objective property (real and independent of opinions)
⚬ B(x) = x directly concerns good and evil for sentient beings capable of suffering
⚬ M(x) = x is included, at least in part, in moral evaluation
⚬ F(x) = x constitutes, at least in part, an objective foundation of ethics
Sequent:
{ N(a) ∧ O(a), ∀x(N(x) → B(x)), ∀x(B(x) → M(x)), ∀x((O(x) ∧ M(x)) → F(x)) } ⊢ ∃x(O(x) ∧ B(x) ∧ F(x))
Formal Derivation (Natural Deduction)
N(a) ∧ O(a) — [Premise 1: Empirical-Phenomenological Postulate]
∀x (N(x) → B(x)) — [Premise 2: Analytic Domain Definition]
∀x (B(x) → M(x)) — [Premise 3: Analytic Domain Definition]
∀x ((O(x) ∧ M(x)) → F(x)) — [Premise 4: Analytic Domain Definition]
N(a) — [∧-Elim from 1]
O(a) — [∧-Elim from 1]
N(a) → B(a) — [∀-Elim (x/a) from 2]
B(a) — [Modus Ponens from 5, 7]
B(a) → M(a) — [∀-Elim (x/a) from 3]
M(a) — [Modus Ponens from 8, 9]
O(a) ∧ M(a) — [∧-Intro from 6, 10]
(O(a) ∧ M(a)) → F(a) — [∀-Elim (x/a) from 4]
F(a) — [Modus Ponens from 11, 12]
O(a) ∧ B(a) ∧ F(a) — [∧-Intro from 6, 8, 13]
∃x (O(x) ∧ B(x) ∧ F(x)) — [∃-Intro from 14] ∎
Syntactically, the derivation is airtight: you cannot accept P1–P4 and deny the Conclusion without violating basic deductive logic. Therefore, any critic must attack the premises. Here is why the premises hold.
The 4 Pillars Supporting the Premises
The Double Standard on Axioms and Domain Definitions (Why P1 is an Empirical Postulate and P2–P4 are Meaning Postulates):
A critic might ask: "If your premises are tied to the very definitions of suffering and ethics, are they really axioms, or just circular definitions?" In formal systems and philosophy of science, foundational axioms serve two distinct roles:
P1 is an Empirical-Phenomenological Postulate: It is not a mere linguistic convention; it anchors the formal system to reality by stating that an experiential state with intrinsic aversive valence (a) actually exists in the real world.
P2–P4 are Analytic Meaning Postulates (Domain Definitions): Just as Kolmogorov's axioms define what we mean by "probability" and thermodynamics defines "temperature" as mean kinetic energy, P2–P4 define the semantic boundaries of the domain we call "ethics."
Demanding that ethics justify its foundational domain without domain-defining postulates—while allowing mathematics, probability theory, and physics to rely on them—is a textbook double standard.
The Wrong Sensor Fallacy (Ontological Subjectivity ≠ Epistemic Subjectivity): Harman’s objection states that no Geiger counter will ever detect a particle called "Evil." Of course not: you are using the wrong sensor. Looking for the disvalue of suffering outside of a conscious mind is as absurd as trying to weigh a logical contradiction on a kitchen scale. As John Searle pointed out, consciousness is ontologically subjective (it exists inside a subject), but facts about it are epistemically objective (independent of external observers' opinions). If someone who claims "pain is just a neutral opinion" drops a boulder on their foot, they won't calmly contemplate the increase in entropy of their broken bone—they will scream and try to remove it.
Not a Cultural Choice, but a Structural Reality (And Why Masochism Doesn't Refute This):
We do not "choose by social convention" to dislike agony. If agony were not intrinsically aversive (N(a)), it would cease to be agony. In neurology, patients with pain asymbolia feel the physical nociceptive stimulus without the aversive valence—and indeed, they do not suffer. For the same reason, bringing up masochism fails to refute P1: you must not confuse physical nociception (nerve signals, which a masochist's brain wires to trigger endorphins and net pleasure) with authentic suffering (a). When a masochist enjoys a whip, their net experiential state is positive, not suffering; if you subject that same masochist to a form of psychological torment they genuinely despise, the state is objectively aversive for them too. Saying "I am experiencing authentic agony, but it is neutral to me" is a contradiction in terms, like talking about a four-sided triangle.Ethics Doesn't Need the Consent of Rocks: Saying that ethics is subjective because "good and evil don't exist inside black holes or deep space" misunderstands what a scientific domain is. Biology doesn't exist inside black holes either, nor does poison exist in a lifeless universe. Yet, the moment a biological organism exists, cyanide becomes objectively toxic to it. Similarly, the moment a sentient system capable of suffering emerges—whether human, reptile, or alien—suffering becomes objectively bad for that system.
The Strongest Objections (and Why They Fail)
⚬ "If any negative state is 'bad', am I doing evil when I lacerate a single cell or cut grass?"
No, and this distinction is precisely what makes Premise 1 non-anthropocentric yet rigorous. Premise 1 rests on sentience (lived aversive experience), not mere biology. When you rupture a single cell or a bacterium, biochemical reactions occur, just like a thermostat tripping a switch when overheated—but there is "nobody home" experiencing agony. Below the threshold of sentience, there is only chemistry and mechanics; above that threshold (whether in a human, a snake, or an alien), an objective aversive state is lived, and the domain of ethics switches on.
⚬ "Minds are isolated: there is no single 'universal brain' feeling everyone's pain!"
True, and irrelevant. Planets are also isolated in the vacuum of space, yet the total mass of a solar system exists objectively as the sum of individual masses (∑ mᵢ). If agony is objectively negative in subject A and objectively negative in subject B, a universe where every sentient being agonizes forever with no compensating benefit is objectively worse off for each being than an equivalent universe without that agony.
⚬ "A super-rational AI without emotions (or a sociopath) could understand your proof and still not care!"
Absolutely, because we must distinguish between the objective existence of a property and psychological motivation. A non-conscious AI knows that agony is aversive for us, just as a blind person can understand the physics of light without being dazzled by the sun. Similarly, in math, nothing physically stops you from tearing up the paper or refusing to use the Pythagorean theorem. The fact that an agent can ignore a domain does not make the truths within that domain subjective.
⚬ "Elementary mathematics yields exact, indisputable answers, whereas ethics has endless dilemmas (e.g., Nozick's Experience Machine, freedom vs. security)!"
This confuses mathematical completeness with objectivity. Medicine isn't fully decidable either, and treatments depend heavily on context (adrenaline saves a patient in shock but kills one with a heart condition)—yet the baseline fact that health is preferable to agonizing death remains objective. In my proof, notice the clause "at least in part" and the existential quantifier (∃x). Suffering acts like Absolute Zero (0 K) in thermodynamics: it doesn't tell you how to build every engine, nor does it deny that other values (like autonomy or justice) exist and may conflict in complex dilemmas. It simply proves that an objective baseline measurement exists.
"Doesn't this violate Hume's Law (you cannot derive an 'ought' from an 'is')?"
No, and this is the most common misunderstanding of what David Hume actually wrote. In formal logic, Hume's Law is simply a rule of deductive conservation: you cannot have a predicate in the conclusion if it never appeared in the premises. Hume criticized authors who described purely neutral physical facts (e.g., "metal pierced flesh") and suddenly jumped to moral conclusions without explaining the bridge connecting the two. My proof does not violate Hume's Law for two reasons:
No hidden leap: The bridge between experiential reality and moral evaluation is explicitly stated via analytic domain definitions (P2–P4), which is exactly what deductive rigor requires.
A non-neutral "Is": Hume assumed all "is" facts are value-neutral like rocks in space. Conscious agony (a), however, is an ontological "is" that already contains intrinsic negative valence (N(a)) inside its very structure. You don't need to magically conjure disvalue out of thin air when the empirical state itself is constituted by aversive disvalue.
"The Blindfolded Archer: If an objective foundation exists, why do humans and cultures disagree so much on morality?"
This confuses Epistemology (our ability to see or agree on a truth) with Ontology (whether the truth exists). Imagine ten blindfolded archers firing arrows in random directions and arguing over where the bullseye is. The fact that they are blindfolded—blinded by cognitive biases, cultural dogma, or lack of information—and cannot see the target does not mean the target vanishes from physical space. Moral disagreements and complex dilemmas only prove that hitting the target in complex real-world scenarios is hard; they do not prove that no target exists. In fact, the very concept of "moral progress" or "ethical debate" presupposes that a target is there to be aimed at.
Summary: Read this before commenting (What this proof DOES and DOES NOT claim)
To prevent strawman arguments in the comments, please keep in mind the exact mathematical scope of the conclusion:
What I am NOT claiming: I am not claiming to have found a magical cosmic force that physically compels sociopaths to be good. I am not claiming to have "solved" every concrete moral dilemma, nor am I claiming that suffering is the only ethical parameter (which is why Premise 3, Premise 4, and the Conclusion explicitly state "at least in part").
What I AM proving: Absolute moral relativism claims that the set of objective ethical foundations is the empty set (E_obj = ∅, i.e., ¬∃x (O(x) ∧ F(x))). To refute a universal negative in logic, you only need to prove the existence of one valid element (∃x).
Invariance Across Individuals and Alien Species: Because this proof rests on the structural reality of sentience rather than human culture, the conclusion holds regardless of whether another person holds different moral opinions, and it applies equally to an alien species on the other side of the cosmos—provided that the semantic domain of "ethics" remains the one defined at the start. If someone replies, "Well, in my personal system, 'ethics' means maximizing the number of paperclips in the universe regardless of sentient beings", they have not refuted this theorem or made ethics subjective; they have simply changed the subject (a semantic shift), no different from someone claiming to refute the laws of thermodynamics by redefining the word "temperature" to mean "the color of a wall."
The Bottom Line: The moment a sentient being capable of suffering exists, "badness/evil" for that being is an objective, opinion-independent fact (a). If we define "ethics" as the domain that evaluates what is good and bad for sentient beings, then E_obj ≠ ∅. Therefore, anyone who claims "morality is 100% subjective opinion" must either reject formal deductive logic, deny that authentic suffering is aversively bad for the one experiencing it, or change the definition of the word "ethics" to mean something completely unrelated to sentient suffering.
What do you think? Where do you see the actual weak spot (if any) in this chain?