In the first note I applied set/class distinction and T-schema hierarchies to certain metaphysical issues. In this note I will first quickly summarise how I applied them to some of Kant’s thinking and then will try and show how they help when we consider ethical rather than metaphysical dilemmas. So what follows first is a more detailed breakdown of each of Kant’s four antinomies, showing how each might be clarified (or dissolved) using tools from modern set theory (particularly ZFC’s set/class distinction) and semantic tools like Tarski’s hierarchy and the T-schema. I will also relate this (and this I didn’t do originally) to Cantor’s handling of infinity to show how later developments in mathematics avoid Kant's paradoxes by more carefully distinguishing between levels of reasoning and objects.
Kant’s first antinomy is : the World has a beginning in time / The World has no beginning in time. Kant believes both the thesis and antithesis here can be proven, generating a contradiction. However, from a modern standpoint, we can reinterpret this ‘world’ using formal tools. If one tries to model the ‘world’ as a totality (like a set), then the assumption of a beginning or not refers to properties of that set. But in ZFC (Zermelo-Fraenkel set theory with the Axiom of Choice), there is no such thing as ‘the set of all things’, the cumulative hierarchy of sets is open-ended, forming a proper class. The distinction is crucial: sets can be members of other sets; proper classes cannot. Thus, ‘the world’ as a totality must be modeled not as a set but as a proper class (such as the universe V of all sets). Asking whether V has a beginning in time is ill-posed because it would require us to quantify over all time, all events, and all causality within a framework that is not properly defined at a single level. Kant’s paradox arises because of what Tarski would call a violation of the ‘semantic hierarchy’ whereby you are trying to assert something about the totality from within that totality. When carefully formalised, the contradiction dissolves: one must ask whether particular well-defined models of spacetime have a beginning, and those models do, sometimes. But the totality of all such models cannot be treated as a single object subject to ‘having a beginning.’
Kant’s second antinomy is : Every composite substance is made of simples / No composite substance is made of simples. This turns on the notion of simplicity and composition. Kant presents a contradiction based on the infinite divisibility of matter. But once again, the ambiguity is over the totality of substances and the kind of space they occupy. Cantor's work on the infinite gives a rigorous foundation to ideas of divisibility: the continuum is uncountably infinite, and any interval of it has the same cardinality as the whole. But ZFC ensures that the real numbers are a set, not a proper class, so we don’t get into paradoxes like the set of all points of extension. The idea of a ‘simple’ could be formalised as an indivisible element (like an atom in ancient thought or a urelement[i] in set theory), but ZFC generally avoids urelements and assumes every object is a set. More importantly, the key is that we cannot simultaneously claim the composite (say, matter or space) to be both infinitely divisible and composed of simples without specifying the rules of composition. Kant fails to distinguish the level of language talking about ‘everything in space’ from the formal system defining the space (as a manifold, or set, or measure space). The paradox thus vanishes when you distinguish between the base level of analysis (a model of space) and the meta-level statements about composition. Tarski’s hierarchy keeps these apart and avoids incoherent self-reference.
Kant’s third antinomy is: There is freedom (spontaneity) / There is no freedom, only natural causality. This antinomy centres on causality and agency. Kant sees a contradiction between determinism and the possibility of free action. But again, the problem lies in failing to distinguish between levels: is ‘freedom’ a property of events within the system, or a description from outside it? In Tarskian terms, this is like confusing an object-level truth (this event is caused by X) with a meta-level principle (some events are not caused). ZFC doesn't speak directly to freedom, but semantic hierarchies help here: the tension arises because we demand that causality be complete (a total function from past to future) and yet leave room for a ‘gap’ in this function. In physics, probabilistic systems (like in quantum mechanics) have built-in uncertainty, and they are still causal in a technical sense. The point is that once we define a system with rules, we cannot also smuggle in exceptions without inconsistency, unless we go up a level and say ‘this system was chosen’ or ‘constructed’ with such exceptions. Kant’s mistake is demanding completeness and exceptionality from the same level of analysis.
Kant’s fourth antinomy is: A necessary being (God, world-substance) exists / No necessary being exists. This is perhaps the closest to traditional metaphysical paradoxes. Again, the paradox comes from a confusion of levels. To assert the existence of a ‘necessary being’ is to make a meta-level claim: not just that something exists, but that it cannot not exist. However, in logic (especially modal logic), ‘necessity’ is a modality applied to propositions within a logical system. It’s meaningful only relative to a model. ZFC avoids these issues by not assuming any metaphysical necessity but claiming that existence is always relative to a model. One can define objects that are ‘necessary’ in some sense within a model (e.g., the empty set is necessary because it’s part of the axioms), but one cannot globally quantify over all models without falling into paradox. Once again, Tarski’s hierarchy saves us: ‘X exists necessarily’ must be understood in terms of a truth predicate for a specific model. If we ask whether ‘the necessary being exists’ as a totalising claim, we again try to express something that belongs to a higher level within a lower one, generating contradiction.
Cantor’s revolution in set theory is essential here and again his approach revolves around different levels. He showed that infinite sets can be rigorously handled by distinguishing between levels of infinity (countable, uncountable, inaccessible, etc.). He also faced paradoxes, like the Burali-Forti paradox (the ‘set of all ordinals’ cannot exist as a set), which led to later formalisations distinguishing between sets and proper classes in ZFC. The idea is that we can talk about ever-larger collections, but not all such collections are sets. This reflects a key idea shared with Tarski: you cannot capture ‘everything’ within a single level without contradiction. So when Kant confronts apparent contradictions about the totality of time, space, or freedom, he is, by modern lights, attempting to form sets or apply truth predicates at levels where these concepts are undefined. That is why Hamkins might, following Tarskian and ZFC-style thinking, insist that the problem lies not in the world or the content of these claims, but in the imprecise and self-crossing formulations. Once you use modern formal tools to clean up the language and separate levels appropriately, the contradictions vanish. We don’t end up necessarily agreeing with Kant’s conclusions in the Critique of Pure Reason if we recognise that the antinomies arise not from the nature of reason itself, but from illicit attempts to totalise what can only be modeled at successive levels. The apparent depth of the paradoxes is often just a byproduct of an overly ambitious or collapsed semantic framework.
Ok, so now I want to try and see if this kind of argument is fruitful when applied outside of traditional metaphysical problems. In what follows I try and apply it to ethics and at first to the problems of consequentialist ethics, particularly utilitarian dilemmas. I argue that failures to respect levels of reasoning or domain restrictions can generate apparent paradoxes or morally repugnant decisions that might, like Kant’s antinomies, dissolve under more precise formulation. Consequentialist theories, especially utilitarianism, aim to evaluate the morality of an action by its overall consequences, typically in terms of aggregate welfare or happiness. But notorious problems arise when scenarios are constructed that seem to justify terrible acts (e.g., torturing an innocent person) if they yield a large enough good. Principles are applied universally, without recognising level distinctions (e.g., applying the same calculus to personal decisions and to the design of moral systems). Infinite aggregations or totalities are involved (e.g., maximising utility for all sentient beings across time and space). These can lead to ethical conclusions that feel wrong, or at least extremely counterintuitive, suggesting either a flaw in consequentialism or in how we are modeling the problem.
Let’s analogise ‘sets’ to well-defined domains of moral reasoning like individuals, communities, or bounded scenarios. A ‘class,’ by contrast, might be thought of as the totality of all morally relevant beings or all possible consequences across time. The problem can then be set up like this. Classical utilitarianism often implicitly assumes we can reason about ‘the good of all sentient beings’ as if that were a well-defined, summable set. But this is like trying to form ‘the set of all sets,’ which we know leads to paradoxes in logic (e.g., Russell’s paradox). We then confront an ethical parallel. When you apply utilitarian calculus to ‘all sentient beings ever,’ you're effectively treating a proper class (an open, unbounded, non-membered totality) as if it were a well-structured, totalisable set. This overextension leads to breakdowns like the repugnant conclusion (Parfit), where adding billions of barely happy lives is counted as better than fewer flourishing ones. So, like in set theory, you need to restrict the domain of ethical calculation, define what counts as a morally countable ‘set’ of outcomes, and avoid treating the ‘class’ of all future consequences as a computable object. Tarski distinguished between object-level and meta-level uses of language, especially in the context of truth. Similarly, we can distinguish between action-level and system-level uses of ethical reasoning. Object-level ethics: ‘In this case, should I lie to save a life?’ Meta-level ethics: ‘Should a general policy permit lying to save lives?’ Utilitarian fallacies often arise from collapsing these levels.
For example, we calculate at the object level (‘torture will help’), without realising that doing so subverts the meta-level rules (the system of justice, rights, trust). Alternatively, we apply meta-level abstractions (maximise total utility) to cases where object-level distinctions matter (individual dignity, agency, fairness). This is analogous to the liar paradox: saying ‘this sentence is false’ collapses truth levels and leads to contradiction. In ethics, saying ‘this act is right because it increases good,’ while undermining the very system of moral rules that defines ‘good,’ leads to moral contradictions or breakdowns in intuitions. Take for example the proposal that torturing one innocent person to save many fulfils a consequentialist ethical stance. At the object level, consequentialism may say ‘yes, do it.’ But at the meta-level, allowing such actions undermines the system of rights and protections that creates moral stability. Just as in Tarski's scheme, you can't mix these levels without confusion. So the claim is that consequentialist paradoxes often arise from flattening ethical reasoning across levels, much like liar-type paradoxes in semantics.
Consider the problem of infinite value. Should we sacrifice present happiness for the possibility of trillions of future lives being slightly better off? Or can we construct ‘lexical orderings’ of value to avoid Parfit’s repugnant conclusion? These debates resemble the issues Cantor and ZFC set theory resolved with the hierarchies of infinity and the rejection of a ‘set of all sets.’ The ethical analogue requires that we distinguish between bounded, manageable ethical domains (sets), and idealised moral totalities (classes). We must avoid reasoning that treats the totality of possible futures or agents as a computable whole. Failing to do this leads to ethical versions of Russell’s paradox: if we must maximise good for all possible futures, and if all outcomes are possible, then every choice becomes both justified and unjustifiable.
From this perspective, the failure in consequentialist ethics is not necessarily in the consequentialist framework, but in how it's often formalised and applied. By importing tools from modern logic and semantics, we see how ill-posed ethical dilemmas mirror poorly formulated semantic or set-theoretic sentences. They feel paradoxical but result from improper abstraction. Restricting domains (like distinguishing sets from classes) avoids global paradoxes and forces us to define moral reasoning locally and contextually. Maintaining level distinctions (like object/meta, action/system) helps avoid collapsing rules that should be kept distinct, thus avoiding moral contradictions. In summary: many philosophical puzzles in ethics, especially the disturbing conclusions of consequentialism, may not reflect problems in moral truth but rather in the syntax of ethical reasoning. Just as Tarski taught us to separate levels of truth to dissolve semantic paradoxes, and ZFC taught us to distinguish sets from classes to avoid logical contradiction, we may need a formal ethics that respects hierarchies of reasoning and bounded moral domains, to avoid misleading conclusions that arise from treating ethical concepts as if they were universalisable in a naïve or totalising fashion.
We can extend this formal approach, using set/class distinctions and Tarskian semantic levels, to analise Rawlsian ethics and deontological moral theories, particularly Kantianism. These frameworks, like consequentialism, also risk confusion or paradox when levels of discourse are mixed or universality is improperly formalised. A precise meta-theoretical architecture, mirroring ZFC and Tarski, can help clarify their structure and avoid confusion. Rawls’s A Theory of Justice proposes the original position: a hypothetical, impartial standpoint from which individuals, behind a ‘veil of ignorance,’ choose principles of justice. These principles are to govern the basic structure of society. His theory is not consequentialist; it is contractualist and procedural focused not on outcomes but on fairness of the system that generates them. But Rawls still faces meta-level problems analogous to those in naive consequentialism. For example we can ask whether the original position coherently represent all persons, does it define a set of persons, or a universal class of rational agents and can the principles derived in the original position self-apply to their own justification? These echo issues in set theory. Like Russell’s paradox, if the original position is meant to represent all possible rational choosers, and it chooses the rule by which those choosers judge, we risk circularity. The concept of ‘all rational agents’ might be improperly treated as a set, when it should be modeled as a class, an open-ended, schema-level construct.
To resolve this, we should recognise that Rawls is best read as constructing a meta-theoretical model: the original position does not represent particular people, but a higher-level standpoint outside the structure of the world. It is akin to a meta-language, not an object-level speech act. So we can identify a Tarskian Structure in Rawls whereby we model the original position in analogy with Tarski’s hierarchy. Level 0 (Object level): Actual institutions, laws, policies, distributions of resources. Level 1 (Moral level): Norms used to evaluate those institutions. Level 2 (Meta-moral level): The original position itself, a device to select the correct norms. If we try to collapse these, e.g., claim that the norms generated at Level 1 should justify the process that created them, we commit a category mistake, akin to letting the liar sentence quantify over its own truth predicate. Rawls is largely careful about this, but interpretations of Rawls often err by reifying the original position as a set of agents within society, rather than as a meta-structural stance. This misreading generates pseudo-paradoxes, e.g., ‘Why would anyone in real life agree to these principles?’ which confuse the formal, class-level perspective with empirical, set-level actors.
Now consider Kantian ethics. Kant's Categorical Imperative states: ‘Act only on that maxim whereby thou canst at the same time will that it should become a universal law.’ This imperative is often read as a semantic universalisation whereby each moral judgment must hold at all times for all rational beings. However, naive formulations lead to paradoxical outcomes when applied to morally ambiguous maxims, e.g.: ‘May I lie to save a life?’ ‘May I kill one to save many?’ and so on. Here again, the problem is one of level confusion. The imperative is meta-level: it concerns the logical form of rules that apply across all situations. But the testing of maxims often happens at the object-level, with particular examples. When we try to apply the Categorical Imperative directly to object-level cases without accounting for the higher-level structure of the imperative we get results that seem contradictory or counterintuitive. Worse, some moral formulations seem self-referential, like: ‘The rule that all universalisable rules must be followed’ which are an analog of the liar sentence. In set-theoretic terms, Kant treats ‘the moral law’ as if it could be a universal set of correct actions. But again, such a totality is ill-formed. If we instead treat the moral law as a generating schema, defined at a meta-level like Tarski's truth predicate or ZFC’s comprehension axioms (e.g., ‘for any definable maxim φ, if φ is universalisable, then it is permitted’), then we avoid paradox. Just as ZFC bans sets that are too large or circular, we must ban maxims that attempt to define their own moral legitimacy.
Many moral paradoxes arise not from deep flaws in ethical reasoning, but from logical and semantic confusion, failing to respect the boundaries between levels of language and between sets and classes. By adopting a framework modeled on ZFC and Tarski we prevent self-referential collapse in ethical formulations and we ensure that moral universals are treated as schema-level constraints, not empirical aggregations. We clarify why certain dilemmas, like torture for the greater good, are structurally incoherent, not merely counterintuitive Thus, classical problems in ethics such as consequentialist dilemmas, Rawlsian procedural universality, and Kantian deontology, can all benefit from semantic hygiene informed by formal logic. Just as logic became stable after distinguishing sets from classes and separating truth levels, ethics too can gain clarity by respecting these formal distinctions.
Let’s apply the set/class distinction and Tarskian levels of moral evaluation to a real-world ethical dilemma. Suppose a high school teacher wants to slightly alter a student's grade to help them get into university. The student is bright but disadvantaged, and the teacher feels this act of ‘cheating’ is justified to correct systemic unfairness. From a naive consequentialist view, the teacher weighs outcomes in terms of the utility gain. On the one hand, the student thrives at university and escapes poverty. On the other hand there may be a utility loss as a more ‘deserving’ student might be displaced and institutional integrity is undermined. This seems to support cheating, depending on how outcomes are valued. But it also opens the door to problematic universality: if every teacher cheats, the system collapses. So we seem caught in a paradox between doing good and preserving fairness. But this paradox arises from level confusion.
Let’s analyse it using the formal ethical architecture modeled after ZFC set theory and Tarski's hierarchy. Step 1: Clarify Levels of Moral Language. We must distinguish the different levels. Level 0: Object-level action - the teacher edits a grade. Level 1: Norm-level evaluation - should teachers edit grades to help deserving students? Level 2: Meta-norm level - what rules or procedures should generate permissible norms? Much like how Tarski bans sentences that talk about their own truth within the same system, we must avoid moral reasoning that lets an agent decide whether their own exception is permissible.
Step 2: Set/Class Distinction in Ethics. Treating moral rules as if they apply to all cases uniformly, without recognising when exceptions create new rule-classes, leads to contradiction. The teacher reasons: This act is justified for me in this case. But if we universalise it to all such cases, it collapses system integrity. So we must ask: is the justification a set-level rule (‘edit grades for students in need’) or is it a class-level schema (‘establish general, justifiable procedures for exceptions’)? The teacher, acting alone, is creating a set-level exception without meta-level legitimacy. Just as in ZFC, where a ‘set of all sets’ is disallowed, a ‘rule for all justified exceptions’ can't be built from object-level data, it must be externally generated, through meta-level consensus (e.g., institutional policy).
Step 3: Tarskian Clarity Prevents Illusions. By failing to distinguish levels of moral evaluation, the teacher experiences a false dilemma. This is like the liar paradox: the sentence (‘this act is justified’) creates an illusion of coherence while subverting the rule it appeals to. Using a Tarskian hierarchy, we can say moral evaluation (truth of ‘this act is justified’) cannot happen at the same level as the act. Permissibility must be determined by a procedure defined at a higher level, like institutional rules, peer deliberation, or public norms. Otherwise, each actor becomes their own moral lawgiver, just as each sentence assigning its own truth-value creates paradox.
Step 4: Philosophical Clarity. We avoid the contradiction by recognizing that the rule ‘I may cheat for good ends’ is a pseudo-rule, like an illegal set in ZFC. A real ethical rule must be meta-legitimate: justified via class-level schema that others can access and apply. Institutions create formal structures (like Tarski’s semantic levels) that maintain coherence in judgment. If this is right then this teacher’s dilemma feels morally compelling, but it is structurally flawed. By taking justice into their own hands, the teacher enacts a norm at the wrong level. Like creating the set of all sets or asserting a sentence’s own falsehood, this leads to ethical incoherence masquerading as compassion. Just as ZFC bans pathological sets and Tarski banishes self-applying truth-claims, we must design ethical systems that restrict moral self-exemption. Exceptions must come from higher-level procedures, not from individual actors forming ad hoc rules. So this case, like the liar paradox or Russell’s paradox, teaches us not that ethics is broken but that it needs semantic discipline and formal layers, just like mathematics and logic.
How would the set/class distinction and Tarskian truth hierarchy respond to Sidgwick’s idea of esoteric morality, the claim that some moral truths or practices should not be made public, because their disclosure would undermine the greater good. In The Methods of Ethics, Henry Sidgwick famously claims that utilitarianism may require secrecy: for example, if telling the public that lying is sometimes justified leads to more lying overall and moral decay, then the truth, that lying is sometimes best, should be withheld. This leads to what he calls esoteric morality: a justified moral principle that is not publicly shareable. This presents a paradox. A rule (e.g., ‘Lie when it produces the best consequences’) is true, but making it known would undermine its very utility. The formal challenge this presents is about self-application and level collapse and thus produces a tension structurally similar to the liar paradox.
The rule (‘Sometimes lying is good’) is true in some instances, but when applied universally, it undermines moral trust and thus invalidates itself. This is what Hamkins and Tarski would call a level collapse. In Tarskian terms, we are trying to assert a meta-level truth (about what is really right) within the object-level discourse (everyday moral language). But this generates contradiction. In ZFC set theory, it’s like trying to define the set of all sets that don’t contain themselves, an analogue to Russell’s paradox. Just as such sets are banned, rules that invalidate themselves when made public are not legitimate moral rules unless properly stratified.
To resolve this, we introduce semantic levels of moral discourse. Level 0: Practical moral action (do I lie or tell the truth?) Level 1: Public ethical rules (lying is wrong) Level 2: Meta-ethical principles about exceptions or moral engineering (when should truth-telling norms be relaxed for global utility?) The error in Sidgwick’s framing is that he treats esoteric morality as if it could be a rule at level 1, but it is really a level 2 strategy, a meta-level governance of rules, not a rule itself. Trying to implement level-2 rules at level 1 (e.g., everyone knows the rule is to lie when it helps) leads to paradox, much like asserting ‘this sentence is false’ in the object language. In set theory, we distinguish between sets which are concrete collections we can reason about directly and proper classes that are too big or unruly to be sets, but still real structure, like the class of all sets. In ethics public moral rules are like sets: they are shared, applicable, enumerable. Esoteric strategies are like classes: not implementable at the same level; they must operate at a meta-level to preserve coherence.
So Sidgwick’s esotericism corresponds to a class-level governance of public norms. It is not a contradiction so long as the two levels remain distinct. But when philosophers or policymakers collapse these levels (e.g., ‘Let’s all publicly agree that sometimes we should lie for good’), then contradictions arise. The Tarski/ZFC framework implies that meta-moral procedures can exist (e.g., secret intelligence decisions, moral triage, asymmetric knowledge), but that these must be carefully isolated from public moral schemas. In practical terms a society may designate institutions (like emergency ethics boards, war-time triage protocols) to make non-public decisions, But these must be formally bounded, like proper classes are bounded in ZFC. This avoids paradox while respecting the insight that not all truths are publicly deployable.
Sidgwick's esoteric morality, while emotionally and practically compelling, flirts with paradox because it confuses levels of ethical language, trying to make meta-rules act as public rules. That’s like importing class-level structure into the set-level world of public morality, which creates instability. Using Tarskian truth levels and ZFC distinctions we can formalise the idea that some ethical knowledge belongs at a meta-level, prevent logical collapse by isolating semantic layers, and avoid endorsing what appears to be moral deception by grounding it in higher-order procedural legitimacy, rather than ad hoc discretion. So the solution is not to reject esoteric reasoning but to architect it properly, with clear meta-ethical infrastructure, just like mathematics manages semantic paradox.
So let’s now apply the set/class distinction and Tarskian levels of truth to the real-world ethical case of a teacher secretly lying to benefit a student, for example, falsifying a grade or bending a rule so that a disadvantaged but promising student can access an opportunity (such as a scholarship or elite program). This is the kind of ‘benevolent cheating’ that can feel morally intuitive but institutionally dangerous. This case echoes the Sidgwickian dilemma where the teacher believes the lie produces a better outcome (justice for one overlooked student). But generalising this behavior (if all teachers cheated for their students) would collapse the institution of fair assessment. This is the moral equivalent of a semantic paradox: what looks like a morally true sentence (‘Lying here helps justice’) invalidates the very system that makes it intelligible (‘Academic justice depends on truth and fairness’).
To understand this, apply Tarski’s insight: paradox arises when we let sentences refer to themselves or speak at the wrong semantic level. The object-level of morality (Level 0) is where the teacher acts. The institutional norms (Level 1) are about fair grading, transparency, and equality. The meta-level (Level 2) is where we ask: should institutions sometimes allow exceptions or override rules in edge cases? If the teacher moves a Level 2 rationale (‘sometimes we override justice for a better cause’) down to Level 0 without institutional authorisation, we have a level collapse, akin to a liar sentence (‘this sentence is false’) asserting a truth-value from within itself. In this way, her lie disrupts the formal coherence of the system. It feels justified but acts as a paradox-generator inside an otherwise consistent structure. In ZFC set theory, sets are elements you can manipulate within the system. Proper classes are larger collections (e.g. the class of all sets) that cannot be manipulated as elements without contradiction.
A student’s situation is a set-level ethical object: you can respond to it using known rules (grades, evaluation). But a global justification like ‘I know when exceptions are right’ is a class-level moral claim. It's a stance about how the whole system should be bent or transcended. Trying to smuggle a class-level override into the set-level operations (e.g., falsifying a grade while pretending it fits the rules) causes ethical incoherence, much like trying to define the ‘set of all sets’ in naive set theory results in paradox. From Hamkins’s perspective, the teacher’s moral feeling, that the lie is the right thing to do, may be a structural illusion created by insufficiently precise levels of moral reasoning. It’s not that she’s wrong in a deep way, rather, it’s that the formulation of her ethical reasoning is too naïve, collapsing important distinctions between individual justice and institutional rules, between ethics of care and ethics of fairness, and between meta-level design principles and object-level behaviors. Without separating these layers, she produces ethical contradictions, akin to how the liar paradox arises from mixing semantic levels.
Using this layered model, exceptions must be structured at the meta-level: that is, built into the institutional design (e.g., via special appeals panels, context-sensitive policies), class-level sanctioned, not via ad hoc judgment, but through transparent higher-order procedures and protected from self-reference so that rule-bending doesn’t destroy trust in the rule system itself. For example, if the teacher feels compelled to help the student, she should appeal to or help create a meta-level mechanism (e.g., discretionary committees for disadvantaged students), not override the rules herself. This preserves moral intent while avoiding paradox and systemic harm.
Just as Tarski showed that truth requires stratification into semantic levels, and ZFC shows that collections must respect hierarchical distinctions, ethics too must honor distinctions between individual decisions and system-level governance if the analogy holds. When we fail to respect those boundaries, our best intentions, like the teacher’s act of care, generate ethical contradictions and systemic instability. This doesn’t mean care or exceptions are wrong, it means they need the right level of ethical architecture.
[i] An urelement contains no elements, belongs to some set, and is not identical with the empty set
