Conscious sexual fetish taxonomy

This post is about sexual themes; it quotes someone else’s blog post about oral sex, and briefly comments on the fact that I found that it seemed to provide a division of the possible conscious motivations for eroticizing something.

Three pure worldviews

As I see it, there are three pure worldviews, regarded as fundamental orientations for your philosophical arguments. They are as follows.

1. Current science. The idea is that, no matter how your philosophical arguments turn out, they must support what is held in current science, or the views that seem to motivate the research programs of current scientists even if they are not officially part of scientific theories. This is sometimes defended by an appeal to the “demonstrated success” of science in providing understanding of the world and predictions about it, but as I see it, this is the same worldview that goes back to the Epicurean and Democritean atomists, who had similarly “scientific empiricist” views long before any success of that research program was evident to everyone. These are people who think empirical inquiry into the efficient, spatiotemporal causes of things is the ultimate way to understand them, and whatever our deep philosophical theories say about things, it must support this sort of inquiry and the most intuitive conclusions from it. “We must be able to explain empirical science in light of our theories, with as little revision as possible.”
2. Historical tradition. These are people who see an intellectual tradition spanning all of history, of which they are the heirs—often including the most famous historical thinkers such as Plato and Aristotle, Thomas Aquinas, Leibniz and Kant, etc. They believe philosophy must be, if not a priori, at least mostly not dependent upon the development of scientific instruments and paradigms, so that, if clearly intelligent people in the distant past believed something, there must be some deep truth in their analyses. It is important to them that, however their philosophical arguments turn out, they must be able to understand how Plato’s and Aristotle’s and others’s ideas can be reinterpreted in light of what they are now saying, keeping their essential core of truth. They want their perspective to be in respectful conversation with the great thinkers of all ages, not just recent academics or scientists. “We must be able to explain historical tradition in light of our theories, with as little revision as possible.”
3. Intuition. These are people who view the two above ideas with suspicion, because they seem to subject philosophical inquiry to an external authority, as if you are first looking at science or tradition and then rationalizing a view which is similar to them. They think that, since the argument from authority has no place in philosophy, the philosopher must build his views only from what seems plausible to him, without trying to square it with anything current or previous. This idea of seeking to believe only what seems plausible to oneself, in a rather informal and unspecified sense, is what is now known in academia as intuition. These people, being quite ready to point out mistakes in both current science and the great thinkers of historical tradition, are the most characteristic endorsers of such a view as panpsychism, which is neither favored by scientific materialists nor by traditional religions, but which vindicates both the intuitions about consciousness seeming fundamental and the intuitions about consciousness seeming reducible. “We must be able to explain our intuitions in light of our theories, with as little revision as possible.”

The fact that the above three pure worldviews seemed to roughly correspond (in a vague analogy) to the Aristotelian material cause, efficient cause, and formal cause, respectively, made me think of whether there might not be a worldview corresponding to the final cause. This would be a focus not on vindicating the empirical contents of our thoughts, nor their historical origins, nor their formal constitution, but on their ultimate goal or purpose. It is conceivable to me that you could seek to formulate your philosophy with the goal that it should match what will be thought by people in the future, and this would be a unique worldview which is different from the ones above. The reason why I think this is not a pure worldview is that no one can predict the future without drawing on materials from the present, and those materials will ultimately be from one of the other three. So the hypothetical future-oriented worldview is necessarily composite.

Postulate Sets for Logical Calculi

This blog post is a translation from Polish notation into modern notation of Appendix 1, “Postulate Sets for Logical Calculi”, from Arthur Prior’s Formal Logic. It contains a wealth of axiom systems from different sources, many of which are little known today. Since Prior gave citations of the literature where he found these systems, the post also transcribes Prior’s Appendix 2, “Select Bibliography”, though making it a new numbered section within the text.

To do this, I first transcribed the appendix (see plaintext transcription here) and then translated. Any inaccuracies are my fault.

Although this blog can display LaTeX formulas, I have decided that, since the main use of having this resource is to easily copy and paste the axioms, using Unicode symbols was preferable. However, I have kept Prior’s references between sections, in case something is off with those.

Noteworthy is the inclusion of C.I. Lewis’s modal systems S1 through S8 (apparently S6 is due to Alban and S7–S8 to Halldén, per SEP). Prior’s rendering is different from the one found, as of now, in John D. Cook’s blog and in the SEP article by Roberta Ballarin, and is more accurate. Cook and Ballarin had apparently looked at the appendix 2 to Lewis and Langford’s Symbolic Logic and copied the axioms named there as part of the systems; in addition to this, Cook silently changed the strict implication (⥽) to material implication (→). This method of transcription was faulty, since the axiom list as given by Lewis and Langford’s appendix doesn’t capture how they used the symbols in the actual body text. Their appendix itself says that S1 “contains all the theorems of Sections 1–4 in Chapter VI”, which should have made Cook and Ballarin pause, since theorem 18.4, within section 4 of chapter VI (page 163), is the formula ⌜p ⥽ ◇p⌝, which is given by Prior as the sixth axiom of S1. “Materialized”, this is ⌜p → ◇p⌝, a form of what is now known as the Axiom T of modal logic (sometimes written, equivalently, as ⌜□p → p⌝). The Cook/Ballarin version of S1, especially after Cook’s materialization of the implications, has no modal operators at all, which I did think was strange (isn’t S1 a system of modal logic?), but only thought to question after seeing Prior’s transcription of the Lewis–Langford S-systems. Prior also gives Modus Ponens as an inference rule rather than an axiom (as Lewis and Langford had given it), which is now the custom.

Neither Symbolic Logic nor Prior’s rendering mention axiom K or the rule of Necessitation being added to either S4 or S5, but it is widely held (as in the SEP article) that both had both, so I’m not sure what’s going on with that. Were K and Necessitation even originally part of Lewis’s systems, or were they only added by other authors later?

Goodness by participation

Sometimes, in natural theology, the following strong argument pattern is used (where F is a predicate):

Divine infinity (DI):
It’s purely good to be F
∴ God is infinitely F

Sometimes, this weaker pattern is used instead:

Creator outranking (CO):
It’s purely good to be F
Some creature, C, is F
∴ God is F (God is at least as F as C is F)

In the Discourse on the Method, CO is justified by appeal to these general principles:

D1. More perfect things cannot be caused by less perfect things.
D2. More perfect things cannot depend on less perfect things.

Both D1 and D2 seem to be implausible. D1 seems to have a counterexample in evolution. D2 seems to have a counterexample in various cases of wholes depending on their parts.

But it seems we can support a more localized version of CO with what I’ll call a “giving-perfections account” of creation. This says simply that, if there is a creator of the world, then this creator creates the world by giving creatures a limited version of some of his own perfections. This seems defensible and lets you use CO without having to defend DI.

This may also be called, seemingly equivalently, a “participation account” of creaturely goodness. This is to say that, when a creature has some perfection or goodness, it has this goodness by participation in its creator.

Aside from the Discourse on the Method, here is a different example of implicit application of CO: Paul Weingartner argues in his Omniscience: From a Logical Point of View, p. 6, that if angels are logically and deductively infallible (they cannot commit logical errors) as Thomas Aquinas says that they are (ST I.58.3), then it is also impossible that God, “who has created them”, could commit an error in matters of logic. In the part in quotation marks, CO is implicitly relied upon.

Appendix (2025-10-30)

This appendix is to point out a possible parallel between the giving-perfections account and Plato’s views. The SEP’s article on properties, written by Francesco Orilia, says:

Plato appears to hold that all properties exemplify themselves, when he claims that forms participate in themselves. This claim is crucially involved in his so-called third man argument, which led him to worry that his theory of forms is incoherent (Parmenides, 132 ff.). As we see matters now, it is not clear why we should hold that all properties exemplify themselves (Armstrong 1978a: 71); for instance, people are honest, but honesty itself is not honest (see, however, the entry on Plato’s Parmenides, and Marmodoro forthcoming).

The SEP does not explain why Plato thought this, and maybe Plato’s texts are not clear on the matter. I conjecture, however, that Plato thought this because of a view parallel to the giving-perfections account: the idea is that “you can’t give what you don’t have”, so if the forms are responsible for why particular things instantiate properties, then the forms must themselves instantiate the properties that they impart to things. For instance, if honesty is not itself honest, then it can’t make other things honest.

This idea is exactly parallel to the giving-perfections account if we assume that the Platonic forms are always forms of things that it is purely good to be, e.g., that there is a form of Justice and a form of Courage, but there is no form of Burglary. This is to construe the doctrine of Platonic forms as adhering to the privation theory of evil, so that evil always consists in falling short of a form, not in instantiating an evil form. Certainly many Platonists believed this, although the Platonic texts that support it might not be so clear.

The Platonic linguistic convention about property self-exemplification also falls naturally out of Donald Williams’s trope theory. Williams understands the concept of predication or inherence in terms of trope parthood via the following definition:

a is F ≝ an f-trope is part of a

If we use the classical mereological parthood relation, which is reflexive, then every f-trope is part of itself and, therefore, every f-trope is F. If we think of the property F as the sum of all f-tropes, then similarly F itself instantiates F, and therefore exemplifies itself. Of course, it is possible to define both the property and its predication differently, e.g., someone could use the CEM proper parthood relation instead, which is irreflexive. But the point is that in trope theories like Williams’s, property instantiation by ordinary concrete objects is derivative from primitive abstract objects that themselves instantiate the properties which they impart, just as in the herein conjectured interpretation of Platonism, and just as in the giving-perfections account of creation.

Preference semantics

This is a taxonomy of human preferences, which are human mental features. In theories of such features, it is fundamentally important to distinguish the uncontroversial mentalistic attributions from those attributions that are more contested. For instance, when I was talking about whether an observed action is emotional, I gave the example that in some cases it is uncontroversial to say that crying is an emotion-displaying behavior, whereas some other attributions can be more contested, such as in a dispute whether a deserting soldier was moved by overwhelming fear or by a more calculated plan to preserve himself. In this theory, this fundamental distinction features as the distinction between enacted and unenacted preferences, where enacted preferences are the uncontroversially attributed ones.

Enacted preferences are subdivided between revealed preferences (what Rothbard called demonstrated preferences) and bound preferences. Revealed preferences are uncontroversial because they are nothing other than the action itself; as long as an action was truly an action in the sense of something done consciously by the agent (a question about which there is usually little doubt), then certainly everyone agrees that in some sense the agent wanted to do the action, although it may be a rather weak sense. Out of all attributions of preferences, revealed preferences are the least empty but most blind, having the best semantics but the worst predictive power. Bound preference is my own name for a preference which is codified into a contract. Although all language is vague, indeed even the language of contracts, what happens in contracts is that the question of what the language means about human preferences is submitted to the judge’s interpretation, so that it is the convention that any hard dispute is settled one way or the other by the judge, so that, even though there may be different views on what precisely the parties had intended to commit themselves to, the only view that matters is the judge’s, so that their preference is bound to his interpretation of their language.

Unenacted preferences are those that are inferred to exist beneath an action that does not uncontroversially display it, for instance, if Alice wears a band T-shirt, Bob may infer that Alice is a fan of the band, and possibly further infer that Alice enjoys spending her time listening to music more generally. Although all preferences are in some sense inferred, we reserve the name of inferred preference (simply speaking) for those that are inferred from something other than verbal language, since there is no better name for those, and we should like to distinguish them from stated preferences, which are inferred from verbal language. A further kind of unenacted preference is what I’ll call postulated preference, which is where you say something is in someone’s true interest in spite of what everything about their behavior seems to communicate that they want. For instance, a parent may enforce a kid’s bedtime in spite of the kid’s protestations because the parent thinks the kid actually wants to feel well-rested the next day, and simply has a poor grasp of the causal connection with regard to their bedtime.

So these are the kinds of preferences:

• Enacted preference
• Revealed preference (shown by action)
• Bound preference (contracts)
• Unenacted preference
• Stated preference (verbal)
• Inferred preference (nonverbal)
• Postulated preference (“true interests”)

Political left and right

This post explains my view of political left and right based on this source and this source (pp. 182–186), which I had usually sent directly for people to read, but which no one reads when I send them, so I figured maybe I should write my own thing.

Liberty cap, copied from this article at JSTOR Daily.

The idea of political left and right comes from the French Revolution, which was a conflict between the aristocracy and the bourgeoisie, where the proletariat was entirely uninvolved. There was the Right, which wanted to preserve throne-and-altar statist absolutism as well as an actually-legally-frozen caste-hierarchy where the ruling class is supported by war, and there was the Left, which supported the bourgeoisie in its fight against the aristocracy, defending radical liberty, markets, peace, and secularism. The Right defended privilege, and privilege was understood in its true etymological sense of priva+lex or “private law”, a law that applies only to a certain group of persons instead of applying equally and universally, which is to say, actual legal privileges formally given to a legally-defined nobility; there was no notion of someone being “privileged” by simply being born with any advantage whatsoever.

Confusion was created historically due to the socialists, a movement that arose only later, successfully propagandizing themselves as left-wing even though they weren’t exactly that: they professed the ends of freedom, withering away of the state, peace, high living standards, administration of things not men, class-analysis of rulers vs. producers, etc; but the means they actually wanted to use to achieve those ends were statism, collectivism, central planning, community control over the individual. So they didn’t fit into the spectrum at all, or they were a kind of center, but they wanted to look progressive so they framed themselves as the left-wing, and their propaganda succeeded.

To reduce the confusion as ecumenically as possible, the political compass was created, which gave the socialists the “economic left” while adding a separate authority axis. So we have the Historical left-and-right and the Compass left-and-right, which are, at least, clearly understandable, but oriented roughly opposite from each other. And nothing binds people to use any particular conception when they speak of left-and-right, so if someone appeals to left-wing values by citing people who were historically known to be on the left, this is still persuasive. So it is basically indeterminate in people’s minds whether regulatory interventions are left or right-wing, it depends whether you frame it as an instantiation of hierarchy or try to frame the government as somehow really standing for the people in that context.

Many libertarians think the liberty–authority spectrum is most important but accept the socialists’ framing of themselves as left-wing, so they think of themselves as radically right-wing. (Stephan Kinsella is one such libertarian, who gets offended if you call him a left-winger.) Conversely, you have the aeons–archons spectrum (depicted below) where egalitarianism is blended into the liberty–authority spectrum, and the most radical left idea would be to somehow merge all humans into one thing. (The aeons–archons spectrum frames itself as a crazy “transcended” meme, but its central portions underlie how many people subconsciously think, as a result of a common particular mix of historical awareness and socialist propagandistic confusion.)

The aeons–archons political spectrum meme, artist unknown.

In this context it is indeterminate whether libertarians are left-wing or right-wing. As Walter Block emphasized in the title of a not entirely great article, libertarianism is unique. This idea that libertarianism is properly neither left-wing nor right-wing, which Block calls “plumb line libertarianism”, was shared by the late great Jeff Riggenbach, who hosted a great podcast, The Libertarian Tradition, covering many historical pro-liberty theorists who might be seen as on either “side” by current lights, but who Jeff rightly saw as firmly libertarian. It was also shared by Mr. Libertarian himself, Murray Rothbard, who famously aligned himself with the so-called New Left during the Cold War, due to his overriding antiwar concerns preventing him from wanting to utterly destroy and devastate the Soviet Union (as the conservatives of the time would have wanted it), however unjust its political arrangement may have acknowledgedly been. People who have not read Rothbard on these issues think he “switched sides” throughout his life. As he explained it thoroughly in The Betrayal of the American Right, he was just sticking to his convictions. (His article on Left and Right is also great, and is my other main source here.)

I think of myself as historically left-wing, culturally left-wing (on issues such as LGBT rights, immigration, etc) and “economically” “right-wing” per the compass usage which I don’t really accept, since it implies some vague association between privilege/hierarchy in the old/true sense of it and in the newfangled confused socialist senses of it. As an example of a problem with the compass usage, protectionism is very culturally and historically right-wing, since it wants to protect our nation from foreign upstarts (and secure an actual literal legal privilege to freeze the status of our current captains of industry in relation to those upstarts), but if we focus on how it involves government control over free enterprise, then it’s “economically left-wing” per the compass. I don’t buy it, but whatever; certainly most libertarians today have been driven by their anticommunism to think of themselves as very right-wing, so it’s hard to fight the tide. There is, of course, no meaning to left-wing and right-wing simpliciter, and it is confusing to use it in any meaning, but sometimes I use it, mainly when it is clear that the context is American politics regarding issues (mostly cultural issues) where we can draw a clear line between the two main political parties. It is fraught to extend this into a broader-perspective political theory.

I don’t strictly mind being called either left-wing or right-wing, but I really prefer not being called right-wing given the ideas it might give off about my cultural values (which I worry I don’t emphasize clearly enough), whereas given how I’m very clear about my laissez-faire economic policy views (which are, in the American context, not even fully a Republican thing anyway), I’m mostly happy to be called left-wing, although of course, I don’t insist anyone call me that if they find this hard to buy, like, whatever, go off. I don’t call myself either thing.

Axiomatic Modal Stoicism

This blog post formalizes my conception of Stoicism using propositional modal logic.

This post examines how Stoicism interacts with the assumptions of Psychoanalysis and Behaviorism. Pictured in the illustration are the representative figures of these ideas: respectively, Seneca the Younger (center), Sigmund Freud (left), and B.F. Skinner (right). Of course, the post examines these ideas in a rather abstract sense that might not be attributable to these authors.

• Syntax and semantics
• Axioms for modal logic and Stoicism, and their philosophical justification
• Modal axiom schemes
• Rules of inference
• Stoic axioms
• Justification of Stoic axioms
• Theorems and proofs (P+R+K+T fragment)
• Lemmas (P+R+K+T fragment)
• Theorems (P+R+K+T fragment)
• Psychological methodology axioms and their philosophical justification
• Why a Stoic can endorse Psychoanalysis (Ps)
• Why a Stoic can endorse Behaviorism (Bh)
• How to read the choice
• Theorems and proofs (Ps/Bh fragment)
• Lemmas (Ps/Bh fragment)
• Theorems (Ps/Bh fragment)

Syntax and semantics

The language is first-order propositional modal logic. The definition ◇φ ≝ ¬□¬φ is used freely.

The language is interpreted under a novel way, which once explained, will justify the use of axioms K and T. Although in other contexts I may endorse the use of S5 and the kitchen sink, other axioms were omitted for economy and because I’m not always sure how to interpret the theorems which they would prove.

The interpretation is that all propositions are the attribution of a predicate to a given observed action. The propositions of interest are “the action is Emotional” (E) and “the action is morally Bad” (B). Stoicism asserts a relationship between these attributions which will be explained, justified, and worked out in detail. To aid this explanation, the modal operators are introduced, interpreted in a unique way. Given an action-attribution A, when A was attributed to an action in an observable uncontroversial way, we say □A: for instance, crying is necessarily emotional (□E), and murder is necessarily bad (□B). To say A ∧ ¬□A is interpreted as saying that the action was inwardly emotional although it did not show it (E ∧ ¬□E), or that the action was morally moved by bad motives although it was not observably a bad action (B ∧ ¬□B). The assertions of Stoicism are then clearly stated as the axioms P and R, suggestively named Passion and Reason, which are explained and justified below.

Axioms for modal logic and Stoicism, and their philosophical justification

Classical propositional logic is assumed, and appeals to its tautologies (contraposition, explosion, ∧-intro, etc.) are called PC in proofs.

Modal axiom schemes

K: □(p→q)→(□p→□q)
T: □p→p

T should clearly be true under my interpretation of the modal operator: if something is manifest, then it is (actually) the case. K means manifestness respects implication, which also seems plausible enough.

Rules of inference

US, Uniform Substitution: ⊢ φ ⇒ ⊢ σ(φ)
MP, Modus Ponens: α, α → β ⊢ β
N, Necessitation: ⊢ φ ⇒ ⊢ □φ

The use of Necessitation may seem too strong for an observability operator, but as I see it, whoever believes the axioms will believe them to be analytic, part simply of the meaning of emotionality and badness attributions.

Stoic axioms

Stoicism consists in the axioms P and R:

P, Passion: □E → □B
R, Reason: B → E

These axioms are meant to formalize the informal notion of Stoicism, which is characterized as the belief that actions are morally bad if, and only if, they are moved by Passion rather than Reason. The axioms are justified below.

Justification of Stoic axioms

The justification will employ some propositions which will not ultimately be kept as axioms or mentioned in theorems or proofs. For instance, to justify the formalization, it seems helpful to mention a proposition meaning “the action was moved by Reason”, which, since the letter R is already taken by our axiom R which we intend to justify, I will gloss as “the action was Wise” and abbreviate to W. Then Stoicism clearly supports the Dichotomy:

D, Dichotomy: E ∨ W

The Dichotomy says that every action is moved either by emotion, or by reason, or both (inclusive disjunction). The Dichotomy is not yet a full statement of Stoicism, it just asserts one of its doctrines: besides emotion and reason, there is no third type of motive that can be attributed to an action. (For instance, if we attribute the action to demonic possession, then the true agent was the demon, and we again have the question whether the demon acted rationally or emotionally, or both.) Passion is, if not equivalent to emotion, at least a kind of emotion; if someone believes in “rational emotions”, they need not object yet, since E ∧ W is still possible under this axiom. A fuller statement of Stoicism is added by TR:

TR, Thick Rationality: W→¬B

As the gloss that called a reason-moved action Wise had already hinted, if a Stoic has attributed an action to Reason, then he does not believe that it was morally Bad. The Stoic believes in “thick rationality”: if an action correctly chose the means to pursue the agent’s ends, but the agent’s ends were not themselves good ends, then the agent was irrational in his choice of ends, and his action was irrational as a result.

But from D and TR we have our Axiom R.
Proof: From TR (W→¬B) take the contrapositive to get B→¬W; assume B, then ¬W. From D (E∨W) and ¬W, Disjunctive Syllogism yields E. Thus from B we derived E, so by →-introduction B→E, i.e., R. ∎

Axiom R represents that if a Stoic has called an action morally Bad, then he must attribute it to Emotion, since Reason is simply not available for Bad actions. A similar informal consideration supports P: if a Stoic can conclusively call an action Emotional just from observing it, this must be because he has already ruled out Reason as a motive for it, which means that he is looking at a manifestly morally Bad action. After all, to suppose that we ever have □E ∧ □W is to suppose that there exist observably overdetermined actions, where both motives are observably attributed to an action even though either motive would be, under Stoicism, sufficient to explain it. So now we have R and P both justified by our informal beliefs about Stoicism, as desired.

A Stoic who believes further that all emotions are Passions might also endorse the converse of R, i.e., E→B. This collapses all emotion-attributions into badness-attributions. To keep our assumptions light, we are not assuming this here. In the section on psychological methodology, it will follow as a theorem (part of T10) when Behaviorism, my preferred psychological theory, is assumed.

Theorems and proofs (P+R+K+T fragment)

Some lemmas are used to speed up proofs.

Lemmas (P+R+K+T fragment)

L1 (Converse Passion). ⊢ □B → □E
Proof:

1. ⊢ B → E (R)
2. ⊢ □(B → E) (1, N)
3. ⊢ □B → □E (2, K) ■

L2 (Box Equivalence). ⊢ □E ↔ □B
Proof: From P: □E→□B and L1: □B→□E by PC obtain the biconditional. ■

L3 (Reason—Contraposition). ⊢ ¬E → ¬B
Proof: From R: B→E by PC (contraposition). ■

L4 (Necessitated Contraposition). ⊢ □¬E → □¬B
Proof:

1. ⊢ ¬E → ¬B (L3)
2. ⊢ □(¬E → ¬B) (1, N)
3. ⊢ □¬E → □¬B (2, K) ■

Theorems (P+R+K+T fragment)

T1 (Possible Badness Requires Possible Emotion). ⊢ ◇B → ◇E.

Proof: ◇B → ◇E ≡ (¬□¬B → ¬□¬E) which is the contrapositive of L4 (□¬E→□¬B). PC gives the contrapositive, then rewrite with ◇. ■

Remark: The converse, ◇E → ◇B, is not derivable. It has a countermodel: M = (W,R,V) with W = {w₀,w₁}, R = W × W (so ∀x∀y xRy), V(E) = {w₁} and V(B) = ∅ – hence M, w₀ ⊨ ◇E ∧ ¬◇B.

T2 (Possibly Dispassionate Just When Possibly Innocent). ⊢ ◇¬E ↔ ◇¬B.

Proof: By L2, ⊢ □E ↔ □B, hence by PC ⊢ ¬□E ↔ ¬□B, i.e. ⊢ ◇¬E ↔ ◇¬B. ■

T3 (Manifest Passion Condemns). ⊢ □E → B.

Proof: P gives □E→□B; T (with p:=B) gives □B→B; compose by PC: □E→B. ■

T4 (Manifest Vice Reveals Passion). ⊢ □B → E.

Proof: L1 gives □B→□E; T (with p:=E) gives □E→E; compose by PC: □B→E. ■

T5 (Emotion May Require Public Badness). ⊢ ◇(E → □B).

Proof: Let A := □(E ∧ ¬□B).

• Tautology t1: (E∧¬□B)→E. By N and K: A → □E. With P: □E→□B, so A → □B.
• Tautology t2: (E∧¬□B)→¬□B. By N and K: A → □¬□B. By T (p:=□B): □¬□B→¬□B, so A → ¬□B.
• From (A→□B) and (A→¬□B), PC yields ¬A. Thus ¬□(E∧¬□B). Now, ¬□(E∧¬□B) ≡ ◇¬(E∧¬□B) and by PC/US, ¬(E∧¬□B) ≡ (E→□B). Hence ◇(E→□B). ■

T6 (Badness May Require Public Emotion). ⊢ ◇(B → □E).

Proof: Mirror of T5 using L1 instead of P. Let A′ := □(B ∧ ¬□E).

• (B∧¬□E)→B ⇒ A′→□B; with L1: □B→□E, so A′→□E.
• (B∧¬□E)→¬□E ⇒ A′→□¬□E ⇒ (with T, p:=□E) A′→¬□E.
• PC: (A′→□E) & (A′→¬□E) ⇒ ¬A′. Thus ¬□(B∧¬□E) ≡ ◇¬(B∧¬□E) ≡ ◇(B→□E). ■

T7 (Cold Vice Impossible). ⊢ ¬◇(B ∧ ¬E).

Proof: By N on R: ⊢ □(B→E). Using PC/US, (B→E) ≡ ¬(B∧¬E); by N+K this yields ⊢ □¬(B∧¬E), i.e. ⊢ ¬◇(B∧¬E). ■

T8 (Covert Vice Requires Covert Passion). ⊢ (B ∧ ¬□B) → (E ∧ ¬□E).

Proof: From R we have B→E, so from B infer E. From P we have □E→□B; by PC (contraposition) obtain ¬□B→¬□E, so from ¬□B infer ¬□E. Conjoin by PC to get (E ∧ ¬□E). ■

Psychological methodology axioms and their philosophical justification

The Stoic core (P and R) is deliberately neutral about how inner attributions (E, B) are evidenced. The two “methodology” schemata say what you must think about the relation between inner states and their public marks if you want to use AMS as a model of inquiry into character:

Ps, Psychoanalysis: ◇¬(E→□E) ∧ ◇¬(B→□B)
It is possible for Emotion and Badness to be present without being manifest.

Bh, Behaviorism: □(E→□E) ∧ □(B→□B)
Necessarily, if Emotion or Badness are present, they are manifest (in principle) as such.

These are contraries rather than contradictories because our evidential situation could, in principle, be mixed or indeterminate.

Why a Stoic can endorse Psychoanalysis (Ps)

On the present reading, □ is an observability operator: □A means there are uncontroversial, public criteria that settle A for the action at hand. Ps says only that sometimes those criteria underdetermine the truth about motives and moral quality. This is a modest and very Stoic-friendly thesis.

1. Opacity of assent. For Stoics, the moral core of action lies in assent—the inner commitment that makes an impulse ours. Assent can be swift, conflicted, or suppressed without leaving unmistakable behavioral residue. One can act with a Stoic face while inwardly submitting to a turbulent evaluation; conversely, one can perform an outwardly admirable deed from a vicious maxim. That is exactly the content of ◇(E ∧ ¬□E) and ◇(B ∧ ¬□B): sometimes the motivational reality outruns what observers (or even the agent) can certify.

2. Self-deception and social masking. Agents can misconstrue or conceal their motives—for status, harmony, or fear. The philanthropist moved chiefly by spite toward a rival, the polite insult delivered with a smile, the calm saboteur who harms by omission: each illustrates how inner Emotion or Badness can be present though the public checklists do not light up.

3. Methodological humility. Ps is not a metaphysical posit about hidden homunculi; it is a research policy: do not assume that the public marks exhaust the moral or emotional facts. That policy fits R (Bad → Emotional) and P (□Emotional → □Bad): the Stoic linkage between passion and vice can hold even when the passion or the vice do not surface in an uncontroversial way. In the Ps regime you therefore expect, and methodologically allow for, cases of inward passion without manifest signs and inward vice behind respectable conduct. (This is precisely what our theorems T11 and T12 will record at the modal level.)

Why a Stoic can endorse Behaviorism (Bh)

Bh takes a different tack: it operationalizes the vocabulary. It says, in effect, “we will only count as ‘Emotional’ or ‘Bad’ those attributions that admit public criteria strong enough to settle them.” Under this stance, E and B are not hidden properties to which behavior gives fallible clues; they are roles defined by their outward criteria. Hence □(E→□E) and □(B→□B) are analytic of how we are choosing to use the words in inquiry.

1. Publicness and accountability. If moral and emotional classifications are to guide law, pedagogy, or communal correction, they must rest on intersubjectively checkable marks. “Hidden badness” that leaves no behavioral trace becomes, on this policy, a misuse of Bad rather than a genuine counterexample. This secures clean evidential pipelines: attributing E or B already licenses—and indeed collapses into—their manifestability (hence our theorem T9: E↔□E and B↔□B, even necessarily so).

2. Guardrails against mind-reading. By building □ into the very use of E and B, Bh avoids speculative diagnostics about motives. That is a virtue if you worry that the Stoic critique of passion otherwise tempts us to over-interpret ordinary actions. Combined with P and R, this yields a sharp, behaviorally anchored ethics: necessarily, what counts as Emotional counts as Bad, and conversely (our theorem T10). The theory becomes a calibration norm for observers rather than a depth psychology.

3. Not metaphysics, but operational choice. Bh does not deny that people have inner lives; it declares that for the purposes of this theory’s attributions, only what can, in principle, be publicly settled will count. The box thus records a convention about evidence, not a claim that private states do not exist.

How to read the choice

Both axioms are live options because they address method, not the Stoic core:

• Ps prioritizes explanatory depth: it leaves room for inner assent and vice to outrun public marks, aligning with the Stoic focus on the hegemonikon (the ruling faculty). Expect hidden passion/vice to be possible, and treat attributions as defeasible by deeper interpretation.
• Bh prioritizes intersubjective reliability: it identifies moral and emotional predicates with their public criteria, making the theory action-guiding, teachable, and legally tractable, at the cost of collapsing the inner/outer distinction for E and B.

Either stance is consistent with P and R; they are incompatible with each other because one builds in underdetermination while the other bans it. In that sense AMS functions as a core Stoic logic that can be coupled with a hermeneutic (Ps) or an operational (Bh) methodology, depending on what you want your theory to do.

Theorems and proofs (Ps/Bh fragment)

Lemmas (Ps/Bh fragment)

L5 (Box–Conjunction). ⊢ (□A ∧ □B) → □(A ∧ B)
Proof: Tautology t: A→(B→A∧B). By N: □t. By K twice: from □A get □(B→A∧B), then with □B get □(A∧B). ■

L6 (◇–Monotonicity). ⊢ □(A→B) → (◇A → ◇B)
Proof: From PC: (A→B)→(¬B→¬A). By N and K: □(A→B)→□(¬B→¬A)→(□¬B→□¬A). PC (contraposition): □(A→B)→(¬□¬A→¬□¬B), i.e. □(A→B)→(◇A→◇B). ■

(Recall L2: ⊢ □E ↔ □B, hence by PC ⊢ ¬□E ↔ ¬□B.)

Theorems (Ps/Bh fragment)

T9 (Behaviorist Transparency). Bh ⊢ □(E↔□E) and Bh ⊢ □(B↔□B); hence Bh ⊢ (E↔□E) and (B↔□B).

Proof: E-part:

• From T: ⊢ □E→E, so by N: ⊢ □(□E→E).
• Bh gives □(E→□E).
• By L5: □[(E→□E) ∧ (□E→E)].
• PC tautology: [(E→□E)∧(□E→E)]→(E↔□E); by N+K and MP: □(E↔□E). 

B-part is identical with E/B swapped.

By T on each: □(… )→(… ), so Bh ⊢ (E↔□E) and (B↔□B). ■

T10 (Behaviorist Collapse). Bh ⊢ □(E↔B) (hence Bh ⊢ E↔B).

Proof:

• From L2 and N: ⊢ □(□E↔□B).

• From T9: Bh ⊢ □(E↔□E) and □(B↔□B).

• PC tautology (transitivity): (X↔Y)∧(Y↔Z)→(X↔Z).

  1. With X:=E, Y:=□E, Z:=□B, by N+K and L5: □(E↔□B).
  2. With X:=E, Y:=□B, Z:=B, again N+K and L5: □(E↔B). Finally T yields the unboxed E↔B. ■

T11 (Psychoanalytic Opacity). Ps ⊢ ◇E ∧ ◇¬□E and Ps ⊢ ◇B ∧ ◇¬□B.

Proof: E-part:

• PC: ¬(E→□E) ↔ (E∧¬□E) gives ⊢ ¬(E→□E)→(E∧¬□E); by N and L6: ◇¬(E→□E)→◇(E∧¬□E).
• PC: (E∧¬□E)→E and (E∧¬□E)→¬□E; by N and L6: ◇(E∧¬□E)→◇E and ◇(E∧¬□E)→◇¬□E.
• From Ps: ◇¬(E→□E); chain the arrows to get ◇E ∧ ◇¬□E.

B-part is identical with E/B swapped using Ps’s second conjunct. ■

T12 (Psychoanalytic Cross-Opacity). Ps ⊢ ◇(E ∧ ¬□B) and Ps ⊢ ◇(B ∧ ¬□E).

Proof: First show the E-claim.

• From L2 and PC: ⊢ ¬□E→¬□B. Hence ⊢ (E∧¬□E)→(E∧¬□B) (PC).
• By N and L6: ◇(E∧¬□E)→◇(E∧¬□B).
• From T11 (under Ps): ◇(E∧¬□E). So Ps ⊢ ◇(E∧¬□B).

The B-claim is symmetric using ⊢ ¬□B→¬□E. ■