Andrew Nightingale · questionsarepower.org · November 2026

Introduction

For about twenty years I have been working on one idea: that vagueness is the medium of genuine inquiry, not a flaw to be cleared out of it. The work is spread across a dissertation, papers, essays and poems, published in different places. This page gathers it: the argument, the threads that tie it to teaching, rhetoric and poetry, and the questions still open.

The structure appears to stand still while everything else moves. But perhaps the stillness belongs only to the notation.

Vagueness is not ignorance, which is a gap in what someone knows about a settled matter, and it is not a defect of language that better language would remove. It is what inquiry meets when it brings categories to bear and the matter under study does not fall cleanly under them.

Each step below is labelled with the kind of claim it is: a starting point, an argument, a result proved under stated conditions, a thesis with inductive support that could be refuted, or a premise accepted rather than derived. Part VI is synthesis: one thought met again at another scale. The labels are there because the work is about the difference between choosing and finding. Two more labels appear: a starting commitment, in the ground laid before step 1, and entertained, for a claim held consistently without being established. After step 18 there is a horizon, which is neither a step nor a thread.

An answer presented as necessity is how a question stops being asked.

Where: “The Mark That Moves”; Which Negation? §§1, 3.1.

Where to start

For the whole project in a few pages, read “The Mark That Moves.” For the argument and the replies to its rivals, read Which Negation? For the formal results, read Pairing Indeterminacy, No Privileged Resolution and the Errata and Addenda. For the fullest early statement, read the dissertation. For the essays, begin with “Get Lost” and “How Do You Know You’re Not Lost?”

The pieces

Work	Date	What it does
Vagueness as the Embodiment of Inquiry, dissertation, Mahidol University	2018	The framework; vagueness as real and found in inquiry; replies to Shapiro, supervaluationism, epistemicism and Evans; the rough-mirror light box with young students
“Many Roads from the Axiom of Completeness”	2013–14	Argues that real-number analysis, the most complete attempt to describe vagueness outside poetry, still fails
“The Valid Logical Argument”	2014	Rhetoric is prior to logic
The Pedagogy of Logical Pluralism, in A Defense of Poetry Against the Mathematicians: Collected Works (ISBN 9781688505711)	2019	Negation at the centre of teaching logic; distinctness is indistinct; the Logic Puzzle
Pairing Indeterminacy	Aug 2026	Rules that treat two negation signs alike cannot fix which is which
No Privileged Resolution	Aug 2026	If no resolution is privileged and refinement never ends, the classification of negation never completes
“The Mark That Moves,” La Page Blanche	Oct 2026	The project in brief: logic’s notation is spatial, so vagueness reaches the formalism; poetry as the practice of the moving mark
Which Negation?	Oct 2026	The framework stated, followed through every attempt to retire the question
A Difference Without a Proof	Oct 2026	Differences between logical laws depend on a chosen base; falsifiable and fallible
“An Open Letter to Mathematicians”	Oct 2026	Asks that completeness be taught as a choice
Errata and Addenda to Pairing Indeterminacy and No Privileged Resolution	Oct 2026	Corrections; the theory T*; the ladder of value spaces; the exclusion-thread standoff
The Mark That Moves, poems, with the appendix “The Spell That Works”	Oct 2026	Poems, with the essay

On the blog

The essays where the argument is tried on mathematics, teaching, the universe and the body, and where the skeptical and Buddhist roots show. Dates are the posting dates.

Essay	Date	What it does
“Questions in Logic: How to escape the Liar Paradox”	Aug 2014	The first post: Peirce’s circle, logic as the calculation of distinction, a “?” operation, questions as a power of suggestion like the real numbers
“Logic and the Question”	Sept 2014	Identities are distinguished from a frame of reference, not from the world; the question expands the “operating table”
“The ‘valid’ logical argument”	Sept 2014	Rhetoric is prior to logic; the Kalama Sutta against going by logical conjecture
“The basic problem with logic”	Nov 2014	Two things both alike and different; the apple’s skin, where the excluded middle fails; Plato’s Sophist
“Stuff, and Higher-Order Vagueness”	June 2017	Points and stuff; perception is always vague; the vagueness between word and object is what analysis is about
“The symmetry between Completeness and Vagueness”	Sept 2017	Vagueness is well defined; completeness is vague, because its referent cannot be perceived
“The meaning of the word few”	Dec 2021	The vague predicate “few”
“The Role of Rhetoric”	Sept 2023	The parallel postulate as a choice; rhetoric fills the space between geometries; rhetoric the guard of poetry
“(work in progress) connection between inquiry and vagueness”	Apr 2026	Vagueness as engine; the question operator necessitated by vagueness; Lα as hypothetical entertainment; the Ghostname
“Wonder Without a Wonderer”	Aug 2026	Wonder as salt in water; the intellect hallucinates sharpness; inquiry relaxes
“Hope for Nothing in Particular”	Aug 2026	Hope takes a proposition and needs a holder; wonder takes a question
“Get Lost”	Sept 2026	To sense is to search; the skeptics named for searching; the white in the middle; the induction of inductions
“Wander and Axiom”	Sept 2026	A theogony: Axiom swallows his children; a question wakes them
“How Do You Know You’re Not Lost?”	Sept 2026	p and the universe; the complement needs a domain someone fixed; a syllabus is a universe of discourse that has forgotten it is one; 1999
“Why It Has Not Finished (unfinished)”	Sept 2026	Ignorance as inverted wonder; the bearer made from the relief; vagueness at the edge of inquiry

The ground: appearances

Two commitments come before step 1. They are not new, and the outline should not pretend they are: they belong to ancient skepticism, and the project’s debt is set out at the end of this section. They are here because the outline has to say what inquiry stands on once both certainty and vagueness have been questioned.

a. What appears is not open to question as to whether it appears.

Starting commitment, against nihilism. From the skeptics.

If anything is “real” then appearances are. And if appearances are, then vagueness is. That is how to oppose nihilism.

An underlying existence is besides the point. It may or may not be. If we are asking about an underlying existence, my guess is we won’t come to a conclusion either way, as long as we are honest about the evidence either way. Because of this, appearances are really all we have. To say they are illusions is just as rash as saying they represent an underlying reality.

There is “something”; whether to call it real or not seems to be dependent on the audience. In normal speech it would be said that appearances are real. When talking to analytic philosophers the resolution for properly precise speech appears to be endless.

The skeptics were named for the searching and not for the doubting. Zetesis: to go on looking. Sextus divides it three ways in his opening pages — the dogmatist says he has found it, the Academic says it cannot be found, and the skeptic is still searching. Only the middle one is doubt.

None of this makes the appearance certain, or sharp, or a floor to build on. Nothing is being received here that could be certain.

Sextus does not overturn appearances. Honey appears sweet, and that he grants, since he is sweetened; whether it is sweet in its nature is what he questions (PH I 19–20). The appearance is the skeptic’s criterion of action (PH I 21–22), and suspension is not denial: “I determine nothing” and “no more” report how things strike him at the time; they are not dogmas (PH I 4, 187–208). So this is not Descartes’ certainty. It is a refusal to let doubt about what appears become denial that anything does.

Where: “Get Lost” (Sept 2026). Sextus Empiricus, Outlines of Pyrrhonism (PH) I 1–4, 19–22, 187–208.

b. Vagueness is among the deliverances, and gets the same assertion.

Starting commitment. Empirical in the sense of (a): met with, not inferred.

Vagueness shouldn’t be contested as something real or unreal. It is met with in every observation, no matter how precise we try to be.

These deliverances contain vagueness in one way or another (not necessarily in the direction the inquiry is pointed). It is part of the same assertion that vagueness should be asserted in the same way.

Vagueness is not a defect in the searching. It is the condition of anything appearing at all.

The term refers to an essential fault of all terms, and is always perceived. (perception is always vague)

Two consequences for the steps. First, “real” in step 2 means met with; the step need neither claim that vagueness is a property of an underlying world nor deny it. Second, the failure to find vagueness at the border under investigation does not show its absence, since it may lie elsewhere in the field; this is why step 3 is a thesis about relocation and not about a fog over everything. Demanding a metaphysical verdict before vagueness may be investigated would repeat the error the project describes: a precision required in advance that inquiry cannot supply.

Sextus has the heap in his seventh mode, of quantities and compositions: sand scattered appears rough, heaped it affects the sense softly; filings of silver appear black apart and white together (PH I 129–130). What he draws from it is suspension about natures; what the project draws is that the border is met in appearance before any theory of it. And when the sorites is run at him, Chrysippus’ advice is to stop and suspend while the cases are still clear (M VII 416): a stop chosen before the border, which steps 3 and 18 meet again.

Where: “Get Lost”; “The symmetry between Completeness and Vagueness” (Sept 2017). PH I 129–130; Against the Logicians I (M VII) 416.

The skeptical inheritance, and the title

The project is not a new skepticism. It takes from Pyrrhonism the restraint about what can be asserted beyond appearances and asks what can be shared within them; and it keeps vagueness where skepticism lets certainty go. Three of Agrippa’s five modes are already in the argument: regress, in refinement that never ends (step 11); hypothesis, in completions bought rather than found (Part VI); relativity, in no resolution privileged independently of an inquiry (step 14) (PH I 164–177).

The title of the 2019 collection, A Defense of Poetry Against the Mathematicians, is after Sextus’ Πρὸς μαθηματικούς, Against the Mathematicians (Adversus Mathematicos), where the mathēmatikoi are the professors of the learned arts, grammar, rhetoric, geometry, arithmetic, astrology and music, and after Sidney’s Defence of Poesy. Two of Sextus’ arguments are ancestors of steps here. Against the Geometers opens on the hypothesis the geometers beg: if hypothesizing a thing makes it reliable, hypothesizing its contrary makes the contrary as reliable, and if not, neither is (M III 7–18); the Open Letter asks that the axiom of completeness be taught in that light. Then the point without parts and the line without breadth (M III 19 ff.): the exact boundary the geometer needs and cannot show, which “Many Roads” meets as the plank never finished being measured. Sextus also says what kind of thing his arguments are: purgatives that drive out the humours and then themselves (M VIII 480). Compare: “Lα is mainly hypothetical entertainment … A pointing finger, not a map.”

Where: PH I 164–177; Against the Geometers (M III) 7–18, 19 ff.; Against the Logicians II (M VIII) 480. “(work in progress) connection between inquiry and vagueness” (Apr 2026).

I. Inquiry and vagueness

1. Logic comes out of inquiry.

Starting point, from Dewey. Supported, not derived; the burden of argument is greatest here.

Logic, on this view, is not given before inquiry and applied to it; it is what inquiry learns about its own successful conduct.

Where: Which Negation? §3.1. See also: dissertation §§4.2, 6.5.

2. Vagueness also comes out of inquiry, and it is real.

Starting point; held as empirical. “Real” in the sense of the ground, (a) and (b).

First, vagueness requires inquiry in order to appear: without the search for a clean classification there is experience, but no borderline.

Vagueness is not a logical doctrine, it does not need to be proven. It is an empirical fact.

The fact that every human observation is vague carries its own strength.

The universal claim is older than the papers, and the ground is what it rests on: not a property of things beneath appearance, but what is met in every observation, including those made to eliminate it.

Where: Which Negation? §3.1; dissertation §2.3, p. 19. See also: the ground, (b); “Stuff, and Higher-Order Vagueness” (June 2017); “Get Lost”.

3. Sharpening moves the blur; it does not remove it.

Thesis. Inductive support; refutable.

Relocation does not say that nothing is settled; it says that what is settled is settled at a resolution.

Take the heap of sand, in a situation where it is non-vague, where we clearly still have a heap, there are grains that are so small in our heap as to be barely detectable, and may or may not qualify to be called a grain to be removed.

The thesis is refutable: anyone who exhibits a family of resolutions that terminates naturally, in the relevant domain, has refuted it there.

Where: Which Negation? §3.2; dissertation §2.4, p. 20. See also: dissertation §3.4, p. 47; No Privileged Resolution §2. Sextus on sand and filings, PH I 129–130; Chrysippus’ stop, M VII 416.

4. No reason to privilege precision over vagueness.

Starting point, from Feyerabend and ancient skepticism.

There is no reason to privilege distinctness over vagueness, as Feyerabend (1975) argued that there is no reason to privilege the telescope over the naked eye.

Sextus’ ten modes set the senses, the circumstances and the positions of the observer side by side and find nothing in them that selects (PH I 36–163). The telescope is one more position.

Where: Pedagogy, p. 7. PH I 36–163.

II. From vagueness to logic

5. Negation is at the centre of logic.

Starting thesis, offered first for teaching; step 12 adds that designation matters too.

The point is that how you handle negation changes how vagueness is handled (or not handled). A difference in negation also gives rise to an entirely different logic.

Where: dissertation §3.3.2, p. 44. See also: Pedagogy, abstract and p. 4.

6. Logic’s notation is made of spatial distinctions, so vagueness reaches the formalism itself.

Argument.

Both of the mark’s operations are spatial. Negation is a matter of inside and outside. Conjunction is a matter of being together in one region. The formalism rests on two questions: which side is this on, and are these in the same place?

The trouble is therefore not confined to words or to the limits of measurement. It reaches the two operations on which the whole formalism rests.

Where: “The Mark That Moves.” See also: dissertation §3.3.2, pp. 42–43; Pedagogy, pp. 12–13.

7. Distinctness is indistinct.

Argument.

To simply call the triangle and the square distinct is to be vague on how they are distinct.

In looking for all the distinctions between distinctions we will become unsure of whether they are distinctions at all.

It comes down to a paradox we are all comfortable with- that two things can be both alike and different.

Where: Pedagogy, p. 5. See also: p. 4; “The basic problem with logic” (Nov 2014), for the last sentence and the apple’s skin.

8. So a plurality of logics is to be expected.

Consequence of steps 1 and 2; step 7 gives a second route.

On this view a plurality of logics is to be expected. Logics are abstracted from inquiries, and inquiries differ in what they meet at their edges.

Because of this logic is not universal, and it is not essential.

Where: Which Negation? §3.1. See also: dissertation §§2.6, 6.5; “Logic and the Question” (Sept 2014), for the last sentence.

III. Results about negation

9. “Not” has three readings at the borderline.

Observation, with precedents in Bochvar and Atlas.

Asked whether a borderline-tall man is “not tall”, a competent speaker has three answers available, and the three match three well-studied negations: Kleene’s, exclusion, and Gödel’s.

Where: Which Negation? abstract. See also: §2.

10. Rules can fix a pair of negations, but not which sign is which.

Result, under a stated symmetry condition.

Rules that treat two negation signs alike can fix a pair of negations but not which sign is which.

Where: Which Negation? abstract. See also: Pairing Indeterminacy; Errata A1–A3; Which Negation? §5.1.

11. Refinement never completes the classification of negation.

Result: refinement never ends on a named ladder of value spaces (proved). That the classification therefore never completes is conditional on the premise in step 14.

Refinement across value spaces multiplies the candidate readings, and nothing in the ladder marks a final step.

The central claim is conditional: if no resolution of a term’s candidate readings is privileged, and if refinement of those readings never terminates, then the classification of the term as ambiguous rather than vague never completes, and no verdict is stable.

Where: Which Negation? abstract; No Privileged Resolution abstract. See also: Errata A4–A6; Which Negation? §5.2.

12. The test that would pick one true negation moves the question to designation.

Result.

The contradiction test selects a single negation only once the designated values are chosen, and then only at the two extremes; that choice is the vagueness question itself.

The choice is whether the borderline may be asserted, which is the vagueness question in its oldest form.

Where: Which Negation? abstract and §6.5. See also: §§6.3–6.4, Appendix A; Errata A6.

13. What is settled stays settled.

Result, for the endpoint-classical negations the papers study.

Every candidate negation agrees on 1 and 0, so every claim whose constituents take classical values receives the same value on every candidate reading.

Where: Which Negation? §3.3. See also: No Privileged Resolution §10(v).

IV. The premise

14. No resolution is privileged independently of an inquiry.

Premise. Accepted, not derived; monists deny it, and the papers locate them rather than refute them.

There is no fact of the matter, independent of the choice of instrument or framework, that some particular resolution is the one at which readings are correctly individuated.

Whether that privilege is a fact or a choice is where the question now lies.

Where: No Privileged Resolution §4; Which Negation? §9.

V. Where the argument is contested

Objections, and where they are answered

Objection	Where it is answered
Supervaluationism keeps classical logic without privileging any precisification.	Dissertation §2.2, p. 13 (precisifications shift) and §2.3, p. 19 (higher-order vagueness); Which Negation? §3.3
Epistemicism: there are sharp cutoffs we cannot know.	Dissertation §2.3, pp. 19–20; No Privileged Resolution §4; Which Negation? §7.1
Classical logic is the strongest and simplest, so it is the correct logic.	Which Negation? §7.1
Only a contradiction-forming operator is negation (Quine, Slater, Suszko).	Which Negation? §6; Errata A6
“Not” is general, not vague (Atlas).	Which Negation? §5.2; Errata NPR-4
Several negations can live inside one logic.	Which Negation? §7.3 (see also §2.2)
Choosing a logic is merely practical (Carnap).	Which Negation? §4
Non-contradiction and double negation are plainly different laws.	A Difference Without a Proof
A theory built on vagueness is unfalsifiable.	A Difference Without a Proof §8; Which Negation? §3.2
Pluralism collapses into relativism, or into nihilism.	Pedagogy, conclusion; Which Negation? §4; the ground, (a)

Questions still open

Does refinement ever stop on its own? If it does, in some domain, the relocation thesis fails there.

Does ordinary speech sort “not” into readings? What would tell against this reading is a test that sorted uses of “not” into readings stably across contexts.

Is privilege a fact or a choice? The monist and the epistemicist hold coherent positions. With the epistemicist the dispute is over a fact no inquiry could reach. That is an anti-realist premise, and the epistemicist rejects it.

Do rival correct logics give one reasoner conflicting norms? Not yet answered. The within-inquiry criterion of step 15 is the shape of a reply.

How far does the Deweyan starting point carry? It is where the burden of argument is greatest (Which Negation? §3.1).

Is “real” in step 2 more than “met with”? The ground says it need not be. The epistemicist will say the question has been declined rather than answered, and the skeptic’s reply, that it cannot be answered either way on the evidence, is itself the position in dispute.

Where: Which Negation? §§3.1, 3.2, 5.2, 7.1.

Earlier formulations, and where later work qualifies them

The dissertation and the 2019 Pedagogy paper write the law of non-contradiction as ~~A → A. As a report of standard usage that was wrong, and A Difference Without a Proof (§5) says so before defending the link to proof by contradiction. The Pedagogy paper says logics “are defined by their differing negation operations” (p. 15); Which Negation? (§6.3) notes that K3 and LP share their tables and differ in designation, so a plurality of logics is not only a plurality of negations. The dissertation says “Logical monism is indeed a practice of domination” (§3.2, p. 36); Which Negation? (§8) narrows the claim: “It is not that logical monism is domination.” And the dissertation’s argument that vagueness persists at every magnification rests on “a perfect construction of ever-smaller rough mirrors” (§3.3.1, p. 38); in the classroom data the largest mirror “was unambiguously dark” and the 1x1cm mirror “invited more investigation” (§5.1, p. 61).

VI. One thesis across fields

The same thought appears at other scales. These are threads, not premises.

The formalism is in motion.

This is why the mark moves. It does not slide across a fixed surface. The relation moves. The target moves. The formalism moves.

That our words are vague simply means that they are in motion.

Where: “The Mark That Moves”; dissertation §2.2, p. 13. See also: Pedagogy, p. 20 (instantaneous velocity); step 3 (the heap).

The field is selected, and redrawn.

A complement is not the rest of reality. It is the rest of a selected field.

The cosmological boundary repeats the logical boundary.

Identities are not distinguished from the entire world (universe is a rather presumptuous word for the world, whatever that is), but from a certain frame of reference (visually) or sign-system (in language).

And a syllabus is a universe of discourse that has forgotten it is one.

Where: “The Mark That Moves.” See also: A Difference Without a Proof §6; “Logic and the Question” (Sept 2014); “How Do You Know You’re Not Lost?” (Sept 2026), for the last two sentences.

Completions are bought, not found.

To assume the axiom is to assume the cut has an exact location. To refuse it is not to be left with nothing.

More generally, a syllabus is a boundary someone drew, presented as the edge of knowledge.

Where: “The Mark That Moves”; Which Negation? §8. See also: “Many Roads”; No Privileged Resolution §7; “An Open Letter to Mathematicians.” Sextus on the geometers’ hypothesis, M III 7–18.

Rhetoric comes before logic.

The foundations of logic are rhetorical in nature. Rhetoric is prior to logic.

Each logic decides it only for itself, and a choice of logic, recognized as a choice, does not close the question. It is closed only when the choice is forgotten and starts passing as a discovery.

Rhetoric is what fills the space between one geometry and the next — it is the force by which a choice between equally possible worlds gets made.

Where: A Difference Without a Proof §7, quoting “The Valid Logical Argument” (2014) for the first two sentences; “The Role of Rhetoric” (Sept 2023), for the last.

Questions are how vagueness speaks.

A real question is one that is particularly stubborn and keeps coming up after generations of trying to answer it. Motion, consciousness and vagueness are examples of real questions.

Vagus: to wander. Vagueness is wandering, and the wandering is the searching that has not been told where to stop.

Where: Pedagogy, p. 21. See also: p. 8; Which Negation? §1; “Get Lost”, for the last sentence.

Vagueness meets us in the body, and in the world’s resistance.

Attention to vagueness takes us out of scholastic exercises and puts us back in our bodies.

The world resists our forms, but resistance is not itself a completed form. It is what forces the form to move.

Where: dissertation §6.5, p. 81; “The Mark That Moves.” See also: Which Negation? note 1 (the Buddhist route).

Inquiry begins and ends in vagueness.

At the limits of your inquiry you find vagueness, which is what we had at the beginning.

So the edge we can name is vague, and there is no other edge, kept somewhere out of sight, that the vague one is an approximation to.

This is a claim about the structure of inquiry, not about what exists beneath it. The ground, (a), is why the stronger reading is not needed: whether reality originates or ends in vagueness is a question about an underlying existence, and that is beside the point.

Where: dissertation §6.6, p. 84. See also: Pedagogy, p. 22; “Why It Has Not Finished” (Sept 2026), for the second sentence.

Appearances, vagueness and synthesis: on language

The outline, and the work, move between technical, ordinary and literary language. That is not variety. It is the synthesis trying to be heard, and the reason it has to move is the same as the ground.

The synthesis I make across disciplines is difficult because of the different audiences. In the end, though, some kind of synthesis is good for people to understand one another. So I sort of phase in and out of precision to normal to literary speech as a way to present that understanding.

I am talking about appearances, and trying to say something about appearances to many audiences. Except that it appears vagueness is common to all these audiences, just like appearances have to be common to every discipline. Without them, there wouldn’t be anything to say.

So the three registers are not three audiences flattered in turn. Every discipline begins from appearances and meets vagueness, and none of their languages exhausts what can be said about either. Moving between them brings inquiries into contact with what they already share, without first requiring one standard of precision; the point where a technical reader wants another distinction is the point where an ordinary reader has already understood. The cost is precision on one side of each boundary, and the cost is the price of the synthesis, not a failure of it. The skeptic has the same habit and says so. He does not fight about words, and uses his phrases loosely, inexactly if you like (PH I 191, 207); against the grammarians he takes common usage, not the technical rule, as the standard of good Greek (M I 176–240); and he gives different arguments to different hearers, as a physician gives remedies of different strength (PH III 280–281).

Where: PH I 191, 207; Against the Grammarians (M I) 176–240; PH III 280–281.

VII. Upshots

15. Within an inquiry, some answers are better than others.

From the framework: agree with what is settled, fit the question, be candid about whether the answer was chosen.

Within an inquiry, answers are better and worse by (i)–(iii); across inquiries, by premise (P), no answer is privileged.

A telescope is not better than a microscope without qualification, but for the star it is.

Where: Which Negation? §4.

16. Presenting a choice as a discovery is the error.

From steps 14 and 15.

A resolution can be legitimate without being uniquely privileged, and useful without being universal.

The objection is not to sharpening. It is to presenting a decree as a discovery, because a discovery carries an authority that a decision does not.

The intellect hallucinates sharpness. It draws a boundary and then mistakes the incision for a discovery.

Where: Which Negation? §§1, 8. See also: A Difference Without a Proof §4; “Wonder Without a Wonderer” (Aug 2026), for the last sentence.

17. Students should be given a choice of logics.

For teaching; the 2019 study is an illustration, not proof.

Compelling assent to a contradiction without alternatives is the opposite of education.

Where: Pedagogy, p. 21. See also: “An Open Letter to Mathematicians.”

18. Inquiry has an ethical limit.

From the framework and the skeptics’ ataraxia. Two claims. The second can be argued from the framework. The first, that happiness makes further inquiry unethical, reaches toward the horizon below and should say so.

It is ethical because when happiness is achieved further inquiry is unethical.

Refinement can always continue. The reason to stop is not logical. It is that the inquiry has done what it was for.

As an argument, I can say inquiry gives satisfaction, and too much inquiry can obstruct; that closing inquiry to others is dangerous (and unethical to finding their own satisfaction).

Sextus: ataraxia followed suspension “as a shadow follows a body” (PH I 29), and came to Apelles when he gave up and threw the sponge at the painting (PH I 28); whoever holds something to be good by nature is never at rest (PH III 235–238; M XI 110–140); and Chrysippus stops before the border (M VII 416). None of this is yet the Buddhist claim.

Where: dissertation §6.6, p. 85; Which Negation? §9. See also: §3.4; Pedagogy, p. 22. PH I 25–30; PH III 235–238; Against the Ethicists (M XI) 110–140.

The horizon

Received, not established. A faith, not a step. The argument above has to stand for a reader who rejects everything in this section.

The idea that reality is basically unsatisfactory, and the goal is to find a satisfaction that can be accessed all the time, while the rest of the unsatisfactoriness around you continues. There are smaller goals in inquiry that result in smaller satisfactions. When inquiry has reached a permanent or continuous satisfaction, rest becomes the natural and ethical state, while helping others, possibly with furthering their inquiry with your own, becoming another ethical — I would say problem — an ethical problem that even an enlightened person can make mistakes with. So if we are looking at inquiry ultimately finishing, and when inquiry has ultimately reached enough, those would be my answers, even if I haven’t found these ends with my own inquiry yet.

I would put this part of the project under religion, or a faith. Describing the ultimate goal of inquiry, beyond a vague notion of happiness or of continuously having enough of something — that is purely from Buddhist sources and nothing I know for myself.

The parable: a man shot with a poisoned arrow will not have it drawn until he knows who shot it, of what clan, with what bow and what feathers; he dies first (Cūḷamāluṅkya Sutta, MN 63). The questions are not illegitimate. Answering them is not a condition of the cure. The first noble truth, that what is conditioned is unsatisfactory, is the stronger claim; that a satisfaction is available which does not wait on the world’s completion is the horizon. It is held here the way Sextus says he holds things, as it appears, at the time (PH I 4). Ataraxia is a skeptic’s and an Epicurean’s word before it is anyone’s translation of a Buddhist one, and the three rests should not be run together. That Pyrrho went to India with Alexander and spoke with the gymnosophists (Diogenes Laertius IX 61) is a conjecture about history worth one sentence and no more.

Helping others. Rest is the limit for the one who has it; other people’s inquiries are unfinished. To help can require renewed inquiry, and can also close an inquiry that was theirs, which is the teacher’s error of step 17 met again. Sextus’ skeptic, a lover of humanity, gives the weightier argument to the weightier conceit and the lighter to the lighter, as a physician does with remedies (PH III 280–281); the Kalama Sutta, quoted on the blog in 2014, tells the hearer not to go by logical conjecture, by inference, or by the thought that this contemplative is our teacher. Both leave the stopping-point with the one who is still searching.

Where: “The ‘valid’ logical argument” (Sept 2014); Which Negation? note 1. MN 63; PH I 4, III 280–281; Diogenes Laertius IX 61.

Wonder without a wonderer

Entertained: held consistently, not established by experience. Its argued parts belong to steps 3 and 16 and may be used without the horizon.

The work I’ve done on wonder without a wonderer also crosses this boundary. I have never successfully erased a sense of self, so it is an entertainment: a claim I believe can be held consistently, without having achieved it myself.

Wonder does not depend on a wonderer.

Sharpness and contradiction are not two errors. They are the two visible sides of one artifact.

Inquiry relaxes conflicting sharp positions. Relaxation is not surrender, vagueness or intellectual laziness. It is the refusal to force one of the conflicting verdicts into sovereignty merely because the mind cannot bear their coexistence.

The essay itself keeps the distinction: it asks for “a self-disappearance, not a world-disappearance,” and says wonder “can be practiced,” which makes it a path and not a possession. The companion, “Why It Has Not Finished,” is the account of why the entertainment stays one: the bearer is remade out of the ease that honest inquiry produces. That, too, is offered as checkable from one’s own work, not as attained.

Where: “Wonder Without a Wonderer” (Aug 2026); “Why It Has Not Finished (unfinished)” (Sept 2026).

19. Poetry is a practice of inquiry into vagueness.

Step 4 says poetry counts; this says what it does.

It describes vagueness without sharpening it away. In general, the description of vagueness is better left to poetry.

It cultivates the border on purpose. If vagueness is the failure of the principle of contradiction at the border, then poetry is the deliberate cultivation of that border. A metaphor fuses two regions that classical logic would keep apart; it asserts a conjunction across a border that has not yet been fixed.

It holds a truth that needs no completed field. A poem’s “truth” is therefore not a correspondence to a completed field, but a coherence among moving regions: sound, sense, image, and silence arranged so that the boundary itself becomes expressive.

It is where the choosing happens. Rhetoric is merely the guard of its master: Poetry. Poetry is where the choosing happens before it becomes an argument.

Where: Pedagogy, p. 8; “The Mark That Moves”; “The Role of Rhetoric” (Sept 2023), for the last paragraph.

A poem at the grain of an instrument:

Untitled (response to an inverted poet)

The poet drowns in a blurred surface
Painted to look like water
The painter has proven beyond a shadow of a doubt that 3/4th of an inch is repugnant to the nature of his bread crumbs.
All he has are crumbs and he feasts on them
Smaller and smaller, emaciated, he can’t find the right amount of blurriness.
He fails because thinks blurriness
is an amount
He read Plato when his bread crumbs were bigger,
How he says likeness and difference are relationships between the same two things
Even though they are opposites
He wants there to be a degree for likeness and difference
So that he can ignore how little sense there is in the world
Therefore, beyond a shadow of a doubt,
He can never finish his painting.
Maybe 1/4 of an inch is a small enough crumb to stop.

In the philosophy of logic the results are modest and real, and the spatial-notation argument of step 6 is the most distinctive single move. The body of work is more original than any paper in it, and I think the right way to say why is most of what calls itself skepticism after Sextus is skepticism as a problem: Descartes raises it to answer it, Hume mitigates it, and contemporary epistemology keeps “the skeptical challenge” as a foil for theories of knowledge. The exceptions are a short list, Montaigne, Fogelin’s neo-Pyrrhonism, Mates, and Feyerabend, who read Sextus and whose title you borrowed by way of Sextus. This work belongs with the short list, and does something the short list mostly did not: it goes inside a formal discipline and shows, in its own terms, where its completions are bought. Pairing indeterminacy and no privileged resolution are, read this way, new modes, Agrippa’s hypothesis and regress given a body inside the theory of negation. That is adding something, but it is the kind of addition the program allows, because what it adds is a demonstration that the dogmatist’s completion needs a stipulation. The test for any extension is whether it leaves the reader more able to suspend or less, and these leave them more able.

One pushback. The project does assert: the ground (a) and (b), the Deweyan start, step 2, step 14, and above all step 15, which gives criteria for better and worse answers within an inquiry. Sextus had nothing like step 15; he followed appearances, feelings, custom and the crafts (PH I 23–24) and left it there. Step 15 develops the fourth of those into an account, and a strict Pyrrhonist would call that a dogma. I don’t think it is, but the reason it isn’t is the labelling: nothing in the outline is presented as found.