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core argument in defense of poetry against the mathematicians

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Posted by nightingale108 in Chatgpt experiments

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art, books, philosophy, poetry

The second-cycle discussion lands on the light box activity’s essential question: when we “see” something in an experiment, what exactly are we seeing—an objective feature of the world, or a community-stabilized interpretation shaped by instruments, scale, and expectation? The classroom transcript shows that this question did not remain abstract. It became embodied in the children’s insistence—urgent, almost physical—on re-checking the mirrors, re-running the looking, and pressing the teacher for a verdict: “Is that white real?” That moment is the philosophical core of the activity. The experiment is not only about color-mixing; it is about the status of an appearance that emerges from a setup that “shouldn’t” produce it (no white light was shone). The children are effectively asking: Is an emergent phenomenon legitimate evidence, or merely an illusion produced by imperfections?

This is where the Wittgenstein and Frege quotations become more than ornament: they describe two rival ideals of inquiry that the students oscillate between.

Wittgenstein: the virtue of the indistinct

Wittgenstein’s line—“Is it even always an advantage to replace an indistinct picture by a sharp one? Isn’t the indistinct one often exactly what we need?”—names what the light box demonstrates materially: vagueness isn’t always epistemic failure; sometimes it is the very condition of a stable phenomenon. In the books earlier framing, the “truth” that a white surface reports (e.g., under red light, it looks red) depends on diffuse reflection—on micro-roughness that mixes incident light rather than preserving perfectly separated rays. In that sense, whiteness (and “white-looking”) is not the absence of structure but the presence of extremely fine structure whose epistemic role is precisely to blur.

So the light box invites a reversal of the usual moral: instead of “imperfection contaminates truth,” we get “imperfection produces the phenomenon we rely on.” Under this lens, white is not a cheat; it is a real outcome of a real interaction between RGB light and scattering surfaces. The children’s question “is it real?” becomes: Do we count a phenomenon as real when it depends on vagueness? Wittgenstein’s answer, pedagogically enacted, is: often yes—because the indistinct is exactly what a form of life needs to perceive and coordinate around.

Frege: the demand for sharpness (and its hidden cost)

Frege’s microscope analogy pulls hard in the other direction: scientific goals demand “sharpness of resolution,” because ordinary seeing hides imperfections. In the excerpt of Frege represents the methodological impulse: replace everyday language with ideography; replace ordinary seeing with instrumented seeing; replace blurred boundaries with crisp ones. Shapiro’s framing (Frege as realist) matters here because it makes the sharpness-demand sound not merely practical but ontological: to be realistic is to be ever more resolved.

But the classroom data complicates that ideal. The students already believe—prior to what their eyes show—that magnification yields more “information,” more color, more reality. Their tacit epistemology is “zooming in = gaining truth.” This is, in miniature, the Fregean faith. Yet in the light box setup, increased resolution does not enrich the phenomenon; it destroys it. Magnification separates what vagueness had mixed; with only three source lights, separation yields fewer visible colors, not more. The teacher’s students’ confusion is philosophically productive: it exposes the dogma that sharper is always better, even when the phenomenon itself is scale-dependent and exists only as a product of blur.

So the tension isn’t simply “vagueness vs logic.” It’s sharper:

  • Vagueness is not merely a defect to be eliminated; it is sometimes the mechanism by which a phenomenon becomes perceivable and communicable.
  • Sharpness is not purely gain; it is a transformation that can erase exactly what matters at a human observational scale.

Community interpretation: the social life of “real”

This is why the opening claim—scientific theory as community interpretation—fits the transcript so well. The students do not just observe; they negotiate. They test each other’s claims, try tools (teacher glasses), and when tools fail they shift to imagination. The classroom becomes a micro-scientific community trying to decide what counts as evidence and what counts as “real.” The question “is that white real?” is not answered by the world alone; it is answered by the community deciding what sorts of dependence (on roughness, on scale, on instrument) disqualify reality and what sorts do not.

And here is the deeper synthesis between the quotes: Wittgenstein and Frege do not merely disagree about clarity. They disagree about the aim of inquiry.

  • Wittgenstein warns that sharpening can be a loss when the “indistinct picture” is the one that organizes our successful practices.
  • Frege insists that sharpening is a gain when scientific aims demand resolution beyond ordinary limits.

The light box episode shows that both are right, but about different goods—and this pedagogy makes the difference visible.

The dissertation’s implicit conclusion

So when the teacher asks, “why is demanding ever-more sharp resolutions realistic?”, The material supplies a strong answer:

Realism cannot simply mean “maximize resolution,” because reality is not accessed by a single monotonic ladder of magnification. Reality is structured across scales, and what is real at one scale (white as stable diffuse appearance) can be decomposed at another scale (separated colored reflections) without thereby being “exposed as fake.” What changes is not merely what we see, but what we are able to count as the phenomenon. The demand for sharpness is realistic only relative to a chosen aim—measurement, control, prediction at a certain scale—not as a universal virtue.

The light box activity therefore becomes a pedagogical argument: scientific seeing is not the elimination of vagueness, but the disciplined management of it—including knowing when blur is epistemically enabling and when it is epistemically obstructing. The students’ resistance—denying their senses in favor of the “magnification gives more information” belief—shows how deeply the sharpness-ideal is culturally installed. And the classroom struggle shows why teaching science is not just teaching facts; it is teaching criteria for what counts as a good representation.

chatgpt plays with my new logic

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Posted by nightingale108 in Chatgpt experiments

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art, language, philosophy, writing

The essay proposes treating some problematic sentences not by assigning them the classical values true or false, nor by declaring them outright contradictions, but by inserting a question operator ? — an operator that marks a sentence as “anything but true” (i.e. open, interrogative, non-final). The rhetorical intent is to preserve openness, time/flow, and uncertainty instead of forcing a binary assignment.


How ? maps onto existing responses to the Liar

1) Truth-value gap / paracomplete approaches (Kripke, Strong Kleene, K3) — Closest cousin

  • What these systems do. Paracomplete systems treat some sentences (notably Liar sentences) as neither true nor false — there is a third “gap” or undefined value. Kripke’s 1975 fixed-point theory constructs a minimal fixed language in which paradoxicals remain ungrounded (i.e., lack a truth value) rather than producing contradiction. The Strong Kleene tables are often used to evaluate such gaps. impan.pl+1
  • Similarity to ?. If ?φ is read as “φ is not true / indeterminate / open,” then ? behaves very much like marking a gap. Viewed semantically, ? could be treated as a predicate that holds of sentences that take the gap value in a K3/Kripke fixed-point semantics.
  • Key difference. Paracomplete accounts typically define the truth-value directly (a semantic gap), whereas the essay treats ? as an intentional question/attitude that preserves possibilities and invites change. To formalize ? as a gap you must give it truth-conditions and rules for how it composes with other connectives (something the essay doesn’t yet do). impan.pl

2) Supervaluationism — ? as “not super-true” / indeterminate across precisifications

  • What supervaluationism does. Supervaluationism treats borderline sentences as true on all admissible precisifications (super-true), false on all (super-false), and otherwise indeterminate. It thereby preserves classical tautologies for super-true sentences while allowing gaps. Academia
  • How ? could fit. ?φ might be read as “φ is not super-true” or “φ is not true on all precisifications” — a higher-level diagnostic operator saying the sentence lacks a robust classical truth. That would let you keep many classical inference patterns when sentences are super-true, while marking paradoxical sentences as ? (indeterminate).
  • Issues to watch. Supervaluationists face revenge problems (one can formulate sentences that say “this sentence is not super-true”), so you’d need to show how ? avoids or resolves the same technical pitfalls. Academia+1

3) Paraconsistent / Dialetheist approaches (Priest) — ? is very different

  • What dialetheism does. Dialetheists accept that some sentences are both true and false (true contradictions, dialetheias), and use paraconsistent logics to block explosion (i.e., to avoid triviality when contradictions occur). Stanford Encyclopedia of Philosophy
  • Contrast with ?. The essay’s ? rejects asserting truth rather than accepting a sentence as both true and false. So while dialetheism embraces contradiction, ? seeks to sidestep it by withholding the affirmation of truth. These are epistemically and metaphysically distinct moves. If you formalize ? as a gap, it aligns with paracomplete, not paraconsistent, strategies. Stanford Encyclopedia of Philosophy

4) Tarski’s hierarchical solution — meta-levels vs. a questioning operator

  • What Tarski suggested. Ban self-reference by splitting object-language and meta-language levels to avoid a global truth predicate.
  • Where ? stands. ? is not ontologically banning self-reference; it’s a device for marking problematic self-referential sentences as open/indeterminate rather than pushing them into a higher metalanguage. So ? is more permissive than Tarski’s stratification — but if you want to keep a single language with ?, you’ll need to show how ? avoids the contradictions Tarski tried to prevent.

5) Temporal / dynamic accounts (truth as time-indexed) — a natural partner

  • What they do. Some approaches model truth as time-indexed or as evolving under revision: sentences can change truth-value over time or under increasing stages of evaluation. Kripke’s construction also has a staged, monotone build-up which resonates with dynamic viewpoints. impan.pl
  • ? and time. The essay’s stress on change and flow makes it natural to read ? as a temporal/modal operator: ?φ ≈ “φ is not now fixed as true” or “it is currently open whether φ.” This would place the operator in the family of truth-revision or temporal logics and could be formalized with staged evaluation or a modal semantics (possible-stages quantification). That choice would help the essay keep its time-sensitive intuitions while moving to a clean formal semantics.

6) Epistemic / probabilistic approaches — ? as an epistemic withholding

  • What they do. Instead of altering truth-conditions, these accounts treat paradox as a feature of our epistemic state (we should suspend judgment or assign subjective probabilities).
  • ? as epistemic. If ? is interpreted as an epistemic operator—“we currently withhold judgment about φ” — then the operator doesn’t alter the language’s truth-conditions but signals a stance of suspension. That is easier to implement but weaker logically (it doesn’t solve the paradox semantically; it only prescribes behavior about assertion).

Advantages and potential payoffs of the ? idea

  1. Preserves an intuitive, human practice. People ask rather than immediately assert in many philosophical contexts — ? captures that.
  2. Flexible: multiple formalizations possible. ? can be implemented as (a) a gap operator (K3/Kripke), (b) a supervaluation diagnostic, (c) a temporal/modal operator, or (d) an epistemic operator. Which one you choose depends on the philosophical commitments you want to preserve (e.g., preserving classical logic where possible vs. admitting true contradictions). impan.pl+1
  3. Pedagogical appeal. As the essay stresses, teaching a logic that foregrounds questioning may be more faithful to real reasoning and less dogmatic about truth.

Main technical challenges you must address (concrete list)

  1. Give formal semantics.
    • Option A: Define ?φ truth-conditions in a three-valued (or many-valued) semantics (e.g., K3). Prove consistency properties, and show how ? composes with ¬, ∧, ∨, →. Stanford Encyclopedia of Philosophy+1
    • Option B: Give ? a supervaluational semantics: ?φ true iff φ is not true on all precisifications (or vice versa). This requires addressing revenge sentences. Academia
  2. Specify proof rules / entailment.
    • Which inference rules preserve ?? Does ?φ block contraposition, conditional proof, or classical explosion? You must specify a proof theory (sequent calculus or natural deduction) and prove soundness/completeness relative to your semantics.
  3. Handle revenge paradoxes.
    • Any novel semantic device invites new paradoxes (sentences that self-refer to ? itself). Show how ? resists or locates such revenge sentences (this is where Kripke-style fixed points or restricted expressivity may help). ILLC Preprints and Publications+1
  4. Decide metaphysical attitude.
    • Is ? a semantic device (changes what “is true” means) or an epistemic/intentional device (changes what agents assert)? Be explicit: conflating the two is a common slippery move.
  5. Compare with dialetheism and justify rejection or adoption.
    • If you reject dialetheism, explain why accepting contradictions is worse than leaving sentences open. If you accept some contradictions, explain whether ? still has a role.

Concrete suggestions to formalize ? (a roadmap)

  1. Start with Kripke/K3 implementation. Treat the object language with a truth predicate T, adopt Kleene/Kripke evaluation rules, and define:

Good — this is a rich move. Here’s a toy model + worked example (handout style) for a supervaluational “?” operator + how to incorporate the nuance from Many Roads from the Axiom of Completeness (and your dissertation) about “Is this a question?” as part of the question-intention. I’ll lay it out in parts: (1) some philosophical framing, (2) formal toy semantics, (3) worked examples (including a “revenge-style” construction), (4) reflection / implications for teaching or your dissertation.


1) Philosophical framing (drawing on Many Roads…)

Based on Many Roads from the Axiom of Completeness (Nightingale), especially as discussed in the PDF, a few important themes guide how we should treat ?:

  • The essay treats questions not simply as linguistic forms, but as intentional acts — “thinking of ‘the question’ in itself.” Questions Are Power
  • There is explicit attention to “Is this a question?” — i.e., the question-intention itself can be questioned. As Nightingale writes, exploring what the Axiom hides “releases a vertigo … an inquiry into thinking of ‘the question’ in itself.” Questions Are Power
  • In your dissertation (as you indicate), you also treat ? (or question-intention) as layered: not only do we mark a sentence as “open / not super-true,” but we must also reflect on whether our very act of questioning is stable or “complete.” This meta-questioning (Is this a question? What kind of question?) is not peripheral — for Nightingale, it’s essential.

So: the ? operator should not just mark indeterminacy of truth, but also bear a second-order character: it signals questioning not only of the statement’s truth, but of the act of questioning itself.


2) Formal toy semantics for ? (supervaluation + meta-questioning)

Here’s a minimal formal setup to capture both indeterminacy and a reflexive question-intention. This is meant for a handout or a “classroom toy model”; it’s not a full dissertation-length system, but enough to illustrate and test the concept.

2.1 Language

  • Let L be a propositional / first-order language with a truth-predicate T(x) (or just a propositional “sentences as objects” style).
  • Introduce a unary operator ? applied to well-formed formulas φ: ?φ.
  • Introduce a second-order operator ?? (optional) to mark question-reflection: ??φ reads, “I question whether φ is the kind of question it claims to be” (i.e., question-about-question).

2.2 Precisifications (supervaluationist setup)

  • Define a set of admissible precisifications Π. Each precisification π∈Π is a classical interpretation of L (assigning truth-values in {T, F}) for each atomic sentence, including sentences with T.
  • But not all self-referential / higher-order question-reflection sentences need to be allowed in all precisifications. We can restrict Π so that for any π∈Π:
    • If a sentence involves ??, its interpretation in π must respect a stability clause: π must assign truth in such a way that question-intentions do not collapse trivially into “true / false only.” (This mimics restricting precisifications to avoid very pathological self-referencing “I am not a question” loops.)
    • Alternatively: allow all, but track second-order indeterminacy (see below).

2.3 Semantic clauses

Define the supervaluation semantics for ? and ?? as follows:

  • A sentence φ is super-true if it is true in all π∈Π.
  • φ is super-false if it is false in all π∈Π.
  • Otherwise, φ is indeterminate.

For the question operators:

  1. ?φ (first-order question) is super-true iff φ is not super-true.
    • Intuitively: ?φ = “It is not the case that φ is unambiguously (in all precisifications) true.”
    • ?φ is super-false iff φ is super-true.
    • In other cases (if φ is indeterminate), ?φ may itself be indeterminate (depending on exactly how you set up composition).
  2. ??φ (meta-question) is super-true iff there is at least one precisification π such that in that precisification, the act of questioning φ (i.e., interpreting ?φ) does not correspond to a “stable question”. Formally:
    • Let’s say in each π, there’s a predicate or evaluation criterion Qπ​(φ) that determines whether in π, ?φ is treated as a legitimate question (i.e., nontrivial questioning, not just “φ false / true”).
    • Then: ??φ is super-true if Qπ​(φ) fails in at least one π.
    • ??φ is super-false if Qπ​(φ) holds in all π.
    • Otherwise, ??φ is indeterminate.

(This is a toy clause — in a full system you would need to define exactly what “legitimate questionhood” means in each precisification.)


3) Worked Examples (Toy Handout)

Here are some example sentences + how they might be evaluated under this toy semantics.

Example A: Simple non-paradoxical sentence

Let p = “It rains.”
Consider ?p.

  • In each π∈Π, p is either T or F (classical).
  • Suppose in all precisifications, p is sometimes true, sometimes false (i.e., it’s not fixed). Then p is not super-true.
  • So ?p is super-true (because the semantic clause says: ?φ is super-true if φ is not super-true).
  • This matches our intuition: “It is not unambiguously true that it rains” — a genuine question-intention.

Example B: Liar-style sentence (revenge-type)

Let L = “L is not super-true.” (the canonical super-laier). Now consider:

  1. ?L — “I question whether L is (super-)true.”
  2. ??L — “I question whether ‘L is not super-true’ is itself a stable question.”

Evaluation under toy semantics:

  • For some π∈Π, you might assign L = T; for others, L = F. That is typical for a revenge-style situation. So L is indeterminate (neither super-true nor super-false).
  • Then ?L is super-true (because L is not super-true in every precisification).
  • But what about ??L? That depends on whether in some precisifications, ?L is not “stable” as a question. If in some precisifications, Q_\pi(L) fails (i.e., we interpret ?L not simply as a “this is uncertain” but as a mis-question, or a destabilized questioning act), then ??L is super-true. That means: “Yes, I even question whether my own question ‘L is not super-true’ is a proper question or stable act of questioning.”

This avoids a direct contradiction: you don’t force L to be super-true or super-false, but you allow that the question-intention (?L) is itself non-final; and then you explicitly reflect (??L) on that instability.


4) Reflection / Implications for Teaching or Dissertation

Here’s how you might use this toy model in your dissertation, or in a classroom (or both):

  1. Pedagogical tool:
    • Present students with L and ?L. Ask them: “Is ?L a better way to handle the Liar than just declaring L undefined?”
    • Then pose ??L: have them reflect: “What does it mean to question one’s own question? Is there a kind of ‘meta-uncertainty’?”
    • This helps concretize the idea from Many Roads… that questioning itself is not monolithic — it can be questioned, destabilized, refined.
  2. Dissertation development:
    • Use the toy semantics to formalize a portion of your argument, showing that the ? operator (plus maybe ??) can be given a precise, supervaluationist semantics.
    • Use the restriction on precisifications (or the stability clause) to mirror your philosophical argument from Many Roads…: not all “questions” are legitimate — question-intention itself requires reflection.
    • Then analyze revenge paradoxes (like the Liar) in light of ??: show that some revenge sentences become higher-order indeterminate rather than outright contradictory.
    • Finally, you can connect this to pedagogy: how teaching ? and even ?? can help students develop a more nuanced understanding of logic, truth, and inquiry — not just false / true, but questioning stability.

Ancient Cave Paintings

15 Saturday Jun 2024

Posted by nightingale108 in Questions in Logic

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Tags

animals, art, poetry

If you'll allow my own special crudeness
A disability of being born a caveman
In a world where we have become powerful.

I like deer and buffalo.
I don't get hungry as often as you do, you have to eat all the time
yet my hunger is deeper.

My work is a triumph, it is pure magic
To make a likeness
On how animals move and still themselves.
there is nothing more excellent.

Everyone is a genius; I mean that; we jostle for attention.

I tried to follow this world, not knowing the many worlds under this thin veil. the one the Goddess changes to suit her mood. Cling to her veil and get swept away

(the Goddess is busy being glorious, voluptuous, serene.)

Genius does not depend on competition or collaboration.
It does not depend on what other people are doing or what they have or believe. 

The pioneers that get ignored, enumerated.

1) A monkey's hands are a pure genius.
2) A bird's beak is genius
3) The designs of spiders
4) The Stygian hollows of a wasp nest
5) sloths are lazy? Whatever it is they do is genius.
...

Some say our magic gets more and more real,
As if real or unreal was something I could weigh in my hand.

I see these animals and plants as they are to me,
their liquid intelligence commanding such graceful movements
stooping for water, hunting and praying to escape a hunt
why am I not recognized as being among them?

Is my magic still excellent?
even if I find myself in this time?

we still need our own liquid grace, our houses like the wasps,
we need the Art of the Sloth more than we know.

Now the old magic is called vandalism.
Is it because I stoop for the water and food I find
in an urban wilderness? I join the fox and the bird in drinking from a puddle in the park. What is good enough for them, is good enough for me.

To be truly wild is to live like a flame
brilliant, fragile
I feared for my life among cavemen,
and if I made a mistake I would be dead.

we have greater fear now

fear made us live, goading us to nourish our senses, of smell, of bare touch on soft cold earth, the brush that paints dew on our skin.

Plants appeared mighty then. A plant for every illness, every wellness, every star in the ancestral night sky. Their deep magic was dominant, not to be enslaved. A factory conformity of plants, called farming, should we allow that kind of life into our circle, where some of us are weeds? What does it mean to live as a farmer, and not a hunter?

Fear is collectively generated.

We cannot blame a few men or one god.

the colors I have touched on a cave wall, my magic of likenesses
On the subject of grace in the animal life, Now
I cannot paint them in a way that they are 20,000 years old.

My work earns destitution, donations of fear disguised as care, and a place among the gods... the one we created so we could deposit our fears into him.

such monstrous collective activity. 

yet, I accept your fear because that is what you need. 

I will be that foolish god for you, because a caveman knows not to guard his precious bulk against all the pain that courage brings.

I anoint you with a prayer for grace, and

"There is a hell of a good universe next door, let's go." --ee cummings

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