Your cognitive sword is skepticism, propelling you forward thrusting and parrying at the devious world of deception?

"A scratch and my arm's off, but the other impels a sword." — ucarr

I figured I could count on you to carry on.

Consider: ∧². This is the higher order of conjunction. So, the conjunction of conjunction might be written as a+ba+b. — ucarr

Non of this is well-formed. Might as well write "§⊥φ±".

There are no laws prohibiting the multiplexing of a=a. — ucarr

Yes, there is. Substitution is extensional. Indeed, that's the very definition of "=".

Definition 1.1 (Extensionality). If A and B are sets, then A= B iff every element of A is also an element of B, and vice versa. — Open Logic, p. 25

I think I'm done here.

Consider: ∧². This is the higher order of conjunction. So, the conjunction of conjunction might be written as a+ba+b. — ucarr

You quote me incorrectly. Here's the undistorted quote.

Consider: $∧^2$. This is the higher order of conjunction. So, the conjunction of conjunction
might be written as $a+b^{a+b}$. — ucarr

Higher order conjunction (across symmetry) suggests itself as a central component of mind emergent from brain. If there's truth in this conjecture, then it might be the type of symmetric extension that empowers your mind to understand the logical rules you cite as your refutations of my conjectures.

I respect your decision to walk away from our engagement here. Your input has motivated me towards a degree of logical clarity I couldn't've achieved without you. Thank-you for your time and energy.

I don't think your work here is done. For that to be the case, you need to write a logical proof establishing that the two quotes below confirm extension by substitution is disjoint from identity.

There are no laws prohibiting the multiplexing of a=a.
— ucarr
Yes, there is. Substitution is extensional. Indeed, that's the very definition of "=". — Banno

Definition 1.1 (Extensionality). If A and B are sets, then A= B iff every element of A is also an element of B, and vice versa. — Open Logic, p. 25

Your proof must counter-narrate:

Likely the most simple symmetry element is identity, represented by E (from the German word "einheit", meaning unity). Identity is the symmetry element of existence; all objects have this symmetry element, even if they have no other symmetry element. — Spectroscopy Online

I never got an answer to any of my questions.

In the framework I use, truth is not a metaphysical essence but a relation intrinsic to our practices of justification. To say a proposition is true is to claim that it holds up under the public criteria of a form of life, viz., that it connects belief with what obtains in the world. Truth marks the point where our language intersects with reality and is further illuminated by understanding: not merely that the world is as the proposition says, but that we can see how and why this is the case. The correspondence is real and, in some language-games, legitimately pictorial, e.g., where mapping, modeling, or measurement aim to reproduce structure or proportion. Yet even there, “picturing” works only because it is guided by understanding: without grasping how the representation functions, no degree of accuracy would amount to knowledge. Understanding is easily overlooked because it seems built in, but it is what allows us to apply the criteria of truth, to distinguish success from coincidence, evidence from echo. What makes a proposition true is the state of affairs that obtains; what makes that truth knowable is the grammar of our interaction with it, governed throughout by understanding. In this sense, truth is both discovered and articulated, anchored in reality and shown through our capacity to comprehend its order.

Formal definitions of truth, though indispensable in logic, leave this fuller picture out. Tarskian or semantic schemas (“‘p’ is true if and only if p”) capture the structure of truth but not its life. They specify conditions of equivalence but remain silent about how truth functions within inquiry, how it guides belief, sustains correction, and grounds public justification. Formal accounts strip truth of human context: they can model consistency but not meaning, accuracy but not understanding. What they describe is the form of truth’s operation, not its practice. Truth, as lived and recognized, is not a symbol in a metalanguage but what’s embodied in our forms of life (our language games), the point where the world’s order and our conceptual order momentarily coincide.

We are homosexual at an early age" – why is that suddenly true? — Astorre

Homosexuality supporting later heterosexuality is one of my conjectures that is subject to refutation. — ucarr

I never got an answer to any of my questions. — Astorre

You've gotten a response to each and every post you've addressed to me. As I say above, my conjecture about sexual identity ideation is subject to refutation. Possible refutation confers legitimacy upon conjecture.

My post is about a=a, or identity. Sexual identity ideation spins out from this center as one of the core identities of the human individual: gender identity. The young child learns basic attributes of his identity. As he comes to awareness of sexual difference, he seeks esteem for his own group first. This seems natural to me because, as I've said, you must learn to love yourself before you are equipped with the self-esteem to begin to love the very different other. Whether or not the individual advances beyond the island of his own gender and, crossing over to the other side, discovers and consummates the nirvana embedded in love beyond selfhood is an open question.

Statistically, it's supposed to be the case that nine out of ten do, with one out of ten, or ten percent of the population, being homosexual.

All of this is possibly refutable. I expect you, now, to bring on the counter-narrative, if you have one. This instead of you continuing to attack such trivia as my diction, or the other inflated, reputation-building rhetorical device, attacking the opponent's methodology while abstaining from entering the trench war. The authentic battle is down in the trenches where the fighting rages over the logic of the premises and the viability of the propositions arising from them. My post is filled with possibly refutable propositions. Do you attack their logical details, as Banno does? No. You attack the diction of my sentences instead of their logic and conformity to reality, as evidenced below:

It's like an exercise in the aesthetics of symmetry and transformation that remains at the level of abstract contemplation. You wrap basic arithmetic in a poetic veneer, calling it the "dynamism of identity" and the "emergent property of truth," but what's next? — Astorre

What do you have to say about the logic of symmetry and transformation presented as the dynamism of identity? Have you read about this, or heard it being discussed? You imply it's cliché, but you cite no standard references. You ask, "Where is the breakthrough beyond what is already known?" Might the blossoming of human identity into symmetry and transformation from the extensional substitution of a=a nevertheless unitary be the breakthrough fusion of QM uncertainty you're looking at but not seeing?

My Identity Manifesto is filled with attack points. Have you read it? If you have, why are you attacking me instead of attacking my propositions?

My general impression of your narrative says, "You want to pair the metaphysics of knowledge relationships (p →q), as dynamically governed by an emergent and energetic inter-relation, viz., truth, with empirical experience. Dynamical, energetic identity transformations across space and time forming symmetries that conserve identity and support an enduring POV embody the living experience of truth.

We gaze into the looking glass and learn to live with our mirror-image devilish playmate.

My general impression of your narrative says, "You want to pair the metaphysics of knowledge relationships (p →q), as dynamically governed by an emergent and energetic inter-relation, viz., truth, with empirical experience. Dynamical, energetic identity transformations across space and time forming symmetries that conserve identity and support an enduring POV embody the living experience of truth. — ucarr

In other words, truth isn’t some hidden essence, it’s what happens when our justified beliefs line up with the facts of the world, or the way the world is. We test truth through shared practices (Wittgenstein's language games, which are governed by implicit rules), our forms of life, where we check, correct, and agree on what counts as evidence. In some cases, like science or mapping, truth can be pictured or measured, but even there it works only because we understand what the picture means and how it connects to reality. Understanding (JTB+U) isn’t optional; it’s what lets us tell genuine truth from lucky coincidence.

Formal theories of truth, like those used in logic, capture a structure but not its lived reality. They can show when a statement fits certain conditions but can’t explain how truth operates in lived reality, how it shapes belief, correction, and meaning. Truth, as we actually experience it, isn’t a Tarski formula (“p” is true iff p.) but a practice. There's a philosophical bridge between ontology and epistemology: the world has its own structure (what obtains), and we have our structures of reason, language, and justification. Truth is the point where those two orders (the world and epistemology) align.

Your cognitive sword is skepticism, propelling you forward thrusting and parrying at the devious world of deception? — ucarr

And what is your proposed better alternative to that?

Your cognitive sword is skepticism, propelling you forward thrusting and parrying at the devious world of deception? — ucarr

And what is your proposed better alternative to that? — Copernicus

I have no better alternative to propose. I'm not judging your outlook. Skepticism is a worthy attitude given our world so fraught with deceptions. Like other useful things, it needs to be carefully controlled, lest good turn to bad. Life tricks us at both ends. Too trusting and we get duped; too skeptical and we get deprived.

No, in posting my previous communication, I was attempting to better understand you. When I have some idea how the other person tends to see the world, that helps me understand individual statements which I can then put into context.

Holism

• The math operators are the questions; the equal sign is the answer; the variables and constants are the subjects

• Within this environment, the truth is dynamic identity symmetrical and conserved. It is the emergent whole arising from the interplay of subjects, questions and answers, and the math logic that integrates their dynamic functions

• Subject_Question_Answer form a trio that animates creation.

• The unsearchable fundamental is identity.

• The math operators are identity operators that ground zero and one. This binary duo is sufficient to represent all of creation

• N + Additive Identity (0) = n; N – Subtractive Identity (0) = n; N * Multiplicative Identity (1) = n; N / Divisive Identity(1) = n

• Truth outside of temporal dynamism is neither created nor destroyed, but only revealed

• Identity outside of temporal dynamism is neither created nor destroyed, but only revealed

• The immortal soul of an existing thing outside of temporal dynamism is neither created nor destroyed, but only revealed

• The immortal soul has expression as the invariant point of a topological manifold