Is there an Ultimate Logic?

[watsup]

I haven't. Can you give an example of where the rule is violated?

Who said it was violated? I was making fun of your claim that A=A somehow shows that there is a God.
And if you want to know more about Bizarro World, grab some Superman comics.

 

[ataraxia]

Well no, that isn’t the only argument. I agree it is the most coherent explanation.

Why more coherent? Seems pretty wildly speculative and outlandish to me.

Can you imagine an alternate world where A ≠ A?

“x = x” is a statement of the law of identity, one of the three classic laws of thought in Aristotelian logic. It's often taken as axiomatic in classical logic, meaning it’s not proven but assumed. But not all systems of logic accept it without question. It is just a convention of classical logic.

In non-classical logics—such as paraconsistent logic, quantum logic, or fuzzy logic—identity behaves very differently or breaks down altogether. These systems are internally consistent and empirically and pragmatically useful (e.g., in quantum computing and AI), which undermines the idea that the classical law of identity is a necessary universal. Entirely different systems of logic, often contradictory, seem to apply when dealing with different scenarios or contexts. Often, like in quantum mechanics, we don’t even understand WHY there are such differences in the systems of logic in these different contexts- we just know that that’s what we observe and that’s what works in that context. That seems to be good enough reason- necessary AND sufficient reason.

That’s why it seems logic is better understood as a human invention for modeling various experiences and observations than as any single and universal divine law.

 

[Gozaburo]

Why more coherent?

I've laid out that argument a couple of times. Should we relitigate here once again?

x = x” is a statement of the law of identity, one of the three classic laws of thought in Aristotelian logic. It's often taken as axiomatic in classical logic, meaning it’s not proven but assumed. But not all systems of logic accept it without question. It is just a convention of classical logic.

In non-classical logics—such as paraconsistent logic, quantum logic, or fuzzy logic—identity behaves very differently or breaks down altogether. These systems are internally consistent and empirically and pragmatically useful (e.g., in quantum computing and AI), which undermines the idea that the classical law of identity is a necessary universal. Entirely different systems of logic, often contradictory, seem to apply when dealing with different scenarios or contexts. Often, like in quantum mechanics, we don’t even understand WHY there are such differences in the systems of logic in these different contexts- we just know that that’s what we observe and that’s what works in that context. That seems to be good enough reason- necessary AND sufficient reason.

That’s why it seems logic is better understood as a human invention for modeling various experiences and observations than as any single divine law.

Classical logic's axioms hold at a metalevel, that's why they're called logical axioms. They're not arbitrary. Non-classical logics still rely on these axioms to even get off the runway and - ultimately - do not end up violating the laws of logic (the opposite, they rely on them) to reach conclusions.

 

[Gozaburo]

Best John McEnroe shout: YOU CANNOT BE SERIOUS!. that you actually believe that identity proves your God.

If after all of this back and forth this is what you understand the depth of the argument to be there's really no point in having a dialogue.

 

[watsup]

If after all of this back and forth this is what you understand the depth of the argument to be there's really no point in having a dialogue.

I understand that A=A means that there is a God is a circular argument at absolute best and, as such, has no more merit than any other figment of imagination God no matter what sort of snake oil you are trying to sell. No one at all is buying it, and especially when the “dialogue” is strictly hemmed in by your pre-selected philosophical paradigms.

 

[Gozaburo]

I understand that A=A means that there is a God is a circular argument at absolute best and, as such

Well this isn't the argument so you flunked.

 

[watsup]

Well this isn't the argument so you flunked.

I am not the one making up imaginary entities and trying to “prove” them with philosophical meandering. You have flunked every test that has been given you by those who have grounding in philosophy.

 

[Gozaburo]

I am not the one making up imaginary entities and trying to “prove” them with philosophical meandering. You have flunked every test that has been given you by those who have grounding in philosophy.

If you can’t even understand the arguments then how are you able to decipher who’s winning the debate?

Maybe just sit this one out bud.

 

[ataraxia]

I've laid out that argument a couple of times. Should we relitigate here once again?

You have laid out one possible hypothesis or narrative to explain why the laws of classical logic hold. I admit it is *A* logical possibility. It’s a cool story and internally logically consistent. But it’s not the only possible hypothesis and there’s nothing logically necessary about it.

But as we are showing here, this hypothesis doesn’t seem to hold up in trying to explain ALL the phenomena we see in this world beyond the every-day “common sense” world (the classical world). So it’s a hypothesis which fails. That’s OK- that happens all the time. In science, when that happens, you just dust yourself off and move on.

And you also have admitted that it’s not the only logical possibility. There are many other possible, logically consistent possible hypotheses and narratives we could try to come up with to try to explain these phenomena. Which is right? Who knows right now? We just don’t know. I guess we have to keep using our imagination yo come up with better hypotheses and narratives, also internally logically consistent, to hopefully try to explain these broader range of phenomena we are observing. That’s work under progress right now. But it’s true we don’t have a good one yet to replace the old classical one yet.

And that’s OK- we don’t know everything- we never have, and probably never will- but we do know some things, and we use those things as tools to keep probing, keep learning, and keep trying to survive, and even thrive, where we can. That’s how we have always done it.

There’s nothing logically contradictory, inconsistent, or circular about that.

Classical logic's axioms hold at a metalevel, that's why they're called logical axioms. They're not arbitrary. Non-classical logics still rely on these axioms to even get off the runway and - ultimately - do not end up violating the laws of logic (the opposite, they rely on them) to reach conclusions.

Saying that all logics ultimately rely on classical axioms is like saying all languages rely on Latin grammar—it reflects a historical starting point, not a necessary foundation. Just as non-Euclidean geometry doesn't secretly rely on Euclid to make sense, non-classical logics can be internally coherent without assuming classical identity or non-contradiction- which they don’t.

Calling the axioms of classical logic 'metalevel' doesn’t prove they’re necessary—only that they’re foundational within one logical framework and construct. Other systems have different foundations and are equally internally consistent- and it’s not just made-up random logic: they apply in different contexts in the real world and work just as well in those contexts as classical logic in our every-day “common sense” world and experiences with which we are most familiar.

But there’s no neutral metalevel from which to declare classical logic the arbiter of all possible reasoning.

For example, in quantum computing, the law of the excluded middle doesn’t necessarily apply. In fuzzy logic, identity and contradiction can both be partial. These aren’t toy examples—they’re used in real technologies and physical models. That suggests classical logic is just one tool among many, not a universal gatekeeper or gold standard.

And in quantum computing, we don’t even really understand WHY that logic works the way it does. It’s just the way we have seen things to work in the quantum realm- that’s as far as our knowledge and observations take us- and that’s good enough logical foundation with which to build powerful supercomputers- no different than the chimp who just knows that the hard rock is a good enough tool with which to crack nuts. What more does he need to know to keep cracking those nuts? Rocks and quantum logic are both tools we use to accomplish tasks.

 

[Gozaburo]

Calling the axioms of classical logic 'metalevel' doesn’t prove they’re necessary—only that they’re foundational within one logical framework and construct. Other systems have different foundations and are equally internally consistent- and it’s not just made-up random logic: they apply in different contexts in the real world and work just as well in those contexts as classical logic in our every-day “common sense” world and experiences with which we are most familiar.

But there’s no neutral metalevel from which to declare classical logic the arbiter of all possible reasoning.

The problem is you literally can’t even make a coherent argument without presupposing the axioms in question. To even suggest alternative possible models, you assume these axioms to form coherent sentences. You can suggest they’re arbitrary and not foundational, but you can’t do so without having an irrational and incoherent position.

You have laid out one possible hypothesis or narrative to explain why the laws of classical logic hold. I admit it is *A* logical possibility. It’s a cool story and internally logically consistent. But it’s not the only possible hypothesis and there’s nothing logically necessary about it.

But as we are showing here, this hypothesis doesn’t seem to hold up in trying to explain ALL the phenomena we see in this world beyond the every-day “common sense” world (the classical world). So it’s a hypothesis which fails.

Can you demonstrate where the hypothesis fails? Again, I’m not opposed to accepting an argument that has more explanatory power, is internally consistent, and is more coherent.

“Just is” and the blind assumptions of hard empiricism are not better arguments. Sense data as an epistemic starting point is not a better argument.

Obviously I accept there are other arguments about the possibility of knowledge, I just don’t think they’re good ones.

 

[ataraxia]

The problem is you literally can’t even make a coherent argument without presupposing the axioms in question. To even suggest alternative possible models, you assume these axioms to form coherent sentences. You can suggest they’re arbitrary and not foundational, but you can’t do so without having an irrational and incoherent position.

You're right that in this conversational context—using human language, reason, and debate—we're drawing from the toolkit of classical logic. But that doesn’t prove classical logic is the universal ground of all possible reasoning. It just shows that classical logic is well-suited for this context, the same way classical Newtonian mechanics is well-suited for driving a car.

But just like we wouldn't use classical Newtonian physics to describe black holes or subatomic particles—because it breaks down there—we shouldn't assume classical logic is the only framework capable of making sense of reality. In contexts like quantum physics, fuzzy systems, or inconsistent databases, classical logic not only fails but can give dangerously misleading results.

Saying “you can’t argue without classical logic” is like saying “you can’t move without Newtonian physics.” It's true that it works fine for traffic and walking to the grocery store- but fails at black holes, electrons, quantum computing, etc, etc.... Context matters. As the French philosopher Jacques Derrida said: “There is nothing outside the text (context).”

So when you say “you can't make a coherent argument without classical logic,” it's like saying “you can’t measure time without Newtonian absolute time.” It certainly works quite well for a while and in certain everyday contexts—but Einstein and quantum mechanics proved it's not universal. Context reshapes what coherence even means.

And also, when we use classical logic to talk about non-classical logics, it's a bit like using English to describe Chinese grammar. There is nothing inconsistent about that. It works for translation and meta-level discussion, but it doesn’t mean Chinese grammar and vocabulary depend on English grammar and vocabulary to function. There is no meta-grammar, and no evidence of a universal lawgiver for the laws of grammar or for any universal vocabulary. Our laws of grammar and our vocabularies are man-made and always contingent. Likewise, non-classical logics can be internally coherent and useful without secretly somehow relying on classical axioms. They don't. They have been constructed so that they can and do stand independently on their own premises and observations.

Can you demonstrate where the hypothesis fails? Again, I’m not opposed to accepting an argument that has more explanatory power, is internally consistent, and is more coherent.

The hypothesis that the laws of classical logic are universal is what fails. We have found through observation and experience that they are not universal. So we have had to come up with other logics, based on other premises and observations, to explain those other phenomena in those other realms. But the observations are coming first- our attempts to create premises for and construct new systems of logic to try to understand, explain, and predict those observations have only come later. But WE are making these systems of logic up, just like our systems of vocabulary, categorization, and language. They are all man-made and contingent. And we change them as we need to.

And with that hypothesis also goes the hypothesis that we NEED such logical universals as a foundation with which to make sense of our empirical observations- to somehow "ground" them. Empirical observations don't need grounding. They are primary and come first- the basic foundations and premises of our systems of logic which we construct on top of them as foundations. The systems of logic we are creating to understand and make sense of our observations them is built on those experiences- it's not the other way around. Godel, Wittgenstein, the logic of quantum mechanics, etc, etc.... all seem to confirm this, from many different perspectives and starting points of argument.

Obviously I accept there are other arguments about the possibility of knowledge, I just don’t think they’re good ones.

We can argue about which ones we currently think are better or worse, based on our latest understandings, experience, and "common sense"- but the fact that you accept that there are other possibilities takes away the argument that there is anything logically necessary about your hypothesis.

 

[Gozaburo]

But just like we wouldn't use classical Newtonian physics to describe black holes or subatomic particles

A particularly bad analogy because Newtonian physics is a descriptive model, not prescriptive, defining coherence itself.

Saying “you can’t argue without classical logic” is like saying “you can’t move without Newtonian physics.” It's true that it works fine for traffic and walking to the grocery store- but fails at black holes, electrons, quantum computing, etc, etc.... Context matters. As the French philosopher Jacques Derrida said: “There is nothing outside the text (context).”

Derida is saying meaning is derived from textual or cultural contexts, not fixed truths. The laws of logic apply across language, across culture, across all sociological contexts, so this is another bad example.

And also, when we use classical logic to talk about non-classical logics, it's a bit like using English to describe Chinese grammar. There

Same thing here. Languages are conventional with arbitrary rules.

The hypothesis that the laws of classical logic are universal is what fails. We have found through observation and experience that they are not universal. So we have had to come up with other logics, based on other premises and observations, to explain those other phenomena in those other realms. But the observations are coming first- our attempts to create premises for and construct new systems of logic to try to understand, explain, and predict those observations have only come later. But WE are making these systems of logic up, just like our systems of vocabulary, categorization, and language. They are all man-made and contingent. And we change them as we need to.

Again, non-classical logics still assume the laws of logic at a metalevel. To give some clear examples of what I mean: Quantum uses A=A for states and LEM post-measurement; fuzzy sums A ∨ ¬A to 1; paraconsistent keeps LEM, etc. You haven't demonstrated this is not the case.

And with that hypothesis also goes the hypothesis that we NEED such logical universals as a foundation with which to make sense of our empirical observations- to somehow "ground" them. Empirical observations don't need grounding. They are primary and come first- the basic foundations and premises of our systems of logic which we construct on top of them as foundations. The systems of logic we are creating to understand and make sense of our observations them is built on those experiences- it's not the other way around. Godel, Wittgenstein, the logic of quantum mechanics, etc, etc.... all seem to confirm this, from many different perspectives and starting points of argument.

I don't agree that empirical observations don't need grounding, nor do I grant you that this claim is true, though it is a recognized position often called naïve empiricism.

First of all, I don't think what you're saying is what Godel, Wittgenstein, or quantum mechanics points out. Godel and Wittgenstein certainly were not naive empiricists and - on the contrary - their findings, if anything, damage the naive empiricist worldview more than support it. Kant identified almost 250 years ago that a priori categories (like identity, causality, etc.) structure experience - observations aren't "raw" but shaped via theory-laden logical principles, which require an epistemic ground. To even claim "observations don't need grounding" assumes logical coherence to produce an argument i.e. you're using grounded logic to deny grounding.

 

[watsup]

D

If you can’t even understand the arguments then how are you able to decipher who’s winning the debate?

Maybe just sit this one out bud.

Makes no difference. Your philosophical meandering doesn’t show that there is a God of actuality, only a God of your imagination, just like every God ever proposed by a human. It’s just a different sort of superstition on your part.

 

[ataraxia]

A particularly bad analogy because Newtonian physics is a descriptive model, not prescriptive, defining coherence itself.

Absolutely—Newtonian physics is descriptive. But so is logic. The claim that logic is "prescriptive" only makes sense within a framework that already treats coherence, identity, and non-contradiction as inviolable. That’s circular. The point of the analogy wasn’t that logic is physics—but that different models are useful in different domains, and insisting one model defines coherence *for all domains* is like saying Euclidean space defines all geometry.

“Defining coherence” isn’t the same as being metaphysically necessary. Coherence is a property within a system, not proof that the system maps directly onto ALL reality in some final way. Other systems define coherence differently (e.g. paraconsistent logics), and they’re still logically valid.

Derida is saying meaning is derived from textual or cultural contexts, not fixed truths. The laws of logic apply across language, across culture, across all sociological contexts, so this is another bad example.

True—Derrida was primarily concerned with language and meaning. But that’s the point: meaning—even logical meaning—is mediated through language, symbols, and interpretation. We never access a “pure logic” outside of signs and frameworks. And that idea—that we can’t appeal to context-free universals—applies just as much to logic as it does to linguistics. That’s why even logical axioms get revised or recontextualized in different systems (e.g. quantum logic, fuzzy logic, modal logic).

To quote Wittgenstein:
"The limits of my language mean the limits of my world."
"Even logical truths only function within a language game- they are not outside of grammar, they are part of it."

Same thing here. Languages are conventional with arbitrary rules.

Sure—natural languages are arbitrary in terms of grammar or syntax. But formal logic is also a constructed system, not revealed metaphysical necessity. Peano arithmetic, ZFC set theory, modal logic—all are rigorously constructed, but none are immune to revision or replacement. The fact that we can create multiple, non-equivalent logical systems—each internally valid—shows that logic is not “non-arbitrary” in the metaphysical sense, only in the intra-system sense.


In other words, logic is conventional at the level of system choice, even if it becomes rigid within that system. We just construct and choose the system that seems to work best within the context in which we are working. And if we find it is not working anymore because of certain observations, we then contruct another logical model to make sense of those further observations. But we are making this stuff up. Reality is under no obligation to always follow those rules under all circumstances. It's always contingent on the context.

 

[ataraxia]

First of all, I don't think what you're saying is what Godel, Wittgenstein, or quantum mechanics points out. Godel and Wittgenstein certainly were not naive empiricists and - on the contrary - their findings, if anything, damage the naive empiricist worldview more than support it. Kant identified almost 250 years ago that a priori categories (like identity, causality, etc.) structure experience - observations aren't "raw" but shaped via theory-laden logical principles, which require an epistemic ground. To even claim "observations don't need grounding" assumes logical coherence to produce an argument i.e. you're using grounded logic to deny grounding.

Kant’s insight about theory-ladenness is important—and I’m not denying it. But what that actually shows is that *all knowledge is mediated*, including logic itself. Kant was not defending logical absolutism—he was describing the conditions under which human experience is structured, not declaring metaphysical necessity.

In fact, modern pragmatists like Sellars, Quine, and Putnam show that even Kant’s a priori categories are up for revision, in light of scientific developments. Quantum physics, to use the example we have been talking about, radically challenges traditional logical categories and notions of causality and identity.

So if even Kant's categories evolve with science, observations, and theory, then logic can't be a fixed metaphysical anchor or grounding- it's a shifting frame, pragmatically responsive - in turn based on context, observation, experience, and utility. Using a system to show the boundaries of the system isn't incoherent—it's insightful. That's what Gödel, Turing, and even Wittgenstein did. Recognizing that the ground shifts doesn’t require being groundless—it just requires intellectual humility about what counts as foundational, and an openness to new ideas, models, and seeing the world.

But as I talk to you, it is starting to become clear that I don’t think what’s really bothering you is grounding in logic itself. What’s bothering you is the absence of a final, all-encompassing answer—a Theory of Everything (or TOE, as the physicists like to call it- something which they will admit is a pretty ambitious project). But, what you are looking for is even bigger and even more ambitious that THAT: a TOE not just in physics, but something that also explains ethics, consciousness, society, meaning, and all existence itself. That’s certainly a very understandable and a deeply human impulse: we want closure, a unified picture, something that makes sense of everything. But we’re not there—and we may never get there. But simply slapping on a label like “God,” “absolute logic,” or “metaphysical grounding” on that gap doesn’t resolve the uncertainty. It doesn’t offer any real explanatory power or coherence—it just rebrands the unknown as if it were known. That’s not grounding anything. That’s just putting a name on your discomfort with ambiguity and ignorance. We may just have to learn to make ourselves comfortable in such ambiguity and not knowing everything. That always leaves us open to new ideas, new observations, and new models. That lack of certainty may not just be a weakness and a bug, but the feature that leaves us open to learning more.

If anything, insisting on a single universal logic or metaphysical ground risks flattening and impoverishing such richness of human inquiry, where multiple models (mathematical, ethical, cultural, psychological) coexist—not always neatly, but often usefully.

I don't know if I quoted you one of my favorite quotes from the late Nobel laureate physicist Richard Feynman before, but even if I did, it's worth repeating, because I think it captures this sentiment and mindset of modern science. (see next post for it, it's kinda long)

 

[ataraxia]

(con'd from my previous post):
"The scientist has a lot of experience with ignorance and doubt and uncertainty, and this experience is of very great importance, I think. When a scientist doesn't know the answer to a problem, he is ignorant. When he has a hunch as to what the result is, he is uncertain. And when he is pretty darn sure of what the result is going to be, he is still in some doubt. We have found it of paramount importance that in order to progress we must recognize our ignorance and leave room for doubt. Scientific knowledge is a body of statements of varying degrees of certainty — some most unsure, some nearly sure, but none absolutely certain.
Now, we scientists are used to this, and we take it for granted that it is perfectly consistent to be unsure, that it is possible to live and not know. But I don't know whether everyone realizes this is true. Our freedom to doubt was born out of a struggle against authority in the early days of science. It was a very deep and strong struggle: permit us to question — to doubt — to not be sure. I think that it is important that we do not forget this struggle and thus perhaps lose what we have gained.

If we take everything into account — not only what the ancients knew, but all of what we know today that they didn't know — then I think that we must frankly admit that we do not know.
But, in admitting this, we have probably found the open channel. Such humility and admission of ignorance may not be a weakness, but a strength. This is not a new idea; this is the idea of the age of reason. This is the philosophy that guided the men who made the democracy that we live under. The idea that no one really knew how to run a government led to the idea that we should arrange a system by which new ideas could be developed, tried out, and tossed out if necessary, with more new ideas brought in — a trial and error system. This method was a result of the fact that science was already showing itself to be a successful venture at the end of the eighteenth century. Even then it was clear to socially minded people that the openness of possibilities was an opportunity, and that doubt and discussion were essential to progress into the unknown. If we want to solve a problem that we have never solved before, we must leave the door to the unknown ajar.

We are at the very beginning of time for the human race. It is not unreasonable that we grapple with problems. But there are tens of thousands of years in the future. Our responsibility is to do what we can, learn what we can, improve the solutions, and pass them on.
...It is our responsibility to leave the people of the future a free hand. In the impetuous youth of humanity, we can make grave errors that can stunt our growth for a long time. This we will do if we say we have the answers now, so young and ignorant as we are. If we suppress all discussion, all criticism, proclaiming "This is the answer, my friends; man is saved!" we will doom humanity for a long time to the chains of authority, confined to the limits of our present imagination. It has been done so many times before.
...It is our responsibility as scientists, knowing the great progress which comes from a satisfactory philosophy of ignorance, the great progress which is the fruit of freedom of thought, to proclaim the value of this freedom; to teach how doubt is not to be feared but welcomed and discussed; and to demand this freedom as our duty to all coming generations."

Richard Feynman - Wikiquote

en.wikiquote.org

 

[Gozaburo]

Absolutely—Newtonian physics is descriptive. But so is logic. The claim that logic is "prescriptive" only makes sense within a framework that already treats coherence, identity, and non-contradiction as inviolable. That’s circular. The point of the analogy wasn’t that logic is physics—but that different models are useful in different domains, and insisting one model defines coherence for all domains is like saying Euclidean space defines all geometry.

“Defining coherence” isn’t the same as being metaphysically necessary. Coherence is a property within a system, not proof that the system maps directly onto ALL reality in some final way. Other systems define coherence differently (e.g. paraconsistent logics), and they’re still logically valid.

Can you conceive of a domain where the laws of logic are descriptive or where coherence is system-relative without assuming the laws in question?

True—Derrida was primarily concerned with language and meaning. But that’s the point: meaning—even logical meaning—is mediated through language, symbols, and interpretation. We never access a “pure logic” outside of signs and frameworks. And that idea—that we can’t appeal to context-free universals—applies just as much to logic as it does to linguistics. That’s why even logical axioms get revised or recontextualized in different systems (e.g. quantum logic, fuzzy logic, modal logic)...

Yeah we've been through this one too. Even if we excuse that Wittgenstein presupposes a number of metaphysical categories to even get his argument off of the ground, he then concludes that meaning in words is always contextual and even somewhat arbitrary which, presumably, also applies to the argument he is making!

In other words, logic is conventional at the level of system choice, even if it becomes rigid within that system. We just construct and choose the system that seems to work best within the context in which we are working. And if we find it is not working anymore because of certain observations, we then contruct another logical model to make sense of those further observations. But we are making this stuff up. Reality is under no obligation to always follow those rules under all circumstances. It's always contingent on the context.

As you know, I agree with Quine's suggestion that all worldviews are built on top of a web of presupposed beliefs. The challenge I'm putting forth is for you (or anyone else) to build a worldview which doesn't rely on the laws of logic as essential and necessary axioms.

Kant’s insight about theory-ladenness is important—and I’m not denying it. But what that actually shows is that *all knowledge is mediated*, including logic itself. Kant was not defending logical absolutism—he was describing the conditions under which human experience is structured, not declaring metaphysical necessity...

To be clear: I'm not a Kantian, I was merely invoking him to demonstrate that naive empiricism is bunk.

But as I talk to you, it is starting to become clear that I don’t think what’s really bothering you is grounding in logic itself. What’s bothering you is the absence of a final, all-encompassing answer—a Theory of Everything (or TOE, as the physicists like to call it- something which they will admit is a pretty ambitious project). But, what you are looking for is even bigger and even more ambitious that THAT: a TOE not just in physics, but something that also explains ethics, consciousness, society, meaning, and all existence itself...

I don't think this assessment is fair because you're acting as-if I'm arbitrarily inserting God (like the fallacious god-of-the-gaps argument) instead of providing a sound transcendental argument for God's necessity and attempting to prove it via impossibility of the contrary epistemically speaking. Put very succinctly: either knowledge is accidental or it is purposeful. Since calling knowledge 'accidental knowledge', accidental meaning, accidental laws, accidental logic, et. al., which are all an oxymoron and self-defeating, since knowledge, meaning, laws, logic, inference, etc. all preclude accident in their definitions. Consequently, the nontheist view cannot justify any of its assumptions about the world, knowledge, arguments, laws, and logic; in fact, it assumes the theistic view of purpose/intentionality to even talk about these things.

Equating my argument to 'god-of-the-gaps' argumentation or an arbitrary insertion of God means that you're not truly willing to assess the depth of the critique.

 

[ataraxia]

Can you conceive of a domain where the laws of logic are descriptive or where coherence is system-relative without assuming the laws in question?

Sure: the domain of classical logic. When the observations on the behavior of electrons was studied, it became clear that they were not following that kind of logic. It necessitated creating a whole new system of logic based on different premises.

Yeah we've been through this one too. Even if we excuse that Wittgenstein presupposes a number of metaphysical categories to even get his argument off of the ground, he then concludes that meaning in words is always contextual and even somewhat arbitrary which, presumably, also applies to the argument he is making!

Sure. I could see us potentially observing and learning things in the future where Wittgenstein is proven wrong. But even THAT would be yet another model- contingent on yet further observation

As you know, I agree with Quine's suggestion that all worldviews are built on top of a web of presupposed beliefs. The challenge I'm putting forth is for you (or anyone else) to build a worldview which doesn't rely on the laws of logic as essential and necessary axioms.



To be clear: I'm not a Kantian, I was merely invoking him to demonstrate that naive empiricism is bunk.

I don’t think this assessment is fair because you're acting as-if I'm arbitrarily inserting God (like the fallacious god-of-the-gaps argument) instead of providing a sound transcendental argument for God's necessity and attempting to prove it via impossibility of the contrary epistemically speaking. Put very succinctly: either knowledge is accidental or it is purposeful. Since calling knowledge 'accidental knowledge', accidental meaning, accidental laws, accidental logic, et. al., which are all an oxymoron and self-defeating, since knowledge, meaning, laws, logic, inference, etc. all preclude accident in their definitions. Consequently, the nontheist view cannot justify any of its assumptions about the world, knowledge, arguments, laws, and logic; in fact, it assumes the theistic view of purpose/intentionality to even talk about these things.

Equating my argument to 'god-of-the-gaps' argumentation or an arbitrary insertion of God means that you're not truly willing to assess the depth of the critique.

I appreciate that you're not appealing to a crude “god-of-the-gaps” move, but to a transcendental argument—that knowledge, logic, and meaning presuppose intentionality and purpose, and that only theism can provide that ground. That’s a much stronger and more interesting claim. But I still don’t think it holds up- for a few reasons:

First, the either/or framing—either knowledge is purposeful or it’s accidental—is too rigid. It assumes that purpose must come from a mind like ours, writ large. But that’s importing human categories into metaphysics. Why should “purpose” or “intentionality” be the only valid framework for coherence? That’s a projection, not a proof. Logic, laws, and inference may simply emerge from the structure of the universe—or from the way our minds have evolved to model that structure—not from an external will.

Second, calling non-theistic knowledge “accidental” misrepresents how naturalistic accounts work. Most modern epistemology, from Quine to Sellars to Brandom, treats knowledge as a social/pragmatic process that evolves through correction, feedback, and coherence—not a top-down gift from a purposeful being. It’s not "accidental," it’s emergeny—just like language, ethics, or scientific theories.

Third, you say that inference and logic "preclude accident in their definitions." But that's true within a logical system—not across metaphysical systems. You're presupposing the conclusion: that logic must be grounded in a purpose-giver. But we can also explain the coherence of logic from within the system of human cognition, shaped by evolution, culture, and utility. It's not that logic is random—it's that it’s context-bound and plural.

Finally, you claim that the non-theist “assumes the theistic view” just to reason at all. But that feels like a definitional trap—like saying, “you can’t argue without secretly believing what I believe.” It closes off real dialogue. From a pragmatist or post-structuralist view, meaning and coherence are contingent but functional, not necessarily grounded in a timeless, personal intelligence.

In short: I hear you saying that reason itself points to God. I’m saying that reason may not need a metaphysical origin to function. Maybe it just needs a context, a community, and a commitment to self-correction.

 

[ashurbanipal]

You are moving goal posts by mixing and matching the actualities of the universe such as particular shapes with the human construct of logic. The shape existed in the universe but logic did not since it is a man-made system resulting from the thought and intelligence of the evolution-produced biological brain. Two different tracks—the existence of the universe and man-made systems.




My argument is that mathematics and all of its particular language, symbols, and numbers were constructed by humans in their endeavor to understand the world and the universe in which they reside.

The position you are describing is called formalism. The idea is that logic and mathematics are just (as you say) human-made systems with rules a little akin to the rules of a game; they're merely arbitrary. Now, this symbol-game may well have utility, but that shouldn't distract us from the fact (claim the formalists) that logic and mathematics are just fancy symbol-games that are not real in any sense.

There's a pretty good argument against this position and in favor of some kind of realism for maths/logic. Here's how it goes:

Let's define what we mean by "real." It's hard to fully define, but one thing we can say about what is real is that what is real does not yield to human desire in any direct sense. I may focus really hard on the idea that there's a suitcase with fifty million dollars in my closet--but no matter how much I focus, no matter how much I wish it were the case, no matter how I visualize it, that just doesn't happen. Reality pushes back against what I want to be the case.

Now, Kurt Godel proved, in (I think) 1933 that any symbol-system sufficiently robust to represent quantified predicates (that is, sentences that make claims like "All X's are Y's" or "Some Y's are Z's" and so on) can be both sound and complete. No matter how much we wish for such a system, it simply cannot be done. But then, that means that there's something real about such a system--the systems push back against our desires.

 

[ataraxia]

then, that means that there's something real about such a system--the systems push back against our desires.

Sure- reality and observations structure our systems of logic and push back. They are even the inspiration and origin for our systems of logic. There are pragmatic limits to the systems of logic we can come up with- it has to correspond to our observations.

What is our observations change and grow, we have found that we have to modify, and even completely overhaul our systems of logic. For example, the logic of Euclidean geometry and Newtonian physics seemed absolutely unstable. It was sad of Euclid and Newton that they had glimpsed the mind of God.

But Einstein‘s relativity showed that the Universe is not really at all Euclidean nor Newtonian. The basic postulate and premises of these systems did not match the observations we were starting to make. So we had to come up with a different system of logic, different set of rules to explain how things work on that different scale of high velocity and high gravity.

Quantum mechanics has been doing the same with laws of logic as basic as the law of identity, or causation. So we have had to design an entirely different set of logical laws to explain those phenomena in the subatomic realm.

And what still remains quite a mystery is how small subatomic particles behave under high velocity, and gravity. A lot of weird things happen there, such as in black holes, or trying to explain the origin of the universe, that cannot be explained by the logic and postulates of ANY of our current systems, including quantum mechanics or relativity. We have come up with some possibilities, such as strength theory or quantum loop gravity. But while these are internally, consistent and coherent systems, it’s not considered science, because they do not rest on what is considered the most bedrock promises, the inputs to the logical system, which is observation.

So that’s why, for example, one of the pioneers of strength theory, Edward Whitten, was given to Fields metal in mathematics (the equivalent of the Nobel prize for mathematicians), and not the Nobel prize. His mathematical model for string theory is logically amazing and sophisticated. But as of now, that’s all it is. It is not science until that is grounded and observation.

So although grounded in reality and limited by it, these logical systems are all just imaginative attempts to try to understand the universe, predict it, and even learn to manipulate it. They are imaginative and clever, but always contingent and man-made.

They are not a glimpse into the mind of God, nor evidence of one.

 

[ataraxia]

The position you are describing is called formalism. The idea is that logic and mathematics are just (as you say) human-made systems with rules a little akin to the rules of a game; they're merely arbitrary. Now, this symbol-game may well have utility, but that shouldn't distract us from the fact (claim the formalists) that logic and mathematics are just fancy symbol-games that are not real in any sense.

There's a pretty good argument against this position and in favor of some kind of realism for maths/logic. Here's how it goes:

Let's define what we mean by "real." It's hard to fully define, but one thing we can say about what is real is that what is real does not yield to human desire in any direct sense. I may focus really hard on the idea that there's a suitcase with fifty million dollars in my closet--but no matter how much I focus, no matter how much I wish it were the case, no matter how I visualize it, that just doesn't happen. Reality pushes back against what I want to be the case.

Now, Kurt Godel proved, in (I think) 1933 that any symbol-system sufficiently robust to represent quantified predicates (that is, sentences that make claims like "All X's are Y's" or "Some Y's are Z's" and so on) can be both sound and complete. No matter how much we wish for such a system, it simply cannot be done. But then, that means that there's something real about such a system--the systems push back against our desires.

Even language and vocabulary, using words to try to categorize different phenomena, like “this is a monkey”, “this is a tree”, “the his is a car”- are man-made constructs. We are trying to find the essence of what these things are and put a label on them to make the world easy to navigate. We would be overwhelmed if we paid too much attention to the difference in particulars of each case of those things. But when we get down to it, we find the edges of these categories are fuzzy, and they bleed into all sorts of surrounding categories.

I think the clearness of these concepts that we created is where Platonic thinking begin to take shape originally. You want to find the essence and ideals of these words that we use.

But it turns out we create these words and categories in the first place, as tools to help us navigate our world, and then become self-mystified by them. These categories are not always universal even across languages- hence, the difficulty of trying to translate between them. Different cultures defined things differently. That may even hold across individuals. That is a set up for a lot of cultural and personal misunderstandings sometimes.

Evolutionary biology, has shown that the category of monkey is not a fixed thing. There are lots of genetic differences between monkeys, and overtime, species change and evolve, there are lots of genetic differences between members which anmolify overtime, until they become something entirely different- we find that the original mental category we created for them no longer exists. I think this sort of metaphysical weirdness to our categories is what really bothered a lot of religious people about evolutionary biology when it first came out. Religion has a strong foundation in platonic thought and rigid categories, and Darwin challenged that with his model. (Nietzsche: “Christianity is Platonism for the masses”).

Philosophers, logicians, and linguists started to see this, and most of 20th century philosophy has been a backlash to and an attempt to show the problems with Plato. Outside of Gödel, for example, I think the following works, each approaching a subject from a very different perspective, are very interesting in this regard:

https://www.stephenhicks.org/wp-content/uploads/2019/01/DeweyJ-Influence-of-Darwin-on-Philosophy.pdf

Philosophical Investigations: Wittgenstein, Ludwig: 8601404291777: Amazon.com: Books

Philosophical Investigations [Wittgenstein, Ludwig] on Amazon.com. *FREE* shipping on qualifying offers. Philosophical Investigations

www.amazon.com

Difference and Repetition: Deleuze, Gilles, Patton, Paul: 8581000010135: Amazon.com: Books

Difference and Repetition [Deleuze, Gilles, Patton, Paul] on Amazon.com. *FREE* shipping on qualifying offers. Difference and Repetition

www.amazon.com

 

[ashurbanipal]

Sure- reality and observations structure our systems of logic and push back. They are even the inspiration and origin for our systems of logic. There are pragmatic limits to the systems of logic we can come up with- it has to correspond to our observations.

That doesn't seem likely to be correct. There aren't any natural correlates to the limitations that Godel found for formal systems. Additionally, there are objects within some formal systems that could not have any natural correlate--imaginary numbers, for example. We use imaginary numbers to solve certain problems in engineering and physics, but it's impossible to have 3i oranges, or something like that. The idea that we learn logic from observing the natural world seems to sit rather ill with observations such as that.

What is our observations change and grow, we have found that we have to modify, and even completely overhaul our systems of logic. For example, the logic of Euclidean geometry and Newtonian physics seemed absolutely unstable. It was sad of Euclid and Newton that they had glimpsed the mind of God.

But Einstein‘s relativity showed that the Universe is not really at all Euclidean nor Newtonian. The basic postulate and premises of these systems did not match the observations we were starting to make. So we had to come up with a different system of logic, different set of rules to explain how things work on that different scale of high velocity and high gravity.

I think that seems to be based on a misunderstanding of what logic is. Euclid and Newton both used logic; they don't have their own logics just as such. Euclidean geometry is often used to introduce deductive reasoning to high school students these days, but that's the only connection as far as I can tell. Euclid and Newton built theories using logic; those theories were eventually proven to be wrong (in Newton's case) or less parsimonious than the alternatives (in Euclid's case), but neither theory is dictated by logic or mathematics. Actually, I think that was Lobachevski's point--mathematicians up to about 1830 thought that Euclid's postulates and axioms were mathematical truths--he showed that they are not.

Quantum mechanics has been doing the same with laws of logic as basic as the law of identity, or causation. So we have had to design an entirely different set of logical laws to explain those phenomena in the subatomic realm.

That also does not seem correct. There's no law of identity or causation in logic. There's a function called identity, but that's quite different. There probably is a logic that has as an axiom A is A, but it wouldn't be any kind of mainstream logic since, generally speaking, we don't want predicates (e.g. "is") in our axioms.

And what still remains quite a mystery is how small subatomic particles behave under high velocity, and gravity. A lot of weird things happen there, such as in black holes, or trying to explain the origin of the universe, that cannot be explained by the logic and postulates of ANY of our current systems, including quantum mechanics or relativity. We have come up with some possibilities, such as strength theory or quantum loop gravity. But while these are internally, consistent and coherent systems, it’s not considered science, because they do not rest on what is considered the most bedrock promises, the inputs to the logical system, which is observation.

That's not logic, either. There's no observation that serves as an "input" to logic. I'm not quite sure what would be an input for logic--I suppose maybe you could say that arguments serve as inputs when we use logic to test for validity, but usually, observation is relevant to scientific theories.

So that’s why, for example, one of the pioneers of strength theory, Edward Whitten, was given to Fields metal in mathematics (the equivalent of the Nobel prize for mathematicians), and not the Nobel prize. His mathematical model for string theory is logically amazing and sophisticated. But as of now, that’s all it is. It is not science until that is grounded and observation.

So although grounded in reality and limited by it, these logical systems are all just imaginative attempts to try to understand the universe, predict it, and even learn to manipulate it. They are imaginative and clever, but always contingent and man-made.

They are not a glimpse into the mind of God, nor evidence of one.

Sure, but they're not really systems of logic, or mathematics, at least in the way that I understand systems. They seem to be closer to models rather than systems.

 

[ashurbanipal]

Even language and vocabulary, using words to try to categorize different phenomena, like “this is a monkey”, “this is a tree”, “the his is a car”- are man-made constructs.

Well, that's certainly true. There's no necessary relation between "tree" and the things that are (for example) in my back and front yards. Nor is there such a relation with "baum" and those things, or "dendron" and those things, etc.

We are trying to find the essence of what these things are and put a label on them to make the world easy to navigate. We would be overwhelmed if we paid too much attention to the difference in particulars of each case of those things. But when we get down to it, we find the edges of these categories are fuzzy, and they bleed into all sorts of surrounding categories.

I'm not so sure this is true, or at least, I don't think it's universally true. I can think of some objects that might fit in both of what might be considered exclusive sets (e.g. <tree>, <bush>), but I can also think of sets of natural things that seem quite well defined (e.g. <gold>, <water>, <rock>, <EM radiation>, <star>, <electrons>). I'm having trouble thinking of something that would be kinda rock, kinda not-rock. Seems like something is either a rock, or it isn't.

I think the clearness of these concepts that we created is where Platonic thinking begin to take shape originally. You want to find the essence and ideals of these words that we use.

It seems like something else entirely motivated Plato. In the Phaedo, for instance, he points out that we sometimes look at things like sticks or stones as equal in some ways and not equal in others. I may have two roughly cylindrical stones that happen to be, as closely as we can measure, exactly the same height (or, for that matter, a stonemason may have carved two cylinders of stone and made them exactly the same height). But they are not thereby made equal in all ways. Nothing in the universe is equal in all ways to something else, far as we can tell. But we yet have an idea of equality and we know what it would mean for two objects to be equal in all ways (equal mass, equal spectral reflections, equal dimensions, etc.). Whence comes this idea of equality? It's not found in nature, it's not a thing that we can stub our toe on or anything. And yet, we know how to apply it. There has to be some kind of abstract object, "equality"--a thing that is not itself like a stick or a stone--that we have some kind of access to.

Whatever you think of this argument, it seems clear he's not looking for essences. He's got something else in mind.

But it turns out we create these words and categories in the first place, as tools to help us navigate our world, and then become self-mystified by them.

That was certainly Wittgenstein's (Tractatus) idea; I think most philosophers these days think he was probably wrong about that.

These categories are not always universal even across languages- hence, the difficulty of trying to translate between them. Different cultures defined things differently. That may even hold across individuals. That is a set up for a lot of cultural and personal misunderstandings sometimes.

Plato would, I think, just ask why we should be impressed by this. Perhaps some individuals, and some cultures, just have imperfect access to the forms.

Evolutionary biology, has shown that the category of monkey is not a fixed thing. There are lots of genetic differences between monkeys, and overtime, species change and evolve, there are lots of genetic differences between members which anmolify overtime, until they become something entirely different- we find that the original mental category we created for them no longer exists. I think this sort of metaphysical weirdness to our categories is what really bothered a lot of religious people about evolutionary biology when it first came out. Religion has a strong foundation in platonic thought and rigid categories, and Darwin challenged that with his model. (Nietzsche: “Christianity is Platonism for the masses”).

If you mean what I think you mean, I'd say it's rather more complicated than that. What upset a lot of Christians about Darwin, and that continues to upset them, is that, if evolution by natural selection is right, it's pretty hard to take Genesis 1 and 2 as literal history, and the impulse to take the Bible as literal history arose as an unintended consequence of the Protestant reformation (the medieval Christians wouldn't have been bothered by it and even had some theories of natural kinds that were evolution-like).

 

[ashurbanipal]

Philosophers, logicians, and linguists started to see this, and most of 20th century philosophy has been a backlash to and an attempt to show the problems with Plato. Outside of Gödel, for example, I think the following works, each approaching a subject from a very different perspective, are very interesting in this regard:

Again, I think the story is rather more complicated than that. We ended up turning to materialism by about 1920 in the Anglophone world thanks to four developments in the late 19th and early 20th centuries: the elucidation of the fine structure of the brain by Ramon y Cayal and Roger Sherrington, the development of symbolic logic by Gottlob Frege, Bertrand Russell, Alfred North Whitehead, Alonzo Church, and a few others, and then the development of psychology as a science thanks to William James, Sigmund Freud, Willhelm Wundt, and Jean Piaget, and then finally the rise of science itself. These parallel developments suggested a research program that seemed quite promising: neuroscience would map the entirety of the brain, psychology would do the same for the mind, and the logicans would provide the mathematically-founded array of relations from one to the other. We would thus have a fully worked-out materialist system of the world.

Certainly, if materialism is true, Plato cannot be right in any robust metaphysical sense (though some philosophers like Naomi Reschotko have interpretted him to only mean that we can abstract from the world, not that there are these things floating around in a Platonic heaven called "forms"...but that's an aside), so as a natural consequence of this program, Platonism took a beating. But on the other hand, his philosophy received a boost from science--the idea that there are natural laws is quite a Platonic one. The idea that this piece of copper (which we have never tested) will conduct electricity just as well as that piece (which we have) is a Platonic idea--it's actually one that he makes explicit somewhere, though I can't recall in which of his dialogues he uses the idea of natural law--it may be in the Republic or possibly Laws.

Two problems arose from this program, however. First is that when the older idealisms were dethroned as the reigning ontologies, there was never any definitive contest that played out. Mostly, academics became materialists in the Anglophone world because of the promise of the research program and the unrelenting and charismatic evangelism of Bertrand Russell. Second, cracks began to show in the edifice pretty early--Godel's proof being the first and perhaps the worst of those. Its direct consequence would be that no logical relation array could be complete as to relations between mind and brain. Later, as brain research developed and we began to find weirder and weirder things about what the brain is actually doing, various materialist theories were shown to be false. Type-identity theory doesn't fit with observation at all, and token-identity theory just doesn't explain anything to begin with, so those were out by the 1960s. Putnam's machine-state functionalism was next up, but he himself saw a fundamental flaw with it when he published Representation and Reality in 1988, and it turns out that that problem generalizes to any kind of functionalism. Since that time, materialism has been under increasing pressure because it seems unable to present a coherent view--that is, a view that is non-self-contradictory and that does not contradict observation.

So if the 20th century was a backlash against Plato, the late 20th century and the 21st century has seen a revival of his ideas in semi-new clothing.

The story is a little different for continental philosophy. They became materialists much earlier and for quite different reasons, mainly having to do with Marx's critique of Hegel's understanding of history. I'm afraid my training is in the analytic side of philosophy; I know a little about the continental stuff, but not enough to be confident in writing about it. Certainly, the above is a vast over-simplification, meant only to pick out a few strands and point to how they led to something else.

 

[ashurbanipal]

It occurs to me that maybe I ought to say a little about what logic is. The history of logic began with Aristotle in the Prior Analytics. Logicians in the middle ages worried over some problems that obsessed Aristotle (like how to relate conditional statements--i.e. if...then...statements, to the other logical operators like AND or NOT) and did manage to complete the square of opposition in a manner that would have pleased Aristotle. But dealing with quantified predicates and having a fully worked-out understanding of hypothetical and modus syllogisms remained elusive.

Finally, in 1898, Gottlob Frege published the Begriffschrifft, which came to the attention of Bertrand Russell. Russell realized that Frege had solved the longest-standing problems--again, dealing accurately with quantified predicates and relating conditional statements to the other logical operators, thereby closing the loop on all the recognized forms of syllogism. His system did contain a fatal flaw, which Russell and Whitehead spent a lot of time trying to fix.

What emerged from those early 20th century efforts is this: logic is simply an artificially constructed language with formal definitions of its terms, and those definitions make it easy to understand the truth-relations between propositions. Consider the following three propositions: Socrates is a man, all men are mortal, Socrates is mortal. It seems intuitively clear that if the first two sentences are true, then the third one must also be true. That's a truth-relation between propositions. What logicians had always hoped is to find a way to set the evaluation of natural language arguments on as firm a footing as mathematics, and while that is now known to be impossible, we can check for validity (defined as: if the premises are all true, it is impossible for the conclusion to be false)--that is, we can check whether someone has reasoned correctly or not.

When I first started investigating logic (over 30 years ago now) I thought for sure that it was simply wrong, that it is an overly mathematized approach to the world, a rigid system that tries to apply artificial rules to what is in fact a complex and messy world. I gradually realized that I was wrong. What the logicians of the 20th and 21st century have done is they've modelled human reasoning almost perfectly. There are a few outstanding issues, but they're not ones that usually come up in conversation or debate.

Bertrand Russell and G.E. Moore apparently thought that the then-newly discovered structures of formal logic implied a materialist ontology. Pretty much every logician after them realized, however, that any such implication is downright silly. Logic needs to be as topic-neutral as possible, and the logicians from about 1930 onward went to work to make sure that logic is free from any kind of metaphysical entanglement.

There are a great many misconceptions about logic and what counts as logical. A lot of people think that science is logical and religion illogical or non-logical or some such, but this is just a hold-over from the logical positivists, who thought that we could essentially replace all of philosophy with science plus formal logic and mathematics. They were spectacularly incorrect, but at the time it seemed to be a promising program. Their ultimate failure showed, among other things, the need for logic to float free from metaphysical committments.

Logic these days can handle pretty much any set of ideas, topic, what-have-you. Scientific theories, religious arguments, philosophical arguments, scholarship methods, etc. are not themselves logic. They only use logic--or rather, they are the products of reasoning, and logic is a system we can use to check that that reasoning is valid.