godelian wrote: ↑Tue Jan 14, 2025 12:09 pm
BigMike wrote: ↑Tue Jan 14, 2025 10:10 am
Godelian, your argument seems to conflate the logical structure of a theory with its alignment to reality, but let’s unpack this in a way that addresses the core issue: whether atheism—or more broadly, skepticism of religious claims—needs to operate like a formal axiomatic system to hold validity.
The analogy of an "atheism GPT" and the idea of a theory with arbitrary axioms, no domain, and restrictive conditions doesn't map well onto atheism itself. Atheism isn’t a comprehensive theory or system of axioms; it’s simply the absence of belief in deities, typically due to a lack of evidence. It doesn’t claim a domain, nor does it need to. It’s a position of non-commitment to claims that lack sufficient empirical or logical support.
The conditions you outlined—restrictive axioms, lack of a domain, and arbitrary axioms—might describe a poorly constructed formal system, but they don’t apply to atheism as it functions in practice. Atheism doesn’t deny the possibility of defined objects (e.g., a deity) outright; it questions the evidence and coherence of the claims made about such objects. If someone presents a consistent, evidence-backed model of a deity, atheism could respond within that framework—but until then, it simply remains unconvinced.
In contrast, religious claims often assert a detailed ontology—a domain of gods, spirits, or supernatural phenomena—which can and should be scrutinized using logic, evidence, and critical thinking. The burden of proof lies on those making specific claims, not on those withholding belief due to insufficient evidence.
Your argument that proving an "atheist theory" has a model is "virtually impossible" misses the point: atheism doesn’t require proving a comprehensive theory. It’s not about constructing a positive model but about assessing the claims of others and withholding belief when those claims fail to meet logical or evidentiary standards.
This ties back to the importance of teaching critical thinking rather than dogma. Encouraging children—and societies at large—to evaluate claims based on evidence and reason doesn’t create an "empty model." It creates an open system where beliefs are proportional to the evidence supporting them. Atheism fits comfortably in such a framework, not as an empty theory, but as a stance waiting for substantiation before accepting extraordinary claims.
I was evaluation the situation exclusively within the context of Tarski's semantic theory of truth.
ChatGPT was doing that too.
Your arguments, however, do not stay within the confines of model theory and do not respect its constraints.
There are indeed other truth theories.
These alternative truth theories say nothing, however, about GPT programs or what exactly they prove. You will have to use something else than mathematical logic, model theory, or computer science because these fields will not support your argument.
Godelian, I appreciate your framing of this discussion within Tarski’s semantic theory of truth, but I believe it’s worth addressing why my perspective on atheism as a corollary to the laws of nature transcends the strict confines of formal model theory. The reason is simple: atheism, as I view it, isn't a formalized axiomatic system requiring models in the Tarskian sense. Instead, it aligns with physical laws and principles that underpin observable reality.
The laws of nature—conservation laws and the four fundamental interactions—leave no room for entities or forces that operate outside their scope. Conservation laws, for instance, dictate that energy, momentum, and charge cannot appear or vanish without cause. These principles inherently exclude phenomena like miracles or interventions by a deity that violate these laws. Atheism, in this view, arises naturally from accepting the deterministic, causal framework of physics as the only viable explanation for the universe.
Tarski’s semantic theory, while useful in formal logic and mathematical truth, isn’t equipped to address empirical truths about the natural world. Empirical truth emerges from observation, experimentation, and alignment with physical reality, not from formal structures alone. For example, the conservation of energy isn’t "true" because it fits within a model-theoretic framework—it’s true because it consistently aligns with every observed interaction in the universe.
Religious claims, by contrast, often posit entities or phenomena that contradict these fundamental principles. For these claims to hold validity, they must demonstrate evidence that withstands empirical scrutiny. Without this evidence, atheism remains the default position—not as an "empty theory" but as the logical outcome of aligning belief with the observed constraints of reality.
While model theory can assess internal consistency within formal systems, it doesn't invalidate atheism’s basis in physical laws. Atheism doesn’t need a "model" in the Tarskian sense to remain grounded in the evidence and logic dictated by nature. My argument for atheism as a corollary to conservation laws isn’t about bypassing logical rigor but recognizing the constraints imposed by the universe itself.
Would you agree that physical laws, rather than formal semantics, are the appropriate basis for evaluating claims about the existence of entities purported to operate within or beyond the natural world?
Poor thing.