The lack of deductive closure is not considered an advantage in proof theory. On the contrary, it is considered a pretty much insurmountable problem. In fact, we generally avoid the use of theories that are not closed under logical consequence.
IslamGPT versus BibleGPT
Re: IslamGPT versus BibleGPT
Re: IslamGPT versus BibleGPT
It is Christianity's greatest weakness:
Its failure to close under logic means that Christianity simply has no usable notion of truth.ChatGPT: Why do we avoid the use of theories that are not closed under logical consequence?
We avoid using theories that are not closed under logical consequence because such theories are incomplete, inconsistent, or unreliable for formal reasoning. Here’s why:
Why Non-Closure is Problematic
When a theory is not closed under logical consequence, it has several undesirable properties:
a. Incompleteness
If a theory T is not closed under logical consequence, it fails to include all the statements that are true in its framework. This makes reasoning with T unreliable, as there may be true statements that cannot be derived.
b. Inconsistency Risks
A theory not closed under logical consequence can lead to inconsistencies in its use. If we overlook logical consequences, we might unknowingly accept contradictory statements, especially if the theory's boundaries are unclear.
c. Impairment of Formal Reasoning
Mathematical and logical reasoning relies on systematic deduction. If a theory isn't closed under logical consequence, it hampers the deductive process, as not all relevant information is included. This limits the power of the theory to model and predict phenomena.
d. Ambiguity in Interpretation
Theories that lack closure introduce ambiguity: different users might reach different conclusions about what the theory entails. This undermines the consistency and universality of the theory's application.
Practical Implications
In fields like mathematics, computer science, and philosophy, ensuring closure under logical consequence is essential to maintain rigor and reliability. For instance:
In mathematics, axiomatic systems (like ZFC set theory) are constructed to be closed under logical consequence to ensure all provable statements are included. In computer science, knowledge bases in artificial intelligence are designed to be logically closed to support sound decision-making. In philosophy, formal theories of logic aim for closure to ensure coherence and avoid logical gaps.
Conclusion
Theories not closed under logical consequence are incomplete and may lead to inconsistencies or ambiguities. By working with theories that are logically closed, we ensure that all truths derivable within the framework are accounted for, supporting clear, reliable, and rigorous reasoning.
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Re: IslamGPT versus BibleGPT
This is clearly not true.godelian wrote: ↑Tue Dec 24, 2024 10:11 pmFollowing Luther's attempt at turning Christianity into a scriptural religion instead of a clerical one, Protestant denominations somewhat subscribe to the sola scriptura view. However, that is clearly not what they do in practice.Immanuel Can wrote: ↑Tue Dec 24, 2024 6:28 pm In fact, all Protestant denominations, to one degree or another, depart from this "magisterium" view. That's what makes them Protestant, in fact: the "protest against" the fiat declarations of the Papist magisterium.
I have no idea why you even think it's true...unless you really don't, and are just practicing the Islamically-approved practice of taqqiya, or deception.
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Re: IslamGPT versus BibleGPT
Who cares? Christians don't think the Papal nonsense was authoritative in any way. In fact, sola scriptura means that Luther himself isn't authoritative. Maybe you're just too used to bowing to an authoritarian religion to imagine it could be any other way...is that possible?godelian wrote: ↑Tue Dec 24, 2024 10:17 pmAt his trial in 1521, Martin Luther used the notion of deductive closure as the main argument in his defense. Luther's argument was rejected by the Papal and Imperial prosecutor...Immanuel Can wrote: ↑Tue Dec 24, 2024 10:05 pm Well, what's clear is that your premise was simply untrue. So there's no "deductive" problem with Christian ethics at all.
Well, you'd better lay out "the problem," then...because I would say that there really isn't one at all.I accept the prosecutor's argument because there is otherwise no other solution to the problem.
Re: IslamGPT versus BibleGPT
The problem is that deductive closure is not viable in Christian theology.Immanuel Can wrote: ↑Tue Dec 24, 2024 11:39 pm Well, you'd better lay out "the problem," then...because I would say that there really isn't one at all.
Luther himself ended up also rejecting the notion of logical closure in Biblical morality.
When Philip of Hesse argued that the patriarchs in the Bible are mostly polygamous, and therefore that there is nothing wrong with polygamy, and that he wanted Luther to officiate at his bigamous marriage, suddenly Luther also ended up rejecting these otherwise logical consequences from the Bible.
Hence, the problem is that there is no usable notion of truth in Biblical moral theory. As ChatGPT has pointed out, without deductive closure, truth cannot be discovered. That is the same as stating that Soundness theorem does not apply.
Christian theology does not satisfy Tarski's semantic theory of truth and therefore does not contain particularly much usable truth. In fact, Christian theology is largely in violation of what we mathematically know about the truth.
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Re: IslamGPT versus BibleGPT
godelian wrote:IslamGPT versus BibleGPT
LMFAO
Re: IslamGPT versus BibleGPT
An LLM makes use of deductive closure to produce interpretations and discover the truth. This is not possible in Christian theology because it does not support deductive closure.
The principle of Christian magisterium implies that the clergy will routinely bypass the requirements of logic in their interpretation:
All Christian denominations have in practice adopted the same policy of magisterium.https://en.m.wikipedia.org/wiki/Magisterium
The magisterium of the Catholic Church is the church's authority or office to give authentic interpretation of the word of God, "whether in its written form or in the form of Tradition".
An LLM cannot interpret the Bible because it is not able to bypass logic. That is why BibleGPT does not work properly.
Christianity and reason -- both automatic and human -- are largely incompatible.
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Re: IslamGPT versus BibleGPT
So what you are insisting, is that a bloke (MorHamMad) can come along 600 years later and totally distort the Judaic/Christian texts to suit his desire to have a following of murdering cunts....yet you see some form of 'incompatible' logic within the ORIGINAL holy texts he distorted to achieve his "manhood" ego.
Re: IslamGPT versus BibleGPT
The reason why Biblical theology is incompatible with reason is not so much because of the scriptures themselves but mostly because of the existing body of incompatible interpretations that have acquired force of law under the principle of infallibility of the Church.attofishpi wrote: ↑Wed Dec 25, 2024 3:07 am yet you see some form of 'incompatible' logic within the ORIGINAL holy texts he distorted to achieve his "manhood" ego.![]()
The Torah alone, for example, as the foundation for Jewish law, is certainly not incompatible with reason. Therefore, JewishGPT would almost surely work fine.
The prophet of Islam has managed to transmit a Quran along with a prophetic Sunnah that are suitable for the GPT process to produce a consistent LLM from. He has clearly succeeded where the Christian churches have almost completely failed.
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Re: IslamGPT versus BibleGPT
Islam? From a man that intended to profit, a "man" that distorted the New Testament account of Christ (> 600 years after HIS death), in particular the ENTIRE message Christ died for...LOVE & TRUST.godelian wrote: ↑Wed Dec 25, 2024 3:17 amThe reason why Biblical theology is incompatible with reason is not so much because of the scriptures themselves but mostly because of the existing body of incompatible interpretations that have acquired force of law under the principle of infallibility of the Church.attofishpi wrote: ↑Wed Dec 25, 2024 3:07 am yet you see some form of 'incompatible' logic within the ORIGINAL holy texts he distorted to achieve his "manhood" ego.![]()
The Torah alone, for example, as the foundation for Jewish law, is certainly not incompatible with reason. Therefore, JewishGPT would almost surely work fine.
The prophet of Islam
Ooonooo...and yet I KNOW GOD very personally (and I KNOW MorHamMad is a LIAR)godelian wrote: has managed to transmit a Quran along with a prophetic Sunnah that are suitable for the GPT process to produce a consistent LLM from. He has clearly succeeded where the Christian churches have almost completely failed.

Re: IslamGPT versus BibleGPT
My post is not about the spiritual part of religion.
There are (numerous) questions that rationality cannot reach, such as "Why does the universe exist?' or "Why are we alive?" or "What does God expect from us?".
Rationality is a tool that can deal with some questions. Spirituality is another tool that can deal with other questions.
If your only tool is a hammer, then the whole world will soon start looking like a nail.
The way in which a person can know God is a spiritual question for which rationality will essentially be irrelevant.
I mostly avoid debating spiritual questions because I consider the subject to be highly subjective.
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Re: IslamGPT versus BibleGPT
au contraire
U understand logic, computers..etc
Therefore to understand this entity once it has provided personal empirical evidence of ITS existence, RATIONAL comprehension of GOD is paramount.
Indeed, to even discount that GOD could be an A.I. (from my observations) is to be rather philosophically daft.
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Re: IslamGPT versus BibleGPT
You keep saying that, but not saying what you mean by it. I understand "deduction." I just can't see any kind of warrant for your assumption, and you're not providing any.godelian wrote: ↑Wed Dec 25, 2024 2:12 amThe problem is that deductive closure is not viable in Christian theology.Immanuel Can wrote: ↑Tue Dec 24, 2024 11:39 pm Well, you'd better lay out "the problem," then...because I would say that there really isn't one at all.
That's clearly untrue, and not even remotely hard to disprove. The entire corpus of the Western legal tradition is founded on Torah, for example. That's a matter of historical record, and not at all hard to show. https://lonang.com/commentaries/foundat ... l-history/ , https://users.ssc.wisc.edu/~rkeyser/?page_id=540 , https://www.beasleyallen.com/wp-content ... -we-do.pdf ...Hence, the problem is that there is no usable notion of truth in Biblical moral theory.
I don't think you know what you're talking about at all.
Re: IslamGPT versus BibleGPT
For a starters, the legal traditions in the West are mostly based on Roman law, which is indeed staunchly rational. Next, the Torah is indeed the foundation of Jewish law, which is also rational, but which is largely rejected in Christianity.Immanuel Can wrote: ↑Wed Dec 25, 2024 4:36 am The entire corpus of the Western legal tradition is founded on Torah, for example. That's a matter of historical record, and not at all hard to show.
The gentiles (non-Jews) do not have to abide by Jewish law:
Most of Jewish law is not mandatory for Christians and the Torah is not binding to Christians. Mosaic law, in its entirety, is indeed the foundation for Judaism but not so for Christianity.https://enterthebible.org/passage/acts- ... considered
BIBLE TEXT
Acts 15:1-3
SUMMARY
At a meeting in Jerusalem, “the apostles and the elders, with the consent of the whole church” (15:22) comes to understand that God calls Gentiles to saving faith in Christ without requiring them to be circumcised and keep all Jewish laws.
ANALYSIS
The issue of the mission to Gentiles is first raised in Acts 10 and Acts 11:1-18, when Peter’s report about his vision and encounter with Cornelius convinces believers in the Jerusalem community, not least because of the Spirit’s legitimation. But in Acts 15 the issue must be reconsidered. Some believers from Judea insist that God requires that baptized Gentiles be circumcised (and probably keep food laws). A council is held in which Peter again testifies to God’s plan of salvation for Gentiles through faith in Christ, without the necessity of receiving circumcision or adhering to all Jewish laws. For the sake of harmony in mixed Jewish-Gentile congregations, however, the council recommends that Gentile believers abstain from some “essential” Jewish taboos, namely: “things polluted by idols . . . fornication . . . whatever has been strangled . . . and from blood” (15:20, 28‒29). These forbidden elements were associated with idolatrous practices, such as consuming meat offered to false gods in pagan temple ceremonies (the animals would have also been butchered by strangulation and other methods retaining blood, in violation of kosher practices).
The Jerusalem council’s decision to welcome Gentile believers apart from circumcision is certified as the will of God directed by the Holy Spirit (Acts 15:8-9, 28). At the same time, suspicion about the Gentiles’ lack of adherence to the Torah (Jewish law) continues to be an issue. Suspicion later dogs Paul’s footsteps, as he discovers when he returns to Jerusalem (21:20-25).
On the contrary, as Paul clarifies, by becoming a curse, Christ has freed the Christians from the curse of abiding by a moral theory:
There is no moral theory in Christianity. There is only the magisterium of the Church, which is not closed under logical consequence, and which is not meant to be consistent, but which is still infallible.Galatians 3:13. Christ redeemed us from the curse of the law by becoming a curse for us, for it is written: "Cursed is everyone who is hung on a tree."
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Veritas Aequitas
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Re: IslamGPT versus BibleGPT
No such thing.
Initially, there could be a neutralGpt;
but, from my experience with LLMs it is always:
godelianGpt versus [xGpt]
where x can be any other person.
Example, what is glaring so far is;
VAGpt versus AtlaGpt
VAGpt versus SeedsGpt
especially when each imputes their variable conditions into the discussion.
Ultimately what prevails should be the foundational truth based on a credible FSK.
Godelian is not a true Muslim so his foundation is not credible.
A true Muslim is one who understands the Quran fully and comply fully with the terms of the agreed covenant.