I asked Grok AI, “conclusions that do not logically follow from premises, do they adhere to the laws of contradiction and identity?”

The AI response correctly with:

“Conclusions that do not logically follow from premises, by definition, do not adhere to the principles of:

Law of Identity: If a conclusion changes or misrepresents what is being discussed or the nature of the entities involved in the premises, it fails to respect the law of identity. This law asserts that something is itself and its properties remain consistent. If the conclusion introduces or alters these properties in a way not supported by the premises, it’s not maintaining identity.

Law of Non-Contradiction: If the conclusion contradicts either the premises or itself, it clearly violates the law of non-contradiction, which states that contradictory statements cannot both be true in the same sense at the same time. A conclusion that defies the premises would be contradictory.

For example:

Premise: All dogs have fur.

Non-logical Conclusion: Therefore, some dogs have feathers.

Here, the conclusion does not adhere to:

Identity: It changes or misrepresents what it means to be a dog (with fur) by suggesting they might have feathers.

Non-Contradiction: It contradicts the premise that all dogs have fur by implying some could have feathers.

So, no, conclusions that do not logically follow from premises typically do not adhere to these fundamental laws of logic. “

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This is interesting because Science uses induction, which by definition, the conclusion does not logically follow from the premises. Scientific experimentation, which is affirming the consequent, does not logically follow from the premises. Observation is based on inductive logic.

This means science is a repeated and systematic denying of the laws of contradiction and identity. Scientist will try to get around this by saying we do not change “some” observations in the premise to an “all” in the conclusion, but a to “likely,” or “probable” In my experience they do in fact mean an “all,” because when they publish their journals they restate their past conclusions as Modus Ponens. However, we will ignore this. It still violates the law of contradiction and identity to go from “some” and change it to “likely.” This also is ignoring the other category errors such as “past tense observations” to conclusions about present and future tense., and etc. This is why science is not a body of knowledge.

If the laws of identity and contradiction should be so easily violated, then when Paul says grace, he does not mean grace, but something else like fish. When he says works, he really does not mean works but something else like grace. And so the statement “Jesus is the son of God,” means Jesus is not the son of God. Even though Jesus’ argument (Matthew 22:32) hinged on the identity of a “present tense” premise, it should be fine to conclude in the past tense; therefore God is not the God of the living, because He was the God of Jacob and not that He is the God of Jacob. When the bible says all our sins are forgiven, it is logical to say, they are probably forgiven, right? Induction says it is intelligent to make “past to present,” and “some to probable” interchangeable. Thus, that is how we read the bible, right?

Beyond the direct violation of contradiction and identity, this also leads to skepticism at the epistemology level. And skepticism also denies the law of contradiction.

As a Christian we understand the absolute unmovablity of logic when reading and understanding the bible; and yet, some still think science can produce knowledge, despite it systematically denying the laws of logic.