<quote from Real Faith & Reason>
A Quick Tour of the Trilemma
The logical fallacy of infinite regression:
When someone tries to prove a conclusion C using proof P but has no proof for the proof, this person ends in infinite regression. Infinite regression is a problem with the premise, the proof P.
P proves C. P1 proves P. P2 proves P1. P3 proves P2. (Continue infinitely)
Each P is a premise (proof). C is the conclusion.
This regression of unproven proofs goes on infinitely with no real proof for the proof.
An ungodly thinker says we can trust his reasoning. How does he know? He states an argument to support his reasoning using a premise, but how does he know his premise is true? He has to create a second logical argument to prove his original premise, the premise he used to support his claim that we can trust his reasoning. Of course, he hasn’t gotten anywhere since his second logical argument also has a premise that he must prove. He can then try to prove that premise with another logical argument, but this chain of unproven reasoning goes on forever. Well, not forever, but until he runs out of time. So, he never finds solid ground and never has sound reasoning because not one of his claims can stand on its own. Therefore, he knows nothing since he needs further proof for every claim he makes.
The logical fallacy of circular reasoning:
A persuader starts with what looks like infinite regression, but the infinite regression hooks up to itself in a circle of reasoning. With circular reasoning, the proof for one of the premises is one of the previous premises. Circular reasoning hides the problem of the unproven premise.
P proves C and C proves P.
C proves P, P1 proves P, and C proves P1.
An ungodly thinker says we should trust her reasoning. But how does she know? She uses her reasoning to try to convince us to trust her reasoning, but using her reasoning to prove we can trust her reasoning is circular reasoning.
The logical fallacy of axiomatic thinking:
Axiomatic thinking is just making up stuff and calling it true.
X is true. It just is.
An ungodly thinker says, “I take the validity of my reasoning ability as an axiom.” While we can ask for proof, we won’t get any. The ungodly thinker says, “It’s self-evident, and I don’t need to prove it because it’s an axiom.”
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