Can logic be used to prove any belief?
It depends what you mean by "prove."
Two different concepts in logical argumentation are soundness and validity.
To better explain soundness and validity, I will use an analogy:
In January of 2004, mars rovers “spirit” and “opportunity” landed on mars. 8 years later, another rover, “Curiosity,” landed. Curiosity was ...
Consider logic as a machine taking inputs and yielding outputs.
If the input is false, the output may be true or false.
But if the input is true, the output is 100% true .
This is because the logical machine is designed to be " truth preserving".
Note : Saying that logic is "truth-preserving" is just another way to state that " a reasoning is valid ...
The set of propositions that can be known to be true with 100% logically justified complete certainty are those analytic propositions that are verified as true entirely on the basis of their semantic meaning. These are all anchored in sound deductive inference and semantic tautology.
All propositions that have any empirical aspects are limited by the ...
... it's hard to pinpoint exactly what makes them different from a basic
belief such as 'Deductive reasoning is reliable'. Nonetheless, it
would seem this one is a basic belief that is rational or warranted.
Confidence in the truth or existence of something not immediately susceptible to rigorous proof: dictionary.com/browse/belief