I never have any idea of what point you are trying to make.
It's very simple. On this forum, there are people who claim that they can take any set of words as an axiom and use it as a starting point for their philosophy/epistemology/worldview/whatever. The argument is that since the starting point is an axiom it cannot be proved false and thus cannot be criticized.
However, some axioms are bad because they are self refuting. Here are some examples.
Axiom 1: All truth is unknowable.
Response: If all truth is unknowable, then how can you know that axiom 1 is true?
Refuted.
Axiom 2: All truth is contained in the Bible.
Response: If all truth is contained in the Bible, why isn't axiom 2 contained in the Bible?
Refuted.
Axiom 3: Any statement that cannot be verified (at least theoretically) true or false is meaningless and should be assumed false.
Conclusion: Since "God exists" cannot be verified, it is a meaningless statement and should be assumed false.
Response: If statements that cannot be verified are meaningless, then until you can verify axiom 3 it must be considered meaningless and should be assumed false.
Refuted.
Axiom 3 is the postulate that we're focusing on now because it was the central tenet of a school of thought known as
logical positivism (also called logical empiricism). In the 1920s, some reasonably intelligent atheists got together and figured that since they were smart, they could put science on a sound logical footing, defeat religion once and for all, and usher in a new area of progress for science. You can read all about it at
http://www.philosophybasics.com/branch_logical_positivism.html
Now Loudmouth's claim that: "All facts are demonstrable" is but a hair's breadth from the standard logical empiricism claim that all facts must be verifiable. By making this statement, he has placed himself solidly in the logical empiricism camp.
Logical empiricism is formally dead because it's last known strong adherent recanted in 1967. Among the criticisms leveled at the epistemology were:
* Logical Positivism's insistence on the
strict adoption of the
verifiability criterion of meaning (the requirement for a non-analytic, meaningful sentence to be
verifiable) is problematic, as the criterion itself is
unverifiable, especially for negative existential claims and positive universal claims.
* Almost any statement (except a
tautology or logical truth) is unverifiable in the
strong sense, there is a
weak sense of verifiability in which a proposition is verifiable if it is
possible for experience to render it
probable.
* Distinctions between "observable" and "theoretical" have been challenged as well as the distinctions between analytic and synthetic truths.
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Now all of these philosophical problems have been considered unresolvable by people far smarter than you, Loudmouth, or I. However, if you want to make a novel argument, I'm certainly willing to listen.
However, Loudmouth's argument that the statement cannot be criticized because it's an axiom is hardly novel. It's an example of special pleading, which is defined as: "a fallacy in which a person applies standards, principles, rules, etc. to others while making him or herself (or those he or she has a
special interest in) to be exempt, without providing adequate justification for the exemption."