The central problem for all axiomatic systems that are insufficiently rich (or unable to obtain exterior confirmation definitions as available in empirical science) is self-reference. Thus, the limits imposed at the outset - if one is not aware and doesn't address them - lead to the basic example for the whole self-referential paradigm: the Epemenides' 'all Cretans are liars paradox."
All Cretans are Liars- If the speaker is a Cretan, then the statement is ipso facto unresolvable. If Cretan, then he exists within the so-called abstract, formal system. Yet, he’s making a statement (meta-) about the system. Hence, is he lying? Or is he telling the truth?
This cannot be resolved. It's an undecidable proposition, as Godel’s Incompleteness Theorem (II) applies.
A similar problem of analogous nature is posed for the biblical authoritarian. He finds himself in an impossible “Catch 22” because while he desires to prove to an audience that his book is inerrant and absolute, it’s impossible to do so exclusively within his system of axioms (e.g. quotes) since so many are self-contradictory. Thus, he is left to claim it himself or assert his system of axioms (quotes in biblical books) is “inerrant according to God"- thereby making a meta-statement that emanates from outside the system.
Thus, the biblical authoritarian is left to expect his audience to accept his claims on faith.
What about the realm of science? One can have a theory, for sure, but is there a way to move the theory to fact by escaping the tableaux of meta-statements or claims. Philosopher of Science, Henry Margenau, has noted that in the absence of P-facts and defined C-constructs, any syllogism or argument will have too many meta-statements, and break down to mere circularity.What are these?
Consider E = mc^2, which Einstein equation constitutes a specific formalism for a very particular operational definition linking energy and mass. We say it is a closed formalism, embodying closed symbols and operational definitions. Scientific epistemology allows us to regard E, m and c as constructs, connected via operational definition to what we call P- (perceptual) facts. That is, these facts are based on experimental measurement confirmed numerous times.
Hence, these measurements provide an open avenue out of any would-be tautologies. Thus, we expect a correlation like: C <-> P, re-affirming closure, significance and NO meta-linkage.
Now, consider the generic, open-ended verbal statement: “I see a desk”
Here, there is no connectivity between construct and perceptual fact. The words in quotation marks are a metaphor. The desk is NOT a P-fact, nor is seeing it a P-experience (experience wholly grounded in sensation). After all, a host of attributes (color, size, shape, density etc,.) are omitted, so we are left with an abstraction or mere shell of desk in terms of an actual, material correlate.
The open-ended process above creates a dynamic that yields an effective transition from a recurring complex of attributes, sensations to a simple, bare-bones construct, ‘desk’. This process goes by the name ‘reification’ In effect, the construct ‘desk’ is – as represented- is part of no set or defined ensemble of sensations that can be precisely named, defined. (Since all attributes are omitted). To boil it down, “I see a desk” is devoid of any context since no attributes are assigned. It is left to the beholder or cognite to fill these in.
In an analogous manner, a generic God-claimant or invoker is almost always in the deficient position of reifying what he's talking or writing about. Anytime one uses meta-phrases such as: "God ordained...", Or "God demanded.....", or God did or said such and such...." is trapped by reification. In other words, he's effectively rendered his god a thing. An obvious way out is to either define his God according to at least one C-construct and P-fact, OR - failing that, provide at least one necessary and one sufficient condition for it to exist.
By contrast, anyone who invokes 'E = mc^2' has no latitude or degrees of freedom to fill in anything, and hence invite circularity or reification. Since all P-facts are already defined by specific constructs – which have very exact meaning in physics. (e.g. c= the velocity of light, or about 300,000 km/sec) There is no wiggle room, and this lack of wiggle room means a pre-defined context exists. In contrast to this, the proponent of a vitalist or supernatural cosmos offers a claim that is subjective because the observer must provide an assumed closure - unlike in the case of E = mc^2, where all symbols are fixed.
For example when someone is using generic terms in a discussion like "God", in the absence of filling in what he means by it, then I am left to do what he should have from the outset. The problem is what I arrive at may not be at all what he means!
This subjectivity arises precisely because the claimant (or uninformed recipient of the claim) must fill in the blanks - so to speak - and provide a more complete subjective frame. For all intents, s/he may also give whatever “definition” he wants of supernatural or "living universe", to try to have it every which way, with no accountability. (Unlike a scientist, who – if he claims observation of a new quark or a cosmic string- must show empirical data that consistently shows it, as well as the means to confirm it.)
In the absence of P-facts and a defined C-construct (e.g. which concretely answers : ‘What is a soul?, What specific attributes does it have that are recognized by all) the claimant is in a parallel position to the Cretan. He claims something, even if only a possibility statement, but his system remains open since:
i)He’s not defined what exactly 'soul' means
ii)He has no P-facts to back it up which can be confirmed (independently) outside his reference frame
iii)He uses circular arguments to return to his original claim, e.g. “I have a soul because God created me with one’"
Hence, he is trapped within the realm of meta-statements. At the same time, the supernaturalist may complain egregiously about a Materialist (or mechanist scientist) for not being "open to the cosmos" as “having more than we can detect”.
But the claimant himself hasn’t provided the contextual basis to do that, since he’s only offered an open system (of putative axioms relating to his term) with no closure. No C-constructs, no P-facts. To escape a Godelian loop, the supernaturalist is obliged to:
i)Provide an operational definition for whatever concept, term or entity he invokes (“soul”, “God”, “Hell”, etc.)
ii)Provide one single construct based on (i), showing how this construct makes use of the definition,
iii)Provide a single percept or perceptual FACT that would even allow for it to be compared to a scientific hypothesis- say to explain the same phenomenon. (Energy might be a starting concept here)
The above basic parameters can easily be adjusted in any argument to show that supernaturalism-vitalism doesn’t hold up to logical scrutiny.
One may certainly make claims that are vitalist or supernaturalist in nature, but these must in the end be accepted on faith.