You're right, about first order logic not being all there is to [theology].
We know some things from eyewitness accounts that are judged to be
reliable. But...
Christians have evaluated the eyewitness accounts (such as accounts of
experiencing the presence of God, or an act of God) using techniques of
evaluation that are common in the hard sciences, or in a courtroom.
Christian reasoning, WITHOUT formal logic, is heavily crippled.
Logical models, cut free of the balancing keel of our shared reality,
is also subject to personal bias, and speculation. We reason about
our shared reality, to come up with explanations of Christian doctrines,
even in cases when we cannot demonstrate Christian doctrines
through logic alone.
And, the study of linguistics involves the study of logical human
languages, logically analyzed. Scripture was given to us in human
languages, so logic is involved in the translation and interpretation
of Scripture (I reject the solely mystical approach of "the Holy Spirit
told me that this passage means...").
For Christians who embrace formal logic, there are serious skills to be learned.
As you mentioned, one of the worst errors of starting logic students is that
they make mistakes translating human language into logical notation. This
can be fixed through a lot of practice.
Also, as Christians find out if they study Moral Theory, and the common historical
modes of morality-ethics, human language can refer to groups of related truths,
that cannot be enumerated individually. Most of the 10 Commandments, are of this
type of "super-rule". "You shall not murder a human being" is an example. It is
not a complete listing of all the ways in which we could murder a human being.
Which means that we need an "decision algorithm" (a method to go through) to
evaluate whether or not a specific action is actually "murder".
(Note that all ME (moral-ethical) systems have these general "super-rules",
and that there is no solution for globally determining the comprehensive meaning
of a ME model, for every possible action. This is why building a ME model into
an AI software tool, is a very, very difficult problem to solve.)
---------- ----------
An example: remember Asinov's rules for governing the sci-fi behavior of
a robot...
1 A robot cannot harm a human being
2 A robot cannot allow a human being to be harmed
3 A robot must obey a human being, unless it would be breaking rules
1 or 2
Note that rule 1 cannot be enumerated, as to all the specific behavior that
harms a human being. And, modern pagan culture claims that all sorts of
benefits are Entitled to us, even if God does not hold these "entitlements" to
be human rights. Is a human woman being harmed, if she can't wear 2 inch
fingernails to class? Is an employee harmed during work hours, if they can't
be on social media and texting their friends all day long?
Rule 2 is even more impossible to completely enumerate. Because it deals
with possible future sequences of actions. Can we really PREDICT the future
(including the free will of human beings) accurately enough to evaluate what
COULD cause a human being harm in the future?
Rule 3 is impossible to evaluate and apply, because rules 1 and 2 are impossible
to evaluate.
NOTE THAT "LOVE GOD WITH ALL YOUR BEING, AND LOVE YOUR NEIGHBOR
AS YOURSELF", are just as impossible to enumerate.
---------- ----------
Many ME systems claim to be doing "what is best for the most people".
Of course, no one agrees on the list of things that are "good".
And, no one can agree on the hierarchy of the good things, to prioritize.
And, given a hierarchy of goods (such as the Constitution and Bill of rights,
in a state's fair rule of law), there will ALWAYS be citizens who disagree
with the application of justice TO THEM, although everyone wants "justice"
to be applied to EVERYONE ELSE BUT THEM. (Trump in his legal woes, is
an example of this position.)
We see this dysfunction of disagreement overcome (supposedly), by the
atheistic Communist and Socialist systems, that use a decision algorithm of
"doing what is best for the people". History tells us how terribly this rule
fails, because it is unfalsifiable. It is not a rule. It is not an ME system.
---------- --------
The interesting thing about this topic, is that although there are questions that
are beyond the reach of logic to solve (try reading The Outer Limits of Reason,
by Yanofsky), rejecting reason/logic altogether gets you into a place in which
you cannot reason about the limits of reason, or what the interpretation of
Scripture is, or what the guidance of the Holy Spirit is. You can't even evaluate
what a ridiculous conspiracy theory is. Or reason about what our shared reality is.
Also, rejecting the core logic of Epistemology, means rejecting the evaluation
principles for deciding what evidence there is, in our shared reality. AND,
deciding what good evidence to add to our personal belief system, and
when we need to re-form our personal belief system, because we have found
new sound evidence that contradicts it. (The lack of these sound rules for
re-forming our personal belief system, is why people embrace ridiculous conspiracy
theories. And we see that this is common, among groups that are uneducated,
or who have already rejected intellectual development.)
---------- ----------
As Stephen Meyers has said in Return of the God Hypothesis, most of the hard
sciences are not proven with pure deductive logic (which is what formal logic is),
but are based on inductive thinking, creating hypotheses, and testing them (with
methods that are formulated based on deductive logic).
The philosophers, in discussing what truth is, found their arguments on deductive
logic. There is nothing wrong with deductive logic. And there are algorithmic ways
to transform probabilistic assertions (for example) into deductive logic assertions.
Computer Science has done this, for decades. Even proofs in the approximation
logics, have individual lines of the proof that threshold into TRUE/FALSE (which
is deductive logic).
---------- ----------
I am currently publishing a book on the fusion of deductive logic, a Christian
worldview, and the analysis of modern arguments (based on a Christian
worldview). I know that promotion of products is not allowed on this site.
But, I recognize the importance for Christians to recognize the place of
deductive logic in the orthodox faith, and morality, and how to recognize
flawed modern arguments. No matter how this fusion is made, it remains
a very difficult problem.
But, Christians are not ENTITLED to reject formal logic, even if it is a limited
tool.
And that's my position, on the topic.
