STAN: On Axioms and First Principles

My interlocutor Stan over at Atheism Analyzed is rather graciously attempting to reboot our convo, so for the benefit of those who might've had a hard time following the give-and-take, here's Stan (in deep violet) and yours truly (burnt orange)....

Axioms and First Principles

Scott, OK then, right to the point this time. The question at hand:

“Given that I need a foundation of some support, what principles would you commend, and for what reason? Am I compelled by logic to adopt any, some or all of these principles?”

There are several definitions of the concept, “axiom”. Two seem to fall out:

(a) A precept that is used to support a different claim, but which is itself unprovable, therefore it is assumed valid for the sake of argument. Structure:

“Given N, and assuming A, then P”,
where A is the axiom, unprovable but assumed valid for this instance.

(b) A precept that is self-evident, unprovable, whose negation is self-contradictory.

I think that (a) is the type of axiom to which you were referring. That type of axiom is not known absolutely, but could be considered statistically to be probable, as you said.

Type (b) is a sort of jump off point to the First Principles, which have the following characteristics (maybe more):

First Principles:

(1) Validity is self-evident, or it is “incorrigible” (not correctable).

(2) Unprovable.

(3) Negation is self-contradictory.

(4) Exist as a ‘bottom” element in a regressive analysis, without which an infinite regression would occur.

(5) Generally tautological (definitions).

(6) The circularity of tautology implies a priori comprehension.
For example, the dictionary uses words to define words (it is circular); one must understand some word at some point a priori in order to use the dictionary.


Examples of First Principles:

Euclid
“Things that are equal to the same thing are equal to each other”

Aristotle
"For the same (characteristic) simultaneously to belong and not belong to the same (object) in the same (way) is impossible."

Descartes
“Cogito ergo sum” (I think therefore I am) (also, “I doubt everything, but I think about doubting, therefore I am a thinking being, therefore I am)

The general list of First Principles is both epistemologically and ontologically applicable (i.e. both truth values and existence values).


These are intuitive and incorrigible:

a. Identity: if it is true it is true; if it exists it exists.

b. Non-contradiction: It cannot be both true and false simultaneously. It cannot both exist and not exist.

c. Excluded Middle: It cannot be partially true, partially false. It cannot partially exist.

e. Cause and Effect: For every effect there is a necessary and sufficient cause.


These are probabilistic:

a. The Immutability of math throughout the universe.

b. The Immutability of physical law throughout the universe.

c. The Immutability of physical law throughout time (past and future).

d. The mutability of all levels of verifiability (Gödel's theorems).


There is more detail here. (Note to the reader: The link goes to Stan's site, where you should search for First Principles)

Now to the point. If these things are wrong, then much of rational thought and it’s offspring, empiricism, cannot be thought to provide any valid concepts. So these things are thought to be true….without proof. More to the point they are understood as valid statements, intuitively.

If that last statement is true, then intuition is a valid tool for comprehension of concepts possessing those truth values which exist outside the range of empirical testing or proof.

I stop here, with the understanding that the discussion of erroneous intuition, imagination, self-delusion, and dreams might be next.

For now, is this path as stated so far, reasonable?

As for a box to contain my own philosophical position, radical idealism it is not. Perusing the box categories on Wiki, I suppose that Justificationism comes close. I accept and support the discipline of empirical science. I do not support Naturalism or Materialism which I consider to be false, agenda-burdened, and parasitic to empiricism. Abduction is difficult to support due to the use of wild extrapolations without checks and balances.

And I agree with Einstein’s rebuke to Hume concerning locking out meta-physics by definition:

“…those convictions which are necessary and determinant for our conduct and judgments cannot be found solely along this solid scientific way.For the scientific method can teach us nothing else beyond how facts are related to, and conditioned by, each other. The aspiration toward such objective knowledge belongs to the highest of which man is capable, and you will certainly not suspect me of wishing to belittle the achievements and the heroic efforts of man in this sphere. Yet it is equally clear that knowledge of what is does not open the door to directly to what should be .”

Albert Einstein, Science and Religion, Mein Weltbild, Amsterdam: Querido Verlag, 1934.