For simplicity, I can reduce what I’m saying to:

1) x = x is necessary only if x is necessary.
2) x is necessary.
3) Therefore, x = x is necessary.

That illustrates the bind I was getting myself into arguing with Aaron in regard to a necessary being. “x = x is necessary” is pretty straight forward when it comes to mental entities like x. However, when “x = that particular person/being/existent,” I don’t see how we can escape the qualification “… only if that particular person/being/existent is necessary.” Since that person known as Samuel Clemens is merely possible, how can we even say "Samuel Clemens = Samuel Clemens is necessary"?

I don’t understand what you mean by “discoverable.” Since identity statements are necessarily true if true and necessarily false if false, what we’re discovering via the empirical evidence is what we assumed was a necessarily true statement (Samuel Clemens is not Mark Twain, necessarily) is false. So what we're discovering isn't some unknown necessary truth, but rather what we assumed true was in fact false and hence it's binary true. Maybe that's just splitting hairs, though.

It might help John to try and very precisely define what the difference between a "true statement" and a "necessarily true" statement is. Perhaps giving 5 examples of each category.

You're getting distracted and not addressing the actual argument. Here it is again:

4) IF Samuel Clemens is Mark Twain and Samuel Clemens exists, then Samuel Clemens is Mark Twain necessarily (law of identity).
5) Samuel Clemens is Mark Twain.
6) Samuel Clemens exists.
7) Therefore, Samuel Clemens is Mark Twain necessarily.

This is a valid argument. Therefore, if the premises are true, (7) is also true. Since the argument proving (7) relies on (5) and (6) being true, our level of certitude about the truth of (7) will track our level of certitude towards (5) and (6). Since (7) is a necessary statement, then if (4) is true your thesis that we can't sensibly ascribe probabilities other than 0 and 1 to necessary statements is also false.

You claim that (4) is false (I guess?). That is, you think it is possible that Samuel Clemens is Mark Twain and Samuel Clemens exists, but also that Samuel Clemens is not Mark Twain. That is, you think it is possible that Samuel Clemens is Mark Twain and is not Mark Twain. Please explain.

What I mean by "discoverable through empirical means" is that our knowing whether some claim p is true is done through an empirical investigation, eg in science or history rather than through reason alone as in math and logic. You are implicitly assuming that all necessary claims can only be known through reason alone (i.e. can only be known a priori). I'm proving this false via counterexample.

I dont know what you mean. The existence of things tells you nothing about the existence of god. Why do you think it does?

I dont think any materialist says "Things exist, therefore materialism is true". If they do , they are equally as incorrect as you were(depending on what you are meaning by materialism, I guess).

The bind is a bit worse than I think you imagine it to be. It's not even clear that you have a clear sense of what you mean by the word "necessary" here as you seem to be glossing over it repeatedly.

* When you say "God is a necessary being," what do you think the function of the word "necessary" is? How do you conceptualize the "necessity" of the statement?
* When you say "It is necessary that 2+2=4," what do you think the function of the word "necessary" is? How do you conceptualize the "necessity" of the statement?

You may also want to consider the idea of "vacuous truth" as you continue to explore these ideas, as well as come to terms with "possible universes" as a concept to help you think through your statements.

A square necessarily has exactly four sides.

Mark Twain is not necessarily Samuel Clemens.

I’m not saying that. I’m saying everyone is relying on “everything” to make their case. Consider materialism and idealism: since their respective proponents are relying on the same evidence, how do you determine which one is more probable based on the evidence when they’re both relying on the same evidence?

Okay? Do you have an argument to back up this assertion?

Here's my argument. "Mark Twain" is the name of a person. "Samuel Clemens" is the name of a person. The person referred to by both of these names is the same person. Since people are necessarily identical with themselves, Mark Twain is necessarily Samuel Clemens.

Now, of course it is possible that the names "Mark Twain" and "Samuel Clemens" could refer to different people than they do in actuality. If so, then of course Mark Twain would not be Samuel Clemens. However, (7) is not an assertion about the possibility of who could be referred to by the names "Mark Twain" or "Samuel Clemens," but rather an assertion about the person referred to in the actual world by these names, positing that the person referred to by these names is the same person. That claim, if true, is necessarily true.

That's all I'm trying to do:

4. Objections to Rigidity
(A rigid designator designates the same object in all possible worlds in which that object exists and never designates anything else. This technical concept in the philosophy of language has critical consequences felt throughout philosophy. In their fullest generality, the consequences are metaphysical and epistemological. Whether a statement's designators are rigid or non-rigid may determine whether it is necessarily true, necessarily false, or contingent.)
Various objections to the coherence or usefulness of rigidity have been put forward by specialists in the philosophy of language, though the objections do not seem to have done much to damage the widespread appeal of rigidity, which is commonly taken for granted in mainstream literature from various areas of philosophy. (Whether your typical philosopher is entitled to embrace rigidity is another matter: so there is a case for saying, on grounds independent from the foregoing objections, that rigidity and the necessity accompanying it stand or fall with a robust version of the analytic-synthetic distinction (see note 6). If that case is solid, then either popular Quinean antagonism toward analyticity should prompt the rejection of rigidity or else the appeal of rigidity should prompt the rejection of the familiar antagonism toward analyticity.) What resistance to rigidity there is may be addressed in general terms first, in order to save for its own subsection (§4.2) treatment of objections specifically directed at the application of rigidity to terms for properties, which are especially contended.

Kripke’s Category Error: Why There Are No Necessary A Posteriori Propositions
I will continue Quine’s, Stalnaker’s, and Chalmers’s line of attack using the “argument from propositional ambiguity.” While related, my argument is that single sentence can frame a proposition about a thing-in- itself and also frame a proposition about a mental construct of that thing.

Against the Contingent A Priori
Since Saul Kripke’s Naming and Necessity, the view that there are contingent a priori truths has been surprisingly widespread. In this paper, I argue against that view. My first point is that in general, occurrences of predicates “a priori” and “contingent” are implicitly relativized to some circumstance, involving an agent, a time, a location. My second point is that a priority entails necessity, whenever the two are relativized to the same circumstance. In other words, what is known to be the case a priori (by an agent in a circumstance) could not fail to be the case (in the same circumstance), hence is necessary.

A Posteriori Necessity: Misled by Language?
Kripke's discovery of a posteriori necessity is often invoked as a great discovery in 20th Century Analytic Philosophy. I think it was an important discovery--just not what some seem to have thought it to be. Allow me to explain. Recently, I have been arguing--along with people like Avner Baz and Mark Balaguer--that it is important not to confuse conceptual analysis with metaphysics. The traditional story of Kripke's discovery, if I have it right (and I may not), is that Kripke made a metaphysical discovery: that he discovered really interesting modal metaphysical facts (e.g. water is necessarily H2O) that we come to grasp through empirical discovery (i.e. water's molecular structure). I want to suggest that this is not quite right.

Against the Necessity of Identity Statements
Initially in this essay, I will provide an account of Kripke's claim regarding the necessity of identity statements. I will give a systematic analysis of the structure of Kripke's argument, facilitating an examination of the mechanics of the argument and my critique thereof. My criticism lies in the challenge to Kripke's intuitive claim that proper names are rigid designators, and that therefore the relation expressed in an identity statement between a name and the object it picks out is a necessmy one. I will argue that identity statements (employing descriptions, in names, and in statements in science) are contingent, not necessary, undermining Kripke's notion of the a posteriori identity.

Are you more interested in exploring or defending?

You would be well-served to try to put these statements into your own words. It feels kind of scattershot right now and it's not clear what ideas you're actually trying to bring together into coherence or whether you recognize where they all fit relatively to each other and your underlying claims.

For example, you didn't clarify your position on the two questions that I asked you. That simple language usage may go a long way in bringing coherence to your perspective.

I dont understand what you mean by this, or how it relates to materialism.