How do Latter-day Saints rebut GM Skeptic's objection against the epistemic value of personal spiritual experiences?

Logical fallacies

This argument commits:

• Circular reasoning--personal experience is used as a premise to argue for a conclusion about the validity of personal experience
• Self-refutation--personal experience is used as evidence to show that personal experience is not valid evidence
• Fallacy of division--GM Skeptic states: Because of the exclusive nature of these religions, they can't both be right -- if we grant that this statement is true, it does not mean that everything taught within these religions is false.
• Third-cause fallacy - as already noted by depperm, GM Skeptic appeals to correlation and suggests it requires causation. (Furthermore, explaining how something happens does not necessarily explain why something happens)

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Doctrinal disagreements

• Spirit is matter: the suggestion that something "spiritual" behaves like matter is not a problem for Latter-day Saint beliefs. "There is no such thing as immaterial matter. All spirit is matter, but it is more fine or pure, and can only be discerned by purer eyes" (D&C 131:7)
• Ask & ye shall receive: we don't believe that revelation is intended to be mystical; we believe it is intended to be instructive, and that God answers questions. See an example of this argument here: Quality Revelation Comes From Asking Quality Questions (note this is not an official church source). A response like "yes!" makes a lot more sense if it's clear what the question was.
• God is no respecter of persons: we believe God is willing to witness of the truth to all who are willing to seek Him. We are not surprised by spiritual experiences in other faiths; we believe there are elements of truth therein, even if they do not have the fulness of the Gospel of Jesus Christ:

5 If any of you lack wisdom, let him ask of God, that giveth to all men liberally, and upbraideth not; and it shall be given him.

6 But let him ask in faith (James 1:5-6a)

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Epistemological Musings

All evidence of any form rests upon a foundation of experiential evidence. Whether that evidence came from an equation, a machine, or human senses, take it back a few steps and you’ll end up with a human mind. A human mind developed the mathematical axioms and the machine, and a human mind interpreted information presented by the senses.

We cannot get around experiential evidence. Those who suggest it be excluded from consideration discard their own worldviews along with those of their opponents. Even the claim that something should be trusted because it is reliable is an appeal to experiential evidence.

One of the strengths and weaknesses of experiential evidence is that one individual's experience is not directly accessible to other individuals. If someone else appeals to experiential evidence I may not know if the claim is true or false; this is one reason why aggregators like language and scientific inquiry are so powerful. Language allows people to convey their experiences using mutually understood symbols (like words). Scientific inquiry calls for outlining a process that can be repeated, allowing others to learn--through the experience of testing--what someone else has already learned.

I am not the least bit bothered by the possibility that someone may claim an experience that wasn't real, or may interpret an experience incorrectly--just like I'm not bothered by the possibility that language is sometimes misinterpreted or that good scientific practice sometimes leads to erroneous conclusions that are later overturned. But if the reliability of anything flowing through experiential evidence is subject to error, how can we be sure of anything?

2nd best method: Induction. If something is repeatable, with successive iterations we can raise our level of confidence.

Best method: Reasoning in the absolute. One who can reason in the absolute can rule out all competing possibilities (we fallible mortals cannot do this). If there is an Omniscient & Omnipotent Being who can reason in the absolute, information learned from Him would be epistemologically superior to anything learned from sources that cannot reason in the absolute. The claim that I have learned something by revelation from God would be the most secure statement epistemologically possible for a non-omniscient being (such as myself) to make.

A claim that is one step removed from Someone who can reason in the absolute is epistemologically inferior--that is, between:

1. Abraham says he met with God
2. God says He met with Abraham

Both statements may describe the same incident, but claim 2 is epistemologically superior.

For the same reason, any epistemological claims made by other people--supporting or opposing the existence of God--will never be so powerful as obtaining that answer directly from the source. A Being that has all power would necessarily be able to make Himself known unmistakably. I claim that He has.

Disclaimer--these thoughts are the product of my own study and do not constitute official statements by The Church of Jesus Christ of Latter-day Saints

Post-script

Re the coin flipping objection, flipping a coin many times is in fact a reliable means of demonstrating either:

• This coin is loaded/imbalanced OR
• This coin will on average deliver 50% heads and 50% tails.

Both can be demonstrated with a very high degree of statistical significance if one has the patience.

However, this information is accessed through experiential evidence (as are all observations in science); as a result, using observations about coin flips in order to argue against the usefulness of experiential evidence is logically invalid.