[jason1990]

In my opinion, the only thing a Frequentist can say about the Two Envelope Paradox is what you yourself have already said.

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the amounts in the envelopes are Fixed...each time a Person opens an envelope and sees an amount, the conditional probability of the second envelope being double the amount he sees is either 100% or 0% - he just doesn't know which.

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There is no repeatable experiment in the Paradox. As you said, there is no sequence of envelopes for you to choose from. But neither is there a sequence of people choosing from those envelopes. There's just you and the envelopes and a one time choice. Introducing any kind of repeatable experiment is adding something to the Paradox that wasn't there.

In my opinion, the Paradox is entirely a lesson for Bayesians. The Bayesian equivalent of "I know nothing" is the uniform distribution. If a Bayesian has no information about an unknown quantity, other than the fact that it is a member of some set, then it is common for the Bayesian to assume that the unknown quantity is a random element of that set with a probability distribution such that all members are equally likely.

In fact, many people who have never even heard the word "Bayesian" have made this Bayesian assumption, without even explicitly realizing they are doing so. Anyone who has assumed this has a little Bayesian in them, and this Paradox is a lesson for the Bayesian in all of us.