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You say that you accept the immortality argument. Are you willing to test it?

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No.

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One quick point on your counter to the argument that there is a 0% chance that we would be in the finite present world, given that there is an infinity of time in heaven. Even if there are beth 2 number of observer moments in the present world, either because there are Beth 2 number of observers experiencing worlds like ours, or because our present world is infinitely looped, I still feel like there would be an infinitely greater number of observer moments in heaven. We could just pair every single discrete observer moment in our present world to a discrete observer moment in heaven, and we would still have an infinite number of heaven observer moments left over.

For example, for every looped world consisting of a finite time spent in the present world and an infinite amount of time spent in heaven afterwards, we could pair the moments in the present world in one-to one correspondence with finite moments in heaven, and still have infinite moments in heaven left over. This would be true for every loop, and we could extend the pairing to all other possible Beth-2 observers as well. For every Beth-2 observer, there will be an infinitely greater number of observer moments spent in heaven, even if they spend an infinite amount of time in our present world.

One way around this I suppose would be to argue that the loop is such that we spend a finite amount of time in the present world, then a finite amount of time in heaven, then back to the present world, and so on…

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Kind of late to the party, but for a somewhat historically significant attempt at deducing something like the Trinity a priori, you could check out Vladimir Solovyev's "Lectures on Divine Humanity".

His argument is not really based on considering the Trinity as consisting of three different "people" so much as three different "instances" of the full nature of God expressed at different necessary logical moments within the process of self-awareness in a single infinite and eternal mind.

This is a very traditional type of metaphor for or explanation of the Trinity, with a version found in Augustine's De Trinitate. Something like the Father being God's base existence, the Son his perfect image in self-awareness (and thus the one through whom creation occurs, as a finite expression of that image and a finite revelation of that image to creates beings), and the Holy Spirit as the movement of God's love for the goodness perceived in the act of self-awareness/revelation in the Son.

The claim would be that these three distinct logical moments are all inseparable and thus not "parts" of God, and yet each has as its subject matter the full nature of God, and thus each "instance" contains God's entire being.

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I’m not exactly a Christian but I think you can derive something approaching the Trinity or even the real deal given the unique vantage point of human beings in the universe and God’s relationship to us, as implied by arguments about the nature of the mind, plus a few steps of reasoning about the nature of God’s presence in the universe.

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How?

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A truncated version: God created the universe so He must exist in an ultimate form external to it, ie the Father. Per many apologetics God also is present across time and space like a uniform field enabling things such as free will and the existence of souls, ie the Holy Spirit. If we grant all this then examine the phenomenon of religion, its clear that God has a unique relationship to human beings of all created things. And there is a kind of symmetry between the nature or “interiority” of being a mind and consideration of the edges of the universe. We are kind of epistemically barred from interrogating them in parallel ways, but both questions are also at the very core of who we are, both as a biological drive and in the neutral rational sense. Given the nature of religion and the marked symmetry of the human experience with other aspects of divinity, it makes sense to expect God to reveal Himself in human form.

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"But then the odds that I’d happen to be having these experiences now—which I’ll have for 0% of my total life—is zero."

I think this is wrong. The probability I'm alive now given an infinite afterlife is ~0. But that will be true for any point in the afterlife. If I die and go to heaven or hell or whatever and wait a million years at the end of the million years, I'll think "hey, my 80 years on earth plus a million in heaven" is an infinitesimal share of eternity. The odds of being around now is ~0. This will always be true so I think given the afterlife, we are unable to say existing now is any less likely than at any other point in time. So we can't say our location in time is particularly unlikely given the afterlife.

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