well the Christian argument basically relies on that Jesus defeated Satan by his death and resurrection; because by that he defeated death (because he did not stay dead) and sin (re: discussion had earlier), hence triumphing over the powers of evil. There is obviously more to it. But that is simplest explanation that any person could reasonably understand.
This means not only is Satan disarmed, he is already doomed to destruction (this may also answer the second question in some degree, as his fate is already sealed).
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logically, it will depend on your definitions of God and Satan. I honestly think it doesn't make much sense without reference to the former, but I will give it a shot by contradiction.
remark: We will define Satan as the greatest conceivable evil entity.
If God (YHWH), being intrinsically good, has not defeated Satan, then God is not the most powerful being (and ditto for all others in that category), leaving Satan as the most powerful being, since God was not able to beat him. Then unless we hold to some dualistic (a good God and an evil God) religion, we are left with the conclusion that God is not God, which is absurd.
It does require these two underlying things, which have to be deduced separately:
The main issue I have is it mainly "words" rather than more of an argument, it is hardly airtight, and more of a sketch.
1. That GOD is the most-powerful and greatest (conceivable?) incorruptible being, by definition. (This is just a definition, so it is easy to deduce, in fact this is generally the accepted concept for God, but not always)
2. For the sake of argument, we can use the conclusion that GOD is God (YHWH), or for that matter any God that satisfies by their nature and attributes the above definition. Namely that God is a loving, just God from (1). To actually deduce this properly, is the point of this thread of course, but it is not something that can be just proven, but more so asserted with confidence on the evidence (but one can with sufficient evidence, assert the opposite).
The underlying assumption is that the greatest conceivable being must be good and loving. This assumption is probably just as hard to prove, but is generally accepted. (A proper discussion of this might be a bit beyond what I am trying to address). In fact logically, this is where the argument hinges.
(We can basically say that this can be justified by examining/reducing to simpler things, such as the law-maker tends to set what is good, but this simplification fails because from experience, not all law-makers are incorruptible
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The basic premise of this argument is found by replacing Satan, being the embodiment of evil, with evil itself.
The real question is what attributes would one prescribe to the most greatest conceivable being, well for starters, we would most likely assume depending on how we view the world, certain positive attributes (in our very nature, we esteem good things, such as kindness, charity, justice, truth etc. etc.) would be presumed that the greatest being would have. The real question is how can we prescribe these attributes.
Now if God decided not to deal with evil properly then Frankston we have a problem..., as God is not just
Now if God decided not to keep the promise to deal with evil at some point, then Frankston we also have a problem..., as God is a liar.
which if God is supposed to good, he isn't, so maybe evil is not the most conceivable evil.
Basically, God would not be God, if he did not have the attributes that by definition he should have. The most obvious is omnipotence. In fact what we can deduce directly about the divine without word-twisting is, that if God exists he has to be powerful, but not necessarily loving. While that doesn't disprove God's existence it can indeed.
The converse is also true. If one can systematically disprove all the attributes that are supposed to be there in the lack of God's existence, then you have a proof by contradiction for God's existence. Unfortunately if one only disproves one attribute one can still challenge whether the absence of God leads to.
In the end, you can only prove God's existence and non-existence, if the implications of either claim can be proven or disproven (the latter is stronger).
In fact that is why for instance there are different views of God.