I assume that:
- most christians believe in a single one god (monotheism); and
- that this god is the christian god.
In that case, how do you know that the gods in other monotheistic religions do not exist?
How do you know that there are not multiple gods (polytheism)?
I know I'm late to this discussion, but here goes.
(a) I assume that most christians believe in a single one god (monotheism)
That's safe to assume. It's also safe to assume that they believe in the Trinitarian God.
I exclude from this most unorthodox religions, including, but not limited to The Church of Jesus Christ of Latter-Day Saints (they believe the Trinity is three distinct gods, and also in eternal progression, i.e., "As man now is, God once was; as God is now man may be" [Lorenzo Snow], so that there is an infinite cycle of Gods stretching through eternity), The Church of Christ, Scientist (they deny the Trinity, and God as a personal force), the Jehovah's Witnesses (again, deny the Trinity), and Unitarian Universalists (deny the Trinity and the authority of orthodox Christianity).
(b) I assume that this god is the christian god.
Yep, another safe bet. We don't believe in Cthulhu, if that's what you mean.
(c) In that case, how do you know that the gods in other monotheistic religions do not exist?
Because we have faith in the Bible, and that it is the inerrant and infallible Word of God. We believe that we are guided by the Holy Spirit ["Therefore I want you to understand that no one speaking in the Spirit of God ever says Jesus is accursed! and no one can say Jesus is Lord except in the Holy Spirit." 1 Corinthians 12:3 ESV], and thus know the Truth.
We trust in God when He says: "I am the LORD, and there is no other, besides me there is no God." Isaiah 45:5 ESV
You ask how we know that the gods in other monotheistic religions do not exist, but you said it yourself:
We are monotheistic. Thus we believe other gods do not exist.
(d) How do you know that there are not multiple gods (polytheism)?
Personally, as I am a recent convert, I have travelled in circles were Paganism is practiced.
Ásatrú to be exact. You know, Óðinn, Þórr, Baldr, Heimdallr, Hveðrungr [Loki], Yggdrasill, Bifröst, the Jǫtunn, Jǫrmungandr, Valhöll, Ragnarök, &c., &c.
You know, I wore a Mjǫlnir, and all that good stuff.
I was in the folkish branch, which believes that only the children of the North can follow the Gods of the North (I'm mostly English, Norwegian, and German, so I fit the mold perfectly).
But then I realized something.
My ancestors gave up the Forn Siðr a thousand years ago for a reason.
They threw their idols off the Goðafoss in Iceland,
They built Stave Churches,
All for a reason.
There is a reason why Christianity is the predominant religion in Europe.
There is a reason why Christianity is the worlds largest religion.
It's called the power of the Holy Spirit.
It's called Jesus.
It's called God.
The Old Gods are there if you look for them. But they were converted as well.
That's my two cents, at least.