Not quite. I'm not saying that since there is only one God, any worship directed toward any god is actually worship of the one. What I'm saying is that if you and I choose to worship the same god but we both come to radically different conclusions about that god based upon our personal experience of that god, we are still worshipping the same god.
That's circular reasoning. You can't assume that two folk are woshiping the same God and then use that as evidence that they are actually worshipping the same God.
You're argument boils down to "if we're worshiping the same God then we're worshiping the same God." Well. Duh. But that doesn't support the claim that folk actually are worshiping the same God.
One of us may be doing it wrong, but the worship is still directed at the same "place".
Does not follow.
So if two Jews point toward the Torah and both say "I worship that God", they do. And if a Christian points to those same books and says "I worship that same God (and by the way, here's some more of God's revelation for your perusal)", then she still worships that same God (though she might be doing it wrong).
Now add, "But God didn't actually part the Red Sea, and all those prophecies about a coming Messiah? Forget them" or similar changes, not just "additions" but outright contradictions and you'd be closer.
And if a Muslim points toward the Christian Bible and says "I worship that same God (but really, the final authority on God's full revelation to man can be found in this book I have right here)", then she too is still worshiping the same God, just in a different and possibly incorrect way.
Sorry but that does not follow. Christians worship a God that is the literal father of Christ or a God that took physical form to become Christ (depending on flavor of Christianity). Muslims worship a God that did not do those things.
To play a bit with the Beatles analogy it would be like saying "I'm a fan of John Lennon for writing Octopus's Garden" and someone else saying "I'm a fan of John Lennon for writing Maxwell's Silver Hammer." Since John Lennon didn't write both (in fact, he wrote neither--another possibility that people often neglect in discussions of this kind), even though they use the same name ("John Lennon") for both the author of Octopus's Garden and the author of Maxwell's Silver Hammer they are not talking about the same author since the same author did not write the two songs.
Don't confuse the label with what the label is applied to. Don't confuse the map for the territory.
I guess I'm saying that the individual's intent determines
the object of her worship, even if that worship is fundamentally flawed in some way.
The problem with that argument is that anyone who "intends" to worship what they think is the "one true God" whether that God is YHWH, "Allah," Odin, Loki, Raven, Enlil, Shiva, Tezcatlipoca, or something you or I have never even imagined would, by that argument be
Note that I'm not saying that Jewish, Christian, and Muslim teachings all have to be compatible with one another in order for them all to worship the same God. And I do understand what you mean by stating that the object of worship is determined by the conception help by the worshipper--I'm just coming at the problem from the other direction.
I think it really does come down to a fundamental difference in our respective understandings of "worship". That's cool, though, because I think we've gotten to understand what each other are saying, and that's the fun part anyway.
Actually, I think the difference is more fundamental than that. Here's a little thought experiment for you: can you imagine any worship of what someone believes is "one true God" that would not be worship of the "same God" as that of Christians? If not, then I submit that your definition is such as to be meaningless*. If so, then consider what makes that God different from that of Christians and whether those distinguishing characteristics are fundamentally different from the distinguishing characteristics between Judaism, Christianity, and Islam.
*To be meaningful, a word, statement, argument, or what have you has to have possible situations where it is true and those where it is not. It has to discriminate between categories (true/false, is/is not, etc.). A statement that is always true, say "it is raining or it is not raining" tells you nothing about the world. In formal logic this is called a tautology and it and it's converse, a statement that is always false (a contradiction), are considered logical flaws.