>The axiom that God doesn't exist is exactly on the same level as the one that he does. Both of them require the same type of assumption.
I'm with you on this. On some level, something caused the universe to exist. The explanations are: a Creator did it; or causality has no meaning outside of existence, so a first cause isn't necessary.
Either of those axioms requires an assumption, and once you make such an assumption, everything else is filtered through that lens.
But those are not any kind of axiom, because neither is a self-evident or clearly correct version of truth.
Two poor examples of an axiom are not "on the same level" as axioms.
>Either of those axioms requires an assumption, and once you make such an assumption, everything else is filtered through that lens.
What assumption does atheism make? None.
From the cosmologists' point of view, it is not clear that the cause of our observable universe need be available to our study within that observable universe. There is no assumption being made; it is simply an unanswered question, about which we are unsure we will ever have a useful answer.
>Atheism makes the assumption there is no God (read creator).
>Creationism makes the assumption there is a creator.
No. You are using the word "assumption" incorrectly.
In the scientific sense, I am using both the hypothesis that the creator exists and that the hypothesis creator does not exist to interpret the data of the world, comparing the results, and choosing the one as being more logical and likely. I assume nothing, though, being an inherently imperfect being, I recognize I must make some educated guesses to interpret the data before me -- but that is necessary for employing either hypothesis in the real world.
In a subtle sense, one could say that any hypothesis is a "working assumption" or a "tentative assumption". But, no, it is not the same as a just plain "assumption" as found in any dictionary.
It may be true that some people cut this short this process by making assumptions from the get go. But that is not intrinsic to atheism. Arguably, it is not even intrinsic to theism.
Atheism makes the assumption there is no God (read creator).
No, atheism makes no initial assumptions, and through reason and experimentation comes to the conclusion there is most likely (to a high degree of certainty) no God, at least not as defined by most religions.
Now, your final two sentences...
Both make assumptions. Both have the possibility of being incorrect.
...do not imply the third from last:
There is no difference between the two.
There are many other sorts of differences beyond assumptions and possible incorrectness. From a rational perspective, the evidence supporting one is much more rigorous (i.e. evidence has a higher prior probability and more supporting data to raise posterior probability).
You could assume that if I turn the key in my car's ignition it will start. I could assume that it won't. Both have the possibility of being incorrect. However, one of us has actually tested this, so one of us has better information.
I'm with you on this. On some level, something caused the universe to exist. The explanations are: a Creator did it; or causality has no meaning outside of existence, so a first cause isn't necessary.
Either of those axioms requires an assumption, and once you make such an assumption, everything else is filtered through that lens.