Atheism is the only reasonable, default position to take.

Introduction: First of all, thanks for your clarification. Now I understand the way you use theword "consistency", which is clearly different from the way I use it.I start my second round by responding to what I see as minor questions on my first round andthen I go back to the main argumentMinor Points:Valid PropositionA proposition is valid if it does not entail false. For example, '2=3' is an 'invalid' proposition, becauseit is unsatisfiable* by itself (i.e. any set containing it is unsatisfiable). A proposition 'God exists' isa 'valid' proposition because it is satisfiable by it self, its satisfiability depends on the set ofaxioms one accepts.* Notice that from now on I am going to use the word "satisfiability" to mean "logical consistency" to avoidmisunderstandings.Uniqueness#9 was not clear because of your unclear definition of "consistency", now it is clear, while technicallyspeaking it is still a statement that does not follow logically from the other ones since it uses languagethat has not be defined before, e.g. "reasonable default position". To be technically correct your argumentshould include your account for what is a "reasonable default position" and #9 should show that atheism is theonly one because there is only one: the empty set.Major Points:ConsistencyJust to clarify, in my argument I took your argument as a logical one, since you phrased your argumentin logic-related terms ('logical propositions', 'consistent', 'demonstration', 'axiomatic premises', 'refutation'...).Taking your definition of "consistent", I fail to realize why should #4 be accepted as an axiom, i.e.why should one treat all propositions as equal, when the preliminary definitions clearly state thatone is not obliged to?The Con could argue that it has been defined as an axiomatic premise and that I should accept it as so, but that leads as to the next point.The contradictionEven if you are trying to show that atheism should be accepted as a logical conclusion from your argumentyou do not show why should one accept your argument to begin with. The points #1-#3 do not create anyproblem since they seem to follow from the preliminary definitions, but #4 is stated as being an axiom, even if it is not an "accepted logical principle", and it does not follow from the preliminary definitions.It should therefore be accepted as a 'positive belief' without evidence, but from #7 we should refrainfrom accepting any proposition as true without evidence, and therefore from accepting #4 as true, which is a contradiction.In order to avoid this problem, the Con should present at least some evidence for supporting the acceptance of #4, which he did not do.* Notice that this response only tries to clarify the response I gave in the first round, by treating "atheism is the only reasonable default position" (#9) as a shorthand for "#1-#4 imply #6-#8", so, if we accept#1-#3 as being entailed by the definitions and your argument as being logically correct, the only remaining axiomto be proved to establish the correctness of the proof is #4. **** By #4, I mean your clarified reading for it and the intending meaning that one should treat propositions"consistently", either accepting all of them as positive beliefs or accepting any of them.Conclusion: So, in conclusion, you present an argument, without further evidence, that proves that one should refrain from accepting any proposition as true without further evidence. This therefore includes the proposition "a god or god exists" (and hence supports atheism) but also the proposition "this argument is true" (which contradicts atheism).