Our new cosmological argument for the existence of God weakens the usual Principle of Sufficient Reason premise that every contingent true proposition has an explanation to a weaker principle (WPSR) that every such proposition could have an explanation. Almeida and Judisch have criticized the premises of our argument for leading to a contradiction. We show that their argument fails, but along the way we are led to clarify the nature of the conclusion of our argument. Moreover, we discuss an argument (...) against us based on a principle of alternate explanation incompatible with our WPSR, and show that his argument fails. (shrink)