Final answer:
Aristotle would not consider an argument that is not based on ethos, pathos, or logos, such as an appeal to ignorance, to be a persuasive 'proof' because it is not rationally convincing.
Step-by-step explanation:
According to Aristotle, a persuasive 'proof' must be logically compelling and capable of convincing a rational person of its conclusion. Considering the types of proofs Aristotle identified such as ethos (character), pathos (emotion), and logos (logical argument), the statement that does not qualify as an Aristotelian persuasive proof would be one that is not based on these elements. For instance, an argument that relies on an appeal to ignorance or lacks connection between the truth of a belief and the evidence for that belief, as also mentioned by Harman, would not be deemed a persuasive proof by Aristotle's standards.
Philosophical discussions, such as the existence of deities, often involve various arguments and proofs, many of which can be scrutinized for logical flaws. As per your question, an argument stating that since one cannot provide evidence against the existence of God, thereby concluding God exists, would exemplify a non-persuasive proof because it is an argument from ignorance, which does not satisfy the criteria of rational acceptance based on positive evidence.