The following things cannot be defended with logic, and should be renounced at once:
- Love
- Beauty
- Inner Peace
- Music
- Poetry
- God
These are not comparable.
Love, beauty, etc are emotions that we seek to describe in order to better communicate those emotions between humans. Without a human to communicate the concept of 'beauty' it becomes meaningless, that is it's reality cannot be understood by an independent intelligence. This is not true with 'God', meaning here, I presume, a universal creator standing outside creation.
To explain - a random alien could come to Earth after the end of humanity and read our jottings. Let us assume that they are capable of reading and interpreting our texts. They could understand 'beauty' as meaning 'pleasing to one's senses' but would not, from that, be able to immediately refer to an object we might find beautiful and know that we had found it beautiful.
Conversely, though they can understand the concept of 'God' as universal creator with equal dexterity, the concept of 'God' differs qualitatively in that, had the aliens come into contact with the creator, they would immediately be able to recognise the actual creator as fulfilling the concept defined by us as 'God'.
Put simply, 'beauty' is a relative concept the application of which does not exist independent of humanity, therefore it is incapable of 'proof'. 'God' is an absolute concept that - if real - exists independent of humanity and is therefore capable of proof.
As a result I would logically contend that the OP question is relevant to 'God' but not to 'beauty'.
BFR