I think you should apologize for making this post. There are a lot of important things that aren't mathematically rigorous but are nevertheless worth understanding.
I agree that there are lots of things that are worth understanding but can't be expressed in rigorously logical terms. Things like the subjective experience of falling in love or laughing at a joke or the value of behaving toward others with compassion. Wovon man nicht sprechen kann, darüber muss man schweigen.