Just to add one more category of God’s Creatorhood - he is pictured as a lawmaker. And that’s the one aspect that science is equipped to investigate. It’s odd, though, how partitioning off such lawmaking into a secular pursuit somehow enables people to say that “science now knows that x is not caused by God, by by the laws of nature.”
However, it would be a gross error to decribe God as merely a lawmaker - yet many seem to come close such errors, by saying that God created the world we see entirely through the laws of nature. It seems that in that area, it’s accepted that one can investigate the works of God, but I’m not sure how that is conceptually distinct from any other kind of deduction about his works.
@swamidass
Back on the engineer/artist distinction, I’m not sure how one can maintain that when there was no such distinction through most of human history, until the last century or two: Leonardo was an artist and engineer, Phydias likewise in ancient Greece. And in the Bible, the artisans chosen by God to make the tabernacle (and recognised by Richard Middleton, for example, as being portrayed in conscious parallel to God’s role in the Genesis 1 narrative) and combine both practical and artistic skills by the Spirit of Yahweh:
Then the Lord said to Moses, 2 ‘See I have chosen Bezalel son of Uri, the son of Hur, of the tribe of Judah, 3 and I have filled him with the Spirit of God, with wisdom, with understanding, with knowledge and with all kinds of skills – 4 to make artistic designs for work in gold, silver and bronze, 5 to cut and set stones, to work in wood, and to engage in all kinds of crafts. 6 Moreover, I have appointed Oholiab son of Ahisamak, of the tribe of Dan, to help him. Also I have given ability to all the skilled workers to make everything I have commanded you: 7 the tent of meeting, the ark of the covenant law with the atonement cover on it, and all the other furnishings of the tent – 8 the table and its articles, the pure gold lampstand and all its accessories, the altar of incense, 9 the altar of burnt offering and all its utensils, the basin with its stand – 10 and also the woven garments, both the sacred garments for Aaron the priest and the garments for his sons when they serve as priests, 11 and the anointing oil and fragrant incense for the Holy Place. They are to make them just as I commanded you.’