[betty boop]

Physical laws are approximations.

OK. Actually, I prefer the interpretation of physical law that says the physical laws are descriptions of the regularities that (contingent) nature tends to manifest -- approximations as you say, and not "laws" in the normative or causal sense.

But whatever they are, are they "physical," materially embodied, tangible, matter-based entities that may be isolated and directly observed as such?

[RightWhale]

Here's a question that may be related. What is more real, your house and lot, or the deed to the house and lot in the Recorder's Office?

[js1138]

Laws, scientific or not, are statements, and statements are embodied in physical objects and processes. Some of the laws of physics appear to have unblemished reputations for consistency and validity, but they are nevertheless based on less than complete knowledge of all phenomena. Some are admitted to apply to a subset of known phenomena. For this reason they are certainly not Platonic.

Values like Pi are statements about statements. There is no such thing as a perfect circle, other than the corporation by that name. The Platonic circle and its attributes are axiomatic. They are compelling because we find them useful, but in the space consisting of all possible self-consistent axiomatic systems, an arbitrary number of circles could be defined.

You, of all people should be wary of assuming that the human perception of truth is identical or isomorphic with God's. Our thoughts are prisoners of the structure of our mind, which is indeed physical, and is constrained by its utilitarian upbringing.

My wife likes to say that people tend to adjust their thinking to conform to their peer group. She says this mostly when a politician or judge is suddenly promoted and abandons his/her former ideological roots. The peer group changes and the politician adjusts.

Science, philosophy and theology are an evolving peer group. We think of things like geometry differently now than people did a thousand years ago, even though geometry is among the most static of the disciplines. Statements like the ratio of a circle to its diameter have not changed, but our way of thinking about them have changed. I find it difficult to see an "out thereness" to a circle, when the concept of a circle is an axiomatic statement.