Seeing red

[Angrboda]

What is your notion of what an idea is?   In the physicalist paradigm, ideas are things just as much as a desk or a glass is a physical thing.  If you're saying something different, you need to provide some defense of that instead of just handwaving it aside with the non-informative label 'idea'.  What is an idea in your framework?  You have a referent that doesn't seem to refer to anything.  A signifier without a significand.

You are demanding of a person who does not define the world in thing-ness to define ideas as a thing.  I will not.

So, in your world, an idea is no-thing, and reality is made up of no-things.  Very illuminating.

Materialism is a reduction of all phenomenon to a small set of mathematical principles, with some metaphysics thrown in for good measure.

That it turns out the universe is reducible only to ideas is an etymological problem for you.  You can call black white if you want, but unless you can represent your ideas of essential parts as things with volume, occupying space, and located in specific times, then you are abusing the word horribly.  Essentially, you are taking Idealism and saying "Nuh uh, that was us all along."  But let me say this, if you want to argue that reality consists of mathematical principles, then you're going to have a tough time explaining why mathematical principles have become aware of themselves.

I don't think you know what the word etymological means.  Our understanding of the world consists of ideas.  You are taking this brute fact and using it as a shield against knowledge.  But you do so at a cost, and that cost consists in making your model of the world a useless one.  I may have a tough time explaining self-awareness but so what?  A difficult problem does not equal an insolvable problem.  The evidence from science and medicine is that the mind behaves consistent with it being an object like any other.  Complex in its action, but material.  Your preference for the notion of a world of ideas is nothing more than a strategic retreat from the question of how your mind works.  That materialism explains phenomena outside of mind makes you willing to accept mechanistic explanations otherwise.  Because you personally can't comprehend how ideas can be things, you recoil into a position of epistemic insularity.  You can't solve the problem of consciousness, so you assert that it cannot be solved.  And you retreat into a nest of words that mean nothing, and explain less.

 It explains by breaking apart composite phenomena into parts that explain the composite.  Your breaking everything down into 'ideas' doesn't explain.  It merely leaves the nature of things undefined.  It subsumes, but doesn't reduce.  Is there anything that an idea cannot be?  Is there anything an idea must be?  It seems that under your view, an idea can be anything, so you haven't identified any parts which explain the composite.  That's a weakness, not a strength.  What are the practical limits on ideas in your Idealism?

An idea is an immaterial principle or pattern, either an experience or a principle which molds experience.

Well that's vague.  It's also the resort of the religious.  Ideas are immaterial.  So they really are no-thing. What makes you think ideas are immaterial?