I would consider that Planning, if you're trying to work out what you're building, how it is going to function, etc. Philosophy is pretty abstract, I think. Unless you're talking about theoretical design, in which case, I'm not sure.
I would agree with Carving as a prerequisite, but I think as far as Mathematics or Architecture go, it depends on how you write the skill. If you include installation and commercial use of wood as a part of the definition, then yes, you're going to have to understand architecture and construction. If you keep it to the cutting, shaping, and
groomingErr, not the right word, but hopefully you know what I mean. of wood, then those things aren't going to be as essential.
A quick Wiki search defined Carpentry as follows, but you by no means have to follow such a definition. Just for an idea:
Carpentry is a skilled trade in which the primary work performed is the cutting, shaping and installation of building materials during the construction of buildings
(Also mentioned ships, bridges, framework, etc.)