Okay, I'll play.

Handsaw. Tent. Pot. Matches.

Rationale?

Handsaw:
- A handsaw does the work of many knives and will outlast most
- Builds shelter quickly and efficiently
- Cuts all manner of materials -- trees, washed-up fishing nets, coconuts, green bone for the rich marrow, wet trees for kindling
- Polish one side for signalling (marginal)
- Add small cutting edges by grinding on a big, stationary rock (I have done this)
- Musical instrument for entertainment (tie me kangaroo down!)

Tent:
- A modern tent is a tarp, plus poles, groundsheet, mosquito shelter (malaria, black flies), sun/wind shelter.
- If disassembled, you still have: two waterproof tarps, poles for shelter/fishing/dip nets, fine mesh for minnows/bugs, and lots of thread/cordage

Pot:
- Very hard to improvise this simple item
- Potable water, water collection and transport, crude cooking, boiling scrap cloth for bandages, etc. etc. etc.

Matches:
- Making fire reliably without modern contrivances is pretty darn hard; just try it
- Fire solves a lot of survival problems (potable water, signalling, cleaning, disinfecting, deterring bugs/animals, morale)

Honourable mention -- I'm sad that I have to leave Wilson behind:
- Flotation device
- Water carrier
- Basket for carrying tasty, pinchy crabs
- Hat and sandals
- Lashing and bunjy cords
- Patient counsellor who listens intently to my pacing-and-planning-out-loud sessions, commiserates with my sorrows, and laughs at my inside jokes
(Sorry, Wilson, I'm sorry!)