Philosophical Tools

I know of two 'Philosophical Tools':

• Occam's Razor: Don't use a more complicated explanation than you need.
• Diax's Rake: Don't believe something just because you'd like it to be true.

What else have we got, and what gardening implements can we associate with them?

A list of tools would be really handy. Because when you're stuck, new approaches help. And a list of mental images for complex concepts would help you remember them.

Some handy maxims which need names are:

• If you can't prove something, try to prove the opposite.
• See if you can change the problem to make it easier.
• Specific examples and generalizations illuminate each other.
• Explain your argument to a child, a foreigner, an alien, a computer.
  
• Try to write it down.
  
• Sleep on it.
• Leave it alone and work on something else for a bit.
• Look around, and contemplate nearby objects and how they relate to the problem in hand.

Feynman and Sussman both tried to explain their ideas clearly, to mathphobes and computers. Montaigne explored his ideas through writing. But neither of these things remind me of any tools, or in fact any objects.

Can we go the other way? What about taking a list of tools and thinking what each one would mean if used as a metaphor for a way of attacking a problem.

Here are some tools I can see from where I'm writing:

The mirror, the lantern, the penknife, the swiss army knife, the thing for getting stones out of horses hooves, the pickaxe, the probe, the shotgun, the earplug, the key, the spoon, the zipper, the book, the flask, the camera, the paperclip, the paperweight, the radio, the tape recorder, the fire extinguisher, the magnifying glass.

Do any of these have philosophical connotations?

The radio: tell everyone you know about your argument and see what happens
The earplug: stop reading about other peoples attempts to solve it and see what you can do on your own for an hour or so.
The thing for getting stones out of horses hooves: See if there's a tiny sub-problem that's tractable.
The notebook: write down tiny notes every time you think of a new thing. You don't have to read them later. Just writing will do.
The probe: Find a new way of measuring something about the problem.
Magnifying glass: Just look at one part of the problem in isolation (really good for cryptic crossword clues)

That seems a more tractable approach to finding a list.