[guyomes]

Taking the statement completely out of context, it states : if A implies B, then not A implies not B. This is a logical flaw.

The correct statement from a logical point of view is: if A implies B, then not B implies not A.

In this case, even if writing down your ideas makes them more precise, there might be other methods that make your ideas more precise. Again this is just the logical point of view, out of context.

[nequo]

> Taking the statement completely out of context, it states : if A implies B, then not A implies not B. This is a logical flaw.

The statement in TFA is not that though. Instead, it is "if A implies B, then not A implies not C."

  A: writing about thoughts
  B: thoughts become more complete
  C: thoughts are most complete

If "A implies B" is true, then it also doesn't matter if other methods also make your ideas more complete, because "A implies B" means that writing would make them even more complete, therefore "not C."

[guyomes]

You're perfectly right. It is indeed perfectly logical then. It could be reformulated like this: if f(A) > f(not A) then f(not A) is not maximal.

f: a function indicating how complete the thoughts are.

A: writing about thoughts.

[__0x01]

What books can I read to reason like this?

EDIT: shortened sentence

[nequo]

This might sound strange but a book on real analysis or topology that walks through proofs could be one.

[throwaway55533]

+1, pg is using a pretty typical argument you see in analysis/topology.

If you want to get to real analysis/topology the typical sequence is

1. Logic and Set theory (recommendation: How to Prove It, Velleman)

2. Linear Algebra (don't have a good recommendation)

3a. Real analysis (recommendation: PMA, Rudin)

3b. Topology (recommendation: Topology, Munkres)

I'm not sure I'd recommend learning math. It's an extremely expensive skill -- though pretty valuable in the software industry. People who go learn math are generally just drawn to it; you can't stop them even if you wanted to.

But be aware, (1) you'll have no one to talk about math with. And (2) you'll be joining a club of all the outcasts in society, including the Unabomber.