You say

Even more misleading is the often quoted motto: ‘I think therefore I am.’ This is as illogical as saying ‘I see a dog, therefore I am a dog.’

You should give Descartes more credit. He was no dummy. Ask yourself this: "is it possible to be thinking and not exist?" Put another way, can things that don't exist be thinking? It seems that thinking requires something to do the thinking.

This is very different from the obviously fallacious "I see a dog, therefore I am a dog."

Before you dismiss the great thinkers it's wise first to try to understand them.