This article presents evidence that symbols exist in our minds independent of words. http://artksthoughts.blogspot.com/2009/07/concepts-cognition-and-anthropomorphism.html
Actually, it seems extremely unlikely that words would be required for symbolic thinking, considering that any animal advanced enough to base its actions on thought rather than pure reflex would need to have some kind of symbolic representation of the world.
Concepts exist without words, since words are just one part of a concept, and people with left temporal brain damage can lose access to a word without losing access to the concept.
A "symbol" sometimes means something atomic, which concepts are not. We probably have no symbols in our brains, in this strict sense.
Before language, people must have thought without words. I often have the impression that I have a thought fully-formed in my head, yet I wait to listen to it unfold in words before moving on to the next thought. Perhaps I could think much faster if I weren't addicted to words.
Has anyone developed techniques for thinking without words?
This would have a little in common with Buddhist practices of emptying your mind, but wouldn't be the same thing. For one thing, Buddhists also try to empty their minds of images. More importantly, they are trying not to think, while I'm trying to think - just not unpack everything into words.