I do it every day.

I had previously said no. I was thinking that in order to transfer information to another I would have to use a form of language. That's really not the question. I may see a tree and remember a tree without having a name for it. So that would be yes. Reviewing the question ....YES!

I'd suppose that whatever the means to convey ideas to one another can be defined as language.
Whatever one works out in ones own head to make decisions, I would suppose could as well be defined as ones own inner language.
When I first heard that idea about one could not think without language, in the 60's, I still had clearer memory of when I did seem to think more in imagery than words. By now it is just memory of memory.

I cannot. I do not think in images at all. Words, music, and emotions. And I cannot truly think in emotion and music alone...only feel.

Most of this type of thinking is instinctual. For instance, technically, movement is a way of thought. Our brain sends messages without words that trigger our neurons and muscles. A lot of movement can be done without conscious effort. It's pretty amazing. Emotion is another good example. You don't really "think" sadness, anger, etc. in words. You feel it through wordless thoughts and chemical processes. Considering that everything we do is processed by the brain, it could be said that most actual thought is not language-based. That being said, we CAN consciously think in pictures, music (without words, of course), etc. Someone who is deaf and blind can still think. Animals can definitely still think, in their own way.

Pure music.

Define 'think'

Imagine a computer. It processes information. However, that information then has to be communicated, for which it is translated into a language, whether it is a pattern of lights, a screen read-out or speech generation.
The human brain thinks, without a language in the accepted sense. Then it is communicated, usually in stages, to the consciousness. Hence the illusion of thinking in a language. I personally "think I think" in either English or Swahili, but what I am really receiving is a read-out, and I can choose how it is presented.

Other animals do it all the time.

My favorite podcast (RadioLab) has an hour long show dedicated to this very question...and it is brilliant!! The stories relayed are truly striking. I wholeheartedly recommend this listen to anyone interested in this topic.
A link to the specific episode: [wnycstudios.org]

In fact we do. We think with images, feelings, sensations, sensory awareness, and unsymbolized thinking. Words are just how we attempt to communicate those things with others.