To put it in another way, it does not logically follow that untestable things are not capable of being understood.
Here is why I think it does
follow logically :
1. To understand X is to be familiar with the properties of X.
2. To become familiar with the properties of X, the properties must be examined (tested).
3. For the properties to be examinable (testable), the properties must avail itself, or at least the effects of itself, to sensory scrutiny.
Therefor, if X has properties which are not available to our senses, we cannot understand X.
I think you are missing the importance of your intellect. I'd restate it as follows:
1. To understand X is to be familiar with the essence of X. Properties of X point to the essence of X.
2. To become familiar with the properties of X, the properties must be available to the intellect.
3. Even if the properties of X are unavailable to our intellect, it does not follow that it does not or cannot exist.
Therefore, if X has properties which are not available to our senses or intellect, we cannot understand X and thus cannot make any claims of existence or non-existence of X. Unless you are a skeptical crackpot
How do you test whether you have free will, thoughts, intentionality, qualia etc.
Erm ..well, maybe thats why these things are so poorly understood and debated to death.
But perhaps I'm not the best person to comment on thoughts. I've long ago written them off as non-existant, except notionally, remember?
If a thing or thought is non-existent, then it is non-existent notionally, imaginary and otherwise. Saying a thing is non-existent except notionally is nonsensical, it does not make sense.
But if they do have testable properties, one should in principle be able to understand these notions. And the more about them that can be tested, the better we'll understand them.
You seem to deny that thoughts have ANY properties by fiat since you deny their existence. I am still curious how you think you are able to reason without having thoughts.