Language stands to the mind just like a mirror to the eyes. The mind needs a language to conceive itself. Which might (or not) mean that there is a primitive natural language.

OK, so here's the difference between perceiving and thinking: You perceive when your sensory organs impulses creates mind images, on the other hand, thinking is about to construct mind images without the five senses and organize them as you want. So, a way to prove to someone else that you're thinking could be guessing what this other person is thinking of and how the person thought about it.
For example, if you show to the person a fish tail and a woman and ask him to imagine a creature, it would probably be a mermaid. Of course this was a foolish example, but if you ask something more difficult, with ambiguous answers and explain how to conclude, proving that you are aware of the process,I guess that it's' a good proof.

Following the "default definition", quantity stands for the magnitude of countable and reducible things. I mean, in a geometric view, would be like distance, the space between the initial and the final point. When you're counting something, you're presuming that there's a limit and when you reach the limit you'll be known the quantity.

Also, a x quantity of filler stuff fill in a x quantity of fillable things.
For example, two shoes fits in a box, if you increase the quantity of shoes to 3 shoes, it won't fit any more because it crosses the limit, it can also happen in the negative way. The thing is that with you have an infinitely large box, with an infinite amount of shoes in, no matter how many shoes you take off from the box, it won't change nothing. So talking about quantity doesn't make sense any more.