I can picture four grains without a problem. I merely point out the psychological machinery involved. It helps to have the simplest and most regular global arrangement in mind, even if that geometry of relations is then also suppressed to a large degreed to emphasise the distinctness of each grain. — apokrisis

I believe, that you believe, that you can perceive 4 (or more) seperate grains of sand at any specific time, but I don't know if you're basing your belief on a knowledge of "working-memory" https://en.wikipedia.org/wiki/Working_memory .

Sort of :)

Yep. Zeno’s paradoxes also hinge on this logical issue of trying to reconcile what conventional logic has rent asunder.

Is reality discrete or continuous at base? Or are these just polar extremes that derive from constraints placed on the third thing of a vagueness, a Firstness, a potential?

My argument is that predication is vague. But that is not a problem because we can sharpen it to the degree that pragmatically matters by adding constraints. We can imagine the extreme cases - Platonically or mathematically perfect discreteness or continuity. And then reality can be measured against these contrasting conceptions.

We can see that there are three thing or four things at a glance if they are three or four things like grains or sand or grains of wheat in a flat scatter. Five at a glance is harder - more reliant on a telling structure. Then six needs that structure in the way we can recognise and visualise the six dots making up that number on a rolled die.

If this recognition ability can be demonstrated in experiments, it does not seem so hard to believe that I can actually visualise as I believe that I do.

I also like to (try) to visualize what others believe they can perceive. I realize my perception is not always right - even though I may believe it is.

Yep. Zeno’s paradoxes also hinge on this logical issue — apokrisis

But do you see the difference I just pointed out?

Is reality discrete or continuous at base? — apokrisis

No, the sorites doesn't directly address that.

The sorites starts from the happy reality of being able to order a sequence of objects (grain collections, heads, photos) in correspondence with the natural numbers and to discuss choices of how to superimpose a dramatically smaller ordering on the same objects. — bongo fury

My argument is that predication is vague. But that is not a problem because we can sharpen it to the degree that pragmatically matters by adding constraints. — apokrisis

I'm willing to learn more about Peirce's and/or your theory of vagueness, sharpening and pragmatic constraints, within the limit of my low tolerance for abstract nouns. (This nominalism from which I do suffer.) Meanwhile, you may or may not be interested that Goodman has a detailed theory of those phenomena, which examines how sharpening of an important kind (replicability) is facilitated by vagueness at the edges of syntactic (and potentially also semantic) elements. Which thus explains the fortunate starting point mentioned above. And, I believe (as detailed here), the puzzle itself.