Can you count without using a language?
Try this: Clap your hands or tap on something an arbitrary number of times. Can you tell how many times you did it without "saying" one, two, three in your head?
Even if you pay attention to it, it seems impossible to count without language.
At least not a stream of sensory inputs; small clusters of around 10 or fewer things seem easily countable from just looking at a "snapshot."
Geometry is the best example, anythig beyond the basics has no good common names and still you can do it in your head.
If you slice through a pair of carrots, how many pieces of carrots are there afterwards? (do this simple thing in your head an than read on)
I slice them imaginary and than start counting what I'm left with. The part where I go from 2 carrots to 4 carrot parts happens without words. Anyone doing it differently? You of course have to be self-observing enough to say more than "I just know" :).
But yea, get's more difficult with 73. But even there I might determine "visually" that cutting across a row of carrots halfs each of them. So the 2 in 73*2 ist still determined without words.
There is no conscious calculation performed. The result might be fetched from memory, but there might also be subconscious processes involved. And that seems to be what the argument is about. Grandparent claims we cannot count without language while the article claims we have estimation hardware builtin (that's count-ish, imo). That's not really conflicting, since GP implies a specific counting process that's usually done consciously. Do the clapping, ask someone unsuspecting how often you have clapped, and he'll probably be able to tell the number without concisely counting. Even for a stream of sensory inputs.
But yeah, consciously thinking about something usually involves words for many of us, as that the most common/effective way for our thoughts to interact with the world.
For instance you can use tokens to do counting. If you want to count the number of sheep in a herd you could put a small rock in a bag for every sheep. This bag of rocks will then "represent" the herd. And you can use it to reason about properties of the herd.
If lets say you want to count that all sheep are present you can move the rocks from one bag to another. If you want to split the herd between two peeople you can make two piles roughly the same size and take as many sheep.
You could have another type of object representing months in a year. Then you could assign the rocks to months to ration food.
When you start grouping your tokens in well defined shapes, or introduce tokens of different denominations you are on the slippery slope towards language.
Of course if you count symbols ticking by visually as "language" then yes, at the root the brain is going to use some sort of symbol to represent increasing quantity.