[glaberficken]

Well, I was inclined to agree, but: when we say "count" and "number" we usually mean something very precise and accurate. Such as: "how many oranges are there on the table?". As opposed to when we we ask stuff like: "how many oranges do you think there are on that orange tree?" "You have lived by that tree your entire life, do you feel like it is carrying more oranges than in past years?"

My point is that these 2 activities are clearly different, and that non-humans clearly engage in the last one but I'm not so sure I have ever seen clear evidence they engage in the first one.

[maze-le]

I guess you are right, it is important to differentiate a pure number (one, five, ten thousand) from a fuzzy category of numbers (a bunch, a pack of wolves, some dozen eggs). But, apparently, some animals have the ability to count exact numbers, such as apes:

* https://www.wellbeingintlstudiesrepository.org/cgi/viewconte...

or bees (OK, only to 5, but still):

* https://www.sciencedirect.com/science/article/pii/S258900421...

In these cases I would say -- even if they don't have the ability to tell us that they can reason with exact numbers -- we can observe experimentally that they do. And I don't see any reason to assume that the abstraction that is represented in the animal mind is fundamentally different from our notion of it.

EDIT: That could also be an indication for mathematical Platonism, when I think about it. But alas, as long as we don't observe a species that develops mathematics from the basic forms of countability that would be a stretch too far... Or to put it differently -- if there is a species that could reasons about numbers beyond the basics of counting, given enough time they would also be able to axiomatize mathematics under an equivalent of ZFC Set theory.

[glaberficken]

In those studies I don't see any evidence and clear conclusions that the either the chimps or bees could count.

I see a lot of meandering about methodologies in the chimp paper and if you see the Concusions paragraph you can see how weak it is:

>"CONCLUSIONS: Studies of numerical competence in the chimpanzee continue to provide new insights into the range and capacity for quantitatively based information processing in this species. In general, the rebirth of studies of animal counting currently suggests that this area remains a rich and fruitful source of contributions to our understanding of animal cognition and behavior. And for a truly comparative perspective, it will be important for researchers to challenge their creativity, by continuing to devise new methods for tapping capacities toward counting in a variety of species, including nonhuman primates, rats, birds, and additional new species for whom no data currently exists"

The bee paper is more interesting but it also doesn't reach the conclusion that bees can count. At least it offers a context for the framework used and the conclusions reached.

What they did is simulate a neural network that has the bees visual data as input and prove that a simple "inexpensive" computation can in theory scan quantity of perceived objects.

Well isn't that just the same as proving that a neural network algorithm can simulate an computer accumulator register?

> "Within this framework we have shown that counting and numerical ordering are computationally inexpensive, provided the animal employs an active, sequential scanning of pattern elements."

[Keysh]

The bee paper referenced in the original article (Dacke & Srinivasan 2008) is about real bees, and does a pretty good job of showing that the bees must somehow be keeping numerical track of how many instances of a particular landmark they've passed, at least up to a total of four.