# How Could We Know if Animals Can Think Abstractly?

Michael Egnor

I have laid out in previous posts the evidence that animals are not capable of abstract thought. Furthermore, it is unclear what kind of abstract thought an animal could have, given that animals have no language in which to express abstract concepts. If an animal isn’t thinking about a particular thing or about a word, what would the animal be thinking about?

But the question can be asked: How could we detect abstract thought in an animal?

Here’s how. The experimental design necessary to detect abstract thought in an animal requires a step in the experiment in which the animal would have to think abstractly, without reference to any particular, and act on that abstract thought.

An abstract concept could be selected — say, a mathematical concept like the concept of square root. Mathematics is the paradigm of abstract thought, and it can be tested in animals that lack language by training the animal to select groups of the appropriate number of objects.

Can an ape understand what a square root is? If so, the animal would be capable of abstract thought.

The ape could be shown a picture of 25 objects, and then shown screens containing different sets of objects — a set of 1, a set of 2, and set of 3, and so on. The animal would be rewarded if he selected the set of 5, which is the square root of 25. The training could be repeated with different kinds of objects, still using 25 and 5, until the animal reliably chose 5 objects when shown 25 objects.

Once the animal reliably selected the set of 5 after being shown the set of 25, the animal could then be trained to select the set of 4 when shown the set of 16. Once that task was learned, the task could be repeated with 2 and 4.

Once these tasks of selecting the set of objects equal to the square root of the reference set was learned for a series of square-root pairs, the animal would be tested with novel square roots. Would the animal select 3 objects when shown the set of 9? Would the animal select 1 object when shown the set of 1? Would the animal select 6 objects when shown the set of 36?

This is a real test of abstract thought, because it would require that the animal comprehend the concept of square root abstracted from particulars, and then apply it to new particulars.

I think readers would agree that the likelihood of any animal selecting the square root of the novel square is not above chance, and that no duration of training would change the outcome.

If we want to test abstract thought in animals, it is this design, or an analogous design, that is needed. The experiment must isolate an abstract concept and, by allowing the animal to select particulars, demonstrate that the animal understands the abstract concept independently of the particulars.

It seems obvious, at least to me, that no animal would ever show comprehension of the abstract concept of square root, or of any abstract concept. Animals can’t think abstractly.