There is a story in the Guardian today reporting a study that allegedly shows that certain fish can count to four. My normal first reaction to this sort of wildly implausible claim is that the journalists have gotten the details wrong, but this time they quote a researcher apparently making that wildly implausible claim:
Their numerical ability is on a par with that of monkeys, dolphins and children aged between six months and 12 months. “We have provided the first evidence that fish exhibit rudimentary mathematical abilities,” said experimental psychologist Christian Agrillo, of the University of Padova in Italy.
OK, the researcher only says, or in translation says(?), that their study is evidence of “rudimentary mathematical abilities”, which is much less specific and less mentalistic than “able to count to four” as the Guardian’s James Randerson reports
Fish are able to count to four, according to experiments which involved giving them the option of joining shoals of different sizes.
Call me a pedant, but the experiment does not show that fish can count to four! It shows they exhibit behaviour that can be quantified in various ways. It shows they can be predicted to move to the biggest group of fish when the groups have sizes up to four after which point they are unpredicatable, but those conclusions exploit our mathematical ability not the fish’s. You might just as well say my DNA can count to four because it stops giving me limbs at four, or can count to five because it stops giving me fingers at five. The inference that they are counting is drawn on the basis of a change in their behaviour after a certain point, but the change could be triggered by purely physical causes. Do we say a thermostat can count because it switches the boiler off at a certain temperature? I don’t know what is responsible for the fish’s responding in this way, but I’m pretty confident it’s not a matter of counting anything. Four is a mathematical concept with necessary connections to other numbers and mathematical operations. Only something whose behaviour exhibits a sensitivity to these interrelations with other mathematical terms can be taken to deploy a genuine mathematical concept.
Misunderstandings of this sort show why one or two philosophy courses should be compulsory for psychologists (if the mistake is the researcher’s), or journalists. It is important because stories of this sort feed into the debates about what is so special about humans and what our place in nature is. The latter debates are too important to be choked up with muddled thinking from researchers and lay people.
P.S. The most important science related story in the Guardian today is not this one, of course, but this one.