I asked a similar question recently, and it was closed. So, bear with me.
When two things are materially equivalent we don't add anything to work out how much we have of both together, right? If sentient beings are materially equivalent to human beings, then to work out how much we have of both together we just take the number of human beings there are.
But we do when things aren't materially equivalent. e.g. when neither is a condition of the other, then we just add the amount of both. Gibbons are not great apes, so we have as many hominoids as we have gibbons and great apes.
So how do mathematicians express material equivalence, and do they need logic to express states like the above? They seem very basic to applied mathematics.