[Physicist]

Before this goes on, we first need an objective definition of "family". We have an objective definition of "species" (even though it doesn't always work, e.g. the various species of bears, which are apparently able to produce viable offspring between them). But what constitutes a family?

[gore3000]

We have an objective definition of "species" (even though it doesn't always work, e.g. the various species of bears, which are apparently able to produce viable offspring between them).

The ability to produce viable offspring is the only objective criteria for species. If these bears can do as you say then they are one species just like dogs and wolves are the same species in spite of the apparently large differences between them.

[Ahban]

my family definition: A family is a group of related species, morphologically similiar, who share a set of physical characteristics, which are not posessed in total by any other group.

For the felines for example, they would be placental carnivore mammals that have retractable claws. If I cared to I could find a few more defining traits of the cat family.