I think the problem is encapsulated by the title of this discussion. "Regarding intellectual capacity: Are animals just lower on a continuum, or a distinct difference?" If the distinct difference between human and non-human animals is better put in terms other than intellectual capacity, then would this not be of interest here? Assuming it would be, the title reveals a restrictive assumption, namely that it's all about intelligence and the brain.
I think we
can describe the difference biologically, in something like the way that
@apokrisis and
@Wayfarer have sketched out, but beneath these descriptions there is a deeper conception of human uniqueness directing the investigation, as if we already know what we're looking for. The biological descriptions do not stand on their own, because any biological capacity can be regarded as--and indeed biologically
is--just another species characteristic alongside other unique capacities such as the dance of the bee, the problem-solving ability of corvids, or sonar-directed flight. What gives the biological descriptions
sense in this context is that we are already looking for what makes us different. But crucially there is nothing here that rules out the conclusion that we are not very different after all. Because in a sense, we're not.*
Which is why I want to describe the difference differently. To begin with, it's more than a "distinct difference"; it's a radical discontinuity, and it has to do with society and culture, history and personhood. Framed in terms of intellectual capacity, discussions often end fruitlessly in debates surrounding intellectually disabled people, infants, and so on. The
argument from marginal cases is made to show that humans are not unique in attaining moral status, and although I disagree with its conclusion, it does expose the fallacy of thinking that we can divide humans from non-humans according to certain properties of individuals, as if we grant rights on a case-by-case basis, checking off a list of characteristics, such as intellectual capacity, before we decide to treat a being as a person or not. If we rather see a human as a social person bound up in a culture, the intellectual capacity of individuals drops out of the picture and the intellectually feeble can be seen as part of the moral sphere, the sphere of persons.
History is important here too because it shows that how you understand the question of human uniqueness differs according to what you're interested in. You can discover that humans and animals are on a continuum if the continuity is what you're interested in, that is, if you restrict your enquiry to (ahistorical) biology. There certainly is a continuum in that descriptive context, and you can dismiss the discontinuities if you think they are not fundamental. Everyone would surely agree that our ways of life have changed in important ways over periods of time in which no significant evolutionary changes took place--this is history--so to avoid the conclusion of a discontinuity you would have to dismiss history as unimportant to what we fundamentally are.
So it's about what matters to us. Whether we decide on an overarching continuum or discontinuity depends on which level of description is deemed most overarching. If we see human beings primarily as moral and political agents with the capacity to change the world on the basis of reasons, we will see a discontinuity (this is not to say we cannot arrive at a discontinuity some other way). But if we see human beings as defined by neural capacities, or as determined billiard balls or hostages to their genes, then we will be tempted to see history, reason and morality as just another evolutionary endowment.
* Or, to the extent that a different kind of biology can include or gear into sociology, anthropology, and linguistics without the reductiveness of evolutionary psychology, biology itself
could embrace human uniqueness. I guess that's where
@apokrisis's approach comes in.