Merleau-Ponty's analysis of cognition might suggest the following.
The cognitive process naturally ascribes " inter-actional extension" to every focal concept along a time or space dimension. E.g. the abstract noun "house" cognitively triggers a possible plethora of potential relationships
of the conceiver with that class of objects we call "house" including possession, residence, possible destruction, existence before or after our own etc,etc, only some of which will have significance in real life
contexts. But with the concept of "infinity", there are no "real life" boundary conditions operating to delimit cognitive speculation.
This implies that the concept of "infinity" is generally not a member of the set of functional or pragmatic cognitive concepts, except perhaps in the special case of the mathematics of numbers. In that sense, talking about "an infinity of objects" is a category mistake
as defined by Gilbert Ryle. He might say questions about "an infinity
of objects" is as meaningless as questions about " the location
of the university" whilst wandering around the colleges and libraries of Oxford".
Now add to that angle the non-dualist thought that all concepts logically require a conceiver, then the concept of "infinity" only remains extant whilst conceivers do, therein you have another nail in the coffin.