Is there any reason to imagine that abstract ideas exist when they are nowhere to be found except in language?
No more is known today, for example, about Platonic Forms than upon initial utterance some 2500+ years ago. Metaphysical speculations and justifications simply have not provided the conception with any heuristic merit and as of yet, not a one has been observed or confirmed.
As another example: all points equidistant from a single point upon a two dimensional plane, i.e. a Euclidian circle, can not be observed in the world (from all that we can observer between the scope of quantum decoherence to cosmological and epistemically opaque whole ("black holes"). There are, however, innumerable instances of things which can be described as circular. Be this a limitation of spacetime or due to the use and definition of "point", it seems to me that the only place a Euclidian circle can be found is in its description (language).
Unless we are to imagine that describing a unicorn amounts to invoking its "existence" in the same sense that the computer screens which you and I are viewing this on exist, I think the answer is plainly "no, abstract ideas are only to be found in language".