Is there no way out but exclusion as the meaning of a word? What else could a word denote? A substance? A relation?
Dignāga discuss this problem in the apoha section of his Pramāṇasamuccaya, and so thus his commentator Jinendrabuddhi in his ṭikā thereon (which I had the pleasure to read in a Seminar lead by Helmut Krasser, see here). In the text, an objector suggests that the word might denote a particular (viśeṣya) insofar as it is qualified by something else (a viśeṣaṇa). In this way, one would avoid the fallacy of the word's denoting an individual (which would lead to the paradoxical need of a single word for every single individual and, hence, to the impossibility of communicating at all). When one hears "blue", explains the objector, one immediately expects an integration telling us how much blue it is (blue, bluer or bluest?/nīla, nīlatara or nīlatama?). In the same way, once one hears "existing" (sat), one expects "a pot" or "a cloth" to further qualify this "existing".
But Dignāga holds that either the example does not apply (as explained in a previous post, see here) or that even if it could apply to the case of blue, it would still not apply to the case of what is "existing". In fact, in the case of blue, its degrees are obviously part of it, and hence they can be "expected" as a qualification of it. On the other hand, "a pot" does not share the same universal (jāti) as "existing" and in order to have the former qualify the latter one would be forced to postulate an over-ranking universal above them –which cannot be the case, since it would lead to a regressus ad infinitum. (On this point, see also Sujanasi's interesting comments to the post referred to above.)