In response to the recent explosion of literature on the metaphysics of grounding, some authors (e.g. Daly 2012, Wilson 2014) have expressed skepticism about the coherence or usefulness of this concept. One question that does not seem to have been raised, however, is: how are grounding claims to be established? If one examines the literature, the answer seems to be: by pointing. A handful of stock examples (Socrates and his singleton, a disjunction and its disjuncts) are constantly repeated, but the reader is simply expected to concede the obviousness of the grounding claim. However “intuitive” these claims may seem, pointing to such examples is clearly not sufficient to establish the claim that there is a relation of metaphysical dependence between these entities. In particular, this ostensive method of establishing grounding claims fails to eliminate the possibility that the dependence in question is conceptual. It is clear that in order to grasp the concept <singleton of Socrates>, one must also grasp the concept <Socrates>, and hence that there is a relation of conceptual dependence between the two. But this does not imply that there is a relation of metaphysical dependence between the objects of these two concepts. To see this, consider the concepts <square root of two> and <two>. It is obvious that one must grasp the latter in order to grasp the former, but it is certainly not obvious that the latter grounds the former, i.e. that the number √2 is metaphysically dependent on the number 2. The number √2 is after all simply a real number, and has no intrinsic connection with the number 2; it can even be referred to without employing the concept <two>, for example, by the expression: “length of the hypotenuse of a right triangle whose remaining sides are each of length 1”.
Furthermore, metaphysical dependence cannot follow directly from conceptual dependence, as the direction of dependence may be reversed simply by referring to objects using different concepts: thus <square root of four> depends conceptually on <four>, which, if the inference from conceptual dependence to metaphysical dependence were valid, would imply the 2 depends on 4, but <square of two> depends on <two>, which would imply that 4 depends on two. If grounding is irreflexive, as most of its partisans hold, then at least one of these claims is false. In short, I am suggesting that what is “obvious” in the usual examples of grounding is a conceptual dependence, but this is being illegitimately used as evidence for a metaphysical dependence.
The German logical tradition , from which the term ‘ground’ derives, distinguished between ideal and real grounds (principia cognoscendi and principia essendi vel fiendi) as having to do either with “knowledge in the understanding” or “the thing itself outside thought” (e.g. in Ch. A. Crusius’ Entwurf der nothwendigen Vernunft-Wahrheiten, wiefern sie den zufälligen entgegen gesetzet werden , §34 — see my draft translation here). It is essential that some such distinction be introduced in the contemporary grounding literature in order to avoid illicitly passing from conceptual to metaphysical dependence, or from ideal to real grounding claims. The question of how we are to pass from ideal to real grounding has not yet been addressed within the grounding literature, to my knowledge.