A quick way to question conjunctive accounts

Suppose someone proposes a philosophical account of the form:

• x is F if and only if x is G₁ and x is G₂ and x is G₃.

There is a quick way to question this that I think works most of the time. Just query the proponent: "What if the three conditions on the right hand side are satisfied merely coincidentally?"

The proponent can only give one of two answers while maintaining the biconditional: "Yes, x is still F when the conditions are satisfied merely coincidentally" or "The conditions are of such a nature that they cannot be satisfied merely coincidentally."

But it is implausible that that a coincidental satisfaction of conditions should suffice for a natural concept. Thus, if coincidental satisfaction of the conditions is sufficient for x to be F, pretty likely Fness is a stipulative rather than natural concept.

On the other hand, if the proponent insists that the conditions were so crafted that they cannot be satisfied coincidentally, it is likely that one of two possibilities is the case. The first is that the proponent lacks philosophical imagination, and you just need to think a little bit about how to make the conditions be satisfied coincidentally, and then you'll have a counterexample on hand. Just reflect a bit on Gettier-type cases, and if you're clever you should be able to find something. The second possibility is that the conditions are weaselly by including something like "relevantly" or "non-aberrantly". Here is an example of weaselly conditions:

• x knows p if and only if p is true and x believes p and x is justified in believing p and the anti-Gettier condition is met for x with respect to p.

These conditions cannot be satisfied coincidentally because the anti-Gettier condition is telling us that the first three conditions are satisfied non-coincidentally. But of course this is weaselly, since we aren't told at all about the kind of non-coincidentally that's required. Every coincidence is a non-coincidence from some point of view. So, really, such weaselly conditions need to tell us not just that the conditions are satisfied non-coincidentally, but that they are satisfied relevantly non-coincidentally.

Moreover, in the above example there is a pretty good chance that the weaselly final condition entails the other three. For what it says is basically that the other three conditions are satisfied in an un-Gettiered way! I think this isn't uncommon with weaselly conditions.

Note: In the example, one could try to formulate the weaselly condition as the denial of Gettiering: "and x is not Gettiered with respect to p". Then the weaselly condition wouldn't entail the other three. But then the resulting conditions would be too strict. For suppose that x has two sources of data on p. One source gives knowledge. The other gives Gettiered knowledge. Then x knows p but x is Gettiered with respect to p.

Philosophical accounts whose right hand sides are of the form

• x is F if and only if ∃y(G₁(x,y) and G₂(x,y) and G₃(x,y))

can use the quantification to avoid coincidentality sometimes, but often are subject to a similar criticism.