So I was reading this post over at Brian Weatherson’s blog. In it Weatherson points out quite interestingly that the question of whether a belief should not count as knowledge because it is based on a false presumption is actually quite subtle. Or to put it another way Gettier counterexamples against knowledge in the case of justified true beliefs often turn on the falsity of some justified step in the chain of belief. Weatherson is pointing out that even if your knowledge is based on a false belief in some cases it is still knowledge.

Given the type of examples Weatherson deploys I suggest the answer lies in some application of charity to the believer. Even if the justification an agent is disposed to offer for his belief cites some false fact if there is a true fact in the general region which would suffice in the justification we should credit that as knowledge. For instance (stealing from Weatherson’s example) if an agent justifies his belief that X by citing p&q but q is false and all the agent needs is p we should still count that as knowledge. So while I think this point is worth noting I guess I don’t feel it is of great significance because I tend to think with all of these disposition type terms (belief, knowledge etc..) there is some ambiguity which must be addressed by an application of charity.

However, my goal in this post wasn’t to attack or even respond to Weatherson’s point but to offer my very simplistic analysis of knowledge. This is something that has been floating around in my mind for awhile and it wouldn’t surprise me if it is also somewhere out in the literature but I haven’t seen it there. In short, modulo this issue of charity, why not just define knowledge as justified true belief where every necessary step along the justification is also true? So first I should perhaps explain how I view a justification. Basically I assume a justification is a lot like an inductive version of a proof. Thus it will proceed from certain assumptions moving through intermediate conclusions along the way before reaching the statement in question. Of course since the steps are only inductively and not necessarily deductively valid all the premises can be true and each step be valid yet reach false conclusions (intermediate or final). The Gettier cases rest on the possibility that the final conclusion is true but that some of the intermediate conclusions are in fact false.

It seems to me the obvious answer to this worry is just to require each intermediate step along the justification to be true as well as validly inferred from the preceding deductions. For instance suppose Fred goes to visit Susan. Fred observes a silver Prius in Susan’s driveway and concludes that Susan owns a silver Prius. If, however, the silver Prius in the driveway actually belongs to Susan’s friend Josephine but Susan really does own a car of a similar type and color we have ourselves a Gettier case.

Presumably Fred reasons thusly. There is a silver Prius in Susan’s driveway. It is likely that the car parked in Susan’s driveway is Susan’s. Thus the silver Prius in Susan’s driveway is Susan’s. Hence Susan owns a Silver Prius. Notice how the requirement that every intermediate step in the deduction be true nicely prevents this case of justified true belief from being knowledge. Since ‘the silver Prius in Susan’s driveway is Susan’s’ is false we don’t have a case of knowledge. If on the other hand Fred had known that Susan only let people who owned the same kind of car as her park in her driveway and used this fact to conclude Susan owned a silver Prius it would count as knowledge.

Now a plausible objection is that an invalid chain of reasoning can be massaged into a valid chain of reasoning. For instance if we replace the step in Fred’s reasoning where he infers that the car in Susan’s driveway is the car she drives by the inference that people frequently drive the same type of car that is parked in their driveway it would seem we have a case of justified true belief. However, far from a deficit I think this is actually a strength of this analysis. It is a feature of a proper analysis of knowledge that it should allow the same evidence to constitute knowledge seen in one way and not seen in another one. If Fred is disposed to cite the first inference to justify his belief when asked he doesn’t have knowledge. On the other hand if he really grounds his knowledge in the connection between the car in someone’s driveway and what type of car the individual owns, and isn’t just inferring it from the connection between owning a car and parking it in your driveway, then he does have knowledge.

Still one might protest that an inference like this shouldn’t count as knowledge. After except for the relationship between ownership and parking in the driveway this probabilistic relationship might not exist. However, if one takes this line it is difficult to see how any non-certain knowledge might exist. Given any sort of probabilistic inference about some object it is quite likely that there is some additional information one could specify about the object to make the inference invalid. For instance if you purport to know that someone is dead because they haven’t breathed for 5 minutes likely there is some additional fact, say the number of hairs in their beard or their age in seconds, which they share only with survivors of icy water immersions.