### A False Closure Principle

A Counter Example to the (RMC) Closure Principle

David Doerksen

Closure principles are principles meant to capture the idea that if you know some proposition that entails another, then you can come to know the entailed proposition. As intuitive as this sounds it turns out to be very hard to find the true closure principle. In ‘A closer Look at the Closure Principle’ Michael Blome-Tillmann shows us why he thinks many versions of the closure principle are false. At the end of the paper he presents what he thinks is the correct closure principle. I will only focus on two principles he talks about. They are (MC) and (RMC):

(MC) If you know that p and you know that if p then q, then possibly you know q.

(RMC) If you know that p and you know that if p then q and it is not the case that the set of all the worlds where not q is true are disjoint from the set of all the worlds where your perceptual experience and memory are different then at the actual world.

Dr. Blome-Tillmann thinks that (MC) is false because of what he calls Dretske’s intuition. This is the intuition that you *cannot* deduce the negation of sceptical hypothesis simply from an ordinary world proposition and the knowledge that the ordinary world proposition entails the negation of the sceptical hypothesis. If p is ‘this is a zebra’ and q is ‘this is not a cleverly painted mule’ and if ‘if p then q’ is true, we have a counter example to (MC). I can know p and I can know if p then q, but I can’t come to know q only on the basis of those two propositions. I need something else. The something else is what (RMC) introduces.

In the counter example to (MC) the problem is that in all the worlds where ~q is true, you would have the exact same perceptual experiences and memories in them as you do in the actual world. This means that all the ~q worlds are uneliminated for us. So (RMC) adds that the set of all the ~q worlds and the set of all the eliminated worlds must not be disjoint in order for us to be able to deduce q from knowing p and knowing if p then q. The upshot of (RMC) is that we cannot come to know sceptical hypotheses simply by deducing them from ordinary world propositions and so the sceptic cannot use the principle against us for the conclusion of scepticism (using transmission arguments that is). Here is Michael Blome-Tillmann’s argument:

P1) If (MC) is false for Dretske type intuitions and (RMC) does not have the same problems as (MC) then (RMC) is true

P2) (MC) is false for Dretske type intuitions and (RMC) does not have the same problems as (MC)

C) So, (RMC) is true.

I deny P1. This is because even if Michael Blome-Tillmann is correct about the antecedent, (RMC) is false on other grounds. If we accept Dretske’s intuition then we think we cannot conclude the negation of sceptical hypothesis from deducing them from ordinary world propositions. Presumably the way we come to know the negation of sceptical hypothesis if we have this intuition is by using phenomenal conservatism, inference to the best explanation or if the sceptical world is massively different to our perceptions and memories then they are in the actual world. Consider now a situation in which I know that this is a zebra and I know that if it is a zebra then it is not a cleverly painted mule. We will call the situation A. Now consider all the ~q worlds, that is all the worlds in which the animal is a cleverly painted mule. It is totally plausible that in one of these worlds the mule wasn’t so cleverly painted, but rather it has one extra stripe on it that the actual zebra does. But this means that in one of the ~q worlds our perceptual experience is not the same as it is in the actual world, so the set of all the ~q worlds are disjoint from the set of all the eliminated worlds. So all three conditions of the antecedent of (RMC) are satisfied, but it is still not the case that we can come to know that the animal is not a painted mule on the basis of these three things alone. The fact that the painted mule has one extra stripe cannot make the difference between us being able to tell that it’s a painted mule and not a zebra. Not all the zebras have exactly the same number of stripes. If we were in the situation where it was a painted mule with an extra stripe, we would not be able to say “hey that zebra looking thing has one extra strip then one of the zebra’s does in another situation we could be in, so it must not be a zebra”. That is absurd. But then all we are left for concluding that the animal is not a painted zebra is deducing it from ordinary world propositions that we know, but we already rejected that as a way to come to know that the animal is not a zebra. So this suffices as a counter example to (RMC) and that means that (RMC) is not the correct closure principle. Here is my argument:

P1) Situation A is a situation in which the antecedent of (RMC) is true and the consequent is false.

P2) If (P1) then (RMC) is false.

C) So (RMC) is false.

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