What's the problem with Horizontal Belief Transmission?

15 May 2015

Under what conditions can we say that our beliefs are justified? Imagine for a moment that someone you know believes that vaccinations cause autism. You of course, think that this idea is an utter load of bollocks. So who is right? And how do you know? After all, it’s not like this is a matter of pure logic or axiomatic belief. It seems like every reason you might give in support of your position - that the medical studies that claimed as much were fabricated and the paper that reported it was retracted, that no subsequent scientific study has shown any connection between the two what so every - still has to rely on some justified prior belief.

Philosophers have a neat little way of explaining this process and who is right (or at least justified) - it’s called belief transmission. The idea is simple enough: any belief q is justified if and only if you are justified that some earlier belief p entails q, and that you are also justified in believing p. But how do we know that the entailment belief from p to q is justified? For that, we can rely on process reliability - the idea that beliefs which are the result of some process are justified if and only if that process reliably generates true beliefs.

So your anti-vaxer friend believes that vaccines cause autism because they heard it from their fortune teller. Now you can say that this isn’t justified for the simple reason that believing everything that a fortune teller says isn’t a reliable way to generate true beliefs.

This theory of process reliability and justification transmission is all hunky dory until we consider the idea of group or collective belief. Consider this scenario for a moment:

There are 100 guards in the British Museum. The first 20 justifiably believe that a fellow guard Albert will attempt to steal some precious art (perhaps they overheard him scheming with known thieves). From this, they are justified in believing that some guard will steal some art. The second 20 believe that fellow guard Barry will attempt to steal some art. They are also justified that some guard will therefore steal some art. And finally a third 20 believe that fellow guard Charlie will steal some art, thereby also correctly inferring that some guard will steal some art.

So while only 20% of the group believes A, 20% believes B, and 20% believes C, 60% believes S (that some art will be stolen). S is a justified group belief from one perspective - all who hold that belief are justified - but not another - the group believes S but does not believe A, B, or C.

If a justified group belief is a belief that is held by at least a majority of the group, and is one in which the justification for the belief is transmitted from earlier justified beliefs, then it seems like we have a problem. There appears to be no earlier group belief with which to transmit justification to S. Alvin Goldman certainly thinks it is.

We confront, then, something of a dilemma. The verdict delivered by the horizontal dimension and the verdict delivered by the vertical dimensions conflict with one another. Such a conflict cannot be tolerated in a satisfactory theory of group justifiedness. Which dimension should take priority: the horizontal one or the vertical one?

– Social Process Reliabilism (2014) p18

Goldman uses the lack of justification transference from the horizontal dimension to favour a vertical conception of group belief aggregation. But why should we think horizontal belief transmission here is unjustified? Unlike the doctrinal paradox, it looks like this lack of transfer is simply an oversight.

It’s a logical truth that any proposition or belief p entails the disjunct of it and something else p or q - a form of logical inference know as disjunctive introduction. If I believe that the Lions will win the premiership, then I must also believe that the Lions or the Hawks will win. It’s impossible to believe the first without believing the second.

So what happens when we apply this to group belief? Well, the guards that believe A must also believe A or B or C. The guards that believe B must believe A or B or C. And the guards that believe C must also believe A or B or C. So now we have the situation where the majority believe A or B or C, they are justified in believing A or B or C, and this group belief reliably transfers justification to the belief S - that some guard is going to steal some art.

Now one objection to this is that we don’t have a justified group belief in either A, B, or C to generate the group belief A or B or C. Because A is not a justified group belief, it cannot transfer justification to A or B or C. But this objection would also undercut justified individual beliefs that are the result of belief conjunctions.

Take for example, the belief that Berlin is the capital of Germany. This belief can only be true if one also believes that Germany is a real country, that Berlin is a real city in Germany, and the source of this information say, reading it in an encyclopaedia, is a reliable generator of true beliefs. Take away any one of those prior beliefs and the remainder are insufficient to justify the belief that Berlin is the capital of Germany. It is the conjunct that justifies the belief.

So too with group belief. It might be the case that only 20% of a group believes A but the majority belief in A or B or C is the logical consequence of the conjunction of 20% believe A and 20% believe B and 20% believe C. Horizontal belief transfer seems to work just fine.