Totality and Justification
Totality operators don’t often feature explicitly in discussions in epistemology, but one phenomenon that does receive a good deal of attention is defeat – the way in which evidence supporting a proposition can be overturned or counterbalanced by new evidence that comes to light. Suppose I have a perceptual experience as of a blue vase before me. Am I justified in believing that there is a blue vase before me? Clearly I do have some very strong evidence for this, but whether I’m justified in believing it depends on what other evidence I happen to have. If, for instance, I’ve learned that there is tricky blue light illuminating the vase or that I’ve ingested a hallucinogen, then that would serve to defeat my perceptual evidence.
The most we can really say is something like this: If I have a perceptual experience as of a blue vase before me, and I don’t have any other relevant or defeating evidence, then I would be justified in believing that there is a blue vase before me. While we can’t say anything definitive about what a perceptual experience justifies, we can say something definite about what a perceptual experience justifies if it is the totality of one’s relevant evidence. The totality operator here is indispensible – but there has been little investigation in epistemology of the status or properties of such operators.
It is often said that a rational agent should proportion her degrees of belief to the evidence. Naturally, though, it is the totality of one’s evidence to which one should proportion one’s beliefs – and not just some part of it. Indeed, this is sometimes referred to as the requirement of total evidence. This is another, related, way in which totality operators have relevance for epistemology – in spelling out our obligations as rational inquirers. It’s natural to think that bodies of evidence stand in relations of relative size – that a body of evidence E1 can ‘outstrip’ a body of evidence E2 if E1 includes all of the evidence in E2 and further evidence besides. We will use this relation between bodies of evidence to devise a formal analysis of totality operators, as they occur in epistemology, and use the analysis to shed new light upon their content and logic.