What Infinitism is Contingent On

Infinitism with regards to the depth of graph representing the structure of justification, whether foundational or coherent, whether propositional or doxastic, will be false unless the subject of the content of the belief has the feature of being both infinitely small and infinitely large in some way. This rule of infinitism gets it right for the oft example of believing that “it is 12:00” (or any time). The infinitist points out that there are propositionally infinitely many justifiers. This rule of infinitism gets it right for every case where the infinitist has no response, for example, believing that “I am in pain.” The infinitist cannot respond to that example because it is not necessarily true that the reality of the agent is both infinitely small and infinitely large. It could be the case, but the sciences have still to be agnostic about our reality. In the case of doxastic justification, because the machinery of the human mind is finite in function, it is implausible we hold infinitely many beliefs about anything. In the case of propositional justification, infinitism is only possible when the subject of the belief is at least infinitely large or infinitely divisible.

Notice there could be infinite propositional justifiers for a belief in depth or in breadth, where depth is the weight of the graph and breadth the number of vertices pointing at a proposition. If reality is temporally infinite but not spatially infinite, this would mean that the depth of propositional justifiers would be infinite. If reality is spatially infinite by not temporally infinite, it would mean that the breadth of propositional justifiers could be infinite but the depth would not be (as time “began”). In the case where reality is both temporally and spatially infinite, propositional justification would be infinite in both breadth and depth. In the case where reality is neither temporally or spatially infinite, or is locally limited or isolated in some way, infinitism with regards to propositional justification will be false.