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.

Understanding Epistemology

The word “epistemology”, I believe, looks pretty scary to those unfamiliar with it. Contrast this with “ethics”, another traditional branch of philosophy, where the word is not scary and many, most, perhaps all, people have experience with a way of “doing the right thing.” Understanding ethical issues and dilemmas, in my experience, is more common for people than understanding epistemological issues and dilemmas. For example, it is more likely that a non-philosophically trained person would have an opinion on the ethics of Syrian intervention than an opinion on what newscasters and politicians are justified in believing. The more I learn about the definitions and distinctions of epistemology, the more I think that raising the public understanding of epistemology to the same level as ethics would benefit the public discourse. I will discus how I came to the topic as well as explaining what I learn in an approachable way.

My Background

Since this summer semester, the bulk of what I study at Rutgers has been epistemology, beginning with the course “Theory of Knowledge.” If you look up epistemology in the dictionary, you’ll likely find the definition contains the phrase, “theory of knowledge”, and I learnt that this is because the faculty thought “epistemology” would scare off students with little or not background. By a combination of accident and preference, I have taken the undergraduate introductory epistemology course and I am taking the undergraduate 400-level and the graduate introduction. I like this a lot, I believe this combination will adequately prepare me to interface with problems in epistemology. I’m very excited that my experience has already allowed me to begin reading publications which would have previously baffled me; I am working through Laurence Sosa and Ernest Sosa’s Epistemic Justification.

The Regress Problem

Here is an example of a epistemological problem that I will show that everyone would benefit from understanding.

Think about your beliefs. Pick any one of your beliefs. You very likely have related beliefs, beliefs that come about from this first one and beliefs that justify this first one. For example, if you picked “Obama is the President of the United States”, you might notice that this belief justifies your other belief that “Barack Obama is the first African-American president” and stems from other beliefs like “The United States has a president” and “The United States is a democracy.” Your beliefs have relationships!

In one direction, you have increasingly higher-order beliefs. In the other direction, you have increasingly basic beliefs. Notice that more basic beliefs are related in some way to higher beliefs in a way that justifies them. It would be hard for you to believe that “The United States has no president” and from this, and other beliefs, think that “Barack Obama is the first African-American president.” If you keep tracing how your beliefs are related in the basic direction, what is that you find? Does it end? Does it loop back on itself? Is it infinite?

This question is known as “the regress problem.”

Possible Solutions

I’ll present it more formally. Imagine a graph where every node represents a doxastic or propositional belief held by a single person. The directed vertices between the nodes represent a justification-relationship, where $N_1$ has a vertex pointed at $N_2$ when $N_2$ is justified in some way by $N_1$. When moving from $N_1$ to $N_2$, I say the belief becomes “more basic.” There are three logical possibilities about the structure of such a graph. As you move to increasingly more basic beliefs:

  1. You can reach a set of “most basic beliefs,” philosophers call this foundationalism;
  2. Justification is cyclic, meaning “basic beliefs” can be cyclic, philosophers call this coherentism;
  3. You never reach a set of “most basic beliefs,” justification runs infinitely, philosophers call this infinitism.

Why This Matters

How does this fit in how people talk about belief and justification? Take the issue of Syria. On the topic, it is very common to hear a liberal say of FOX News things like,

FOX New opposes the Syria peace plan because it makes America under Obama seem weak. They’re biased! This fits with their conservative viewpoint.

What that sounds like to me is that our liberal is accusing some “epistemic community” (a piece of jargon to mean institution) has formed a belief which confirms a bias, fits an agenda. I think this is equivalent to saying that FOX News has formed a belief with bad justification. Perhaps the set is locally coherent and contains some truths, but this person’s main problem is that the justification for their opinion doesn’t contain all the facts or similar. This is one example of when being able to understand the epistemological issues of a story equally well as the ethical issues of story, being able to intelligibly answer “Was it moral to make peace with Syria?” and “Am I justified in forming this belief about peace with Syria?” Just as it’s valuable to use ethical words like “rights” and “happiness” (for utilitarians) in public discourse, it’s valuable to use epistemological words like “coherence” and “foundational belief.”