Foundations & Coherence

Here, I explain two leading theories of the structure of knowledge, and why one of them is better.*

[* Based on: “Foundations and Coherence” in A Companion to Epistemology, 2nd ed. (Wiley-Blackwell, 2010), pp. 22-33.]

1. The Regress Problem

If someone claims to know, or even justifiedly believe, A, then it seems apt to ask them what reason they have for believing A. (Hereafter, I’ll just say “know” for “know or justifiedly believe”. The main issue is really about justification for belief, but “know” and “knowledge” are shorter.)

Suppose they cite a reason, B. Then one can ask for a reason for believing B. Suppose they cite another reason, C. Then one can ask for a reason for that. And so on. What happens if we repeat this questioning indefinitely? One of four things:

1. They have an infinite series of reasons, so they can just go on forever citing new reasons.

2. They go in a circle, i.e., at some point they cite as a reason something that appeared earlier in the series.

3. They come to some starting point(s) that needs no reasons, i.e., one or more claims that are known in a way that doesn’t depend on reasons (sometimes called “self-evident” propositions).

4. Their belief ultimately rests on one or more unjustified assumptions, so they don’t know A after all.

These possibilities correspond to four theories about the structure of human knowledge:

1. Infinitism

2. Coherentism (a.k.a. “the coherence theory of justification”)

3. Foundationalism

4. Skepticism

#1 and 4 are highly unpopular. Let’s focus on the two leading views, Coherentism and Foundationalism.

2. Coherentism

Basically, coherentists think that a belief gets to be justified by being supported by an internally coherent system of beliefs, i.e., a system in which many beliefs support each other, explain each other, fail to conflict with each other, etc.

Note: No one doubts that coherence can contribute to justification. The issue is whether coherence alone may suffice for justification, without the need for foundations. Coherentists say yes; foundationalists say no.

2.1. The probabilistic argument

Suppose that the police interview several witnesses to a crime, without letting them confer with each other. If the witnesses independently tell stories that all fit together well, then the police will conclude that those stories are by and large accurate, because if they weren’t generally telling the truth, it’s highly unlikely that their stories would happen to fit together. Similarly, says the coherentist, if you have multiple beliefs from different sources that fit together well, then those beliefs are probably by and large correct.

Background point: Remember that the question is whether coherence alone may suffice for justification. So for the above example to help the coherentist, it must explain how coherence can provide justification without relying on any foundations. So now here are two objections:

Objection 1: Suppose that none of the witnesses individually have any credibility at all, i.e., the probability of A being true given that a witness asserts A just = the prior probability of A being true. This essentially means that you regard each witness as a random guesser. Then if two witnesses assert A, that will still do nothing to raise the probability of A. (Very roughly, if two random guessers both happen guess A, that doesn’t make it any more likely that A is the truth.) So the reasoning of the example presupposes that each individual witness has at least some initial credibility. This is analogous to our individual beliefs starting with at least some foundational justification.

Objection 2: The police in the witness example have to rely on some foundational knowledge (even apart from objection 1). For instance, they must assume that they can know, to start with, that each witness really did assert what the police think they asserted. They would also have to be able to know when a set of assertions count as “coherent” or not, and they would have to know the principles of probability theory. They have to have that knowledge at the start, in order to do the coherence reasoning, so the example fails to explain how coherence by itself could justify anything.

2.2. The input objection

It looks like, on the coherence theory, you could get lots of justified beliefs about the world without having any actual input from the world, e.g., without actually observing anything. That seems wrong.

Possible response: Modify the theory so that you are required to have a set of beliefs and experiences that cohere with each other. This blurs the distinction between coherentism and some traditional, fallibilistic versions of foundationalism.

2.3. The alternate-coherent-systems objection

There could be many conflicting belief systems, each of which is internally coherent. Would we want to say that they are all justified?

Response: The above-suggested requirement (incorporating experiences as well as beliefs) eliminates most of the possible conflicting systems. For any that remain, well, maybe it’s just true that there are multiple rational yet conflicting belief systems.

2.4. How to define coherence?

Fumerton objects that there’s no good account of what “coherence” is.

The weakest account of “coherence” is that a belief system is coherent as long as it’s consistent (doesn’t contradict itself). But this would mean that none of us have coherent belief systems. All rational people have inconsistent belief systems. (Proof: Do you think you have at least one false belief? If you’re rational, you answered “yes”. It follows that your beliefs are inconsistent, since they can’t all be true.)

The strongest account of “coherence” is that a belief system is coherent when every belief in the system is entailed by other beliefs in the system. Say you believe any two propositions, A and B. If you understand basic propositional logic, then you will also believe “A if and only if B”. Congratulations: you now have 3 beliefs such that each one is entailed by the other two. This makes it trivial to get the strongest form of coherence.

Conclusion: The weakest notion of coherence is too strong, and the strongest notion is too weak. So there is no good notion of coherence.

2.5. The circularity objection

Circular reasoning just seems obviously bad. You can’t justify A on the basis of A, nor can you justify A on the basis of B and B on the basis of A, etc. It’s obscure why things would get better if you just make a really big circle.

3. Foundationalism

Thesis: some beliefs (known as “foundational”) are justified in a way that doesn’t depend on reasons, and all other justified beliefs are based on the foundational beliefs.

3.1. Why believe foundationalism?

One reason is that there just seem to be obvious examples. E.g., if you’re in pain, it seems like you just know that you’re in pain; you don’t need reasons or an argument to figure that out. Likewise, if you understand “A=A”, you just see that it’s true.

The other main reason for believing foundationalism is the disjunctive syllogism: infinitism, coherentism, and skepticism are all implausible. Foundationalism is the only viable account of how knowledge might work.

3.2. The arbitrariness objection

The leading “objection” to foundationalism is that putatively foundational beliefs are “arbitrary”, and therefore unjustified, and therefore there can’t really be foundational beliefs.

Though this objection is very popular with undergraduate students, I find it empty. I don’t know what “arbitrary” means. I can think of two obvious interpretations: “arbitrary” means “unjustified”, or it means “not based on reasons”.

Suppose it means “not based on reasons”. In that case, the objection says that putatively foundational beliefs can’t be justified because they’re not based on reasons. That begs the question, blatantly.

Now suppose it means “unjustified”. In that case, the objection says, again, that putatively foundational beliefs are unjustified because they’re not based on reasons. Again, blatantly question-begging.

A more sophisticated worry: presumably, there should be something that differentiates foundational beliefs from random, unjustified beliefs that are also unsupported by reasons. E.g., my belief “A=A” must have some feature, F, that the belief “Purple unicorns live on Mars” lacks, which explains why the former is justified and the latter not. E.g., maybe “A=A” has a special sort of luminous obviousness to it. Whatever F is, it seems like I could cite the presence of F as a reason for my belief “A=A”, thereby showing that “A=A” is not foundational after all.

No, not quite. A foundational belief is defined as one that does not need a reason; it’s not defined as one that cannot have reasons supporting it.

3.3. The bootstrapping problem

Suppose some annoying skeptic asks me for evidence that my sensory perception is reliable. I could just go around looking at objects and gathering “inductive evidence” that my senses are reliable. E.g.: “There’s a cat [known by observation]. My perception tells me that there’s a cat [known by introspection]. So my perception got that one right. Also, there’s a tree. And my perception tells me that there’s a tree. So my perception got that one right too!” Etc. After gathering many cases like this, I generalize to the conclusion that my perception is highly reliable, since it keeps accurately reporting how things are. This is known as “bootstrapping”.

This seems like bad reasoning; it seems objectionably circular. Yet, if perceptual beliefs are foundational, it’s hard to see what’s wrong with the above sort of reasoning. It starts from foundational propositions (all those perceptual beliefs about the environment, plus some introspective beliefs which don’t seem problematic at all), and it reasons linearly from there to the conclusion that perception is reliable.

Notice that this doesn’t just apply to perceptual beliefs. For any class of beliefs that you claim is foundational, you can construct analogous bootstrapping inferences. This is meant to show a problem for foundationalism.

Reply: I don’t know the solution to the bootstrapping problem, but I’m sure the solution isn’t to reject foundationalism, because the problem confronts any theory of knowledge or justification, not just foundationalism. Suppose your theory says that we may acquire knowledge/justification using method M. (M could include reasoning to the belief, it could include the belief’s coherence with your belief system, etc., so this is not limited to foundationalist theories.) A skeptic asks you for evidence that M is reliable. You could then construct a boostrapping argument: You form the belief that P using M, note that M is how you formed it, and conclude that M got the right answer in that case. You then form the belief that Q using M, and again note that M gave you the right answer there. Etc. You then bootstrap to the conclusion that M is reliable.

So I think that if the bootstrapping problem refutes foundationalism, it refutes all theories of knowledge.

3.4. Which beliefs are foundational?

You know the answer to this. If P seems true to you, and you have no reason for doubting it, then you thereby have at least some justification for believing P. (See: 1, 2.)

4. Conclusion

Foundationalism is the correct account of the structure of knowledge.