Tabula Rasa, Axioms, And The Münchhausen Trilemma

How would we know what we know about the hard sciences, if we could only rely on our senses, the techniques from the knowledge we currently know, and nothing else?

If you ask anyone “Which is larger, the Sun or the Moon?”, every educated person will say the Sun and they may even tell you that the Sun is about 400 times the size of the moon, by diameter. An uneducated person will probably remember from school that the sun is bigger or they may not and go with what they see.

Now you ask “Well, they appear to be the same size. So, how do you know that the sun is bigger? How would people have figured this out during ancient times before telescopes and such were invented?”

At this point, the uneducated person may find it puzzling and interesting. The educated person will be offended. “Are you questioning my intelligence? You must be a conspiracy theorist.”

Very few people will actually know the observations which were needed for us to even question whether the sun and the moon were different sizes. Fewer still will know the experiments done and the body of empirical knowledge required to make us certain that the sun is larger. Yet, the educated people are all certain the sun is bigger. They are also certain they have arrived at this conclusion using rational decision making.

There are a lot of educated people who are not very smart. Being mediocre and educated makes people indignant when they are questioned.

Wikipedia: Problem of the Criterion

Wikipedia: What the Tortoise Said to Achilles

Street Epistemology: A Method for Checking Our Understanding

An axiom or postulate is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. Axioms are the most basic conceptual foundation in all proofs, hence they cannot be proven by referencing even more basic statements, since there are none by definition. It is thought that in principle every theory could be axiomatized in this way and formalized down to the bare language of logical formulas.

Note that the order in which axioms are listed matters because previous axioms state concepts that later axioms have to refer to. It would not make sense to establish the Identity Axiom after the Law of Non-Contradiction.

Everyone has assumptions because they are necessary in order to think. It speeds up mental calculations when the brain doesn’t have to consciously realize axioms all the time. For example, we presuppose space, time and causality when we think about physical events. Philosophy involves bringing those assumptions into consciousness. The goal is to make all implicit assumptions explicit, and question them. All humans begin life with unexamined assumptions, but everybody tends to examine different assumptions at different ages due to selective attention, and some people never examine any of them at all since they never needed to examine them, weren’t smart enough to examine them, and were never educated about them.

Assumptions can also make thought experiments and if-then chains of reasoning easier to think about. For example, it would be harder to learn physics without making assumptions for simplifying the problems to aid with learning the topics at hand.

Main Article: StateOfTheNihil’s Solution to the Münchhausen Trilemma.

Wikipedia: The Münchhausen Trilemma.

Foundationalism, coherentism, and infinitism all share the underlying assumption that beliefs are justified solely by other beliefs, in a chain of reasoning. This is where things start to fall apart. Beliefs are not just justified by other beliefs, but also by their relation to subjective experience.

The other problem with infinitism is that if justification is just a chain of beliefs that extends indefinitely, then it is impossible to know what is justified. You can’t demonstrate the chain or conceptualize it. You can only assert it.

Knowledge may seem to be foundationalist since complex concepts depend on simpler concepts, but there’s no reason why this can’t be explained by coherentism instead. It’s not possible to have a purely foundationalist theory of epistemology, though it is possible to start off from a foundationalist-like series of axioms and theorems that cohere to other epistemological knowledge to the point where the entire theory of epistemology justifies and re-affirms the axioms and theorems themselves, which would ultimately be coherentism, not foundationalism.

It’s possible to create new beliefs that are not soundly grounded within a set of basic beliefs, axioms, and assumptions. For example, many American Indians believe that photography could steal a person’s soul. They did not establish this new belief as something that follows from what they already believed. If they cannot explain how what they believe works, yet they choose to hold the beliefs anyway, then they have chosen to believe in something that does not follow from an epistemic foundation because they had to make a new assumption for explaining what they were perceiving. More generally, whenever someone tries to understand why before understanding how, they are breaking the rules of foundationalism and how it’s supposed to work.

Foundherentism is another proposed solution to the Münchhausen Trilemma that’s similar to the one that StateOfTheNihil proposed (which I endorse), but it still falls short because Haack argues that experience’s relation to beliefs is causal, and that causal relationships can also function as a justifying relation. We shall differentiate our proposed solution from Haack’s solution by naming our solution “Empirical Coherentism”.

It’s not possible to build a purely foundationalist theory of epistemology, though it is possible to create a set of axioms and theorems that cohere to other epistemological knowledge to the point where the entire theory of epistemology justifies and re-affirms the axioms and theorems themselves. Every great theory begins with a minimal, yet sufficient set of carefully chosen axioms that implicates a framework of non-contradictory conclusions.

Knowledge tends to look as if it’s structured according to foundationalism when first acquiring it, but every foundationalist system eventually evolves into a coherentist structured system as the acquisition of knowledge progresses. In fact, one of the most defining characteristics of formal education is precisely that it is structured in a foundationalist format, starting from simpler concepts to higher-level concepts. Structuring curriculum in this manner optimizes the acquisition of knowledge.

The foundationalist framework that I am proposing is easy to understand since it can be readily formulated by an understanding of classical logic. This framework also works as something that secular, logical people with different backgrounds can quickly learn and make references to when discussing philosophy. Without a common framework of agreed-upon knowledge, people with completely different life experiences (and educations) may not be able to communicate anything meaningful at all. So a foundationalist framework provides a common point of reference.