This is just a brief post about making some epistemological matters crystal clear:
1. Human knowledge is a form of belief
2. Human knowledge is axiomatic
Human knowledge is a form of belief
belief: An acceptance that something exists or is true, especially one without proof.
Now, some people might argue that a statement S is not a belief. In order for them to demonstrate that S is not a belief, they would have to provide a proof that S is not a belief. This proof would be a set of arguments involving logical or/and empirical/inductive reasoning where the only conclusion is that S is true. However, both logical reasoning and empirical/inductive reasoning themselves rely on the acceptance that other statements are true. In other words, reasoning and empirical reasoning involves holding certain beliefs.
Beliefs: formal logic
So, assume that someone were to prove to me that S is true using a logical argument. This logical argument would only be valid if one accepted the statements that underlie the rules of formal logic. The three statements that underlie formal logic are called the Laws of Thought. One of the statements is “A thing is the same as itself” while the second one goes “It will never be the case that A is true and false”. These statements are believed to be true. And when it comes to the “roots” of logical reasoning, this is far as you can go. I call this “roots” axioms. An axiom is something that is held to be true without the need to provide a proof.
Beliefs: physicalist empiricism
Empiricism is far muddier as it tackles the even muddier area of ontology. Formal logic is something of a discrete world where things are either black or white. But empiricism is more of a grey area where the core idea is that truths about the world can be grasped through the senses, whether natural or augmented by technology, as opposed to rationalism where truths about the world can be grasped through logical reasoning. Empirical reasoning also has its share of statements that mostly relate to ontology. The first one is that whatever we see can be interpreted or made sense of by humans. The second one (for followers of the physicalist school of empiricism) states that physical entities/forces/objects are either physical or material. The third one is that the processes of the universe are measurable to a level of complexity that can be understood by humans.
The first statement, which talks about truth through sensorial experience, relies on statements such as “sensorial experience either is reliable or can be made reliable” being true. How do you prove the reliability of sensorial experience without using sensorial experience to establish the proof? It seems that you can’t if you are a human. Solipsism is one of the ontological stances that denies the reliability of sensorial experience when it comes to matter of truths about the world.
The second statement relies on statements such as “All phenomena that can be observed by us can be measured” and “For practical purposes, phenomena that can’t be observed or inferred from observations does not exist” being true. And in turn, these statements depend on statements such as “Measurability and existence are properties that always go together” being true. Now, as sensible an approach as this is, it inevitably raises the question of how can we establish that measurability is a property of all things that also have the property of existing in this universe? Of course, seeing how measurements are the main way in which we discover knowledge about the universe, it does not seem feasible for us to gain empirical knowledge about the limits of measurability without using measurements. So, we have to take this statement as an axiom.
The third statement relies on statements such as “We are capable of measuring the processes of the universe or we will get capable to do so in our endeavour of empirical knowledge seeking” being true. This statement, in turn, relies on statements such as “The processes in the universe have a complexity C and humans are capable of understanding processes of complexity C” being true. As smart as we are compared to other life forms in this planet, the idea that you are smart enough to understand the processes of the universe just because your brain makes you do things that no other life form you have seen can do is not currently provable and it does not seem to be true. Surely, our capabilities don’t change regardless of the absence or presence of life forms less capable than us. Of course, you could come up with other statement to rationalise the above statement about complexity but it seems to me that it is just another case of megalomania in our species.
So, as seen above, when looked at in detail, the two main avenues of truth are full of beliefs at their lowest level. Beliefs about the Laws of Thought being true or beliefs about the physicalist ontology being true or beliefs about universal measurability, all these are tools that we use to gain knowledge, we use them on the basis that the set of beliefs we hold are true. And I am not discussing here whether the statements underlying the use of empirical and logical reasoning are true or not. The main idea of this post is that they are beliefs, in other words, they are statements for which we have no proof but nevertheless accept as true.
Human knowledge is axiomatic
Following the conclusion of the previous point, it seems safe to conclude that human knowledge is axiomatic. In other words, if you were to question every factual piece of empirical knowledge or/and every logical statement, you would arrive to the axioms of empiricism and formal logic and you would not be able to go any deeper because axioms form the rock bottom level of our knowledge. The first stone in our pyramid. This is why I cringe every time I see the words “fact” and “belief” opposed to each other. In particular, I see the word “fact” used in a very dogmatic way as something whose truth has been discerned beyond all doubt when, as we have seen, nothing can be discerned beyond doubt by us. Not we the tools we currently have. Instead of saying “S is true”, the logically valid sentence would go: “according to the axioms of empirical/logical reasoning, S is true”. This longer sentence highlights the conditional nature of our statement. It is true insofar as the axioms of our reasoning are true. And this means that we are open to the possibility that were these axioms to ever be proved false, S would be false everything else being equal. Uncertainty, like mortality is something of a constant in our lives, we seek ways to tackle it but denying its pervasive presence in our lives amounts to something akin to denying that A&B is true when A and B are true.