As an undergraduate engineering student, I was taught lots of material that I later found to be incomplete. The facts I was taught were correct, but only in certain circumstances. In some sense, I’ve struggled to identify what my education was. It has left me pondering a fundamental question: What is knowledge?

In Theaetetus, Plato defined knowledge to be a justified true belief [1]. This is the traditional definition of knowledge, and it seems reasonable. If you have evidence for a belief, and that belief is correct, it seems like you can say that you know your belief; i.e. your belief is knowledge.

In 1963, Edmund Gettier showed that Plato’s definition falls short [2]. Gettier gave a counterexample, and counterexamples like it are now known as Gettier cases. Here is one: an observer is looking at a hill and sees an animal that looks like a goat. The observer states “There is a goat on that hill.” The observer has a belief (there’s a goat on that hill). And he has justification for that belief (his view). He is mistaken, though; the animal that the observer sees is actually a dog. If that were the entire story, then we could say that the observer’s belief is incorrect, and so it isn’t knowledge. However, there is a goat on the hill that is hidden from the view of the observer. And so, the observer’s belief is correct. However, it doesn’t seem like knowledge since the observer’s justification was flawed.

Where do we go from here? One natural next step is to question all of our senses. Is any of this reality? We could all be plugged into the Matrix or living in an artificial reality [3]. And since our only evidence of causality is a set of causal experiences, perhaps we can’t even rely on that. This is a philosophy known as Skepticism [4].

Skepticism seems like the only provable choice, and so it seems like the only defendable one. And although this is the case, I don’t think that it leaves us with an operational definition of knowledge (in the sense that we are left saying we can’t know anything). So let us assume that causality holds (i.e. that the laws of physics remain the same over time) and proceed to seek out a definition of knowledge that holds with this assumption.

In 1963, Karl Popper created a new definition of knowledge: an ability to predict the future with high probability (which he called science). For example, Einstein used his general theory of relativity to predict how light bends near large masses. In 1916, he thought of a way to test his theory by observing Mercury when it was positioned next to the sun during a solar eclipse [6]. Three years later, during a solar eclipse, Mercury appeared exactly where he predicted. An ability to predict the future is a very appealing definition for scientists and engineers. A statement like “this building will withstand a 7 point earthquake” is a valuable quantified prediction.

And yet it seems incomplete. I can look at a red shirt, say “that’s a red shirt”. I would be stating a fact (knowledge) without making a prediction of the future. In other words, not all knowledge is science.

This led me to Contrastivism; a philosophy that alters the definition of knowledge. Conventionally, a statement of knowledge has a proposition and a subject. For example, “that shirt is red;” the shirt is the subject, and the proposition is that the subject is red. “Mercury will appear at location X in the sky during the next solar eclipse;” the subject is Mercury and its location in the sky is the proposition. Contrastivism changes the definition of knowledge to one of comparison: a subject, a proposition, and a constrast [7]. In Contrastivism, one compares two possible knowledge statements, and the one that’s more probable (better justified) is considered known. (If neither options are justified, we say we don’t know.) For example, “That shirt is red, not black” or “There’s a goat on the hill, rather than the hill not having a goat on it.” The hill is the subject, the proposition is that there’s a goat on it, and the contrast is that there’s no goat on the hill.

Let us consider the situation of a murder mystery in a locked room with two people in it, one is holding a gun. We can say, “The person with the gun killed the victim, rather than the victim committed suicide.” But how do we know an alien didn’t teleport into the room, commit the murder, and frame the person with the gun? We don’t. Instead we say, “The person with the gun killed the victim, rather than an alien.” We can say this because it is more probable that the person with the gun committed the murder. Another statement we can say is “The person with the gun killed the victim, rather than any other reasonable possibility,” meaning that the person with the gun is the most likely the murderer in comparison to all other possibilities we’re willing to consider. And an even shorter way of saying this is “The person with the gun killed the victim.”

And so we’ve arrived at our operational definition of knowledge. Knowledge is a justified statement that is most probable in comparison to other possibilities.

[1] http://plato.stanford.edu/entries/plato-theaetetus/

[2] Gettier, Edmund L. “Is justified true belief knowledge?” Analysis 23.6 (1963): 121-123.

[3] http://www.theverge.com/2016/6/2/11837874/elon-musk-says-odds-living-in-simulation

[4] http://plato.stanford.edu/entries/skepticism/

[5] Popper, Karl. Conjectures and Refutations: The Growth of Scientific Knowledge. Routledge, 2014.

[6] Andreasen, Nancy C. “Einstein: His Life and Universe.” American Journal of Psychiatry 165.12 (2008): 1615-1616.

[7] http://www.iep.utm.edu/eth-cont/