How Do We Know That We Know What We Know?
It’s important to note that I am not a philosopher. Some of what we’re about to delve into is pretty heady. I’ve done my best to distill things down while keeping the meat. Any mis-interpretations or mis-representations are solely my own.
The title for this entry says it all. How can we know that something we know or believe to be true actually is true? We are surrounded by information, some of it true, some of it false, some of it only applicable to certain situations or circumstances. How are we to tell which set of data or facts is correct relative to everything else?
Fortunately, there is a discipline within philosophy that deals with exactly these questions: epistemology. Like most things philosophical, the word epistemology is derived from the Greek ‘episteme’, meaning knowledge, and logos meaning ‘logical discourse’ (1). Historically epistemology has dealt with 3 fundamental questions (1):
What is knowledge and what do we mean when we say we know something?
What is the source of knowledge and how do we know if it’s reliable?
What is the scope of knowledge and what are it’s limitations?
We’ve been working on epistemological questions for a very long time. Plato, Aristotle and Socrates worked on these problems and never arrived at a resolution. Later Descartes, Hume and Kant gave it a whirl. In more modern times Noam Chomsky, Ayn Rand and Terence McKenna joined the ranks (2). The nature of knowledge and knowing is slippery. I think this is an area we will never fully settle.
Philosophy, then, necessarily interacts with science. Scientists are often confronted by an extremely difficult question to answer: “How do you know?” And here we come to a fork in the road, each side of which must be examined. On the one side we have science itself; a collection of ‘facts’ about some subject (1). On the other side we have the philosophy of science which describes the processes and philosophical underpinning related to those facts and their discovery (1). In this post we are going to look at the philosophy of science.
What are the philosophical processes and underpinnings that help us understand which data are real and which are not? In the scientific process, we can boil this question down to roughly 4 philosophical approaches. These are sometimes used in conjunction and help us arrive at a scientific hypothesis. The 4 approaches are (1):
Each of these has its own strengths and weaknesses.
Rationalism is a system that relies on a construct called a syllogism. Syllogism is a form of reasoning in which a conclusion is drawn from two statements or premises that are assumed to be true (3). There are three major types of syllogism with a few different subforms (3). Here, we’re going to look at 2 forms: modus ponens and modus tollens.
Modus ponens is an affirmation and generally follows the form:
If A is true, then B is true (major premise)
A is true (minor premise)
Therefore B is true (conclusion)
Modus tollens, on the other hand, is negation and follows the form:
If A is true, then B is true (major premise)
A is not true (minor premise)
Therefore B is not true (conclusion)
At this point we need to discuss two things: validity and truth. A syllogism is valid if its conclusion follows from the premises. A syllogism is only true if the information it contains is consistent with fact (4).
Consider the following:
Major premise: all mammals are warm blooded
Minor premise: dogs are mammals
Conclusion: therefore, dogs are warm blooded
The above syllogism is both valid and true. All mammals are warm blooded - it’s part of the definition of a mammal. Dogs are mammals. And we know dogs are warm blooded as a consequence.
Now consider this (1):
Major premise: if I can find the north star, I can use it to find north at night
Minor premise: the north star is the brightest star in the night sky
Conclusion: the brightest star in the night sky points north
Is this syllogism valid? Yes, the conclusion follows both premises. Is it true? No. Those who are astronomically minded will see the error. It’s a commonly held misconception that the north star is the brightest star in the night sky. Actually Polaris (the north star) is 46th in brightness (5). The brightest star in the night sky is Sirius A which points either southeast, south or southwest depending on the time it’s observed (5). This rationalization doesn’t hang together as true because it’s built on faulty information. So, if you’re ever lost at night and someone suggests you find your way by following the brightest star, go in the opposite direction of that person and you’ll do ok. The lesson here is: just because something sounds logical doesn’t mean that it’s true. It’s fair to question the factual basis of each premise.
From the perspective of science, a rational argument is problematic because it’s empty (1). Go back to our mammal-dog example from above. We have to know our premises are true and, at that point, the conclusion is usually foregone. We are only making explicit something we already knew.
Moving on to Reliabilism. Under this way of thinking we are justified in knowing something is true only if that something is arrived at using reliable cognitive processes that extend beyond human reason (1). We see reliabilism a lot in Boolean logic and mathematical proofs. Consider the following proof of the additive property of equality from algebra (6):
Let a, b, c and d be members of set S and ‘=‘ be a relationship on that set
Let d = a + c
Then d = b + c (because a=b in step 2)
d = d
a + c = d
Therefore a + c = b + c
Most of us take the above property completely for granted, but at some point all of the rules of algebra, geometry, calculus and higher maths are ‘proven’ in ways similar to this. There’s no bias in this type of exercise and little room for misconception as in the premises of rationalism.
That said, we have to be careful not to break any mathematical or logical rules. Consider the following (7):
a^2 = ab (multiply both sides by a)
a^2 - b^2 = ab - b^2 (subtract b^2 from both sides)
(a + b) (a - b) = b (a - b) (factor)
a + b = b (cancel)
2b = b (substitute and combine terms)
2 = 1 (cancel common terms)
The above seems perfectly fine, right? Wrong. We violated a rule of algebra. See if you can find it (I’ll put the answer in footnote 8). Unless we’re paying close attention and understand the mathematical and logical rules in play very well, we can end up creating a situation that appears to be true but is actually false.
Coherentism tells us that knowledge is secure when its ideas support one another to form a logical construct (9). In other words knowledge is certain only when it coheres with similar information (1).
I have to be honest, this was a difficult one to distill down to relatable examples. After reading through several sources I felt like I had a pretty good handle on coherentism, but I was still kind of at a loss for how to describe it simply. Negative cases were pretty easy to come by, as we’ll see shortly. Positive cases tended to be fairly elaborate. So, like I always do when faced with this type of situation, I shut the computer down and went away to do something else. After a while (no, I’m not going to tell you how long it took), it hit me: a good chunk of our justice system, particularly the circumstantial case, is built on this philosophical approach.
Suppose a crime has been committed and reported to the police. There were no eye witnesses and no camera footage. How do we go about solving the case and putting the proper person in jail? Well, we may try to collect physical evidence (hair, blood, finger prints, etc.), we may look for who had a motive to commit the crime, we may look more closely at those who had a motive and see who doesn’t have an alibi for the time the crime was committed and so on. One of these pieces, on its own, isn’t enough to justify taking away a person’s freedom. But, as the pieces collect, they begin to paint a picture or point a finger towards the likely culprit (assuming we are interpreting and connecting things properly).
And, of course, this provides an excellent negative case as well. We have all seen news stories where an innocent person is set free after serving time in prison for a crime they did not commit. Humans can draw connections that don’t exist, make leaps that are unsupported and interpret information in a non-logical way. We can be told connections exist where they do not and cognitive bias leads us to the conclusion that the person telling us these connections exist is credible, so we go with it.
Of the four philosophical methods, coherentism is, to me, the method in to which it is easiest to introduce error. Let me give you a simple example: prior to Nicolaus Copernicus (1473-1543) (10), all the astronomical observations and theories in science pointed to the fact that the earth was the center of the solar system and probably the center of the universe. This belief was supported by a set of logical, at the time, facts and reasoning. Of course, we now know this model of the solar system, and probably the universe, is entirely untrue.
Lastly we have empiricism which provides one of the foundations for modern science. Empiricism says that all sciences (and therefore the knowledge derived therefrom) are based on experience and observation (11). In science an empirical approach seeks to create hypotheses, or educated guesses, against which further observations and tests can be performed.
Here we need to take a bit of a side track. One of the issues that plays havoc with public understanding of science is the difference between hypothesis and theory. An hypothesis examines available evidence and attempts to create an explanation (12). So far so good. Here’s the tricky bit: an hypothesis, if it’s to be of any value, must be testable or falsifiable in some way. In other words, examining the evidence and making an untestable pronouncement or statement is not the creation of an hypothesis nor is it science. A theory is an hypothesis that has been tested a lot and never been shown false (13). In science we never prove anything ‘true’, we only show that in certain circumstances and within the limits of our current ability to make observations, something hasn’t been shown not true.
Science then, unlike the public interpretation of it, is always changing. New technologies enhance the way we make observations. We come up with new observations to make about existing phenomenon. We come up with new questions to ask about existing phenomenon. Everything is always open to questioning. There is no such thing as ‘settled science’. Science itself is an inherently unsettled and unsettling process. Every hypothesis is subject to falsification followed by either revision or being thrown on the trash heap of failed hypotheses. Every theory is subject to revision or complete overturning, and this can happen at any time.
All things scientific are tentative. What is accepted at any give time represents the consensus view of institutional science (1) - coherentism anyone?
Since empiricism is based on experience and observation, it also has the potential to lead us down the wrong path. Eye witness testimony is based on personal observation and many studies have shown the issues with human ability to recall. Cognitive bias and the way the sub-conscious processes complex information causes memory to be distorted, particularly in stressful circumstances. Humans are not robots with perfect recall nor are our eyes cameras that simply take snapshots of the world around us to be stored in the brain and called up at a later date.
To wrap this up then, modern science is built largely on empiricism. We use rationalism, reliabilism, and coherentism as a check against the biases that can come from personal observation. This means we’re interested primarily in knowledge gained through observation and experimentation.
Wenning, C. (2009). Retrieved from http://www2.phy.ilstu.edu/pte/publications/scientific_epistemology.pdf
List of Epistemologists. Retrieved from https://en.wikipedia.org/wiki/List_of_epistemologists
Syllogisms. Retrieved from http://changingminds.org/disciplines/argument/syllogisms/syllogisms.htm
Nordquist, R. (23 June 2019). Definition and Examples of Syllogisms. Retrieved from https://www.thoughtco.com/syllogism-logic-and-rhetoric-1692167
50 Brightest Stars (2020). Retrieved from http://astropixels.com/stars/brightstars.html
McAdams, David E. Additive Property of Equality. (12 April 2009). All Math Words Encyclopedia. Life is a Story Problem LLC. Retrieved from https://www.allmathwords.org/en/a/additivepropofequality.html
Algebra Sleuth: Proof that 1=2. (2023). Retrieved from https://www.education.com/activity/article/Algebra_Sleuth_Proof_that_1_2/
At the beginning of this ‘proof’ we defined a=b. Between steps 4 and 5, we simplify by dividing by a - b to cancel terms. Since a=b, a - b must be zero and we cannot divide by zero.
Coherentist Theories of Epistemic Justification. (9 March 2021). Stanford Encyclopedia of Philosophy. Retrieved from https://plato.stanford.edu/entries/justep-coherence/
Nicolaus Copernicus. (8 January 2023). Retrieved from https://en.wikipedia.org/wiki/Nicolaus_Copernicus
Scientific Empiricism. (2022). Retrieved from http://www.dictionary.com/browse/scientific-empiricism
Hypothesis vs Theory. Retrieved from https://www.diffen.com/difference/Hypothesis_vs_Theory
What is the difference between hypothesis and theory? Retrieved from https://www.quora.com/What-is-the-difference-between-Hypothesis-and-Theory