Consistency as the Criterion of Truth

Consistency as the Criterion of Truth

8th Sep 2020
Reading Time: 8 minutes
Epistemology, Philosophy

How do we know when something is true?

What does it mean to know? How do we define true?

In 1963, American philosopher Edmund Gettier published one of the shortest, most influential, and most controversial papers in epistemology, titled Is Justified True Belief Knowledge? In it, he provides counter-examples to the criteria for knowledge put forth by philosophers Plato, Roderick Chisholm, and A.J. Ayer, who each discussed definitions of knowledge as a justified true belief (JTB for short).

The basic idea of Justified True Belief is that there are three essential criteria for knowledge: a belief, a justification for that belief, and that the belief is true. If a proposition fails to meet all three criteria, then it is not knowledge.

Whether or not JTB was ever widely accepted by philosophers or anyone else as a gold standard for knowledge is debatable, to say the least. In his 2016 paper The Legend of the Justified True Belief Analysis, Dr. Julien Dutant, a lecturer in philosophy at King's College London, dismembers the questionable history of how the JTB criteria ended up in every introductory philosophy textbook as the "traditional" Western definition of knowledge. It seems likely that Gettier's arguments against JTB had more to do with popularizing it than any of its supposed advocates.

In his 1963 paper, Gettier provided a couple of thought experiments to illustrate cases where a person might have a justified true belief but still not have knowledge. Gettier's counter-examples to JTB, and others inspired by them, have become known as Gettier Problems. These problems posit elaborate scenarios where a person has a belief and a justification for it, and where the belief happens to be true, but it is true for a completely different reason.

In his book Theory of Knowledge, first published in 1966 and revised in 1977 and 1989, Roderick Chisholm offers a simple Gettier problem that illustrates how they disprove the JTB criteria: imagine that you see what appears to be a sheep in a field. You believe there is a sheep in the field, and you have a good justification for that belief. However, what you saw was actually a dog that had been disguised as a sheep. But, out of your sight in another part of the field, there is an actual sheep. Therefore, your justified belief that there is a sheep in the field is true, but not for the reason you think it is.

Moti Mizrahi, a professor of philosophy at Florida Tech, ably points out the logical flaws underlying Gettier problems in his 2016 paper Why Gettier Cases Are Misleading:

Gettier cases are misleading insofar as they merely appear to be cases of epistemic failure (i.e., failing to know that p) but are in fact cases of semantic failure (i.e., failing to refer to x).

In the case of the sheep in the field, your belief is not merely that the field contains a sheep, but that a specific sheep exists in that field - the one you saw. By exploiting vagueness in the way we commonly discuss philosophical propositions in everyday language, it's possible to conflate the justfied belief in one sheep with the actual existence of a different one. What you believed was not merely that the field contained any one interchangeable sheep; you believed specifically that you observed a particular sheep, in a particular part of the field, at a particular time. The mistake would quickly be revealed by further investigation, even if it did raise disturbing new questions about who disguised the dog as a sheep.

A real-life example of a Gettier problem further illustrates why the apparent logical paradox of the sheep in the field does not exist at all when more specific language is used. In the 1960s, astronomer Peter van de Kamp and his team began publishing papers claiming to have discovered evidence of a planet around Barnard's Star, a nearby red dwarf about six light-years from the Solar system. van de Kamp and his colleagues had spent years carefully observing the star, looking for tiny variations in its position on their photographic plates that might indicate the presence of a planet.

The use of astrometry - precise measurements of the positions of stars in the sky - to discover unseen stellar objects had been in use since 1844. That year, Friedrich Bessel published his observations of the wobbly motion of two nearby stars, Sirius and Procyon, and inferred that they must be binary stars with companions too dim to see. Bessel's discoveries would wait decades for confirmation, when the development of better telescopes would reveal that both Sirius and Procyon have white dwarf companion stars.

A century later, Peter van de Kamp thought he saw a similar wobble in Barnard's Star using the 24-inch telescope in the Sproul Observatory at Swarthmore College in Pennsylvania. He concluded that the wobble was due to the influence of a large, Jupiter-like planet. In 1963, he published a paper estimating the planet's mass as 1.6 times larger than Jupiter's, with an orbital radius of 4.4 astronomical units. In 1969, he published another paper claiming that the star actually had two planets, with masses of 1.1 and 0.8 Jupiters.

van de Kamp and his team continued to publish observations and theories about the planetary system of Barnard's Star for over a decade until his retirement in 1972, but attempts by other astronomers to confirm their results were unsuccessful. Studies by Wulff-Dieter Heintz, van de Kamp's successor at Swarthmore College, revealed that the observations were actually the result of regularly scheduled cleanings of the telescope, and van de Kamp's "discovery" was dismissed as untrue.

Decades later, in 2019, an international team of astronomers led by Ignasi Ribas of Spain announced the discovery of a planet around Barnard's Star, discovered through the use of doppler spectroscopy over 20 years of observations. Their discovery, now named Barnard's Star b, bears no resemblance to van de Kamp's planets. A "Super-Earth", b is estimated to weigh in a around 3.2 Earth masses, with an orbital radius of 0.4 astronomical units.

So, Peter van de Kamp was right - there is a planet around Barnard's Star. However, he was wrong, because the planet that is actually there did not match his observations and conclusions. Did Peter van de Kamp know there was a planet around Barnard's Star? Obviously not. He had a justfied belief that was true - but only if phrased in a very general way. He didn't simply beleive there was some planet in orbit of that star, he believed in and published about specific planets, based on faulty observations, that turned out not to exist.

In the exact same way, the sheep in the field thought experiment - and most Gettier cases - rely on imprecise language to create apparent paradoxes where in fact there are none. Gettier problems are the Gordion knots of epistemology; convoluted linguistic wordplay disguised as philosophical paradoxes, which can be quickly cut through by trivial investigation.

However, Gettier problems can help illustrate the actual fallacy of the JTB criteria for knowledge, which is: who knows? Belief can't exist without a believer, and so knowledge requires a knower. Gettier problems rely on constructing scenarios where the full facts are hidden from everyone except whoever's telling the story. This omniscient narrator is conveniently placed to relate the embarrasing reality behind the characters' misapprehensions. But who is this smug and all-knowing reporter?

This may seem like a silly objection at first, because we are so used to the conceit of an omniscient observer with complete access to the truth, and who can therefore determine in call cases who is right and who is wrong about any given proposition. This all-seeing author is present in fiction and nonfiction alike, in books we read and stories we hear all our lives, so it's no wonder we accept its presence without question, just as we accept the existence of fungible generic sheep.

But the existence of an all-knowing participant in these thought experiments is a strong ontological assertion. When we ask whether our characters "know" whether something is true that we are provided as a given, we are implicitly comparing their knowledge to the knowledge of a hypothetical observer with perfect information. In reality, we rarely have the opportunity to check our conclusions against an infallible source of truth.

If we retold Gettier problems without the benefit of a pansophical perspective, we would end up with a story more like the discovery of Barnard's Star b than the story of a dog in sheep's clothing. When you report seeing a sheep in the field, people may believe you or not, and only further observations - preferably by other, impartial individuals - can add to or detract from the strength of the case. Even though the new evidence for a planet orbiting Barnard's Star is very good, it still may turn out to be wrong. Astronomers would love to be able to verify their findings against authoritative data - but if they could, why would they need their telescopes at all?

This is the real problem with the JTB criteria for knowledge -  the impossibility of verifying the Truth criterion. If you have a well-justified belief and want to test whether it's true or not, how do you do that? Any test you could make would also be subject to further questioning: "How do you know A is true? Because B. How do you know B is true? Because C." and so on forever.

Sextus Empiricus, a famous Pyrrhonian Skeptic philosopher of the second century A.D., identified this same problem:

Those who claim for themselves to judge the truth are bound to possess a criterion of truth. This criterion, then, either is without a judge's approval or has been approved. But if it is without approval, whence comes it that it is truthworthy? For no matter of dispute is to be trusted without judging. And, if it has been approved, that which approves it, in turn, either has been approved or has not been approved, and so on ad infinitum.
 - Sextus Empiricus, Against the Logicians
   translated by R.G. Bury

Sextus' concept of a "criterion of truth" became one of the central issues in epistemology, called the Problem of the Criterion. There are many proposed solutions to this problem, among them the Coherence, Correspondence, and Pragmatic theories. I propose another, which I think of as Consistency.

Briefly stated, if a proposition is consistent with everything else we think we know, forming a logical and integral worldview, then it is more likely to be true.

In my previous post on epistemology, I laid out some of the very basic concepts of Bayesian thinking. In Bayesian epistemology, a proposition becomes more likely the more evidence it has to support it. Each piece of evidence, in turn, has its own probability of being true based on the evidence that supports it, and so on. This creates an interdependent web of probabilities, in which related propositions can reinforce or refute each other.

Cromwell's Rule reminds us that we must always leave some room for doubt, and so all knowledge exists only in estimates of certainty, not absolutes. As a result, no network of interconnected, probabilistic knowledge will never converge completely. As Wittgenstein says in his book Philosophical Investigations, "Explanations come to an end somewhere." If we forfeit any possibility of achieving absolute metaphysical certainty, the question becomes simply where and when we decide to stop digging. At what point is our knowledge "good enough"?

In future posts, I hope to expand on this question as it applies to the Three Worlds. Each of the three ontological realities have branches of philosophy that seek to develop consistency within them. The philosophy of seeking consistency in the objective reality was called Physics by Aristotle, though we now refer to it more commonly as Science. Theories of Ethics pursue consistency in the subjective experience, and Politics deals with how we collectively determine our intersubjective truths.

In an upcoming ontology post about objectivity and objective reality, I plan to expand on the idea of the inaccessibility of objective truth. Not to argue that it doesn't exist, but to explore the consequences of our limited ability to comprehend it.

© 2020 Craig A. Butler
First Posted: 8th Sep 2020
Last Updated: 23rd Nov 2020