By way of example, consider the moons of Jupiter. I can testify that last time I checked, Jupiter had moons. The vast preponderance of the evidence suggests that the major moons have been there for millions of years. All the available evidence indicates that in 1610, at the time Galileo first said Jupiter had moons, it did in fact have moons.
In this sense, we can define a notion of truth. This is meant to be an objective (not subjective) notion of truth. To me, the term “fact” is more-or-less synonymous with “truth”.
We must evaluate separately the truth of each proposition, such as the narrow question of whether Jupiter has moons. In contrast, we do not pretend to know the whole truth about a complex situation.
Now let us consider how knowledge differs from truth:
This example shows that knowledge can change with time, and can be very unevenly distributed. By way of contrast, note that the truth didn’t change in 1610; only the knowledge changed.
The notion of an ideal truth, of which our knowledge is only an imperfect shadow, is not exactly new. See e.g. reference 1.
Knowledge can be formulated in various ways, some better and some worse. For example,
Statement 3 is not true. There are numerous additional moons, too small to be seen using telescopes of the sort available in 1610.
Let us consider item 4. It is simultaneously less precise and more reliable (compared to item 3), because it doesn’t stick its neck out quite so far. It does not attempt to capture the complete truth, and thereby avoids complete falsity. Statement 3 is very precise, but false. Statement 4 is an inequality, not an equality, so it is more vague. Although vagueness is something of a disadvantage, it is preferable to falsity.
Alas, statement 5 is not quite true, either. If you look just once, there are several things that could go wrong. First of all, you won’t be sure at first glance what’s a moon and what’s a background star; they just look like bright dots. What’s worse, there is a very real possibility that less than four moons will be visible. Sometimes one or more moons will be hiding behind the planet, or in its shadow. You can solve these problems by making repeated observations over a period of hours or days. You will see that the moons move (quite unlike stars) and soon you will see four of them.
Science is useful because it makes predictions. (For more about scientific methods, see reference 2.) We see from this example that our knowledge and our predictions depend partly on observations, and partly on theory. To understand the moons of Jupiter, we invoke a great number of theoretical ideas, such as:
There is an interesting contrast: Truth is something to be discovered. Knowledge is not so much discovered as invented.
That is, much scientific activity revolves around cobbling up models that capture some aspects of the truth with some degree of fidelity. Often this involves a process of successive refinement, such as:
Science is mostly about knowledge. Models are part of our knowledge. Sometimes a model represents the observations only imperfectly. Moreover, even if a model represents all the presently-available observations perfectly, we cannot assume it represents the truth. At some point in the future, hitherto-unobserved data may dramatically change our knowledge.
Galileo had trouble persuading “The Powers That Be” to believe that Jupiter had moons. They didn’t want Jupiter to have moons, and some people have a powerful ability to not see what they don’t want to see.
Here belief denotes more-or-less the same thing as knowledge, but by connotation it calls attention to the fact that people are often willing to believe things that cannot possibly be true.
Sometimes people believe the truth, but all-too-often they believe things that cannot possibly be true. According to some measures, more people in the US believe in astrology than believe in evolution (reference 4). Wacky beliefs are reflected in people’s actions, not just in what they say they believe. In the US, people spend ∼10 billion dollars per year on homeopathic medicines, magnetic “therapy” bracelets, and similarly wacky forms of “alternative” medicine.
In some simple cases, knowledge is sufficiently well established that it can pass for absolute truth (in some narrow domain). As I like to say, we don’t know everything there is to know about the moon, and we don’t know everything there is to know about green cheese, but we know enough to be quite sure that the moon is not made of green cheese. A similar thought is expressed by the saying that you should keep an open mind, but not so open that your brain falls out.
Generally, though, issues are more complex (as discussed in section 4), and those who claim to possess infallible inerrant “truth” are cranks, unaware of their own limitations, monumentally immodest and arrogant.
It is particularly comical to observe how different cranks hold wildly incompatible incompatible beliefs. They each claim to possess infallible inerrant “truth”, but really they have no idea what truth is. This phenomenon is well portrayed in the story about the holy war between the Little-Endians and the Big-Endians (reference 5).
As Daniel Patrick Moynihan was fond of saying: “Everybody is entitled to their own opinion, but they’re not entitled to their own facts”.
As mentioned above in connection with green cheese, knowledge is in some cases sufficiently well established to pass for absolute truth.
More commonly, though, knowledge is inexact. Knowledge does not need to be exact to be useful. For example, we are told that the radius of the earth is approximately 4000 miles. That value is not exact, but it is close enough for a range of practical purposes. Indeed we know that the earth is not exactly spherical, so that any question about “the” radius is unanswerable, in principle, if you want to get picky about it. But nevertheless we can construct a spherical model of the earth. A spherical model is only approximately faithful, but it is good enough to be useful for a wide range of practical purposes.
In some cases where the spherical model is not good enough, ellipsoidal models can be used. Continuing down this road, we can construct a long sequence of progressively more complicated, progressively more faithful models.
This allows us to address some age-old questions: Is truth discovered, or invented? Is knowledge discovered, or invented?
As for truth, some philosophers speak of real, absolute, ideal truths that are not invented but may eventually be discovered. In contrast, as for knowledge, the vast bulk of our knowledge is in the form of models that are clearly invented.
In any case, I don’t think this distinction tells us anything about truth that we didn’t already know. It is easy – too easy – to say that the truth remains unchanged while we adapt our models to fit the truth ... but on a day-to-day basis we don’t know where the boundary is between what’s changeable and what’s not. For example, before 1908 almost everybody was sure that we lived in a three-dimensional space, and that three was obviously and unchangeably the true answer. Then one fine day Minkowski made a pretty convincing case for four dimensions. What was previously considered exact suddenly became an approximation.
Do not confuse the model with the truth. The model may be more or less faithful to the truth, but (except maybe in very special cases) it will never be the truth.
The truth, as the word is used here, is absolute and ideal. Jupiter has moons, and has had moons for millions of years, quite independent of whether Galileo or anybody else knew the truth.
However, truths are more useful when somebody knows them, so it is important to create and disseminate knowledge.
It would be silly to discuss what “Society” believes. Society is very inhomogeneous and knowledge is very unevenly distributed. Here’s one important example among many: In 1944, the truth was that codebreakers in Bletchley Park were reading a great deal of the Nazis’ high-level encrypted communications. A few people knew this, but “society” in general didn’t know this – not in England, Germany, or anywhere else.