Karl Popper had an interesting relationship with “defining terms.” On the one hand, he felt quite strongly that it was wrong to do so:
I do not believe that exactness or precision are intellectual values in themselves; on the contrary we should never try to be more exact or precise than the problem before us requires (which is always a problem of discriminating between theories). For this reason I have stressed that I’m not interested in definitions; since all definitions must use undefined terms, it does not, as a rule, matter whether we use a term as a primitive term or a defined term.Objective Knowledge: An Evolutionary Approach p. 58
Yet he spent considerable time dwelling on certain definitions. He was, for example, famous for his attempts to precisely define science (the boundary problem) and verisimilitude.
Popper consistently renounced the importance of words. It purportedly led Popper to claim that a true Critical Rationalist is always ready to continue the conversation in the other party’s vocabulary. (Not that I was able to find such a quote.) And he had no problem allowing labels applied to him that were historically the opposite of his ideas:
Words do not matter, and I do not really mind if even a thoroughly misleading and mistaken label is applied to me.Myth of the Framework, p. 74-75
Popper goes on to accept that such labels as ‘positivist’ (Myth, p. 75) and ‘inductivist’ (Myth, p. 104) so long as you can recognize that when applied to him they mean something quite different than how they were historically used.
In this post, I’m going to attempt to summarize Popper’s view of what I call Word Essentialism (Popper preferred the term “Methodological Essentialism” but I find this less descriptive). Word Essentialism is the philosophical error of thinking words have definitive definitions and thus carefully defining your terms will lead to precision of thought.
Forms and Essences
The philosophical error of Word Essentialism is rooted in Plato’s Theory of Forms or Ideas.
Think of a triangle. You probably pictured three perfectly shaped lines that form a closed shape. Plato would argue that in reality, you have never encountered a true Triangle, but only approximations of the concept. Yet you have no problem picturing in your mind a perfect triangle, despite having no experience with one. This idea led Plato to imagine a realm of Forms or Ideas where ideas are “more real than all the ordinary things which are in flux [in physical reality], and which, in spite of their apparent solidity, are doomed to decay.” (Open Society 1, p. 25)
Plato believed that there could only be a single Form for any one concept. This (or so it seemed to Plato) followed logically from the fact that should you have, say, two Forms of the perfect ideal bed, then whatever similarities that existed between those two Forms must of necessity be a single separate Form that defines what a bed is.
If things are similar because of some virtue or property which they share, for instance, whiteness, or hardness, or goodness, then this virtue or property must be one and the same in all of them; otherwise it would not make them similar.The Open Society and Its Enemies Vol. 1, p. 28
This view led Plato to think that:
If all things are in continuous flux, then it is impossible to say anything definitive about them. We can have no real knowledge of them, but, at the best, vague and delusive ‘opinions’.The Open Society and Its Enemies Vol. 1, p. 28
Word Essentialism: The Platonic Ideal of Definitions
Plato’s Theory of Forms and Ideas solved, for Plato, this problem by allowing people to learn about the essence of the idea (which existed as a real thing in the realm of Platonic Ideas) rather than the imperfect, decaying, and influx approximations that existed in the real world, of which no truths could ever exist permanently. This led Plato and his followers to seek out Universal Definitions which Plato believed, if found, would determine the real nature of the Form or Idea. (Open Society 1, p. 29-30)
…a description of the essence of a thing they all called a ‘definition’” according to Plato.Open SocietyThe Open Society and Its Enemies Vol. 1, p. 31
Methodological Essentialism is the “theory that it is the aim of science to reveal essences and to describe them by means of definitions…” (Open Society 1, p. 32)
Under this understanding of science, the ultimate aim of science would be “compilation of an encyclopedia containing the intuitive definitions of all essences… their names together with their defining formula.” (OS2, p. 12)
For example, Essentialism claims that an important question might be “What is a puppy?” and that the correct answer is to exhaustively describe the essence of “puppiness” by answering something like “A puppy is a young dog.” Though to make it exhaustive, this might require us to go on to describe exactly what defines a dog. (Open Society 2, p. 10,13-14)
By comparison, Popper advocates for Methodological Nominalism (which I shall call “Word Nominalism”) which sees the aim of science as merely “describing how a thing behaves in various circumstances, and… whether there are any regularities in its behavior.” (Open Society 1, p. 32)
So to Popper questions like “What is energy?” or “What is an atom?” were pretentious and unnecessary for science while questions like “How can the energy of the sun be made useful?” was the real aim of science. (Open Society 1, p. 32)
This view lead us to a different role for definitions in science. Modern science thinks the important question is “What shall we call a young dog?” and the correct answer is “For the sake of brevity, let’s call a young dog a puppy so that we don’t have to keep saying ‘young dog’.” (OS2, p. 10,13-14)
Can Language Be Made More Precise Via Definitions?
Methodological Essentialism leads to the false belief that “language can be made more precise by the use of definitions.” (Open Society 2, p. 17)
Popper gives an example of why this can never work by (in true Popperian style) starting with the assumption that it can work. He then follows the idea to its logical conclusions.
Imagine politicians debating such ideas as ‘democracy’, ‘liberty’, ‘duty’, and ‘religion.’ Then imagine we require all politicians in the debate to define how they understand those terms so that they can’t use rhetoric to fool us.
Imagine one politician that defines ‘democracy’ as ‘the rule of the general will’ or ‘the rule of the spirit of the people.’ The politician has complied with the requirement to define his terms about as well as we might realistically expect, yet now we aren’t really any better off because we need to know what he means by ‘rule’, ‘people’, ‘will’, and ‘spirit.’ (Open Society 2, p. 18) Yet people would be naturally hesitant to ask for these definitions because it’s obvious that to do so will just lead to an infinite regress. (i, p. 17-18) So defining one’s terms upfront doesn’t seem to solve the very problem that we want it to.
How Word Nominalism Solves the Problem
Can Methodological Nominalism solve this infinite regress? Popper says it can. And it does so by simply not taking any of its words too seriously and dealing with the inherent vagueness of words only when necessary.
For the nominalist position there is no difficulty which corresponds to the infinite regression [of Methodological Essentialism]. As we have seen, science does not use definitions in order to determine the meaning of its terms, but only in order to introduce handy shorthand labels. And it does not depend on definitions; all definitions can be omitted without loss to the information imparted. It follows from this that in science, all the terms that we really needed must be undefined terms. (Emphasis in original.)The Open Society and Its Enemies Vol. 2, p. 18
Popper entirely rejects the need to make precise the meanings of our terms:
…philosophy, which for the twenty centuries has worried about the meaning of its terms, is not only full of verbalism but also appallingly vague and ambiguous, while a science like physics which worries hardly at all about terms and their meaning, but about facts instead, has achieved great precision. This, surely should be taken as indicating that, under Aristotelian influence, the importance of the meaning of terms has been grossly exaggerated. But I think that it indicates even more. For not only does this concentration on the problem of meaning fail to establish precision; it is itself the main source of vagueness, ambiguity, and confusion.The Open Society and Its Enemies Vol. 2, p. 19
In science, we take care that the statements we make should never depend upon the meaning of our terms. Even when the terms are defined, we never try to derive any information from the definition, or to base any argument upon it. This is why our terms make so little trouble. We do not overburden them. We try to attach to them as little weight as possible. We do not take their ‘meaning’ too seriously. We are always conscious that our terms are a little vague (since we have learned to use them only in practical applications) and we reach precision not by reducing their penumbra of vagueness, but rather by keeping well within it, by carefully phrasing our sentences in such a way that the possible shades of meaning of our terms do not matter. This is how we avoid quarreling about words.The Open Society and Its Enemies Vol. 2, p. 19
Popper goes on to give examples of how science might use terms like ‘wind’ or ‘sand-dune’ which are quite vague but then gets scientific precision by saying something like ‘dunes between 4 and 30 feet high’ or ‘window of a velocity of between 20 and 40 miles an hour’. (Open Society 2, p. 19)
Why Lack of Precision Can’t Be Resolved Via Defining Things Better
Popper admits that lack of precision in terms may lead to trouble. He gives the example of what ‘simultaneity’ means in physics and how Einstein had to reform the word’s meaning before a correct physics theory was possible. But that problem could hardly have been solved by physicists more carefully defining what they meant by ‘simultaneity’ upfront. (Open Society 2, p. 20)
Why Defining Terms Reduces Understanding
Popper goes on to claim that philosophy’s deep-rooted belief in Methodological Essentialism was precisely what led to philosophies like scholasticism and mysticism (and I’m tempted to add ‘postmodernism’) which ‘despair in reason.’ (Open Society 2, p. 21) This is because “…a quarrel about the question whether the definition was correct, or true, can only lead to an empty controversy about words.” (Open Society 2, p. 18)
Did Popper Successfully Define His Terms with Precison?
So why did Popper spend so much time ‘defining his terms’ in the cases of ‘Science’ and ‘Verisimilitude’?
In the case of ‘science,’ Popper was reacting to the claims of Karl Marx that Communism was ‘Science.’ He could see that Communism was ‘unfalsifiable’ and was attempting to work out how that made it effectively ‘not a science.’ And in the case of ‘Verisimilitude’, he explains that the common sense understanding of ‘nearness to the truth’ has become suspect and he wished to introduce a formalization of the concept to show it was still a legitimate concept. (Objective Knowledge, p. 59-60)
How successful was Popper in his aims? It seems to me that the results were mixed at best. His rehabilitation of the common sense understanding of ‘nearness to truth’ seems to have few criticisms. But today the notion of the boundary of science being ‘falsifiability’ seems to me to have been largely misunderstood.
Yet I feel that Popper had the right idea here. The goal is not precision in language, but precision in concepts necessary to explain your theory. “Falsification” and, to an extent “Refutation,” conjure up images in people’s minds that don’t really match what Popper was trying to get at. They imagine a single standalone theory being refuted by a single false observation – an idea contradicted by the Duhem-Quine thesis. (See Logic of Experimental Tests by David Deutsch for discussion.)
Deutsch improved on Popper’s language here by introducing the concept of good explanations being ‘hard-to-vary’ rather than ‘falsifiable.’ The real problem with Communism as a theory wasn’t that it wasn’t science because it wasn’t ‘falsifiable’ but that Communists had no problem constantly re-imagining Communism to match any imaginable observation.
Popper never made the mistake of insisting that his was the sole and only definition of ‘science’ and that anyone that was using the word otherwise was simply mistaken. Unfortunately, many that try to use Popper’s criterion for science today make just that mistake. 
But you can’t really claim Popper was wholly unsuccessful either, given that many do read him and come away with a correct understanding of his theory of knowledge and its relevance to science.
Popper used definitions not as way to define words, but as a way to refine his own theories. Where he could, he introduced new terms as shorthand for his concepts. In other cases, such as ‘verisimilitude’ his explicit goal was to rehabilitate the common sense understanding of the concept, so introducing new terms wouldn’t have made sense for his purposes. Thus he reused an existing term and risked some level of later misunderstanding inherent in reusing lay terms in a more formal setting.
Deutsch and Definitions
I wonder what Popper would think of David Deutsch’s books where he actually puts together a glossary of terms for each chapter, often taking common words and narrowing the penumbra of the word for his purposes.
For example, Deutsch defines “Creativity” as “The capacity to create new explanations.” (Beginning of Infinity, p. 30) This is very useful if taken in the Popperian light of Deutsch choosing to use the word ‘creativity’ as a shorthand for a more narrow concept he wishes to introduce (in this case, the unique ability humans have to create explanatory knowledge.) But choosing to narrowly redefine a common term like this has led to some confusion when fans of Deutsch’s books mistakenly think that the word ‘creativity’ can only refer to this definition and all others are wrong.
The word ‘creativity’ pre-exists Deutsch by many centuries and has never been used to solely refer to ‘the capacity to create new explanations.’ Much of what we consider ‘creativity’ today – such as art and music – is actually largely inexplicit knowledge that has yet to be put into explanations. This also leads to problems when fans of Deutsch want to refer to creativity as requiring explanatory knowledge and then become confused when they realize evolution is quite ‘creative’ but has no explanatory knowledge. (See the discussion of such an incident here.) 
And yet, I doubt Popper would have felt Deutsch made a mistake by including a glossary of terms. If you want to refer to the concept of the capacity to create explanations, there is no existing English word for that concept and ‘creativity’ strikes as close as possible to being a great shorthand for it. Making up an entirely new word won’t always do the trick. (Creativization? Creativination? It just doesn’t roll off the tongue well…) The mistake was only to assume the word has no other uses in real life.
Words Are Theory-Laden
An interesting twist on all this is the realization that words are themselves theory-laden, though sometimes inexplicitly so.
Think about the word “intelligence” as in “Artificial Intelligence.” The word “intelligence” had been in use for centuries and yet no one really knew what it meant precisely. But that didn’t stop us from using the term correctly despite its vagueness. In fact, if you had to specify with precision what “intelligence” was before you made a word for it, you’d still not have the word and your language would be deficient. Natural language is rich and useful because it’s vague, not despite it.
But we all have an inexplicit, though vague, concept of what ‘intelligence’ is. Moreover, we usually recognize it when we see it. The word “intelligence” refers to situations where we recognize it.
It is interesting to note that when the field of “Artificial Intelligence” began the researchers attempted to more precisely define what “intelligence” was so that they could start a research program around it. The intuitive but inexplicit notion of “intelligence” wasn’t formal enough to work with.
The main ‘definition’ they settled upon was that to be “intelligent” was to “act rationally.” Seeing that Economics already had a working definition of “rational,” they adopted the view that “intelligence” is to take “the best possible action in a situation.” (Artificial Intelligence: A Modern Approach, p. 30) In other words, to optimize to your goals.
This isn’t necessarily a bad definition of “intelligence” in that it captures some of the inexplicit ways we use the word “intelligence” quite nicely. To make an “intelligent decision” does mean something like making the best possible (or close to the best possible) one in a situation.
But I conjecture that this view of ‘intelligence’ is one of the main reasons why Artificial Intelligence was developed solely towards narrow AI rather than Strong AI (aka AGI). The way they chose to define “intelligence” mattered to what they researched. When we finally understand what AGI really is, we’ll look back with some humor at the narrow way AI research tried to define it as solely ‘optimizing goals.’
Science has no choice but to start with the sometimes vague and inexplicit concepts contained in natural language. It does not proceed by carefully defining words, but by carefully defining concepts – and often creating entirely new words to attach to those concepts as a handy shorthand. This is a subtle but important difference. There is a need to precisely figure out how humans creatively create new explanations, not to carefully define the word “intelligence” which often really does just refer to optimizing one’s goals.
 On the confusion caused by trying to narrow the penumbra of the word “creative” to be specifically the creation of explanatory knowledge created by Universal Explainers: After I wrote this article, but before it was published, someone in the 4S email group brought to my attention this interview with Deutsch. It’s interesting that Deutsch here claims that “artificial evolution” has no “real creativity.” The implication seems to be that “biological evolution” therefore does. Later on, he explicitly states, “We now know that science is conjectural and creative, as creative as any human activity. The same is true with evolution.” But if “creativity” is really “the capacity to create new explanations” then biological evolution has no creativity because biological evolution doesn’t evolve explanations.
It’s always tempting to reduce the “penumbra of a word’s vagueness” to try to make yourself more precise. Sometimes this is even helpful. But most likely even you won’t stick with your own more precise definition later.
 Popper never made the mistake of insisting that his was the sole and only definition of ‘science’
Here is an example:
This criterion of demarcation between empirical and non-empirical theories I have also called the criterion of falsifiability or the criterion of refutability. It does not imply that irrefutable theories are false. Nor does it imply that they are meaningless. But it does imply that, as long as we cannot describe what a possible refutation of a certain theory would be like, that theory may be regarded as laying outside the field of empirical science. (The Myth of the Framework, p. 88)
In other words, Popper actually only claimed that falsification was the boundary between ’empirical science’ and non-empirical ideas. However, see this post for discussion about how even this has been challenged.