2.6 Definitions

Category: Logic and Mathematics

Keywords: definitions, symbol, symbols, definition, meanings, meaning, term, meaningful, symbolic, define, defined, meaningless, operations, implicit, usage

Number of Articles: 316
Percentage of Total: 1%
Rank: 44th

Weighted Number of Articles: 532.9
Percentage of Total: 1.7%
Rank: 9th

Mean Publication Year: 1950.1
Weighted Mean Publication Year: 1957
Median Publication Year: 1950
Modal Publication Year: 1934

Topic with Most Overlap: Meaning and Use (0.0442)
Topic this Overlaps Most With: Analytic/Synthetic (0.0437)
Topic with Least Overlap: Duties (0.00047)
Topic this Overlaps Least With: Population Ethics (0.00286)

A scatterplot showing which proportion of articles each year are in the definitionstopic. The x-axis shows the year, the y-axis measures the proportion of articles each year in this topic. There is one dot per year. The highest value is in 1934 when 5.2% of articles were in this topic. The lowest value is in 1884 when 0.3% of articles were in this topic. The full table that provides the data for this graph is available in Table A.6 in Appendix A.

Figure 2.23: Definitions.

A set of twelve scatterplots showing the proportion of articles in each journal in each year that are in the Definitionstopic. There is one scatterplot for each of the twelve journals that are the focus of this book. In each scatterplot, the x-axis is the year, and the y-axis is the proportion of articles in that year in that journal in this topic. Here are the average values for each of the twelve scatterplots - these tell you on average how much of the journal is dedicated to this topic. Mind - 1.8%. Proceedings of the Aristotelian Society - 1.4%. Ethics - 0.8%. Philosophical Review - 1.7%. Analysis - 2.5%. Philosophy and Public Affairs - 0.3%. Journal of Philosophy - 2.2%. Philosophy and Phenomenological Research - 1.8%. Philosophy of Science - 2.4%. Noûs - 1.1%. The Philosophical Quarterly - 1.2%. British Journal for the Philosophy of Science - 1.2%. The topic reaches its zenith in year 1934 when it makes up, on average across the journals, 5.4% of the articles. And it hits a minimum in year 1891 when it makes up, on average across the journals, 0.3% of the articles.

Figure 2.24: Definitions articles in each journal.

Table 2.17: Characteristic articles of the definitions topic.
Table 2.18: Highly cited articles in the definitions topic.


At first when I saw this topic come up, I assumed that it would be part of the influence of positivism. If positivism is going to work, a lot of terms need to be defined along with a theory of definitions. And the timeline, especially on the single graph, checks out for that explanation. But I’m not sure that’s all of what is going on. When looking through the notable articles that are clearly about definitions, such as the Dubs or Reid articles mentioned above, they don’t seem super positivist. They don’t seem openly hostile to positivism, but they don’t motivate the search for a theory of definitions with an account of their role in positivist philosophy.

That said, they also don’t come up with things that would pass muster by contemporary standards as theories. I’m going to quote Dubs’s conclusion at length because I can’t really summarize it otherwise:

The foregoing summarizes the important features of what I find necessary for definition. To recapitulate: definitions are of various types, depending upon what function they are to fulfil. Dictionary definitions attempt to explain a meaning to a person who is ignorant of it. The three requirements for such a definition are commensurateness, understandability, and usually) conceptuality. Scientific definitions attempt to enable the exact identification of cases of a term in experience or thought. There are two requirements: commensurateness and definition only in terms previously defined. Such definitions are conceptual or non-conceptual. Conceptual definitions, in any developed science, form an elaborate hierarchy, the creation of which is sometimes an extremely difficult task. Non-conceptual definitions may be causal definitions, denotative definitions, or semi-denotative definitions. In a few sciences, essential definitions have been achieved; most definitions are merely nominal. I hope that the foregoing account of definition fits the varied facts of scientific and logical usage and constitutes an intelligible and consistent account of definition. (577)

I mean, sure definitions are conceptual or nonconceptual; that doesn’t seem like a stunning conclusion. And more generally, what we get here feels more like a shopping list than a sharp account. But it’s still something, and Dubs does make some good points along the way about the mischief that philosophers can do with badly drawn definitions.

One other thing to note about this topic is that it is very American. The articles here are primarily by US authors in US journals. And for all my complaints about Dubs, there is a kind of professionalism to the American writers that isn’t always shared by their British contemporaries. I suspect this professionalism is not always admired by those who look to philosophy for deep insight. But there is a sense here, in a way that there isn’t in the earlier topics, that we’re getting early versions of philosophy as it is now done.

This topic is helpful for seeing the difference between the raw counts and the weighted count. The weighted count is much higher, as seen above. This is because every time someone introduces a definition in their paper (as such), the model gets a bit excited and thinks that it is a paper on definitions. It quickly figures out that this probably isn’t the case, but it can leave a residual probability. Those residuals add up, and eventually the topic is the ninth highest by weight out of the ninety. And that’s why even though there are very few papers in these journals that are in any sense on definitions since the 1980s, the graph doesn’t go to zero. All those times the model thinks it is 2 or 3 percent likely that a paper is about definitions add up, and the result is a graph like this one.