2.51 Mathematics

Category: Logic and Mathematics

Keywords: mathematics, arithmetic, numbers, mathematical, proofs, infinity, axioms, counting, infinitely, theorems, proved, prime, proof, hilbert, numerical

Number of Articles: 420
Percentage of Total: 1.3%
Rank: 23rd

Weighted Number of Articles: 333.3
Percentage of Total: 1%
Rank: 40th

Mean Publication Year: 1978.7
Weighted Mean Publication Year: 1974.9
Median Publication Year: 1982
Modal Publication Year: 1993

Topic with Most Overlap: Sets and Grue (0.0422)
Topic this Overlaps Most With: Sets and Grue (0.0335)
Topic with Least Overlap: Emotions (0.00019)
Topic this Overlaps Least With: Duties (0.00025)

A scatterplot showing which proportion of articles each year are in the mathematicstopic. 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 1883 when 2.8% of articles were in this topic. The lowest value is in 1885 when 0.0% of articles were in this topic. The full table that provides the data for this graph is available in Table A.51 in Appendix A.

Figure 2.121: Mathematics.

A set of twelve scatterplots showing the proportion of articles in each journal in each year that are in the Mathematicstopic. 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 - 1.4%. Proceedings of the Aristotelian Society - 0.9%. Ethics - 0.1%. Philosophical Review - 0.8%. Analysis - 1.1%. Philosophy and Public Affairs - 0.1%. Journal of Philosophy - 1.1%. Philosophy and Phenomenological Research - 0.4%. Philosophy of Science - 1.4%. Noûs - 1.4%. The Philosophical Quarterly - 0.8%. British Journal for the Philosophy of Science - 2.6%. The topic reaches its zenith in year 1883 when it makes up, on average across the journals, 2.8% of the articles. And it hits a minimum in year 1885 when it makes up, on average across the journals, 0.0% of the articles.

Figure 2.122: Mathematics articles in each journal.

Table 2.137: Characteristic articles of the mathematics topic.
Table 2.138: Highly cited articles in the mathematics topic.

Comments

When I did a new model run, one of the first things I checked was whether the model had found the philosophy of mathematics topic. And the quickest way to check for that was whether it had clearly put the two big Benacerraf papers in the same topic. Most models passed this test, but some of them did so less clearly than others. This model run just passes the test. Here are the probability distributions over the ninety topics for the two articles.12

Table 2.139: Table 2.140: Paul Benacerraf, “What Numbers Could Not Be.”
Subject Probability
Mathematics 0.3073
Ordinary language 0.2166
Sets and grue 0.1680
Meaning and use 0.0633
Denoting 0.0370
Personal identity 0.0226
Universals and particulars 0.0220
Verification 0.0208
Norms 0.0202

That makes sense—it is a philosophy of mathematics article, but it is largely about sets, and it can’t escape the fact that it’s written during the era of ordinary language philosophy. But the second table is a closer run thing.

Table 2.141: Table 2.142: Paul Benacerraf, “Mathematical Truth.”
Subject Probability
Mathematics 0.2001
Truth 0.1713
Ordinary language 0.1198
Norms 0.0744
Knowledge 0.0637
Radical translation 0.0587
Concepts 0.0539
Definitions 0.0465
Theories and realism 0.0347
Analytic/synthetic 0.0246
Verification 0.0245
Justification 0.0216
Propositions and implications 0.0207

Again, this sort of makes sense—the article is about truth. But the model is much less sure how to classify this article, as evidenced by the number of topics that get a probability between 4.6 percent and 7.4 percent.

What the model is working with is a conception of philosophy of mathematics that is centered around two debates. One is the nature of infinity, the other is the nature of proof. That’s not a terrible take on twentieth-century philosophy of mathematics, but it does mean that papers like “Mathematical Truth” get treated as less than fully paradigmatic.

I mostly look at how big a topic is by eyeballing the twelve journal graph. But in this case that would be highly misleading. Because this topic is spread across many journals, and many years, those twelve lines look like they barely have a pulse. But the tables show that, depending on size is measured, this is the twenty-third or fourtieth biggest topic. So many other topics are concentrated in a small number of journals or times, and they make a bigger visual impact than topics like this that keep chugging along.

  1. Remember that these tables are cropped at 2%; the model assigns probabilities to all 90 topics but I’m not showing them all here.↩︎