2.7 Propositions and Implications

Category: Logic and Mathematics

Keywords: propositions, proposition, entailment, implication, contradictory, entails, negation, entail, disjunction, denial, propositional, negative, contradiction, conjunction, implies

Number of Articles: 480
Percentage of Total: 1.5%
Rank: 13th

Weighted Number of Articles: 480.8
Percentage of Total: 1.5%
Rank: 13th

Mean Publication Year: 1952
Weighted Mean Publication Year: 1960.8
Median Publication Year: 1955
Modal Publication Year: 1969

Topic with Most Overlap: Deduction (0.0551)
Topic this Overlaps Most With: Deduction (0.0429)
Topic with Least Overlap: Evolutionary Biology (0.00023)
Topic this Overlaps Least With: Evolutionary Biology (0.00071)

A scatterplot showing which proportion of articles each year are in the propositions and implicationstopic. 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 1905 when 5.6% of articles were in this topic. The lowest value is in 1886 when 0.0% of articles were in this topic. The full table that provides the data for this graph is available in Table A.7 in Appendix A.

Figure 2.25: Propositions and implications.

A set of twelve scatterplots showing the proportion of articles in each journal in each year that are in the Propositions and Implicationstopic. 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 - 2.8%. Proceedings of the Aristotelian Society - 1.5%. Ethics - 0.2%. Philosophical Review - 1.4%. Analysis - 3.4%. Philosophy and Public Affairs - 0.1%. Journal of Philosophy - 1.1%. Philosophy and Phenomenological Research - 1.2%. Philosophy of Science - 0.9%. Noûs - 1.7%. The Philosophical Quarterly - 1.4%. British Journal for the Philosophy of Science - 0.5%. The topic reaches its zenith in year 1933 when it makes up, on average across the journals, 7.4% of the articles. And it hits a minimum in year 1886 when it makes up, on average across the journals, 0.0% of the articles.

Figure 2.26: Propositions and implications articles in each journal.

Table 2.19: Characteristic articles of the propositions and implications topic.
Table 2.20: Highly cited articles in the propositions and implications topic.


Note that the scale in the second graph is thrown off by the very high numbers from the early years of Analysis. This is, as seen at the top of the page, one of the larger topics in the study, despite the graphs looking quite low.

This overlaps a lot with deduction. Indeed, it is possibly best to simply regard them as part of the same topic. Fortunately, to do that one doesn’t have to do much more than change the scales on the graphs, because their distribution over time, and over journals, is pretty similar.

This topic gets implication rather than validity, which is moved to deduction. Therefore, the logical works in it are a touch earlier. But it also gets proposition, so it picks up a bit more weight from more contemporary work on propositions. Here, for instance, is the table for Jeff King’s paper “Designating Propositions.”

Table 2.21: Jeffrey C. King, “Designating Propositions.”
Subject Probability
Sense and reference 0.4068
Propositions and implications 0.1335
Ordinary language 0.0935
Mathematics 0.0542
Deduction 0.0466
Belief ascriptions 0.0430
Sets and grue 0.0365
Truth 0.0307
Norms 0.0270
Composition and constitution 0.0233
Explanation 0.0203

It mostly goes with sense and reference. That topic, despite its Fregean name, appears much later in our story. But note that the model can’t quite shake the idea that it should be placed in this topic. It’s this kind of assessment that keeps the graphs for this topic from really collapsing.