Logic in analytic philosophy: a quantitative analysis

Abstract

Using quantitative methods, we investigate the role of logic in analytic philosophy from 1941 to 2010. In particular, a corpus of five journals publishing analytic philosophy is assessed and evaluated against three main criteria: the presence of logic, its role and level of technical sophistication. The analysis reveals that (1) logic is not present at all in nearly three-quarters of the corpus, (2) the instrumental role of logic prevails over the non-instrumental ones, and (3) the level of technical sophistication increases in time, although it remains relatively low. These results are used to challenge the view, widespread among analytic philosophers and labeled here “prevailing view”, that logic is a widely used and highly sophisticated method to analyze philosophical problems.

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Notes

  1. 1.

    By “early,” “middle” and “late” we mean the origins of analytic philosophy, the period from the mid-30s to the mid-70s, and the last forty years, respectively. The expression “late analytic philosophy” was introduced in Weatherson (2014) and analyzed in Bonino and Tripodi (2018).

  2. 2.

    The interview was given in 1994 and was first published in Edmister and O’Shea (1994).

  3. 3.

    For a comprehensive survey of logical methods in philosophy, see Pettigrew and Horsten (2011).

  4. 4.

    This was the title of a series of conferences organized at the University of Turin since January 2017: see https://dr2blog.hcommons.org.

  5. 5.

    Notice that by ‘representative’ we do not mean that each and every article in the corpus is an analytic philosophy article, but only that the corpus consists mainly, though not exclusively of articles in analytic philosophy.

  6. 6.

    In a recent interview Moretti clarifies: “The term ‘digital humanities’ means nothing. Computational criticism has more meaning, but now we all use the term ‘digital humanities’—me included. I would say that DH occupies about 50 percent of my work” (Moretti 2016).

  7. 7.

    This kind of distant reading is applied, for example, in Moretti (2009) to literary corpora and in Bonino and Tripodi (2019) to philosophical corpora.

  8. 8.

    Arguably, also Petrovich (2018) belongs to this line of research.

  9. 9.

    For the original quotation see Wittgenstein (1953).

  10. 10.

    Available at https://philindex.org.

  11. 11.

    Notice, however, that the 4284 articles contain some duplicates, that is articles shared by the purposive sample (2553) and the dataset drawn from the Philosopher’s Index (1622). Thus, we cannot say that we read exactly 4284.

  12. 12.

    The analysis revealed that the Philosopher’s Index classification is actually biased in that, for instance, it tends to exclude articles in which logic plays only an instrumental role.

  13. 13.

    All this means that, with the exception of the total number of articles, all the results concerning the subdivisions of articles in groups such as logic, instrumental, logical sophistication, and so forth are estimated values, obtained in the following way: \(n = a + 5b\), where n is the estimated value for group X, a is the number of articles belonging to X in the Philosopher’s Index dataset, and b is the number of articles belonging to X recognized in the purposive sample but not present in the Philosopher’s Index dataset. Obviously, b is multiplied by 5 because the sample amounts to the 20% of the entire corpus.

  14. 14.

    The second clause of M3 is based on the consideration that the qualification “highly sophisticated” must be assessed relative to the overall development of logic as a discipline: since logic arguably becomes more sophisticated over time, the level of sophistication required in order to be considered high should also raise over time. Therefore, if analytic philosophy is to be regarded as highly sophisticated from a logical perspective, one should expect that the level of sophistication of the logic that is present in analytic philosophy also increases over time.

  15. 15.

    In very few cases, when we did not reach a clear and shared conclusion, we left the decision open. For example, if we were hesitant as to whether consider a given paper belonged to the philosophy of language or the philosophy of logic, we assigned the value 0.5 to each of the alternatives, rather than the value 1 to one of them.

  16. 16.

    The interested reader is referred to http://openlogicproject.org/.

  17. 17.

    One may wonder why \(\mathsf {FOL}\) and \(\mathsf {NCL}\) are treated as equally sophisticated to begin with. The main reason is that none presupposes the other—although both presuppose \(\mathsf {PL}\). One can, for instance, approach the study of first-order logic without knowing anything about modal (propositional) logic; viceversa, one can study modal (propositional) logic independently from first-order logic.

  18. 18.

    To be sure, it would have been possible to evaluate the fulfillment of M1 by making reference to the purposive sample alone. Yet we chose to make the calculations on the basis of the combinations of the two datasets (i.e. purposive sample and Philosopher’s Index dataset) in order to preserve as much uniformity as possible in our data. Luckily enough, the difference between the two calculations is just 0.98%, which—by the way—seems to confirm that the 20% purposive sample is statistically rather reliable.

  19. 19.

    Notice that Archive for Mathematical Logic and Mathematical Logic Quarterly are successors of Archiv für mathematische Logik und Grundlagenforschung and Zeitschrift für mathematische Logik und Grundlagen der Mathematik, respectively, and were published since the 1950s. The articles, however, were mainly in German.

  20. 20.

    Conditions (1), (2) and (3) above, which provide a more through explanation of the idea of instrumentality expressed in M2, must not be confused with the annotation rules. In fact, they would not be operational enough. We are confident that our annotation rules are able to select a class of articles that is approximately equivalent to the class which would be ideally selected by (1), (2) and (3).

  21. 21.

    This example allows us to clarify a subtle point concerning our distant reading methodology. One could argue that von Wright conceived of (deontic) logic as an instrument of philosophy, an instrument that provides a Carnapian explication of (deontic) concepts. One could try to defend this claim, for example, by pointing out that although von Wright became a pupil of Wittgenstein, he never ceased to be heavily influenced by the Carnapian ideas he received as a young man in Finland by his former teacher, Eino Kaila (von Wright 1989). In the present article we chose to focus mainly on the paper under consideration, without necessarily considering any further, external information (however interesting and correct it may be). Rather, we closely adhered to the annotation rules. Therefore, von Wright’s article has been attributed to the logic proper category.

  22. 22.

    Things are somewhat different in Britain, but we will not be concerned with these subtler differences here.

  23. 23.

    One may think that the idea of taking the decrease of the lowest level of logical sophistication as an evidence of the emergence of analytic philosophy presupposes the prevailing view. In particular, it presupposes M3. And since we use the decrease of level \(\mathsf {0}\) to assess the prevailing view, one may object that there is a circularity in our analysis. To address this issue it should be noted that behind the idea that a decrease of level \(\mathsf {0}\) can explain the emergence of analytic philosophy there is the assumption, largely independent of the prevailing view, that the logic of Dewey, Bradley or Hegel is not the kind of logic that analytic philosophers are normally interested in; most of them would not even count this as logic. If so, when we find an article discussing the logic of Dewey, Bradley or Hegel, it is reasonable to assume that in most cases its author is not an analytic philosopher. Now, the assumption that analytic philosophers are not interested in non-mathematical logic is perhaps implied by the prevailing view, but it certainly does not imply it. Therefore, our analysis does not presupposes the prevailing view for the simple reason that the prevailing view is a view about the role of logic in analytic philosophy and the articles at level \(\mathsf {0}\) that disappeared were not arguably written by analytic philosophers.

  24. 24.

    A full-text search on JSTOR reveals that “Dewey” occurs in 305 articles published in The Journal of Philosophy from 1941 to 1960, and in 140 articles from 1961 to 2010, whereas in The Philosophical Review it has 89 occurrences in the former period and only 9 occurrences in the latter period. Notice that for The Journal of Philosophy 305 occurrences of “Dewey” in the period 1941–1960 is a significant result, compared to the occurrences of “Russell” (199), “Whitehead” (155), “Carnap” (95) and “Wittgenstein” (66).

  25. 25.

    See also Katzav (2018).

  26. 26.

    One of the obstacles to a straightforward answer to this question is that “a little” is a relative notion. One could devise methods to establish some standards, considering for example the presence of logic in a corpus of French or German journals. Should these additional data reveal that logic is present in, say, 10% of the corpus, it would be fair to conclude that the prevailing view is, in a certain sense, confirmed. Unfortunately, at the moment we are not able to give even a rough estimation of how much logic is present in other corpora and we leave this task to future work.

  27. 27.

    There are, of course, differences among the founding fathers. It is worth noting, incidentally, that Russell (in a more elementary way) and Carnap (in a more sophisticated way) had somewhat innovative positions, since they anticipated the view of mathematical logic as a fundamental instrument for philosophy. The case of Carnap is particularly interesting: in the 1950s, he used logic as an instrument in his confirmation theory (Carnap 1950) and he also provided an attempt to axiomatize biology for philosophical purposes (Carnap 1954), based on the work previously done by Joseph Henry Woodger (Woodger (1937), which in turn had been deeply influenced by Carnap and Tarski’s writings). Carnap famously called such an instrumental role of logic “explication”.

  28. 28.

    Interestingly enough, a logician such as von Wright, who belonged to a different generation, would have on the contrary been surprised by this data, since he had conjectured a different trend: “I shall not predict—he wrote—what will be the leading trends in the philosophy of the first century of the 2000s. But I think that they will be markedly different from what they have been in this century, and that logic will not be one of them. If I am right, the twentieth century will even clearer than now stand out as another Golden Age of Logic in the history of those protean forms of human spirituality we call Philosophy” (von Wright 1993b, p. 23).

  29. 29.

    However, Williamson might consider the rise of quantified modal logic a confirmation of his point of view, rather than an alternative account. According to him, the development of modal logic as metaphysics is one of the most distinctive features of scientific and professional analytic philosophy in the recent years (Williamson 2007, 2013).

  30. 30.

    Here are the results with respect to the entire corpus, namely, \(\mathsf {LOG}\) plus non-logical articles (level \(\mathsf {2}\): 1.90% in the 1940s; 3.31% in the 1950s; 4.41% in the 1960s; 6.43 % in the 1970s; 4.23% in the 1980s; 3.85% in the 1990s; 3.26% in the 2000s. Level \(\mathsf {3}\): 1.14% in the 1940s; 3.36% in the 1950s; 5.48% in the 1960s; 7.94% in the 1970s; 5.61% in the 1980s; 4.85% in the 1990s; 5.53% in the 2000s).

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Appendix

Appendix

The level of sophistication of \(\mathsf {Other}\)

\(\mathsf {Other}\) at level \(\mathsf {0}\) and \(\mathsf {1}\)

  \(\mathsf {Other} \, \mathsf {0}\) \(\mathsf {Other} \, \mathsf {0} / \mathsf {Other} \; (\%)\) \(\mathsf {Other} \, \mathsf {1}\) \(\mathsf {Other} \, \mathsf {1} / \mathsf {Other} \; (\%)\)
1941–1950 24 40.34 29.5 49.58
1951–1960 47 58.75 28 35
1961–1970 12 14.72 54 66.26
1971–1980 8 16.67 26 54.16
1981–1990 2 5.88 25 73.53
1991–2000 2 8 22 88
2001–2010 2 13.33 10 66.67
1941–2010 97 28.28 194.5 56.70

\(\mathsf {Other}\) at level \(\mathsf {2}\) and \(\mathsf {3}\).

  \(\mathsf {Other} \, \mathsf {2}\) \(\mathsf {Other} \, \mathsf {2} / \mathsf {Other} \; (\%)\) \(\mathsf {Other} \, \mathsf {3}\) \(\mathsf {Other} \, \mathsf {3} / \mathsf {Other} \; (\%)\)
1941–1950 3 5.04 3 5.04
1951–1960 5 6.25 0 0
1961–1970 8 9.82 7 8.59
1971–1980 8 16.67 6 12.50
1981–1990 4 11.77 3 8.82
1991–2000 0 0 1 4
2001–2010 2 13.33 0 0
1941–2010 30 8.75 20 5.83

\(\mathsf {Other}\) at level \(\mathsf {4}\).

  \(\mathsf {Other} \, \mathsf {4}\) \(\mathsf {Other} \, \mathsf {4} / \mathsf {Other} \; (\%)\)
1941–1950 0 0
1951–1960 0 0
1961–1970 0.5 0.61
1971–1980 0 0
1981–1990 0 0
1991–2000 0 0
2001–2010 1 6.67
1941–2010 1.5 0.44

The level of sophistication of \(\mathsf {Discipl}\)

\(\mathsf {Discipl}\) at level \(\mathsf {0}\) and \(\mathsf {1}\).

  \(\mathsf {Discipl} \, \mathsf {0}\) \(\mathsf {Discipl} \, \mathsf {0} / \mathsf {Discipl} \; (\%)\) \(\mathsf {Discipl} \, \mathsf {1}\) \(\mathsf {Discipl} \, \mathsf {1} / \mathsf {Discipl} \; (\%)\)
1941–1950 17 14.05 74 61.16
1951–1960 22 9.54 110 47.72
1961–1970 15 5.65 123 46.33
1971–1980 10 4.43 69 30.53
1981–1990 6 4.33 42 30.32
1991–2000 0 0 42 34.85
2001–2010 3 2.31 40 30.77
1941–2010 73 5.93 500 40.58

\(\mathsf {Discipl}\) at level \(\mathsf {2}\) and \(\mathsf {3}\).

  \(\mathsf {Discipl} \, \mathsf {2}\) \(\mathsf {Discipl} \, \mathsf {2} / \mathsf {Discipl} \; (\%)\) \(\mathsf {Discipl} \, \mathsf {3}\) \(\mathsf {Discipl} \, \mathsf {3} / \mathsf {Discipl} \; (\%)\)
1941–1950 21 17.35 9 7.44
1951–1960 44 19.09 50.5 21.91
1961–1970 50 18.83 70.5 26.55
1971–1980 56 24.78 82 36.28
1981–1990 33 23.83 38.5 27.80
1991–2000 36 29.88 38.5 31.95
2001–2010 25.5 19.61 32 24.62
1941–2010 265.5 21.55 321 26.06

\(\mathsf {Discipl}\) at level \(\mathsf {4}\).

  \(\mathsf {Discipl} \, \mathsf {4}\) \(\mathsf {Discipl} \, \mathsf {4} / \mathsf {Discipl} \; (\%)\)
1941–1950 0 0
1951–1960 4 1.74
1961–1970 7 2.64
1971–1980 9 3.98
1981–1990 19 13.72
1991–2000 4 3.32
2001–2010 29.5 22.69
1941–2010 72.5 5.88

The level of sophistication of \(\mathsf {Instr}\)

\(\mathsf {Instr}\) at level \(\mathsf {0}\) and \(\mathsf {1}\).

  \(\mathsf {Instr} \, \mathsf {0}\) \(\mathsf {Instr} \, \mathsf {0} / \mathsf {Instr} \; (\%)\) \(\mathsf {Instr} \, \mathsf {1}\) \(\mathsf {Instr} \, \mathsf {1} / \mathsf {Instr} \; (\%)\)
1941–1950 3 4.13 57.5 79.31
1951–1960 3 2.15 105 75.27
1961–1970 1 0.32 232 73.89
1971–1980 1 0.41 138 56.10
1981–1990 0 0 123 64.91
1991–2000 0 0 136 65.86
2001–2010 2 0.52 257 66.93
1941–2010 10 0.64 1048.5 67.56

\(\mathsf {Instr}\) at level \(\mathsf {2}\) and \(\mathsf {3}\).

  \(\mathsf {Instr} \, \mathsf {2}\) \(\mathsf {Instr} \, \mathsf {2} / \mathsf {Instr} \; (\%)\) \(\mathsf {Instr} \, \mathsf {3}\) \(\mathsf {Instr} \, \mathsf {3} / \mathsf {Instr} \; (\%)\)
1941–1950 6 8.28 6 8.28
1951–1960 16 11.47 15.5 11.11
1961–1970 37 11.78 40.5 12.90
1971–1980 51 20.73 54 21.95
1981–1990 24 12.67 39.5 20.84
1991–2000 25 12.11 37.5 18.16
2001–2010 31.5 8.20 68 17.71
1941–2010 190.5 12.27 261 16.82

\(\mathsf {Instr}\) at level \(\mathsf {4}\).

  \(\mathsf {Instr} \, \mathsf {4}\) \(\mathsf {Instr} \, \mathsf {4} / \mathsf {Instr} \; (\%)\)
1941–1950 0 0
1951–1960 0 0
1961–1970 3.5 1.11
1971–1980 2 0.81
1981–1990 3 1.58
1991–2000 8 3.87
2001–2010 25.5 6.64
1941–2010 42 2.71

Sub-disciplines in which logic is an instrument

  Epistemology (%) Phil. of language (%) Phil. of mathematics (%)
1941–1950 7.14 28.57 4.29
1951–1960 7.64 22.22 5.56
1961–1970 17.04 23.79 6.75
1971–1980 6.94 30.20 3.27
1981–1990 20.11 23.28 10.05
1991–2000 23.50 22 15.00
2001–2010 15.79 21.32 5.26
1941–2010 15.01 23.98 7.08
  Philosophy of mind (%) Moral/political philosophy (%)
1941–1950 7.14 0
1951–1960 3.47 17.36
1961–1970 0.64 9.32
1971–1980 6.53 16.32
1981–1990 4.23 0
1991–2000 5 0.50
2001–2010 0.53 5.26
1941–2010 3.12 7.47
  Phil. of science (%) Metaphysics (%) Others (%)
1941–1950 4.29 48.57 0
1951–1960 20.83 22.92 0
1961–1970 4.82 32.80 4.84
1971–1980 11.43 24.90 0.41
1981–1990 7.94 28.04 6.35
1991–2000 6.50 23 4.50
2001–2010 9.21 40 2.63
1941–2010 9.03 31.25 3.06

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Bonino, G., Maffezioli, P. & Tripodi, P. Logic in analytic philosophy: a quantitative analysis. Synthese (2020). https://doi.org/10.1007/s11229-020-02770-5

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Keywords

  • Analytic philosophy
  • Quantitative methods
  • Logic