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Reference in the Land of the Rising Sun: A Cross-cultural Study on the Reference of Proper Names

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Abstract

A standard methodology in philosophy of language is to use intuitions as evidence. Machery, Mallon, Nichols, and Stich (2004) challenged this methodology with respect to theories of reference by presenting empirical evidence that intuitions about one prominent example from the literature on the reference of proper names (Kripke’s Gödel case) vary between Westerners and East Asians. In response, Sytsma and Livengood (2011) conducted experiments to show that the questions Machery and colleagues asked participants in their study were ambiguous, and that this ambiguity affected the responses given by Westerners. Sytsma and Livengood took their results to cast doubt on the claim that the current evidence indicates that there is cross-cultural variation in intuitions about the Gödel case. In this paper we report on a new cross-cultural study showing that variation in intuitions remains even after controlling for the ambiguity noted by Sytsma and Livengood.

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Notes

  1. One might worry that although the difference is statistically significant, it is not very large. Indeed, according to Cohen’s h, the effect size is given by h = arcsin(0.565) – arcsin(0.315) = 0.280, which would ordinarily be classified as a small effect. However, it is not especially clear that the usual interpretation of effect size is appropriate in this context. Whether an effect of this size is philosophically interesting depends on the details of the arguments launched from its foundation.

  2. Online responses were collected through the Philosophical Personality website (philosophicalpersonality.com).

  3. Participants were counted as having more than minimal training in philosophy if they were philosophy majors, had completed a degree with a major in philosophy, or had taken graduate-level courses in philosophy.

  4. Participants in Stage 1 were 73.8 % female, with an average age of 35.2 years, and ranging in age from 18 to 79 years old. Participants in Stage 2 were 45.7 % female, with an average age of 20.1 years, and ranging in age from 18 to 39 years old. Participants in Stage 3 were 75.1 % female, with an average age of 36.9 years, and ranging in age from 18 and 79 years old.

  5. A χ 2 test of independence indicates that Probe and Response are associated for Americans (χ 2 = 42.54, df = 3, p = 3.08e-9). Fisher’s exact test yields a p-value with the same order of magnitude (p = 2.25e-9). We tested the expectation—derived from Sytsma and Livengood’s results—that the four probes would be ordered by the proportion of (B) answers from least to greatest like John’s Perspective, Original, Narrator’s Perspective, and Clarified Narrator’s Perspective. Hence, we conducted three one-sided tests of proportions. We do not correct for multiple comparisons here, since some authors argue that such corrections are unnecessary when comparisons are planned in advance (see for example, Chapter 22 in Motulsky 2010). The reader may make whatever corrections seem prudent. We found that the proportion of (B) answers in the John’s Perspective probe was statistically significantly smaller than the proportion of (B) answers in the Original probe (χ 2 = 15.99, df = 1, p = 3.17e-5) and that the proportion of (B) answers in the Original probe was statistically significantly smaller than the proportion of (B) answers in the Clarified Narrator’s Perspective probe (χ 2 = 3.38, df = 1, p = 0.033). However, we could not reject the hypothesis that the proportion of (B) answers in the Narrator’s Perspective probe was equal to the proportion of (B) answers in the Clarified Narrator’s Perspective probe (χ 2 = 0.141, df = 1, p = 0.353). At the request of an anonymous referee, we also calculated 95 % confidence intervals for the proportion of (B) answers for each probe. The intervals are (0.466, 0.624), (0.239, 0.396), (0.490, 0.654), and (0.601, 0.759) for the original, John’s perspective, narrator’s perspective, and clarified narrator’s perspective probes, respectively. Using a uniform prior, we also calculated 95 % highest-density credible intervals for the proportions to be (0.470, 0.622), (0.241, 0.391), (0.494, 0.652), and (0.607, 0.757). Finally, using a prior informed by the results reported in Sytsma and Livengood (2011), we calculated 95 % HDIs for the proportions to be (0.431, 0.550), (0.236, 0.353), (0.512, 0.634), and (0.653, 0.763).

  6. A χ 2 test of independence failed to detect any association between Probe and Response for Japanese speakers (χ 2 = 2.45, df = 3, p = 0.485). Fisher’s exact test yields a similar p-value (p = 0.488). We used simulations based on the proportions observed among English speakers to estimate the power to detect a similar effect at the 0.05 significance level with our Japanese sample sizes. Probe and Response were associated according to a χ 2 test at the 0.05 significance level in 928 out of 1,000 simulations. They were associated according to Fisher’s exact test at the 0.05 significance level in 933 out of 1,000 simulations. We calculated 95 % confidence intervals for the original, John’s perspective, narrator’s perspective, and clarified narrator’s perspective probes to be (0.196, 0.424), (0.191, 0.453), (0.262, 0.539), and (0.279, 0.558), respectively. Using a uniform prior, we calculated analogous 95 % highest density credible intervals to be (0.199, 0.413), (0.195, 0.439), (0.268, 0.527), and (0.285, 0.547).

  7. One-sided χ 2 tests of proportions showed that the proportion of (B) answers in the Original probe was statistically significantly smaller for Japanese than for Americans (χ 2 = 10.71, df = 1, p = 0.00053), the proportion of (B) answers in the Narrator’s Perspective probe was statistically significantly smaller for Japanese than for Americans (χ 2 = 4.35, df = 1, p = 0.0186), and the proportion of (B) answers in the Clarified Narrator’s Perspective probe was statistically significantly smaller for Japanese than for Americans (χ 2 = 10.74, df = 1, p = 0.00053). We could not reject the hypothesis that the proportion of (B) answers for the John’s Perspective probe was the same for Americans and Japanese (χ 2 = 0, df = 1, p = 0.5). An anonymous referee worried that the differences we would like to attribute to culture might actually be due to systematic differences in the gender and age composition of the samples. The Americans we sampled were more likely to be female than the Japanese we sampled, and they were more likely to be older. In order to control for the gender disparity, we did the following 1,000 times: We randomly selected a sub-sample from our American female participants so that we had a new, smaller sample that was 50 % male and 50 % female—basically in line with our Japanese sample; we then made the same comparisons as above and recorded how often we got a significant result at the 0.05 and at the 0.001 levels in each case. The results were as follows: In all 1,000 repetitions, the percentage of (B) answers to the Original probe among the Japanese was statistically significantly smaller than the percentage among the Americans at the 0.05 level, and in 424 of those, the Japanese percentage was statistically significantly smaller at the 0.001 level; in no repetitions was the percentage of (B) answers to the John’s Perspective probe statistically significantly smaller among the Japanese at either the 0.05 or 0.001 level; in 776 repetitions, the percentage of (B) answers to the Narrator’s Perspective probe, the Japanese percentage was statistically significantly smaller at the 0.05 level, and in 2 of those the Japanese percentage was also smaller at the 0.001 level; finally, in all 1,000 repetitions, the percentage of (B) answers to the Clarified Narrator’s probe among the Japanese was statistically significantly smaller at the 0.05 level, and in 715 of those the Japanese percentage was also smaller at the 0.001 significance level. We found it practically impossible to directly control for the differences in age composition without serious loss of power. However, we controlled indirectly by fitting a logistic regression model predicting responses based on age using our Western data. If the difference in age distributions mattered, we would expect to see a significant coefficient for age in the model. But age was not a statistically significant predictor of participant responses for any of the four probes (with p-values of 0.790, 0.802, 0.940, and 0.468). Hence, we have reason to doubt that differences in the age compositions of the two samples accounts for the differences in responses.

  8. It is worth noting that our study did not specifically control for a third potential confound that has been pressed in the literature—that MMNS’s original Gödel probe question is ambiguous with regard to asking about the speaker’s reference or semantic reference of John's use of the name “Gödel” (Ludwig 2007; Deutsch 2009). Nonetheless, while this ambiguity is distinct from the perspectival ambiguity, it is plausible that the two narrator's perspective probes clarify it as well, as discussed by Sytsma and Livengood (2011). Further, Machery et al. (2013) present independent evidence that the speaker's reference/semantic reference ambiguity does not explain away the cross-cultural variation found by MMNS.

  9. We conducted a Cochran-Mantel-Haenszel test for conditional independence to compare the responses in Stages 1 and 3. Specifically, we tested the null hypothesis that Stage (either 1 or 3) and Response (either A or B) were independent conditional on Probe (1–4). We could not reject the null hypothesis (M 2 = 0.347, df = 1, p = 0.556). By contrast, the same test using data from Stages 1 and 2 did reject the null hypothesis (M 2 = 21.24, df = 1, p = 4.05e-6). And the null hypothesis was rejected when the data from all three stages were analyzed together (M 2 = 23.59, df = 2, p = 7.55e-6).

  10. One-sided χ 2 tests of proportions showed that the proportion of (B) answers in the Original probe was statistically significantly smaller for Japanese participants than for American participants (χ 2 = 15.29, df = 1, p = 4.61e-5), the proportion of (B) answers in the Narrator’s Perspective probe was statistically significantly smaller for Japanese participants than for American participants (χ 2 = 11.41, df = 1, p = 3.65e-4), and the proportion of (B) answers in the Clarified Narrator’s Perspective probe was statistically significantly smaller for Japanese participants than for American participants (χ 2 = 3.10, df = 1, p = 0.0393). As before (see Footnote 5), we did not correct for multiple comparisons. We calculated 95 % confidence intervals for the reverse-translated probes in Stage 3 to be (0.514, 0.681), (0.140, 0.276), (0.591, 0.746), and (0.484, 0.648). Similarly, assuming a uniform prior, 95 % highest density credible intervals for the reverse-translated probes are (0.518, 0.678), (0.141, 0.270), (0.596, 0.745), and (0.488, 0.645).

  11. Parallel to what we did in Stage 1, we conducted three one-sided tests of proportions in order to test an expected ordering for the proportion of (B) answers in the reverse-translated probes. As before, we do not correct for multiple comparisons. We found that the proportion of (B) answers in the John’s Perspective probe was statistically significantly smaller than the proportion of (B) answers in the Original probe (χ 2 = 45.97, df = 1, p = 6.00e-12). The proportion of (B) answers in the Original probe was smaller than the proportion of (B) answers in the Narrator’s Perspective probe, but the difference was not statistically significant (χ 2 = 1.38, df = 1, p = 0.120). And the difference between the Narrator’s Perspective probe and the Clarified Narrator’s Perspective probe did not even run in the right direction (χ 2 = 3.105, df = 1, p = 0.961).

  12. Participants were 74.1 % female, with an average age of 34.7 years, and ranging in age from 18 to 78 years old.

  13. A 95 % confidence interval is given by (0.616, 0.772). A 95 % credible interval based on a uniform prior is given by (0.621, 0.770). A one-sided χ 2 test of proportions showed that the proportion of (B) answers in the corrected Clarified Narrator’s Perspective probe was statistically significantly smaller for Japanese participants than for American participants (χ 2 = 12.05, df = 1, p = 2.60e-4). We carried out a sub-sampling scheme identical to the one described in Footnote 7 in order to control for differences in gender composition. We found that in 1,000 out of 1,000 repetitions, the percentage of Japanese (B) answers was statistically significantly smaller than the percentage of American (B) answers at the 0.05 level, and we found that in 513 of those 1,000 repetitions, the percentage was smaller at the 0.001 significance level.

  14. We think the degree to which one should lose confidence in the overall results is small even if the Clarified Narrator’s Perspective probe is dropped from consideration, since the other three probes did not appear to have any translation problems.

  15. To further test the source of the problem with the reverse-translated Clarified Narrator's Perspective probe, we simply added the word “fact” to the end of the parenthetical used in Stage 3. We gave the revised probe to 142 American participants online, again adopting the same restrictions used in Stages 1 and 3. Participants were 62.7 % female, with an average age of 43.0 years, and ranging in age from 18 to 82 years old. As predicted, the percentage of (B) answers for the revised version of the probe—60.6 %—is higher than we found for the unrevised probe in Stage 3. A 95 % confidence interval is given by (0.520, 0.686). A 95 % credible interval based on a uniform prior is given by (0.524, 0.683). More importantly, the percentage of (B) answers is not statistically significantly different from the percentage found for the English baseline version of the probe in Stage 1. A χ 2 test of proportions showed that the proportion of (B) answers for the version of the reverse-translated Clarified Narrator's Perspective probe with “fact” added was not statistically significantly different from the proportion for participants in Stage 1 (χ 2 = 1.64, df = 1, p = 0.200). Further, it is statistically significantly higher than the percentage found for the translated probe in Stage 2. A one-sided χ 2 test of proportions showed that the proportion of (B) answers for the version of the reverse-translated Clarified Narrator's Perspective probe with “fact” added was statistically significantly higher than the proportion for Japanese participants in Stage 2 (χ 2 = 4.95, df = 1, p = 0.013). In 1,000 repetitions designed to control for the difference in gender composition, we found a statistically significant difference in the predicted direction 943 times at the 0.05 level but never at the 0.001 significance level.

  16. For example, Sytsma and Livengood (2011, 330–331) argue: “Before seeing any data, there was just as much reason to predict that East Asians would be more likely than Westerners to answer (A) on the basis of the epistemic ambiguity as there was for Machery et al. to predict a difference on the basis of different semantic intuitions. Interestingly, this claim follows from the very same body of empirical work that Machery et al. point to in framing their prediction that Westerners and East Asians would differ in their intuitions about the Gödel probe.... In particular, they call on the work of Nisbett et al. (2001) indicating a range of cultural differences, which they collect under the heading of ‘holistic vs. analytic thought’.... Holistic thought is supposed to be characteristic of Easterners.... Analytic thought is supposed to be characteristic of Westerners.... The more holistic way to read Machery et al.’s Gödel probe is in terms of the beliefs that would be ascribed to John by his interlocutors. The more analytic way to read the probe is in terms of the beliefs that we the readers have as informed by an omniscient narrator.”

  17. The expertise defense is discussed briefly in MMNS’s original paper; see also Machery 2012a, 2012b.

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Appendix

Appendix

Stage 1, Pre-Translation:

Suppose that John has learned in college that Gödel is the man who proved an important mathematical theorem, called the incompleteness of arithmetic. John is quite good at mathematics and he can give an accurate statement of the incompleteness theorem, which he attributes to Gödel as the discoverer. But this is the only thing that he has heard about Gödel.

Now suppose that Gödel was not the author of this theorem. A man called “Schmidt” whose body was found in Vienna under mysterious circumstances many years ago, actually did the work in question. His friend Gödel somehow got hold of the manuscript and claimed credit for the work, which was thereafter attributed to Gödel. Thus he has been known as the man who proved the incompleteness of arithmetic.

Most people who have heard the name “Gödel” are like John; the claim that Gödel discovered the incompleteness theorem is the only thing they have ever heard about Gödel.

Question for Original Probe:

When John uses the name “Gödel,” is he talking about:

  1. (A)

    the person who really discovered the incompleteness of arithmetic?

  2. (B)

    the person who got hold of the manuscript and claimed credit for the work?

Question for John’s Perspective Probe:

Having read the above story and accepting that it is true, when John uses the name “Gödel,” does John think he is talking about:

  1. (A)

    the person who the story says really discovered the incompleteness of arithmetic?

  2. (B)

    the person who the story says got hold of the manuscript and claimed credit for the work?

Question for Narrator’s Perspective Probe:

Having read the above story and accepting that it is true, when John uses the name “Gödel,” is he actually talking about:

  1. (A)

    the person who the story says really discovered the incompleteness of arithmetic?

  2. (B)

    the person who the story says got hold of the manuscript and claimed credit for the work?

Question for Clarified Narrator’s Perspective Probe:

Having read the above story and accepting that it is true, when John uses the name “Gödel,” would you take him to actually be talking about:

  1. (A)

    the person who (unbeknownst to John) really discovered the incompleteness of arithmetic?

  2. (B)

    the person who is widely believed to have discovered the incompleteness of arithmetic, but actually got hold of the manuscript and claimed credit for the work?

Stage 2, Japanese Translation:

ジョンという人物がいたとしよう。ジョンは大学時代に、ゲーデルとは、算術の不完全性と呼ばれる、ある重要な数学の定理を証明した人物である、と教わった。ジョンは数学が大変得意であり、不完全性定理についてその正確な内容を述べることができる。ジョンはその定理の発見者はゲーデルだと思っているが、彼がゲーデルについて聞いたことがあるのはこれだけだった.

ここで、ゲーデルはこの定理の考案者ではなかったと想定してみよう。実際には、「シュミット」 と呼ばれる男――その遺体はウィーンにおいて何十年も前に不可解な状況で発見された――がその業績を成し遂げたのである。シュミットの友人であったゲーデルは何らかの手段をもちいてその手稿を手に入れ、その業績を自分のものだと主張したのである。以来、その業績はゲーデルのものとされている。こうして、彼は算術の不完全性を証明した人物として知られることになった.

「ゲーデル」 という名前を聞いたことのある人のほとんどはジョンと同じである。つまり、ゲーデルについて聞いたことがあるのは、ゲーデルが不完全性定理を発見したということだけである.

Question for Original Probe:

「ゲーデル」 という名前を使うとき、ジョンが語っているのは誰についてか?

  1. (A)

    算術の不完全性を本当に発見した人物

  2. (B)

    手稿を手に入れ、その業績を自分のものだと主張した人物

Question for John’s Perspective Probe:

上のストーリーが実話だったとしよう。「ゲーデル」 という名前を使うとき、ジョンは自分が語っているのは誰についてだと思っているか?

  1. (A)

    算術の不完全性を本当に発見した人物

  2. (B)

    手稿を手に入れ、その業績を自分のものだと主張した人物

Question for Narrator’s Perspective Probe:

上のストーリーが実話だったとしよう。「ゲーデル」 という名前を使うとき、ジョンは実際のところ誰について語っているのか?

  1. (A)

    算術の不完全性を本当に発見した人物

  2. (B)

    手稿を手に入れ、その業績を自分のものだと主張した人物

Question for Clarified Narrator’s Perspective Probe:

上のストーリーが実話だったとしよう。ジョンが 「ゲーデル」 という名前を使うとき、あなたは彼が語っているのは実際のところ誰についてだと思うか?

  1. (A)

    算術の不完全性を本当に発見した人物 (ジョンはこのことを知らない)

  2. (B)

    算術の不完全性を発見したと広く信じられているが、実際には、手稿を手に入れ、その業績を自分のものだと主張した人物

Stage 3, Reverse-Translation:

Suppose that there is a person named John. In college, John was taught that Gödel is the person who proved an important theorem in mathematics, called the incompleteness of arithmetic. John is very good at mathematics and is able to describe the precise content of the incompleteness theorem. John believes that the discoverer of the theorem is Gödel, but this is all he has heard about Gödel.

Now suppose that Gödel was not the originator of the theorem. In reality, the man named “Schmidt”—whose body was found many decades ago in Vienna under mysterious circumstances—accomplished the work in question. Gödel, who was Schmidt’s friend, somehow obtained the manuscript and claimed that it was his work. The work is thereafter attributed to Gödel. In this way, he has come to be known as the one who proved the incompleteness of arithmetic.

Most of the people who have heard the name “Gödel” are like John. That is, what they have heard about Gödel is only that Gödel discovered the incompleteness of arithmetic.

Question for Original Probe:

When he uses the name “Gödel,” whom is John talking about?

  1. (A)

    The person who really discovered the incompleteness of arithmetic

  2. (B)

    The person who obtained the manuscript and claimed that it is his work

Question for John’s Perspective Probe:

Suppose that the above story is true. When he uses the name “Gödel,” whom does John think he is talking about?

  1. (A)

    The person who really discovered the incompleteness of arithmetic

  2. (B)

    The person who obtained the manuscript and claimed that it is his work

Question for Narrator’s Perspective Probe:

Suppose that the above story is true. When he uses the name “Gödel,” whom is John really talking about?

  1. (A)

    The person who really discovered the incompleteness of arithmetic

  2. (B)

    The person who obtained the manuscript and claimed that it is his work

Question for Clarified Narrator’s Perspective Probe:

Suppose that the above story is true. When he uses the name “Gödel,” whom do you think he is really talking about?

  1. (A)

    The person who really discovered the incompleteness of arithmetic (John does not know this)

  2. (B)

    The person who is widely believed to have discovered the incompleteness of arithmetic but in reality obtained the manuscript and claimed that it is his work

Question for First Edited Version of Clarified Narrator’s Perspective Probe:

Suppose that the above story is true. When he uses the name “Gödel,” whom do you think he is really talking about?

  1. (A)

    The person who (unbeknownst to John) really discovered the incompleteness of arithmetic

  2. (B)

    The person who is widely believed to have discovered the incompleteness of arithmetic but in reality obtained the manuscript and claimed that it is his work

Question for Second Edited Version of Clarified Narrator’s Perspective Probe:

Suppose that the above story is true. When he uses the name “Gödel,” whom do you think he is really talking about?

  1. (A)

    The person who really discovered the incompleteness of arithmetic (John does not know this fact)

  2. (B)

    The person who is widely believed to have discovered the incompleteness of arithmetic but in reality obtained the manuscript and claimed that it is his work

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Sytsma, J., Livengood, J., Sato, R. et al. Reference in the Land of the Rising Sun: A Cross-cultural Study on the Reference of Proper Names. Rev.Phil.Psych. 6, 213–230 (2015). https://doi.org/10.1007/s13164-014-0206-3

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