Abstract
Having formulated the axioms of the theory, it is now time to proceed to its theorems. In this chapter, I shall take the laws as my starting point and deduce several theorems from them. Each theorem will be illustrated by relevant historical examples.
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Notes
- 1.
As with the zeroth law, the modified versions of both the theory rejection theorem and the method rejection theorem (discussed below) were suggested by Rory Harder during the seminar of 2013. In their initial version, both of the rejection theorems assumed that the classical logical notion of inconsistency is the universal and unchangeable criterion of compatibility. As we already know, this assumption is untenable. For details, see section “The Zeroth Law: Compatibility”.
- 2.
- 3.
See Lindberg (2008), pp. 54, 309–310.
- 4.
For details, see Garber (1992), pp. 63–69, 130–136.
- 5.
For discussion, see Brooke (1991), pp. 275–320.
- 6.
This is not surprising since, as I have stressed in section “Time, Fields, and Scale”, disciplinary boundaries are both transient and ambiguous.
- 7.
- 8.
This is an interesting topic for professional historical research. When exactly was natural astrology exiled from the mosaic? What theories replaced natural astrology in the mosaic? Was it replaced by some physical theory and, if so, which one and when?
- 9.
Refer to section “The Third Law: Method Employment” for discussion.
- 10.
The case is discussed in section “The Third Law: Method Employment”.
- 11.
There is an interesting theoretical question that calls for further study: is every theory rejection necessarily synchronous with some method rejection? I confess that, at the moment, I don’t have a clear-cut answer to this question.
- 12.
See Lindberg (2008), pp. 49–52.
- 13.
See more on this transition in section “Mosaic Split and Mosaic Merge” below.
- 14.
See Lakatos (1970), pp. 10–11.
- 15.
See Lakatos (1968) for a nice discussion of the history of probabilism.
- 16.
It is important to understand that the contemporary Bayesianism, which is essentially an heir to probabilism, has given up the task of assigning objective probabilities. See Howson and Urbach (2006), p. 45. Consequently, contemporary Bayesianists realise that theory assessment is a comparative procedure.
- 17.
- 18.
- 19.
- 20.
- 21.
See Popper (1934/59), pp. 32–33, 61–63.
- 22.
Popper (1963), p. 322.
- 23.
See Popper (1963), pp. 151, 322–330.
- 24.
- 25.
See Kuhn (2000), pp. 112–115.
- 26.
Although in his (1977), pp. 320–339, Kuhn attempted to introduce five transhistorical values which presumably guide theory assessment across paradigms, it is clear that the attempt was a flop, for he ended up making these values paradigm-dependent. For discussion, see Laudan (1984), pp. 14–20, 30–32.
- 27.
- 28.
Einstein (1953), p. vii.
Unfortunately the vices of the traditional interpretation are still being repeated in popular accounts. Take for instance Mark Steel’s BBC lectures. Albeit ingeniously hilarious, they propagate the same old errors by presenting the case as if it were “the brilliance of a few” versus “the dogmatism of churchmen”.
- 29.
- 30.
See Lindberg (2008), pp. 115–117, 339–342.
- 31.
For my explication of the Aristotelian-medieval method, see pp. 139 ff.
- 32.
See section “Mosaic Split and Mosaic Merge” below.
- 33.
- 34.
- 35.
- 36.
- 37.
This is another illustration of what happens when historical research is not guided by a proper theory.
- 38.
See Nadler (1988), p. 241.
It is worth pointing out that Arnauld didn’t exactly invent this patch; he merely exploited a well-known medieval strategy. In fact, some 400 hundred years before Arnauld, a very similar strategy was used to reconcile the Aristotelian natural philosophy with Christian dogmas such as “God’s omnipotent” or “God created the world”. See Lindberg (2008), pp. 240–243, 251–253; Grant (2004), pp. 216–217.
- 39.
- 40.
See Vartanian (1953), p. 42.
- 41.
See, for instance, Fara (2003), pp. 488, 491–492.
- 42.
See section “Sociocultural Factors” below for discussion.
- 43.
See, for instance Biagioli (1996), p. 201.
- 44.
See Kuhn (1977), pp. 290–291, 322–328. I should mention, however, that none of the cases discussed by Kuhn is a genuine instance of inconclusiveness. What Kuhn ignored in his examples (such as Ptolemy vs. Copernicus, or phlogiston vs. oxygen) is that, in actual practice, theories are assessed by the method of the time and not by Kuhn’s own five criteria. Once we assess Kuhn’s cases by the methods employed at their respective times, we come to realize that the examples were chosen erroneously.
- 45.
See Laudan (1984), pp. 26–39, 43–45, 62.
- 46.
Brown (2001), p. 20.
- 47.
- 48.
See Laudan (1984), pp. 5, 11, 25, 33.
- 49.
See Weinberg (2003), p. 150.
- 50.
See section “The Third Law: Method Employment” for discussion.
- 51.
There is also the third option, which I shall discuss in section “Mosaic Split and Mosaic Merge”.
- 52.
Note, however, that I have presented this community-oriented version of the story only for illustrative purposes – it is irrelevant to the actual deduction of the necessary mosaic split theorem.
- 53.
There is an interesting theoretical question that calls for further study: is it possible for a mosaic to split as a result of the employment of two incompatible methods? In other words, does mosaic split always result from theory acceptance or can it also result from method employment?
- 54.
Refer to the discussion of the Eucharist episode in section “Contextual Appraisal”.
- 55.
Cummings (ed.) (2011), p. 681.
- 56.
See Gascoigne (1989), pp. 54–55. As with almost all dates of theory acceptance, a more precise data is required here.
- 57.
See Brockliss (2003), pp. 45–46, (2006), p. 260.
Vartanian gives a slightly later date: on his reckoning, the Cartesian natural philosophy was included in the curricula of the University of Paris only in the 1710s. See Vartanian (1953), p. 41. However, the rule of thumb suggests that in such matters we have to rely on the more recent scholarship.
Also, McLaughlin mentions that the theory was officially recognized only in the 1720. See his (1979), p. 569. However, it is safe to say that this was merely post factum recognition by the authorities of what had been already apparent: by the time of the official recognition the theory had been systematically taught in Paris for two decades.
- 58.
See Schmitt (1973), p. 163.
- 59.
See Frängsmyr (1974), p. 31.
- 60.
See Gascoigne (1989), p. 146.
- 61.
- 62.
Although it must be pointed out that in the Dutch Republic Newton’s theory acquired a very special flavor. See Jorink and Maas (eds.) (2012).
- 63.
- 64.
My reading holds only if the two mosaics had not been split earlier than the 1680s. Whether the Cambridge and Oxford communities shared the same mosaic before 1680s, or whether they had different mosaics is for HSC to establish.
- 65.
Refer to section “The Third Law: Method Employment” for my explication of the Aristotelian-medieval method.
- 66.
Bunge (1962) provides a nice discussion of different species of intuitivism and shows why it is doomed.
- 67.
In case the community expects theories of scientific change to provide some novel predictions, necessary mosaic split can be considered one such prediction of this TSC.
- 68.
See the timeline on page 208.
An interesting historical question arises here: when did the three mosaics merge? Possibly, it had to do with the rejection of respective theological propositions. If that is the case, then the task is to find out when theology was exiled from the mosaic.
- 69.
It is probable that the other protestant mosaics, such as that of German scientific community, also merged with those of Dutch and Swedish mosaics. This can be revealed only by proper historical research.
- 70.
See, for instance, Cohen (1985), pp. 182–183.
- 71.
- 72.
- 73.
See Terrall (1992), p. 234.
- 74.
Again, it needs to be emphasized that my historical hypotheses are to be taken with a grain of salt as they are presented only for the purpose of illustrating the theorems of the TSC. Only professional historical research can establish whether my historical hypotheses hold water.
- 75.
See, for instance, Newton-Smith (1981), pp. 222, 245–246, 269.
- 76.
See section “The Third Law: Method Employment” for details.
- 77.
- 78.
- 79.
Worrall (1989), p. 387.
- 80.
See, for instance, Abímbólá (2006), p. 55. Zahar calls it “stability thesis”. See Zahar (1982), p. 407. In addition, when Bayesianists argue that scientific reasoning is conducted in accordance with the axioms of probability, they tacitly subscribe to the static method thesis. See Howson and Urbach (2006).
- 81.
As I have noted earlier, the whole contemporary discussion on the role of novel predictions has the static method thesis as one of its premises. See section “The Second Law: Theory Acceptance” for details.
- 82.
See, for instance, Freedman (2009), p. 314.
- 83.
See Shapin (1996), p. 4.
- 84.
See section “The Third Law: Method Employment” above, pp. 142 ff.
- 85.
Worrall (1989), p. 386.
- 86.
- 87.
This has been pointed out by Rory Harder during the seminar of 2013.
- 88.
See section “The Zeroth Law: Compatibility” for discussion.
- 89.
See Burgess (2009), pp. 99–100.
- 90.
This is another example of an interesting historical question that would probably have never arisen if not for TSC.
- 91.
Hacking, for instance, mixes in one big bowl many disparate methods (some of them even not being methods in our technical sense) and then goes on asking rhetorically “Where then is this splendid specific of science, the scientific method?” See Hacking (1996), p. 64. Freedman too doesn’t seem to be distinguishing between procedural and substantive methods and, as a result, quickly arrives at the dynamic methods thesis without touching upon the case of procedural methods. See Freedman (2009), pp. 317, 320.
- 92.
The question was suggested in 2012 by William E. Seager in a private conversation.
- 93.
There are also other interesting historical questions concerning the initial state. Was there one initial mosaic or were there many different initial mosaics? Which elements did the initial mosaic(s) contain? When did the mosaic(s) originate? Naturally, all these questions are to be tackled by HSC.
- 94.
There is a noteworthy technical detail: logically speaking, the nonempty mosaic theorem that we have deduced earlier is a deductive consequence of the necessary method theorem: if any mosaic necessarily contains at least one method, then it logically follows that any mosaic contains at least one element.
- 95.
See my explication of the Aristotelian-medieval method on pp. 139ff.
- 96.
For other oft-cited prerequisites of science, see Hansson (2008).
- 97.
See section “Static and Dynamic Methods” for discussion.
- 98.
See section “Construction and Appraisal” of Part I for discussion.
- 99.
See Lakatos (1971), pp. 102, 114, 118–121. Naturally, for Lakatos, methodology is a twofold normative-descriptive discipline. See section “Descriptive and Normative”.
- 100.
This is in tune with Garber’s criticism of Lakatos’s approach. See Garber (1986), p. 98.
- 101.
The question of the role of sociocultural factors in method employment is extremely interesting and calls for separate research. At this point we can only notice that there is a good chance that they do play role in method employment; this seems to be suggested by the underdetermined method change theorem. Obviously, this needs to be carefully studied.
- 102.
There is an open historical question concerning the initial implicit expectations of the ancient Greek community (if there ever was one united ancient Greek community). Even if it turned out that their initial requirements were extremely vague, it would still be interesting to explicate those requirements and determine the degree of their vagueness.
- 103.
See section “Mosaic Split and Mosaic Merge” for discussion.
- 104.
See Bernard (2005).
- 105.
See section “Mosaic Split and Mosaic Merge”.
- 106.
See Krementsov (1997).
- 107.
There is also the open question of the status of normative propositions (including those of methodology) in the mosaic. Can normative propositions such as those of methodology or ethics be part of the mosaic? If so, how do they become prescribed, i.e. what logic governs their entrance into and rejection from the mosaic?
- 108.
See section “The Third Law: Method Employment” for discussion.
- 109.
For GCP, see Kolman et al. (1998).
- 110.
Of course, only professional historical research can reveal the distance between the methodology of a field and the method actually employed in that field. This is yet another question which would most likely remain unasked if there were no TSC.
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Barseghyan, H. (2015). Theorems. In: The Laws of Scientific Change. Springer, Cham. https://doi.org/10.1007/978-3-319-17596-6_5
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