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Ian Hacking's new book *Why is there philosophy of mathematics at all?", see here, contains many interesting ideas. One of the ideas is the dichotomy of two distinct models for the development of a science. One is the butterfy model. A biological organism follows a course of development that is predetermined to a certain extent by its genetic make-up. The example of butterfly was chosen I think because of the dramatic changes a butterfly undergoes (cocoon, etc), unlike, say, an elephant; yet even those dramatic changes are written into the script so to speak.

The other model is the Latin model of development of a natural language like Latin. Such development obviously is affected by historical factors and contingencies of human behavior.

Hacking seems to think that scholars often view mathematics as following a butterfly model, whereas he himself seems to argue in favor of the Latin model.

So to summarize, my question is: does Hacking's Latin model really apply to mathematics?

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    $\begingroup$ A small question: In "people generally view [...]", does "people" designate laypeople, mathematicians, or some other (majority) group? $\endgroup$ – Danu Jan 13 '16 at 16:12
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    $\begingroup$ @Danu, Hacking seems to imply that this includes many historians and mathematicians. I doubt it many laypeople would be interested in the question :-) If you like I can provide some examples of scholars adhering to such views. $\endgroup$ – Mikhail Katz Jan 13 '16 at 16:26
  • $\begingroup$ Hacking's metaphors seem to be alluding to "postmodern" vs. "Whiggish" approaches to historiography of science. We had an extensive discussion of them here hsm.stackexchange.com/questions/2857/… Hacking's view of history was influenced by Kuhn, although his philosophy is less relativistic and closer to Lakatos, which the "Latin" metaphor reflects. While language's development is influenced by social and cultural factors it is also driven by external needs of dealing with the world. $\endgroup$ – Conifold Jan 15 '16 at 21:52
  • $\begingroup$ Given that the zeta function helps to understand something about primes, Hacking is asking is this an inevitable devlopment of the number concept (from integer to complex function) or is it serendipity - butterfly or history? -that's what I saw by just leafing (not reading) through the book. Perhaps the question should be reformulated. $\endgroup$ – sand1 Jan 16 '16 at 22:17
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Mathematics is a language (and a culture), as such it isn't constrained by any "predetermined path" mandated by some genome makeup. I'd strongly say mathematics (and all science, as part of human culture) follows the "Latin" scheme (which itself is also part of the same cultural development).

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    $\begingroup$ Thanks for your answer. I have the impression that traffic here is a bit slow. I think this question is suitable for MSE as well. We could try to develop a formulation that may lead to a more in-depth discussion if you are interested. $\endgroup$ – Mikhail Katz Jan 13 '16 at 15:30
  • $\begingroup$ However, MSE is not for "opinion" questions, nor for discussion. So you will need to ask about whether there are other books or papers on butterfly/Latin or something. $\endgroup$ – Gerald Edgar Jan 14 '16 at 16:23

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