Abstract
The paper argues that there is a fruitful analogy to be made between classic pre-analytic Euclidean geometry and a certain kind of mechanism models, called ideal mechanisms. Both supply necessary truths. Bunge is of the opinion that pure mathematics is about fictions, but that mathematics nonetheless is useful in science and technology because we can go “to reality through fictions.” Similarly, the paper claims that ideal mechanisms are useful because we can go to real mechanisms through the fictions of ideal mechanisms. The view put forward takes it for granted that two important distinctions concerned with the classification of fictions can be made. One is between ideal and non-ideal fictions, and the other between social and non-social fictions. Pure numbers, purely geometric figures, and ideal mechanisms are claimed to be ideal and social fictions.
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- 1.
Apart from Bunge (1964), see also in particular (Bunge 1997, 2004, 2006, Ch. 5). In a “Personal Postscript” in Bunge (1997), he presents “a brief account of my struggle with the concepts of mechanism and mechanismic explanations” (ibid. p. 458). For me, Bunge (1964) was a seminal paper. The notion of mechanism has ever since the end of the 1960s played an important role in my philosophical endeavors. In Johansson (2004 [1989], Ch. 14) it is central. Subchapter 14.3 has the heading “Mechanisms and their parts.” The views about mechanisms stressed in the present paper were first outlined in Johansson (1997).
- 2.
In many contexts the expression ‘material model’ is used, but, as far as I know, Bunge uses it only on one occasion (Bunge 1967, p. 146). I take him to mean that material systems become material models only when being part of “conceptual and semiotic systems.”
- 3.
A co-author and I have, partly influenced by Bunge (see footnote 1), ever since the 1990s stressed the importance of distinguishing in medicine between mechanism knowledge and correlation knowledge. See Johansson and Lynøe (2008, Ch. 6); we did earlier put forward the distinction in similar but much smaller books in Swedish in 1992 and 1997, and in Danish 1999.
- 4.
What today are called theorems, Euclid calls propositions. In my discussion I disregard the fact that Euclid’s first three Postulates are not statements that describe a state of affairs as existing; they state that it is always possible to draw, produce, and describe, respectively, a certain kind of geometric figure.
- 5.
According to ACM1, if W1 rotates clockwise, W2 rotates anti-clockwise, and if W2 rotates anti-clockwise, W3 rotates clockwise just as W1 does.
- 6.
According to ACM1, if all the three wheels are mutually connected and rotating, then one of the wheels must be able simultaneously to rotate in two opposite directions, which is a contradiction.
- 7.
In fact, I have the much stronger view that the property dimension of shape cannot be quantified. See Johansson (2011), where a proof to this effect is given. So far, no one has been able to find a mistake in the proof, which relies on transfinite mathematics.
- 8.
- 9.
There have in this decade been some discussions about whether certain scientific models should be regarded as fictions or as analogous to fictions See for instance Contessa (2010), Frigg (2010), Toon (2010), Morrison (2015), and Bueno et al. (2018). But in none of these papers and books is my thesis that certain models can contain necessary truths put forward.
- 10.
- 11.
- 12.
I discuss them in Johansson (2015, sects. 6 and 7), and I think they point towards what might be called a property view of the natural numbers.
- 13.
For a comprehensive discussion of Weber’s ideal types, see von Schelting (1934). He finds distinct kinds of ideal types in Weber. Along one dimension, von Schelting divides ideal types into “causal-real” and “non-causal ideal,” and along another into “generalizing” and “individualizing.”
- 14.
My analysis of how it can be possible for different persons to refer to the same individual fiction is presented in Johansson (2010). It differs from Bunge’s, but it also differs from “the pretence theory of fiction” and “the make-believe theory of fiction.” Both the latter have been used in discussions of fictional models in science; see Frigg (2010) for the first and Toon (2010) for the second.
- 15.
In the sixth section, I briefly compare Bunge’s and Popper’s conceptions of approximate truths. A comparison between Bunge’s view of what is “neither objective nor subjective in an ontological sense” and Popper’s view of his so-called “world 3” would lay bare a further striking similarity between them.
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Acknowledgements
For useful comments on a preliminary version, I would like to thank Rögnvaldur Ingthorsson, Ingemar Nordin, and Christer Svennerlind.
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Johansson, I. (2019). Mechanism Models as Necessary Truths. In: Matthews, M.R. (eds) Mario Bunge: A Centenary Festschrift. Springer, Cham. https://doi.org/10.1007/978-3-030-16673-1_14
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