Abstract
The scattered and pervasive variability of material objects, being a conspicuous part of the very experience of early-modern and modern science, challenges its purely theoretic character in many ways. Problems of this kind turn out in such different scientific contexts as Galilean physics, chemistry, and physiology. Practical answers are offered on the basis of different approaches, among which, in particular, two can be singled out. One is made out by what is often called an ‘art’ (thus not a science, rather an informed practice) of experiments. From the Renaissance until J. H. Lambert’s writings of the 1750–1760s, we can follow a train of reflections on the art of making experiments that deal precisely with the persistence of contingency in the material objects of pure science. The other is the analysis of contingency in probabilistic terms. They develop subsequently and eventually meet, as it can be seen precisely in Lambert’s work: among the first to pursue this path are Jakob Bernoulli and Leibniz.
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Notes
- 1.
See, for instance, Yeo 2014, 91–95.
- 2.
“Vita brevis: ars longa: occasio praeceps: experimentum fallax: iudicium difficile est” (Hippocrates 1494, a3v).
- 3.
On contingency and laws of nature, see chapters 1, 2, and 7 of Daston and Stolleis (2008). On the historical evolution of observation as a canonical form of learned experience in late medieval and early modern Europe, see Pomata and Siraisi (2005), Gaukroger (2006), and chapters 1–3 in Daston and Lunbeck (2010). On the context and development of a culture of experimental facts in sixteenth- to eighteenth-century England, see Shapiro (1979, 1983, 2000). We are considering observation of the “normal” variability of things; of course “monsters” and “wonders” pose even more complex problems (see Daston and Park 1998), yet these are outside the scope of this chapter.
- 4.
Dialogo sopra i due massimi sistemi del mondo, tolemaico e copernicano (1632, nine years after Il saggiatore); Discorsi e dimostrazioni matematiche intorno a due nuove scienze attenenti alla mecanica e i movimenti locali (1638).
- 5.
- 6.
For the sake at least of testifying to the influence of these works, I shall be using coeval English translations of Galileo.
- 7.
“Fix it well in your mind, that in the highest distances, that is v.g. the height of Saturn, or that of the fixed Stars, very small errors made by the Observator, with the instrument, render the situation determinate and possible, infinite and impossible. This doth not so evene in the sublunary distances, and near the earth” (Galilei 1661, 265; OG 7, 317).
- 8.
In the Italian text: “ferma scienza” (OG, 8, 276).
- 9.
Ars is considered an habitus intellectualis in the whole Latin Aristotelian tradition on the basis of Eth. Nic. VI. It is remarkable that, in contrast to Bacon and certain strands of Aristotelianism, the pertinent instrument is not a “logic.”
- 10.
Although using a not dissimilar definition, the most important contemporary German philosopher, Christian Wolff, is surprisingly deaf to any practical aspect of these issues: for him, very simply, “Ars experimentandi est, qua experimentis veritates eruuntur”—i.e., the art in which we find truths by means of experiments, as a subdivision of the ars inveniendi a posteriori, in a sort of belated Ramist treatment of the ars inveniendi in general (Psychologia empirica, §459; Wolff 1732, 357–58).
- 11.
“Innumerabiliter […] innumerae erunt variationes, quibus corporum naturalium omnium, potestati artificis subjectorum, status artificialis mutari potest” (Müller 1721, 7).
- 12.
“Corpus naturale non nisi sub certis conditionibus et circumstantiis, quid et quantum agere vel pati possit, prodit ac demonstrat” (Müller 1721, 7).
- 13.
Not without a conspicuous, maybe inevitable share of idealizations; see Wood (1980).
- 14.
And it is even more important to “consider the contingencies, to which experiments are obnoxious, upon the account of circumstances, which are either constantly unobvious, or at least are scarce discernible till the trial be past” (Boyle 1772, 1:334). On the role of contingencies and experimental miscarriages in Boyle’s scientific program, see Sargent (1994).
- 15.
Henry Power’s experimental philosophy joined “claims for experimental liberty and devotion” (Shapin and Schaffer 2011, 304). Power put great weight indeed on experimentation: “the true Lovers of Free, and Experimental Philosophy […] are the enlarged and Elastical Souls of the world” (Power 1664, 191). See also the still useful Cowles 1934.
- 16.
“Propositum fuit Auctori monstrare eximium usum quem in vita civili habet ea. Matheseos pars, a paucis hactenus tractata, quæ de probabilitatibus dimetiendis agit” (Bernoulli 1713, n.n.).
- 17.
On the connection of primeval probability theory and such questions of civil and political import, see Poovey (1998).
- 18.
My italics. This passage (“since such events are contingent by their own nature”) was the only appearance of the term “contingent” in the text of the Logique. On the pre-Port Royal and pre-Pascalian history of rational methods of dealing with uncertainty, see Franklin 2001.
- 19.
Plainly for God, and in general for any omniscient being, “chance” does not exist. Incidentally, Bernoulli’s first studies had been in theology.
- 20.
This is a first approximation to distinctions that will be crucial in probability theory, to which, yet, Bernoulli’s concepts are not perforce to be mapped: “There is no need to foist a single probability idea on to Bernoulli” (Hacking 1975, 149). On the peculiar way in which both Bernoulli and Lambert kept in view nonadditive notions of probability, see Shafer (1978).
- 21.
“Superest methodus investigandi per inductionem, sed cum omnia percurrere nequeamus, artis est eligere præ cæteris examinanda, et hoc jam reducitur ad Analogiam; et in eo consistit tota ars experimentorum” (A VI, 3, 425).
- 22.
“Sed simpliciter experimenta quaerere dato subjecto, hoc faciendum est, ope jam cognitorum experimentorum per analogiam” (A VI, 3, 425).
- 23.
“Ars faciendi Hypotheses, sive Ars conjectandi diversi generis est, huc pertinet ars explicandi Cryptographemata, quae pro maximo haberi debet specimine artis conjectandi purae et a materia abstractae, unde regulae duci possunt quas postea etiam materiae applicare liceat” (A VI, 3, 426).
- 24.
In the terms of Aristotelian tradition, upon which Leibniz so often relies, it is a matter of dialectical reasoning, instead of demonstrative. Conclusions are not necessary, in this case, but probable, basing on, so to say, inconclusive inferences. The distinction is also presented as one “between examination of matters of necessity and examination of contingencies” (Jardine 1991, 118).
- 25.
“A gifted mind ignorant of the doctrine of chances but able to apprehend the fact that evidence and causation are in different categories could perfectly well start measuring epistemic probability. The proof of this is that Leibniz did” (Hacking 1975, 85).
- 26.
“Reasons are either proofs, or presumptions, or semi-proofs (semiprobationes) or probabilities” (A VI, 4, 2167; Dascal 2007, 53).
- 27.
Marcelo Dascal has pointed to Leibniz’s frequent use of the word “balance” and its synonyms (Dascal 2008, 68–69).
- 28.
May I refer on this to Pasini (2016).
- 29.
One must agree at least with the second part of this comment: “By ‘a kind of logic’, Leibniz means a calculus of probabilities, whose development he foresaw with his usual prescience. […] Yet once again, Leibniz overstates the virtues of formalization and its role in practical deliberation” (Grosholz 2008, 176).
- 30.
To circumvent this problem, some interpreters have invested in what Hacking (1975, 138) called “the probability-possibility-facility-creatability nexus,” which is a rather weak solution, at least because it seems to impose either epistemic or practical limitations on the Creator, or to misread important Leibnizian texts (as, e.g.,., in Krüger 1981).
- 31.
This allows him to negate any special role of the “opinion of weighty authorities,” which can contribute to the likelihood of an opinion, but “does not produce the entire likelihood by itself” (NE IV, 2, 14; RB, 373) as regards the nature of things. For instance, Copernicanism was decidedly likely even when Copernicus was isolated in his opinion.
- 32.
- 33.
“I have been assured that a lady at a well-known court saw in a dream the man she later married and the room where the betrothal took place, and she described these to her friends, all before she had seen or known either the man or the place. This was attributed to some secret presentiment or other; but chance could produce such a result since it happens rather rarely; and in any case the images in dreams are a little hazy, which gives one more freedom in subsequently relating them with other images” (NE IV, 11, §11; RB, 445).
- 34.
“Kansse oder expectative hollandisch, puto esse ex Gallico chance germanice exprimerem Schanße, wie man sagt die schanße verlieren oder verscherzen” (A IV, 6, 705).
- 35.
A pioneer of the study of lotteries, Gataker, admitted that the word “chance” could by some be “utterly condemned, and held foolish and heathenish,” yet it was a term “according to the iust analogie and proportion of Tongues and Languages, used by the Holy Ghost himselfe in Gods booke both in the Old and New Testament” (Gataker 1627, 9–10). On him see Daston (1988, 155).
- 36.
As it is hinted at by, for example, this passage: “The question of how inevitable a result is, is heterogeneous from—i.e., cannot be compared with—the question of how good or bad it is. […] The fact is that in this as in other assessments which are disparate, heterogeneous, having more than one dimension (so to speak), the magnitude of the thing in question is made up proportionately out [en raison composée] of two estimates […] As for the inevitability [grandeur] of the result, and degrees of probability, we do not yet possess that branch of logic which would let them be estimated” (NE II, 21, § 67; RB, 206–7).
- 37.
Leibniz to Jacob Bernoulli, December 3, 1703: “Difficultas in eo mihi inesse 84 videtur, quod contingentia seu quae ab infinitis pendent circumstantiis, per finita experimenta determinari non possunt […] quis dicet, an sequens experimentum non discessurum sit nonihil a lege omnium praecedentium? ob ipsas rerum mutabilitates. Novi morbi inundant subinde humanum genus” (GM 3, 83–84).
- 38.
“That is why geometers have always held that what is proved by induction or by example in geometry or in arithmetic is never perfectly proved”; even “if one tried a hundred thousand times, […] one can never be absolutely certain of this unless one learned the demonstrative reason for it, something mathematicians discovered long ago. […] In fact, there are experiments that succeed countless times, and ordinarily succeed, yet in some extraordinary cases we find that there are instances where the experiment does not succeed” (GP 6, 504–5; AG, 190).
- 39.
This idea (that depends much on the definition of a “regular” line) returns often in Leibniz’s writings, together with the optimistic notion that all curves can have an analytical expression: see, for example, §6 of the Discours de métaphysique (A VI, 4, 1537–1538).
- 40.
“Datis quotcunque punctis inveniri possunt lineae infinitae per ipsa transientes. Quod sic demonstro: Postulo (quod demonstrari potest) datis quotcunque punctis inveniri posse lineam aliquam regularem, per ipsa transeuntem. Inventa illa esse ponatur et sit A. Sumatur jam aliud punctum inter data, sed extra hanc lineam; et per puncta initio data et punctum novum transeat linea, quod fieri potest per idem postulatum: hanc necesse est esse diversam a priori, at tamen per eadem transire puncta data, per quae prior. Et cum punctum infinities variari possit, etiam aliae atque aliae in infinitum lineae erunt possibiles. His autem punctis comparari possunt casus observati et lineae regulari regulae seu aestimationes ex casibus ducendae” (GM 3, 84).
- 41.
“Utilissima est aestimatio probabilitatum, quanquam in exemplis juridicis politicisque plerumque non tam subtili calculo opus est, quam accurata omnium circumstantiarum enumeratione” (GM 3, 83).
- 42.
“Quod Doctrina de probabilitatibus aestimandis in materiis juridicis non sola circumstantiarum enumeratione, sed eodem illo ratiocinio et calculo indigeat, quo alias in sortibus aleatorum comparandis uti solemus, docent me variae quaestiones de Assicurationibus, de Reditibus ad vitam, de Pactis dotalibus, de Praesumtionibus, aliaeque” (GM 3, 87).
- 43.
“Quod si nunc loco urnae substituas corpus humanum senis aut juvenis, quod fomitem morborum in se velut urna calculos continet, poteris eodem modo determinare per observationes, quanto ille quam iste morti sit vicinior” (GM 3, 88).
- 44.
“Rationem inter numeros morborum etsi infinitos determinare possumus finitis experimentis non praecise, sed quantum ad praxin sufficit accedendo subinde propius donec error insensibilis fiat” (GM 3, 91).
- 45.
See nonetheless McClaughlin (1996) for an investigation of French Cartesian empiricism.
- 46.
- 47.
On the historical development of the doctrine of apocatastasis from its Stoic origins to Christian adaptations see Ramelli 2013. Bernoulli (1713, 53; 2006, 177) had also been using the term in a weaker sense, for the return of the lots to their original states in a game continued for long enough (apocatastasis sortium).
- 48.
There is some Origenism in the background of these discussions, that saw Leibniz debate with people like Petersen and Overbeck on the theme of universal renovation and salvation; see Costa 2014.
- 49.
It is in reality a self-reply to a concern he expressed in the preceding paragraph: “So if the same experiment is taken to have been repeated infinitely, it is clearly right (omni iure licet) to consider the mean among all to not differ from the truth. This is apart from defects of instruments” (Lambert 1760, §279; 2001, 96).
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Pasini, E. (2019). Ars experimentandi et conjectandi. Laws of Nature, Material Objects, and Contingent Circumstances. In: Omodeo, P.D., Garau, R. (eds) Contingency and Natural Order in Early Modern Science. Boston Studies in the Philosophy and History of Science, vol 332. Springer, Cham. https://doi.org/10.1007/978-3-319-67378-3_15
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