Abstract
This paper aims to advance two claims. First, it aims to show that Hume’s argument against the rationality of induction is sound. However, I claim that the conclusion does not follow merely from the self-defeating attempts to justify the rule of induction, unlike traditional readings of the argument. Rather, the skeptical conclusion must also take into account Hume’s argument that the secret powers that are present in bodies and give rise to sensible qualities are unknowable. The paper’s second aim is to show that Newtonian induction escapes Hume’s secret powers argument, given that it includes a transductive inference, from observable phenomena to the powers present in the ultimate parts of matter. Consequently Hume’s argument against the rationality of induction does not demonstrate the non-rational nature of Newtonian induction.
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Notes
E refers to (Hume 1975) and SBN refers to Hume (1978). Quotes taken from https://davidhume.org/.
For Hume the inseparability of ideas is the foundation for demonstrative reasoning: “In order therefore to know, whether abstraction implies a separation, we need only consider it in this view, and examine, whether all the circumstances, which we abstract from in our general ideas, be such as are distinguishable and different from those, which we retain as essential parts of them” (T 1.1.7.3, SBN 18-9). See also De Pierris (2015, Section 2.2).
T refers to the original edition of the Treatise, Hume (1978). Quotes taken from https://davidhume.org.
Commentators sometimes object to Hume’s argument by claiming that turning to the PUN to support the RI amounts to the demand that the RI be turned into a deductive argument. That is, they claim that Hume commits himself to a deductivist conception of justification. However, it seems to me that this charge is misguided. One might say that introducing the PUN merely amounts to claiming that inductive inferences are reliable–that is, that they are likely to produce true results. See Millican (1995, 108) for a similar rebuttal.
See also De Pierris (2015, 2.4).
See Otero Perez (2008) for a similar use of Carroll’s paradox as an analogy for inductive justification.
I thank one of the reviewers for referring me to Hanna’s succinct treatment of the logocentric predicament.
Lange (2008, Section 5) also mentions externalist means or taking a naturalist approach towards epistemology to justify inductive schemes of inference (e.g., Van Cleve (1984) and Otero Perez (2008)). If we presume that there are external reasons or causes that show that RI is reliable, the rule circularity involved in the justification of induction is not a vicious epistemic circularity.
Schliesser (2017) in a blog post discusses the role of the SPA in Hume’s argument against induction. Schliesser places Hume’s argument in relation to the explanatory models of Early Modern philosophy, where essences, inherent natures, or active principles are taken to be the origin of the effects of natural bodies on other bodies. Thus we may think of Hume’s argument as undermining the explanatory ideals of 17th- and 18th-century science.
Although Hume’s account of the inductive method appears to align with Francis Bacon’s account of induction, it seems as if Bacon’s thinking about induction is much more embedded in matter theory than most commentators realize. Bacon argues that observations and experiments are designed to find the connection between forms and natures. Bacon’s notion of nature mostly correlates with a simple sensible quality. However, the notion of form seems to relate to those active principles in corpuscles that give rise to changes in corpuscular forms. Thus, forms are not necessarily sensible qualities; they may exist below the realm of observable qualities. Moreover, while Bacon argues that observations and experiments ought to reveal that certain forms are necessary and sufficient for certain natures, he does not imagine this connection to be that of a cause-effect relation, but rather thinks of it as an identity relation between an unobservable corpuscular arrangement and observable qualities. An example would be the correlation between corpuscular motions and heat. Thus it is not clear that Hume’s argument undermines even Baconian induction. I elaborate on this reading of Bacon in (Unnatural Acts: The Transition from Natural Principles to Laws of Nature in Early Modern Science, unpublished).
Based on their interpretation of Rule IV for the Study of Natural Philosophy, Ducheyne (2012), [82 n. 151, n. 152] and Walsh (2017) think that Newton takes his conclusions in the Principia to carry certainty, undermining those commentators who take Newton as thinking of his scientific theories as probable at best. According to Ducheyne and Walsh, perhaps Newton takes mathematics to be so central to his analysis of phenomena as to render his arguments non-ampliative or purely demonstrative. This claim takes its cue from the proper translation of the Latin text of Rule IV. The text is usually translated as saying that the results of inductive inferences should be taken as “either exactly or very nearly true”. But the proper translation, according to Ducheyne, should be “either exactly or as most closely as possible true”. This opens the possibility that Newton takes his theory to be certain and, if any corrections are required because of future observations, that the theory be made to cover a smaller scope or made less general rather than be corrected. Contrary to Ducheyne and Walsh, I think that, even with the translation corrected, the correct interpretation is that his results can be approximations to the true descriptions or are only probably true.
The Area Law states that the radius to the satellite from a central body covers equal areas in equal periods of time.
According to Kepler’s Harmonic Rule the period of completing satellite’s orbit is proportional to the mean radius to the power of 3/2, or t2 ? R3.
See Ducheyne (2005) for this reading of Newton’s method.
In the explication of the definition of Quantity of Matter, Newton says, “For the present, I am not taking into account any medium, if there should be any, freely pervading the interstices between the parts of bodies. Furthermore, I mean this quantity whenever I use the term “body” or “mass” in the following pages. It can always be known from a body’s weight, for – by making very accurate experiments with pendulums - I have found it to be proportioned to the weight, as will be shown below” (Newton 1999, 404).
It is plausible to assume that, initially, by “body” Newton means whatever it is that can generate sensory impressions on the human mind. The notion of body is that which can be manipulated in experiments or influenced so as to generate sense-impressions on the human mind, whether by direct or indirect means. This notion is confirmed by a little creation story that Newton articulates in the De Grav. In this story, Newton imagines God creates bodies by rendering certain regions of space impenetrable. He also imagines that God allows those impenetrable regions to move about, colliding and interacting according to the laws of motion dictated by God. Newton argues in the De Grav that we can take these impenetrable regions to be bodies, as long as they meet certain conditions: “(1) that they be mobile… (2) that two of this kind cannot coincide anywhere, that is, that they may be impenetrable… and (3) that they can excite various perceptions of the senses and the imagination in created minds, and conversely be moved by them” (Newton 2004, 28–29). Given that Newton takes both mobility and impenetrability to be shown as universal by Rule III, the only a priori notion of body that is left takes a body to be that which can generate perceptions in created minds.
A discussion of criteria and principles of individuation is beyond the scope the paper, which Brading takes to be relevant to the problem that is solved by taking laws to be constitutive of the notion of body. I may add that in Newton’s thinking, laws of nature are constitutive of the notion of action. The individuation of action requires both laws of nature and the notions of absolute space and time. He then takes bodies to be defined by the types of actions that they generate. So laws of nature are constitutive of bodies, but only indirectly, via their constitution of actions. Moreover, the notions of impenetrability and mobility, and centripetal forces, are epistemically crucial in individuating bodies and the qualities that can be attributed to them. But we should also recognize that, while all laws of nature are constitutive of the notion of bodies, not all laws are essential in articulating criteria or principles of individuation.
Achinstein (2010) argues, for example, that there are non-formal aspects of Newton’s induction that must be taken into account to understand the nature of Newtonian induction. But he does not explain the relation between the non-formal aspects and the transductive inference.
In a recent paper, Biener and Schliesser (2017) argue that there is a tension between the universality claimed by Rule III for laws of nature and a certain passage in Query 31 of the English edition of the Opticks. In the passage, Newton claimed that God could have varied the sizes, shapes, densities, and forces of particles, which would as a result vary the laws of nature, and created different kinds of worlds governed by distinct laws. Biener and Schliesser claim that this suggests that laws of nature are contingent for Newton and dependent solely on God’s will. It seems as if this suggestion undermines the universality insisted on in Rule III. Biener and Schliesser resolve the tension by differentiating between the context of constructing a natural philosophy versus a metaphysical context. For the purpose of grounding a science of our world, Rule III implies that certain qualities and laws are universal. The metaphysical context is one where the modality of laws of nature is explored and their contingent nature articulated. This reading seems plausible, except that it is not clear what Newton means by different worlds that exist in different regions of space – what then are the criteria by which a world is isolated or insulated from other worlds? Is there a principled way in which a particle of one world is screened off from entering another world? The law of inertia implies, at least, that particles in our world, if they are able to get detached from the attractive forces in our world, will eventually be able to penetrate any world in any direction in space. It seems to me that the suggestion in Query 31 is simply incoherent. There is no way to correlate between “worlds” and laws of nature that inhabit these worlds, unless these worlds are somehow metaphysically isolated. However, Newton did not provide any criteria for isolating or individuating worlds. It is odd that Newton would genuinely think that the universality of laws of nature could somehow be limited to particular regions of the universe.
I thank one of the reviewers for pointing out this possibility.
The relationship between Hume and Newton is complex. On the one hand, Hume describes himself in the Treatise as someone who is carrying out a Newtonian style investigation of the human mind. On the other hand, he is critical of core aspects of the Newtonian project, including the nature of absolute space and time, the reality of forces, and the universality of laws. See Schliesser (2007), De Pierris (2012), Hazony and Schliesser (2016), and Slavov (2016) for an assessment of the relation between Newton and Hume.
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This article belongs to the Topical Collection: EPSA17: Selected papers from the biannual conference in Exeter
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Belkind, O. In defense of Newtonian induction: Hume’s problem of induction and the universalization of primary qualities. Euro Jnl Phil Sci 9, 14 (2019). https://doi.org/10.1007/s13194-018-0241-5
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DOI: https://doi.org/10.1007/s13194-018-0241-5