Newton’s 4th Rule for Natural Philosophy
Kirsten Walsh writes…
In book three of the 3rd edition of Principia, Newton added a fourth rule for the study of natural philosophy:
- In experimental philosophy, propositions gathered from phenomena by induction should be considered either exactly or very nearly true notwithstanding any contrary hypotheses, until yet other phenomena make such propositions either more exact or liable to exceptions.
- This rule should be followed so that arguments based on induction be not be nullified by hypotheses.
Arguably this is the most important of Newton’s four rules, and it certainly sparked a lot of discussion at our departmental seminar last week. Let us see what insights we can glean from it.
Rule 4 breaks down neatly into three parts. I shall address each part in turn.
1. Propositions (acquired from the phenomena by induction) should be regarded as true or very nearly true.
While the term ‘phenomenon’ usually refers to a single occurrence or fact, Newton uses the term to refer to a generalisation from observed physical properties. For example, Phenomenon 1, Book 3:
- The circumjovial planets [or satellites of Jupiter], by radii drawn to the centre of Jupiter; describe areas proportional to the times, and their periodic times – the fixed stars being at rest – are as the 3/2 powers of their distances from that centre.
- This is established from astronomical observations…
Newton uses the term ‘proposition’ in a mathematical sense to mean a formal statement of a theorem or an operation to be completed. Thus, he further identifies propositions as either theorems or problems. Propositions are distinguished from axioms in that propositions are not self-evident. Rather, they are deduced from phenomena (with the help of definitions and axioms) and are demonstrated by experiment. For example, Proposition 1, Theorem 1, Book 3:
- The forces by which the circumjovial planets [or satellites of Jupiter] are continually drawn away from rectilinear motions and are maintained in their respective orbits are directed to the centre of Jupiter and are inversely as the squares of the distances of their places from that centre.
- The first part of the proposition is evident from phen. 1 and from prop. 2 or prop. 3 of book 1, and the second part from phen. 1 and from corol. 6 to prop. 4 of book 1.
Newton appears to be using ‘induction’ in a very loose sense to mean any kind of argument that goes beyond what is stated in the premises. As I noted above, his phenomena are generalisations from a limited number of observed cases, so his natural philosophical reasoning is inductive from the bottom up. Newton recognises that this necessary inductive step introduces the same uncertainty that accompanies any inductive generalisation: the possibility that there is a refuting instance that hasn’t been observed yet.
Despite this necessary uncertainty, in the absence of refuting instances, Newton tells us to regard these propositions as true or very nearly true. It is important to note that he is not telling us that these propositions are true, simply that we should act as though they are. Newton is simply saying that if our best theory fits the available data, then we should regard it as true until proven otherwise.
2. Hypotheses cannot refute or alter those propositions.
In a previous post I argued that, in his early optical papers, Newton was working with a clear distinction between theory and hypothesis. In Principia Newton is working with a similar distinction between propositions and hypotheses. Propositions make claims about observable, measurable physical properties, whereas hypotheses make claims about unobservable, unmeasurable causes or natures of things. Thus, propositions are on epistemically surer footing than hypotheses, because they are grounded on what we can directly experience. When faced with a disagreement between a hypothesis and a proposition, we should modify the hypothesis to fit the proposition, and not vice versa. Newton explains this idea in a letter to Cotes:
- But to admitt of such Hypotheses in opposition to rational Propositions founded upon Phaenomena by Induction is to destroy all arguments taken from Phaenomena by Induction & all Principles founded upon such arguments.
3. New phenomena may refute those propositions by contradicting them, or alter those propositions by making them more precise.
This final point highlights the a posteriori justification of Newton’s theories. In Principia, two methods of testing can be seen. The first involves straightforward prediction-testing. The second is a more sophisticated method, which involves accounting for discrepancies between ideal and actual motions by a series of steps that increase the complexity of the model.
In short, Rule 4 tells us to prioritise propositions over hypotheses, and experiment over speculation. These are familiar and enduring themes in Newton’s work, which reflect his commitment to experimental philosophy. Rule 4 echoes the remarks made by Newton in a letter to Oldenburg almost 54 years earlier, when he wrote:
- …I could wish all objections were suspended, taken from Hypotheses or any other Heads then these two; Of showing the insufficiency of experiments to determin these Queries or prove any other parts of my Theory, by assigning the flaws & defects in my Conclusions drawn from them; Or of producing other Experiments wch directly contradict me…
From Experimental Philosophy to Empiricism: 20 Theses for Discussion
Before our recent symposium, we decided to imitate our early modern heroes by preparing a set of queries or articles of inquiry. They are a list of 20 claims that we are sharing with you below. They summarize what we take to be our main claims and findings so far in our study of early modern experimental philosophy and the genesis of empiricism.
After many posts on rather specific points, hopefully our 20 theses will give you an idea of the big picture within which all the topics we blog about fit together, from Baconian natural histories and optical experiments to moral inquiries or long-forgotten historians of philosophy.
Most importantly, we’d love to hear your thoughts! Do you find any of our claims unconvincing, inaccurate, or plainly wrong? Do let us know in the comments!
Is there some important piece of evidence that you’d like to point our attention to? Please get in touch!
Are you working on any of these areas and you’d like to share your thoughts? We’d like to hear from you (our contacts are listed here).
Would you like to know more on some of our 20 claims? Please tell us, we might write a post on that (or see if there’s anything hidden in the archives that may satisfy your curiosity).
Here are our articles, divided into six handy categories:
General
1. The distinction between experimental and speculative philosophy (ESD) provided the most widespread terms of reference for philosophy from the 1660s until Kant.
2. The ESD emerged in England in the late 1650s, and while a practical/speculative distinction in philosophy can be traced back to Aristotle, the ESD cannot be found in the late Renaissance or the early seventeenth century.
3. The main way in which the experimental philosophy was practised from the 1660s until the 1690s was according to the Baconian method of natural history.
4. The Baconian method of natural history fell into serious decline in the 1690s and is all but absent in the eighteenth century. The Baconian method of natural history was superseded by an approach to natural philosophy that emulated Newton’s mathematical experimental philosophy.
Newton
5. The ESD is operative in Newton’s early optical papers.
6. In his early optical papers, Newton’s use of queries represents both a Baconian influence and (conversely) a break with Baconian experimental philosophy.
7. While Newton’s anti-hypothetical stance was typical of Fellows of the early Royal Society and consistent with their methodology, his mathematisation of optics and claims to absolute certainty were not.
8. The development of Newton’s method from 1672 to 1687 appears to display a shift in emphasis from experiment to mathematics.
Scotland
9. Unlike natural philosophy, where a Baconian methodology was supplanted by a Newtonian one, moral philosophers borrowed their methods from both traditions. This is revealed in the range of different approaches to moral philosophy in the Scottish Enlightenment, approaches that were all unified under the banner of experimental philosophy.
10. Two distinctive features of the texts on moral philosophy in the Scottish Enlightenment are: first, the appeal to the experimental method; and second, the explicit rejection of conjectures and unfounded hypotheses.
11. Experimental philosophy provided learned societies (like the Aberdeen Philosophical Society and the Philosophical Society of Edinburgh) with an approach to knowledge that placed an emphasis on the practical outcomes of science.
France
12. The ESD is prominent in the methodological writings of the French philosophes associated with Diderot’s Encyclopédie project, including the writings of Condillac, d’Alembert, Helvétius and Diderot himself.
Germany
13. German philosophers in the first decades of the eighteenth century knew the main works of British experimental philosophers, including Boyle, Hooke, other members of the Royal Society, Locke, Newton, and the Newtonians.
14. Christian Wolff emphasized the importance of experiments and placed limitations on the use of hypotheses. Yet unlike British experimental philosophers, Wolff held that data collection and theory building are simultaneous and interdependent and he stressed the importance of a priori principles for natural philosophy.
15. Most German philosophers between 1770 and 1790 regarded themselves as experimental philosophers (in their terms, “observational philosophers”). They regarded experimental philosophy as a tradition initiated by Bacon, extended to the study of the mind by Locke, and developed by Hume and Reid.
16. Friends and foes of Kantian and post-Kantian philosophies in the 1780s and 1790s saw them as examples of speculative philosophy, in competition with the experimental tradition.
From Experimental Philosophy to Empiricism
17. Kant coined the now-standard epistemological definitions of empiricism and rationalism, but he did not regard them as purely epistemological positions. He saw them as comprehensive philosophical options, with a core rooted in epistemology and philosophy of mind and consequences for natural philosophy, metaphysics, and ethics.
18. Karl Leonhard Reinhold was the first philosopher to outline a schema for the interpretation of early modern philosophy based (a) on the opposition between Lockean empiricism (leading to Humean scepticism) and Leibnizian rationalism, and (b) Kant’s Critical synthesis of empiricism and rationalism.
19. Wilhelm Gottlieb Tennemann was the first historian to craft a detailed, historically accurate, and methodologically sophisticated history of early modern philosophy based on Reinhold’s schema. [Possibly with the exception of Johann Gottlieb Buhle.]
20. Tennemann’s direct and indirect influence is partially responsible for the popularity of the standard narratives of early modern philosophy based on the conflict between empiricism and rationalism.
That’s it for now. Come back next Monday for Gideon Manning‘s comments on the origins of the experimental-speculative distinction.
Should we call Newton a ‘Structural Realist’?
Kirsten Walsh writes…
At our symposium last week, someone wondered if we can characterise Newton as a ‘structural realist’. It is certainly anachronistic to attempt to interpret Newton’s epistemic stance in light of the present-day scientific realism debate. But the sin of anachronism may be forgiven, if it advances our understanding. So let us see what advantages this interpretation may provide.
Briefly, structural realism is the view that epistemically, a scientist should only commit herself to the mathematical or structural content of her theories, and remain sceptical about the unobservable entities posited by those theories.
To characterise Newton as a structural realist, one might make the following argument:
- P1. Newton is a realist about his theories, but not about his hypotheses.
P2. Newton’s theories make claims about theoretical structures, whereas his hypotheses make claims about unobservable theoretical entities.
C. Therefore, Newton is a realist about theoretical structures, but not about unobservable theoretical entities.
Firstly, consider Newton’s hypothesis/theory distinction. In a previous post I argued that Newton claims that his doctrine of light and colours is a theory, not a hypothesis, for three reasons:
- T1. It is certainly true, because it is supported by (or deduced from) experiment;
T2. It concerns the physical properties of light, rather than the nature of light; and
T3. It has testable consequences.
In contrast, he attaches no special epistemic merit to his corpuscular hypothesis because:
- H1. It is not certainly true, because it is not supported by experiment;
H2. It concerns the nature of light; and
H3. It has no testable consequences.
T1 and H1 support P1. They tell us that Newton is a realist about theories because they can be shown to be true on the basis of experiment. Moreover, he is not a realist about hypotheses because they cannot be shown to be true on the basis of experiment. This highlights an important feature of Newton’s methodology: Newton is only epistemically committed to those things that are demonstrated experimentally.
T2 and H2 appear to support P2, but only if the ‘entity/structure’ distinction maps onto Newton’s ‘nature/physical properties’ distinction. Prima facie, it does. While Newton probably wouldn’t have been comfortable with the entity/structure distinction, the structural realist debate is often framed in terms of the nature/physical properties distinction. For example, here’s how the Stanford Encyclopedia of Philosophy describes the structural realist position:
- Structural realism is often characterised as the view that scientific theories tell us only about the form or structure of the unobservable world and not about its nature. This leaves open the question as to whether the natures of things are posited to be unknowable for some reason or eliminated altogether.
So it looks like the argument for characterising Newton as a structural realist is well-supported by Newton’s distinction between theory and hypothesis. But what do we gain by characterising Newton in this way?
Chris Smeenk recently pointed out to me in an email that the structural realist label identifies a distinctive feature of Newton’s methodology. Namely, that he is epistemically committed to his abstract mathematical structures. He is not an instrumentalist about his theories, but neither is he a realist about the nature of the phenomena they describe. This might shed some light on the optical debate of the early 1670s, for unlike his contemporaries, Newton does not think there is a contradiction in believing that his theory of light is true, while not committing himself to any particular doctrine regarding the nature of light.
Is this a large enough pay-off to warrant the offence of anachronism? What do you think?
In this brief post, I have only considered Newton’s attitudes to his own theories. There are other questions to be raised in connection with structural realism, for example, is Newton a structural realist about the history of science? In other words, what is Newton’s epistemic commitment to the theories of his predecessors? I shall leave this question for another time.
On another note, we were very pleased with how last week’s symposium went. We look forward to telling you all about it next Monday.
Newton’s Early Queries are not Hypotheses
Kirsten Walsh writes…
In an earlier post I demonstrated that, in his early optical papers, Newton is working with a clear distinction between theory and hypothesis. Newton takes a strong anti-hypothetical stance, giving theories higher epistemic status than hypotheses. Newton’s corpuscular hypothesis appears to challenge his commitment to this anti-hypothetical position. Today I will discuss a second challenge to this anti-hypotheticalism: Newton’s use of queries.
Newton’s queries have often been interpreted as hypotheses-in-disguise. But in his early optical papers, Newton’s queries are not hypotheses. In fact, he is building on the method of queries prescribed by Francis Bacon, for whom assembling queries is a specific step in the acquisition and development of natural philosophical knowledge.
To begin, what is Newton’s method of queries? In a letter to Oldenburg, Newton explains that
- “the proper Method for inquiring after the properties of things is to deduce them from Experiments.”
Having obtained a theory in this way, one should proceed as follows: (1) specify queries that suggest experiments that will test the theory; and (2) carry out those experiments.
He then lists eight queries relating to his theory of light and colours, e.g.:
- “4. Whether the colour of any sort of rays apart may be changed by refraction?
“5. Whether colours by coalescing do really change one another to produce a new colour, or produce it by mixing onely?”
He ends the letter, saying:
- “To determin by experiments these & such like Queries which involve the propounded Theory seemes the most proper & direct way to a conclusion. And therefore I could wish all objections were suspended, taken from Hypotheses or any other Heads than these two; Of showing the insufficiency of experiments to determin these Queries or prove any other parts of my Theory, by assigning the flaws & defects in my Conclusions drawn from them; Or of producing other Experiments which directly contradict me, if any such may seem to occur. For if the Experiments, which I urge be defective it cannot be difficult to show the defects, but if valid, then by proving the Theory they must render all other Objections invalid.”
While Newton’s method of queries is experimental, it does not appear to be strictly Baconian. For the Baconian-experimental philosopher, queries serve “to provoke and stimulate further inquiry”. Thus, for the Baconian-experimental philosopher, queries are part of the process of discovery. However, for Newton, queries serve to test the theory and to answer criticisms. Thus, they are part of the process of justification.
Newton uses queries to identify points of difference between his theory and its opponents. For example, in a letter to Hooke he writes:
- “I shall now in the last place proceed to abstract the difficulties involved in Mr Hooks discourse, & without having regard to any Hypothesis consider them in general termes. And they may be reduced to these three Queries. [1] Whether the unequal refractions made without respect to any inequality of incidence, be caused by the different refrangibility of several rays, or by the splitting breaking or dissipating the same ray into diverging parts; [2] Whether there be more then two sorts of colours; & [3] whether whitenesse be a mixture of all colours.”
And in a letter to Huygens, Newton says:
- “Meane time since M. Hu[y]gens seems to allow that white is a composition of two colours at least if not of more; give me leave to rejoyn these Quæres.
“1. Whether the whiteness of the suns light be compounded of the like colours?
“2. Whether the colours that emerg by refracting that light be those component colours separated by the different refrangibility of the rays in which they inhere?”
In both cases, Newton is using queries to steer the debate towards claims that can be tested and resolved by experiment. On both occasions, Newton devotes a considerable amount of space to discussing the experiments that might determine these queries.
These early queries are not hypotheses. Rather, they are empirical questions that may be resolved by experiment. This is not merely a matter of semantics. In the same letter to Hooke, Newton demonstrates this by distinguishing between philosophical queries and hypothetical queries. A philosophical query is one that can be determined by experiment, a hypothetical query cannot. Newton argues that philosophical queries are the only acceptable queries. He equates hypothetical queries with begging the question.
In his later work, Newton’s queries become increasingly speculative, suggesting that they function as de facto hypotheses. Does Newton ultimately reject his early ‘method of queries’?
Next Monday we’ll have a guest post from Greg Dawes on Galileo and the Experimental Philosophy.
