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Tag Archives: natural philosophy

Astrology and the novatores, part 3

Juan Gomez writes…

This is the final post on my first series on the debate between scholastics and novatores in early modern Spain. In the first post of the series I introduced two figures who had a heated debate concerning the status of astrology: Martin Martinez representing the novatores, and Diego de Torres Villaroel defending the scholastics. We saw that Martinez calls for a ban on astrology on methodological grounds. He criticizes those scholastics (specifically Villaroel) who rely on astrology for writing only from their imagination with no regard for observation and experiment.

In the second post of the series we looked at Martinez’s arguments in more detail. We focused on his rejection of the application of astrology in natural philosophy. His attack revolves around the claim that the astrologers explain natural phenomena by referring to obscure causes where the phenomena in question are clearly accounted for by referring to evident causes. He shows that in medicine and natural philosophy there is no need to consult the stars.  Villaroel was offended by this attack on astrology and promptly published his reply, Entierro del Juicio Final, y vivificacion de la astrologia (Burial of the Final Judgment, and revitalization of astrology).  Juicio Final was the title of Martinez’s attack, and in today’s post we will examine Villaroel’s attempt to bury it.

Villaroel sets out to respond to Martinez’s criticisms and show that astrology in fact is useful for our natural, moral, and political inquiries.  We saw Martinez complain about the practice of placing celestial bodies as the causes of natural effects, in particular when it comes to explaining the ailments of the human body. Surprisingly, Villaroel responds to this criticism by saying that these are not mere conjectures, but are actually founded on observation and experience:

That Astrologers assign to each body part its Planet, or its star Sign, is not as dissonant as the Doctor [Martinez] judges; since in fact the analogy and conformity between the temper of the planets, and the cold, dry, wet, and warm parts of the wind, are such qualities not by the devotion of Astrologers, nor by their words, but because God made them that way, giving each its temper and quality: observation and experience, the mother of knowledge (which Martin lacks), has taught us so, as it taught our Masters; if not, let’s ask the Doctor: why is chicory cold? I believe he will answer, because God made it so, and gave it such quality. And I would ask further: has God told you which quality it has? No sir, he will answer (he is not so holy as to have revelations), experience has taught it to me and so have all Medical Authors. Well we astrologers say the same about the qualities of the Planets and Stars.

Despite Villaroel’s insistence that it is through experience and observation that astrologers know the qualities of the planets and their effect on the human body, there is no reference at all to an observation account to support the claim. Instead, Villaroel blames Martinez for not properly studying the work of the authors cited by astrologers (traditional scholastic figures, such as Aquinas and Galen), and so his ignorance leads him to his unfounded criticism.

In fact, it is this ignorance, Villaroel claims, that leads Martinez to think that astrologers refer to occult causes to explain natural phenomena:

I encountered then a Cartesian rascal, who told me with a hollow cough while stroking his beard: those influences you confer to the Stars are either occult qualities, which means you do not know if they exist, or they are evident qualities, and if so you are mistaken in not pointing them out. I replied to the Cartesian, identifying that his argument was as much of a cheat as him, and said: they are occult qualities to you, to Martin, and to all others who, not having studied them, ignore them completely, and because they appear occult to the ignorant, it does not follow that they do not exist, and they are evident qualities to those of us who have studied them, and we are not in error, since we point them out in our almanacs.

Villaroel insists on replying to the criticisms by pointing out Martinez’s supposed ignorance, and instead of supporting his argument with data, he focuses on quoting authors that recommend the study of astrology to insist that Martinez is not only ignorant, but also a terrible physician. Villaroel refers to passages from the work of Galen, Avicenna, and Hippocrates, where they all comment on the necessity of the study of astrology for the proper exercise of medicine. But other than the quotes, Villaroel’s claims are not backed up by observation and experience, despite his claims that such is the source of the astrologer’s knowledge.

This debate between Villaroel and Martinez has an interesting feature: it shows that there was more to the experimental/speculative divide than mere rhetoric. Both our authors use the rhetoric of the new philosophy, placing experience and observation as the only true source of knowledge; but while Martinez does refer to observational data to back up his explanations, Villaroel does not go beyond the authority of scholastic figures and their texts.  What we have here is a clear case of the two sides in the ESD, where the experimental methodology supported by Martinez is contrasted with the speculative ways of Villaroel. Stay tuned for further posts on the ESD in early modern Spain!!

Astrology and the novatores

Juan Gomez writes…

In one of my previous posts regarding early modern Spain I referred to Martin Martinez, a physician who was an avid promoter of the experimental method. Today I want to examine a debate he had regarding the rejection of astrology. In this blog we have provided many illustrations of the methodological statements typical of those who promoted and adopted experimental philosophy. We have shown the insistence in rejecting the work of those that rely solely on speculation, but we have not yet seen any examples of the work of speculative philosophers. The case of astrology in 1720s Spain can shed some light on the kind of speculative science rejected by experimental philosophers like Feijoo and Martinez.

Besides the comments he added supporting Feijoo’s work, Martinez wrote a whole essay (Juicio final de la astrologia (The final judgment of astrology)) rejecting astrology in 1727. He distinguished between astronomy and astrology: while in the former “the regular movement of the stars is observed…times are computed, lunar cycles determined, and eclipses are predicted”, in the latter astrologists “feign a volume (only intelligible to them) in the heavens where they find written mundane events, wars, famine, pests, shipwrecks, harvests, diseases, and all other fortunes of human life.”

In the comments he makes defending Feijoo’s work, Martinez clarifies that the problem with astrology is that it is not founded in observation and experience:

“Upon reflection, according to what reasoning, or experience, do the astrologists found their imagined influxes of the stars and planets? On what grounds do they know that Mars burns, and Saturn cools? They probably say, because Mars is red and Saturn grey: though according to this they should also say that carnations burn and quicklime cools; and if they say they experience heat coming from Mars, I do not understand how they know it comes from it, and not from another cause.”

Martinez goes on listing a number of claims astrologists make, in particular related to the effects the movement of the planets and stars, eclipses, and comets have on the health of individuals. But Martinez is directing his claims to one individual in particular, Diego de Torres Villaroel, a mathematician and astrologist who published yearly almanacs with predictions under the pseudonym “el gran Piscator de Salamanca”. Leaving the calendars aside, Torres also published an essay containing his ideas on the nature of the earth and the heavens. The text was first published in 1724 under the title Viaje fantastico del gran Piscator de Salamanca (The fantastic journey of the great Piscator of Salamanca), and then again in 1739 as Anatomia de todo lo visible e invisible (Anatomy of all that is visible and invisible). It is this book that Martinez targets, and will serve as our illustration of the kind of speculative philosophy the novatores rejected.

Torres’ essay gives an account of the structure and composition of the earth and the heavens, all this prompted by an eclipse which occurred on May 22, 1724. The explanation of the constitution of both spheres of the universe (heaven and earth) is given through a story where the great Piscator travels to the depths of the earth and then upwards to the heavens, illustrating to his fellow travellers all the details of both spheres. As is clear from various passages, Torres’ claims are never supported by observations, but only by the musings of his mind and astrological calculations. The opening lines of the dedicatory epistle highlight the speculative nature of the work:

piscator

“Hand over hand the soul, without resorting to the use of the external senses, and reason, in arms of a jobless idleness, let fantasy to its word, and running through the spaces of imagination it recited in their theatre the following story.”

Torres acknowledges that he writes from his imagination, but asserts that he reaches the same conclusions others (like Kepler, who studies “the cosmic machine”) have:

“With no other guide but my imagination, and sleeping like a log, I have completed the same journeys [as Kepler and Kircher].”

Although lines like the ones just quoted give the impression that Torres must be speaking metaphorically, it seems that his ‘discoveries’ had no other foundation that the inspiration he got from studying astrology. In the opening lines of the story, a character contrasts the method of astrologists like Torres to those who studied the eclipse by means of observation:

“How is it that you, Mr. Astrologist, in an eclipse whose nature and effects have excited the North and their less lazy Observers have been writing about, you do nothing other than note down in your Prediction the simple calculation of the time and the day?”

Torres defends himself, and convinces his companions to go on a journey through the earth and the heavens in order to understand the nature of eclipses and their effects on human events. In their journey through the earth the astrologist points out where hell and purgatory reside deep down where there is no influence of the heavenly bodies. Then they travel upwards to the heavens, where the astrologist explains the different levels, how all is made of ether, and its effects on the earth. He explains how when a comet is “of the nature of Saturn”, it “causes colds, leprosy, haemorrhoids, paralyses, and chronic diseases”; if it is dominated by Mars on the other hand, it causes “cruel dysentery, rotten fevers, delirium, haemorrhages…”

I could go on drawing on passages from Torres’ book, but the ones quoted above are enough to illustrate the opposition to astrology that the Spanish novatores insisted on. It is important to remember that figures like Feijoo and Martinez had a genuine worry regarding the influence of astrology. Unlike our present time, in the early decades of the eighteenth century astrology was still considered by many as a genuine science, and it was this (more than the almanacs) that motivated the novatores to call for a ban on astrology.

Scholasticism and natural science in early modern Spain

Juan Gomez writes…

One of the most exciting tasks of my research has been to track the introduction and reception of the ESD in early modern Spain. I have illustrated the adoption and praise of the spirit of experimental philosophy in various texts by the Spanish Novatores, and I looked in a bit more detail at the work of Benito Feijoo (posts 1, 2, and 3). In spite of the insistence to abandon scholastic and Aristotelian methods and science, the progress of natural philosophy in early modern Spain lagged in comparison to the rest of Europe. In fact, the Novatores themselves recognized this lack of progress, as is clear from a letter by Feijoo which I will be sharing with you today.

In 1745 Feijoo published a collection of letters, most of them responding to a range of criticisms directed against his Teatro Critico Universal. Letter 16 in the second volume of that collection is Causas del atraso que se padece en España en orden a las Ciencias Naturales (Causes for the backwardness of Spain regarding the Natural Sciences). Feijoo gives six reasons (causes) for this backwardness, in all of them placing the blame on the scholastic philosophers and their way of thinking.

The first cause is the narrowness of most of the teachers, whom Feijoo describes as “Everlasting ignorants, set on knowing only a few things, for no other reason that they think that there is nothing else to know, aside from those few things they know.” Feijoo goes on to describe this kind of teacher, who only knows scholastic logic and metaphysics, and laughs when hearing words like ‘new philosophy’ or ‘Descartes.’ However, when asked to explain the claims of the new philosophy or those held by Descartes, they stay silent because they have no knowledge of them. (Note: experimental philosophy and new philosophy are not identical, even though the former was sometimes referred to by the latter name. For example, Descartes was commonly regarded as a new philosopher, but not so much as an experimental philosopher.)

People like the teachers described above have spread throughout Spain a disdain for ‘the new’, the second cause identified by Feijoo. They think that, since every sacred doctrine labelled ‘new’ is rejected immediately for being suspicious, the same rule applies for theories about the natural world. So they must reject the teachings of Galileo, Huygens, and Harvey, as well as all the new instruments and machines developed in the seventeenth century, holding on to their scholastic and Aristotelian science as the one true system. Feijoo comments that this attitude backfires, since rejecting anything because it has been labelled ‘new’ entails that there could never have been any progress in natural science (the Aristotelian system was also ‘new’ at some point).

But aside from rejecting the new philosophy because it is ‘suspicious’, the Spanish scholastics also reject it because all it presents is “a few useless curiosities.” (This is the third cause given by Feijoo.) What the scholastics do not realize, Feijoo tells us, is that under this criterion their theories lose against those of the modern: “Which would be more useful: to explore in the physical world the works of the Author of Nature, or to investigate through large treatises derived from the Entity of Reason, and logical and metaphysical abstractions, the fictions of human understanding?” Feijoo also contrasts between the method of learning in the confines of the classroom of the scholastic, and that of the modern, based on experiments and observations.

The fourth cause rests on the mistaken notion held by the scholastics that the new philosophy is identical to Cartesian philosophy. Feijoo comments that although Cartesian philosophy might be new philosophy, new philosophy is not Cartesian philosophy, the same way men are animals but animals are not men. Highlighting the ESD, Feijoo goes on to divide philosophy into two kinds:

“Philosophy, taken in all its extension, can be divided into Systematic and Experimental. The Systematic has many different members, e.g. Pythagoric, Platonic, Peripatetic, Parascelsistic, or Chemical, that of Campanella, that of Descartes, that of Gassendi, etc.”

Feijoo clarifies that he advocates not that the Spaniards embrace one of the former systems, but rather that they do not close their eyes to “Experimental Physics”, which:

“without regard for any system, investigates the causes through the sensible effects; and where it cannot investigate the causes, it settles for the experimental knowledge of the effects… This is the physics that reigns in Nations: the one cultivated by many distinguished Academies as soon as it emerged in France, England, Holland, Etc.”

The achievements of this experimental physics are illustrated by the discoveries regarding our knowledge of the properties of air, of fluids and mechanics, all of them unattainable by relying on the physics of the schools.

Feijoo identifies as the last two causes the mistaken idea that the new philosophy clashes with religion, and the jealousy and pride of the scholastics in Spain that prevented them from accepting the triumphs of other men of science from different European nations. I will not examine them here. Instead I want to conclude the post by pointing out that, not only there is enough evidence to confirm the presence of the ESD (at least in some form) in early modern Spain, but also that it can provide us with an interesting framework to interpret the development of natural philosophy and science in early modern Spain.

Defining Early Modern Experimental Philosophy (2)

Alberto Vanzo writes…

In my last post, I raised the question as to whether there is any methodological view that was shared by all or most early modern experimental philosophers. To paraphrase Bas Van Fraassen, is there any statement E+ such that

    To endorse the method of (early modern) experimental philosophy = to believe that E+ (the experimentalists’ methodical dogma)?

As those of you who have followed this blog for a while will know, early modern experimental natural philosophers claimed that we should reject hypotheses and speculations (that is, roughly, natural-philosophical claims and theories) and rely instead on experiments and observations. In this post, I will discuss whether this claim, suitably understood, is the experimentalists’ methodical dogma. What does their rejection of hypotheses amount to?

The statement that we should reject hypotheses does not mean that we should avoid learning natural-philosophical claims and theories. On the contrary, according to Robert Hooke, learning hypotheses is beneficial because it helps us to devise new explanations and raise questions:

    the Mind will be somewhat more ready at guessing at the Solution of many Phenomena almost at first Sight, and thereby be much more prompt at making Queries, and at tracing the Subtilty of Nature, and in discovering and searching into the true Reason of things […]

Experimental philosophers also allow us to entertain claims and theories for the sake of testing them. Robert Boyle states in a letter to Oldenburg that natural histories should include “Circumstances” such that their “tryal or Observation” is “necessary or sufficient to prove or to invalidate this or that particular Hypothesis or Conjecture”.

Boyle’s statement makes clear that he allows for the acceptance of a natural-philosophical claims that are proven by “tryal [experiment] or Observation”. The claims in question must be those that are expressed by substantive or – in Kantian terms – synthetic a posteriori statements. Experiments and observations cannot prove analytic a priori statements. These are hardly the kind of statements that concerned experimental philosophers. Assuming that the analytic/synthetic distinction is tenable, accepting analytic a priori statements as true seems to be a harmless move anyway.

In the light of this, we may be tempted to paraphrase the rejection of hypotheses as follows:

    [A] Only commit to those substantive (as opposed to analytic) claims and theories that are warranted by experiments or observations.

[A] is in line with experimental philosophers’ rejection of arguments from authority, epitomized by the motto of the Royal Society: “nullius in verba“, which can be loosely translated as “take no man’s word for it”. [A] entails the rejection not only of arguments from authority, but also any kind of a priori arguments for substantive natural-philosophical claims – for instance, the arguments that Descartes used in the Principles of Philosophy to establish that material objects are made up of corpuscles. [A] has the welcome effect of classifying Descartes where, in my view, he belongs: outside of the movement of experimental philosophy, even though he too gathered natural-philosophical observations and performed some experiments.

However, [A] is inconsistent with the fact that many experimental philosophers were committed to substantive claims, like the corpuscularian and mechanist hypotheses, that were hardly warranted by the then extant empirical evidence. Boyle or Montanari did not seem to be concerned to provide detailed empirical arguments for corpuscularism or mechanism. However, they did not regard their acceptance of these views as being inconsistent with their commitment to experimentalism.

In view of this, I suggest replacing [A] with [B]:

    [B] Only firmly commit to those substantive claims and theories that are warranted by experiments and observations

and claiming that experimental philosophers like Boyle and Montanari did not firmly commit to corpuscularism and mechanism. They only weakly, tentatively, provisionally commit to these views, even though they were confident that future discoveries would dispel any doubt on their truth.

Is it correct to say that experimental philosophers’ commitments to mechanism and corpuscularism was typically weak, provisional, tentative? Are there other claims on the natural world that experimental philosophers firmly endorsed, even though the then available empirical evidence did not warrant them? Can a clear distinction between weak, provisional, tentative and strong, definitive, firm commitments be drawn, and if so, how? If you have any suggestions on how these questions should be answered, please let me know in the comments or get in touch. Answering these questions is important to establish if my suggestion that [B] represents a suitable candidate for the experimentalists’ methodical dogma is persuasive.

CFP: Aristotelian Natural Philosophy in the Early Modern Period

From Lucian Petrescu:

 

The Sarton Centre for History of Science and the Department of Philosophy and Moral Science, Ghent University announces a conference on

23-24 May 2013

with the theme

Aristotelian natural philosophy in the early modern period

Early modern philosophers liked to debate about Aristotle just as much as medieval scholars. They had different sources to fuel their discussions: from the humanist preoccupation with a pristine Aristotle and a purification of a corpus perceived as corrupted to the very medieval doctors that others sought to forget. This conference aims at reconstructing the various ways in which Aristotle’s natural philosophical books were read and used to nourish various philosophical agendas.

We welcome papers on any topic related to late medieval and early modern natural philosophy (roughly 1300-1700) that can contribute to a better understanding of the reception of Aristotle in the period. Papers focussing on the reception of less prominent books of the /corpus aristotelicum/, such as the /Meteorologica/ or the /Parva Naturalia/, are especially welcome.

For paper submissions, please send an abstract of 500 words by *January 15th*, in English or French, to Lucian Petrescu <lucian.petrescu@ugent.be> and Maarten van Dyck <maarten.vandyck@ugent.be>.

Invited speakers: Daniel Andersson (Oxford University / Babes-Bolyai University Cluj), Roger Ariew (University of South Florida), Paul Richard Blum (Loyola University Maryland), Helen Hattab (University of Houston), Carla Rita Palmerino (Radboud University Nijmegen).

Contact: Lucian Petrescu and Maarten Van Dyck.

Oldenburg and Newton on ‘Experimental Philosophy’

Kirsten Walsh writes…

During the debate following the publication of Newton’s first paper, Newton provided a set of eight queries, in an attempt to steer the debate towards a satisfactory conclusion.  When Henry Oldenburg, Secretary of the Royal Society and Editor of the Philosophical Transactions, published Newton’s queries, he added the following introduction:

    A Serie’s of Quere’s propounded by Mr. Isaac Newton, to be determin’d by Experiments, positively and directly concluding his new Theory of Light and Colours; and here recommended to the Industry of the Lovers of Experimental Philosophy, as they were generously imparted to the Publisher in a Letter of the said Mr. Newtons of July 8. 1672.

However, Newton didn’t describe his own work as ‘experimental philosophy’ until 1713, when he added the General Scholium to the Principia.  He wrote:

    … and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy.  In this experimental philosophy, propositions are deduced from the phenomena and are made general by induction.

In 1672, would Newton have been comfortable with Oldenburg’s label ‘experimental philosopher’?  Or did he consciously avoid the label, as Alan Shapiro suggests, in order to distance himself from the methodology of the early Royal Society?

Oldenburg on ‘Experimental Philosophy’

Henry Oldenburg (1619-1677)

To begin, what did Oldenburg mean by ‘experimental philosophy’?  Let’s look at his prefaces to each issue of the Philosophical Transactions.

Firstly, Oldenburg was talking about the Baconian experimental philosophy.  In the 1672 Preface, Oldenburg chose to adopt Bacon’s term, ‘Operative Philosophy’, which he used interchangeably with the term ‘Experimental Philosophy’.  And he wrote:

    But, when our renowned Lord Bacon had demonstrated the Methods for a perfect Restauration of all parts of Real knowledge … The success became on a sudden stupendious, and Effective philosophy began to sparkle, and even to flow into beams of bright-shining Light, all over the World.

Moreover, in 1671, Oldenburg advocated Abraham Cowley’s Baconian-vision for the Royal Society.  In his book, Proposition for the Advancement of Experimental Philosophy, Cowley proposed that the Royal Society appoint professors who were:

    bound to study and teach all sorts of Natural, Experimental Philosophy, to consist of the Mathematicks, Mechanicks, Medicine, Anatomy, Chymistry, the History of Animals, Plants …. and briefly all things contained in the Catalogue of Natural Histories annexed to My Lord Bacon’s Organon.

(Incidentally, in a previous post on this blog, Peter Anstey has identified this as the first English book to use the term ‘experimental philosophy’ in its title.)

Secondly, Oldenburg had in mind an experimental philosophy that emphasised the construction of natural histories.  For example, in 1669, Oldenburg wrote:

    …we then made an Attempt of laying some Foundation for the Improvement of real Philosophy, and for the spreading of Useful knowledge; in publishing Advices and Directions for the writing of an Experimental Natural History…

Thirdly, Oldenburg had in mind an experimental philosophy that attempted to recover ancient knowledge.  For example, in 1671, responding to critics of the experimental philosophy, Oldenburg wrote:

    they call it contemptuously the New Philosophy; when as yet perhaps themselves are not ignorant, that ‘tis so old as to have been the Discipline in Paradise; and from the First of Mankind … to have been practised and countenanced by the Best of Men…

Moreover:

    … we may not lay aside the other expedient, which is so helpful to explicate the Old Wonders of Art, and Old Histories of Nature; namely, To inquire diligently The things that are; What Rarities of Nature, and what Inventions of Men are now extant in any parts of the World.

To summarise, Oldenburg had in mind an experimental philosophy that:

  1. Followed Bacon’s method;
  2. Constructed natural histories; and
  3. Investigated ancient knowledge.

Newton on ‘Experimental Philosophy’

Isaac Newton (1642-1727)

Would Newton have approved of this way of describing his work?

Certainly Newton would have approved of being broadly aligned with the experimentalist philosophers, as opposed to the speculative philosophers.  In his ‘Queries Paper’, he wrote:

    … the Theory … was evinced to me … not by deducing it only from a confutation of contrary suppositions, but by deriving it from Experiments concluding positively and directly.

And in the first paper, he wrote: “And I shall not mingle conjectures with certainties”.

While Newton didn’t construct natural histories, he may have approved of the Baconian overtones of the label.  For, as I’ve discussed previously, Newton’s 1672 queries resemble Baconian queries.

Newton may even have approved of the suggestion that his method had ties to the Ancients.  For example, as early as 1686, in his Preface to Principia, Newton emphasised the influence of the Ancients:

    Since the Ancients (according to Pappus) considered mechanics to be of the greatest importance in the investigation of nature and science and since the moderns – rejecting substantial forms and occult qualities – have undertaken to reduce the phenomena of nature of mathematical laws, it has seemed best in this treatise to concentrate on mathematics as it relates to natural philosophy.

So, I think Newton would have approved of Oldenburg’s label, even though later on, when he came to describe his own experimental philosophy, the emphasis was quite different.  For example, in Query 31 of the Opticks, Newton wrote:

    This Analysis consists in making Experiments and Observations, and in drawing general Conclusions from them by Induction, and admitting of no Objections against the Conclusions, but such as are taken from Experiments, or other certain Truths.  For Hypotheses are not to be regarded in experimental Philosophy.

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…