Skip to Navigation Skip to Content Skip to Search Skip to Site Map

Monthly Archives: July 2014

Colloquium: Principles in Early Modern Thought

University of Sydney

27–29 August 2014



Engraved word map by Leonhard Euler

  • Professor Peter Anstey (Sydney), ‘Principles: the Contours of a Concept’ & ‘Principles of Religion’
  • Mr Joe Campbell QC (Sydney), ‘Principles & the Development of English Equity Law’
  • Professor James Franklin (UNSW), ‘Early modern Mathematical Principles’
  • Professor Daniel Garber (Princeton), ‘Principles in Leibniz’s Philosophy’
  • Professor Michael LeBuffe (Otago), ‘Principles of Spinoza’s Philosophy’
  • Professor William R. Newman (Indiana), ‘Chymical Principles’
  • Professor Sophie Roux (ENS, Paris), ‘Principles in French Philosophy’
  • Professor Kiyoshi Shimokawa (Gakushuin, Tokyo), ‘A Conflict of Principles: Hume versus Modern Natural Lawyers’
  • Dr Alberto Vanzo (Warwick), ‘Principles in Italian Natural Philosophy’
  • Ms Kirsten Walsh (Otago and Calgary), ‘Principles in Newton’s Natural Philosophy’


Colloquium Sponsors:

This colloquium forms part of Professor Peter Anstey’s ARC Future Fellowship project on ‘The nature and status of principles in early modern philosophy’. It is sponsored by the School of Philosophical and Historical Inquiry and the Sydney Centre for the Foundations of Science.


Colloquium Organisers:

  • Professor Peter Anstey
  • Professor Stephen Gaukroger


Places are limited.

Click here to register


Program (Download PDF of the program here):

Wednesday 27 August:

9.00           Peter Anstey, ‘Principles: the Contours of a Concept’

10.30         Coffee Break

11.00         James Franklin, ‘Early modern Mathematical Principles’

12.30         Lunch

1.30           Joe Campbell, ‘Principles & the Development of English Equity Law’

3.00           Break

3.30           William Newman, ‘Chymical Principles’

5.00           End of Day


Thursday 28 August:

9.00           Sophie Roux, ‘Principles in French Philosophy’

10.30         Coffee Break

11.00         Kiyoshi Shimokawa, ‘Principles of Natural Jurisprudence’

12.30         Lunch

1.30           Alberto Vanzo, ‘Principles in Italian Natural Philosophy’

3.00           Break

3.30           Peter Anstey, ‘Principles of Religion’

5.00           End of Day


Friday 29 August:

9.00           Michael LeBuffe, ‘Principles of Spinoza’s Philosophy’

10.30         Coffee Break

11.00         Kirsten Walsh, ‘Principles in Newton’s Natural Philosophy’

12.30         Lunch

1.30           Daniel Garber, ‘Principles in Leibniz’s Philosophy’

3.00           Conclusion

7.00           Colloquium Dinner


Location:   Darlington Centre H07, Boardroom

Contact:    Prof Peter Anstey

Phone:       61 2 9351 2477


Register: Here

‘Epistemic amplification’ and Newton’s laws


Kirsten Walsh writes…

In my last post, I considered the experimental support Newton offers for his laws of motion. In the scholium to the laws, Newton argues that his laws of motion are certainly true. However, in support he only cites a handful of experiments and the agreement of other mathematicians. I suggested that the experiments discussed do support his laws, but only in limited cases. This justifies their application in Newton’s mathematical theory, but does not justify Newton’s claims to certainty. In this post, I will speculate that the laws of motion were in fact better established than Newton’s discussion suggests. I introduce the notion ‘epistemic amplification’ – suggesting that Newton’s laws gain epistemic status by virtue of their relationship to the propositions they entail. That is, by reasoning mathematically from axioms to theorems, the axioms obtained higher epistemic status, and so the reasoning process effectively amplified the epistemic status of the axioms.

I am not arguing that epistemic amplification captures Newton’s thinking. In fact, Newton explicitly stated that epistemic gain was not possible. For him, the best one could achieve was avoiding epistemic loss. (I have discussed Newton’s aims of certainty and avoiding epistemic loss here and here.) I suggest that, objectively speaking, the epistemic status of Newton’s laws increases over the course of the Principia.

To begin, recall that Newton has two projects in relation to the laws:

  1. The specification of the laws as the axioms of a mathematical system; and
  2. The justification of laws as first principles in natural philosophy.

Let’s consider the first project. In addition to the support of mathematicians and the experiments that Newton cites, it is plausible that the epistemic status of the laws increases by virtue of their success in the mathematical system: in particular, by entailing Keplerian motion. Kepler’s rules and Newton’s laws of motion have independent evidence: as we have seen, Newton’s laws are weakly established by localised experiments and the ‘agreement of mathematicians’; Kepler’s rules are established by observed planetary motion and were widely accepted by astronomers prior to the Principia. Newton’s laws entail Kepler’s rules, which boosts Newton’s justification for his laws. Moreover, Newton’s laws provide additional support for Kepler’s rules, by telling us about the forces required to produce such motions. The likelihood of the two theories is coupled: evidence for one carries over to the other. So Newton’s laws also boost the justification for Kepler’s rules. Thus, Newton achieves epistemic gain: the epistemic status of the laws, qua mathematical axioms, has increased by virtue of their relationship to Kepler’s rules.

Now let’s consider the second project – the application of the laws to natural philosophy. Again, the discussion in the scholium justifies their use, but not their certainty. I now suggest that these laws, as physical principles, gain epistemic status through confirmation of Newton’s theory. This occurs in book 3, when Newton explicitly applies his mathematical theory to natural phenomena. As I have previously discussed, the phenomena (i.e. the motions of the planets and their moons) are employed as premises in Newton’s argument for universal gravitation. However, the phenomena also support the application of the mathematical theory to the physical world: they show that the planets and their moons move in ways that approximate Keplerian motion. As we saw above, the laws of motion entail Kepler’s rules. So, since the phenomena support Kepler’s rules, they also support the laws of motion. So this is a straightforward case of theory-confirmation.

There is also scope for theory-testing in book 1. Each time Newton introduces a new factor (e.g. an extra body, or a resisting medium), the mathematical theory is tested. For instance, the contrasting versions of the harmonic rule in one-body and two-body model systems provides a test: it allows the phenomena to empirically decide between two theories, one involving singly-directed central forces, the other involving mutually-interactive central forces. Similarly, the contrasting two-body and three-body mathematical systems provide a test: they allow the phenomena to select between a theory involving pair-wise interactions and a theory involving universal mutual interaction. Moreover, in the final section of book 2, Newton shows that, unlike his theory, Cartesian vortex theory does not predict Keplerian motion. Thus, the phenomena seem to support his theory, and by extension the laws of motion, and to refute the theory of vortices. Again, the laws seem to gain support by virtue of their relationship to the propositions they entail.

To summarise, Newton claims that his laws are certainly true, but the support he gives is insufficient. Here, I have sketched an account in which Newton’s laws gain epistemic status by virtue of their relationship to the propositions they entail. ‘Epistemic amplification’ is certainly not something which Newton himself would have had truck with, but the term does seem to capture the support actually acquired by Newton’s laws in the Principia.  What do you think?