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The Experimental Role of Hypotheses in Newton’s Principia

Kirsten Walsh writes…

In the first edition of Principia (1687), book 3 contained nine hypotheses.  But in the second edition (1713), Newton re-structured book 3 so that it contained only two hypotheses.  All but one of the old hypotheses were simply re-labelled.  Those that specified explanatory constraints were called ‘Rules of Reasoning’, those that were simply unsupported generalisations were called ‘Phenomena’, and only the assumptions about nature were called ‘Hypotheses’.

1st edition 2nd edition
Hypothesis 1 Rule 1
Hypothesis 2 Rule 2
Hypothesis 3 Replaced by Rule 3
Hypothesis 4 Hypothesis 1
Hypothesis 5 Phenomenon 1
Hypothesis 6 Phenomenon 3
Hypothesis 7 Phenomenon 4
Hypothesis 8 Phenomenon 5
Hypothesis 9 Phenomenon 6
Lemma 3 Hypothesis 2

Table: Book 3 changes from 1st to 2nd editions.

These changes seem to indicate that Newton’s attitude to hypotheses changed dramatically between 1687 and 1713 – probably in response to Leibnizian criticisms and Cotes’ editorial comments.

On this blog, I have given you many reasons to suppose that, as early as 1672, Newton was working with a clear epistemic distinction between theories and hypotheses.  More recently, I have argued that in fact, Newton was working with a three-way epistemic distinction between theories, which are certain and experimentally confirmed, hypotheses, which are uncertain and speculative, and queries, which are not certain, but provide the proper means to establish the certainty of theories.  I call this division Newton’s ‘epistemic triad’.  I argued that hypotheses perform a distinctive and vital supporting role to theories and queries, and that this role is an enduring feature of Newton’s methodology.

Today I’ll compare the roles of hypotheses and rules of reasoning in book 3, and argue that Newton’s attitude to hypotheses c.1713 was a refinement of his attitude c.1687, but not a dramatic change.

To begin, consider hypothesis 1 (2nd edition): “The centre of the system of the world is at rest.”

Upon introducing this hypothesis, Newton explained that:

    “No one doubts this, although some argue that the earth, others that the sun, is at rest in the centre of the system.  Let us see what follows from this hypothesis.”

This is a simplifying assumption.  From this hypothesis, in conjunction with Corollary 4 of the Laws of Motion,

    “The common centre of gravity of two or more bodies does not change its state whether of motion or of rest as a result of the actions of the bodies upon one another; and therefore the common centre of gravity of all bodies acting upon one another (excluding external actions and impediments) either is at rest or moves uniformly straight forward”,

Newton derived Proposition 11:  “The common centre of gravity of the earth, the sun, and all the planets is at rest.”

This enabled him to calculate the motions of the planets – that is, to deduce the observational consequences of his theory.  I consider this to be the chief role of hypotheses, and it is experimental.

Now compare this with how Newton uses his rules of reasoning.

Rule 1 states:  “No more causes of natural things should be admitted than are both true and sufficient to explain their phenomena.”

And Rule 2 states:  “Therefore, the causes assigned to natural effects of the same kind must be, so far as possible, the same.”

In his discussion of Proposition 4, Newton explained:

    “And therefore that force by which the moon is kept in its orbit, in descending from the moon’s orbit to the surface of the earth, comes out equal to the force of gravity here on earth, and so (by rules 1 and 2) is that very force which we generally call gravity.”

These rules didn’t help Newton to deduce the observational consequences of his theory in the same way as his hypothesis 1.  They provide an important supporting role for his theory, but it is not an experimental role.

To the second edition, Newton also added the General Scholium, in which he (in)famously declared  “hypotheses non fingo”.  Recently I argued that, in this passage, Newton was not railing against hypotheses in general, but rather, against the use of ‘causal hypotheses’ to illustrate more abstract theories.  Given that the first edition did not contain any causal hypotheses, I consider this addition to indicate Newton’s increasing conviction in his method, rather than any dramatic change.

So finally, to summarise the developments between the first and second editions of Principia:

In the first edition:

  • Hypotheses are temporarily assumed, untestable propositions that provide a supportive role; and
  • There are no causal hypotheses.

In the second edition:

  • Hypotheses are temporarily assumed, untestable propositions that provide a supportive experimental role;
  • Other temporarily assumed, untestable propositions are given other labels to distinguish them from hypotheses; and
  • Emphatically, there are no causal hypotheses.

I see these changes as developments of Newton’s epistemic triad, rather than dramatic methodological changes.

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