QuestionsCan science explain everything?I frame no hypotheses: science establishes laws, not ultimate causes
Can science explain everything?True, but not everything

I frame no hypotheses: science establishes laws, not ultimate causes

"Hypotheses non fingo"

Isaac Newton 1643 · 1727A physicist and mathematician who founds mechanics on an absolute, true and mathematical time and space.
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What it claims

Science establishes with certainty that gravity exists and acts according to laws that account for the motions of the heavens and the sea, but the cause of that force lies beyond what it can establish. "To us it is enough, that gravity does really exist, and act according to the laws which we have explained."

Why

Gravity has been shown to exist and follow laws; its cause was not deduced from the phenomena, so it stays outside science.

The same idea through history
Francis Bacon1620Bacon already asks us to climb by degrees from facts to principles, rather than first inventing general causes.
Isaac Newton1713In the General Scholium, Newton declines to put forward a hypothesis about the cause of gravity: what is not deduced from the phenomena has no place in experimental philosophy.
Isaac Newton1693In his letter to Bentley, Newton makes clear that he did not say gravity is innate to matter: it must have a cause acting by laws, and he leaves his readers to judge whether that agent is material or not.
Pierre Duhem1906Duhem shows that Newton's method is not pure induction: a law is never drawn from facts alone.
In short

"I frame no hypotheses: science establishes laws, not ultimate causes" is an argument by Isaac Newton (Principia, 2nd ed. (1713), General Scholium; letter to Bentley (1693), 1713) on the question "Can science explain everything?" (answer: true, but not everything). Its claim: Science establishes with certainty that gravity exists and acts according to laws that account for the motions of the heavens and the sea, but the cause of that force lies beyond what it can establish. "To us it is enough, that gravity does really exist, and act according to the laws which we have explained.". According to AskPhilosophy's logic check (Z3 solver), the argument is valid only if one grants a premise the author leaves unstated (P4). AskPhilosophy presents 3 objections, 3 of them with a documented reply, and the original text behind each premise, checked word for word.

Principia, 2nd ed. (1713), General Scholium; letter to Bentley (1693)
Valid with an implicit premise

Newton has just explained the tides, the orbits of the planets and the fall of stones with a single force, gravity. What produces it? He admits he does not know, and he turns this into a principle: he will frame no hypotheses. What can be deduced from the phenomena is asserted; what cannot is not invented. For Newton, science gives sure truths about how things behave, but it stops before the question of the ultimate why.

P1Gravity acts on bodies according to their quantity of matter and decreases as the square of the distance. But the cause of these properties could not be discovered from the phenomena.
P2Whatever is not deduced from the phenomena is an hypothesis, and hypotheses, whether metaphysical or physical, have no place in experimental philosophy.
P3In experimental philosophy, particular propositions are inferred from the phenomena and then made general by induction. This is how the laws of motion and of gravitation were discovered.
P4 · implicit premiseWhat is thus deduced from the phenomena by induction is genuinely known: these are true laws of nature, not mere convenient fictions.
So science establishes with certainty that gravity exists and acts according to laws that account for the motions of the heavens and the sea, but the cause of that force lies beyond what it can establish. "To us it is enough, that gravity does really exist, and act according to the laws which we have explained."

click a premise to reject it

If you accept every premise, logic forces you to accept the conclusion. So the debate is about the premises.
Checked by a logic solver: the premises cannot all be true while the conclusion is false.
Without the implicit premise: Without P4, one could accept all the rest and say: Newton's laws are also calculating tools, not truths. Then science would establish nothing true, neither about the cause nor about the laws.
The argument is valid. P1 says the cause was not deduced from the phenomena; P2 makes it an hypothesis with no place in science; P3 says the laws, by contrast, are deduced; P4 (hidden) says what is thus deduced is really established. The conclusion follows: true laws, a cause out of reach.
Analogy. A doctor finds that a medicine lowers fever in every observed case. He can assert it and prescribe the exact dose. Why does it work? As long as it has not been observed, he does not make it up. Newton does the same with gravity.

Objections

3

Each objection is a conversation: click to see who replies and where the debate stands.

Gottfried Wilhelm Leibniz 1716 · attacks premise 4

Leibniz judges that a force acting at a distance with nothing to explain it is not a true law but an "occult quality" or a perpetual miracle. For him, a regularity is natural only if it can be explained by the nature of things: without a cause, Newton's law is not yet known.

a defender replies
Samuel Clarke defender of the argument · 1716
Clarke replies that a manifest quality is not "occult" because its immediate cause is unknown: the phenomenon itself, attraction, is established by observation and experiment, and its laws are known. If someone one day explains it by a mechanism, he will be thanked; meanwhile, denying the fact because its cause is unknown would be strange reasoning.
Where the debate stands (our summary)The disagreement is about what counts as knowledge. For Leibniz, to understand is to explain by the nature of things. For Clarke and Newton, a law established by experiment is already knowledge. Physics followed Newton for two centuries; general relativity (1915) then offered a geometric explanation of gravity, which in turn leaves questions open.
Pierre Duhem 1906 · attacks premise 3

Duhem argues that the law of gravitation is not drawn from the phenomena by induction: it even contradicts the Kepler laws it claims to start from. If Newton's theory is exact, those laws are false. It stands by the agreement of the whole theory with observation, not by pure deduction.

a defender replies
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William Harper defender of the argument · 2011
Harper argues that Newton does not induce naively. His "deduction from the phenomena" is a method of successive approximations: assuming the theory, the gap between observed orbits and Kepler's law yields new measurements, which in turn become evidence for the law. It is not a circle but a way of turning data into evidence.
Where the debate stands (our summary)Duhem is right on a point few contest: Kepler's laws are only approximate and Newton's theory corrects them. The disagreement is about the nature of the method: for Duhem the theory is confirmed as a whole system; for Harper the Newtonian method yields stronger evidence than Duhem allows.
Pierre-Simon de Laplace 1814 · attacks the conclusion

Laplace imagines an intelligence that would know all the forces of nature and the position of every being: it would embrace in the same formula the motions of the heavenly bodies and those of the lightest atom, and nothing would be uncertain for it. He adds that the human mind, through its discoveries in mechanics and geometry joined to universal gravitation, keeps drawing nearer to this intelligence, from which it will nevertheless always remain infinitely far. Our reading: for Laplace nothing in nature in principle escapes the laws science seeks; the limit Newton sets would be a limit in fact, not in principle.

a defender replies
see the argument
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Emil du Bois-Reymond defender of the argument · 1872
Du Bois-Reymond takes Laplace's image of the all-knowing mind to set limits: natural science will never explain the essence of matter and force, nor how consciousness arises from matter. His formula, "ignoramus et ignorabimus", we do not know and we shall not know, fed a long debate.
Where the debate stands (our summary)An open point. Laplace's programme has flourished (relativity, quantum mechanics) but has met limits it did not expect. Whether to speak of a limit in fact or in principle for questions such as the origin of the laws or consciousness remains debated.