QuestionsCan science explain everything?The eternal mystery of the world is its comprehensibility
Can science explain everything?True, but not everything

The eternal mystery of the world is its comprehensibility

The miracle of the comprehensibility of the world

Albert Einstein 1879 · 1955The physicist of relativity: simultaneity depends on the observer, and there is no 'now' valid for the whole universe.
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What it claims

Science really succeeds, but its very success is a fact it presupposes and cannot explain: a question remains that lies beyond its reach.

Why

Our concepts are creations of the mind, yet the world lets itself be ordered by them: science presupposes this fact, it cannot explain it.

The same idea through history
Immanuel Kant1787Kant: we know of things a priori only what we ourselves put into them. Einstein salutes this idea, but does not take it as an explanation.
Albert Einstein1936Einstein puts the point in an aphorism: the eternal mystery of the world is its comprehensibility.
In short

"The eternal mystery of the world is its comprehensibility" is an argument by Albert Einstein (Einstein, 'Physics and Reality' (1936); 'Space and Time in Pre-Relativity Physics' (1921), 1936) on the question "Can science explain everything?" (answer: true, but not everything). Its claim: Science really succeeds, but its very success is a fact it presupposes and cannot explain: a question remains that lies beyond its reach. According to AskPhilosophy's logic check (Z3 solver), the argument is valid only if one grants a premise the author leaves unstated (P3, P4). AskPhilosophy presents 3 objections, 2 of them with a documented reply, and the original text behind each premise, checked word for word.

Einstein, 'Physics and Reality' (1936); 'Space and Time in Pre-Relativity Physics' (1921)
Valid with an implicit premise

A physicist of genius ends up astonished at what works for him. In 1936 Einstein writes that the eternal mystery of the world is its comprehensibility, and he speaks of a 'miracle'. He does not say that science is false: he says that it works, and that the fact that it works is what it cannot explain. An important precision: he uses 'comprehensible' in the most modest sense, that of an order put into sense impressions by concepts and the relations between them. His astonishment is therefore not about the final truth of science, but about the fact that such an order is possible at all. A caution: the two-part formula ('eternal mystery', then 'miracle') comes from one text, but its translations vary a great deal between collections.

P1Science succeeds: by means of concepts and relations between them, we bring order into the totality of our sense experience. This is the deliberately modest sense of 'comprehensible'.
P2This universe of concepts cannot be deduced from experience by logical means: it is, in a sense, a creation of the human mind, without which no science is possible.
P3 · implicit premiseSo nothing, in logic or in experience, guarantees in advance that experience will let itself be ordered by our concepts: a world without order was conceivable.
P4 · implicit premiseEvery scientific explanation already presupposes this order (laws, concepts that apply): science therefore cannot explain it without arguing in a circle.
P5That experience can be ordered in this way leaves us in awe, but we shall never understand it: it is, Einstein says, the eternal mystery of the world, a miracle.
So science really succeeds, but its very success is a fact it presupposes and cannot explain: a question remains that lies beyond its reach.

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.
Valid with two hidden premises, P3 and P4. The debate concerns them. Against P3, some say our mind imposes order on experience (Kant), others that theories that do not work disappear (van Fraassen), others that our concepts are tailored to our sensations (Mach). Against P4, one can answer that science can explain some regularities by deeper ones, and that only the last remains unexplained. Note that the conclusion is modest: Einstein does not say that a non-scientific answer exists, only that science gives none.
Analogy. Imagine being handed a padlock and a key you made at random in your workshop, without ever having seen the padlock. The key opens it. One could say: never mind, it opens. Einstein stops at this fact: why does a key made by the mind fit the lock of the world? The objections amount to saying that the lock may have been made for us, or that keys that do not open are thrown away.

Objections

3

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

Kant (the mind puts order into experience) 1787 · attacks premise 3

We know of things a priori only what we ourselves put into them. The order of nature is therefore not a lucky accident: it comes from the way our understanding forms all possible experience.

Einstein replies
Einstein 1936 · What Einstein concedes
Einstein grants it in part: it is, he says, one of Kant's great realizations that the setting up of a real external world would be senseless without this comprehensibility. He makes it a condition of science, not the end of the mystery.
The debate goes on (our summary) A Kantian would answer that 'condition of all possible experience' is precisely the explanation. A follower of Einstein would answer that this explains why we cannot think a world without any order, not why the precise laws of physics, which Kant could not have known, apply to the world.
B
Bas van Fraassen (selection among theories) 1980 · attacks premise 3

The success of scientific theories is no miracle, and it is not even surprising to a Darwinian mind: they live in a harsh competition, and only the successful ones survive. We see theories that work because the others have been abandoned.

no reply
Einstein never answered this objection.
The debate goes on (our summary) A follower of Einstein would answer that selection explains why current theories work, not why among possible theories there were regularities so simple to find. Wigner (1960) expresses a similar astonishment about mathematics, but he does not reply to van Fraassen, who writes twenty years later.
E
Ernst Mach (economy of thought) 1883 · attacks premise 2

Science is an economy of thought: our concepts are convenient summaries of our sensations. They are made to fit experience because they come from it. There is therefore no mystery in their applying to it.

Einstein replies
Einstein 1921 · What Einstein says in advance
Einstein agrees on one point: concepts have no justification other than representing the complex of our experiences, and they are not independent of the nature of experience, as clothes are not of the form of the body. But he also grants that the universe of ideas probably cannot be deduced from experience by logical means: it is, in a sense, a creation of the mind.