Please bear with me, as I am self-studying philosophy as a beginner. My questions are about the limitations of empirical science.

During my reading of some books, I've come across statements of the form 'science can't prove (beyond reasonable doubt) X'.

What kind of limitation is this? Is that an epistemological or ontological constraint?

It seems to me that they are epistemological statements about science, since it's about the things we can't possibly know. Or maybe it's essential to science that we can't know some things? Does that change the answer?

In the same vain, what about the statement that science can't prove that we live in a simulation (like The Matrix or an elaborate dream)? This is a statement that stems from the book The grand design by Stephen Hawking and Leonard Mlodinov, 2010.

Is this another kind of limitation? It seems to me that 'living in a Matrix-like world' is an ontological statement about the world, but claiming that we can't know it, is an epistemological claim.

  • I'm curious where you got those two examples that are supposedly not provable by science?
    – Cell
    Oct 12, 2019 at 12:30
  • @Cell I got those examples from a book from Maarten Boudry, a Belgian philosopher of science. The book is called: "Waarom de wereld niet naar de knoppen gaat". The book is not translated in English yet. Some of his influences are Steve Pinker, Richard Dawkins and David Deutsch. It's a book that's about optimism, progress in times that are perceived as otherwise. Oct 12, 2019 at 13:24
  • Not translated in english? That's too bad. To be honest, as someone who is in science academia those claims sound like nonsense. The only reason those examples could be seen as controversial is because there is a lot of variability and uncertainty in studying climate and biology. It has nothing to do with metaphysics.
    – Cell
    Oct 12, 2019 at 14:13
  • @Cell I should have added that he began the chapter with those controversial statements. That's a rhetoric device, to get attention of the reader. He writes indeed that science has not proven those examples, but then he goes on to write that there's enough evidence that it would be foolish to claim otherwise. Oct 12, 2019 at 14:34
  • 2
    But in science "proven" and "true beyond a reasonable doubt" are synonyms. Only in logic and math is there absolute certainty because they involve taking true statements and rearranging to say the same thing differently.
    – Cell
    Oct 12, 2019 at 14:42

3 Answers 3


We always have to keep in mind that science makes models of the universe. It does not 'prove' truths or facts or do anything of that nature. This is the case with mathematics as well, though it's harder to see because the things mathematics models are far more abstract; I'd even go so far as to say that modeling is the basic activity of reason. Science is generally defined by the fact that it both generates and tests its models on empirical observations — we look at the world to create models, and then we look at the world again through the lens of our models to use, correct, and refine them — but empirical observations merely guarantee that our models are functional, not that they are true.

Technically speaking, epistemology and ontology are both forms of metaphysics, in the sense that they deal with first principles, so the question you're asking isn't quite sound. But if I had to choose I'd say it is a problem of epistemology. The problem, really, is the age-old observation that a map is not the territory it maps. Science is a kind of map of the material universe, and it can never quite capture the universe it aims to cover. Worse, it's often a map of territory we cannot directly see: e.g., gravity, for which we have well-defined models (except at the extremes), but few clues as to its substance. We are in the unenviable position of tapping out many of our scientific maps like blind men — think of the Large Hadron Collider as a high-tech cane poking at things we can't see — and because of that many people stray into thinking that the map is the thing being mapped (i.e., that science is 'true'). But no, epistēmē and ōn (knowledge and essence) are always separated.


The older view was that causality was like goodness, it was something that had no proper empirical existence. It's not like a stone in the road that one just comes across. The issue rests on some from of distinction between experience and intellect. Causality, like goodness, may have a real existence in the world, but must be derived through reasoning and is not directly available even to the "eyes of the soul." Hume and Kant destroyed, and then Schopenhauer obliterated the metaphysical certainty in causality.

Epistemology in the context of Anglo-English and the currently dominat analytic tradition is a vague term, questions concerning knowledge. In the German tradition it was a term that grew out of the post-Kantian reflection on the subject matter implied by the word Transcendental. The issue of the conditions for any possible experience (not merely for human or "subjective" experience). Kant said that the negation of the principle of causality is not syllogistically contradictory. Because one can speak consistently of an ex nihilo event (of creativity coming into the daily flow of things). Schopenhauer thoroughly demonstrated the faultiness of both Hume and Kant from the perspective of sound reason, which had not yet been demoted to the status of mere subjectivity.

When Popper introduced his famous statement of the Problem of Induction in a scientific context, which is somewhat contested in its status, he seemed to speak epistemologically in the inexact Anglo-American sense. If one tries to make his statement exact, into a formal epistemological principle, still in Anglo-British terms, the statement that one can test for conditions of falsification, but not conditions of verification, becomes meaningless (the vague notion of "corroboration" comes in as a common sense surety). Because a break in a causal chain doesn't prove that the chain won't be reestablished and then never broken again. Or, that the chain once broken won't always threaten to return to the old observed regularity. It becomes merely a working assumption wanting for the apodictic certainty of mathematical objects.

The term ontology was often used interchangeably with the term metaphysics in the tradition. And its use has become quite anarchical in our own time. The variety of uses being limited on the one hand by the most powerful thinkers, e.g., Heidegger, and on the other by the analytic philosophy departments now in control of the university proper (in contradistinction to the numerous independent actors within the university system).


In your last sentence you seem to have found the heart of the matter: science can tell us things about things that can be completely unrelated to it. The epistemological limitation is a quality of that relationship, not of the object itself (an object that, like the potential simulation of this reality, can have ontological implications) - science does not somehow emulate its object.

As science is by its nature based on empirical evidence, it naturally cannot take account of things that cannot be measured. Metaphysics is by its very nature immeasurable¤.

The opinion that science can't prove something to be a fact (a 'fact' being an a posteriori label) can have multiple underlying reasonings, but the one I'm most familiar with is the idea that for something to be a fact it needs to be that way and not any other (always). But science obviously cannot prove the future of things.
This could be considered a semantic limitation, even, since the meaning of 'fact' as we now know it is based on what can be proven by science in the first place (or at least to be "something that has actually occurred"+, merely implicating reoccurrence).

I do wonder where you got your definition of 'proving', as it seems inherently false: (the logic behind) mathematics is abstract, whereas science analyses that which is physical.
Besides that, the idea that science (or prove) gives guarantees seems a bit off to me: a guarantee suggests a statement with the intent of assurance. This seems to contradict scientific scepticism. The history of science has told us that things are rarely set in stone (take only the idea of Euclidean space, or the dichotomy of time and space).

(I'm also curious where you picked up the statement that it can't be proven that smoking causes cancer.)

¤ Against my better judgment, not by its very definition, apparently: https://www.etymonline.com/word/meta-
+ https://www.etymonline.com/word/fact

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