# Can science prove statements to be true?

I know that mathematics can prove certain statements to be true, which we call theorems. But what about science? Can science prove statements to be true? Note, just because a statement can't be proven to be true by science does not mean it is not true. I am merely asking whether science can prove the truth of statements. Of course, this depends on what we mean by "prove". Also, have any philosophers written about this issue?

• What do you make of the sentence 'The mass of the Moon is less than the mass of the Earth'? Or how about 'The Thames is shorter than the Nile'? Dec 22, 2023 at 22:45
• This question hinges on a polysemy around Prove. See analogous polysemy around law. Dec 23, 2023 at 15:37
• Mathematics does not prove statements to be true, only that some statements are equivalent to or imply some others. At best you can establish that A implies B. Then if you determine that A is true, B is also true Dec 23, 2023 at 15:40
• YES. Subject to revision. Anyone else like to give an answer? I'm not sure that this is the place for Nonduality. Dec 26, 2023 at 21:34

Yes, certain types of non-mathematical statements can be proven, depending on what meaning of 'prove' you have in mind.

Mathematics is a formal system, so that proof is essentially a matter of demonstrating that a statement is consistent with the axioms and rules of deduction. In an analogous way you can prove the correctness of other statements which are related to systems of rules. For example, you can prove the validity of a move in chess by referring to the rules of the game; you can prove that a person with a given income is obliged to pay a given amount of tax by referring to the prevailing tax code.

Other types of accepted proofs are associated with evidence of various sorts. You can proof the validity of the statement 'it is raining' by looking out of your window. You can check the truth of the statement 'Bertrand Russell won the Nobel Prize for Humorous Fiction' by consulting accepted authorities. Science can play a role in providing that kind of evidence to support a decision about whether a give statement is true.

What science cannot do is to prove unrestricted general statements, since its method of verification typically relies on physical evidence, so the validity only stretches as far as the evidence does. For example, we cannot prove that the speed of light always has a given value- all we can say is that in the various tests that have been performed, its speed has been found to have a given value, subject to some degree of experimental error.

• Comments have been moved to chat; please do not continue the discussion here. Before posting a comment below this one, please review the purposes of comments. Comments that do not request clarification or suggest improvements usually belong as an answer, on Philosophy Meta, or in Philosophy Chat. Comments continuing discussion may be removed. Dec 26, 2023 at 22:16

A common form of mathematical proof is 'showing it cannot be otherwise' (ie proof by contradiction - if you can show that the negation of your statement leads to contradiction then it is impossible that it be false)

If you mean by 'proof' something like the above then scientific statements notoriously can't be proven since there's no way of showing from our epistemic perspective that they must necessarily be true. And many practising scientists explicitly reject the literal truth of their theory anyhow - on one popular view it's rational to disbelieve your best theory on the grounds that you're confident that a better, different one is around the corner.

Two dissenting voices:first, Descartes really did believe that scientific knowledge could we achieved with infallible certainty (because God would be a deceiver if humans could investigate to the best of their powers and still get it wrong). Second, you could argue that 'proven' just means 'adequately tested' - which I guess is now the sense in which it's used in makeup ads that use the phrase 'clinically proven'...

• As for apodictic scientific knowledge, I think Kant and Hegel would be much better examples. Descartes only has thw category of knowledge "by divine light", there's not much to get from him about scientific knowledge specifically imho. Dec 31, 2023 at 21:57
• Apart from the fact that Descartes specifically presents his project as one of getting knowledge in "natural philosophy" (what we now think of as science) on a footing of certainty. And (as a point of order) Descartes doesn't only believe in knowledge by divine light/intuition - empirical knowledge is also possible once God's existence is proved. Last two meditations make that clear. Jan 1 at 1:22

No. This is the analytical path:

1. Reason is the set of thinking rules, which is not formal. When I reason, I follow certain thinking rules, which are not formal (e.g. written). Consider here that sometimes I make mistakes. Those are not yet logical, but rational mistakes.
2. Logic is the formal expression of rational rules. That is, this is a set of written and logically consistent rules (notice that the consistency of logic is provided by... logic; that's why many philosophers, like Russell, sustained that logic is circular, tautological). Here, there are no logic mistakes (ideally). Logical rules are consistent, rational rules are not necessarily logically consistent, but they tend to be, in a person that has survived. When we speak of logic, we mean essentially propositional logic and all forms of logic that emerge from it (e.g. predicate logic, fuzzy logic).
3. Logic organizes judgements around in two groups: truth and falsehood. Truth is very complex to define, however, it can be considered that rationally (metaphysically), truth is just a group of consistent judgements, and empirically (physically), truth is the set of rules of experience (obtained by means of the senses) that are consistent with the logical truth.
4. Mathematics is just a metaphysical extension of logic. Truth in mathematics exists due to Logic.
5. Science is a set of empirical truths. Notice that two groups of judgements have been defined: physical (empirical) and metaphysical (rational). Science addresses ONLY empirical truths. Metaphysical truth (e.g. God exists) is not scientifically verifiable.

Now, for the question:

Can science prove statements to be true?

The question is quite ambiguous and vague. However:

• If an statement is purely rational, yes, provided that the sufficient logic (e.g. the elementary objects like truth, falsehood, and the necessary rules, like Modus Tollens, etc.) and dependent axiomatic systems (e.g. mathematical axioms) contain all required elements to reach the judgement (e.g. 7+5=12 is true).
• If an statement only contains rational and empirical elements, yes, provided that the sufficient logic (e.g. propositional logic), dependent axiomatic systems (e.g. Laws of Thermodynamics) and empirical facts contain all required elements (e.g. chemical reactions tend to minimize the free energy of the system.).
• If an statement contains metaphysical elements which are not part of logic (e.g. aesthetics), no. Science cannot address metaphysical facts (e.g. "La Gioconda transmits feelings of sadness" is true...).

When we say that something is "proven," we mean that it conforms to certain rules of objectivity. Logic has one set of rules that help us determine the validity of an argument. Mathematics has another set of rules, but it is built off of logic and can't contradict it. Natural science, in turn, has a set of rules that includes a contingent element that is based on experience, but must conform to logic and mathematics which supply objectivity. This is why we can say that the proposition, "the Earth is round," is both contingently and objectively true.

In logic, we say that the premises are sound based on the evidence and the form used to reach the conclusion is valid based on logic. Therefore, "proven ".

If prior to the invention of mobile phones, there was a statement such that recordable images of the natural world can be stored and displayed for future observation.

That proposition or statement can be proved as a product of science by reading this as my expression of an answer to your question.

If by the word "prove" you mean show to be true or good, then the answer is no for science and maths. Any argument has some assumptions and some rules for going from assumptions to results. The assumptions of the argument might be wrong and the rules might also be wrong, so they can't prove the conclusion to be true. This was pointed out by Karl Popper in "Realism and the Aim of Science", especially Chapter I and in "On the Sources of Knowledge and of Ignorance" in "Conjectures and Refutations" and also

Knowledge, including scientific and mathematical knowledge, is created by guessing solutions to problems and criticising those solutions until only one is left and it has no known problems. Popper called this critical rationalism (CR).

The Duhem-Quine problem isn't an issue for CR. If an experimental results clashes with a theory then the result might be wrong, or might have been misinterpreted or whatever. The way to handle that is to come up with a guess about the solution to the problem that has independently testable consequences, e.g. - if you think your telescope's optics are distorting your view of a planet and making it look like a theory might be wrong, then it should also distort your view of other objects.

Depends on what you mean by 'prove'. There are a number of good responses here. Dcleve brought up the main contention between logical empiricism and positivism and Karl Popper and his beliefs about falsification in his theory of critical rationalism. The positivists said yes, and Popper said no. After Quine, you have an array of positions about what science can do and what it is in practice, such as the views of Imre Lakatos. What can be said with certainty is that Popper is usually understood to have undermined confirmationism and verificationism so if science proves claims, it does so at best tentatively.

The key turning point philosophically in your question is what is meant by proof. Proof means many things to many people. In order to understand what you mean by proof, you would have to explain your views on evidentialism. From WP:

Evidentialism is a thesis in epistemology which states that one is justified to believe something if and only if that person has evidence which supports said belief.1 Evidentialism is, therefore, a thesis about which beliefs are justified and which are not.

Let us say, then, that generally science produces claims that are far more reliable and useful than pseudoscience or religion in the domain of discourse about the physical world. You can't pray rockets into space, and certainly astrology offers no guidance. Physics on the other hand can land a VCR on the moon with amazing accuracy. In this sense, science is successful because it relies heavily on empirical evidence which has a partner in philosophy called the correspondence theory of truth. Science tends to produce claims that are far more difficult to falsify and are far more robust in creating change in the world, a topic that is understood by philosophy of mind as direction of fit.

So for all intents and purposes, in general conversation, science proves statements about empirical matters to be true with the caveat that further information might show science has made a mistake. Thus science generally proves claims true about the physical world, but no claim is beyond revision, improvement, or falsification. This is consistent with the epistemological position called fallibilism (IEP).

The truthfulness of the mathematical proofs depends on the underlying axioms. For example, Euclidean geometry is based on the following 5 axioms:

1. A straight line may be drawn between any two points.
2. Any terminated straight line may be extended indefinitely.
3. A circle may be drawn with any given point as center and any given radius.
4. All right angles are equal.
5. For any given point not on a given line, there is exactly one line through the point that does not intersect the given line.

The above axioms are assumed to be true -- and all subsequent proofs are conditional on the axioms holding true.

The natural sciences have similar foundations. They are based on certain assumptions about our reality -- and all scientific proofs are, therefore, conditional on those assumptions holding true. These are the assumptions as I see it:

1. There is only one objective reality that we all share and belong to. That is, we assume that we are not dreaming it all up, that we weren't spawn into existence 10 seconds ago with our memories implanted, etc.
2. This reality is deterministic. Things do not happen at random, but every event was caused by some past event. The laws of nature prescribe how exactly causes create their effects. Those laws are immutable.

To sum it up: scientific proofs are possible but they depend on the above assumptions.

Logical Positivism was premised on the idea that both science and logic verify claims. Karl Popper pointed out that science can never verify anything, it can only fail to falsify it. There is virtually no dispute that science cannot do verifications. Popper put falsification at the core of science, where it remains.

Note that Popper considered all observations and facts to be tentative, not certain. "Facts" are the hypotheses that we have enough confidence in to use to anchor and test other hypotheses.

However, multiple critics of Popper's falsification attacked the principle that science can do falsification either. Kuhn looked at the history of science and showed that paradigm shifts were at best only loosely related, and more commonly basically unrelated to newly discovered facts that could falsify a theory. Paul Feyerabend pointed out the radical difference in methods of science in different fields and different maturities of a field. Willard Quine, in the Quine-Duhem thesis, pointed out that all theories are always underdetermined by evidence, so no certain falsifications are ever possible either. Extending Quine-Duhem to the hypotheses we take as facts -- none of theme are certain either, so we cannot have certainty even of our data. Poppers strict approach to falsification may be an aspiration, but it is not actually achievable.

Popper admitted this himself in his later years, and proposed an alternative method of doing science, which relied upon cental and ancillary hypotheses, rather than falsification. One could compare rival collections of hypotheses by the degree of predictability they offer. The more potential states of the world that a central plus ancillary collection that matches our data predicts could not happen, the better the hypothesis. This is a rephrasing of Occam's Razor.

Imre Lakatos proposed a more structured variant on this alternative from Popper, where a family of core plus ancillary assumptions is called a Research Programme. Research Programmes are used in an active field, where ther are always a lot of open questions. The more useful advances that a Research Programme enables, the more "progressive" it is, while the more unresolved questions it has to carry as unresolved, and the more ad hoc ancillary hypotheses it must take on to deal with surprizing observations, the more "regressive" a Programme is. There can be multiple rival Research Programmes being pursued in a field, and their adoption or abandonment is based on the judgement of their users on how progressive or regressive they are.

Popper and his ally Lakatos, with these alternatives, conceded that science can do neither verification nor falsification, although it DOES still do testing. The interpretation of test results though, is a far more judgment based process than simple verification or falsification implies.

So, no. The consensus of philosophers of science is that Science can neither verify a truth nor achieve an absolute falsification.

• Wow. A short summary of the decades of 20th century debate on this very question, plus names of the leading philosophers and movements involved got DOWNVOTED!! Wow. Tough crowd. Dec 22, 2023 at 23:02
• wow indeed. a true disincentive for me putting in my one cent's worth! Dec 30, 2023 at 1:50
• Very true! 😃 👍 Dec 31, 2023 at 20:08
• That's a misunderstanding of the Duhem-Quine thesis. The thesis says that any statement of a theory can be held to be true in light of any evidence because it doesn't have any observational consequences by itself. This doesn't mean that a whole theory is never falsifiable - a theory has observational consequences and can be falsified. The only challenge that the Duhem-Quine thesis poses for falsificationism is that: (a) a theory understood as something that you can find in textbooks has to be supplied by auxilliary assumptions (about instruments etc.) to produce observational consequences.
– user71009
Jan 29 at 14:38
• @Dcleve (b) an amendment to an already well-established theory cannot be falsified independently. We falsify the whole theory (in conjunction with the amendment). Because our knowledge of biology, chemistry etc. depends on physics, this means that potentially discoveries in any science can have an effect on physics and other fundamental natural sciences. Popper thought it's more granular.
– user71009
Jan 29 at 14:40

Imagine you have a Lego castle you built, and you want to know if it's strong enough to hold a toy dragon. Science can't give you an absolute "yes" or "no" answer, like a magic spell. Instead, it's like testing the castle with different weights:

Small Lego people: If even tiny figures make the towers wobble, it's a warning sign! This is like scientific experiments that find weaknesses in an idea.

Bigger Lego creatures: If a medium-sized griffin makes the walls crack, it's more evidence the castle might not be strong enough. More experiments add to the picture.

The big dragon: If the dragon sits on the castle and it STANDS STRONG, that's like a lot of scientific evidence supporting the idea. But what if a bigger dragon comes along? Science is always open to new tests.

So, instead of a final "true" or "false," science gives us confidence levels based on evidence, like your castle tests. The more tests it passes, the stronger the idea.