# Difference Between Evidence and Proof

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What's the difference between evidence and proof?

I think a lot of evidence can lead to proof.

Also, proving and disproving of a model is important to keep science, scientific.

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Proof is absolute. You can do that in math, where you can take a premise and a set of rules, and apply them.

In science, the process is inductive. More than one explanation might be consistent with the evidence, but we won't know until more evidence is obtained. Such as with phlogiston — worked with preliminary data, but then evidence was uncovered that was inconsistent with the model.

It is the job of scientists to try and exclude all but one explanation, but there's always the chance that the known science is incomplete, and there is more science to be revealed. Such as happened with relativity and quantum mechanics.

However, there is a point at which you have to concede that it is exceedingly unlikely that a model is wrong, owing to all the evidence in support of it. It is similar to Stephen Jay Gould's description of "fact"

In science, 'fact' can only mean 'confirmed to such a degree that it would be perverse to withhold provisional assent.' I suppose that apples might start to rise tomorrow, but the possibility does not merit equal time in physics classrooms.
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A proof will never change. Evidence weighs on the balance of probabilities that can lead to high confidence but always leaves the door open.

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21 minutes ago, swansont said:

t is the job of scientists to try and exclude all but one explanation, but there's always the chance that the known science is incomplete, and there is more science to be revealed. Such as happened with relativity and quantum mechanics.

Isn't it rather the job of scientists to 'prove' an explanation (like a quantum interpretation or a quantum-gravity model) and in doing so, debunk  the other explanations?

Another difference between proof and evidence is that proof is less/not open for interpretation. Many fields of evidence concerning biological evolution are open for interpretation but the evolution theory not so much.

Scientific knowledge is imo always incomplete, the knowledge 'constantly' grows.

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4 minutes ago, Itoero said:

Isn't it rather the job of scientists to 'prove' an explanation (like a quantum interpretation or a quantum-gravity model) and in doing so, debunk  the other explanations?

No, because:

5 minutes ago, Itoero said:

Scientific knowledge is imo always incomplete, the knowledge 'constantly' grows.

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32 minutes ago, Itoero said:

Isn't it rather the job of scientists to 'prove' an explanation (like a quantum interpretation or a quantum-gravity model) and in doing so, debunk  the other explanations?

A quantum interpretation is not something you can prove; it's not actually science. It's an interpretation of science.

In general, it's not my job to debunk someone else's claim, as such. It's their job to make their claim stand up to scrutiny, which includes debunking other explanations. Nobody is likely to come along and find deviations from Newtonian gravity for human-scale interactions — we have too much evidence that it's correct, so we have tremendous confidence in it. The deviations are in the more extreme cases, where GR differentiates itself from Newtonian physics. Something new would have to somehow give different predictions from GR, and confirm them experimentally, in order to be accepted. They have to give everyone a reason to pay attention to it.

So they would have to show their results are different from accepted theory, and credible — that's it's not the result of a shoddy experiment, or some confounding effect that's skewing the data. (which happens — see BICEP2 or the superluminal neutrino results, for example)

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1 hour ago, Itoero said:

Scientific knowledge is imo always incomplete, the knowledge 'constantly' grows.

You say this, and yet I doubt your sincerity. You still seem to rebel against the idea that "proof" isn't what science is looking for. I think you still believe this:

2 hours ago, Itoero said:

I think a lot of evidence can lead to proof.

Also, proving and disproving of a model is important to keep science, scientific.

I've lost track of the number of threads where people explained the reasoning behind theories and why the methodology looks for the best supported explanations, and yet you opened this thread to repeat your belief. You seem to really want to believe things can be proven. Maybe you could explain why?

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5 hours ago, Itoero said:

What's the difference between evidence and proof? I think a lot of evidence can lead to proof.

If you accept discovery of a particle as proof for a particle, then that is pretty much the usage of the terms in particle physics, where "evidence" is a certain amount of statistical significance and "discovery" is a certain larger amount of statistical significance (example link for explanation: https://blogs.scientificamerican.com/observations/five-sigmawhats-that/). That usage of the terms is, however, very field-specific. Other fields may have problems to quantifying statistical evidence.

5 hours ago, swansont said:

Proof is absolute. You can do that in math, where you can take a premise and a set of rules, and apply them.

When I was a young math student, I thought about the same. Then in a seminar a professor asked me "what is a proof" and I told him something about a series of logical arguments that start from a given set of axioms. His reply was roughly "err .. yes, that too, ... maybe. But mostly it is an argument that other people accept as true". I think his understanding of "proof" may be the better one (keeping in mind that "other people" referred to mathematicians in this case, who tend to be very rigorous/conservative about accepting things as true).

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29 minutes ago, timo said:

When I was a young math student, I thought about the same. Then in a seminar a professor asked me "what is a proof" and I told him something about a series of logical arguments that start from a given set of axioms. His reply was roughly "err .. yes, that too, ... maybe. But mostly it is an argument that other people accept as true". I think his understanding of "proof" may be the better one (keeping in mind that "other people" referred to mathematicians in this case, who tend to be very rigorous/conservative about accepting things as true).

Isn't a proof an argument that can't be contradicted? Whatever path you take, you always end up in the same place.

Edited by StringJunky
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7 hours ago, Itoero said:

What's the difference between evidence and proof?

Evidence doesn't make the yeast bloom and leaven the bread

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1 hour ago, timo said:

When I was a young math student, I thought about the same. Then in a seminar a professor asked me "what is a proof" and I told him something about a series of logical arguments that start from a given set of axioms. His reply was roughly "err .. yes, that too, ... maybe. But mostly it is an argument that other people accept as true". I think his understanding of "proof" may be the better one (keeping in mind that "other people" referred to mathematicians in this case, who tend to be very rigorous/conservative about accepting things as true).

I think that is quite similar to the more colloquial usage that aligns with SJG's definition of "fact"

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1 hour ago, StringJunky said:

Isn't a proof an argument that can't be contradicted? Whatever path you take, you always end up in the same place.

Not 100% certain what you mean. "Can't be contradicted" is not the same as "proven", especially in math. Any unproven theorem in math, say an unproven Millenium Prize Problem, is proof of this (silly pun intended). Because if they could be contradicted (more specifically: we knew a contradiction to the statements) then they were proven wrong. Accepting an argument as true is a much stronger statement than not contradicting it.

Taking the liberty to modify your statement to "a proof is an argument that everyone [sane and knowledgeable implied] has to agree on" that is not too far away from what I said. The main question is where "everyone" lies in the range from "everyone in the room" to some infinity-limit of everyone who has commented and may ever comment on the statement. This limit would indeed be a new quality that distinguishes proofs from facts (to use the terms swansont suggested in this thread's first reply. I could understand if people chose this limit as a definition for a proof. But it looks very impractical to me, since I doubt you can ever know if you have a proof in this case (... but at least you could establish as a fact that something is a proof ... I really need to go to bed ... ).

Fun fact: For my actual use of mathematical proofs at work, "everyone" indeed means "everyone in the room" in almost all instances. For me, the agreement of that audience would not be enough to call something a fact . (Okay... off to bed, really ....).

9 minutes ago, swansont said:

I think [your former professor's definition of a proof]  is quite similar to the more colloquial usage that aligns with SJG's definition of "fact"

It is, indeed. Maybe with an extra grain of elitism for not needing observations but relying on the thoughts of peers alone.

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2 hours ago, timo said:

Not 100% certain what you mean. "Can't be contradicted" is not the same as "proven", especially in math. Any unproven theorem in math, say an unproven Millenium Prize Problem, is proof of this (silly pun intended). Because if they could be contradicted (more specifically: we knew a contradiction to the statements) then they were proven wrong. Accepting an argument as true is a much stronger statement than not contradicting it.

Taking the liberty to modify your statement to "a proof is an argument that everyone [sane and knowledgeable implied] has to agree on" that is not too far away from what I said. The main question is where "everyone" lies in the range from "everyone in the room" to some infinity-limit of everyone who has commented and may ever comment on the statement. This limit would indeed be a new quality that distinguishes proofs from facts (to use the terms swansont suggested in this thread's first reply. I could understand if people chose this limit as a definition for a proof. But it looks very impractical to me, since I doubt you can ever know if you have a proof in this case (... but at least you could establish as a fact that something is a proof ... I really need to go to bed ... ).

Fun fact: For my actual use of mathematical proofs at work, "everyone" indeed means "everyone in the room" in almost all instances. For me, the agreement of that audience would not be enough to call something a fact . (Okay... off to bed, really ....).

It is, indeed. Maybe with an extra grain of elitism for not needing observations but relying on the thoughts of peers alone.

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-Many things are proven in science: Evolution theory, the expanding of the universe, gravitational lensing,  red shift, blue shift, subatomic particles, atoms, molecules, the fact that light exists out of photons, Rayleigh/Compton scattering,...

Science doesn't deal with 100% proof but it does deal with proof. Everything in science can change, things which are proven are less likely to change.

You can have a look how 'scientific' papers often use 'proof'.https://www.nature.com/search?q=proof

-In an experiment/study you do exclude measurements/explanations/observations/models which seem invalid. But it depends what field you are in. String theory,  Loop quantum Gravity, quantum gravity models can't be disproven or  just excluded.  When one model is somehow proven, other models loose their scientific value and will disappear from the world of science.

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4 minutes ago, Itoero said:

When one model is somehow proven, other models loose their scientific value and will disappear from the world of science.

I think that is the problem with this definition of proof. For example, Newtonian gravity hasn't (and won't) disappear because we have a better ("more proved"?) theory of GR. So the "proofs" of Newtonian gravity still hold, even though we know it is "wrong".

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1 hour ago, Itoero said:

Science doesn't deal with 100% proof but it does deal with proof.

This right here is why I think you're wrong. You take a solid definition of proof (100%) and then decide to also use it to describe what science looks for (best current explanation). You insist it means both things, and to me that muddies the water unnecessarily, and robs a great word of its clarity.

As far as others using it in papers, I also blame lazy definitions. Perhaps they don't use "theory" because so many folks like you insist that it can also mean something else, in this case "something I dreamt up while showering".

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10 hours ago, Itoero said:

You can have a look how 'scientific' papers often use 'proof'.https://www.nature.com/search?q=proof

OK, I looked at the first page of search results. I counted:

• 11 times 'proof-of-concept'
• 1 time 'proof-of-principle'
• 1 time 'formal proof'

None of them is a hint that the authors mean 'scientific proof'. As a database administrator, I sometimes make 'proof-of-concepts', showing that a certain solution in principle could work. (So I think that 'proof-of-principle' and 'proof-of-principle' mean the same.)

In general, observations and experiments support scientific theories, or shows them wrong (at least int the form the theory has at the moment). And when the support is very strong, one could say that a theory is proven. But there is always the chance that it will turn out that a theory is only valid in a certain domain, and must be changed to include other domains.

11 hours ago, Itoero said:

When one model is somehow proven, other models loose their scientific value and will disappear from the world of science.

I think you should be more specific on this 'somehow'... And mostly theories are rejected, because they cannot explain certain observations. But all this scratches just the surface. Already read the philosophy of science of Imre Lakatos?

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1 hour ago, Eise said:

So I think that 'proof-of-principle' and 'proof-of-principle' mean the same

Ups... I meant "So I think that 'proof-of-principle' and 'proof-of-concept' mean the same"

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On 18/09/2018 at 1:53 PM, Itoero said:

What's the difference between evidence and proof?

I think a lot of evidence can lead to proof.

Also, proving and disproving of a model is important to keep science, scientific.

I don't see what the fuss is about.

Surely evidence is just data.

But only data that is or may be, relevant to some sort of investigation.

Any other data, including data that starts off in the may be relevant  category but is subsequently ruled irrelevant is not evidence.

Note that this explanation requires the context of an investigation (Scientific, legal, philosophical. whatever).

Hypotheses or explanations for the evidence may be proposed and in the context of investigation,  the rational deduction of the best hypothesis called a proof.

Different standards and criteria are applied to different types of investigation so there are many different types of proof.
There is no one size fits all.

One thing to note is that the evidence stands separate from the hypotheses and proof so that both of these may change, whilst the evidence remains at least part of the evidence and so that new evidence can be added to or removed from the data.

A good discussion of this process in Science is to be found in this book

Edited by studiot
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• 3 weeks later...

On ‎21‎/‎09‎/‎2018 at 10:01 AM, Eise said:

think you should be more specific on this 'somehow'... And mostly theories are rejected, because they cannot explain certain observations. But all this scratches just the surface. Already read the philosophy of science of Imre Lakatos?

I don't mean that this is for all models. When for example the holographic is 'proven' then other models are not disproven but lose their scientific value.

On ‎21‎/‎09‎/‎2018 at 10:01 AM, Eise said:

None of them is a hint that the authors mean 'scientific proof'.

That's  your interpretation and you should read the OP again. I did not use the term 'scientific proof'.

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14 hours ago, Itoero said:

That's  your interpretation and you should read the OP again. I did not use the term 'scientific proof'.

You asked about the difference between evidence and proof in the context of science, so this would seem to be just a semantic argument that you didn't use that specific phrasing, and yet it's precisely what was implied.

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15 hours ago, Itoero said:

I don't mean that this is for all models. When for example the holographic is 'proven' then other models are not disproven but lose their scientific value

If by "proven" you mean "having more evidence than another competing theory" then this might be true. But, actually, no it isn't.

GR is "more proven" than Newtonian gravity (it can explain things that Newtonian gravity gets wrong for example), but Newtonian gravity has not lost its scientific value.

Your description seems to be almost the exact opposite of how science works. A theory is not rejected because another one is "proven" but when it can no longer explain the evidence. For example, for a long time there was a debate about whether the big-bang or the steady-state model (or models) was more accurate. This was resolved when the CMB was discovered. Not because this "proved" the big-bang model but because it disproved the alternatives (they could not explain this evidence).

So a theory or hypothesis loses its value when it can no longer explain the evidence.

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4 hours ago, Strange said:

If by "proven" you mean "having more evidence than another competing theory" then this might be true. But, actually, no it isn't.

GR is "more proven" than Newtonian gravity (it can explain things that Newtonian gravity gets wrong for example), but Newtonian gravity has not lost its scientific value.

Your description seems to be almost the exact opposite of how science works. A theory is not rejected because another one is "proven" but when it can no longer explain the evidence. For example, for a long time there was a debate about whether the big-bang or the steady-state model (or models) was more accurate. This was resolved when the CMB was discovered. Not because this "proved" the big-bang model but because it disproved the alternatives (they could not explain this evidence).

So a theory or hypothesis loses its value when it can no longer explain the evidence.

You might find it hard to reject Newtonian Physics, since it is a limiting case of Einstinian.

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2 hours ago, studiot said:

You might find it hard to reject Newtonian Physics, since it is a limiting case of Einstinian.

Quite.

Nearly all new theories are refinements of the ones they “replace”.

Edited by Strange
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On ‎13‎/‎10‎/‎2018 at 1:36 PM, swansont said:

You asked about the difference between evidence and proof in the context of science, so this would seem to be just a semantic argument that you didn't use that specific phrasing, and yet it's precisely what was implied.

You are wrong. Evidence and proof used in science are not necessary 'scientific'. The meaning of evidence and proof changes depending on the context the words are used in.

Edited by Itoero

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