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What's the difference between "evidence" and "proof"? I've noticed that the word "evidence" is often used in English as if it meant proof. For example,

...there is evidence of human existence in Saudi Arabia dating back 20,000 years

It looks like in this sentence there is no place for any doubts that humans existed in Saudi Arabia 20 000 years ago. If so, then the word "evidence" here, as far as I understand, can be replaced with the word "proof". Or is it like there are some nuances here that I, as a non-native speaker of English, am not seeing?

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    Your sentence actually makes it clear that there is room for doubt, because it used the word evidence. You are now saying "they write evidence, but I want to read proof. Why don't they write proof?" – oerkelens Oct 21 '14 at 7:52
  • Suggested reading: en.wikipedia.org/wiki/Raven_paradox – cobaltduck Oct 21 '14 at 13:30
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    @cobaltduck - I have read about this paradox about half a year ago, but I don't quite understand where you see the connection between the Raven paradox and my question. Can you, please, elaborate? – brilliant Oct 21 '14 at 13:49
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    Just to add to some of the excellent answers, proof only really exists in math. In the real world almost nothing can be truly proven, which is why you'll usually see the word evidence instead, especially in a scientific context. Evidence lends support to a hypothesis (or eventually theory), but those conclusions are always open to change when new evidence is found. – Nicholas Oct 21 '14 at 14:28
  • This green apple is evidence that all Ravens are black. It is not proof. More of a side-bar, then a direct relation to your question. – cobaltduck Oct 21 '14 at 21:12
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In the simplest terms, proof is conclusive but evidence isn't. Evidence is more of a suggestion.

In your example sentence, the use of evidence is to make it clear that there are other possibilities, such as maybe the dating being wrong, or the evidence not being human in origin.

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    I'll confess -- I used my WABAC machine to go back there and plant the evidence. – Hot Licks Oct 21 '14 at 18:50
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Some fine answers already, but to add a simple explanation:

Evidence may be used to form a theory or hypothesis.

Additional evidence may refine such a theory.

Proof shows the theory to be a fact.

Example: Adding one apple to a basket with another apple results in a basket with two apples in. This could be proof that 1+1 is indeed equal to 2, but only evidence that 2+2 may equal 4. We might say that adding another two apples (hopefully resulting in 4 apples in our basket) has shown proof of our theory, or that the theory has been proven.

In your example the author is saying that the evidence (e.g. maybe carbon dated pottery or the like) has led to the theory that humans existed in Saudi Arabia for at least the last 20,000 years. But just like any other theory, the conclusion built upon the understanding of this evidence may be incorrect, and even the understanding, or dating may be incorrect.

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    "hopefully resulting in 4 apples in our basket" - :) :) :) – brilliant Oct 21 '14 at 8:50
  • The continued answers on this question has reminded me that various disciplines do indeed play with the meaning of proof and theory, usually to facilitate discourse. In law, proof may oft mean as digitig & ornello describe; A scientific theory is often taken as fact, though are still not quite 100% immutable, e.g. the big bang theory which was created as a prediction of the standard model. But the SM is only based on our imperfect observations and also predicts dark, matter, dark energy and dark flow, of which a lot of scientists are still very sceptical of.. remember 'aether'? – Toby Oct 21 '14 at 15:33
  • "...is only based on our imperfect observations and also predicts dark, matter, dark energy and dark flow, of which a lot of scientists are still very sceptical of.. remember 'aether'?" - Yes. I absolutely agree with you about that. – brilliant Oct 21 '14 at 15:45
8

Evidence means:-

A thing or things helpful in forming a conclusion or judgment: The broken window was evidence that a burglary had taken place. Scientists weigh the evidence for and against a hypothesis. [American Heritage Dictionary via the Free Dictionary].

Proof means:-

The evidence or argument that compels the mind to accept an assertion as true. [American Heritage Dictionary via the Free Dictionary]

In some fields of enquiry (Law, or the Sciences) a preponderance of evidence, and a lack of evidence to the contrary, would be regarded as a proof of some statement or assertion. In others (Mathematics or Logic), no amount of evidence is a proof. Only a proof:-

a. The validation of a proposition by application of specified rules, as of induction or deduction, to assumptions, axioms, and sequentially derived conclusions.

b. A statement or argument used in such a validation.

would suffice.

  • "In some fields of enquiry (Law, or the Sciences) a preponderance of evidence, and a lack of evidence to the contrary, would be regarded as a proof of some statement or assertion" - So, if while I were sleeping in a car with an open window and somebody stabbed a pedestrian on the street to death and threw the knife into my car and ran away, and there were no evidence that I was not the murderer, then that would be considered as proof that I was the killer?! But that would be a terribly wrong judgment then! – brilliant Oct 21 '14 at 8:28
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    @brilliant - Yes, it would be a wrong judgment. But one must distinguish between proof in a) the legal sense and b) the scientific sense. The standard for a scientific or mathematical proof to be generally accepted as valid is much higher than that often presented (or accepted) by a prosecutor, defence lawyer, judge or jury member. If you were wrongly convicted of murder, many different factors could have contributed to the assembled evidence perversely being equated with proof when it could be interpreted differently, or exonerating evidence at the crime scene might have been overlooked. – Erik Kowal Oct 21 '14 at 9:02
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In probabilistic terms, evidence increases the probability that a proposition holds, relative to its value without such evidence, whereas proof raises the probability to certainty.

If Y is evidence for X, then

P(X|Y) > P(X)

If it's proof of X, then

P(X|Y) = 1

(Strictly speaking, a probability of 1 isn't quite the same as certainty, but that kind of mathematical pedantry is out of scope for EL&U...)

  • What does P stand for in your formulas? Probability or proof? I guess it's probability. If yes, then can it be more than 1? – brilliant Oct 21 '14 at 14:18
  • @brilliant It's probability. No, it can't be more than 1. But 1 doesn't mean certainty: the probability that I'm not exactly 1m70cm tall is 1, but it's not certain. – chiastic-security Oct 21 '14 at 14:21
  • Can it be less than 1 then? Or it's 1 if there is some probability and 0 if it's absent? – brilliant Oct 21 '14 at 14:29
  • @brilliant For all practical purposes, 0 means it's certain not to happen, 1 means it's certain to happen, and a value in between means it might happen. The closer to 1 it gets, the more likely it is; so 0.5 means it's 50/50. (The distinction between 1 and certainty is a red herring: I shouldn't have mentioned it.) – chiastic-security Oct 21 '14 at 14:31
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    Further "P(X|Y)" should be read as "the probability of X given Y". – tobyink Oct 21 '14 at 19:37
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In order to make a case, you need evidence and an argument. Evidence without argument is just a pile of uninterpreted facts. Argument without evidence is just assertion.

When you have a case, the next question is how convincing that case is. Is the argument a good one? Is the evidence open to other interpretations? Whether the case is proof or not depends on the standard of proof you are looking for. In UK civil court cases, a case is considered proof if it is true "on balance of probabilities", that is, if the court is persuaded that the claim is more likely true than not true. In criminal cases, a case is not considered proof unless it is "beyond reasonable doubt" -- the evidence and arguments are so good that no reasonable person would doubt it. And in mathematics, even that level of proof isn't good enough: something has to be shown to be true beyond possibility of contradiction (ok, I'm blurring the distinction between "evidence" and "axioms" on that last one).

What all this comes down to is that "proof" is a sliding scale, but that wherever you are on it, evidence alone is only one part of a proof.

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In basic terms, evidence + best argument = proof. 'Evidence' can be either physical or testimonial.

In criminal law, the basic evidence is only part of the case. If the prosecution can make a better argument based on the evidence available (bullets, blood, DNA, footprints, fingerprints) than the defense can to explain these things away, you have 'proof', i.e., 'beyond a reasonable doubt'. So, if the prosecution can make a better case than the defense, they have proved their case. 'Proof' has to come up to a standard, which varies according to the kind of case it is ('beyond a reasonable doubt' for some cases, or 'preponderance of the evidence' for others).

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Evidence is some fact that supports a theory. There may also be other, incompatible theories that would also be supported by the same evidence, so either of them may still be right or wrong.

Once there is proof, that means that there is enough of the right evidence that it all supports the theory, and it's not possible that it's not true.

Maybe you believe that Earth has the shape of a cylinder. You travel all the way around it in a ship, and end up at the same spot! Evidence for the theory that Earth is a cylinder, because if it's a cylinder, then that would be possible.

But it's also evidence for the theory that it is a sphere. But then people find the poles, they travel around it in several different directions, and eventually we go into space -- lots of evidence against the cylinder, in fact enough to prove that it's not a cylinder at all (this is just an example, I'm quite sure it was easy to prove Earth is not a cylinder much earlier :-)).

Eventually we gather so much data with satellites et cetera that we know exactly what the shape of the earth is, and it's almost a sphere, but slightly flattened. We know so much about it that that can be considered proven.

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Consider the following phrases

  • some evidence
  • partial evidence (including: additional evidence)
  • evidence
  • overwhelming evidence
  • convincing evidence
  • ultimate evidence
  • definite evidence
  • ...
  • ...
  • proof

But anything more than a proof is less than a proof (e.g. ultimate proof is not a proof).

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“Evidence" is the proof without armor, a strong indication.

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    This post would be improved by explaining why you suggest this term, for example, by providing a dictionary definition or examples in the wild. I encourage you take the site tour and review the help center for additional guidance. – Nathaniel Nov 6 '15 at 19:34

protected by tchrist Nov 7 '15 at 12:16

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