Consider this:

  1. Evidence is the foundations of proof.
  2. So, enough evidence creates proof.
  3. However, how much evidence is needed to make proof depends on the concerning persons' circumstances, predispositions and the topic at hand.
  4. Because of this, different people disagree on how much evidence is needed for proof - i.e. the threshold between evidence and proof is debatable.
  5. Therefore, if proof is debatable, nothing can be proof, as it goes against it's own definition.

Can anyone argue against this?

Note: The words proof and evidence are used in the court sense, not the typical philosophical sense.

  • 4
    This makes sense under an informal, colloquial definition of "proof", but as is usually used in philosophy, the word proof doesn't have the meaning you've imputed to it.
    – Dave
    Oct 21, 2014 at 18:25
  • @Dave Edited. This question is OK otherwise though?
    – woff
    Oct 21, 2014 at 18:39
  • Given that this is philosophy.SE, seems like you should be asking about these words in the philosophical sense, and should ask somewhere else for whether it would be true in that sense, no? Oct 21, 2014 at 21:25
  • Look at @adhoclobster's answer. He had the same analogy, with a different example, yet that is fine. I also added a note earlier, so I don't understand why you say this is the wrong site.
    – woff
    Oct 21, 2014 at 21:45
  • 1
    In the court sense, you are obviously wrong. In most places the criterion is "proof beyond reasonable doubt"; many people have been convicted according to this criterion, so obviously there is proof.
    – gnasher729
    Oct 22, 2014 at 16:43

7 Answers 7


One possible objection is that you're claiming something doesn't exist merely because people have varying abilities for recognizing (or not) said candidate existant (which you seem to posit in premise 2).

  1. A heap of sand is made up of grains.
  2. So, a certain number of grains of sand comprises a heap.
  3. However, how many grains are needed to make a heap depends on vague perceptual, semantic rules or guidelines which may not be followed by all people in all situations to their full degrees.
  4. Because of this, different people disagree on the number of sand grains needed for a sand heap.
  5. Therefore if a heap is vaguely defined, it must be the case that no heaps actually exist.

Does this really follow? Seems to me that there's a pretty big leap in 5. I take issue especially with "If proof is debatable, nothing can be proof."

  • I like this answer(+1). Any (finite) heap of sand can be linearly ordered, and the set of all (finite) heaps can be well-ordered by size (=number of grains). Therefore, since well-ordering guarantees a "least member" (=smallest heap), there should be an answer. I think this is related to Berry's Paradox.
    – nwr
    Oct 21, 2014 at 19:56
  • Thanks for the response. I actually asked this because of my own wandering thought train sparked by religious studies in class.
    – woff
    Oct 21, 2014 at 20:50

It is such an intriguing argument though I find it hard to buy your premise 1 and 2. In my understanding, the evidence you are talking about here means the possible basis for a belief or a disbelief, such as testimonium in Latin sense. What is vague here is what you mean by "proof." Personally, I tend to interpret "proof" as "demonstrandum." Since you will want to say that proof is a complete ground for a belief or disbelief, i.e., we can claim that proof <=>a belief or a disbelief. Then proof is a demonstration about a belief or disbelief. Therefore, evidence does not create proof, evidence is solely an attempt to demonstrate a belief or a disbelief.


There are two types of proofs that would be considered legitimate within philosophy and science: logical proof and empirical proof.

Logical proof reasons from axioms within a logical system such as mathematics. Mathematics appears to underlie many natural laws. Such proofs do not require evidence but operate using the rules the system follows.

Empirical proof can establish basic existence of an entity or force, subject to experimental error, or that a particular entity or force has been observed to have a particular property under the conditions that held true when it was measured. You cannot trangress beyond this. If you observe a hundred white swans and no swans of other colours, it does not prove all swans are white, or even that most swans are white. At best you can regard the existence of white swans as proven. If all swans you observed in a given area at a certain time period were white, this may lead you to assign a higher probability of encountering white swans than you assign to other colours, but, crucially, you can never assign zero probability to the possibility of multicoloured swans.

Courts generally require that claims be established "beyond reasonable doubt". This is, as you say, something that will vary considerably from person to person. Even assuming the individuals deciding on the claims accept scientific standards of proof, and assuming they assign probabilities very similarly, what, precisely, constitutes "reasonable doubt"? Opinions will differ. Averaging out these opinions makes up a great part of the value gained from having juries and panels of judges.


Evidence can establish proof that a theory is wrong. If I find a white crow, then I have conclusively proven that "all crows are black" is wrong.

Proving a theory emperically is logically equivalent to proving that all opposing theories are wrong. If an opposing theory could be correct, then clearly we cannot have proven that our theory must be correct.

For example, we have proven that "The Earth is round" because all other possible shapes for the Earth have been ruled out by evidence. It cannot be flat, it cannot be a cube, it cannot be a torus, because we have experimental evidence showing those shapes do not match reality.

Likewise, we have proven "The Earth is about 4.5 billion years old" because all other possible theories about the age of the earth have been ruled out by evidence. (The theory "The Earth is actually 6,000 years old, but God made it appear exactly as if it were 4.5 billion years old" is by definition experimentally indistinguishable from "the Earth is 4.5 billion years old" and as such, does not count as a separate theory).

Likewise, there is no theory other than Evolution that explains the evidence we see in biology. There is no theory other than Anthropogenic Global Warming that explains what evidence we see in climate studies.

So, to answer your question, "enough evidence" means we have enough evidence to eliminate all other opposing theories.

  • The above applies in court as well as in science. To prove to a jury that person X murdered person Y, the prosecutor must eliminate the theories "persson Y was not murdered" and "somebody else murdered person Y". Oct 23, 2014 at 16:08

There are two measures of truth at play:

     (1) phenomenological matching
     (2) ontological matching

See Massimo Pigliucci's Essays on emergence, part I:

Batterman takes on an alleged (as it turns out) case of reduction of a phenomenological to a more “fundamental” theory: the relationship between classical thermodynamics (phenomenological) and statistical mechanics (fundamental). The fact is, “the quantities and properties of state in orthodox thermodynamic equations appear largely to be independent of any specific claims about the ultimate constitution of the systems described,” which would seem to cast some doubts on the simple version of the reduction story. As Batterman puts it, “Reduction in this context typically is taken to mean that the laws of thermodynamics (the reduced theory) are derivable from and hence explained by the laws of statistical mechanics (the reducing theory) ... [but] there are very good reasons to deny that all thermodynamic (and hydrodynamic) phenomena are reducible to “fundamental” theory,” and these reasons have to do with phase transitions (solid and liquid, liquid and gas, etc.).
Batterman directs his reader to the role played by renormalization group theory within the context of condensed matter theory. This is because renormalization theory “provides an explanation for the remarkable similarity in behavior of ‘fluids’ of different molecular constitution when at their respective critical points.” It turns out, experimentally, that there is a universal pattern that describes the behavior of substances of very different micro-constitution, an observation that — suggests Batterman — would make it puzzling if the right explanation were to be found at the lower level of analysis, in terms of the specific micro-constitution of said fluids.

What science shows is that different ontologies can produce extremely similar phenomenologies. And so, unless you can discern the phenomenology with sufficient precision, you simply cannot know which ontology undergirds the phenomena. And so, (1) may be permanently impossible. Evidence may never, ever give 'proof' of (2). It can, however, establish that (1) is the case. That's done all the time, and is expressed by the phrase, "The model matches the evidence quite well."


One could point out that you are presenting a logical argument, i.e. evidence, to prove that there is no such thing as proof. You create a paradox: If your argument is valid, there is no such thing as "proof", so any claim that you have proven your point is inherently self-contradictory. :-)

But that said ... A classic philosophical musing is to ask, "What can we know for certain?" Of course we can quickly dismiss "I read it in a book" or "My teacher told me" as proof: Maybe the book or the teacher is mistaken or lying. You say you saw it with your own eyes? But we have all seen optical illusions. How do you know that what you saw in this case was real and not an illusion? You have a rigorous logical argument that proves it true? But how can you be sure that there is no flaw in your logic? We have all seen others duped by flawed arguments. Maybe you can even recall a case where you were convinced by a logical argument yourself but later concluded that the argument was wrong. What makes you think that your logic is infallible? Etc.

Thomas Aquinas once argued that he is confidant that he, himself exists. After all, he said, I may be deceived about many things. But I can't be deceived about my own existence, because in order to be deceived, I must exist. But beyond that ... In real life, we all have some things that we would say we are 99+% sure of. I'm quite sure that gravity exists, and that 2+2=4, for example. But how sure am I that the planet Neptune exists? Or that the cosine of 30 degrees = 1/2? I'd put them pretty high, but I'd be a little more tentative. I've seen pictures of Neptune on TV ... but then I've seen pictures of the planet Tatooine on TV too. I've probably seen a proof of the cosine of 30 somewhere, but I don't remember it. To come down many steps: I doubt that bigfoot exists. But I wouldn't bet my life savings on it. Etc. My point being, Can we really say that we have ABSOLUTE, 100% proof of anything? Any such argument must ultimately rest on philosophical beliefs about the nature of reality, and about logical arguments, and I think that any intelligent, honest person would have to admit that he can't be 100% certain of these things.

So I conclude that it's not a simple yes/no question, the point is proven or it is not. It's a matter of, just how convincing is the proof? 50%? 80%? 90%?

Our courts routinely talk about "levels of proof". The highest standard is "proof beyond a reasonable doubt". That's the standard used in criminal cases. The idea is that, yeah, someone could always bring up some unanswered question, so there's always some room for doubt. As one lawyer put it, "It's POSSIBLE that invisible Martians suddenly appeared in the locked room, killed the victim, shoved the bloody murder weapon into the hands of the defendant, and then disappeared just as the police broke down the door. But probably not." At the other extreme is "preponderance of evidence". This is the standard used in civil suits, and it means "which side was more convincing". If you think there's a 51% chance that side A was in the right, then you must rule in favor of side A, even though you believe it is very very close.

We all apply such standards all the time -- not so rigorously named, but the same idea. Before I buy a house I make very sure that I know what I am buying, that all the paperwork is done correctly, etc -- and then I buy insurance just in case I'm wrong. I go to nowhere near as much work before buying a box of cookies. If a friend said they tasted good, I may risk a couple of dollars and buy them. If they turn out to taste awful, so I throw them away. I haven't lost much, so I don't need to spend weeks studying the question. Etc.


Evidence is the foundations of proof.

So, enough evidence creates proof.

There is an invalid jump between the first two statements there. There is also an issue over whether the argument is even sound as opposed to valid in the first place.

Proof really entails that, given certain evidence (read 'sound assumptions'), a conclusion is valid, or logically true. It doesn't mean merely that there is a lot of evidence.

The first premise in the Original Poster's argument there is rather under-qualified. Evidence constitutes the sound (true) assumptions of an argument. The validity of the argument, in conjunction with it being sound (i.e. the assumptions involved being true), involves proof. However, the validity of an argument does not involve an amount of evidence (read an amount of true assumptions).

For example, that we know that:

  • John visited the cellar and the attic.

    ... constitutes both evidence and proof that:

  • John visited the cellar.

If we know the first sentence is true, we have enough knowledge to validly infer the second without knowing it independently. Taking the first as a piece of evidence is sufficient on its own to prove the second - given the valid argument that A + B --> A.

However, true evidence that:

  • John likes football
  • John has a name associated with males
  • John has a girlfriend
  • John is six foot four
  • John shaves their face

does not constitute proof that John is a man. She may be a woman. Large amounts of evidence do not in any way constitute proof. The amount of true evidence is not the issue. It is what true evidence in conjunction with what valid argument you have, that proves.

You can provide as much true evidence that I'm a miserable crook as you want, it doesn't merely on the basis of being a large amount of evidence prove that I'm a miserable crook - unless the evidence is a) true, and b) forms part of a valid argument showing that I am.

In short:

  • evidence is not the sole foundation of proof

  • no amount of evidence is equivalent to proof

  • our predispositions do not make arguments valid, so they do not affect the statement above.

  • there is no blur between evidence and proof. A sound, valid argument constitutes proof. Evidence however is just an assumption in a proof.

However - I am completely willing to be proved wrong!

  • I'm inclined to agree insofar as a formal definition of proof is concerned, but isn't there a certain colloquial sense in which proof consists of evidence in large quantities? For example, what else can popular biologists mean when they suggest we the public (non-scientists) should be inclined to believe the Theory of Evolution is true due to how much evidence there is in its favor? Oct 22, 2014 at 2:19
  • 1
    @adhoclobster Well, the question there is should you believe things on the basis of evidence alone? The answer, I reckon, is yes. There's nothing wrong with taking large amounts of evidence as a basis for believing something. The evidence just doesn't constitute proof that what we believe is true, that's all. Oct 22, 2014 at 12:19
  • Hmm, I think you're attacking a bit of a straw man. You seem to be making much of quantity of evidence as opposed to persuasiveness. But I would think that any rational definition of evidence must weigh it by its persuasiveness. If I am listing to a debate on whether X is true, I can't imagine saying, "The 'yes' side gave 10 arguments while the 'no' side gave only 4, so it must be true." Surely I would consider how persuasive each of those arguments are and not just count them.
    – Jay
    Oct 24, 2014 at 18:51
  • @Araucaria I said that I thought you said that the original poster said that the quantity of evidence was the issue. That sentence should clear up any confusion.
    – Jay
    Oct 26, 2014 at 1:58
  • @Jay OK I get what you meant.. Yes, If the questions edited that way, then there should be an issue about the quality of the evidence. But that still makes the conjunction of 1 and 2 in the argument invalid. In fact it just makes 2 plain wrong. I don't think there's any question that 2 isn't wrong, even if we substitute in a different meaning for proof. Oct 26, 2014 at 10:45

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