This post originally appeared on ZeMing M. Gao’s website, and we republished with permission from the author. Read the full piece here.

In the upcoming trial of COPA v. Wright, COPA sets out to prove that Dr. Wright is not Satoshi, while Dr. Wright provides evidence that he is.

How do you prove a negative?

There is a misunderstanding about “negative proof,” especially among the supporters of Dr. Wright. The saying is that it is impossible to have “negative proof.”

Let’s first leave the case-specific evidence aside and consider it purely from a logical point of view.

In philosophy, science, and logic, it is recognized that “Argument from Ignorance” (ad ignorantiam) and “Argument from Absence” (Argumentum ex silentio) are logical fallacies where the “absence of evidence” is taken as “evidence of absence” to disprove a claim.

That is, it is fallacious logic to take the absence of evidence for a statement as evidence that the opposite statement is true or the absence of evidence against a proposition as evidence that the proposition is true.

Sometimes, “Argument from Ignorance” and “Argument from Absence” are called “negative proof,” and in this sense, “negative proof” is impossible because it is based on the logical fallacy.

However, in COPA v. Wright, COPA’s claim is not necessarily the kind of negative proof based on an “Argument from Ignorance” or “Argument from Absence,” which would be too obvious to pursue seriously.

What COPA sets out to do is to negate a claim by Dr. Wright that he is Satoshi. It is “proof of a negative,” different from the “negative proof” defined above.

For convenience, let’s still call what COPA needs to prove “negative proof.”

The kind of “negative proof” COPA needs to bring is not logically fallacious or impossible.

That is, at least logically, it is possible for COPA to establish negative proof of Dr. Wright’s Satoshi claim.

Any statement or proposition, if it is factual or scientific in nature, must be at least theoretically possible to be proven wrong, negated, or falsified. This is the “principle of falsifiability” in science.

Because Dr. Wright’s claim that he is Satoshi is factual in nature, it must be falsifiable or has the potential to be proven wrong.

COPA’s unspeakable pain

Therefore, COPA isn’t so foolish that they are pushing a proposition that is outright fallacious and illogical from its onset. They want negative proof of Dr. Wright’s claim. What they want is not a logical fallacy, at least not on its face, because it is possible to have such a negative proof.

But the trouble is that, in all the Particulars of Claim (POC) of COPA, there is absolutely nothing that even alleges, let alone proves, a legitimate and logical “negative proof” to Dr. Wright’s positive claim.

On the contrary, every allegation that COPA has made and presented to the court is designed to avoid having such negative proof rather than pursuing it. It focuses on circumstantial evidence of tangential issues away from the core.

COPA’s allegations can be put into two major categories:

  1. Dr. Wright failed to prove that he was Satoshi in the past.
  2. Dr. Wright has committed forgeries.

The problem is that these allegations, even if proven to be true, all fall into the strict category of “Argument from Ignorance” (ad ignorantiam) or “Argument from Absence” (Argumentum ex silentio), which is known to be a logical fallacy.

It confuses “proof of something negative about a claimant” with “negative proof of a statement made by the claimant.” It further confuses “negative proof of a supporting statement” with “negative proof of the end statement” (see below for the distinction between a supporting statement and the end statement).

Real negative proof

The logical way to establish a negative proof of a positive claim is to prove either impossibility or direct contradiction inherently arising from the claim rather than rely on circumstantial evidence of events that carry negative implications to the claimant.

Real negative proof is not only possible but can also be essential in many cases.

Consider the following simple example:

You have a car. The car has only one original key, but you are missing it.

The claim: Bob says he has the original key to your car.

A false negative proof: you search Bob’s hands and pockets and don’t find the key, and proclaim that you have proven Bob’s claim is wrong. (This is classic “Argument from Ignorance” because you have not exhausted all possible places Bob might have kept the key.)

Another false negative proof: you point to evidence that Bob has lied in the past about where he kept the key. (This is an example of “Argument from Absence” because Bob’s lying about where he kept the key just means he has failed to provide evidence that he has the key, but such absence of evidence does not contradict or exclude the possibility that he does have the key.)

A true negative proof: Alice shows up and presents the key in her hand. (This is an example of proof of impossibility because there’s only one original key, which Alice has, making it impossible for Bob to also have the key.)

Consider another example:

The claim: Bob says he took the famous photo of “Tank Man” during the Tiananmen Square protests in 1989.

A false-negative proof: you find that Bob could not produce the original film of the photo.

Another false negative proof: you find evidence that Bob said things in the past that seemed to be sympathetic to the Chinese Communist Party.

A true negative proof: you discover the evidence that during the entire month of June 1989, Bob was stationed in Berlin and never went to China. (This is an example of proof of impossibility.)

Another true negative proof: Jeff Widener shows up with all evidence that it was he who took that photo. (This is an example of proof of contradiction.)

Therefore, it is possible to have a negative proof, but one should not confuse a false negative proof with a real one.

True negative proof in the context of Satoshi’s identity

The above is not a mere academic discussion. An excellent example of negative proof in a specific context of Satoshi’s identity is illustrated by Jameson Lopp.

Mr. Lopp wrote a piece to present negative proof of the claim that Hal Finney is Satoshi. He used the specific and approvable activity time frames of Satoshi and Finney to prove that it is impossible for Finney to be Satoshi because he could not be running a 10-mile race in Santa Barbara, California, on Saturday, April 18, 2009, at 8 AM Pacific time, while simultaneously sending 32.5 BTC to Mike Hearn via a verifiable transaction as Satoshi did.

What Mr. Lopp presented was legitimate negative proof.

Although nothing involving humans can be 100% certain, this is the strongest type of “reverse alibi” evidence to disapprove a claim of Satoshi.

The same is true with Dr. Wright’s Satoshi claim.

A simple and valid negative claim can shut him down.

For example, why doesn’t COPA extend the discovery to find one or more windows (periods) of provable activities of Satoshi and Dr. Wright to show a contradiction or impossibility?

Such windows do exist. Find Dr. Wright’s travel itineraries from 2008 to 2010 and compare them with Satoshi’s known activities. Just finding one occasion in which Dr. Wright was on a flight while Satoshi was active online would have provided very strong negative proof. The burden would fall completely on Dr. Wright to refute the negative proof.

There is no fundamental barrier for COPA to make such a discovery. In fact, there is no reason to suspect that Dr. Wright might refuse to comply with such a discovery request.

Or, why can’t COPA focus on Satoshi’s evidently necessary skills, such as the knowledge of computer science, programming language, and cryptography, and illustrate by contrast that Dr. Wright does not possess such skills?

Or, why can’t COPA point out the level of Satoshi’s involvement in the Bitcoin project was so high from late 2008 to 2010 that it would necessarily require a full-time involvement, and therefore, any person who claims to be Satoshi could not have been in another employment at the same time?

Just a single negative proof would create an incredible amount of legitimate pressure on Dr. Wright’s claim.

Yet, COPA produces no such negative proof. Zero.

Instead, COPA focuses on circumstantial evidence for negative events (which, as discussed above, is different from negative proof), such as failure to prove the past or alleged forgery.

Why? It certainly cannot be that COPA and its lawyers are so ignorant that they don’t understand the difference.

It is simply because there is no such negative proof in the case of Dr. Wright. It is not that negative proof is inherently impossible (as many have misunderstood), but because, in the specific case of Dr. Wright, there simply is no legitimate negative proof based on either impossibility or direct contradiction.

Jameson Lopp, who gave strong negative proof to reject the Hal Finney Satoshi claim, has not produced concrete negative proof of Dr. Wright’s claim. There is certainly no lack of motivation or resources. Mr. Lopp is one of the strongest deniers of Dr. Wright’s Satoshi identity claim.

In fact, no one in the world has. See the next section for more on this point.

It’s the reality that speaks.

A smearing campaign is, therefore, the only thing left for COPA to do. The second-best choice for COPA is to find Dr. Wright’s culpability of a scandalous nature (such as fraud or deception) and then use it to discredit (impeach) him and all his evidence. Such a tactic will largely rely on subjective confusion and psychological impact rather than sound and objective logic, but it still could be effective. It’s proven to be extremely effective in the sphere of social media, and it could also be effective in the courtroom. It may be much harder to confuse a court than people on social media, but it is possible, especially when the court has to face an overwhelming amount of information and confusing complexities of the related issues. See the key in COPA v. Wright.

Negative proof, its fundamental nature, and practical implications

As said above, negative proof can be logical, and it isn’t hard to understand.

But how come there is so much confusion surrounding it?

People are not confused by the general definition of negative proof but are confused by actual applications involving a logical structure of multiple layers of statements.

From an abstract point of view, proof is always about a certain statement, namely whether the statement is true or false.

The world we live in requires a variety of basic elements, including time, identities, relations, states, conditions, events, and values, to be adequately described. However, when it comes to proof of truth, everything that needs to be approved can be abstracted as a statement or a structure of statements.

Therefore, all proofs are about the truth or falsity of a certain statement. In that, every statement may have a positive proof or negative proof, or lack thereof. It is very simple at this abstract level.

The complexity arises because the statements we encounter in human life are not unrelated items scattered on a flat surface. They are hierarchical.

The basic structure of a hierarchical statements can be illustrated as follows:

hierarchical statements

In the above example, we have multiple layers of supporting statements b1, b2, c1, c2, c3, etc., which collectively support the end statement A1, the ultimate conclusion of this particular logical structure. Of the supporting statements, some are in the middle, which can be a sub-end statement (such as b1 and b2) supported by the lower statements (c1, c2, c3).

Every discussion, debate, or argument has its own logical structure of statements, like the one above. A legal case tried in the courtroom is no exception.

So where does the confusion come from?

Most confusion comes from invalid cross-statement applications and cross-layer
applications of a certain proof.

For example, when a negative proof is provided to negate supporting statement b1, one could be misled to conclude that all other supporting statements (e.g., b2) are also negated and further conclude that the end statement A1 is negated. In this case, even if the negative proof regarding supporting statement b1 is valid, the conclusion about the other statements, especially the end statement A1, is erroneous.

Therefore, the problem is not that negative proof is categorically illogical but that people often make invalid or illogical cross-statement jumps and even cross-layer jumps based on an otherwise valid negative proof of a certain supporting statement. If the negative proof of the supporting statement is even invalid, to begin with, that is a different story because such invalid proofs are usually rather transparent. They can be argued and debated, either refuted or established, but they don’t cause logical confusion. It is the invalid application of limited proof across statements or even across layers that causes confusion. Skillful debaters often use such tactics to mislead people.

In the case of Satoshi’s identity, we may have the following structure (oversimplified for illustration):

Identity inline

If Dr. Wright wants to prove he is Satoshi, he must meet the burden of proof to positively prove that his statement is true.

COPA may attack any particular statement in the above structure of statements to prove that the statement is untrue. If successful, it would be negative proof of that particular statement. Every successful negative proof weakens Dr. Wright’s evidentiary structure that supports his claim. Such attacks, if substantiated, are both logical and legitimate.

But one should not jump from negative proof of one statement to another, especially not from a supporting statement in a sub-layer to the end statement in the final layer.

It is important to note that, in each layer, negative proof of one statement just takes out that statement. Unless there is an inherent logical connection to other statements in the same layer, the other statements may continue to provide support to the statement in the upper layer. Assuming otherwise is committing a logical error of argument from ignorance or argument from absence.

Evidentiary rules indeed allow impeachment of a witness through the impeachment of a statement by the witness. These rules, however, are very strictly and narrowly defined. Impeachment of a witness may discredit other statements the same witness makes and solely supports but does not discredit a statement made by the same witness if the credibility of the statement depends on another independent source. Further, it does not discredit statements made by others, even if the statements are related to the impeached witness.

Even if COPA takes out all relevant supporting statements by point-to-point negative proofs, it only means that Dr. Wright has failed to meet his burden of proof to prove that he is Satoshi, but does not mean that COPA has met its burden to prove that Dr. Wright is not Satoshi.

From the above illustration, it is clear that the only way for COPA to prove Dr. Wright is not Satoshi is to provide direct negative proof to refute the end statement “Wright is Satoshi.” To do that, it must reason for logical impossibility and contradiction rather than resort to sentimental ambiguity.

If Dr. Wright really is not Satoshi, such negative proof must exist.

In fact, such a negative proof can be easily applied to an arbitrary person who claims to be Satoshi. For example, Satoshi is certainly a native or at least highly professional English speaker. Any claimant who doesn’t have a level of commensurate mastery of the English language would face immediate negative proof. Likewise, Satoshi certainly has a high level of knowledge in computer sciences and cryptography. Any claimant who doesn’t have such knowledge faces immediate negative proof.

The only reason why such negative proof is unavailable in Dr. Wright’s case is because he evidently meets all these requirements.

However, there are more specific characteristics known of Satoshi that could pose a meaningful challenge to even a claimant like Dr. Wright.

As Jameson Lopp demonstrated in his article, activity patterns during specific times may present very strong negative proof against a claimant whose pattern does not match that of Satoshi.

Yet, as said above, COPA does not even make an effort to find a negative proof to the end statement but rather focuses on negative proofs of the sub-layer supporting statements, hoping that the court would be led to jump across the layers to reach a logically invalid but psychologically effective conclusion.

In fact, outside the courtroom, no one else has found any convincing negative proof against Dr. Wright’s claim. So far, the closest thing is one notorious episode in which someone anonymously signed a message claiming Wright was a fraud using the private key of some addresses found in the list provided by Dr. Wright to the court. But it wasn’t the real negative proof at all. There is no proof that those addresses associated with the key used in the signature are “Satoshi addresses” – addresses known or proven to be that of Satoshi. Even if those addresses at one point in time belonged to Satoshi, there is no evidence that they still belonged to Satoshi at the time of the signature. Those addresses were found to be listed in the large list of address inventory provided by Dr. Wright to comply with a court order but are not even formally attested to be Dr. Wright’s addresses, let alone proven to be Satoshi’s addresses.

Therefore, that detracting signature is a negative proof to negate the statement “Dr. Wright owns this address,” but not negative proof to negate the end statement “Dr. Wright is Satoshi.” This incident itself shows the importance of understanding the structure of logical statements in any argument and how easily invalid negative proofs can mislead the world due to people’s failing to have such a proper understanding.

Negative proof of a negative claim

But let’s turn the table around. COPA’s claim is a negative claim that Dr. Wright is not Satoshi. Can Dr. Wright provide negative proof of COPA’s negative claim?

He can. And he should.

Note that here, the negative proof of a negative claim has the same result as the positive proof of a positive claim but arrives at it from a different angle. The latter is to directly prove that Dr. Wright is Satoshi, while the former is to prove it indirectly by showing that the statement “Dr. Wright is not Satoshi” cannot be true because it causes impossibility or contradiction, or at least unlikely to be true because it leads to improbable conclusions.

Every piece of evidence is a statement, but there are also silent statements:

What ought to be there but is not.

This is often called “negative evidence,” which is different from “negative proof.”

In the case of Dr. Wright, the statement that “Dr. Wright is not Satoshi,” when combined with the silent statements, logically leads to the following strange conclusions:

If Dr. Wright is not Satoshi, then the real Satoshi has existed in a social vacuum except for his temporary online presence from October 31, 2008, to December 2010. He is completely silent in the face of an imposter making an all-out effort to steal his name and his work.

Even if his own total silence could be explained by assuming that he’s dead, the total silence of everyone in the world who is related to him or represents him means that Satoshi had no family, no friends, no heirs, no agents, no representatives who can vouch for him.

If Dr. Wright is not Satoshi, then Satoshi did not live a real life or have any social life. His entire social circles and connections are silent or dead. His classmates, roommates, and teachers from all the schools he went to, from kindergarten to university, and his companions, friends, and colleagues all never existed or have completely disappeared. All his school records, university records, formal academic qualifications, employment records, driver’s license, tax records, and any other government records, bank records, credit history, or anything a normal citizen could have enjoyed or relied upon cannot make any appearance or connection as if they never existed. None of the equipment he used, such as computers, and none of his online activities, such as Internet posts, can surface to make a statement as if they never existed or totally disappeared. He had no distant or close family ties and no caring grandparents. He had no employment number in any country and had never worked to earn a salary. He had no associations or hobbies, didn’t play sports, and had no social connection of any kind that could produce one person who would vouch for him when needed.

But all that screams an extreme form of impossibility because such a human being is either a total myth or someone whose real identity is wrongfully rejected.

After over a decade of development and accumulation, one but only one proposition has emerged that could resolve the above impossibility. That resolving proposition is simply this:

Satoshi is Dr. Wright.

Once one allows that proposition, all factual and logical difficulties, including the above-illustrated impossibility, disappear. The Satoshi universe suddenly comes into order, connects with reality, and makes sense.

But the world continues to reject the only reasonable proposition. It is because the world does not follow facts and logic but rather impressions, sentiments, emotions, narratives, personal beliefs, preferred values, and entrenched economic interests. Jameson Lopp is an example. Knowledgeable and having obviously investigated the Satoshi matter well beyond most others, he presumptively excludes the possibility that Dr. Wright is Satoshi. It is because he has his own beliefs and values regarding what Bitcoin should be as a system, and Dr. Wright is in every bit contrary to that value system.

COPA is the corporate Mr. Lopp and more. COPA may also be influenced by value beliefs and ideologies but is more driven by entrenched economic interests.

The human witnesses

A large portion of the trial of COPA v. Wright will focus on multiple documents, each equivalent to a statement. From an evidentiary point of view, it is necessary to contest these documents as long as they are deemed relevant. But I hope the judge does not get lost in the forest.

Besides the documents, the firsthand human witnesses are critical.

Up until today, the world has relied on human testimonies. There were a lot of injustices in this human system, but overall, we did fine because human conscience has been and is still operative.

This is especially so when it is a trial court witness under oath. There is a good reason that all common law-based legal systems have very strict evidentiary rules about witnesses, differentiating a firsthand witness from hearsay and factual evidence from an opinion.

The importance of this cannot be over-emphasized. It is very common for people to confuse the evidentiary value of factual evidence and opinion evidence. “Factual” does not mean you must accept it. It means that the evidence is factual in its nature, in contrast to a mere opinion. For example, in the event of a fire at 10 AM, if a witness says, “I saw a man wearing a red jacket entering the building around 9:50 AM,” that testimony is called factual evidence. Whether you believe the witness is telling the truth or not, or whether this leads to the conclusion that the fire was caused by arson, is a different matter, but the testimony is factual in nature. In comparison, if another person says, “I believe John Smith probably started the fire because I believe he is a bad guy,” that is an opinion. The person could be very much right about John Smith, but what he said is not factual evidence.

Opinions can be created, manipulated, spread, and become codependent, and people don’t necessarily violate their conscience when they stand by an opinion.

In contrast, factual evidence is independent. If it is false, it has to be manufactured by the witness himself in a positive violation of the person’s conscience.

Often, factual evidence is irrefutable because it is simply there in the public’s eyes. How one uses the evidence to draw a conclusion depends on how one estimates probabilities, but the evidence itself is factual, and you can’t simply brush it away as if it were somebody’s opinion.

But alarmingly, our society is quickly becoming so corrupt and cynical that it can no longer trust human testimonies, even the testimonies under oath bearing a man’s conscience. The destructive trend will continue to grow until blockchain has started to reshape our world. A provable and immutable global timechain is urgently needed, not to replace human conscience, but to protect and preserve it.

I’m glad that Dr. Wright chooses to prove it in a courtroom using normal human and social evidence because that is the kind of evidence that not only relies on humanity but also gives meaning to humanity in return.

I hope the court gives humanity a chance.

The Bayesian probability estimate based on the totality of evidence

All the above discussions consider each piece of evidence separately as if they were independent from each other.

In real life, however, identities, relationships, and events are related. Evidence does not come in parallel slots but interrelated pieces that stack up upon one another to cumulatively and progressively change the estimate of the probability of a proposition.

This is the teaching of Bayes theorem. When properly estimated using Bayes theorem, multiple pieces of evidence, which each standing alone may not give the proposition a probability too much higher than 50%, can quickly stack up to result in a near certainty of the proposition. See Mathematical Proof that Dr. Craig S. Wright is Satoshi Nakamoto.

Summary

COPA can win the case if it provides convincing negative proof.

But it won’t.

In the trial of COPA v. Wright, it is all clear that COPA doesn’t have a case because they’re not even trying to provide a clear and logically legitimate negative proof, like what Jameson Lopp did to Hal Finney. All COPA hopes to rely upon is a phyop. It’s not because they don’t understand the logic, but precisely because they do and are blocked by the reality: negative proof to Dr. Wright does not exist because Dr. Wright is Satoshi.

On the other hand, what’s more interesting is if and how Dr. Wright can meet his burden of positive proof.

Watch: Exchange corruption and CZ fines, COPA trial, Mining Bitcoin and Halving

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