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In the current climate of argumentative discourse, where one party makes a controversial claim and attempts to logically convey the veracity of that claim, through explanation, to another party that holds the same claim false, one can effortlessly see the importance of an algorithm that would systematically allow for the two aforementioned parties to demonstrate to each other, once and for all, who is correct, or at least more correct, of the two parties. After all, principles of logic dictate that a fact cannot both be true and false simultaneously; this is referred to in conventional logic as a contradiction, and cannot take place, at least assuming the axioms set forth in conventional logic. For this reason, when one party holds a claimed fact P0 true, and another holds the same claimed fact P0 false, that claim can only hold one objective truth value, either true or false, at a time. (It is important to note here that opinions, like the opinion, "Burger King is better than McDonald's," can be treated as fact for the purposes of the algorithm, as the algorithm specified does not distinguish, or need to distinguish, between fact and opinion for the purposes of reaching agreement. Facts and opinions are both claims that a party can hold true or false, and the party holds them true or false for their given reasons; the algorithm is only concerned with those particular aspects while it is being carried out for the purposes of reaching agreement. The only difference is, when an opinion is in dispute, there is no "objective truth" to be found at resolution time concerning the claim. In that case, the "more correct opinion" is simply the opinion that was originally held true by just one of the parties at the start of the algorithm, and both parties ended up holding it true upon reaching agreement at the termination of the algorithm.) Regardless of whether a fact or opinion is the subject of the disagreement, however, the "correct" (or at least "more correct") claim, typically either P0 or ~P0 (not P0), will surface at the end of the algorithm as the claim that both parties hold as true.
Until the present time, conventional dialog was the sole tool for reconciling these disagreements. However, in argumentative discourse, conventional dialog has several shortcomings that showcase the need for an algorithm like the one referenced: namely, conventional dialog doesn't always "work". More specifically, conventional dialog can, and usually will, end with both parties still in disagreement, even in disputes where the claim in dispute is a fact, as opposed to an opinion. In such cases, as stated above, the given claimed fact P0 can only hold one objective truth value at a time (true or false), so in such instances where a fact is in dispute, and one party holds the claim true, and the other party holds the same claim false, one party is right concerning the topic, and the other party is wrong. In small matters, leaving a party wrong about a claim is probably of little consequence, however as the claim P0 gains perceived importance in the minds of the involved individuals, such as the P0 claim, "The US Election was (or was not) stolen," the ramifications of leaving individuals wrong on the given topic has a precedent of being deadly. Because of this, the utility of an algorithm designed to serve this specified purpose is self-evident. Applications of such an algorithm could vary widely, from simple marital disagreement resolution; to reaching agreement about claims of election fraud, whether the election was actually fraudulent or merely perceived as fraudulent; to allowing for The United States Congress itself to be virtually always unanimous moving forward with all legislation; and a potential for solving every disagreement in between.
This exposition outlines a method that proposes to serve that very purpose: to reach agreement between two parties, regardless of the topic chosen or the parties involved in the discussion. The term "to reach agreement" can be understood to mean that this algorithm proposed is not about compromise; this algorithm begins with the two disagreeing parties, where one party holds claim P0 true, and the other party holds claim P0 false, and aims to change one party's mind about claim P0, such that both parties finish the algorithm together both holding P0 true, or both holding P0 false.
To that aim, the exposition herein begins with simple premises that can be considered virtually universally agreed-upon, and logically leads the reader to conclude the following:
1) When the party trying to prove their claim true (hereafter "The Convincer") answers, "Why?" on claim P0, this allows The Convincer to work backwards to form a small two-column proof, as is seen in fundamental Geometry or Logic courses, and this proof consists of two premises (as asking, "Why P0?" generates two premises), P1 and P1→P0 (P1 implies P0, or "If P1, then P0,"), such that anyone that accepts P1 and P1→P0 as true will and must also accept P0 as true.
2) If The Convincer has no answer when asked, "Why P0?", then The Convincer has found what is referred to as an Ultimate Premise (hereafter "UP"), and The Convincer can and must prove this UP P0 to others via simple demonstration.
3) If The Convincer is recursively asked, "Why?" on any claims that get generated, until all newly-generated premises are either UP's, or are already held true by the disagreeing party (hereafter "The Skeptic"), then this scenario induces a very unique and special property between the given P0 claim and its corresponding UP's: in the event that The Skeptic holds all of The Convincer's UP's true, then The Skeptic will and must accept every claim in the why-proof chain as true, which means The Skeptic will and must also accept The Convincer's original P0 claim as true (even though The Skeptic had initially disagreed with the original P0 claim, holding it false, hence the disagreement and the reason for implementing the proposed algorithm in the first place).
4) Upon simple demonstration, The Skeptic will virtually always accept The Convincer's given UP(s), for reasons that are potentially survival-related and/or evolution-related.
5) Assuming The Convincer is correct about P0, once The Convincer has generated each corresponding UP in this manner, such that The Skeptic will and must accept the original P0 claim as true if they accept all of the corresponding UP's as true, and The Convincer has demonstrated the truth of each UP, one by one, then The Convincer will have proved to The Skeptic that The Convincer's original P0 claim is correct. The Skeptic, having once held the original P0 as false, will then hold the original P0 as true, effectively having reached agreement about claim P0 between The Convincer and The Skeptic.
6) If The Convincer turns out to be wrong about the original claim P0, or The Skeptic is at least more right than The Convincer, then The Skeptic will be able to why-prove or simply demonstrate at least one of The Convincer's UP's false. This will invalidate The Convincer's why-proof chain, which will cause The Convincer to change their mind about the original claim P0, which causes agreement to be reached between The Convincer and The Skeptic, with both The Convincer and The Skeptic holding the original claim P0 false at resolution time.
This exposition then explores conclusions and ramifications stemming from these findings.
The question, "Why?", while simple in nature, has large implications when it comes to proving claims in argumentative discourse. The following simple example illustrates a situation in real-life where the algorithm takes place naturally in very brief quantities:
"You should be rushing around to get to school!" The mother exclaims. (Claim P0)
"Why?" The child questions.
"Because it’s 8:00am, Derek, not 7:00am!" (Claim P1)
The mother then thinks to herself, "And if it's 8:00am, not 7:00am, then you should be rushing around to get to school." (Claim P1→P0)
The child, Derek, then realizes their mother is right, and begins to rush around in order to get to school on time.
When the individual trying to prove P0 (hereafter "The Convincer") is making attempts at proving their point, and the individual questioning the point (hereafter "The Skeptic"), asks, "Why P0? Why should Derek be rushing around to get to school?" The Skeptic is, in effect, saying, "For this P0, find a P1 statement and an, 'If P1, then P0,' (P1→P0) statement, such that P1 and P1→P0 (P1 implies P0) are both true [for you, the answerer]." The claim P1 is then the answerer's reason why the claim P0 is true, and P1→P0 is the warrant claim that makes P1 into the cause of P0 for them. In the real-life example with Derek and his mother above:
The P0 original claim was:
"Derek should be rushing around to get to school!"
The P1 reason why claim was:
"(Because) It’s 8:00am, Derek, not 7:00am!"
The P1→P0 warrant claim connecting the reason claim and the original claim was:
"(And) if it’s 8:00am, not 7:00am, then Derek should be rushing around to get to school!"
In this example, The Convincer, by answering, "Why?" has worked backwards to create a small two-column proof, just like the type that is conventionally taught in the Geometry or Logic classroom setting, and this proof proves The Convincer's original Claim P0 "right". ("Right", in this sense, simply means true while the premises, in this case P1 and P1→P0, hold true or are otherwise assumed to be true.) The logical proof that the mother formed via answering why looks as follows:
Proof 1:
| Step | Claim | Reason |
|---|---|---|
| 1 | P1: "It is 8:00am, not 7:00am." | Premise (Demonstrated) |
| 2 | P1→P0: "If it is 8:00am, not 7:00am, then Derek should be rushing around to get to school!" | Premise (Previously Agreed Upon) |
| 3 | P0: "Derek should be rushing around to get to school!" | Modus Ponens, Step 1 and 2 |
Hence proved.
All the mother had to do was demonstrate that it's 8:00am and not 7:00am, by having Derek check a clock or two, and the mother was able to show that she was right: Derek should be rushing around.
Notice that if anyone accepts both P1 and P1→P0 from Proof 1 above, they will and must also accept P0. So, if asked, "Why P0?" and the answerer has an answer, then they can work backwards to find a P1 and a P1→P0, that prove P0 such that anyone that accepts P1 and P1→P0 as true, via demonstration, assumption, or another method, will and must accept P0 as true also.
One may question at this point what happens if The Skeptic asks, "Why P0?" and The Convincer has no answer. This would happen if P1 was substituted in for P0, and The Convincer was asked, "Why P1? Why is it 8:00am?" In this case, there is no reason for it to be 8:00am; this fact is true without having a reason for it to be so. The Convincer in this case just knows that it is 8:00am from their experience, like in checking the clock, or in eras preceeding clocks and their precise time measurement, checking the position of the sun in the sky, etc. As can be seen from cases like the current time, seeing a true or potentially true claim (hereafter "Assumption") to be the case through experience is how an Assumption is believed when the Assumption holder has no other reason for believing it. When the Assumption holder has no other reason in this way, then logic and reason ultimately rely on one's senses. (One's senses is how the Assumption holder experiences these Assumptions to be the case.) So if the answerer has no answer to, "Why P1?", then the answerer has found that for them, their P1 is an Ultimate Premise (hereafter "UP"). This particular claim, "It is 8:00am," is an UP because it is held true without a reason for doing so. (That is the Litmus Test: Assumptions are regular Assumptions if the Assumption holder maintains that they have a reason for holding the Assumption true. Assumptions are UP's if it is held true, but the holder themself agrees that they hold it true for no reason.) In the case of UP's, they are held true only because the holder has experienced the UP to be the case (such as is the case of the UP: "It is 8:00am.") If the Assumption holder only holds it true because it was personally experienced to be the case, then their only method for showing this UP to be true, is for the Assumption holder to give the other party that experience; to have the other other party experience that UP to be true, as well. Currently, simple demonstration is the only known method for getting other parties to also experience that UP, and get that other party to accept that UP as true. For that reason, if the answerer has no answer to, "Why P1?", then the answerer (and/or The Convincer) can and must prove their UP P1 to others via simple demonstration.
Available to The Convincer are three methods that can be used when trying to prove to The Skeptic a Claim P0, P1, etc. (Call it Claim Px.) One or more of the following methods may be used in tandem by The Convincer to prove Claim Px to the Skeptic:
Method 1: Nothing To Prove
The Convincer is to use this Method when The Skeptic already agrees with the Px that The Convincer is trying to prove, in which case
there is nothing to prove.
OR
Method 2: Form A Small Why Proof
The Convincer is to use this Method when The Skeptic disagrees with the Px that The Convincer holds true, and when asked, "Why Px?", The Convincer
has an answer. In this case, The Convincer's why answer yields a Py and a Py→Px, such that The Skeptic will and must accept
Px as true if they accept both Py and Py→Px as true, via assumption, demonstration, further why-proving, etc.
OR
Method 3: Perform A Simple Demonstration
The Convincer is to use this Method when The Skeptic disagrees with the Px that The Convincer holds true, and when asked, "Why Px?",
The Convincer only holds Px true because they have experienced it to be the case, and for no other reason.
In this case, The Convincer must show The Skeptic (if possible) that Px is true via simple demonstration. Assuming Px is true and
The Convincer is able to simply demonstrate Px, then they do so, and The Skeptic then experiences Px to be true for themselves, as well.
The Skeptic then accepts Px as true, and agreement has been successfully reached regarding the claim Px.
During the course of disagreement resolution via the proposed algorithm, every time a Method 1 or a Method 3 scenario is reached, The Convincer and The Skeptic end up reaching agreement (assuming again that any Method 3 simple demonstrations can be conducted), and thus the discourse ends in agreement. In similar disagreement resolution discourse, every time a Method 2 scenario is reached, The Convincer expresses their Px claim in terms of two other claims, Py and Py→Px, creating a situation in which The Skeptic will and must accept Px as true, provided they accept Py and Py→Px as true, again via assumption, demonstration, or some other proof method, including proof Method 1, Method 2, or Method 3 described above.
During Method 2 use, the small why proof that gets formed is highly beneficial, as long as The Skeptic accepts both of the newly-generated claims, Py and Py→Px. However, The Skeptic may not accept both. In the situation where Py and Py→Px are not both accepted as true, the same three Methods described above (Methods 1, 2, and 3) can be used to also prove just Py, just Py→Px, or both. To prove Py or Py→Px, The Convincer would simply substitute Claim Py (or Claim Py→Px) as the new Px, and prove this new Px, in the same manner that the original Px was proven, using Method 1, 2, or 3 from above.
This concept of recursively proving Px, then Py, then Pz→Py, etc. can be best illustrated using another example. Example A, which illustrates this concept, can be found at the link below:
Click Here To Start Example A (JavaScript must be enabled for the example to work.)
Example A demonstrates the straightforward process that The Convincer can follow to prove the original P0 claim, the process taking place as follows: The Convincer answers, "Why P0?". This generates two new premises. For each premise that gets generated, The Convincer leaves the premise alone if The Skeptic already agrees with it (making use of Method 1 from above). If The Skeptic does not agree with the premise, but The Convincer has no answer when asked why, then The Convincer also leaves the premise alone, as the intent is to simply demonstrate the premise later, via Method 3 from above. If The Skeptic does not agree with the premise, but The Convincer does indeed have an answer when asked why, then The Convincer answers why for that premise, and in doing so forms another small why proof to prove that premise. This latest why-answering yields two more premises. The Convincer continues answering why for each new premise, where necessary. The Convincer continues answering why in this manner, until each and every generated premise is either: a) proven via Method 1 above, such that The Skeptic already agreed with the premise upon hearing it; b) proven via Method 2, such that The Skeptic will and must agree with the premise (call it Px) if they agree with The Convincer's two reason claims, Py and Py→Px; or c) slated to be proven via a Method 3 simple demonstration.
If this method is carried out, as was done in Example A above, then the why proofs will be set up in a unique and special way: this series of small why proofs form a chain. This why proof chain then ultimately depends on a small handful of UP's.
In Example A, the mother's why proof chain depended on one UP and on one Previously Agreed Upon Premise that she had to remind Derek of:
The UP:
"It is 8:00am, not 7:00am." (P1)
The Previously Agreed Upon Premise:
"If Derek is late, then he's grounded!" (P5a)
In the discourse that ensues while carrying out this method, The Skeptic already holds any Previously Agreed Upon Premises true, they may just need to be informed or reminded. But such is not the case with the UP's. There is disagreement over the truth of the UP's, but there is a very unique and special property among the given P0 claim's collection of corresponding UP's: in the event that The Skeptic holds all of The Convincer's UP's true, then they will and must accept every claim in the why-proof chain as true.
Their acceptance will propagate all the way down to The Convincer's original P0 claim:
"Derek should be rushing around to get to school!"
From the Example A why proof Traversal, it is apparent that The Skeptic's acceptance will indeed propogate all the way down to P0. In other words, if The Skeptic holds all of The Convincer's UP's true, then they will and must hold The Convincer's original P0 claim true: The Convincer has set up their why proof chain in this special manner for this very reason. Thus, assuming that The Convincer is able to demonstrate all of their UP's as true, then they will be able to prove any (right) P0 to any other person (Skeptic), using this series of small why proofs that they have compiled.
One may wonder at this point whether The Convincer will be able to successfully carry out their simple demonstrations, and manage to get The Skeptic to accept all of their UP's as true. For this reason, it is important at this juncture to more closely examine the senses and experiences, since the senses and experiences are what is relied on when dealing with UP's, where the UP is held true only because of the Assumption-holder's experience, and no longer due to logic and reason.
While navigating everyday life, the Assumption holder's senses, experiences, and logical reason are the three chief truth discernment tools that the Assumption holder has, if they are not the sole tools at their disposal. For example, the Assumption holder can see, hear, touch, remember, and otherwise experience that certain aspects of life are true, and then using logic, they can form conclusions based on the experienced truths acquired. As seen above, after asking the Assumption holder why enough, the Assumption holder eventually runs out of reasons, and the reason chain runs out. Once the reason chain runs out, the Assumption holder's senses and experiences are virtually all they have left to discern truth with.
For this reason, when discerning truth, there is virtually nothing else to ultimately rely on besides one's senses and experiences. Naturally, the Assumption holder (or The Skeptic) will therefore trust their senses and experiences over anything else. For that reason, in the event of an apparent contradiction, where the Assumption holder's senses are notifying them of one truth, in a firsthand account, that contradicts with their previously formed conclusions, then the firsthand account from their senses will take priority and win out, and they will accept that firsthand account to be true over the previously held beliefs. The account must be a firsthand account here, however. Any data from a secondhand account, like studies published by others, will not suffice here. An example would be: a given Assumption holder may trust even the President Of The United States that the rustle they see in the bushes "over there" is just the wind. They may be thoroughly convinced and unwavering in their belief: that the rustle is just the wind. When the lion jumps out, however, and they see the lion with their own two eyes, their senses and experiences take priority and win out over the existing conclusion they held. Seeing the lion was able to demonstrate what hours of explanation never could: namely, that rustle in the bushes is in fact, a lion, and not just the wind.
This example showcases that the Assumption holder will virtually always accept what their senses are telling them: they accept what is personally experienced. In a firsthand account like this, the Assumption holder does not ignore data that is experienced personally. Perhaps there are survival and/or evolutionary reasons why this is the case, as evidenced in the "lion in the bush" example. Regardless of the reasons for this being the case, in the algorithm/method described herein, The Skeptic is experiencing The Convincer's UP firsthand, so The Skeptic will virtually always accept what their senses are directly telling them. The Skeptic will not ignore the data that The Convincer has them experience firsthand in this manner.
As previously stated, with UP's, the sole known method for showing The Skeptic said UP is to get The Skeptic to experience the event personally, which is how the Assumption holder/Convincer came to accept this UP to be true, as well. The Skeptic will therefore be experiencing the event firsthand, and for the reasons stated above, The Skeptic will virtually always accept what they experience through The Convincer's simple demonstration. Put in other terms: The Convincer carrying out the given demonstration will cause The Skeptic to firsthand-experience each UP that The Convincer has generated, which The Skeptic will then virtually always accept to be true for the reasons furnished above. The Convincer's simple demonstration(s), then, will virtually always prove all of their UP's to The Skeptic one by one.
As mentioned earlier, The Convincer, having followed the algorithm/method outlined above, will have formed and set up a series of small why proofs in a unique and special manner, such that: if The Skeptic accepts all of The Convincer's generated UP's as true, then The Skeptic will and must accept The Convincer's original P0 claim as true. Then, as the "lion in the bush" example illustrated, The Convincer can then carry out each simple demonstration to prove each UP to The Skeptic one by one, and The Skeptic will accept virtually all of The Convincer's UP's. In doing so, The Convincer has proved to The Skeptic that The Convincer's original P0 claim is true, for any correct P0 claim, independent of the P0 claim chosen, and independent of The Skeptic's initial beliefs on the matter.
One may wonder at this point what happens, however, if The Convincer were to set up a why proof chain, and The Convincer turned out to be wrong. In those instances, the other discussion party, the more right party of the two (hereafter "The Right Party"), would be able to why-prove or simply demonstrate at least one of the other party's (hereafter "The Wrong Party's") UP's false. The follow-up disquisition at this link explores in detail the scenario where The Convincer turns out incorrect; however, the results of the disquisition above remain unaffected: when The Convincer answers why to form a series of small why proofs, whether The Convincer or The Skeptic is ultimately correct (or "more correct") on the original P0 claim topic at hand, The Right Party ends up able to correct The Wrong Party about The Convincer's original P0 viewpoint claim, independent of the P0 claim chosen or the initial beliefs of The Convincer or The Skeptic.
