Download To prove then, requires

PROOF
A. To “Prove” Defined
Prove - to establish the truth or genuineness of, as by evidence or argument: to prove
one's claim.
To prove then, requires
1) Person A, asserting a claim to another mind.
2) Person B who does not initially take the claim to be the case,
3) a claim,
4) an attempt by Person A to persuade Person B to accept the claim (an argument
or evidence must be presented), and
5) Person B accepting the claim as a result of the attempt to persuade.
Let us look at each of the elements.
1) There needs to be a person. All claims are made by minds. Even if the claim is
seen in a newspaper, a brochure, a menu, or a sacred text, it must have
originated with a mind. Theoretically, this mind could be a human, an angel,
even God. The claim must be directed to others, consciously desiring to have
others read or listen to the claim and argument.
2) Person B, who, previous to the attempt to persuade does not accept the claim.
If Person B already accepts the claim, then no proving has occurred. Despite
the assertion in a well written and quite informative website on the subject of
proof http://theautonomist.com/aaphp/permanent/proof.php
- when the word is used to describe a one-person proof, the narrowing and
limiting phrase “to yourself” is required. (even then, I submit, it can be
understood as having two parties – I know this is kinda silly, but it is akin to
someone talking to himself. There is only one person… but they are acting
like there are two. The same is true in this case…the person is acting like one
part of him is talking to another part of him…as if the rational part of his mind
is attempting to convince his emotions that he should leave his lover. It is just
a play on words, of course…but even here, there are still two “parties”.
3) There needs to be a claim. A claim is an assertion about reality. It must be in
the form of a declarative, descriptive sentence and must assert some fact about
the past or the present. If person A says that licorice is her favorite candy, then
that is a claim. It asserts something about reality. If she says that licorice is the
best candy, this is also a claim. If she says that all people should eat licorice,
this is not a claim, but a prescription, not asserting anything about past or
present reality; rather she is talking about how reality ought to be.
4) The argument must be presented with a purpose of having the other person
agree with the claim and agree with the claim as a result of the proof. If there
is just a claim with no supporting argument or evidence, and Person A desires
Person B to adopt the position, then they are assuming that Person B will
simply accept the claim as a bald assertion, and the acceptance occurs simply
on the basis of Person B trusting the veracity of Person A. In short, they take it
by faith. Proof, by definition, involves bringing in a rational argument or
evidence that encourages Person B to see the reasonableness of the argument
and then change their mind on the basis of the argument or evidence.
For purposes of this paper, the term argument refers to the logical elements
introduced to accomplish the persuasion. The elements come in the form of
other sentences. Acceptance of these other sentences is accomplished by
various means of support. There can be supporting claims. These claims, just
like the initial claim, need to be supported unless they are self-evident or
undisputed. If they are, then the work is finished; the argument is complete. If
the supporting claims are not self-evident or undisputed, then these claims
must be supported by further claims or evidence. Evidence comes in the form
of plainly visible and conspicuous things actually presented to the senses or
non-present presumed things that are presented to the mind. Either way,
however, evidence refers to otherwise plainly visible and conspicuous things
that exist in objective reality. (For a fuller discussion on things, you may read
my paper “On Things, Space, and Time”). For the present, a simple definition
should suffice: a thing = a real object that can be detected by the senses and
examined by others minds. For use as evidence, the thing must be at least
semi-permanent (so as to be around long enough to serve as evidence) and
available for inspection (e.g. the bruise on the face of John is proof that her
face received a blow). In practice, for the purpose of proof, the evidence does
not have to be immediately available if the existence of such objects are
assumed as universally agreed upon as existing ( e.g. “Tailbones are proof that
humans evolved.”)
5) The other person must then, as a result of the argument or evidence, be in a
state of having been persuaded and now holds the assertion in their head also.
There must be a change in the thinking of Person B, and this change must
have come as a direct result of the claim and argument.
Proving is an action, the word prove is a verb. It is something that happens in time
and space and must involve two minds and some specific type of event that has
happened involving both of them.
Proof – 1) an argument or evidence sufficient to establish a thing as true, or 2) to
produce belief in its truth. This is a noun. Definition 1 is a noun describing proof
as a tool in establishment and is a combination of the claim and argument 3 & 4
above. Definition 2 is a noun describing the effect of the tool and is an event that
involved the use of 3 & 4 with the result of 5. Either use is acceptable although
the first is much more common. In logic, a proof typically refers to just the claim
and argument. In real-life situations, proof can also include the result (e.g. “proof
has occurred”) although the more common way of expressing this would be to say
that something was proven (simply using the past tense of the verb to prove. e.g.
She proved her point ).
B. Types Of Proof
1. Analytic Proof (proof by definition / adduction without the need for evidence).
Analytic proof is based on the principles of internal consistency, the use of
axioms, presuppositions, and logical argument.
In Geometry, you have a system with set rules of proof and axioms.
 Axiom 1: Triangles are defined as containing a total of 180 degrees
within the three angles
 Given 1: There is a figure designated as Triangle Q
 Given 2: Triangle Q has one angle (angle A) that is given as
measuring 30 degrees
 Given 3: Triangle Q has another angle (angle B) that is given as
measuring 60 degrees
 Apply Axiom 1 to the givens
 Therefore, the third angle (angle C) is 90 degrees.
Using a internally consistent set of rules, and a specific set of “givens” as to the
measurements of angles A and B, it is capable to “prove” that angle C is a 90
degree angle. You do not need to see Triangle Q, either as a figure drawing or a
real object that is a triangle. All you need to know are the rules and the “givens”.
Essentially, for analytic proofs, you are simply working with given definitions,
axioms, and logic as the means of proof. An internally consistent system allows
for this type of proof.
The same is the case for all mathematical proof, no matter if it is geometry,
algebra, calculus, or any higher branch of mathematics. There is simply no need
to appeal to any external realities or evidence to prove anything.
This analytic proof is common to many fields of inquiry, each having its own set
of definitions, axioms, presuppositions, and rules. For someone to present an
argument to a person in one of these fields, she would have to know the system if
she wanted to have the proof have any effect. As many of you are aware, some of
the proofs in fields from particle physics and quantum mechanics to astrophysics
and astronomy are so complex that scarcely anyone outside the field has the
faintest notion of what is being proved and how. In these types of fields involving
higher level mathematics, claims about real life can be proven, i.e. be accepted by
some others in the community even with no follow-up scientific testing… but
there are also those who only provisionally accept the analytic proof, and wait for
sing on for sure when the scientific data comes in to confirm (demonstrative
proof… see below). Einstein proved mathematically that time would slow down
as speed increased… but many rejected the theory as nothing more than a
mathematical proof… but then later jumped on the bandwagon when space travel
allowed the theory to be tested… and confirmed.
2. Demonstrative Proof (proof that requires production of evidence in support of the
logical argument) This type of proof also uses definitions, axioms,
presuppositions and logical argument, but it relies on bringing in real objects as
evidence to support an assertion. Take the following scenario. Tom, seeing
Johnny wearing his friend Bob’s coat, accuses Johnny of stealing Bob’s coat.
Johnny’s claim is that he did not take the coat. His argument is as followsClaim: Johnny did not steal Bob’s coat.
Argument:
a. Given 1: Johnny is in possession of Bob’s coat.
b. Definition 1: Stealing means taking another person’s
property without the owner’s permission.
c. Supporting Claim 1: Bob gave Johnny permission to
borrow his coat. (This supporting claim is not axiomatic. It
is not true by definition or presupposition; therefore it must
be supported by demonstration.)
d. Production of evidence: Johnny produces a piece of paper
with a handwritten note, signed by Bob, stating that he was
giving Johnny the right to borrow his coat.
e. The evidence establishes Supporting Claim 1.
f. Logically connecting Given 1, Definition 1, and the
undisputed Support Claim 1, it must follow that Johnny did
not steal Bob’s coat – the claim is proven.
Correct?
No. The claim is not proven. A proof was given. A proving was attempted. We
have the presence of a proof (argument or evidence sufficient to establish a thing
as true, or to produce belief in its truth), but it does not follow that anything was
proven. For that to be the case, Tom must now, as a result of the proof, have
changed his mind. He previously held that Johnny stole the coat, and for there to
have had anything proven, Tom would have to now 1) hold that Johnny did not
steal the coat, and 2) hold that as a result of the proof.
You see, Tom may not accept the evidence of the note. Tom may rightly or
wrongly not hold that the signature is really Bob’s. Whether the signature is
authentic or not is not the point here. If Bob rejects the evidence, then Johnny has
not proven to him that he did not steal the coat. Johnny offered up a proof that he
considered being sufficient to support his claim; it may be sufficient in many
other people’s minds, but not in Tom’s, therefore nothing has been proven to
Tom. A proof was offered and laid out, but rejected, therefore nothing was
proven.
Keep in mind that there was simply no way for Johnny to prove his claim by mere
axiom or logical rules. The supporting claim had to be established by producing
evidence – actual things – to complete the proof. This claim required a
Demonstrative Proof, not merely an Analytic Proof. This requires the
establishment of external consistency, or conformance to something in the real
world.
Also, keep in mind that as many people that exist on the planet, that may be as
many different things needed to prove something. You and I might accept the
claim. We may not doubt the authenticity of the evidence. Tom may have been
very familiar with Bob’s handwriting and simply reject the authenticity of the
note. It is simply not enough that a proof has been provided. Each of us has our
own standards of proof that we require. Many of us have not thought through the
whole idea of what standards of proof we have set up in our minds… we simply
accept stuff or not.
Proving then, has both an objective and subjective element. The objective element
is the argument itself. It may be internally sound, using the axioms and arguing
using the proper structure and form, but that does no mean the other person is
convinced. We, from the outside, might look at the proof and be convinced by
it… having considered it to be an irrefutable argument. But another person, for
subjective reasons on his own, might reject the same argument. In this situation,
nothing was proved. A proof was offered, but it was not effective.
We see this all the time in the courtroom. Lawyers offer up evidence for the jury
to see. Sometimes it convinces them, sometimes it does not. Either way, however,
the courts have devised very detailed and strict rules about evidence – about what
evidenced can and cannot be brought in, and how it has to be offered to the court,
how it is substantiated as to its grounds, and in what manner it may be presented
to the jury. In a sense, this is not at all unlike the realm of science. The scientific
method requires objectivity, testability by others, and confirmability by
dispassionate, objective minds.
Let us return to the stolen coat scenario above. Let us say that the claim and proof
are given to another party, Edna. And for the new scenario, let’s say that Edna is
shown by Demonstrative Evidence that the note has been verified by a
handwriting expert that the note is genuine. He hears the claim, agrees with the
definition, has been presented the argument, and has been shown the
handwriting…and even takes the expert testimony as convincing… and still does
not accept the claim. Would you consider her stubborn-minded? I suspect that you
would. You would wonder what was it in her head that kept her from accepting
the claim? You might judge the proof to be objectively convincing… that is that
anyone who has half a brain should be convinced by it. You might wonder what it
is in Edna that keeps her from accepting this claim on the basis of the proof.
The thing is, there are many reasons why people refuse to accept claims…
probably as many as there are people on the planet. We all have things in our
heads and out hearts that keep us from accepting claims…even blatantly obvious
ones. I recall a student coming to me years ago and asking my counsel on a
matter. He was from Viet Nam, and was raised in a Buddhist household. Here in
the states, he had gotten hooked up with a group known as Campus Crusade and
had been to several of their meetings. He enjoyed the people and listened
carefully to their claims that Christianity was the right religion and their
encouragement that he should convert. According to him, he was mostly
intellectually convinced that their claims were true. The problem was that he
knew that if he converted, his family back home would reject him… totally…
actually act as if he were dead… and never have any contact with him again. This
was a devastating thought to him… and it rightly scared him to death. Hence, he
came to me to seek help in his struggle. He had a wall up in his heart… and the
wall did not allow the argument to penetrate to his mind.
You see, there are many, many reasons why people are not convinced by
arguments. Sometimes they might be open and honest and tell you what the wall
is, sometimes they might not. Sometimes they might tell you what the wall
is…when in fact it is something else that they are not sharing with you. Someone
who is very adept might be able to get the real wall out in the open and get them
to drop it…but it is never guaranteed. Never. Sometimes the walls are so tied to
deep and powerful emotions and values that simple logic and evidence will never,
on their own, get through. And when they don’t…. no proving has
occurred…only the offering of proof.
What kinds of things serve as walls? Let me list out a few of the most common:
 Acceptance could cause harm to one or more important relationships
 Acceptance could cost one a job, position, opportunity, and etc.
 Acceptance could cause one to be thought of less favorably… as being
weak-minded, soft-willed, unintelligent, and etc.
 Acceptance would require a major paradigm shift in life which would
require rethinking many other things
 Acceptance would contravene a deeply held value
 Acceptance would expose them to emotional harm
All of these walls involve “cost”… and that is the real crux of the matter.
Acceptance of some things can be quite costly… and to many people acceptance
is just too expensive. In the stolen coat scenario, let’s say Edna had been offered
to coat for little cost by Johnny…so if it were stolen, then she is going to be out a
cheap coat. In the case of my Vietnamese student, acceptance could cost him his
entire family.
So… if we believe that we are in the presence of a solid argument…and yet see
someone rejecting it, we always have to ask ourselves what is the hidden wall that
is keeping it from getting through. We need to ask, what is this going to cost them
to accept this argument?
A woman might have a fella in her life that had previously been unfaithful.
Suppose he confessed and professed his change of heart and renewed devotion
and fidelity. Suppose… this might be hard to believe of course… but suppose that
she wanted to believe him…but had some doubts. Would a mere claim on his part
result in acceptance on her part? Would she not, in fact, like to have some
demonstrative evidence from him…like him canceling his membership with those
three online dating services? There is a direct proportionality here. The greater the
possible cost of acceptance…when the claim turns out to be wrong…the greater
the need for a high amount and quality of the demonstration of evidence
supporting the claim or subclaims. If being wrong is going to hurt a ton… we
need more solid evidence.
A final note: One may accept a claim without it having been proved. If Johnny
made the claim to his brother, and his brother considered Johnny to be a
completely trustworthy source, then he could accept the claim and adopt the new
position purely as an act of faith in the source, without reference to any “proof”.
In this case, nothing was proven, he just took it by faith.
Definitions
Analytic Proof = proof by definition / adduction without the need for evidence.
Axiom = a statement or principle which is generally accepted to be true, but is not
necessarily so (typically used in specific disciplines)
Demonstrative Proof = proof by production of evidence in support of a logical argument
Evidence = physical things brought forth to another person for the purpose of
establishing a claim.
Internal Consistency Δ– how well statements within a system of thought harmonize
with each other
External Consistency Δ– how well statements within a system of though match up
with reality
Presupposition = something assumed to be true in advance without having any proof
(typically not tied to a specific discipline)
Proof = 1) an argument or evidence sufficient to establish a thing as true, or 2) to
produce belief in its truth.
Prove = to establish the truth or genuineness of, as by evidence or argument, in the
mind of another