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December 30, 2009

By Dr. Gary S. Day

 What is Proof?

 It is not a simple affair to establish truth, though the need for proof is great in today’s society which has seen an amazing growth of understanding in science, history, technology, litigation and other disciplines of discovery.  Convincing evidence is brought about when an assortment of evidence is subjected to cross-examination and truth is established from the process.  This process becomes more complex when one realizes that each field of study or knowledge has its own set of methods for the mining of truth, its own tools that are used for the excavation of its proofs and its own rules or canons by which proof is established.  For “proof” does not mean the same thing, in the physical sciences, mathematics, logic, or in historical study or in legal investigation.  The same difference is found in disclaiming assertions, among the various fields of study.  On top of this, it is not possible to disprove many assertions, especially the assertions in the historical and archeological data. 

 The drawback in this complexity is that many are not equipped to handle the arguments put forth or don’t understand the processes of proof, though they may need to use proofs in dealing with others.  Also it is common for the masses to disregard proof in their everyday lives, but the student of the Bible, science or other disciplines of knowledge gathering has no such luxury.  Knowing the principles in the various aspects of proof used in differing topics and the criteria for proof, evidence, logic and illogic should be a keen concern to those serious about apologetics or politics, etc.  The criteria for proof is necessary for the Christian apologist to understand because the Bible is often attacked using the proofs from one field to support their arguments in another, where such proof might be inappropriate or totally invalid.  Blindness to this tactic can easily derail an otherwise strong apologetic case. 

 There are at least seven types of proof:

1. An axiomatic truth is the most basic and fundamental level of truth for proof, for no more simpler category of truth exists to prove the axiom.  They are universally self-evident truths and function as the most basic axiomatic proof.  Particular Axioms are those axioms related to a particular field, such as quantum mechanics, pharmacology or historiography.  Universal Axiomatic Proofs is a collection of axioms that plays a direct or indirect role in every field of knowledge.  These are self-evident, unchallenged proofs, such as the algebraic formula for an equidistant triangle.  If A= B and C=A, then C=B.

2. The proofs of logic deals with statements that are reduced to their most elemental levels.  When two statements are related in a specific way and are placed next to each other, then certain inevitable deductions follow, which represents the only possible deduction also.  Logical proofing uses the application of logical methodology and the axiomatic principles of logic to deduce truth and to arrive at more universal proofs.

3.  Mathematical proof is divided into Arithmetic, Algebraic and Geometrical Proofs, which need to summon Axiomatic and Logical Proofs to arrive at its proofs.  Newer branches of mathematics have also been developed, having manifold applications in the cutting edge of research and technology.  Proofs in these fields often differ from the methodologies found in, say arithmetic.  And though the basic mathematical groups mentioned above are independent, they also function interdependently.  

Mathematical proofs are universal and without exception within a given system, e.g., rational numbers, but they should only be applied in the realm of mathematics or in those fields that yield their expression through mathematics.  All other uses of mathematics are invalid and illegal.  For example, God is not a mathematical equation, but a person, so mathematics cannot be used to prove or disprove God, or the Trinity. 

4. The most common proof in science and technology is empirical proof, using axiomatic, logic and mathematical proofs, through practical demonstration and assessment.  Repetition of experiments with a large sample base allows for statistical application of analysis and the reduction of errors in the conclusions.  But since Empirical Proof is the most common proof in the physical sciences two erroneous assumptions exists: A) everything can be proved or demonstrated by empirical proof; and B) There exists only empirical proofs.

5.  The Historical-Legal Proof is a key to the study of some sections of Biological science, and every branch of the sociological, psychological and the historical sciences.  Advancements in archaeology, history and forensic science have advanced historical-legal proofs.  For instance, the carbon dating of the Shroud of Turin by three independent laboratories has shown it to be a fake that was made during the fourteenth century A.D.

6.  Legal-logical evidence is collected and used to analyze and reconstruct a single event, like what is conducted during crime investigations.  This evidence is not foolproof, so only those outcomes that are considered undisputed should be used in apologetics.

7.  Relational proof is a special category of proof used everyday.  The reading of a newspaper with an announcement of the firing of a government official is taken as ‘proof’ that he was fired because of the relationship existing between the reader and the reporting of events in newsprint.  The major portion of proof that we absorb everyday is based on relational proof.  This type of proof helps in the discovery of important truths, including the existence of God.

What is not Proof?

The empirical proof form is not the only type of proof that leads to knowledge.   There are at least eight major methodologies that are used as evidence, and the empirical form constitutes only a small portion of proof gathering.  And what many believe to be proof or evidence are not proofs at all, and this is a common problem.  Proof comes is the specific form of a particular methodology.  Empirical proof needs to be empirical, historical proof needs to be historical, and so forth.

Proof is not an argument, for neither are always valid, but there is a distinction between the two.  What follows is a list of activities or positions that some use as “proofs” that would not be accepted as legal proof.

 1.  The refutation of another’s argument on a subject only shows that the argument is flawed, not that you are right.

 2.  Showing the possibility of an effect in a situation is not proof, for an effect can be caused by more than one factor.

 3.  The ability to provoke a mental image-creation does not prove or disprove scientific fact, for what “is” decides what “could be” in empirical data.

 4.  A quote from an authoritative figure or an appeal to popular opinion does not produce proof.  In the former case, experts can be found to support any position, no matter how extreme.  In the latter, such appeal is based upon emotional subjectivity, not objective fact.

 5.  Silence does not support proof, for just because something is not found, seen or heard does not negate the existence of the matter, or prove that something didn’t happen.  For example, radical theologians once said that the portions in Genesis that spoke about domesticated camels weren’t written during Abraham’s time, nor did they exist, because none had been found up until their proclamations.  Subsequently, several decades later, it was discovered that not only were there domesticated camels during Abraham’s time, but they were domesticated camels before Abraham’s time.  So, the foundation those radical theologians used to base their claims about the writing of the passages in Genesis collapsed.

The same erroneous thinking was applied to Moses.  No writing material was thought to exist at his time, therefore (their argument went) Moses couldn’t have written the first five books of the Bible.  The same approach from silence was applied to the mention of the Hittites, who were thought not to exist.  Subsequently, both Biblical representations were found to be true, writing materials were found to exist during the time of Moses and exhaustive evidence for the existence of the Hittites have been unearthed.

6.  Applying analogy from something similar to an investigated matter is not proof about the matter, for proof of a statement or thesis comes from the same statement or thesis, not from something analogous.

7.  Circular reasoning, technically called Tautology, is not proof.  For, like the supposed proof from silence, anything can be “proved” by it.  Circular reasoning was used by the religious leaders when they brought Jesus before Pilate, but when Pilate examined Jesus he declared, “I find no guilt in him.”  In this case the circular reasoning goes: He was arrested so punish him, for he is guilty because he was arrested.  The religious leaders wanted to skip the trial where the proof of his guilt or innocence would come out in legal cross examination. 

8.  The presentation of a theory does not represent proof, for it is an unsubstantiated hypothesis that needs verification that it corresponds with reality.  Theories should not be allowed in any debate against the Bible or to substantiate the Biblical claims.

9.  Hearsay is not evidence of proof, nor are narrated anecdotal quotations or flavorful stories, for each category of truth finding methodology has its own rule for establishing its proof. 

10.  Witty catch phrases or slogans prove nothing.  But they are powerful tools used by advertisers, politicians, activists, propagandists and mind-manipulators that suppress reasoned argument.

11.  Philosophical possibility or explanation is not justified as proof, for such speculation can be used to support or refute any position, in similar manner as the use of an expert’s quotation mentioned above.  Therefore, philosophical speculation cannot be used as proof in empirical, social, Biblical or historical subjects.

12.  Verbal or mathematical models are pictures that help researchers study complex phenomena and invisible objects or entities.  Such model making is an essential part of scientific investigation, gut it is not proof of a matter or reality, in itself.  Although models may be fairly accurate, a model is still a hypothetical and theoretical construct, and the purpose of a scientific model is not to offer proof.   For example, some claimed in the 1960’-‘70’s that the Apostle Paul wrote only four of the fourteen New Testament books attested to him.  This claim was based on computer analysis of the writing.  It was later discarded because it was discovered that the language model for the computer analysis was inadequate.  That same model for computer analysis was used on well known writings and the analysis indicated that the books were not written by their authors either!

What is a Model?

A clear understanding of ‘what science is’ is required to minister effectively today.  Often attacks on Christianity stems from un-established theory and not proven science, and the distinction between the two will solve most problems.  But what is still needed in the category of scientific information is a sound understanding of the “models” in the physical and social sciences.  Understanding the science model helps to dismantle unsubstantiated claims based on “scientific models.”   

Empirical science seeks to understand the ways energy and matter function.  Some understanding of the related properties of a complex structure under study is usually known, such as the properties of electrons when studying atoms.  When extremely complex phenomenon are studied, like weather prediction or language, models are used, sometimes with help of supercomputers.  Yet, models are only intermediary steps in the process of scientific investigation and not the final word.

Descriptive and mathematical models also referred to as qualitative and quantitative models are the two types of model-making used to study complex matters.  Verbal descriptions fall into the descriptive/qualitative model category.  Telling the description of, say an elephant, to someone who has never seen one is an example of this type of model.  These models can’t be expressed in mathematical terms.  And, they are easy to describe for no abstract concepts are needed, yet they’re difficult to analyze.  This is their weakness.

Darwin’s concepts of ‘the survival of the fittest’ and ‘change through gradual adaptation,’ or, the birth of the solar system are examples of this model.  Qualitative models, in the first stage of developing a mathematic model are very useful; but because the human mind is keen on adapting images that do not necessarily correspond with reality in the material world, this model should not be used alone. 

The mathematical or quantitative model accurately represents many physical phenomena, and with higher mathematics, such as calculus, very complex phenomena can be represented.  The prediction of astronomical phenomenon in the universe and the launching and return of vehicles into space are good examples of the successful use of mathematical models.

To make a successful mathematical model, first describe a phenomenon in simple mathematical terms and test it until you yield an ‘approximation.’  Then add more factors and retest it until it yields an ‘approximation.’  Keep adding factors and test until the process yields a model or models that are a satisfactory approximation of the reality of the phenomenon. 

Mathematical models of every phenomena has not been achieved, for the scientific study of nature is an ever changing quest, and once one mystery is resolved, the solving of it unearths ten more, yet, not all phenomena yields to such modeling.  But great advancements have been made through these mathematical models.

In the two types of model-making is found the human attempts to discover nature’s underlying laws, but the models do not represent the final truth.  They are only approximations that are compared with the actual phenomenon, and are accepted or rejected or modified according to the comparison.  This model refining process can take decades or longer to accomplish.  The refinements about the atom have been ongoing for over a century, and may take another century of refinements to fully comprehend its functions.

The use of models in the sciences and technology begins with approximate information in order to harness the complexity of the phenomenon under study, yet even when super computers are employed, the results are still far from perfect.  Handling weather prediction is an example.  However, mathematical models are used to great benefit to business and industry.  For example, the CAT scan was developed after a mathematical model of scanning and reproduction was perfected.

Qualitative models are approximations in appearance which may or may not correspond with reality.  While quantitative models more nearly represent the truth of a matter, depending upon its level of refinements, no model ever perfectly represents the phenomenon they imitate.   A comparison of competing models usually sets one of them apart, if not all are considered equal.  Models are approximations, not evidence.  They cannot honestly be used to establish or to attack the Christian faith.

So, what is and is not capable of Proof?

Legal proofs are often used in everyday life, like using stamps on an envelope and the purchasing of theater tickets, yet people are unaware that their actions involve proof and evidence.  The following information about the capabilities of proof might be helpful:

1.  Universal statements cannot be proven because falsifications of the statements are possible, and proving them is generally impossible.  Assumptions are always made in universal statements.  For instance, “The art of writing was not known at the time of Moses” assumes that all possible information about ancient civilization had been found.  We know this statement to be false today, but Biblical critics espoused this view in the 1800’s.  Universal statements can only be used to discover what existed, not to make claims on what did not exist.  Also, when dealing with questions concerning cultural-political life conditions in Biblical times, remember that only about ten percent of extant archaeological sites have been excavated, and only a small percentage of those sites have been fully excavated.

2.  Universals cannot be proved in the social sciences or in historical science, but can be in the physical science of mathematics.  But mathematics cannot assert proofs in non-mathematical areas; e.g., the doctrine of the Trinity cannot be proved or disproved using mathematics, regardless of the attempts of the Muslim apologist to disprove the Triune Godhead with mathematics.  Also, the universal Laws of other physical sciences, such as chemistry, are much different than those of mathematics, so you must compare apples with apples and oranges with oranges (so to speak).

3. Scientific investigation can prove the existence of phenomenon or objects, or persons, but it cannot often prove their non-existence.

4.  Lack of proof or a gap in information in the various sciences carries no weight, but is where many err; e.g., more is unknown about nature that what is known.  So, when the Christian apologist face critics who attack the Bible, say on an historical basis, he needs to be aware when the “lack of information” is used to ‘prove’ their assertions.  In the past the lack of information was used to claim a certain person or race (e.g., the Hittites) did not exist, but has subsequently been proved incorrect.   The Bible was correct about the existence of the Hittites after all.

5.  The proof of a thesis should belong to the same category of study; logic needs logical proofs, sociological research needs sociological proofs, and so forth.  Each claim is established only by the rules of proof applicable to its own category of study.

6.  Circumstantial evidence is not allowed in a court of law because it is not proof.  It only indicates possibility and at best probability, but not certainty.  Anything uncertain is not proof.  Circumstantial probability does not demonstrate in favor of Biblical statements, nor do they debunk them either. 

Everything in the world can not be proved or disproved; only a well-defined set of things can be proved.  Anything violating the cannons/rules of proof in the respective areas of investigation, e.g., violating historical rules in an historical investigation, is to be rejected regardless of how polished is its presentation.

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