Pro Logica

October 2, 2010

From Perceptions to Truth


Epistemology is the  branch of philosophy concerned with human knowledge, or as is usually stated, “what we know and how we know it”.  As in all topics of philosophy there will never be “the last word”, but that doesn’t keep people from trying, and here is my attempt.

This particular post will discuss the concepts of perception, fact, statement of fact, statement of view, belief, faith, reasoning, proof, history and truth.  I only assume that people (consciences) have a finite existence, i.e., a beginning, middle and an end, can remember their perceptions but not perfectly, can associate a current sense or bodily impression with a previous sense or bodily impression, can reason (some better than others), have a limited herd mentality and communicate with each other about their perceptions.  The ability to communicate among consciences is also variable.  These assumptions embody four key concepts of epistemology: memory, conscience, perception and communication.   Without consciences, memory, perception and communication have no meaning; without memory and perceptions, there is nothing about which consciences can communicate; without memory and communication, consciences can have no common knowledge.


Perceptions are basic units of information residing within the memory of any individual conscience.  There are two kinds, internal and external.

An external perception is a memory of the experience of a simple sense impression: the sight of a single object, the hearing of a single sound, the smell of a particular aroma, the texture of a single touch, any particular taste.  In addition to these five external senses there are internal bodily sensations associated with the appetites such as hunger, shelter and sex and also internal bodily sensations classified by the words ‘pain’ and ‘pleasure’.  These are also treated as external perceptions in the same manner as the sense impressions.  Each of these sense experiences can be qualified in some way by a gradient that can be classified as a strong experience, a weak experience or somewhere in between.  A thought such as “I am hungry”, either silent or spoken is not an external perception precisely because the words, silent or oral, represent the association of at least two separate memories.  While sense impressions and bodily sensations are universally experienced by all consciences, they normally occur in a rapid  sequence of many, or are so quickly associated with past memories that most consciences do not recognize these elementary perceptions as such.

Internal perceptions are more complex.  At a minimum they consist of the remembrance of an external perception mediated through a language.  Basically, any thought that presents itself to the mind of a conscience as a language expression is an internal perception.

An example:  The recognition of a string of words as a sentence is an internal perception, but the memory of the hearing of each individual word without any associations, especially meaning, are external perceptions.  From here on the internal perceptions multiply,some of which are: associating a meaning with each word, associating a meaning to the sentence and associating the sentence with its immediate environment–speaker or written characters.  The perceptions mentioned here are clearly the minimum involved; the listener will normally have many other internal perceptions at hand.

Let”s take a closer look at the above example with regard to communication. Communication between consciences is necessary to create a body of common knowledge between the communicating consciences; it accomplishes that end by transferring knowledge existing in one conscience to another conscience that previously did not have it.  Communication between consciences is primarily accomplished through a  body of knowledge called language, which consists of words, rules of grammar and the meanings associated with the words both by themselves and when strung together using the rules of grammar. This example illustrates the basic problem of communication: words have meanings and that you, as a conscience, will either not understand or misunderstand what I have to say unless your meanings coincide with mine.  This observation, which is an internal perception, tells a reasonable conscience that the first duty of any conscience when disagreeing with another conscience is to make sure that both agree on the meanings of all words and phrases used in their discussion.  Of course, this will not necessarily resolve all differences.  This observation is also why philosophers generally insist on only one meaning per word or concept.  Written communication is especially difficult to grasp because the writer and reader usually cannot communicate directly with one another to resolve any difference of meaning, although an astute reader will take the time to consider whether there will be a big difference of opinion or a small one.

Practically all internal perceptions are simply the remembrance of something by a conscience.  It is to be noted that communication between consciences always involves remembrances, i.e., internal perceptions, i.e., memories of external or internal perceptions.  Since memory is fallible the communicated internal perception may be somewhat different from the actual perception when first formulated.  Also, since consciences can and do lie, the communicated internal perception may not be a faithful representation of the internal perception causing the communication.  Also, two consciences observing the same happening may have entirely antagonistic perceptions of that happening.  These factors, together with the unavoidable difference of experiences between any two consciences, account for the differences of knowledge between any two consciences.  These differences are so great that one can rightly conclude that all consciences were, are and will be unique.   I do not think it would be possible even for identical twins of the same gender to have exactly the same internal and external experiences to enable them to have exactly the same common knowledge and absolutely no other knowledge than that which is common to them both.  Here, I would like to state a couple of ethical points: This uniqueness is reason alone to condemn the willful extinction (murder) of any conscience by another conscience and that elective abortions are always unethical since they prevent and deny a new unique conscience from interacting with and communicating with other consciences.

There is a situation in which an objection to the above might surface.  Suppose a conscience in the company of other consciences utters words or sounds which are interpreted as an experience of an external perception by that conscience.  However, the only valid conclusion is that the utterance came from that particular conscience; there is no way of absolutely knowing more.  The utterance is the result of associating words or sounds with previous experiences and is, therefore. an internal perception.  Further discussion with that conscience might clarify the event but just as likely, it may not.

One further thought on language.  Most consciences will accept a statement declaring that there are many different languages and that these languages are, for the most part, mutually unintelligible, primarily because memories are stored in specific languages.  Despite this, certain consciences have been able to learn more than one language and, consequently, provide a workable translation between speakers of the specific languages.  Anybody who has dealt with translations will tell you that there is no such thing as a perfect translation so there may be some uncertainty in the meaning of any translation.  A conscience versed in one language has to make an extra effort to see that his/her meanings agree with the meanings of the words in the translation offered by the other language.

Internal perceptions may be very complex since language has ways of categorizing knowledge which may lead to a given internal perception actually representing a long series of minor internal perceptions.  The problem here is that the communication of the general internal perception may coincide with another conscience’s general internal perception yet fail to elicit any of the same minor internal perceptions.  There may be absolutely nothing in common except the general perception.


Looking at how newborns learn we can state unequivocally that their initial knowledge consists of the control of their body through the use of play either with other consciences or toys (physical objects) followed by a language which comes strictly from their observation of all those consciences which interact and communicate with it.  This learning usually lasts throughout a conscience’s life time–some deterioration occurring  in old age–but is usually advanced enough by around two years of age that knowledge of other things becomes possible.  There is much variation in this time-line due to both the genetic structure of the new conscience and the environment in which it finds itself.

Keeping in mind that memories are fallible, that observations by consciences of similar events do not necessarily lead to  internal perceptions which coincide in all respects and that consciences are capable of lying, the basic rule of epistemology can be stated as follows:


The first thing you will notice about the rule is the use of the word ‘believe’ rather than ‘know’.  Hopefully this will become clear when the concept of ‘belief’ is discussed later in this essay.  The second unusual feature is the use of the word ‘observation’.  This word denotes an internal perception which has been derived through the process of reasoning, (again discussed later in this essay), and, as such, defines the vast majority of internal perceptions.

Unfortunately there is a caveat to this rule–consciences can and do control what they believe.  It usually takes a startling insight (internal perception)  to change a conscience’s belief and many consciences avoid any circumstances that might result in a convincing insight to change their beliefs.

The rest of this essay concerns itself with terms and concepts related to the communication of beliefs (common knowledge) between consciences, and also discusses some aspects of the scientific method related to the concept of perception as presented here.


From prior discussion, young consciences first learn how to control their bodies and communicate with other consciences and this learning becomes the basic knowledge of all consciences.  While we can talk about these two types of learning as being distinct, in practice they are hardly ever separated.  At the beginning of a conscience’s life, some bodily movements may be spontaneous and some may be precipitated by other bodily sensations.  The spontaneous movements are discovered to be controllable while the movements connected to  sensations are discovered to be interruptible–all of this does not happen in a brief period.  Consequently, words are being learned which bear directly on the controllable aspects of bodily movement.  What happens is an almost simultaneous association of a bodily sensation or controllable movement with a word or phrase which masks the external perception.  These internal perceptions stored in memory constitute a conscience’s basic core of knowledge upon which all further learning and knowledge are then built.  Also during this learning period, knowledge is being imparted to the conscience in the form of communicative expressions from its teaching consciences and this knowledge is believed until such time that the learning conscience learns of contradictions between sources of knowledge.


History is a subject loaded with ‘facts’: “World War II lasted from 1939 through 1945.”, The Declaration of Independence was proclaimed on July 4, 1776.”  Geography is another subject loaded with facts: “Sao Paulo is a city in Brazil.”, The Alps is a mountain range located primarily in the country of Switzerland.”  Most all subjects of consciences’ learning have their ‘facts’, that is their claim, anyway.  A branch of learning that has a chance of not admitting to the existence of ‘facts’ within its purview is symbolic logic; however, it does claim that all mathematical or logical systems which consist of axioms and methods to derive theorems from those axioms belong within its branch of learning.

Many of these facts are imparted into the memory of young consciences through a process of memorization called rote learning.  Much more is imparted by the consciences’ own observation of its environment, by listening to other conscience’s communications, especially that of teachers and other trusted consciences and also by their observations of the artifacts which store these ‘facts’ and the artifacts which are used to illustrate these ‘facts’.  All consciences use these methods, called education, which normally lasts throughout a conscience’s lifetime and many consciences go through their entire life without questioning many of these ‘facts’. From time to time a news item will mention some study in which one of these learned ‘facts’ will be disputed.  While the factual disagreement is big news in whatever branch of learning encompasses that disagreement, it is generally a ho-hum bit of news that plays no important part in the life of those consciences outside of that field of learning.  What is missed by this latter group of consciences is that a curious and inquiring conscience might look at any given ‘fact’ and conclude that the ‘fact’ could be inaccurate or even false.  There is always the possibility that the original communicated expression which is now a ‘fact’ was not a faithful representation of either the original event or view or even of an original internal perception.

A statement of fact is an communicative expression of an internal perception of a conscience which is meant to communicate that conscience’s view about the actual occurrence of a past event.  This communication may be made in order to disseminate knowledge or to deceive another conscience and is determined solely by the communicator.  Even if the objective of the communication is the dissemination of knowledge, the fallibility of memory requires a reasoning conscience to evaluate that statement of fact before incorporating it into its store of knowledge.  A statement of view is any communicative expression of an internal perception which is not a statement of fact;  these most likely would be called value judgments or personal beliefs and, also can be made in order to disseminate knowledge or to deceive.  The word ‘statement’ when used without a qualifier can be either of the above described statements or a communicative expression which contains both a statement of fact and a statement of view.  As per any language, a statement which contains both kinds can be separated into an individual statement of fact and an individual statement of view.  Complex statements containing multiple statements of fact and/or multiple statements of view can always be separated into individual statements of fact and individual statements of view.

In view of the definitions in the preceding paragraph, it is safe to say that the English word, ‘fact’, as normally used within human branches of learning is a total fiction and the ‘facts’ proclaimed in any branch of learning are actually statements of fact or statements of view, and while it is true that many of these statements can have multitudes of references as to their validity, there is absolutely no way to confirm an existent truth to any statement.  To illustrate:

Suppose as a student you decide to skip a day from school and a month or so  later it becomes necessary to know the exact date.  You reach into your memory and retrieve a date, but since it deems to be an important date you attempt to verify it by checking the school’s attendance roll for that particular date but the attendance roll says that you were not present at school on that date.  Looking further, you find that the attendance roll shows that you were absent from school on the following date.  Suppose also that there is no other possible way of  verifying your remembered date.

What can never be known from these circumstances is the exact date on which you skipped school.  Furthermore, it is impossible to know whether your memory failed you, or that the attendance roll is in error or even that both possibilities exist.  Taking all these possibilities into account, you cannot even be sure that you skipped a day from school. This kind of analysis can be applied to all learned statements made by any conscience or artifact which purports to claim a ‘fact’.

But, what about the basic knowledge discussed in the previous section, can they be called facts?  Certainly, one can call a conscience’s bodily sensations or sense experiences a kind of fact, especially to the conscience which experiences them, but they are definitely not facts in the same category as the claimed ‘facts’ of human branches of learning.  A conscience certainly knows when it experiences a bodily sensation or sense perception; it certainly knows how to formulate communicative expressions of its internal perceptions in its learned language–allowing for its gradual learning over a length of time and capacity of learning; it also knows what its beliefs are (unless forgotten) and that these beliefs may be subject to change unless those beliefs are founded upon some universal principle which reason forces it to retain (I’m sure I have not exhausted the list).  Yes, these are facts but facts that identify each unique conscience and whose individual internal perceptions, though expressed in identical language cannot be identical internal perceptions.


Every statement uttered by a conscience has at least three corresponding  internal perceptions: there is an original internal perception, an initial internal perception constructed from the original internal perception and a modification of the initial internal perception.  An original internal perception is one formed completely from external perceptions without any associations from previous internal perceptions.  Since all external perceptions are, practically speaking, instantaneously associated with an internal perception, an experiencing conscience forms an initial internal perception which includes all these associations.  It is highly unlikely that a statement based on an original internal perception would be equivalent to one based on its initial internal perception but one must realize that a conscience will believe that its initial internal perception is the original internal perception.  A modification may be nothing more than a recollection of the initial internal perception and that recollection may be identical in content or it may be somewhat altered due to a memory lapse and therefore not identical in content.  In this latter case the conscience is not even aware that the recollection is not identical to its initial internal perception, i.e., the conscience believes that its recollection is identical to its initial internal perception.  It is most definitely possible that after a series of recollections the resulting internal perception’s statement cannot be capable of conveying the meaning of either the original internal perception or its associated initial internal perception except by mere chance. In this process, it can be seen that a conscience may entirely forget its original initial internal perception while believing that its current version is the correct one.

Keeping in mind that all of a conscience’s memory is couched in a language and that there are at least two aspects of a language which underscore the actual communication between consciences–syntax and semantics–there are certain language constructions within any specific language in which the validity of a statement may not reasonably be denied.  If they are, it is always he result of different experiences being associated with different words and when these misconceptions are cleared up between the discussing consciences there is always found to be no disagreement.  Such statements are called tautologies, and are not to be confused with the tautology defined in a truth-valued logical system.

A conscience, upon retrieving an internal perception, can craft a different internal perception and base its communicative statement on this new internal perception.  If the purpose of the statement based upon the crafted internal perception is to disseminate knowledge contrary to the knowledge that would be disseminated by a statement based upon the internal perception which was used as a basis for the crafted internal perception, that conscience will be said to have lied and that the lie (the ‘crafted’ statement) is an attempt to deceive another conscience.

I can sum up these last two sections by saying that any statement uttered by a conscience is either a tautology, belief or a lie.  Of course, a long complex statement can contain one or more  of each and all of these.  The nature of tautologies renders the concept as irrelevant to the rest of this essay.


I can remember that when I was young I was always pummeled with a lot of ‘facts’  from my parents, relatives, teachers and friends; remembered most of them and got good grades in school.  Not every conscience can get good grades in school but a lot of ‘facts’ are imparted to teach individual conscience and received by them as knowledge, i.e., they believe these ‘facts’.  There is no reason not to unless some communication uttered by a conscience indicates otherwise.  At this point, the conscience confronted with contradictory statements has three options relative to its own store of beliefs: it may disregard the contradictory statement, it may replace its existing belief with the contradictory one or it may keep both with the knowledge that a controversy does exist.  If one of the first two options is chosen, it is primarily done on faith, meaning that the choice was made because the source of the accepted statement is more trusted than the other source.  Suffice to say at this point that the uniqueness of consciences precludes any general procedure as to why a conscience so decides.  It is also safe to say that a conscience which chooses one statement over a conflicting one will, oftentimes forget the conflicting one, especially if a relative long interval of time occurs between the pertinent recollections.


Mankind is said to possess a rational faculty, but just what is a rational faculty?  Choices: A tendency to categorize and/or organize, a predilection to form rules and laws, the act by a conscience of using its memory to formulate an internal perception different from any existing ones, the ability to make an abstraction out of a specific internal perception, a propensity to label two successive events as cause and effect, the use of given procedures for determining conclusions from a set of assumptions.   I’m sure that other consciences could come up with a few more choices and that even I might if I thought about it for a longer period.  It seems to me that the first three choices are primary in that the others can be seen as specific applications of them and I have a tendency to believe that any other choice offered would be seen in the same light.  Reasoning can be defined as the act of exercising a conscience’s rational faculty, and as noted in my assumptions a highly variable ability which therefore contributes to a conscience’s uniqueness.

The definition offered here defines reasoning as a process which occurs wholly and totally within and by an individual conscience, and oftentimes, it’s done on the fly, i.e., in conversation with other consciences.  Considering the uniqueness of individual human consciences, it is safe to say that no two individual consciences ever exercise their rational faculty in the same way all the time.  Nevertheless, human consciences have crafted a branch of learning which purports to abstract the process of utilizing the rational faculty, and this branch of learning’s name is usually referred to as ‘Logic’ or ‘Logic Systems’.  Since this essay is about epistemology, there is no need to enter into a detailed description of ‘Logic’ to which I have not the detailed information to do any justice to the subject, but some discussion is necessary to properly define the word ‘proof’.

Of all the subbranches of Logic, the word ‘proof’ appears in the subbranch of ‘Deductive Logic’.  A major assumption of logic can be stated thusly,  “A statement can only have a derived validity within a system of statements  having a set of statements assumed to be valid called axioms with a fixed method or methods of crafting a resultant statement different from the axioms and the statement can actually be crafted (be a theorem) using those methods.  This actual crafting of the statement is then said to constitute the proof of the statement in the specific logical system.  Changing the axioms or the methods of crafting will usually result in a system with a different set of theorems but not necessarily.  In the vernacular, statements true in one logical system may not be true in in a slightly different one.  Of course, Aristotle would not have phrased it that way since the idea of separate and/or fictitious logical systems were probably unknown or latent at that time.  Normally, when a conscience demonstrates its proof and this so-called proof is not part of a fictitious logical system with definite axioms and methods of proof, it presents a series of statements which purport to show its reasoning so as to justify the validity of the last statement in the series.  The rules of deduction can be somewhat vague and the receiving conscience may agree that the proof is valid or disagree, either with the method used for validating, i.e., methods of proof, or with the actual meanings of any statement in the series or even with a statement (axiom) which was left unstated.  What this means is that most arguments purporting to prove a statement merely give a series of reasons for believing a certain statement.  Practically every argument is just a battle of beliefs.

A thinking conscience might ask, “But what about this post?  Aren’t you arguing from assumptions?”.  Of course the answer is yes, but I have not stated any rules of procedure or methods of proof, nor have I used simple sentence constuctions to clearly formulate a deductive argument.  In short, you are only presented with reasons for my belief.


Since all knowledge of the branches of common knowledge are belief, what does a historian, or any conscience for that matter, do when he/she writes ‘history’.  Most historians would answer by saying that they are presenting events that occurred in the past and even though they are presenting their beliefs about the events which occurred in the past, they would still give a just representation of those events primarily because they would not contradict other sources of the same happenings–repetition is usually reliable.  However, we have seen that a statement of and by itself carries no validity and while repetition is usually reliable, one has to be sure that the repetition does not consist of the exact same source, otherwise there is always the possibility of a mistake, memory failure or even of a lie.  The same could be said for a written source.

If a historian or even any conscience enters into a conversation involving historical events or views, he/she usually has an agenda.  It may be to ‘set the record straight’ but this amounts only to state his/her beliefs and try to convince the other consciences that his/her beliefs are better than theirs.  He/she may succeed if his/her beliefs are judged to be irrelevant to any course of action contemplated by the acceding conscience.  More often one presents his/her historical beliefs to convince other consciences to embark on a certain course of action.  There is no difference when history is written except that the agenda may be bigger and broader in scope.  Consider the branch of history called biography; ever wonder why famous people have more than one, and each one generally presents a different view of the person.  No one uses history or writes about history without some ulterior motive even if only to ‘set the record straight’.  As noted earlier, sometimes new sources are found which cause existing beliefs to be questioned but even then there is no assurance that all consciences will accept the new beliefs.


  • All human consciences do have knowledge of their own bodily sensations and sense experiences.
  • Individual human consciences do learn how to translate their knowledge of these sensations and experiences into complex internal perceptions through the use of one or more modes of communication.
  • Individual human consciences do craft statements out of their personal internal perceptions which are intended for the perception of other human consciences.  These statements can be classified as beliefs or lies.
  • Individual human consciences do know the difference between its own beliefs and any lie which it crafts from that belief at the time of crafting .
  • The memory of any individual conscience is fallible.  Therefore, it is almost impossible for any conscience to know whether a statement uttered by another conscience represents an existing belief, a former belief, a lie crafted from a former belief, a lie crafted from an existing belief or even a lie crafted from a former belief in which the former belief itself has been forgotten.
  • No statement can be proved in any absolute sense except in a formal and fictitious system since a proof is the result of a deductive method of reasoning which depends on axioms, i.e., unproven assumptions.  Normal arguments outside of formal and fictitious systems are thus a series of reasons enforcing the presenting conscience’s belief.

I do believe that these conclusions back up the basic rule of epistemology as formulated earlier.


This section deals with those physical/mathematical/logical systems which attempt to describe a subject among consciences usually referred to as the “real world” (defined below) and whose theorems are not in the form of a probability.  A probability does not say anything definite about something actually occurring.

The internal perceptions of our external perceptions, as communicated between consciences, appear highly uniform giving rise to an assumption that there is something outside of consciences and not directly controlled by the consciences themselves, although the consciences can affect and do control certain aspects of it–for instance, trees are recognized by consciences as objects distinct from consciences and we seem to have the ability to cut them down or prune them or climb them.  This uniform aspect  is usually referred to as the real (external) world and is assumed to exist independently of the consciences communicating their perceptions among themselves; however, there is no way to prove this assertion since the assertion can only exist within the memories of human consciences as common knowledge and the elimination of all consciences would also eliminate any shared knowledge about this so-called real world.  Whatever an individual conscience perceives to be of this external world, that individual conscience must believe that it and any other conscience it interacts with along with any other conscience that may exist are  inseparable from this observational external world.  This observational consensus and the one stated previously about the uniqueness of individual consciences makes it highly unlikely that such an independent external world actually exist.  I do not claim that there is no external world, only that its existence cannot be known by us human consciences however much it is assumed and that the universe as perceived by us human consciences is totally unique.  This assumed independence along with an intuitive passive observation of the external perceptions is what gives science the impetus to assume that a conscience crafted, fictitious, physical/mathematical/logical system exists which will describe all the actions and happenings of this assumed external world including our ability to manipulate it, but since this external world is intimately associated with the consciences that describe it, no conscience crafted system can describe all of it since to do so would involve describing each individual conscience, past, present and future. I have used the word crafted instead of created since I reserve the use of the verb ‘create’ to its metaphysical sense, that of producing something from nothing.  An artist crafts an internal perception of his out of physical media; the independent external world perception was also crafted from combinations of earlier internal perceptions, an example of the use of our rational faculty.

Consciences can and do devise systems which describe parts of this external world and which can be utilized to manipulate aspects of it, but I point out that these systems cannot be perfect models since they assume that all interaction between the physical aspects of the external world, as described by their systems,  and consciences is through the manipulation of “laws” existing independently of and prior to the existence of the consciences which formulate the “laws” in the first place.  Most scientists will claim that they are merely discovering the laws of nature but make no attempt determine why these laws even exist or seem to be immutable.  People who believe in a creator God have no problem with these ideas and from a scientific point of view this immutability is necessary for the advancement of shared or common knowledge among consciences (there is no incompatibility between the views, both require the primacy of conscience).  Whatever the cause, the immutability of the laws of nature is a staple of scientific investigation, since, without it, scientific investigation would be meaningless.  It is to be noted that while the external world’s rules are considered immutable, the physical/mathematical/logical system describing those rules have certainly changed over time, usually by incorporating larger chunks of the so-called external world and presenting the earlier “laws of nature” as approximations of the laws formulated by the newer systems.  This alone refutes the application of immutability to physical laws developed through mathematical/logical principles but doesn’t seem to keep physicists from referring to the laws of nature.

The basic unit of the scientific method is the observation and a physical observation is intimately associated with a process called measurement utilizing the remembrance of many external and internal perceptions.  Consider the simple act of measuring a length; there is the motive, the material to be measured (it may be just space), the ruler (measuring device), the marks on the ruler if such exist and the actual process of using the ruler (it may be longer or shorter than the distance to be measured).  While there are some external perceptions in this particular observation, they go unnoticed since they are bound to the internal perception of the idea of measurement.  In short, a scientific observation is an internal perception and subject to all the vagaries of any internal perception.  As most people know, it can be very difficult to get two measurements to agree and for most everyday situations exact agreement between measurements is not critical.

Another drawback to most current physical/mathematical/logical systems is their use of infinitesimals as basic units for their mechanical aspects.  Infinitesimals got their start when Euclid discovered the theorem that the ratio of the circumference of a circle to its diameter is not a ratio of whole numbers.  Nevertheless, between Euclid and now, a number system has been developed to account for Euclid’s theorem and is usually referred to as the real number system since it is assumed to apply to mathematical systems attempting to describe the so-called external world.  The essential assumptions here are: 1) external world scientific events happen in a space consisting of points, 2) this space extends infinitely out in all directions, 3) a single point has absolutely no physical dimensions, and 4) a continuous infinite line in this space can be represented by the real number system utilizing all its comparison features.  (I have italicized the words continuous and infinite because these are somewhat vague internal perceptions of non-scientific observations by consciences and, hence, their use can cause confusion in consciences not having a scientific bent.  Both these terms have very specific mathematical/logical definitions  which seem to convey a sense of our underlying internal perceptions but also convey a sense of disconnect between the definitions and the perceptions.  The only defense of the rigorous definitions of these concepts is the one which states that these definitions do seem to work.)  The problem here is found in assumption 3 which identifies a point in the space of the external world as an infinitesimal.  Unfortunately infinitesimals are not capable of being an external perception of any human conscience, and while the internal perception of an infinitesimal is used to tell us consciences how the real world behaves and no matter how well it does that, it does not prove that infinitesimals actually exist.  Quantum theories of reality actually point to the idea that infinitesimals don’t exist, but even those theories are suspect since they do use the “real number” system for all their calculations.

As mentioned in the above paragraph, the idea of “infinity” represents a disconnect between its normal human conception and its definition within the mathematical/logical systems used as the basis for all scientific theories including that of the “real number” system.  Let’s start with a popular illustration, that of a hotel with a finite number of rooms against a hotel with an infinite number of rooms.  A potential customer goes to the hotel with a finite number of rooms and asks to be put up, but the manager says, “Sorry, all my rooms are occupied.”  The potential customer then goes to the hotel with an infinite number of rooms with the same inquiry but receives this answer, Sure, but you will have to wait awhile.  The manager then goes to unit one and tells them they will have to move to unit two; while those occupiers are preparing for their move the manager goes to unit two and tells them that will have to move to unit three.  This is done repeatedly until all occupiers have been transferred leaving unit one unoccupied.  The manager now goes to the awaiting customer and places him into unit one.  The implication here is that the needed room is being constructed so that the customer in the last room will have a room to move into.  This is a fine illustration of the intuitive meaning of infinite–there always exists the capacity to add one more to the collection; however, this is not the definition of infinity within the mathematical/logical systems used in scientific methodology.  As understood there, the manager of a hotel with a truly infinite number of rooms would not have to go through the process described for that extra room would have already existed.  The distinction here is between a constructive meaning of infinity versus an existent meaning of infinity, and the mathematical/logical systems using these different conceptions are not equivalent–the so-called “real number” system cannot be formulated within a mathematical/logical system using the constructive definition of infinity.  It is not presently known whether the use of the existent form of the definition even leads to a consistent mathematical/logical system.  This assumes that both systems use the same prior axioms and rules of proof.  I do not intend to get into any involved discussion on mathematical/logical systems within this post since its topic is epistemology.

Getting back to Euclid, we now know that his geometrical system does not apply to the earth’s surface except for very small lengths compared to the earth’s circumference–unfortunately our earth is not a perfect sphere but most everybody agrees that it has a circumference (more about this in the next paragraph).  This is a clear illustration of the progression of scientific knowledge: spherical geometry has replaced Euclidean geometry as the actual geometry of the earth’s surface but Euclidean geometry is a very close approximation to many geometrical problems where distances are small when compared to the circumference of the earth and is used because its calculations are simpler.

The concept of the circumference of our earth leads to another drawback of all scientific systems.  Our earth is not a perfect sphere so its circumference cannot be that of a perfect sphere and spherical geometry, a geometry purported as the method for solving its geometrical problems, is absolutely not the exact science to be used for that purpose, but it is close and close enough for practical applications.  If one examines any scientific system, there is always a discrepancy between the mathematical entities used to describe the particular aspect of the external world under consideration and the external world itself as observed by us human consciences–notably the disagreement of successive observations.  Some observations are thrown out as being “way out” and the rest are then averaged in some way, there being no uniform method of averaging.  Most scientists will admit that these concerns do express doubt that our scientific systems are accurate descriptions of the external world and most will say that there is probably another way to picture the external world but that the current systems are close enough for practical applications.  Many scientists also assume that they will develop other and larger systems  which will reduce the earlier systems to approximations within their new systems.  Essentially all our practical applications of science are approximations of approximations of approximations ad infinitum, possibly.


Finally, we come to the very last concept of this post.  Much normal usage of the word ‘true’ is that of a value judgment which one assigns to a statement made by another conscience, this statement being one which, more or less, coincides with one’s own belief; but epistemologically speaking, truth is a subcategory of an individual conscience’s beliefs.  Truths are not just any beliefs since most beliefs do not call for action by the individual conscience; a truth is a belief by which an individual conscience orders and lives and acts its existence.  Some instances: “I believe in government of the people, by the people and for the people”, “I believe in a government that does not allow class distinctions for any reason”, “I do not believe in a god or any gods”,  “I believe that matter preceded human beings and that moral and ethical laws can be derived from the laws of matter.”, “I believe in a loving god who created us,set us into this world for a finite period of time, masked his presence here, but gave us enough curiosity to find him through his works, and gave us a free will to either accept him or reject him.”.  I could go on but there is no necessity for that.  Truths, in this sense, are very important to individual consciences because they determine a conscience’s relations to other consciences; however, epistemology does not give us any methods for determining those truths which are best cultivated for the social process.  That determination is explored in the subjects of religion, morals and ethics and the only statement that epistemology can offer to those fields is the uniqueness of each individual human conscience.


While all common knowledge consists of beliefs, these beliefs are the only thing that consciences can communicate about; so , whether there is a so-called real world or not, consciences do need to act as if their beliefs do matter.  The uniqueness of consciences dictate that the common knowledge between any two consciences will differ from that of any other conscience with either or of any two other consciences.  This presentation shows that reasoning needs to be applied as to the believability of any statement made by a conscience before incorporating that belief into one’s core knowledge.



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