THE TRUTH in all caps means the one truth, the ultimate truth, or what ever the actuality actually is. By participating in PiALOGUE we are able to triangulate all aspects of knowledge and/or opinion or get closer and closer to a common understanding of what is actual which in my diagram is the circular π in the middle with the smaller trangulated colored circles leading up to an ever increasing understanding of the general nature of the THE TRUTH.
Table of Contents
What Is Veritology?
Veritology is a subject (and word) that I have invented to describe
the study of methods for proving the validity of
It is important to distinguish the need to validate our tentative
and theories, from the process of formulating them. The former is
the subject of Veritology, the latter is the subject of the discipline
that I call Speculation Science.
Veritology is philosophically much more important than Speculation
For example, suppose my crystal ball were to reveal to me a theory of
that unifies Relativity and Quantum Mechanics. If the theory were
proved to be true, it would be no less so because it came from my
ball, than if it had come through the usual process of scientific
This act of enlightenment by the crystal ball may simply have been an
fortuitous event. Such an extraordinary stroke of luck does not
the importance of the fact that we have made a gigantic breakthrough in
theoretical physics. In short, aside from issues of efficient use
of our time, and the obvious scientific value in investigating the
of intelligent systems, what do we care of the source of our knowledge,
as long as it is true?
On the other hand, proving or demonstrating that a belief system or
theory is true is of immense importance. If a belief does
not reflect the truth, of what use is it, other than to be an amusing
or a psychological prop such as a rationalization? False beliefs,
such as "this herb is not poisonous", can be outright dangerous.
Since the time of Socrates and Plato, one of the primary goals of
has been the search for truth. Yet philosophers have
merged and confused the quest for truth with the act of
They have asked simply how we "know" truths, lumping belief formulation
and validation together under one subject. It is time to focus
inquiry on the subject of Veritology, and leave Speculation Science to
Before we can investigate methods for proving our knowledge to be
we must first investigate the concept of truth itself.
a rigorous definition of truth is available, thanks to the efforts of
investigators in the area of Mathematical Logic. I will present
only a summary of the mathematical concept of truth. For a
analysis, see any modern text on Mathematical Logic such as Enderton
The language of so-called First Order Logic deals primarily with
sentences with a subject, predicate, and optionally one or more
These sentences can then be combined with logical operators such as
"or", "implies", etc. The subject and objects can be variables,
are "Quantified" (to use the proper jargon), with qualifiers such as
all" or "there exists a". For example, the statement "All men are
mortal", would be written in mathematical logic: "For all X: If X is a
man then X is mortal". The actual mathematical notation would use
special symbols instead of an English sentence, but this is a good
illustration for our point. Mathematical Logic has strict rules
forming its statements. Any statement that is formed using these
strict rules is called a Well-Formed Formula, or WFF for short.
One key to mathematical logic is that each predicate corresponds to
an attribute or relation, or what philosophically is often called a Universal.
For example, the word "mortal" stands for the property of
Another key concept is that of a Model. A Model consists of two
1) A Universe of Discourse, which is the set of all things that exist
the Universe (real or imaginary), and 2) A complete set of attributes
relations that apply to and between every thing in the Universe of
Armed with these concepts, we can now define Truth. A WFF in
Logic is said to be True if for every sentence in the statement, either
explicit or implied (by a Quantifier), the statement has the following
Strictly speaking, the Universe of Discourse for Logicians can be any
that they wish to mentally explore, but for philosophical truth, the
of Discourse is clearly the real, physical Universe (past and
Likewise, the Model is the physical Universe, along with all attributes
and relations which have ever held or will ever hold for all real
- Every subject or object symbol in the statement corresponds to a
of the Universe of Discourse (this is true by definition for Quantified
- Every predicate symbol in the statement corresponds to a relation
- The subject and objects of each sentence do indeed have the
by the predicate in the Model.
A Priori and Analytic Proof
Philosophical tradition, especially since the time of Kant, has
between several kinds of knowledge. These must be examined before
methods for obtaining truth can be addressed. The first
dating back to Plato, is to distinguish innate knowledge from knowledge
learned by experience. For example, since we have the ability to
reason, knowledge of logic can be said to be innate, while knowledge of
the mating habits of fireflies comes from experience.
The modern terms for these types of knowledge are "a priori"
for innate knowledge, and "a posteriori" for knowledge from
Traditionally, these terms have applied to how we come to "know",
both how we formulate beliefs and how we demonstrate that our beliefs
true. Since validation and speculation should really be treated
I will be careful to distinguish proof from belief when discussing
Another dichotomy introduced by Kant is that of analytic vs.
statements. Analytic statements are those which, using the
of Mathematical Logic, are true or false in all Universes of
or equivalently from Model
Logic, are necessarily true or false. Such statements
are also often called tautologies if true, or contradictions if
Synthetic statements are all other statements. Thus "nothing can
both be and not be" is analytic, while "all crows are black" is
As with all knowledge, the issue of whether or not we come to
a statement a priori is inconsequential. The real
is whether or not we can demonstrate the statement to be true a
One obvious instance of a demonstration that we can make without
is to prove that a statement is a tautology. However, this
that we know that Mathematical Logic, the method of proof that the
is a tautology, is valid. Unfortunately, we can't do any kind of
reasoning without assuming that reason itself (the mental equivalent of
Mathematical Logic) works, so our belief in Logic is hopelessly
Thus, it would seem that tautologies fail as instances of statements
for which there is a priori proof. However, given the one
assumption that Logic is indeed valid, then all tautologies are indeed
provable a priori, since we don't need experience to tell us
two of something plus two of something makes four of something.
despite its ultimate circularity, Logic
does seem to rest on a stronger foundation than most strictly circular
knowledge. It can be embedded in Set Theory, which is a theory of
Metaphysics that to some degree is testable by observation. We
certainly observe instances of the entities required to derive the laws
of Mathematical Logic.
By definition, analytic truths are tautologies, so (if Logic is
all analytic statements are provable a priori. The
remains, are there other statements that are provable a priori
are not analytic? Contrary to Kant's conclusions, the answer
seem to be no. A synthetic (non-analytic) statement is a statement that
is true or false particularly in our Universe. How can we prove
that is true in our Universe but not necessarily in others without
Thus, it would appear that we can make the following claim about a
priori and analytic truths:
The assumption of the validity of Logic is one of the two great
which must be made by Veritology, the other being the that at least of
some laws of Physics are constant with time and will continue to hold in the future. I
will discuss this assumption in more detail below.
- The property of being a statement which is provable a priori
exactly equivalent to the property of being a true analytic statement.
- The provability of true analytic statements, or tautologies,
assumption that 1st-Order Mathematical Logic is valid.
A Posteriori and Synthetic
Since a priori truths are equivalent to analytic truths,
by definition all statements are provable either a priori or a
posteriori, and since by definition all statements are either
or synthetic, if follows that a posteriori truths, or those
require experience to prove them, are equivalent to synthetic truths
statements which are not tautologies or contradictions). The
then, is how do we prove a posteriori, or synthetic,
The short answer is: the only way to demonstrate the truth of a
statement is by using the Scientific Method. In the
I will present a very preliminary defense of this belief.
I qualify it as preliminary due a lack of education in the area of the
Philosophy of Science. Once my education becomes more complete, I
will revisit this essay and adjust it as needed.
The Scientific Method has been so successful, that for
purposes I believe that it is safe to assume that it is a valid
With this assumption, there are apparently three areas that should be
The purpose of the Scientific Method is to demonstrate the validity of
a theory under a set of fixed circumstances. It is a process of
experimentation in order to expand the set of circumstances for which
theory is valid, or to find a set of circumstances which invalidate the
theory. The method consists of five basic steps:
- What exactly is the scientific method?
- Is there reason to believe that it does not work, and if so, why?
- Is the Scientific Method the only method of proving synthetic
This simple summary does not take into account error or fraud, but is
enough to communicate the general idea behind the method.
- Initial sensory observations - If no theory exists, then a survey
area to be theorized must be made.
- Induction - By whatever means (see above and Speculation
a theory to match your observations.
- Sanity Check - Test your theory with all of the observations from
(1). If any of them fail, go back to step (2) and try again.
- Form Predictions - Select a set of new experimental parameters
not covered by the observations in step (1), and determine the outcome
predicted by the theory.
- Test Predictions - Make experimental observations of actual
the new set of experimental parameters. If the results do not
the theory, go back to step (2), and come up with a new one (your old
has been falsified). If the results do match the theory,
the range of your theory has been extended to the new set of
Now go back to step (4) to further test your theory.
There are a number of philosophical arguments that have been raised
against the validity of the Scientific Method, among them being:
Despite the last complaint, common sense would dictate that all of
issues are resolvable: the human condition has simply improved too much
thanks to science to write it off as impotent. All but item #5
be resolvable by further analysis. Regarding #5, as Hume pointed
out 300 years ago, we have no choice but to grant the constancy of
nature as an assumption. However, we bet our lives every day that this assumption is correct.
- The simple steps described above to not do justice to the vast
specific types of investigation which fall under the umbrella term
- An infinite number of theories can fit any particular set of data.
- Their is always the potential for error and fraud which I glossed
- It is impossible to exactly achieve a desired set of experimental
as is required by step (5) above
- There is no basis for proving that the exact same experimental
will produce the same set of results.
- There is no generally accepted quantitative measure of
Maybe the apparent progress of science is just an illusion, and we
do not understand the universe any better than we did 2000 years ago.
What of other methods of learning about the external world?
The Scientific Method is a method for using our senses, or "sense data" as
Bertrand Russell (1959) calls it, to learn about the external
We use a miniature or personal version of it for everyday
I know of no other method that can correctly be used to validate
beliefs about the external world using sense data. Other methods
may claim to do so (such as religious revelation or crystal ball gazing),
but until they can be tested via the crucible of repeatability and
independent duplication, we must treat them with a skeptical eye as highly suspect.
Thus, on careful analysis, there are two kinds of truths, a method
for proving each kind of truth, and a basic assumption on which each method
is based. This is summarized by the following table:
Method of Proof
||1st Order Logic is valid
||Some things in Nature are constant.
This is an impressive accomplishment to the credit of modern
The age-old problem of truth has been reduced to two assumptions, both
of which are strongly suggested by ancillary evidence.
- Enderton, H.B., A Mathematical Introduction to Logic,
San Diego, CA (1972).
- Rosenburg, A., The Philosophy of Social Science, Westview
Boulder, CO (1995).
- Russell, B., The Problems of Philosophy, Oxford
New York (1959).