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.

Veritology: The Philosophy of Truth

Table of Contents

• What Is Veritology?
• Truth
• A Priori and Analytic Proof
• A Posteriori and Synthetic Proof
• Conclusion
• References

What Is Veritology?

Veritology is a subject (and word) that I have invented to describe the study of methods for proving the validity of knowledge.    It is important to distinguish the need to validate our tentative beliefs 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 Science.  For example, suppose my crystal ball were to reveal to me a theory of physics 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 crystal ball, than if it had come through the usual process of scientific "induction".   This act of enlightenment by the crystal ball may simply have been an extremely fortuitous event.  Such an extraordinary stroke of luck does not diminish 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 functioning 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 fantasy, 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 philosophy has been the search for truth.  Yet philosophers have traditionally merged and confused the quest for truth with the act of speculation.  They have asked simply how we "know" truths, lumping belief formulation and validation together under one subject.  It is time to focus philosophical inquiry on the subject of Veritology, and leave Speculation Science to science.
 

Truth

Before we can investigate methods for proving our knowledge to be true, we must first investigate the concept of truth itself.  Fortunately, a rigorous definition of truth is available, thanks to the efforts of past investigators in the area of Mathematical Logic.  I will present here only a summary of the mathematical concept of truth.  For a rigorous analysis, see any modern text on Mathematical Logic such as Enderton (1972).

The language of so-called First Order Logic deals primarily with simple sentences with a subject, predicate, and optionally one or more objects.  These sentences can then be combined with logical operators such as "and", "or", "implies", etc.  The subject and objects can be variables, that are "Quantified" (to use the proper jargon), with qualifiers such as "for 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 enough illustration for our point.  Mathematical Logic has strict rules for 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 mortality.  Another key concept is that of a Model.  A Model consists of two things: 1) A Universe of Discourse, which is the set of all things that exist in the Universe (real or imaginary), and 2) A complete set of attributes and relations that apply to and between every thing in the Universe of Discourse.

Armed with these concepts, we can now define Truth.  A WFF in Mathematical 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 three properties:

1. Every subject or object symbol in the statement corresponds to a member of the Universe of Discourse (this is true by definition for Quantified variables)
2. Every predicate symbol in the statement corresponds to a relation in the Model
3. The subject and objects of each sentence do indeed have the relation symbolized by the predicate in the Model.

A Priori and Analytic Proof

Philosophical tradition, especially since the time of Kant, has distinguished between several kinds of knowledge.  These must be examined before methods for obtaining truth can be addressed.  The first tradition, 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 experience.  Traditionally, these terms have applied to how we come to "know", meaning both how we formulate beliefs and how we demonstrate that our beliefs are true.  Since validation and speculation should really be treated separately,  I will be careful to distinguish proof from belief when discussing these terms.

Another dichotomy introduced by Kant is that of analytic vs. synthetic statements.  Analytic statements are those which, using the paradigm of Mathematical Logic, are true or false in all Universes of Discourse, or equivalently from Model Logic, are necessarily true or false.  Such statements are also often called tautologies if true, or contradictions if false.  Synthetic statements are all other statements.  Thus "nothing can both be and not be" is analytic, while "all crows are black" is synthetic.

As with all knowledge, the issue of whether or not we come to believe a statement a priori is inconsequential.  The real question is whether or not we can demonstrate the statement to be true a priori.  One obvious instance of a demonstration that we can make without experience is to prove that a statement is a tautology.  However, this presupposes that we know that Mathematical Logic, the method of proof that the statement 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 circular.

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 that two of something plus two of something makes four of something.  And, 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 can certainly observe instances of the entities required to derive the laws of Mathematical Logic.

By definition, analytic truths are tautologies, so (if Logic is valid) all analytic statements are provable a priori.  The question remains, are there other statements that are provable a priori but are not analytic?  Contrary to Kant's conclusions, the answer would 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 anything that is true in our Universe but not necessarily in others without observing it?

Thus, it would appear that we can make the following claim about a priori and analytic truths:

• The property of being a statement which is provable a priori is exactly equivalent to the property of being a true analytic statement.
• The provability of true analytic statements, or tautologies, rests on the assumption that 1st-Order Mathematical Logic is valid.

A Posteriori and Synthetic Proof

Since a priori truths are equivalent to analytic truths, since by definition all statements are provable either a priori or a posteriori, and since by definition all statements are either analytic or synthetic, if follows that a posteriori truths, or those which require experience to prove them, are equivalent to synthetic truths (those statements which are not tautologies or contradictions).  The question then, is how do we prove a posteriori, or synthetic, statements.

The short answer is: the only way to demonstrate the truth of a synthetic statement is by using the Scientific Method.  In the following, I will present a very preliminary defense of this belief.  However, 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 practical purposes I believe that it is safe to assume that it is a valid method.  With this assumption, there are apparently three areas that should be explored:

• 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 truths?

1. Initial sensory observations - If no theory exists, then a survey of the area to be theorized must be made.
2. Induction - By whatever means (see above and Speculation Science), formulate a theory to match your observations.
3. Sanity Check - Test your theory with all of the observations from step (1).  If any of them fail, go back to step (2) and try again.
4. Form Predictions - Select a set of new experimental parameters that was not covered by the observations in step (1), and determine the outcome predicted by the theory.
5. Test Predictions - Make experimental observations of actual results with the new set of experimental parameters.  If the results do not match the theory, go back to step (2), and come up with a new one (your old theory has been falsified).  If the results do match the theory, then the range of your theory has been extended to the new set of parameters.  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:

1. The simple steps described above to not do justice to the vast number of specific types of investigation which fall under the umbrella term "science".
2. An infinite number of theories can fit any particular set of data.
3. Their is always the potential for error and fraud which I glossed over above
4. It is impossible to exactly achieve a desired set of experimental conditions, as is required by step (5) above
5. There is no basis for proving that the exact same experimental conditions will produce the same set of results.
6. There is no generally accepted quantitative measure of "scientific progress".  Maybe the apparent progress of science is just an illusion, and we really 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 world.  We use a miniature or personal version of it for everyday experience.  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.
 

Conclusion

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:

Experience Class	Logical Class	Method of Proof	Assumption
a priori	analytic	Mathematical Logic	1st Order Logic is valid
a posteriori	synthetic	Scientific Method	Some things in Nature are constant.

This is an impressive accomplishment to the credit of modern philosophers.  The age-old problem of truth has been reduced to two assumptions, both of which are strongly suggested by ancillary evidence.
 

References

• Enderton, H.B., A Mathematical Introduction to Logic, Academic Press, San Diego, CA (1972).
• Rosenburg, A., The Philosophy of Social Science, Westview Press, Boulder, CO (1995).
• Russell, B., The Problems of Philosophy, Oxford University Press, New York (1959).