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First published in the proceedings of the 4th Annual Conference of the
Altshuller Institute for TRIZ Studies (TRIZCON 2002), April-May 2002
Part I: Logical Positivism
Michael S. Slocum, K.O.St.I., Ph.D.
Vice President of Science and Engineering
Ontro Inc.
13250 Gregg Street
Poway, CA 92064
P 858.486.7200
F 858.486.7204
mslocum@ontro.com
Editor’s Note: Dr. Slocum has authored this paper as an
exploratory work demonstrating a novel application for TRIZ (Su-Field modeling
specifically). It is intended to act as a stimulant for the development of
additional novel utilizations of TRIZ. Any interest in this particular line of
research should be directed to Dr. Slocum. Dr. Slocum intends to complete this
series in 10 parts. The next philosophy to be deconstructed is open for
suggestion.
ABSTRACT
Substance-Field modeling can be used in order to deconstruct philosophical
worldviews. The construction of a philosophy and even the language used to relay
the concepts can be diagrammatically deconstructed ( a la Carnap or
Wittgenstein) in order to demonstrate the technical or physical contradiction
that was resolved by the great thinker. Direct correlations with Substance-Field
analysis will be made. A model for logical constructions will be presented as
well as a standard algorithm for the decomposition and development of logical
arguments.
Logical Positivism (LP): LP emerged from Austria and Germany during the
1920’s and was primarily focused on the logical analysis of Scientific
knowledge. LP denied the soundness of metaphysics1 and traditional philosophy;
the LP’s asserted that many philosophical problems are indeed meaningless.
According to LP, there are two sources of knowledge: logical reasoning and
empirical experience. The former is analytic a priori, while the latter is
synthetic a posteriori.2
Figure 1.0
A statement is meaningful if and only if it can be proved true or false by
means of experience - this assertion is called the Verifiability Principle.3
Figure 2.0
Empirical Experience Required by LP to Indicate Knowledge
The absence of an observable phenomenon would indicate a failure to meet the
verifiability principle or possible a measurement and/or detection problem. The
connection between objects (S1 and S2) may exist but be unobservable. This
would yield a situation in which the connection could be pointed a priori
utilizing logical reasoning.
Figure 3.0 [Hurley]
The unobserved phenomenon is pointed to exist (~M) based on
logical reasoning. This process can be demonstrated as:
When we are confident that understanding of a situation is precise?
Obviously, if and only if we are able to precisely describe the conditions in
which it is possible to answer in the affirmative, or respectively, the
conditions in which it is necessary to answer with the negative. The meaning
of a situation is defined only through the specification of those conditions.
The definition of the circumstances under which a statement is true is exactly
equivalent to the definition of its meaning. “… a statement has a meaning if and
only if the fact that it is true makes a verifiable difference.”4
Figure 4.0
~M exists if and only if the interaction between S1 and S2 is
modified in some manner by ~M. If three is no interaction (see Figure 1.0) then
~M does not exist.
The strength of the verification relies on the strength of the experiment of
observation. Metaphysical statements are meaningless. The traditional role of
philosophy is also meaningless, the only role of philosophy is the clarification
of the meaning of statements.
Figure 5.0
M, M’, or M” do NOT exist without a corresponding F,
F’, or F”. The validity of M rests on the strength of the logical construct
under lying it (see Figure 3.0).
Philosophy, then, is the activity by means of which the meanings of
statements/interactions is clarified and defined. If Substance-field modeling is
indeed efficient at this clarification and definition then you could call it a
philosophical methodology. A scientific theory is an axiomatic system that
obtains an empirical interpretation through appropriate statements called rules
of correspondence, which establish a correlation between real objects and the
abstract concepts of the theory.
Figure 6.0
a and a’ are abstract concepts while S1 and S2 are real
objects. The Su-field model, they also indicate the correlation between real
objects and abstract concepts. M is synthetic and a/a’ are analytic.
The language of a theory includes two types of terms: observational (M) and
theoretical (a or a’) (see Figure 6.0). The statements of a theory are divided
into two groups: analytic and synthetic. Observational terms denote objects or
properties that can be directly measured (or observed), while theoretical terms
denote objects or properties we cannot observe or measure but can only be
inferred from direct observations (see Figure 6.0).
As a (or a’) is observed directly or indirectly (if possible) it moves from
the realm of abstract and theoretical to the realm of real and observable. To
maintain the abstract component, a new Su-field model must be created:
Figure 7.0
Analytic statements are a priori and their veracity is based on the syntax of
the language; contrarily, synthetic statements depend on experience (also the
only method to acknowledge their veracity) (see Figure 6.0).
This construction concerning the structure of scientific theory was proposed
by Reichenbach and Carnap in 1928.5
6The main points of this structure are:
- DISTINCTION BETWEEN OBSERVATINAL AND THEORETICAL TERMS
- DISTINCTION BETWEEN SYNTHETIC AND ANALYTIC STATEMENTS
- DISTINCTION BETWEEN AXIOMS AND RULES OF CORRESPONDENCE
- DEDUCTIVE NATURE OF SCIENTIFIC THEORIES
Figure 8.0
Rules of correspondence give an empirical meaning to theoretical terms and
all analytic, while theoretical axioms express the observational portion of the
theory and are synthetic. A theory must be a deductive system or syntax
degrades.
Figure 9.0
The effects of the premise(s) or the conclusion
The arrangement in Figure 9.0 would also remain valid for the Su-field model:
7Figure 10.0
If the relationship between S1 and S2 is incorrect, then the
S1-S3 correlation will be affected. If a’ or b are invalid then the F-F’
correlation will be invalid.
The distinction between observational and theoretical terms depend on the
verifiability principle. A statement is meaningful only if it is verifiable;
but, in scientific theories, there are many statements which are not
verifiable8. These statements are too abstract for a direct test (meaningless).
According to Schlick, the principles of a scientific theory are not statements,
but rules of inference; hence, the problem of meaning does not arise9. Another
solution was proposed by Neurath: the terms which belong to the abstract
language of a scientific theory are explicitly definable in a restricted
language whose terms describe directly observable and theoretical terms arose.
Carnap realized that theoretical terms are not definable by observational
terms. All theoretical terms are removable from a scientific theory.
This hypothesis is supported by two resultants of formal logic:
- 1.0 Craig Theorem
- 2.0 Ramsey Statement
Craig Theorem
Let A and B be two sets of statements, so that B is a logical consequence of
A. Craig proved that (i) there is a set C of statements whose terms are common
to A and B, (ii) C is a logical consequence of A, and (iii) B is a logical
consequence of C. Therefore, if A is the set of axioms of a scientific theory
and B is the set of observational statements implied by A, then there is a set
C, whose terms are common to A and B and thus they are the observational terms
which occur in the axioms, so that C entails B and is a consequence of A.
Therefore, it is possible to translate a scientific theory into a purely
observational language without any loss of deductive power.
Figure 11.0
Craig Theorem
Figure 12.0
Craig Theorem as it applies to Su-field Modeling
Ramsey Statement
The Ramsey statement was utilized by Carnap for the division of the axioms of
a theory into two sets: A and R, so that R contains only observational terms and
expresses the empirical portion of the theory, while A is analytic and defines
the meaning of theoretical terms. Given a theory T, it is thus possible to build
a theory T’ without theoretical terms so that T and T’ are equivalent with
respect to observational statements, that is every observational statement. O is
a logical consequence of T if and only if it is a logical consequence of T’.
Figure 13
Ramsey Statement
Figure 14
Ramsey Statement as it applies to Su-field analysis
Consider the observational steps (R) as the substances involved (S1 and S2)
and their interaction (if physically manifested). The theoretical aspect (A) is
supposed as the force (Fx) driving the physical manifestation (M). The prime
proven yielding Fx as a resultant, according to Ramsey, would then be
equivalent, at least in concept, to Fy if Mx is equivalent to My. This principal
may allow for the simplification of comparative analysis of Su-field models (as
the theoretical aspect, A, need not be considered).10
Logical Positivism assumes that a theory is a deductive system. Therefore,
observational techniques would yield data indicative of the deductive path that
will result in a perceived reality that closely mimics actual reality.
This enhances the importance of the measurement and detection standards found
in Class 4 of the 76 Standard Solutions.
I have attempted to provide an analysis of logical positivism based on
Substance-field analysis. Clearly, I could continue as I have merely covered a
few of the primary tenants of logical positivism. This work will continue as I
seek the correlations between Su-Field analysis and other philosophies.
Author Biography:
Michael S. Slocum, K.O.St.I., Ph.D.
Vice President of Science and Engineering
With over 14 years of research and development experience at ITT Space and Special Projects and the U.S. Army Military Intelligence, Dr. Michael Slocum has become an expert in Problem Solving, Research and Development, Engineering, and Quality. In Dr. Slocum's career, he has worked on the TITAN missile, SeaWolf submarine, Trident submarine, International Space Station, and numerous satellite programs. Most recently, Dr. Slocum served as Principal and Chief Scientist of The Inventioneering Company where he specialized in solving previously intractable technical problems.
Dr. Slocum studied at the U.S. Army Intelligence School and Trinity College where he earned his Ph.D. in Physics. He currently is an Adjunct Professor at North Carolina State University where he teaches a graduate course on the Theory of Inventive Problem Solving. Dr. Slocum is
an editor of the TRIZ Journal (www.triz-journal.com). Dr. Slocum is a member
of the ETRIA Global Coordination Group, the New Technology Review Panel of the
NFPA, Sigma Xi, IFT, SPE, New York Academy of Sciences, ASM, the American
Physical Society, American Chemical Society, and several other relevant
professional societies. Dr. Slocum was recently knighted in recognition of his
contributions to science and society.
___________________
Endnotes:
- Metaphysics: Traditionally, metaphysics refers to the
branch of philosophy that attempts to understand the fundamental nature of all
reality, whether visible or invisible. It seeks a description so basic, so
essentially simple, so all-inclusive that it applies to everything, whether
divine or human or anything else. It attempts to tell what anything must be
like in order to be at all.
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- Synthetic a priori does not exist (a fundamental thesis of
modern empiricism).
(back to article)
- Verifiability Principle: It is not possible to establish a
logically durable building on verifications [a verification is an
observational statement about immediate perception], for they are already
vanished when the building begins. If they were, with respect to time, at the
beginning of the knowledge, then they would be logically useless. On the
contrary, there is a great difference when they are at the end of the process;
with their help the test is performed… From a logical point of view, nothing
depends on them; they are not premises buy a firm end point. (M. Schlick, ‘Über
das Fundament der Erkenntnis’, in Erkenntnis, 4, 1934).
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- M. Schlick, “Positivismus and Realismus” in Erkenntnis, 3,
1932.
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- H. Reichenbach, “Philosophic du Raim-Zeit
Lehre”, 1928.
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- R. Carnap, “Testability and Meaning,” Philosophy of
Science, 3, 1936, and 4, 1937
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- If conclusion is still true then arguemnt is valid; else,
argument is invalid.
(back to article)
- For example, quantum particles or gravitational fields
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- “Die Kausalitzaumt inder Gegenzaumertigen Physik”, Die
Natursuissenschafter, 19, 1931.
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- Although Popper would emphasize the theoretical aspect,
A, as a necessary component of scientific concepts.
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