Peircean philosophy of science is an abundant intellectual treasure.
Charles Sanders Peirce was competent in logic, mathematics and different
branches of science, including astronomy, chemistry, physics, geology, and
meteorology. He was versed in most of the ancient and contemporary schools of
thought in logic (Brent, 1993). Peirces's writings provide many insightful
applications to psychologists and educational researchers. The thesis of this
paper is that by applying Peircean notion of truth and reality, qualitative and
quantitative methods are cooperative rather than competitive. In the view of
Peircean logical system we may say the logic of abduction (firstness) and
deduction (secondness) contribute to our qualitative or conceptual
understanding of phenomena (Hausman, 1993), while the logic of induction
(thirdness) adds quantitative details to the qualitative or conceptual
knowledge.
Qualitative and Quantitative disparities are centered around the issues of
prescriptive and clear-cut answers verses descriptive languages; and single and
objective reality verses multiple and subjective realities (Langenbach, M.;
Vaughn, C. & Aagaard, L., 1994; Erlandson, Harris, Skipper & Allen,
1993). The gap between qualitative and quantitative research might be filled
by multiple approaches which employ abduction, deduction and induction
altogether. The first section of this paper will discuss several assumptions
of the Peircean philosophical system in an attempt to reconcile the differences
in qualitative and quantitative research. The second part of this paper will
evaluate the strengths and weaknesses of these three logical processes under
Peircean direction.
Premises of Peircean Philosophy of Science of Peircean Philosophy of Science
Anti-Cartesian-Cartesian
Anti-skepticism.
One of the assumption of Peircean philosophical system is anti-Cartesian
skepticism. DesCartes (1641/1964) doubted everything, even his own existence.
In his view, knowledge originates from doubts and questioning. Peirce (1868)
rejected the Cartesian tradition by arguing, "We cannot begin with complete
doubt." (p. 140) Rather he ensured what Hegelians deny--we don't have to be
certain of everything in order to know something. In "The Fixation of Belief,"
(1877) Peirce said that we are satisfied with beliefs rather than doubts.
Although knowledge is fallible in nature, and in our limited lifetime we cannot
discover the ultimate truth, we will still fix our beliefs at certain points.
This is why Peirce's epistemology is considered the percussor to pragmatism.
At the same time, Peirce did not encourage us to relax our mind and not pursue
further inquiry. Instead, he saw seeking knowledge as an interplay between
doubts and beliefs, though he did not explicitly use the Hegelian term
"dialectic."
Unfortunately, William James took Peirce's notion of satisfaction of
beliefs but overlooked the struggle between doubts and beliefs. James argued,
"The true is the name of whatever proves itself to be good in the way of
belief...is only the expedient in the way of our thinking." (1898/1975, p.42;
1909/1927, vii) In other words, for James the issue is not what is truth, but
what we believe is truth. Gullvaag said that American pragmatism is, to a
great extent, a result of James' misunderstandings of Peirce (cited in Coppock,
1994). Also, John Dewey took Peirce's notion of "fixing beliefs" and develop
instrumental pragmatism for "fixing situations." In other words, for Dewey the
issue is not what is truth metaphysically, but what would work under a specific
circumstance. Peirce strongly resented both James' psychological pragmatism
and Dewey's outcome-based instrumentalism, and thus Peirce renamed his
pragmatism as "pragmaticism" in order to distinguish himself from James and
Dewey (Smith, 1978).
Anti-foundationalism and Anti-reductionism
.
Besides skepticism, Peirce (1868) also disagreed with DesCartes on
foundationalism. Peirce showed a firm rejection against the Cartesian posture
of laying the foundation of epistemology on the unchanged self-consciousness (I think therefore I am) and innate ideas. DesCartes' discovery of analytical
geometry and Cartesian co-ordinates led to the notion that knowledge can be
reduced to logico-mathematical methods, which is based on human innate
operational structure (Piaget, 1971). For Peirce, reducing our perception of
this complex world to certain elements or foundations such as
self-consciousness and pure logic, will deny the continuity and universality of
events.
Truth and Reality
These issues regarding foundations are essentially ontological: What is
the nature of reality? On what ultimate grounds can knowledge be built?
Sometimes Peirce's position seems to be inconsistent in this regard. Peirce
stated that hardness is not an attribute of an object until we measure it
(1878a). However, this statement should not be interpreted as a position that
there is no objective reality. What Peirce implied was that knowledge is a
social construct. The concept of hardness is a result of our test and
measurement, however, truth is not just a social construct (Parker,
1994).
Peirce made a distinction between truth and reality. Truth is the
understanding of reality through a self-corrective inquiry process by the whole
intellectual community across time. On the other hand, reality is the
existence independent of human inquiry (Wiener, 1969). In terms of ontology,
there is one reality. In regard to methodology and epistemology, there is more
than one approach and one source of knowledge. Reality is "what is" while
truth is "what would be." One of the differences between pragmatism and
pragmaticism can be viewed as orientation to truth and reality. Dewey and
James adopted a subjective and humanistic view to truth i.e. knowledge is a
human and social construct and it can be known without a transcendental
standard. For Dewey "the problem of philosophy is not how we can come to know
an external world, but how we can learn to control it and remake it, and for
what goals" (Durant, 1926/1961, p.523). In contrast, Peirce introduced a
metaphysical dimension into pragmaticism and implied a universal and
transcendental standard (Apel, 1981). For Peirce the inquiry of knowledge is a
form of free association or creative thinking that resemble the Divine mind
(Oakes, 1993), or the Hegelian "Absolute Spirit" (Margolis, 1993).
Knowledge is Cumulative and Self-corrective
Unlike Thomas Kuhn's (1962) emphasis on paradigm shift, Peirce stressed
the continuity of knowledge. First, knowledge does not emerge out of pure
logic. Instead, it is a historical and social product. As mentioned before,
Peirce disregarded the Cartesian attitude of doubting everything. To some
extent we have to fix our beliefs on those positions that are widely accepted
by the intellectual community (1877).
Kuhn proposed that the pattern of inquiry is a process of new frameworks
overthrow outdated frameworks. Peirce, in contrast, considered knowledge to be
continuous and cumulative. Rescher (1978) used the geographical-exploration
model as a metaphor to illustrate Peirce's idea: The replacement of a
flat-world view with a globe-world view is a change in qualitative
understanding, or a paradigm shift. After we have discovered all the
continents and oceans, measuring the height of Mount Everest and the depth of
the Nile river is adding quantitative details to the qualitative understanding.
Although Kuhn's theory looks glamorous, as a matter of fact, paradigm shifts
might occur only once in a century or a few centuries. The majority of
scholars are just adding details to existing frameworks. Knowledge is
self-corrective insofar as we inherit the findings from previous scholars and
refine them.
Implications to Qualitative and Quantitative Research
In this paper the intent is not to settle all debates between qualitative
and quantitative research. Nevertheless, the preceding premises of Peircean
philosophy sheds some light on the dispute.
Pragmatic and Clear Cut Answers?
Quantitative approach is not a quick fix
First, quantitative research methods are apt to Peirce's pragmaticism
rather than James or Dewey's pragmatism. For pragmatic reasons statistics does
produce clear-cut answers. However, in a case of hypothesis testing, fixing an
alpha cutoff does not imply that the case is closed and no further inquiry is
needed. On more than one occasion, I have heard people say that qualitative
research is more difficult than quantitative because in the former the data is
messy and the answer is not clear-cut. Unfortunately, a decision based upon
rejecting the null or not gives a picture that statisticians are finding an
easy out or seeking for a simple answer.
Balancing model and error is struggle between belief and doubt
Quantitative research is neither James' psychologism nor Dewey's
instrumentalism. First, the goal of statistics is not to produce a quick fix
to make us feel good. Second, statistics will not just stop at what works and
what cannot work. Rather, it will go further to find out why something works
and why something doesn't. In addition, statisticians who provide a quick fix
may not do exploratory data analysis at all. Exploratory data analysis, like
qualitative study, handles messy data. The process of balancing smooth and
rough, fit and residual, or model and error can be viewed as Peircean's
interaction between doubt and belief. The commonality between qualitative
study and exploratory data analysis will be discussed later.
Realist and Truth Seeking?
Some writers created the unnecessary polarity of perspective seeking
(qualitative research) verses truth seeking (quantitative research) (Langenbach
et al., 1994; Erlandson et al., 1993). Langenbach et al. even said that
quantitative researchers who accept "truth seeking ontology" contend that
ultimately there exists one best answer.
Multiple approaches are not ontological but epistemological
First, it is doubtful whether statisticians accept that there exists only
"one best answer." Second, "one best answer" is not an ontological concern.
Asking whether the mansion of a wealthy man has one million dollars is one
question; asking which is the best way to break into the house and steal the
money is another question. When qualitative researchers look for multiple and
subjective realities, this is an epistemological issue. When quantitative
researchers accept an objective reality, this is in regard to the ontological
dimension. In practice, most quantitative researchers still use multiple
approaches to address multiple realities. In other words, quantitative
researchers do look for perspectives. As mentioned before, in Peircean system
the term "truth" is not the same as ultimate reality. If we refer to
quantitative methods as a means of truth seeking, we should see the truth as
the understanding of reality, but not the reality itself. We make decisions
based upon statistics due to pragmatic reasons--so called fixing our beliefs at
certain points. However, we pass our findings to subsequent researchers so
that details can be added and mistakes can be corrected.
The nature of knowledge is not social but transcendental
Qualitative researchers adopt "perspective seeking" and "descriptive
language," which are socially constructed. The misuse of this approach may
lead to radical nominalism, which was opposed by Peirce (Parker, 1994).
Nominalism views the core issue of epistemology as the use of terminology, and
there is no logical mapping between the language and the reality. Whether a
theory is acceptable or not relies highly on its compatibility with the
"standard language." I would stand with Peirce's pragmaticism--beyond the
subjective and humanistic level of understanding of knowledge, there should be
a transcendental level at the underlying logic and structure of reality, in
Kantian term, the "internal structure of meaning."
Reality is inter-subjectivity
I would go beyond Peirce to suggest a unity between truth and reality,
truth and perspective, and the humanistic world and the transcendental world.
Perspective seeking verses truth seeking can be viewed as another version of
the subject-object spilt introduced by DesCartes. Barrett (1986) criticized
this dualism as unnecessary: Most modern philosophers ranging from
phenomenologists to analytic philosophers rejects the Cartesian dichotomy. For
modern philosophers, inter-subjectivity is more suitable to epistemology.
Knowledge is a result of inter-subjectivity--I am a part of reality, and
reality is a part of me; truths carry perspectives, and perspectives contain
truths. The world I know is partly shaped by my input, and being who I am is
partly caused by the input from the world. In this sense, there isn't a
reality entirely independent of human inquiry; neither a perspective without
the influence from the world.
Logical-positivism and Reductionism?
Conceptual works can lead to ontological reductionism
When quantitative research is labelled as "logical-positivism," what
people have in their minds is a reduced world of logic and mathematics
suggested by Russell and Whitehead (1910). Although many scholars discredit
reductionism, Searle (1993) defended the value of ontological reductionism, in
which objects of certain types can be shown to consist of nothing but elements
of other types. For example, genes can be shown to be composed of nothing but
DNA molecules. Searle asserted that in history of science successful causal
inferences tend to lead to ontological reductions. When people criticize
reductionism, they pinpoint its weakness of leaving essential features out.
But an ontological reduction captures the invariant elements that are
sufficient for representing the whole object.
Data compression is a good metaphor to illustrate Searle's position. If I
use a software compactor such as Stuffit, Compact Pro or PKZIP to reduce the
size of a file, later the entire file can be recomposed without any data
truncation. But if I use a "lossy" method such as JPEG or MPEG to pack a
graphic file, details will lose at the stage of decompression. One should not
decline to use Stuffit or Compact Pro after their pictures lost the image
quality through JPEG or MPEG compression. By the same reasoning, one should
not disbelief ontological reductionism while they have problems with
non-ontological reductionism.
However, the goal of ontological reduction is at the stage of conclusion,
not at the process of inquiry. In other words, ontological reduction is the
end but non-ontological reduction is the means. Data reduction methods in
statistical procedures are no doubt non-ontological reductions i.e statistical
numbers resulted in data reduction methods are a distorted representation of
the world. Like JPEG and MPEG, data reduction sacrifices some details, but so
are other languages and symbols, even "descriptive language." Actually, every
research approach is reductive in nature, otherwise the huge chuck of
information will be burdensome to researchers. Take the lossy method as an
analogy again. Although JPEG and MPEG trim off some pixels during compression,
the reconstructed images are still sharp enough to recognize, for the lost
details are too small to be detectable by human eyes. The important point is
to transmit the whole picture, not the combination of every piece of detail.
By the same token, researchers want to see a big picture rather than tons of
data.
Peirce recognized the existence of an ontological and metaphysical
reality. In regard to quantitative research methods, the inquiry concerning the
conceptual aspect is capable of pointing to the direction of ontological
reduction. In this view, exploratory data analysis, which contributes to
conceptual understanding, has no contradiction with Searle and Peirce's
position.
Quantitative research is not a one-way reduction
In deed, quantitative research as a whole is harmonious with Searle and
Peirce's notions. It is a misunderstanding to see quantitative research as a
one way reduction of complex phenomena to numbers. One of the goals of
quantitative research is to find the optimal balance between parsimony and
goodness of fit. During the process of exploratory data analysis, a careful
statistician always goes back and forth to add variables to or take variables
out of the model. I see no evidence that statistics is a one way
reduction.
Fallibilism
In Peirce's view, knowledge is fallible in nature but continuous inquiry
makes knowledge self-corrective. Quantitative understanding builds on
qualitative understanding, and they can correct each other. Rescher (1978)
interpreted that for Peirce the process of qualitative induction can be
correctively monitored by quantitative induction. For instance, as more and
more patients are infected with HIV from heterosexual activities, our
conception that AIDS is only a disease of homosexuality is changed. Rescher
contented that "Peirce is thus at once with Sir Ronald Fisher in declaring that
the theory of statistical inference in general, make key contributions to the
scientific induction." (p.13)
On the other hand, qualitative understanding can correct quantitative
knowledge by pointing out new directions that have been neglected. For
example, in economics unempolyment and inflation used to be explained by the
Philip's Curve and Fisher equation, but later the phenomenon that high
unemployment rate and high inflation rate occur at the same time stimulated the
introduction of new theories such as the Supply Side Economics. Many
statisticians are highly aware of the fallible nature of the discipline.
Statistics is not just measurement, but is also concerned with measurement
error. Many statistical endeavors can be viewed as the effort to find out
additional error in relations to the least error. I see no evidence that
statistics is regarded as a form of absolute measurement.
Actually, quantitative and qualitative methodologies share more common
grounds rather than conflict in regard to epistemology: They both admit that
there is more than one way to approach reality; there is a continuity between
qualitative and quantitative understanding; there is a tension between the
complex world and the reduced model; there is a fallible nature of all
inquiries, and thus conclusions are tentative rather than final. More
importantly, they both attempt to break down the data and reconstruct them into
a pattern. In the process of pattern-seeking, they both use symbolic
representations. Qualitative research applies language while quantitative
research employs numbers. Neither is more descriptive or reducing than the
other one.
Peircean Logical System
Exploratory data analysis, which aims at suggesting a pattern for further
inquiry, contributes to the conceptual or qualitative understanding of a
phenomenon. Although it deals with numbers, the ending point is not
statistical figures. Rather the product is the hypothetical insight of the
essential feature or pattern of an event. In other words, the major concern is
not "how much," but "what" and "how."
Abduction, the logic suggested by Peirce, can be viewed as a logic of
exploratory data analysis. For Peirce abduction is the firstness (possibility,
potentiality); deduction, the secondness (existence, actuality); and
induction, the thirdness (generality, continuity). Abduction plays the role of
generating new ideas or hypotheses; deduction functions as evaluating the
hypotheses; and induction is justifying of the hypothesis with empirical data
(Staat, 1993).
Abduction
Abduction is not symbolic logic but critical
thinking
Abduction is to look for a pattern in a phenomenon and suggest a
hypothesis (Peirce, 1878a). Despite the long history of abduction, abduction
is still unpopular among texts of logic and research methodology, which
emphasize formal logic. Logic is divided into formal types of reasoning
(symbolic logic) and informal types (critical thinking). Unlike deduction and
induction, abduction is a type of critical thinking rather than symbolic logic,
though in the following example abduction is illustrated with symbols for
simplification:
The surprising phenomenon, X, is observed.
Among hypotheses A, B, and C, A is capable of explaining X.
Hence, there is a reason to pursue A.
Abduction is not Popperian falsification but hypothesis generationis
This process of inquiry can be well applied to exploratory data analysis.
In exploratory data analysis, after observing some surprising facts, we exploit
them and check the predicted values against the observed values and residuals.
Although there may be more than one convincing patterns, we "abduct" only those
which are more plausible.In other words, exploratory data analysis is not trying out everything.
Rescher (1978) interpreted abduction as an opposition to Popper's falsification
(1963). There are millions of possible explanations to a phenomenon. Due to
the economy of research, we cannot afford to falsify every possibility. As
mentioned before, we don't have to know everything to know something. By the
same token, we don't have to screen every false thing to dig out the authentic
one. Peirce argued that animals have the instinct to do the right things
without struggling, we humans, as a kind of animal, also have the innate ability
to make the right decision intuitively.
Abduction is not hasty judgment but proper categorizationis
It is dangerous to look at abduction as impulsive thinking and hasty
judgment. In the essay "The Fixation of Belief," Peirce explicitly disregarded
the tenacity of intuition as the source of knowledge. Also, exploratory data
analysis, as an application of abduction, is not a permit for the analyst to
be naive to other research related to the investigated phenomena (Anthony,
1994). Peirce strongly criticized his contemporaries' confusion of
propositions and assertions. Propositions can be affirmed or denied while
assertions are final judgments (Hilpinen, 1992). The objective of abduction is
to determine which hypothesis or proposition to test, not which one to adopt or
assert (Sullivan, 1991).
For Peirce, progress in science depends on the observation of the right
facts by minds furnished with appropriate ideas (Tursman, 1987). Definitely,
the intuitive judgment made by an intellectual is different from that made by a
high school student. Peirce cited several examples of remarkable correct
guesses. All success is not simply lucky. Instead, the opportunity was taken
by the people who were prepared:
a). Bacon's guess that heat was a mode of motion;
b). Young's guess that the primary colors were violet, green and red;
c). Dalton's guess that there were chemical atoms before the invention of
microscope (cited in Tursman, 1987).
Peirce stated that classification plays a major role in making hypothesis,
that is the characters of phenomenon are placed into certain categories
(Peirce, 1878b). As mentioned before, the Peircean view of knowledge is continuous
rather than revolutionary. Abduction does not attempt to overthrow previous
paradigms, frameworks and categories. Instead, the continuity and generality
of knowledge makes intuition possible and plausible.
Peirce was an admirer of Kant. He endorsed Kant's categories in
Critique of Pure Reason (1781/1969) to help us to make judgments of the
phenomenal world:
1. quantity (universal, particular, singular);
2. quality (affirmative, negative, infinite);
3. relation (categorical, hypothetical, disjunctive);
4. modality (problematic, assertoric, apodeictic).
Also, Peirce agreed with Kant that things have internal structure of
meaning. Abductive activities are not empirical hypotheses based on our
sensory experience, but rather the very structure of the meanings themselves
(Rosenthal, 1993). Based on the Kantian framework, Peirce (1867/1960) later
developed his "New list of categories."
In short, abduction by intuition, can be interpreted as observing the
world with appropriate categories which arise from the internal structure of
meanings. The implications of abduction for researchers is that the use of
exploratory data analysis is neither exhausting all possibilities nor making
hasty decisions. Researchers must be well-equipped with proper categories in
order to sort out the invariant features and patterns of phenomena. The
statistical method, in this sense, is not only number crunching, but also a
thoughtful way of dissecting data.
Deduction
After suggesting a plausible hypothesis, the next stage is to refine the
hypothesis with logical deduction. Deduction is drawing logical consequences
from premises. The conclusion is true given the premises are true also
(Peirce, 1868). For instance,
All As are Bs.
C is B.
Therefore, C is A.
Deduction cannot lead to new knowledge
First, this kind of reasoning cannot lead to the discovery of new
knowledge, because the conclusion has already been embedded in the premise
(Peirce, 1900/1960). In some cases the premise may even be tautological--true
by definition. Brown (1963) illustrated this weakness by using an example in
economics:
An entrepreneur seeks maximization of profits.
The maximum profits will be gained when marginal revenue equals marginal
cost.
An entrepreneur will operate his business at the equilibrium between
marginal cost and marginal revenue.
The above deduction simply tells you that a rational man would like to
make more money. There is a similar example in cognitive psychology:
Human behaviors are rational.
One of several options is more efficient in achieving the goal.
A rational human will take the option which directs him to achieve his
goal (Anderson, 1990).
The above two deductive inferences simply provide examples that a rational
man will do rational things. The specific rational behaviors have been
included in the bigger set of generic rational behaviors.
Deduction does not specify necessary or sufficient conditiondoes
Second, usually inferences made with deductive methods do not specify
whether the premise is a necessary condition, a sufficient condition, or both.
For example, rationality is a necessary condition, but not a sufficient
condition, of making the correct choice. Sometimes people may fail to select
the right alternative because of lack of faith or courage.
Deduction relies on true premises
Third, deduction is fallible as we cannot logically prove all the premises
are true. Russell and Whitehead (1910) attempted to develop a self-sufficient
logico-mathematical system. In their view, not only can mathematics be reduced
to logic, but logic is the foundation of mathematics. In the traditional
hierarchy of knowledge, biology seeks support from chemistry; chemistry needs
proof from physics; physics depends on mathematics. The notion that
mathematics relies on logic implies that all knowledge can be explained by
logic.
However, Godel (1947/1986) found that it is impossible to have such a
self-contained system. Any lower order theorem or premise needs a higher order
theorem or premise for substantiation and it goes on and on; and no system can
be complete and consistent at the same time.
Peirce reviewed Russell's book Principles of Mathematics in 1903,
but he only wrote a short paragraph with vague comments. Nonetheless, based on
Peirce's other writings on logic and mathematics, Haack (1993) concluded that
Peirce would be opposed to Russell and Whitehead's notion that the
epistemological foundations of mathematics lie in logic. It is questionable
whether deductive knowledge sound just because the logic or the mathematics
stands. No matter how logical a hypothesis is, it is only sufficient within
the system; it is still tentative and requires further investigation with
external proof. For instance, according to geometry rules, the sum of three
angles inside a triangle is 180 degree. However, if one applies this premise
of a two dimensional plane to a three-dimensional world, the deductive
conclusion will be totally wrong. When you draws a triangle on this planet
such as starting from North Pole to the west of equator, and stop at the east
of equator, the sum of three angles can be more than 180 degree.
This line of thought posed a serious challenge to researchers who are
confident in the logical structure of statistics. Mathematical logic replies
on many unproven premises. For example, the mishmash of null and alternative
hypotheses; the disputable computation of effect size; the redundancy of
Bartlett's test; the artificial cutoff of alpha level and so on. Statistical
conclusions are considered true only given that all premises that are applied
are true. As a matter of fact, Kline (1990) found that mathematics had
developed illogically with false proof and slips in reasoning. Thus, he called
the deductive proof from self-evident principles in mathematics an
"intellectual tragedy," (p.3) and a "grand illusion" (p.4).
In recent years many Monte Carlo simulations have been conducted to
determine how robust certain tests are, and which statistics should be favored.
The reference and criteria of all these studies are within the
logico-mathematical system without any worldly concerns. For instance, Fisher
protected t-test is considered inferior to the Ryan test and the Tukey test
because it cannot control the inflated Type I error very well (Toothaker,
1993), not because any psychologists or educators made a terribly wrong
decision based upon the Fisher protected t-test. Pillai-Bartlett statistic is
considered superior to Wilk's Lambda and Hotelling-Lawley Trace because of much
greater robustness against unequal covariance matrices (Olson, 1976), not
because any significant scientific breakthroughs are made with the use of
Pillai-Bartlett statistic. For Peirce this kind of self-referent deduction
cannot lead to progress in knowledge. Knowing is activity which is by
definition involvement with the real world (Burrell, 1968).
Actually, statistics is by no means pure mathematics without interactions
with the real world. Gauss discovered the Gaussian distribution through
astronomical observations. Fisher built his theories from applications of
biometrics and fertilizer. Survival analysis or hazard model are the fruit of
medical and sociological research. Item response theory was developed to
address the issue of reducing test bias. For Peirce, deduction alone is a
necessary condition, but not a sufficient condition of knowledge. Instead,
abduction, deduction and induction must work together.
Induction
Induction introduced by Francis Bacon is a direct revolt against
deduction. Bacon (1620/1960) found that deductive reasoners rely on the
authority of antiquity (premises made by masters), and the tendency of the mind
to construct knowledge-claims out of itself. By using a similar metaphor
introduced by anthropologist Clifford Geertz, Bacon criticized deductive
reasoners as spiders for they make a web of knowledge out of their own
substance. Although the meaning of deductive knowledge is entirely
self-referent, deductive reasoners tend to take those propositions as
assertions.
As mention before, propositions and assertions are not the same level of
knowledge. For Peirce abduction and deduction only gives propositions, but
self-correcting induction gives the support of assertions. Carnap took
Peirce's notion that induction is self-corrective and devoted efforts in
building a comprehensive system of inductive logic (Tursman, 1987). However,
we should be cautious not to over-generalize induction as the salvation of
deduction.
Inductive logic is based upon the notion that probability is the relative
frequency in long run and a general law can be concluded based on numerous
cases. For example,
A1, A2, A3 ... A100 are B.
A1, A2, A3 ... A100 are C.
Therefore, B is C.
Induction is inconclusive in infinite time
Hume (1777/1912) argued that things are inconclusive by induction because
in the infinite time there are always new cases and new evidence. Induction
can be justified, if and only if, instances of which we have no experience
resemble those of which we have experience. Take the previous argument as an
example. If A101 is not B, the statement "B is C" will be refuted. Hume even
used more radical examples such as nature may change its course. My examples
are from sociology and economics.
Based on the case studies in the 19th century, sociologist Max Weber
(1904/1976) argued that capitalism could be developed in Europe because of the
Protestant work ethic; other cultures like the Chinese Confucianism are by
essence incompatible with capitalism. However, after World War Two, the
emergence of Asian economic powers such as Taiwan, South Korea, Hong kong and
Singapore disconfirmed the Weberian hypothesis.
We never know when a regression line will turn flat, go down or go up.
Even inductive reasoning using numerous accurate data and high power computing
can go wrong, because predictions are made only under certain specified
conditions (Samuelson, 1967). Due to American economic problems in the early
'80s, quite a few reputable economists made gloomy predictions about the U.S.
economy such as the takeover of American economic and technological throne by
Japan. By the end of the decade, Roberts (1989) concluded that those
economists were wrong; on contrary to those forecasts, the U.S. enjoyed the
longest economic expansion in its history.
Induction is undefinable in a single case
Second, induction suggests the possible outcome in relation to events in
long run. This is not definable for an individual event. To make a judgment
for a single event based on probability like "your chance to survive this
surgery is 75 percent" is nonsense. In actuality, the patient will either live
or die (50%). Also, this is why people in Hong Kong are very anxious about the
construction of a nuclear plant in Daya Bay, South China, even though the
statistic released by the Chinese government shows a very low probability of
accident. In a single event of nuclear melt-down, the chance of survival is
absolutely zero.
Induction generates empirical laws but not theoretical laws
Third, Carnap, as an inductive logician, knew the limitation of induction.
Carnap (1952) argued that induction may lead to the generalization of empirical
laws, but not theoretical laws. For instance, even if we observe thousands of
stones, trees and flowers, we never reach a point at which we observe a
molecule. After we heat many iron bars, we can conclude the empirical fact
that metals will bend when they are heated. But we will never discover the
physics of expansion coefficient in this way. Peirce (1900/1960) held a
similar position: Induction cannot furnish us with new ideas because
observations or sensory data only lead us to superficial conclusions but not
the "bottom of things." (p.878)
Induction is based on generality and law of large numbers
Nonetheless, for Peirce induction still has validity. Contrary to Hume's
notion that our perception of events are devoid of generality, Peirce argued
that the existence we perceive must share generality with other things in
existence. Peirce's metaphysical system resolves the problem of induction by
asserting that the data from our perception are not reducible to discrete,
logically and ontologically independent events (Sullivan, 1991). In
addition, for Peirce all empirical reasoning is essentially making inferences
from a sample to a population; the conclusion is "merely probably (never
certainly) true" and "merely approximately (never exactly) true" (O'Neill, 1993).
Forster (1993) justified this view with the Law of Large Numbers. On one hand,
we don't know the real probability due to our finite existence. However, given
a large number of cases, we can approximate the actual probability. We don't
have to know everything to know something. Also, we don't have to know every
case to get an approximation. This approximation is sufficient to fix our
beliefs and lead us to further inquiry.
Conclusion
In summary, both deduction and induction have different merits and
shortcomings. For Peirce a reasoner should apply abduction, deduction and
induction altogether in order to achieve a comprehensive inquiry. Abduction
and deduction are the conceptual understanding of a phenomena, and induction is
the quantitative verification. At the stage of abduction, the goal is to
explore the data, find out a pattern, and suggest a plausible hypothesis with
the use of proper categories; deduction is to build a logical and testable
hypothesis based upon other plausible premises; and induction is the
approximation towards the truth in order to fix our beliefs for further
inquiry. In short, abduction creates, deduction explicates, and induction
verifies.
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