On Epistemology of the Celestial Realm
Astronomy is the branch of science
concerned with the study
of matter in outer space. The methods of constructing knowledge in
are unlike those which are used in other fields of scientific inquiry.
particularly so because astronomers deal with processes which,
cannot be either explored experimentally or observed given present day
technology. In this paper, Rationalistic tools, like mathematics and
Empirical tools, like sense observations and quantitative measurements,
discussed as complementary approaches for constructing astronomical
the discussion that follows,
it will be shown that for producing a sound and reliable theory in
one must follow a mathematico-deductive pattern of
starting with a
rationalistic approach and developing a general relation describing a
phenomenon. This relation should then be confirmed empirically through specific
observed data. On the other hand, inductively forming a
directly using empirical data in a conventional hypothetico-deductive
model faces a high risk of resulting in inaccurate astronomical
1.2 Scope of Thesis
The argument presented shall work on
the assumption that
nature is uniform, and the analytic rules of logic and mathematics
the physical world as shown by the equations and theorems. Uniformity
Nature implies that an event that occurs at one place and
time will occur
again at any other place and time if the relevant conditions are the
assumption is required for the working of any law.
for the purposes of
discussion, empiricism will be discussed in the context of Direct
where sensory perceptions are a reliable source of information of the
world. This assumption is necessitated for a pragmatic analysis of the
scientific method, as sensory observations are considered essential
for constructing knowledge in the sciences.
as Immanuel Kant pointed out,
‘all our knowledge begins
with experience, but it does not follow that all our knowledge arises
out of experience’. The difference between the two should be
an empirical observation is required to kick-start any search for
even in the case of astronomy. However, the empiricists’ point
this paper is the one that claims that sense datum can be used
construct knowledge vis-à-vis the scientific method in astronomy.
2.1 The Scientific Method
The Scientific Method
is the process by which
scientists construct an accurate representation of the world using a
standard techniques, which help minimize the influence of biased
beliefs on the
development of a theory. Scientists rely on two distinct types of
creating theories and explanations in any field: Inductive
Deductive Reasoning. While inductive reasoning
from a set of finite observations, deductive reasoning is based on a
syllogistic logical arguments, or on a priori
statements, like those in
Diagrammatic flow of Inductive and Deductive Reason
The conventional Scientific Method
makes use of both
inductive and deductive processes to construct theories. It begins with
observations of nature, on the basis of which scientists creatively and
inductively suggest a hypothesis as an explanation. Working with such a
hypothesis, experiments are conducted and logical tests are formulated
would result in certain observations, under the given conditions, if
hypothesis is true. Through such a trial-and-error process, a theory
the observational data and has a predictive capability is worked out.
The Conventional Scientific Method
2.2 Breakdown of
Scientific Method in Astronomy
When the conventional scientific
method is applied to
astronomy, it is noticed that it does not aid one in constructing
theories mainly due to two reasons. Firstly, outer space observations
consist of rare or one-time phenomena, which occur once in a few
Due to this, an inductive pattern is hard to find since the data sample
limited to just a few observations. Secondly, one cannot repeat the
in a laboratory and conduct tests using the same conditions as outer
many cases, it is not even possible to detect or observe a particular
phenomenon directly. For instance, the human race is not
advanced enough yet to explore distances billions of light years away,
being a Type-Zero
civilization at present harnessing only a portion of the energy
our planet (Kaku 2008, 34-53). Since these two major steps of
and ‘observation’ that lend certainty to the scientific process cannot
carried out effectively, the inductive element of this method – when
astronomy – runs a high risk of being inaccurate.
of the fundamental aspects of
astronomy is that there are a number of processes that are
example, a Black Hole is a celestial body whose
gravitational force is
so high that no electromagnetic signal can escape its pull (Wheeler
Since these signals received from outer space objects are the empirical
which an inductive model is built, scientists have no way of
knowledge on a strictly observational basis when dealing with phenomena
black holes, superstrings, quasars, and of the sort.
only way such objects are
detected is through some indirect evidence of their existence. These
high powered X-ray generation from a given point in space, distortions
fields, or even a visible star orbiting an ‘unseen’ companion. But at
time, it should be noted that there are any number of objects that
responsible for X-ray generation and gravitational distortion (which
necessarily be the objects under study). Also, the ‘unseen’ star could
be a star that is too faint to be seen. One cannot be certain of such
evidence as proof for the existence of a particular phenomenon.
conditions is another important step in the scientific method, since it
to derive a relation of what ‘causes’ lead to a particular ‘effect’. It
highly difficult to conduct laboratory tests for laws concerning
bodies as the conditions required for the processes are too extreme to
simulated. For example, one cannot recreate the fusion reactions taking
inside the Sun’s core to understand the mechanism of radiation in
construct multi-dimensional parallel universes. Astronomy is not like
laboratory sciences where the experimentalist is able to vary and
environment or the conditions under investigation. The ‘experiment’ is
process going on out in space, and the astronomer only collects data
‘results’ of that on-going experiment. Apart from this, celestial
generally take millions of years to develop and occur. When dealing
with such a
huge time-span, it is not possible to take a number of observations
different ‘experiments’, or processes going on in space, and then find
pattern in the information received.
it is necessary to
provide an extension to the laboratory laws, or perhaps invoke new laws
non-empirical means to understand and describe such rarely observed and
to simulate phenomena occurring in outer space.
3.1 Deduction as a Possible Solution
Although it is a powerful and
essential tool in science,
inductive reasoning must be treated with skepticism since it is based
limited sample data, and its predictive capacity is restricted to the
repetitive nature of the phenomenon which governs its construction. If
extends a given case to the general by means of induction, he assumes –
very act itself – that induction is actually a workable and correct
is evident that without forming a vicious circle and begging the
generalization from a specific cannot be demonstrated by this process
1997). This is a major logical problem with justification in inductive
reasoning. Induction speaks more of probability in its conclusions than
is, like any other
science, a law-governed nomological study (Kragh 2001,
157-69). Since empirical means can be relied upon only to
extent for cosmological occurrences, it becomes necessary to develop an
entirely deductive theory of astronomical knowledge, which more or less
the element of inadequate experiential ability.
reasoning is perfectly reliable if one has used the correct premises
logical structure. If the foundational statements on which deductive
stands upon consists of self-evident or transcendental truths, the
conclusions will also be axiomatic in nature. The tools of mathematical
and logic can thus aid us in compiling a consistent scientific theory
astronomy (Douglas 1945,
provides evidence to
support this line of reasoning. Johannes Kepler, who solved the problem
planetary motion, initially believed (based on his observations) that
circle – being the perfect curve – was the only path a planet could
later acknowledged that his mathematical results ‘forced’ him to
the planets should be following an elliptical path with the Sun as one
foci (Tarnas 1993).
3.2 Deductive Nature of Mathematics
Mathematical knowledge seems to have
a kind of certainty
that exceeds other forms of knowledge. Since the structure of
based entirely on a system of analytic a priori
statements, it is
noticed that all demonstrations in this field are deductive in nature.
rationalistic consequence of mathematics has immense implications on
of knowledge. For one, we realize that mathematical knowledge requires
which are not based on sense datum. Any general proposition in this
goes beyond the limits of knowledge obtained empirically, which is
limited to what is individual (Slater ed. 1988).
the steps carried out in
formulating a conclusion are mathematically correct, then the claims of
knowledge produced cannot be disproved. This knowledge is then ‘static’
nature, and can be fully relied on as being true.
3.3 Mathematical Construction of
Knowledge in Astronomy
The most powerful method of
advancement in astronomy is to
employ the resources of pure mathematics in attempts to generalize the
mathematical formalism that forms the existing basis of theoretical
These new features should then be interpreted in terms of physical
1973). The application of such a method would lead to the construction
reliable knowledge in astronomy. If a Euclidian triangle is found by
measurement not to have angles totaling 180°, we do not say that we
with an instance which invalidates the summation law of polygon angles.
always preserve the validity of a mathematical truth by adopting some
explanation for the occurrence. This is our procedure in every case in
mathematical truth seems to be confuted. Thus, finding the mathematical
principles governing celestial phenomena will grant our
immense certainty. Once proven, these laws remain as static knowledge
us to make assured advances in astronomy.
mathematical models and
physical equations – which are used as unifying and generalizing
data – astronomical science would cease to function, since all we would
with is a bewildering assemblage of apparently unrelated observations
would try to make sense of using an apparently unjustified common
derived theories suggest the existence of other hitherto unsuspected
phenomena, thus endowing scientific inquiry with a ‘predictive
(Young 1983, 939-50).
For example, from
the gravitational behavior of the universe, it is logically estimated
Matter’ comprises about 25% of natural matter in the form of
interacting massive particles. Dark Matter is a
hypothesized form of
matter particle that does not reflect or emit electromagnetic
particles have not been detected in any form, and are only predicted to
by extensions of our current knowledge about intergalactic
effects. Such knowledge is created to explain structures and phenomena
entirely outside the range of all direct human experiences. Through
rationalistic reasoning, it becomes possible to make assertions, not
cases that we have been able to observe, but also about all actual or
4.1 Extension of System for Knowledge
If knowledge in astronomy is
mathematics, an important implication follows in so much as we can not
formulate astronomical theories by working within the
framework, but can also extend our mathematical means to create
tools for constructing theories outside the
constructing knowledge within
the existing structure, a new theory is devised which is actually a
mathematical extension of the previous theories. It involves tinkering
equations and working out new expressions which might help in
certain phenomenon or process. For instance, accurate observations of
orbit revealed small differences between its predicted motion as per
Newton’s theory of gravity, and its actual motion. Einstein’s general
theory of relativity,
which has its mathematical foundations in Newton’s theory, predicted a
different motion, which was found to be matching with the actual path.
constructing knowledge outside
the existing system, the scope of the subject itself needs to be
formulation of new techniques that increase the application of
astronomy (Hawking 1998). When dealing with certain problems in
Newton realized that the mathematical knowledge existent at that time
inadequate for him to provide possible solutions. Thus, he developed ‘Fluxions’
for the application of his mathematical equations to differentials
nature. This laid foundations for modern-day Calculus.
of mathematical devices then help to extend knowledge in the
4.2 Validation of Rationally
Since mathematically constructed
knowledge is completely
reliable when used with correct premises and suitable steps, it is
that scientists would place undue trust in claims made on a deductive
Mathematical claims need to be carefully examined in order to check
assumptions, or premises, are sound and the reasoning is valid. To
theories, it should be ensured that specifically
predicted observed data
fits well within the explanations of the theoretical framework. Thus,
deductions tested under new observational programmes support the
cast doubt upon their validity. The observations that do not fit into
mathematical framework should be treated as indications that another
explanation is required for the given problem.
an example in astrophysics, the String
Theory enjoys consistency only in a 10-dimensional universe.
hypothesis is a purely theoretical construct with no experimental
support, and its inability to be tested or falsified by near-term
or astronomical observations prevents it to be accepted as ‘knowledge’
the scientific community as of yet (Naeye, 2003,
the concepts empirically is
a critical step in the construction of scientific knowledge, often
profound influence on what is considered knowledge and what is
invalid supposition (Zycinski 1984,
By this ‘empirical testing’, I do not mean that we can entirely trust
observations (since that is the reason we resort to a mathematico-deductive
model for constructing knowledge in astronomy). Rather, after the
of a conjecture in a model, we are better acquainted with the
the sense datum might have undergone before being received by us, and
take these into account while testing our concepts and theories
do not take the observations at face value to construct a theory.
evidence of the senses should
agree with the truths of reason but it is not required for the
these truths. Repeated observations and experiments function solely as
of conjectures or, as Popper would have put it, attempted refutations.
Irreconcilable failures of theoretical predictions to agree with
leads to abandoning of the theory in search of another (Young 1983, 939-50).
Faults, if any, within the
existing mathematico-deductive structure are then
investigated. If no
such discrepancies are found, then new mathematical systems are
is, the system is extended to create knowledge outside
structure. The full appreciation of this explanation makes the relation
theories and observations clear.
The modified Scientific Method for Astronomy
4.3 Epistemological Testing of Knowledge
In Platonic terms, ‘Knowledge’ is
defined as a proposition
that is a justified true belief. Since induction
inductive statement and relies on falsifiable empirical sample data (in
astronomy) for the purpose of justification, it can be safely said that
induction provides us with a true belief, rather than certain
true belief lacks firm grounds, and can therefore be disproved.
the other hand, the justification
for rationally constructed knowledge is provided through specific
empirical observations predicted beforehand. The element of truth
evident since mathematical conjectures are analytic a priori
and hence, the knowledge thereby constructed is true by definition. It
therefore, in the nature of mathematical knowledge that a theorem,
purely on the basis of deductive reasoning using axiomatic truths,
cannot be argued with. One realizes that knowledge can be better
using deductive means as it can be defined
in much more
precise terms than that which is created empirically and inductively in
The relation between mathematics and
astronomy is the
utility of the former in the pursuit of the latter. Perhaps
the reason we
cannot predict anything happening near the singularity region of a
is because our present mathematical laws and equations cease to be
under the conditions prevalent in that area. This leaves us with no
construct our knowledge with.
it is abundantly clear that
our very limited direct experience with the real physical world in no
qualifies us to pontificate upon nature in its entirety. We can
about outer space in an intuitive way using the theories that we
the form of abstract mathematical structures, than those that purely
available empirical information.
5.2 The Pursuit of Knowledge -An After
It is worth noting at this point that
modern commentaries on
the erroneous descriptions of Ptolemy’s model of the universe reveal an
unjustified contempt for a theory that was remarkably successful in
for the then known phenomena of the celestial sphere (Roy and Clarke
theory - or knowledge in general - is something that is a creation of
minds; it has no independent physical existence of its own, but it
explain reality. Pragmatically speaking, Ptolemy’s theory was correct
dependable. But when constructing theories in the sciences, we are
for knowledge which is correspondingly true, that
is, it corresponds to
the actual way the things are in reality. That is
the foremost reason
why we must not be satisfied by merely constructing a pragmatically
which helps us make accurate predictions, or explain observed natural
phenomena; we must endeavor to find the actual mechanism and phenomenon
as it is
happening, even if we cannot observe it.
a leap enables us to
investigate that part of the universe that is beyond the range of our
perception. For such epistemological pursuits, we must make use of
mathematical formulations, for the ‘world’ which they are exploring is
perhaps, as abstract as those numbers and equations.
Anglo-Chinese Junior College
About the Author
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