On Epistemology of the Celestial Realm

Aditya Singh

1.1 Introduction

Astronomy is the branch of science
concerned with the study
of matter in outer space. The methods of constructing knowledge in
astronomy
are unlike those which are used in other fields of scientific inquiry.
This is
particularly so because astronomers deal with processes which,
many-a-time,
cannot be either explored experimentally or observed given present day
technology. In this paper, Rationalistic tools, like mathematics and
logic, and
Empirical tools, like sense observations and quantitative measurements,
are
discussed as complementary approaches for constructing astronomical
knowledge.

From
the discussion that follows,
it will be shown that for producing a sound and reliable theory in
astronomy,
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
generalization by
directly using empirical data in a conventional *hypothetico-deductive*
model faces a high risk of resulting in inaccurate astronomical
knowledge.

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
relate to
the physical world as shown by the equations and theorems. *Uniformity
of
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
same. This
assumption is required for the working of any law.

Also,
for the purposes of
discussion, empiricism will be discussed in the context of *Direct
Realism*,
where sensory perceptions are a reliable source of information of the
external
world. This assumption is necessitated for a pragmatic analysis of the
scientific method, as sensory observations are considered essential
components
for constructing knowledge in the sciences.

Also,
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
understood, since
an empirical observation is required to kick-start any search for
knowledge,
even in the case of astronomy. However, the empiricists’ point
discussed in
this paper is the one that claims that sense datum can be *used
*to
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
set of
standard techniques, which help minimize the influence of biased
beliefs on the
development of a theory. Scientists rely on two distinct types of
analysis for
creating theories and explanations in any field: *Inductive
Reasoning* and
*Deductive Reasoning*. While inductive reasoning
involves extrapolation
from a set of finite observations, deductive reasoning is based on a
system of
syllogistic logical arguments, or on *a priori*
statements, like those in
mathematical conjectures.

*Figure 1*:*
*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
certain
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
which
would result in certain observations, under the given conditions, if
the suggested
hypothesis is true. Through such a trial-and-error process, a theory
which fits
the observational data and has a predictive capability is worked out.

*Figure 2*:
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
reliable
theories mainly due to two reasons. Firstly, outer space observations
usually
consist of rare or one-time phenomena, which occur once in a few
million years.
Due to this, an inductive pattern is hard to find since the data sample
is
limited to just a few observations. Secondly, one cannot repeat the
processes
in a laboratory and conduct tests using the same conditions as outer
space. In
many cases, it is not even possible to detect or observe a particular
phenomenon directly. For instance, the human race is not
technologically
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
available on
our planet (Kaku 2008, 34-53). Since these two major steps of
‘experimentation’
and ‘observation’ that lend certainty to the scientific process cannot
be
carried out effectively, the inductive element of this method – when
applied to
astronomy – runs a high risk of being inaccurate.

One
of the fundamental aspects of
astronomy is that there are a number of processes that are
unobservable. For
example, a *Black Hole* is a celestial body whose
gravitational force is
so high that no electromagnetic signal can escape its pull (Wheeler
1967).
Since these signals received from outer space objects are the empirical
data on
which an inductive model is built, scientists have no way of
constructing
knowledge on a strictly observational basis when dealing with phenomena
like
black holes, superstrings, quasars, and of the sort.

The
only way such objects are
detected is through some indirect evidence of their existence. These
could be
high powered X-ray generation from a given point in space, distortions
in gravitational
fields, or even a visible star orbiting an ‘unseen’ companion. But at
the same
time, it should be noted that there are any number of objects that
could be
responsible for X-ray generation and gravitational distortion (which
may not
necessarily be the objects under study). Also, the ‘unseen’ star could
simply
be a star that is too faint to be seen. One cannot be certain of such
indirect
evidence as proof for the existence of a particular phenomenon.

Experimentation
under varying
conditions is another important step in the scientific method, since it
helps
to derive a relation of what ‘causes’ lead to a particular ‘effect’. It
becomes
highly difficult to conduct laboratory tests for laws concerning
celestial
bodies as the conditions required for the processes are too extreme to
be
simulated. For example, one cannot recreate the fusion reactions taking
place
inside the Sun’s core to understand the mechanism of radiation in
stars, or
construct multi-dimensional parallel universes. Astronomy is not like
other
laboratory sciences where the experimentalist is able to vary and
control the
environment or the conditions under investigation. The ‘experiment’ is
a
process going on out in space, and the astronomer only collects data
from the
‘results’ of that on-going experiment. Apart from this, celestial
phenomena
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
from the
different ‘experiments’, or processes going on in space, and then find
a common
pattern in the information received.

Therefore,
it is necessary to
provide an extension to the laboratory laws, or perhaps invoke new laws
through
non-empirical means to understand and describe such rarely observed and
difficult
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
on
limited sample data, and its predictive capacity is restricted to the
repetitive nature of the phenomenon which governs its construction. If
one
extends a given case to the general by means of induction, he assumes –
in the
very act itself – that induction is actually a workable and correct
process. It
is evident that without forming a vicious circle and begging the
question, a
generalization from a specific cannot be demonstrated by this process
(Russell
1997). This is a major logical problem with justification in inductive
reasoning. Induction speaks more of probability in its conclusions than
deterministic certainty.

Astronomy
is, like any other
science, a law-governed nomological study (Kragh 2001,
157-69). Since empirical means can be relied upon only to
a limited
extent for cosmological occurrences, it becomes necessary to develop an
entirely deductive theory of astronomical knowledge, which more or less
removes
the element of inadequate experiential ability.

Unlike
induction, deductive
reasoning is perfectly reliable if one has used the correct premises
and
logical structure. If the foundational statements on which deductive
knowledge
stands upon consists of self-evident or transcendental truths, the
derived
conclusions will also be axiomatic in nature. The tools of mathematical
theorems
and logic can thus aid us in compiling a consistent scientific theory
for
astronomy (Douglas 1945,
73-88).

History
provides evidence to
support this line of reasoning. Johannes Kepler, who solved the problem
of
planetary motion, initially believed (based on his observations) that
the
circle – being the perfect curve – was the only path a planet could
follow. He
later acknowledged that his mathematical results ‘forced’ him to
conclude that
the planets should be following an elliptical path with the Sun as one
of the
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
mathematics is
based entirely on a system of analytic *a priori*
statements, it is
noticed that all demonstrations in this field are deductive in nature.
This
rationalistic consequence of mathematics has immense implications on
the theory
of knowledge. For one, we realize that mathematical knowledge requires
premises
which are not based on sense datum. Any general proposition in this
subject
goes beyond the limits of knowledge obtained empirically, which is
entirely
limited to what is individual (Slater ed. 1988).

If
the steps carried out in
formulating a conclusion are mathematically correct, then the claims of
the
knowledge produced cannot be disproved. This knowledge is then ‘static’
in
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
astronomy.
These new features should then be interpreted in terms of physical
entities (Dirac
1973). The application of such a method would lead to the construction
of
reliable knowledge in astronomy. If a Euclidian triangle is found by
measurement not to have angles totaling 180°, we do not say that we
have met
with an instance which invalidates the summation law of polygon angles.
We
always preserve the validity of a mathematical truth by adopting some
other
explanation for the occurrence. This is our procedure in every case in
which a
mathematical truth seems to be confuted. Thus, finding the mathematical
principles governing celestial phenomena will grant our
knowledge-system
immense certainty. Once proven, these laws remain as static knowledge
and allow
us to make assured advances in astronomy.

Without
mathematical models and
physical equations – which are used as unifying and generalizing
structures for
data – astronomical science would cease to function, since all we would
be left
with is a bewildering assemblage of apparently unrelated observations
that we
would try to make sense of using an apparently unjustified common
sense.

Moreover,
such mathematically
derived theories suggest the existence of other hitherto unsuspected
natural
phenomena, thus endowing scientific inquiry with a ‘predictive
capability’
(Young 1983, 939-50).
For example, from
the gravitational behavior of the universe, it is logically estimated
that *‘Dark
Matter’* comprises about 25% of natural matter in the form of
weakly
interacting massive particles. *Dark Matter* is a
hypothesized form of
matter particle that does not reflect or emit electromagnetic
radiation. These
particles have not been detected in any form, and are only predicted to
exist
by extensions of our current knowledge about intergalactic
gravitational
effects. Such knowledge is created to explain structures and phenomena
that are
entirely outside the range of all direct human experiences. Through
such
rationalistic reasoning, it becomes possible to make assertions, not
only about
cases that we have been able to observe, but also about all actual or
possible
cases.

4.1 Extension of System for Knowledge
Construction

If knowledge in astronomy is
constructed through
mathematics, an important implication follows in so much as we can not
only
formulate astronomical theories by working *within *the
current mathematical
framework, but can also extend our mathematical means to create
additional
tools for constructing theories *outside* the
existing structure.

In
constructing knowledge within
the existing structure, a new theory is devised which is actually a
mathematical extension of the previous theories. It involves tinkering
with
equations and working out new expressions which might help in
explaining a
certain phenomenon or process. For instance, accurate observations of
Mercury’s
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
slightly
different motion, which was found to be matching with the actual path.

When
constructing knowledge outside
the existing system, the scope of the subject itself needs to be
extended by
formulation of new techniques that increase the application of
mathematics in
astronomy (Hawking 1998). When dealing with certain problems in
physics, Isaac
Newton realized that the mathematical knowledge existent at that time
was
inadequate for him to provide possible solutions. Thus, he developed *‘Fluxions’
*for the application of his mathematical equations to *differentials
*in
nature. This laid foundations for modern-day *Calculus*.
Such inventions
of mathematical devices then help to extend knowledge in the
astrophysical
arena.

4.2 Validation of Rationally
Constructed Knowledge

Since mathematically constructed
knowledge is completely
reliable when used with correct premises and suitable steps, it is
possible
that scientists would place undue trust in claims made on a deductive
basis.
Mathematical claims need to be carefully examined in order to check
that the
assumptions, or premises, are sound and the reasoning is valid. To
validate the
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
theories or
cast doubt upon their validity. The observations that do not fit into
the
mathematical framework should be treated as indications that another
theory or
explanation is required for the given problem.

As
an example in astrophysics, the *String
Theory* enjoys consistency only in a *10-dimensional *universe.
This
hypothesis is a purely theoretical construct with no experimental
evidence for
support, and its inability to be tested or falsified by near-term
experiments
or astronomical observations prevents it to be accepted as ‘knowledge’
within
the scientific community as of yet (Naeye, 2003,
39-44).

Testing
the concepts empirically is
a critical step in the construction of scientific knowledge, often
having a
profound influence on what is considered knowledge and what is
disregarded as
invalid supposition (Zycinski 1984,
137-48).
By this ‘empirical testing’, I do not mean that we can entirely trust
our
observations (since that is the reason we resort to a *mathematico-deductive*
model for constructing knowledge in astronomy). Rather, after the
ratiocination
of a conjecture in a model, we are better acquainted with the
distortions that
the sense datum might have undergone before being received by us, and
we can
take these into account while testing our concepts and theories
empirically; we
do not take the observations at face value to construct a theory.

The
evidence of the senses should
agree with the truths of reason but it is not required for the
acquisition of
these truths. Repeated observations and experiments function solely as
‘tests’
of conjectures or, as Popper would have put it, attempted refutations.
Irreconcilable failures of theoretical predictions to agree with
empirical data
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
explored, that
is, the system is extended to create knowledge *outside*
the existing
structure. The full appreciation of this explanation makes the relation
between
theories and observations clear.

*Figure **3*:
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
presupposes an
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
‘knowledge’. This
true belief lacks firm grounds, and can therefore be disproved.

On
the other hand, the *justification*
for rationally constructed knowledge is provided through *specific*
empirical observations predicted beforehand. The element of *truth*
is
evident since mathematical conjectures are *analytic a priori*
statements,
and hence, the knowledge thereby constructed is true by definition. It
is,
therefore, in the nature of mathematical knowledge that a theorem,
formed
purely on the basis of deductive reasoning using axiomatic truths,
cannot be argued with. One realizes that knowledge can be better
constructed
using deductive means as it can be defined
in much more
precise terms than that which is created empirically and inductively in
astronomy.

5.1 Conclusion

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
black hole
is because our present mathematical laws and equations cease to be
applicable
under the conditions prevalent in that area. This leaves us with no
tool to
construct our knowledge with.

Thus,
it is abundantly clear that
our very limited direct experience with the real physical world in no
way
qualifies us to pontificate upon nature in its entirety. We can
comprehend more
about outer space in an intuitive way using the theories that we
conceive in
the form of abstract mathematical structures, than those that purely
rely on
available empirical information.

5.2 The Pursuit of Knowledge -An After
Note:

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
accounting
for the then known phenomena of the celestial sphere (Roy and Clarke
2003). A
theory - or knowledge in general - is something that is a creation of
our
minds; it has no independent physical existence of its own, but it
helps us
explain reality. Pragmatically speaking, Ptolemy’s theory was correct
and
dependable. But when constructing theories in the sciences, we are
searching
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
true *theory
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.

Such
a leap enables us to
investigate that part of the universe that is beyond the range of our
sensory
perception. For such epistemological pursuits, we must make use of
abstract
mathematical formulations, for the ‘world’ which they are exploring is
also,
perhaps, as abstract as those numbers and equations.

Anglo-Chinese Junior College

Singapore

About the Author

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