What is Science?
Introduction
The intention in this paper is to write down what science means to me after having
attended a philosophy course on the philosophical problems of the natural sciences, in
which a selection of texts by thinkers in the Anglo-American tradition were read and
discussed.i I will stay with the format of my first paper, which dealt with the question
under consideration along three lines of investigation:
1) A radical reflective investigation,
2) Starting from personal experience, and
3) Trying to state a rough hypothesis.
1. A radical reflective investigation
A very important theme in philosophy centers on reflexivity. As I pointed out in my
previous paper the question about science is problematic. Is it fair to pose the question
about science in a scientific manner? Can there be a specific science of sciences, besides
specializations like the history or sociology of science, which would only cover an aspect
of the totality of science? Or should we lend our ear to philosophy and find maybe there a
mode of understanding the totality of science different and independent of the mode of
understanding as used in the sciences themselves? The open question was: “Can
philosophy develop rigorous insights into the nature of science without basing itself on
the procedures or results of any of the particular sciences?” In this part of the paper I will
deal with this theme of reflexivity in three realms:
1) Scientific Reflexivity, in the sense of one science taking another science as its explicit
field of investigation.
2) Philosophical Reflexivity, in the sense of philosophy being the science and art of
reflexivity itself.
3) Personal Reflexivity, in the sense of experimenting with the discussed modes of
understanding as possible modes of self-perception.
1.1. Scientific Reflexivity
Event though the question about the possibility of a non-scientific philosophy of science
is of particular importance, it is not meant as a rhetorical question to refute the
fruitfulness of investigating all the sciences, including philosophy itself, from the
necessarily limited angles of history, psychology, sociology, political science etc. I will
call these kinds of investigations ‘reflexive nodes,’ in the sense that they are intersections
of the sciences--not in a multi-disciplinary cooperative way concentrating on an agreed
upon worldly subject--but where one science takes the other as its explicit field of
investigation. Results can be very interesting as with Russel’s logic of mathematics;
Kuhn’s history of modern science; Popper’s biology of intellectual progress; Bloor’s
sociology of intellectual claims; or, less known (and more or less randomly picked)
Trumpbour’s political scientific investigation of institutionalized science,ii and
Barnes’critical history of World War I and II historiography.iii One of the questions here
would be about the limits of applicability of these programs. There can be no a priori
argument against trying to, so to say, cast the net as far and wide as possible and see what
comes up. But one should object if the endeavor becomes imperialistic and reductionistic.
When that happens it would be appropriate to add ‘–ism’ to the discipline in question,
because it has tried to transform itself from a local methodology to a universal ideology.
For example the late 19th century psychologistic attempt to explain logic and philosophy
in terms of psychological laws; Russel’s logisistic attempt to totally subsume
mathematics under logic; logical positivism’s scientistic attempt to regard philosophical
problems as scientific problems and “drive metaphysics of the stage,”iv and Bloor’s
sociologistic proposal to “investigate and explain the very content and nature of scientific
knowledge” strictly in terms of value-free sociological and psychological causes.v
As an example of an illuminating non-reductionistic reflexive investigation I will make a
little excursion into the reflexive node of the sociology of philosophy pertaining to
logical positivism according to sociologist of philosophies Randall Collins. According to
Collins the movement’s flagship was the Vienna Circle, which was most active during
the inter-bellum in Austria and Germany and was an amalgamation of three networks and
their problematics: 1) German physicists and their discussion about methodological
questions, 2) the Neo-Kantians and their question about the grounds of experience and 3)
mathematician-logicians working with the deep problems uncovered by thinkers like
Frege and Russel. This combination did not provide any lasting consensual solutions to
its inherited problems. On the contrary, it created actually more puzzles and personal
oppositions than it started with. But because the puzzles were so interesting and the
personal oppositions inspired its members to great creativity, the movement acquired a
substantial portion of the attention space within Western philosophy. The main thrust of
the movement was to provide a unification of the sciences taking physics and logic as its
model and guide, which meant creating a philosophy of science, which should be as
logical and testable as any other science. A side effect, and for some members a major
motive, was a militant opposition against anything metaphysical, which was made
possible by the advanced secularized state of academia.vi
Interestingly, the larger historical background of logical positivism also has to do with
reflexivity, especially within the discipline of mathematics. According to Collins it was at
the middle of the 19th century that of all intellectual endeavors it was mathematics that
had achieved “the highest degree of self-consciousness on its structures of argument.”
Subsequently this “new pitch of intellectual reflexivity” set the stage for the emergence
of the major schools of modern philosophy, i.e. positivism, phenomenology and ordinary
language, which all resulted from “interdisciplinary pressures originating in mathematical
science.” vii
The question for me with the Vienna Circle and its legacy are the reasons for its failures
and its successes. Were their failures, like the verification principle, due to the fact that
they applied rules and methods developed within modern physics and logic and tried to
apply them dogmatically in domains like the social sciences, ethics, and metaphysics,
where they would run into insurmountable problems, because these domains require their
own standards of investigation and rationality? And were their successes, like Goedel’s
work in logic, due to the fact that they applied methods eminently appropriate to the field
of logic and mathematics? Though a close reading of the historical sources will reveal a
plethora of different positions within the Vienna Circle--and therefore any generalizations
about its members can be easily refuted--the philosophical point here to be made is that
probably none of the specialized sciences, however logical and empirical their modus
operandi, has within their power the decision to say what is science and what is not. The
laudable aims of simplification, unification and opposition to unprovable statements,
which drove the program of logical positivism, were not met, and its own dogma’s were
finally exposed from within the movement itself. viii
1.2. Philosophical Reflexivity
Here I like to argue that these problems of cross-disciplinary applicability are eminently
philosophical problems and have been one of its major foci.ix Philosophy is not merely
the crucible or midwife of all the sciences, but also reflects on a higher level of
abstraction on the abilities, operations and limits of science itself, and will be able to dig
deeper into the question of ultimate foundations and origin than the specialized
disciplines.x It can be argued that philosophy is the science and art of reflexivity itself,
thrusted towards an ever-subtler abstract-reflexive cognitive self-transparency by its most
able practitioners. In so doing philosophy has developed different insights and tools to
adjudicate territorial disputes between all the different reflexive nodes, identify new
cross-disciplinary possibilities and transgressions, including its own position, knowing
full well that both science and philosophy are quite dynamic and ever changing
enterprises. Philosophy can not adjudicate a priori, as if it could regulate science, but has
to wait till the results of cross-disciplinary scientific and philosophical experiments are
in.xi In short, philosophy is an abstract-reflexive quest for cognitive self-transparency,
which none of the sciences can ever dream of achieving, though they can make this kind
of cognition into a research subject.xii
1.3. Personal Reflexivity
In this section on reflexivity I will try a radical reflection on myself as an enthusiastic
beginner in the field of philosophy of science. I will try to apply a few of the suggested
modes of understanding on my own mode of understanding and in so doing maybe find
deeper layers of motivation for taking this class and engaging in philosophy of science.
The first of alternative understandings, which struck me, was to see myself from the point
of view of evolutionary biology, especially Popperian evolutionary epistemology,xiii as an
unwitting agent in the random production of hypotheses about science. This in order to
increase the probability that any of these hypotheses would survive critical scrutiny and
thereby contribute to science itself as an instrument for survival of the species Homo
Sapiens in its drive to adapt to its environment. Though this idea creates a slight feeling
of depersonalization, and in the end is not satisfactory, it is kind of fun playing with this
self-perception.
Another possible application would be Kuhn’s idea of incommensurability between
paradigms. Within the discipline of philosophy of science this would mean that all the
different schools or paradigms developed to answer the question ‘what is science,’ could
not have a really meaningful discussion amongst each other.xiv This because, even though
they all use the same words like ‘theory,’ ‘fact,’ ‘hypothesis,’ ‘test,’ etc., the meaning of
these words are paradigm-dependent and therefore quite different. So, even when
participants in these discussions use the same words and seem to understand each other
and seem merely to disagree, they are really talking at cross-purposes. Though they think
they are trying to convince the others by rational arguments, they will only be successful
if they induce a non-rational conversion experience.xv Applying this idea on myself
would mean that, though I think I understand most of the texts in the field of philosophy
of science, in reality I really don’t. I endow the words and statements in those texts with
meanings according to my own emerging paradigm of understanding, which is
fundamentally different from the paradigms shaping the presented texts. Before I will
ever be able to fully communicate philosophically about science with another person I
will first have to be converted by another to his paradigm, or convert someone else to my
own version. And even then we will still find ourselves in a solipsistic discours not being
able to connect with others.
The last experiment would be to apply the sense of philosophy presented in 1.2 to myself.
This would mean that I will have to find my own way and voice in the dynamic everchanging multi-logue comprising philosophy by trying to get aligned with this
philosophical thrust towards ever-subtler abstract-reflexive cognitive self-transparency.
Initially this meant, when I started to dabble in philosophy, getting sucked into this
dizzying maelstrom of philosophical positions, counter-positions and meta-positions. But
by going along, reflecting on how I handle philosophical positions, play them out against
each other and reflectively apply them to myself, I acquire certain interpretative skills and
sometimes even reach lucid moments of insight into the process of understanding itself
when I understand a text about understanding.xvi
2. Personal Experience
My personal claim to having done something scientific is a paper in which I compare
twenty different evaluations of the spiritual status of the Indian religious thinker Jiddu
Krishnamurti.xvii I presented the views as accurately as possible, developed a thesis how
they could best be classified, and ended with 8 conclusions. The paper was vetted by
experts in the field of religious studies and was published by an academic journal. The
important scientific lessons derived from this experience were:
a)
a)
b)
c)
d)
observing, understanding and describing the phenomena in question,
recognizing patterns of relevant similarities and differences,
developing a thesis based on the previous activity, and
evaluating the thesis for its effect to bring clarity the field of investigation, and
noting some interesting features brought out by the investigation.
The lesson I learnt was to let facts and patterns of facts speak for themselves, but also to
be creative and experimental in trying to find them. I also learnt that scientific research
can be a legitimate vehicle to insert ideas into larger non-scientific discussions, where the
topics might be more of an ethical, political or philosophical nature.xviii
3. Hypothesis
What happens when I cognize a fact? On a practical common-sense level I think that
facts are out there in the world to be found and are labeled with words according to my
language community. I have learned to identify things and states of affairs as permanent,
or changing, through an elaborate perception-differentiation and language-acquisition
process of trial and error guided by other people, my parents, teachers etc., who have
gone through a similar learning process. Most of the collective stock of knowledge is
accessible to me in the form of texts, containing facts and theories about a world out
there.
Next to this common sense and somewhat static picture I like to propose the following
hypothesis about the human cognitive process. All acts of cognition and their expression
in statements are basically perceptual, whether it is pointing to a thing (that’s a chair),
ascertaining a state of affairs (the chair is green and small), making either a general
statement (people sit in chairs), or a scientific statement (this chairs has a limit of
carrying 1200 lbs.), a scientific theory (all bodies fall towards a center), a scientific
formula (g=9.8 m/s.s). Whatever the level of abstraction, generality or formalization,
every statement is a ‘view’ or suggests a way of looking. The way we see, at the most
basic level, a simple thing is paradigmatic for all the other levels, for all problems
involved in simple perception have their counterpart in all other forms of cognition. The
view I propose is an amalgamation of Advaita Vedanta, Gestalt-theory, Popperian
philosophy, Bohmian epistemology, Husserlian phenomenology and some more ideas,
whose origin I forgot. To see a thing is to superimpose a form on a specific part of a
nebulous changing flux of sense impressions. Though the flux is unitary, it is not without
an inner differentiation and order, which makes it possible to see temporary ‘gestalts’
within its movement. What is seen, or more correctly, superimposed, has a temporary and
provisional structure. A favorite example in Advaita Vedanta to explain superimposition
(Adhyasa) is the rope identified as a snake. In reality there is a rope, but by mistake, one
perceptually superimposes the form of a snake on it. On closer inspection a gestalt-switch
occurs and one finds out it is actually a rope. Another good example to illustrate the idea
of superimposition is the duck-rabbit picture. The picture is merely a drawing of lines,
drawn in such a way that one can see either a duck or a rabbit. But the act of seeing is
really a perceptual superimposition of either the duck- or rabbit-form on the lines
comprising the picture.
A further question might be asked about he status of the lines themselves. In the duckrabbit example the lines are presented as a neutral basis upon which the conjectural
perceptual act superimposes a form. Can this be interpreted as a possibility of attaining
the rock-bottom of experience, only to be attained if one is sufficiently aware of this
faculty to project? Or are those lines superimpositions by themselves? I think the answer
is positive here as far as the search is for discrete and simple experiences. The lines are
superimpositions upon some ink on paper (or a lot of white-out on a piece of black
paper), which all by themselves also share this feature of being provisional
superimpositions, etc., etc. Therefore, there is no bottom, only an infinity of possible
perceptions, one organically flowing from or replacing the other. On the other hand
Advaita claims that even if the perception of a rope as a rope can be correct, in the final
analysis it is a mistaken imposition, the mistake being to see the rope as separate from the
totality of reality, which is Brahman, which only can be seen or experienced when the act
of superimposition comes to a complete halt in meditation.
This idea of superimposition and flux has close parallels with theoretical physicist David
Bohm’s notion about reality and knowledge as a process: “Not only is everything
changing, but all is flux. That is to say, what is is the process of becoming itself, while all
objects, events, entities, conditions, structures, etc., are forms that can be abstracted from
the process.”xix The only reservation I would have with Bohm’s formulation is his use of
the concept ‘abstraction,’ which could be interpreted as a conceptual act of withdrawing
or taking away from the flux, instead of a perceptual act of imposition or endowment
upon the flux, which I think is more correct.
The main reason for this nuance is to explicate the provisional and hypothetical nature of
even simple perceptions in order to account for errors and fallibility. As long as a specific
perceptual superimposition holds in experience, or finds fulfillment there, all is well. But,
as in the case with the rope, experience might deliver little anomalies, which might
indicate a perceptual error to be corrected.
For example the skin has an unexpected color and structure. Actually the color and
structure is one readily associated with a rope, which might motivate the perceptual
gestalt-switch to rope. But, you’re not quite sure, and because the snake might be
poisonous, you have an extra motivation to find out the truth. Therefore you devise a test,
which might decisively settle the issue, and you will set it up in such a way that if it is a
snake you will not get bitten, and if it is a rope, you will not get entangled. The best way
seems to be to give it a quick poke with a stick. If it will react, it is a snake, if it merely
moves along with the stick, it is a rope. Well, the latter happens and by getting closer you
see indeed that the object has all the features of a rope. To really exclude the possibility it
is a snake, you look for defining aspects of a snake, like a head with eyes, and find them
absent.
This procedure of course has all the features of the hypothetico-deductive method,
including some Popperian twists, but then on the level of simple perceptions: the
identification of the phenomenon as snake is as fallible and corrigible as a hypothesis;
certain features can be deduced and tested based on the conjectured identification; there
is a comparing of two plausible identifications; the setting up of a decisive test by a
deliberate search for falsifying instances: if it is a snake, it should not stay passive, if it is
a rope it should not have eyes.
Implied in the foregoing is the whole problematic of the perception of states of affairs as
a higher-level, more complex perceptual act. There is a difference between seeing a chair
as a chair, and seeing the chair as having the color green, or having a certain curvature,
size, or weight etc. If I see a chair I experience a changing manifold of aspects,
comprising a harmonious background to my perceptual foreground of an invariant
identification. It might be expressed in a simple descriptive statement like “that’s a
chair.” A state of affairs is the highlighting of a certain aspect, made possible by a
perceptual gestalt-switch between background and foreground, where an aspect becomes
foreground and the object, of which it is a part, becomes background. Here a whole new
kind of object comes into being: for example, the greenness of the chair, expressed in the
descriptive proposition “The chair is green.” This is as much a perceptual conjecture as in
the case of simple perceptions. Maybe the conjectural aspect might be less obvious,
because there seems to be such directness when experienced. It might not be a chair, but
its greenness is beyond doubt. But the possibility of error indicates its testable and
hypothetical character: the light could be wrong and the color might have been really
green-bleu, or the perceived curvature was really a straight line.
Because non-refuted perceptual conjectures have certain stability, they can be expressed
in language, which is a reporting mechanism for possible perceptions. I say there is a
green chair, and you can verify my claim by superimposing green chair on the
phenomenon I indicate, and see for yourself if the identification holds within your own
flux of experiences. This applies to simple statements, to states of affairs, to comparisons,
and to any higher level of propositions like scientific laws, theories, even philosophical
statements.
With the previous preparations done it might not be a big step to the claim that theoryformation is basically a perceptual process and is not a process of logically combining
basic statements inductively into higher level scientific statements. Theory-formation
starts with a complex conjectural act of perception, a way of looking at the world in a
new way. “What is involved in this act is perception through the mind of abstract orders
and relationships such as identity and difference, separation and connection, necessity
and contingency, cause and effect, etc.” xx These mental perceptions, or insights, can be
enveloped by thought and expressed in language. Therefore the sequence of perception-description--induction--theory-formation, is not correct. The description of the insight is
theory-formation. Induction doesn’t take place. It is falsely separating description and
theory-formation and erroneously inserted between the two.
Facts and theories are the two extremes on a continuum and imply each other in multiple
and complex ways. Facts are relatively simple perceptions of a more sensuous nature and
theories are more complex perceptions, or insights, of a more mental nature. Both have
an inner and outer horizon: Facts have a complex structure of inner aspects, which can be
brought to light, and facts are also situated in an environment with which it has a
dynamic relationship. Insights imply their own perceptions, and are not free-floating
entities, but are organically connected to other insights. The same structure holds for
simple statements and complex hypotheses. Simple statements can be internally analyzed
and have their context within a web of other statements, including hypotheses.
Hypotheses have their own deductions, including simple statements, and are externally
connected with other theoretical entities.
Progress consists of broader and sharper insights following each other. Newtonian
physics doesn’t see sharp any more when it comes to very high speeds or very small
entities. Its successors do, and might even see why their predecessors failed. The view
that new theories are fundamentally different might be due to several factors. Maybe the
ontological status of posited unobservable entities is taken too serious. When Bohr’s
atomic theory had just proven itself it was quikly overtaken by quantum theory. We still
use both depending on context. It might also be that metaphors used in the explanation of
the different theories are incompatible, even while the mathematics might be
compatible.xxi Or, as with a gestalt-switch, people can not switch back anymore and then
are at a loss to re-experience the founding insights of the previous theory.
In this way a holistic picture emerges of an integrated web of simple and complex
perceptions, and a web of simple and complex statements, which together form a totality,
because the latter are verbal expressions of the former. Both are also part of the universal
flux, though I stated before that they were superimpositions upon the flux and therefore
somehow outside of it. This calls for an explanation. The integrating factor of this
picture is insight itself, which can see and act upon this totality, while at the same time
being part of it. So, instead of man confronting the totality of outside experience through
and from within the total web of its language, he can switch between and within the
totality of simple and complex perceptions and their descriptions in statements and
theories, and also reflect reflect philosophically upon this activity itself, which was tried
in this paper.
i
What I missed were texts from the rival Continental tradition. A great source for me is the collection of
papers in Kockelmans, J.J. & Kisiel Th. J. Phenomenology and the Natural Sciences: Essays and
Translations (Evanston, IL: Northwestern University Press, 1970).
ii
Trumpbour, John (Ed.) How Harvard Rules: Reason in the Service of Empire (Boston: South End Press,
1989)
iii
Barnes, H.E. “Revisionism and the Historical Blackout” in Barnes, H.E. (ed.) Perpetual War for
Perpetual Peace: A Critical Examination of the Foreign Policy of Franklin Delano Roosevelt and its
Aftermath (Caldwell, ID: The Caxton Printers, 1953)
iv
Collins, Randal The Sociology of Philosophies: A Global Theory of Intellectual Change (Cambridge,
MA: Harvard U.P., 1998), p. 722.
v
Bloor,David Knowledge and Social Imagery (New York: Columbia University press, 1976), p. 3.
vi
Collins, pp. 717-730.
vii
Collins, p. 695.
viii
Quine, W.V. “Two Dogmas of Empiricism” in Philosophical Review 60/1 (1951), pp. 20-43.
ix
As Collins states: “Creativity in philosophy since the academic revolution of the 1800s has been largely
stimulated by the adjudication of new disciplinary boundaries. The emergence of history of science,
sociology of knowledge, the literary theory of textuality, along with many other actual and potential
combinations, heightens the reflexivity of the intellectual community as a whole. The search for problems,
for energizing points of attention and contention, which is the life of intellectual networks, has turned to
exposing the inner truths claims of the various specialized branches to the alternative perspectives of
different branches.” Collins, pp. 876-877.
x
“[A] scientist must recognize that an essentially different kind of thinking is needed in the self-reflection
on his science, that in fact a leap must be made…” and “[T]here is a side science cannot reach, the essence
and origin of its domain and its mode of knowing, to which thinking in the present situation must give its
attention, which the sciences are incapable of giving to themselves.” Kisiel, Th.J. “Science,
Phenomenology and the Thinking of Being” in Kockelmans, J.J. & Kisiel Th. J. Phenomenology and the
Natural Sciences: Essays and Translations (Evanston, IL: Northwestern University Press, 1970), pp. 169 &
173.
xi
I agree with Arthur Fine to let “science speak for itself,” and to oppose “doctrines that externally limit the
commitments of science,” but at the same time I would argue to let philosophy speak for itself, especially
when cross-disciplinary reflections become dogmatic and reductionistic. These doctrines like Darwinism,
empiricism and logicism, arise from within science itself and have to be exposed by philosophical
reflection. Fine, A. “And Not Anti-Realism Either,” Noûs 18/1 (1984), p 63.
xii
See for example the psychological-philosophical investigations into transpersonal cognition, like the
papers collected in Hart, T., et.al. (eds.) Transpersonal Knowing: Exploring the Horizon of Consciousness
(New York: SUNY, 2000) and Wilber, K. Eye to Eye: The Quest for the New Paradigm (Garden City,
N.Y.: Anchor/Doubleday, 1983). (It is interesting to note that the author most referred to in the Hart
collection is Edmund Husserl.)
“From a biological or evolutionary point of view, science, or progress in science, may be regarded as a
means used by the human species to adapt itself to the environment.” Popper, Karl “The Rationality of
Scientific Revolutions” in Janet A. Kourany (ed.), Scientific Knowledge: Basic Issues in the Philosophy of
Science (Belmont, CA: Wadsworth, 1987) p. 235. This idea has to be applied also to philosophy of science
itself, because it pretends to be carried out according to scientific rules and can be shown to have an impact,
successful or not, on the progress of science.
xiv
It is not quite clear how to classify the different philosophical schools in this matter. Laudan proposes
four generic positions: positivist, realist, relativist and pragmatist. Laudan, L. Science and Relativism: Some
Key Controversies in the Philosophy of Science (Chicago: The University of Chicago Press, 1990), p. x.
Collins (p. 695) would identify three major philosophies: positivism, phenomenology and ordinary
language, all with their own many different philosophies of science. Lakatos classifies by methodology:
inductivism, conventionalism, falsificationism and his own ‘scientific research programmes.’ Lakatos, I.
“History of Science and Its Rational Reconstructions” in Hacking, I. (ed.), Scientific Revolutions (New
York: Oxford University Press, 1981), p. 2. Popper conjectures three positions: instrumentalism,
essentialist realism and his own fallibilist realism. Popper, K. “Three Views Concerning Human
Knowledge” in Popper, K.R., Conjectures and Refutations: The Growth of Scientific Knowledge (New
York: Routledge, 1989).
xv
“… before they can hope to communicate fully, one group or the other must experience the conversion
that we have been calling a paradigm shift…. [In] these matters neither proof nor error are at issue. The
transfer of allegiance of paradigm to paradigm is a conversion experience that cannot be forced.” Kuhn,
T.S. The Structure of Scientific Revolutions (Chicago: The University of Chicago Press, 1970 [1962] ), pp.
150-151.
xvi
The only state beyond this might well be the Hindu Sachidananda (Consciousness-Being-Bliss),
Buddhist enlightenment, or Krishnamurtian choiceless awareness, where all understanding is transcended
in a state of full wakefulness and lucidity.
xvii
Schüller, Govert W. Krishnamurti and the World Teacher Project: Some Theosophical Perceptions
(Fullerton, Ca: Theosophical History Journal, 1997). Available on-line:
http://www.alpheus.org/html/articles/thopv/index.html.
xviii
I could have expanded this section with a detailed analysis of the way I went about writing this paper.
For example I could have tried to dig up extra-scientific motivations in play and/or reconstruct the
chronological development of the thesis to see how facts and theory played out against each other.
xix
Bohm, D. Wholeness and the Implicate Order (London: Routledge and Keegan Paul, 1980), p. 48. Italics
in original. Bohm also leaves open the possibility of a state of consciousness beyond perception and
knowledge.
xx
Ibid. p. 51.
xxi
“And if we envisage a concrete paradigm which draws a crude analogy, then, notoriously, in so far as it
is really crude, it will not be directly comparable with any other crude analogy… It does not hold when the
paradigm in question has become embedded in mathematical form…. Analogies between pieces of
mathematics render them not incommensurable, but conversely, comparable.” Masterman, Margaret “The
Nature of a Paradigm” in Criticism and the Growth of Knowledge (Cambridge: Cambridge University
Press, 1970), p. 80.
xiii