Philosophy math and science curriculum

Philosophy in Math/Science Curriculum
Intesar T. Aba-Conding
Ph.D. Science Education (Biology) Student

Whenever science is taught,
philosophy, to some degree,
is also taught.
Minimally, the teacher’s own
epistemology, or conception of science,
is conveyed to students and contributes
to the image of science that they
develop in class.

 Ways in which philosophy’s presence in science
education has been and can be made more explicit
will be examined.
 It will be argued that by making philosophy more
explicit the goals of good technical science
education can be advanced – children will
understand the subject better – and at the same time
something of the more general cultural and
epistemological dimension odf science can be
conveyed.
 This consideration can be extended to the teaching
of history, mathematics, geography and most school
subjects

Science and Philosophy
 The separation of science education from philosophy
results in a distorted science education.
 From the ancient Greeks to the present, science has been
interwoven with philosophy: science, metaphysics, logic
and epistemology have been inseparable.
 Most of the great scientists - Democritus, Aristotle,
Copernicus, Galileo, Descartes, Newton, Leibnitz, Boyle,
Faraday, Darwin, Mach, Einstein, Planck, Heisenberg,
Schrodinger – were at the same time philosophers.
 Scientists were called “natural philosophers” through to the
end of the nineteenth century. Einstein spoke of the
theoretical physicist as a “philosopher in workingman’s
clothes”

 Metaphysical issues naturally emerge from the subject matter of
science. Historical studies portray the interdependence of science
and metaphysics.
 The Galilean/ Arsitotelian controversy over final causation
 The Galilean/Keplerian controversy over the lunar theory of
tides
 The Newtonian/Cartesian argument over action at a distance
 The Newtonian/Berkelian argument over the existence of
absolute space and time
 The Newtonian/Fresnelian argument over the particulate
theory of light
 The Darwinian/Paleyian argument over design and natural
selection
 The Mach/Planck argument over the realistic interpretation of
atomic theory
 The Einstein/Copenhagen dispute over the deterministic
interpretation of quantum theory – all bring to the fore
metaphysical issues.
 Metaphysics is pervasive in science.

Galileo
 Galileo is an outstanding example of the
scientist/philosopher.
 He made substantial philosophical contributions in a variety of
areas:
 In ontology, with his distinction of primary and secondary qualities
 In epistemology, both with his criticism of authority as an arbiter
of knowledge claims and with his subordination of sensory
evidence to mathematical reason
 In methodology, with his development of the mathematical-
experimenal method
 In metaphusics, with his critique of the Aristotelian causal
categories and rejection of teleology as an explanatory principle.

GALILEO
 It is thus unfortunate that, depite his important
contributions to the subject.and despite his
acknowledge influence influence on just about all
philosophers of the seventeenth century and such
subsequent philosophers as Kant and Husserl,
Galileo makes scant appearance in most histories of
philosophy, and most science texts ignore his
philosophical interests and contribution.

 Science has always been conducted within
the context of the philosophical ideas of
time. This is to be expected.
 Scientists think, write and talk with the
language and conceptual tools available to
them; more generally, people who forms
opinions, are themselves formed in specific
intellectual circumstances, and their
opinions are constrained by these
circumstances.

 Newton said that he was able to see further than others
because he stood upon the shoulders of giants;
 Without Copernicus,Kepler and Galileo, not to mention
Euclid’s geometry, there would not have been a unified
theory of terrestrial and celestial mechanics.
 A scientist’s understanding and approach to the world
is formed by his or her education and milieu; and this
milieu is pervaded by the philosophies of the period.
 From an objectivist point of view, what these claims are
pointing to is the fact that science as a system of
concepts, definitions, methodologies, results,
instruments and professional organization, predates
the individual who comes to work upon and within it.
 Inasmuch as the former embodies philosophical
suppositions, then the work of the scientist will be
shaped by philosophy.

 The connection of science with philosophy, broadly
understood, is promoted in much present-day popular
scientific literature. Books such as
 God and the New Physics (Davies 1983)
 A brief History of Time (Hawking 1988)
 On Human Nature (Wilson 1978).
 The Tao of Physics (Capra 1975)
 The Dancing Wu li Masters (Zukav 1979)
 Those books have been best-sellers and have conveyed, with
sometimes more and other times less understanding, the basic
idea that science affects, and is affected by, other disciplines
philosopy, psychology, theology, biology and more generally the
worldviews of culture.

 The popular literature can provide an occasion for teachers to discuss
the borderline territory between science and philosophy, and to
connect laboratory life with cultural debates.
 Popular authors often neglect details, and sometimes seriously
misunderstand important issues.
 Along with good popular expositions there are numerous shoddly, but
still popular, works that warp public appreciation of the issues.
 Teachers informed by the history and philosophy of science are in a
better position to evaluate the worth of these competing orientations.
 by introducing students to the speculative, metaphysical and ethical
questions that science throughout its history has considered, the
chances of them being seduced by the first guru they meet offering
worldviews a little out of the ordinary will be reduced.
 Students without prior exposure to such debates can be a little like a
country child on his or her first visit to the big city.

 The role of religious belief in the motivation and
conceptualizations of scientists is usually ignored in the
science syllabus.
 Students learn often enough that Newton discovered three
laws, and the formula for them.
 They learn less often that Newton said, when he wrote his
Principia, “ I had an eye upon such principles as might work with
considering men for the belief of a Deity.” and nothing can rejoice
me more than to find it useful for that purpose.
 They also learn that Boyle formulated the important law
connecting pressure and volume of gases.
 They learn less often that he left a provision in his will for a set of
public lectures “for proving the Christian religion against notorious
infidels” and that he believed his own mechanical philosophy
admirably suited for proving the existence of a Designer of the
universe.

 Despite the fact that, historically, the major Western
scientists regarded their work as proclaiming the majesty
of God, little is heard of this in the typical science
classroom.
 There are engaging psychological, cultural and
philosophical stories that are worth telling and exploring.
 No one expects that the long-running issue of science and
religion will be solved in the science classroom, but surely
it can be raised, and some outline of its components and
history be given.
 Senior students, in particular, can benefit from familiarity
with this issue, as it often bears upon their own personal
affairs, and it bears upon discussions in their literature and
history courses.

 The considerable literature generated by the
Philosophy for Children movement suggests that
children are both capable of, and interested in,
pursuing elementary philosophical questions
(Davson-Galle 1990, Lipman 1991, Lipman &Sharp
1978).
 The science classroom provides opportunities to do
this.
 The science must come first, but there is the
opportunity for children to encounter basic
philosophical questions, and to acquire some basic
philosophical skills of an analytic and reasoning
kind.

Philosophy in the Science Curriculum
 Science education is enriched, and is more faithful to its
subject, if aspects of the interesting and complex interplay of
science and philosophy can be conveyed in the classroom.
 There are various ways in which the interplay between science
and philosophy can be conveyed:
 reading of selections from original sources;
 joint projects with history, social sciences, divinity or literature
classes:
 dramatic reenactments of significant episodes in the history of
science:
 essays on selected themes;
 debates on topical matters;
 or low-level philosophical questioning about scientific topics
being studied or practical work being conducted

Philosophy of science
 A branch of philosophy concerned with the
foundations, methods, and implications of
science.
 The central questions of this study concern
what qualifies as science, the reliability of
scientific theories, and the ultimate purpose
of science.
 This discipline overlaps with metaphysics,
ontology, and epistemology, for example,
when it explores the relationship between
science and truth.

 There is no consensus among philosophers
about many of the central problems
concerned with the philosophy of science,
including whether science can reveal the
truth about unobservable things and
whether scientific reasoning can be justified
at all.
 In addition to these general questions about
science as a whole, philosophers of science
consider problems that apply to particular
sciences (such as biology or physics). Some
philosophers of science also use
contemporary results in science to reach
conclusions about philosophy itself.

 This branch of philosophy is handily called the
philosophy of science. Despite its straightforward
name, the field is complex and remains an area of
current inquiry. Philosophers of science actively
study such questions as:
 What is a law of nature? Are there any in non-physical
sciences like biology and psychology?
 What kind of data can be used to distinguish between
real causes and accidental regularities?
 How much evidence and what kinds of evidence do we
need before we accept hypotheses?
 Why do scientists continue to rely on models and
theories which they know are at least partially
inaccurate (like Newton's physics)?

 Though they might seem elementary, these
questions are actually quite difficult to
answer satisfactorily. Opinions on such
issues vary widely within the field (and
occasionally part ways with the views of
scientists themselves — who mainly spend
their time doing science, not analyzing it
abstractly).
 Despite this diversity of opinion,
philosophers of science can largely agree on
one thing: there is no single, simple way to
define science!
 Though the field is highly specialized, a few
touchstone ideas have made their way into the
mainstream.

 Here's a quick explanation of just a few concepts
associated with the philosophy of science, which you
might (or might not) have encountered.
 Epistemology — branch of philosophy that deals with what
knowledge is, how we come to accept some things as true,
and how we justify that acceptance.
 Empiricism — set of philosophical approaches to building
knowledge that emphasizes the importance of observable
evidence from the natural world.
 Induction — method of reasoning in which a
generalization is argued to be true based on individual
examples that seem to fit with that generalization. For
example, after observing that trees, bacteria, sea
anemones, fruit flies, and humans have cells, one might
inductively infer that all organisms have cells.

 Deduction — method of reasoning in which a
conclusion is logically reached from premises. For
example, if we know the current relative positions
of the moon, sun, and Earth, as well as exactly
how these move with respect to one another, we
can deduce the date and location of the next
solar eclipse.
 Parsimony/Occam's razor — idea that, all other
things being equal, we should prefer a simpler
explanation over a more complex one.
 Demarcation problem — the problem of reliably
distinguishing science from non-science. Modern
philosophers of science largely agree that there is
no single, simple criterion that can be used to
demarcate the boundaries of science.

 Falsification — the view, associated with philosopher
Karl Popper, that evidence can only be used to rule out
ideas, not to support them. Popper proposed that
scientific ideas can only be tested through falcification,
never through a search for supporting evidence.
 Paradigm shifts and scientific revolutions — a
view of science, associated with philosopher
Thomas Kuhn, which suggests that the history of
science can be divided up into times of normal
science (when scientists add to, elaborate on, and
work with a central, accepted scientific theory)
and briefer periods of revolutionary science. Kuhn
asserted that during times of revolutionary
science, anomalies refuting the accepted theory
have built up to such a point that the old theory
is broken down and a new one is built to take its
place in a so-called "paradigm shift."

Who's who in the philosophy of science
 If you're interested in learning more about
the philosophy of science, you might want
to begin your investigation with some of the
big names in the field:

Aristotle
 (384-322 BC)
 Arguably the founder of
both science and
philosophy of science.
He wrote extensively
about the topics we now
call physics, astronomy,
psychology, biology, and
chemistry, as well as
logic, mathematics, and
epistemology

Francis Bacon
 (1561-1626)
 Promoted a scientific
method in which
scientists gather
many facts from
observations and
experiments, and
then make inductive
inferences about
patterns in nature

 Rene Descartes
 (1596-1650)
 Mathematician, scientist,
and philosopher who
promoted a scientific
method that emphasized
deduction from first
principles. These ideas,
as well as his
mathematics, influenced
Newton and other figures
of the Scientific
Revolution.

 Piere Duhem
 (1861-1916)
 Physicist and philosopher
who defended an extreme
form of empiricism. He
argued that we cannot
draw conclusions about
the existence of
unobservable entities
conjectured by our
theories such as atoms
and molecules.

Carl Hempel
 (1905-1997)
 Developed influential
theories of scientific
explanation and theory
confirmation. He argued
that a phenomenon is
"explained" when we can
see that it is the logical
consequence of a law of
nature. He championed a
hypothetico-deductive
account of confirmation,
similar to the way we
characterize "making a
scientific argument"

Karl Popper
 (1924-1994)
 Argued that falsifiability is
both the hallmark of
scientific theories and the
proper methodology for
scientists to employ. He
believed that scientists
should always regard their
theories with a skeptical
eye, seeking every
opportunity to try to
falsify them.

 Thomas Kuhn
 (1922-1996)
 Historian and philosopher
who argued that the picture
of science developed by
logical empiricists such as
Popper didn't resemble the
history of science. Kuhn
famously distinguished
between normal science,
where scientists solve
puzzles within a particular
framework or paradigm, and
revolutionary science, when
the paradigm gets
overturned.

 Paul Feyerabend
 (1924-1994)
 A rebel within the
philosophy of science.
He argued that there is
no scientific method or,
in his words, "anything
goes." Without regard to
rational guidelines,
scientists do whatever
they need to in order to
come up with new ideas
and persuade others to
accept them.

 Evelyn Fox Keller
 (1936-)
 Physicist, historian,
and one of the
pioneers of feminist
philosophy of science,
exemplified in her
study of Barbara
McClintock and the
history of genetics in
the 20th century.

Elliott Sober
 Known for his work
on parsimony and
the conceptual
foundations of
evolutionary biology.
He is also an
important
contributor to the
biological theory of
group selection.

 Nancy Cartwright
 (1944-)
 Philosopher of physics
known for her claim that
the laws of physics "lie" —
i.e., that the laws of
physics only apply in
highly idealized
circumstances. She has
also worked on causation,
interpretations of
probability and quantum
mechanics, and the
metaphysical foundations
of modern science.

 ALL PHILOSOPHY OF SCIENCE BEGINS WITH
ANALYTICAL AND LOGICAL MATTERS
 Philosophy begins when students and teachers slow
down the science lesson and ask what these terms
means and what conditions are for their correct use.
 Philosophy is not far below the surface in any
scientific investigation.
 At a most basic level any text or scientific discussion
will contain terms such as
 Law, theory, cause, truth, knowledge, hypotheses,
 Model, explaination, observation, evidence, space,
field, etc.

LOGIC AND SCIENTIFIC REASONING
 Historical studies provide one context in which the
elements of good reasoning can be illuminated.
 Often the same historical examples can also exhibit for
students the “extralogical” dimension of science: the place
that commitment to metaphysics plays in the
determination of theory and research programs.
 Simple student experiments, “black box” exercises and
other activities where students guess unseen connection
from the behavior of seen variables can highlight most of
the logical fallacies and illustrate different interpretations
of events, but these activities do not raise the important
question of how science actually progresses and settles
upon the best of rival theories.

LOGIC AND SCIENTIFIC REASONING
 History does place thinking skills into the broader scientific
context: good scientific reasoning is not reducible to, or
captured by, the rules of formal logic, nor even by the “rules”
of informal logic.
 But the ability to discern interesting departures from logical
thinking on the part of great scientists is dependent upon
being able to recognize what formally correct and logical
thinking is in the first palce.
 The study of basic logic also assists with the promotion of
critical thinking and reasoning skills in school programs.
 Contributors to the Linda Crow (1989) volume, Enhancing
Critical Thinking in the Sciences, discuss specific strategies for
promoting tha amalgam of problem solving, decision-making,
creative thinking and critical thinking skills in the science
classroom.

THOUGHT EXPERIMENTS IN SCIENCE
 Thought experiments have had an important role in
the history of science – witness their use by
 Galileo, Leibniz, Newton, Carnot and, in this century, by
Einstein, Schrodinger and Heisenberg.
 Newton’s thought experiment of the rotating bucket
of water in an empty universe, which he believed
established existence of absolute space and motion,
is one of the most influential conceptual experiments
in the history of science.
 Einstein, in his “Autobiographical Essay,” states how
as a teenager he felt ill at ease about the then-
dominant physical interpretation of Maxwell’s
equations for electromagnetism

 Mach, in his Mechanics, draws attention to one of the great
thought experiments in the history of science, the thought
experiment in Day One of Galileo’s 1638 Discourses
Concerning Two New Sciences, which is directed at
disproving the Aristotelian thesis that bodies in free-fall
descend with a speed that is proportional to their weight.
 Mach’s view of science education was his advocacy of
thought experimentation.
 He said of thought experiments that “Experimenting in
thought is important not only for the professional inquirer,
but also for mental development as such”, not only the
student but “the teacher gains immeasurably by this
method”.
 Thought experiments enabled the teacher to know what
grasp students had on the fundamental concepts of a
discipline.

 Gottfried Leibniz’s 1686 refutation of the Cartesian
doctrine that momentum was the measure of “force
of motion,” or energy, is another influential thought
experiment in the history of science.
 Galileo offers a model of thought experiment for the
classroom. He begins with familiar circumstances, he
conceptualizes these in the old theory, in thought
he extends the familiar circumstances and then he
sees whether the old conceptualizations are
adequate to the new situation, where they are not, he
proposes new conceptualizations and new theories.

THOUGHT EXPERIMENTS AND SCIENCE EDUCATION

Ethics and Science Education
 The interconnection of science and ethics is particularly
clear in contemporary human genetics programs. The
Human Genome Project has three percent of its three-
billion dollar budget allocated to ethical and legal
ramifications
 In addition to the science of the ethical and policy issues
generated by genetic screening and other techniques
occasioned by the Genome Project.
 One hopes that teachers will strive to make ethical
discusiion as sophisticated as the scientific discussion.
This requires that teachers be familiar with the history of
ethical debate and the its major arguments. Teacher can
benefit, and their classes be enriched, by serious
grappling with these ethical and social quetsions.

Ethics and Science Education
 Values intersect with science in different ways.
 There are epistemic values that mainly guide the
scientific research.
 The scientific enterprise is embedded in particular
culture and values through individual practitioners.
 Values emerge from science, both as product and
process and can be distributed among several
cultures in the society.
 If it is unclear what counts as science, how the
process of confirming theories works, and what the
purpose of science is, there is considerable scope for
values and other social influences to shape science.

 Indeed, values can play a role ranging from
determining which research gets funded to
influencing which theories achieve scientific
consensus.
 For example, in the 19th century, cultural values
held by scientists about race shaped research on
evolution, and values concerning social class
influenced debates on phrenology (considered
scientific at the time).
 Feminist philosophers of science, sociologists of
science, and others explore how social values affect
science.

Philosophy math and science curriculum

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