4. • A student who knows that the
argument on pages 64-73, but
who does not feel the force of
its logic, will lack all motivation
to internalize the rules or use
them on other occasions.
• The difference that validity
makes to an argument must be
vividly real to a student if that
student is to see why it matters.
• A student who does not feel the
badness of a bad argument is
unlikely to produce many good ones.
After all, good arguments usually
start out as not-so-good arguments
that don‟t feel quite right.
5. LARVOR
1. Contrast Philosophy with Mathematics using the
work of George Polya
2. Criticism against mainstream English-speaking
Philosophy by saying that it is ill-equipped to think
about the aesthetic and emotive aspects of the
experience of doing and learning Philosophy by
blaming the Enlightenment Era
3. Criticism against the viewpoint that humans are
naturally rational. By rational, he means that
something that is like dispassionate, formal
rationality on display in the end-products of the
mathematical sciences. (R.G. Collingwood)
6. MATHEMATICS VS. PHILOSOPHY
• In Mathematics, there is a
standard distinction between
seeing the validity of the
individual steps in a proof, and
understanding the proof as a
whole.
7. POLYA Desires of an Intelligent
reader of Mathematics:
1.Present step of the
argument is correct.
2.Purpose of the present
step.
• Present step- purpose is to advance the
overall proof strategy
• Connotes that the intelligent reader
must have strategic overview
• Without the strategic overview, even
the most intelligent reader in math
may become bored and dismayed
and it loses the thread of argument
8. BUT, IN FORMAL DERIVATION OF A
MATHEMATICAL THEOREM…
• The purpose of a step may not be clear until
the end, making it still a mysterious one on
how did a certain theorem and proof came to
be.
• May compel assent, but does not answer the
second intelligent reader‟s second
requirements
• Offers no heuristic lessons to students.
• Polya recommends to tell the story on why a
certain theorem or proof came to be.
9. • For Polya, mathematical problem
solving requires a n appropriate
motivational and affective condition.
• You cannot practice the discipline
without a feel for the subject-matter,
where „feel‟ has two senses: an
intuitive grasp and a caring concern.
ax + b
10. PHILOSOPHY
• Like Mathematics,
philosophy demands
commitment, readily
familiar with the
subject-matter and a
vivid sense of logical
relations among its
elements.
• The difference though
is that Philosophy
uses INTUITION.
11. INTUITION MEANS….
• the state of being aware of or knowing
something without having to discover or
perceive it, or the ability to do this
• is the power of obtaining knowledge that
cannot be acquired either by inference or
observation, by reason or experience. As
such, intuition is thought of as an original,
independent source of knowledge, since it is
designed to account for just those kinds of
knowledge that other sources do not provide.
Knowledge of necessary truths and of moral
principles is sometimes explained in this way.
12. ROLE OF INTUITIONS
1.In many philosophical enquiries, pre-
theoretic intuition serves as a test-bed
or evidential field.
2.In addition to using their intuitions
heuristically, philosophy students must
also examine their more spontaneous
reactions to philosophical questions.
13. How do you perceive
the TRUTH?
It is possible that students can understand a question like
this, understand why it matters, and yet no intuitions tugging
them towards one solution or away from another.
14. • Most likely, it is that the students, while
they have feelings about certain
concepts about the truth, do not have
intuition about metaphysics or
semantics to guide their next moves.
• Lacking a sense of direction on the
technical question, they sit still and wait
for guidance.
• Student becomes passive, waiting only
for an instruction and waiting to be
spoon – fed.
• Cannot express their intuitions about
the metaphysics of time for the same
reason that they cannot follow an
instruction to „Open the lid of your
harpsichord.‟
• “Sorry, Sir, I don‟t have one of those.”
15. PHILOSOPHY STUDENTS
• In Philosophy, students
who lack spontaneous
responses to the matter
in hand cannot
participate.
• Articulation and
examination of one‟s
spontaneous intuitive
responses is central
activity but occupies to
much time.
16. SOLUTION…
• Students of any subject must
develop a sense for the
characteristic arguments of their
discipline. They should feel the
„hardness of the logical must.
• This is mainly true in Philosophy
because logic is part of our
subject-matter.
17. • The Philosophy student
must have an intuitive
grasp of logical
structure that is
sufficiently robust for
the student to test
logical theory against it.
• Example:
• A logic student should
feel both the oddness
of material implication
considered on its own
and the neatness of
the system(s) of which
it is part.
18. TO THE TEACHER OF PHILOSOPHY
• How to cultivate those
sense ability of the
students?
• What exercise can we
devise to make
philosophical concepts
and logical relations vivid
to them?
19. • Teachers should offer students problems
at the correct level of difficulty that arise
naturally.
• The teacher should check that the student
understands the problem by asking: What
is the unknown? What are the data? What
are the conditions? Further support should
take the form of general heuristic
questions, such as „do you know a related
problem?‟
• With enough practice of this sort, the
student may internalize the heuristic
questions and develop the confidence,
commitment and intellectual stamina to
tackle more demanding problems.
Poly • “Teaching to solve problems is education
of the will.”
20. THE KNIGHT OF REASON
• English speaking heirs to
the analytic tradition
•They see Philosophy as
something that is nothing
but the activity of
clarification; where other
disciplines have a
definitive subject-matter,
Philosophy has a mission
– to be the knight of clarity
21. • Mystery Monger – a “dealer or
promoter” of “mystery” and
doubtful arguments
• Intellectual chicanery - deception
or trickery, especially by the clever
manipulation of language
22. DERRIDA
• Most zealous clarifiers regard
Derrida as a mystery-monger of
the worst sort, that Philosophy is
supposed to expose and
eradicate.
• Derrida- focused on language. He
attempted to show that language is
consistently shifting and that
traditional way of reading makes a
number of false assumptions
about the nature of texts.
• Suggest that clear speech is
impossible, or at the very least,
indicative of shallowness.
• Derrida fall short of the prevailing
24. Feyerabend, Duhem and
Polanyi
• Insist on the importance of
feeling and passion in
Science
25. FEYERABEND
• Science will not progress if
scientists always approach
their hypotheses with
perfectly disinterested
rationality.
26. PIERRE DUHEM
• Introduced feeling into the very
logic of science.
• Rather than focussing on the
scientist‟s passionate
commitment to an idea, Duhem
emphasized the scientist‟s
feeling for the phenomena,
which he called “good sense.”
27. Good sense – the scientist‟s acquired
knack of judgment, like a mechanic‟s
ear for changes in the tone of an engine
or a doctor‟s ability to diagnose a chest
complaint from the pattern of wheezes
and rasps.
• Experts require trained eyes and ears
as well as a disciplined brain.
28. THOMAS KUHN
• Prevailing scientific theories of the time
influence the training of the scientist‟s
senses and intellect
• Scientist‟s convictions affect the way he
or she perceives the evidence
• The defeat of one scientific theory by
another is not entirely a logical process;
it requires a kind of conversion
experience in the scientific community.
29. DEFENDERS OF SCIENCE
• Rejected as heresy
the suggestion that
feeling plays an
essential role in
scientific practice
because it seemed
to undermine the
rationality of
science.
30. • If feelings
play an
important role
in scientific
practice then
science is not
wholly
rational.
31. WHAT IS WRONG WITH THE ENLIGHTENMENT?
• It makes formal rationality seem
like something we already have,
which we only need use more
carefully.
• Becoming rational largely consists
in removing self-imposed
impediments to the use of one‟s
reason.
• Assumes that formal rationality is
already present in students and
lecturers alike, and needs only to
be drawn out and exercised.
• Experimental pshychology has
shown this to be false.
32. • We humans live first
in a world of
connotations and
LARVOR associations, which
are only later
resolved into
thoughts, facts,
hypotheses and
suchlike.
33. • Dispassionate formal
rationality is not
natural to us, even
when we are
engaged in rational
activities.
34. • Scientists and
mathematicians write up
their theories and
explanations, their
theorems and proofs in
dispassionate language,
but the scientists and
mathematicians must be
passionate, or they would
subject themselves to the
hard rigour of scientific
rationality.
35. COLLINGWOOD TO THE RESCUE
• In order to have a good
foundation in teaching
philosophy and to set aside
the Enlightenment attitude
towards dispassionate
rationality, Larvor used R.G.
Collingwood‟s view of
language written in his
Principles of Arts.
36. PHILOSOPHICAL PSYCHOLOGY
• Sustains an electrostatic metaphor: experiences
and activities (including intellectual experiences
and linguistic activities) have an “emotional
charge.”
• Modern education encourages us to attend to the
sensation at the expense of the emotion
ex: Highly educated adults - can‟t hardly notice
the emotional charge of most of their
sensory experience
Artist and Children – feel the emotional
charge of their experiences keenly.
37. AIM
• To develop a theory of
imagination. Because for
Collingwood, imagination is
the capacity that allows
creatures who feel to
become creatures who
think, write books and
create art.
38. • Like Wittgenstein,
Collingwood claims that
language begins as
emotional expression,
and only later becomes a
vehicle for the
articulation of thoughts.
39. EXAMPLE
No obvious emotive
charge
Phil Younghusband
H2
O
- It will express an emotion
– perhaps boredom or
excitement
- As soon as we take up
„symbolism for some
Maam Patty and Maam purpose, we give it an
Corcoro
emotional charge.
40. CLASSROOM TIPS
1.Take time to respect and develop the
intuitions that students already have
2.Tell the students what is going on
3.Design exercise to induce suitable
intellectual experiences
4.Ensure that all your material is alive
5.Retrace the route to here