Crispin Weston (crispinw@dircon.co.uk)
Mon, 16 Aug 1999 23:49:49 +0100
From: "Crispin Weston" <crispinw@dircon.co.uk> Subject: Learning in the 21st Century Date: Mon, 16 Aug 1999 23:49:49 +0100
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Ania,
Sorry to have been so long in replying, but I have been on holiday for the
last week.
<<the logic is predetermined but the strategies which it generates,
possibly, endless. So we have two factors in the game of thinking (and hence
education): logic and the possibilities that it legitimises
This sounds very circular to me: logic generates possibilities and
possibilities legitimise logic. If logic is my invention, then of course I
might invent some spurious logic which legitimises my own aims. If logic is
external
to me, I do not see how legitimacy comes into it.
<<If one were to push this dichotomy further, one would have to conclude
that maths is the sole field of abstract thinking.>>
The dichotomy I am suggesting is not between Science and Maths but between
induction and deduction: induction being the process of deriving abstract
principles from the observation of concrete particulars; deduction being the
process of deriving concrete particulars from abstract principles. The
difference in respect of our discussion is that induction does not
necessarily show a predictive power, while deduction does. I have already
accepted that even inarticulate infants deal in abstract concepts, so we
have no disagreement there.
<<As for Einstein's logic it is not private either since it took Newton and
guys before and after Newton for Einstein to organise the arguments in a way
that the it possibly allowed to create a different game.>>
Privacy does not imply authorship: private property may be bought, stolen or
inherited. What
I meant by 'private' was that Einstein's logic, according to your argument,
had no existence outside the perception of Einstein. Parallel logical
systems might exist in the minds of others who happen to share Einstein's
cultural inheritance, but, following the metaphor, there is no 'public
space'
in which an absolute, true logic can exist.
Your chess analogy surely does not fit. I accept that games have their own
invented rules. But the whole point of a game is that it does not pretend to
be able to predict the behaviour of the material world. This is the basis of
our everyday distinction between make-believe and real life.
<<Newton's rules are still valid in certain contexts>>
I think your use of the word 'valid' is a bit of a fudge. I would say
Newton's rules are *useful* in
solving problems where the errors which it introduces are infinitesimally
small. But the abstract propositions on which it is based are not *true*. To
be true, a proposition must not only appear to fit some contexts, but
actually fit all contexts.
<<had it been powerful outside the logic on which it builds and hence
all-encompassing, it could tell us why I am wearing today blue and not
green.>>
There is a clear error in your argument here. I do not claim that anyone
does or can know *all* things, and it therefore follows that I do not claim
that anyone has the ability to predict all things. You do nothing to
disprove my assertions by pointing out that there are things which I cannot
predict. All I assert is that *some* people can predict *some* things with a
greater degree of accuracy than could be accounted for by chance. That is
enough to prove the existence of a power of prediction. Do you deny the
truth of this assertion?
<<conclusions are context-dependent...>>
I agree. The fact that I have some abstract understanding about structural
engineering does not mean that I can avoid having to do my calculations
afresh for each new bridge that I design. The same abstract knowledge
produces different conclusions in different contexts. But the abstract
knowledge does not change and is *not* context-dependent.
<< and hence not revealing how things are but attempting to grasp the
relational organisation of different forces>>
I do not see the difference between 'how things are' and 'the relational
organisation of different forces'. If you read my reply to Mireille, you
will see that I describe statements about relationships as the most basic
kind of
abstract truth. Propositions come in the form 'x is y', which is a
description of a relationship between x and y. Logic is entirely about
relationships.
<<Einstein (some may call him physicist, just to show how relative things
are) >>
Einstein was a physicist as well as a mathematician. I do not see how
pointing to this multiplicity can be an argument for relativism. 2 is half
of 4 and a third of 6 and a lot of other things as well. This does not mean
that any of these statements are not true in an absolute sense. In any case,
academic disciplines are only human conventions and I do not claim that
knowledge of what constitutes Maths as distinct from Geography could, of
itself, give anyone any predictive power whatever.
<<but if you follow my model, then it reveals that all models are subject to
revision>>
I agree with this. The fact that I believe in truth and the possibility of
knowledge does not mean that I think that anyone can be sure that their
beliefs do in fact constitute knowledge. We deal in imperfect models whose
truth is at best provisional. But our models *aspire* to reflect truth as
accurately as possible and some appear to us to reflect truth more
accurately than
others. For example, the model which has it that the moon is made of blue
cheese appears to be a poor one (i.e. untrue).
Incidentally, when you say that your model 'reveals' something, it sounds to
me as if you believe that what your model 'reveals' is true. Or do you mean
that your model reveals nothing about the subject of the model, but
only something about your own psyche and cultural inheritance (which
revelation, of course, is itself not true)?.
<<[models] cannot be revised without being understood within the condition
of the contexts which produced them>>
I am more half-hearted about this. Do we have to watch apples falling off
trees to understand the principle of gravity? What I would accept is that
there may be logical prerequisites to understanding: I can hardly learn how
to do long division without knowing how to do subtraction first. I suspect
you, not believing in logic, might prefer the word 'context' to 'logical
prerequisite'.
<< [objectives for education]
(a) allow for understanding in terms which do not obscure the conditions
which declare things valid, and
(b) allow for and value subversion: an informed change which does not lead
to
destruction>>
'Valid' is what I describe above as your fudge for 'true'. Clear and simple
propositions are true or not true unconditionally. If a proposition is
unclear then it may indeed be true in certain circumstances but not others
(e.g. the statement that gravity is of such-and-such a force omits to
specify that this is true of the earth but not of the moon). If a
proposition is complex then parts of it may be true and parts of it may be
unclear or false.
You of course will not accept this view. So let me push you a little further
on your formulation. When I say that I believe something is 'true', you
prefer to say that it is 'valid given certain conditions'. Can you then
answer me this: is a statement in the form 'x is valid given conditions y,
y1, y2...', true? Let me anticipate your answer: --"No", you will reply,
"The statement 'x is valid given conditions y, y1, y2...' is valid given
conditions z, z1, z2..., which statement is itself valid given conditions a,
a1, a2, etc.". I think you must agree that your formula is infinitely
recurring. When you make a statement, do you hold in your head this infinity
of conditions, or do you *of necessity* 'obscure the conditions which
declare things valid'? Your rule (a) is impossible to observe.
I could of course agree with (a) if you would allow me to re-phrase it,
changing 'the conditions which declare things valid' to 'their proofs', or
to be less categorical, 'their evidential basis'. But I have a feeling that
that is not what you meant.
I am not sure I understand (b). If it means that students should not have
learning imposed on them without their agreement, then I would like to agree
because I see learning to think for yourself is an important education goal.
But as an absolute principle, I do not think the rule is an impossible one.
Take the early years. A baby picks up its value system at its mother's
breast and can hardly be expected to make informed decisions about its
learning. Is this early learning wrong? (And if it is wrong, I must not
forget to ask what are the conditions which declare it to be wrong).
<<or between your belief about what it lets you do>>
No. As discussed above, Newtonian physics is all that I am ever likely to
need in the physics department (so it is useful), but I am told that its
propositions are not true.
<<external to me means: ? whether it corresponds to the arguments as we see
them fit or as they are>>
As they are.
<<Do you believe that there is female/male distinction...>>
Yes.
<<...and why?>>
Why do I believe in the distinction or why do I believe there is such a
distinction?
Why do I believe in the distinction? Because I see evidence for it in the
bodies and behaviours of humans and animals. The existence of such a
distinction appears to me to be incontrovertible (which makes me all the
more delighted at the possibility that this perception of mine might be
disproved). You may want to organise society in such a way that the sexual
distinction is not reflected in society, or genetically to modify the human
race so as to eliminate all sexual distinctions, but these are quite
different.
Why do I believe there is such a distinction? I think it has
something to do with the evolutionary advantage of sexual reproduction, the
division of labour, particularly in relation to the rearing of young, and
the management of aggression so as not to be socially destructive. I am
quite sure that anthropologists, biologists or other experts could produce a
fuller answer to mine.
<<You yourself talked about prediction and hence STATISTICS rather than
anything else.>>
No. Statistics are normally (perhaps inevitably: I do not know) based on
empirical research. I talked about
deduction, which is quite different. I do not think Einstein said that
particles had a 60% chance of behaving in such and such a way as they
approached the speed of light: he said they *will* behave in such and such a
way. And his prediction was not based on a single observation of any
particle travelling at these speeds.
<<I will wait for knowledgable conclusions as to how we can record knowledge
onto students.>>
'Transmission' does not imply a passive recipient. If we play catch and I
throw a ball to you, you must actively catch it if the transmission is to
work. What I mean by transmission is that the learning (the ball) comes from
somewhere: either the teacher, or the environment, either cultural (learning
from peers) or physical (learning to ride a bicycle). It is not invented by
the catcher.
I said...
<< To speak in a more positive sense, what I am in favour of is clarity
about our educational objectives and in the measurement of student progress
towards those objectives (which is not to say that total clarity is
achievable, but that it is worth working towards).>>
You replied:
<<I agree and I will maintain that my points (a) and (b) were a good start
worth their expansion.>>
I agree that you show no timidity about defining educational goals. But to
return to a point I made earlier, do you think it is *true* that your
principles (a & b) are good ones? If yes, then I do not understand how you
can describe things as true when you do not believe in truth. If no, then I
do not see how you can honestly advocate principles which you do not believe
to be true. If they are true only for you, then why should I be interested
in them?
I said <<I think it is for the clients of the education system (students,
parents, employers, government) to specify aims:>>
You replied <<hmm, how do we ensure though that the context of these
conclusions is not limited and hence limiting and, in the end, damaging?>>
How do we ensure that the educational objectives pursued by *teachers* are
not limited and, in the end, damaging? There are no guarantees here. I do
not accept that teachers have any particular expertise in the ends of
education. I think dialogue is important and, as the experts in educational
process, teachers having a role in informing that dialogue. Not from on
high, saying 'this is what education should be about', but more along the
lines of 'if you do (a), then the consequence will be (b)', as a civil
servant might inform a minister, or a judge inform a jury. Take another
parallel: that of medicine. If ask the doctor to cure my illness, I do
not want a lecture on what levels of pain I should be prepared to endure. I
would do better to go to a priest for guidance on that subject. I expect the
doctor to ask me what I want: (longevity vs. maximum
pain relief, perhaps) and then to tell me how I can achieve *my* ends.
I said <<I would like to see more technocrats in education, fewer
ideologues.>>
You replied, <<technocracy is idealogy of arrogance and ignorance and I am
certain that on a closer look you would yourself run as far as possible from
such a means:-)>>.
I cannot resist the temptation to ask again, how someone who does not
believe in truth, can nevertheless believe in ignorance?
Having sent my mail, I decided I should not have finished on such a
rhetorical but provocative note. Both technocrat and ideologue have
pejorative uses. But I tried to use the two terms in a more exact and
non-pejorative context: I define a technocrat as someone concerned with
means, and an ideologue as someone concerned with ends. This phrase, then,
is just a summary of the argument above.
I assure you, Ania, I do try to run from arrogance. The chief result of a
belief in truth is the constant awareness that one might be wrong. Is that
not conducive of humility? If I am the author of my own truth, then I can
never be wrong: that, surely, is the seed of arrogance!
Best wishes,
Crispin Weston
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