Is this a valid explanation of my use of
inclusional, dialectical and propositional logics in my living theory of my
educational influence in my learning, in the learning of others and in the
learning of social formations? Do my values carry the hope of Ubuntu for the
future of humanity?
Jack Whitehead, University of Bath,
DRAFT 13 February 2004
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Joao Roe |
Nick Selley |
Margarida Dolan |
i) In who we are and in what we are doing, as shown in the video-clips,we
embody an infinitude of knowledge that we can add to and transform as we live,
learn and research our lives of enquiry.
ii) As we reflect on our experiences and our contributions to the conversation
of the 12th January we experience a feeling of well-being as we experience
the expression of our life-affirming energy and inclusional ways of being.
iii) By viewing ourselves through the lens of a digital video-camera and including
these images in our living educational theories of our own learning and educational
influences we are making original contributions to educational knowledge.
I am thinking here of living educational theories that have the capacity to
explain the education of individuals, the educational influences between individuals
and the education of social formations. I am also thinking of these contributions
in terms of Donald Schon’s (1995) point about the need for a new epistemology
for the new scholarship. In my understanding of an epistemology it is important
to understand the logics in a claim to knowledge (as well as understanding
the unit of appraisal and standards of judgement for use in testing the validity
of the claim to knowledge).
At this point I want to acknowledge a political intent in my writings. To
explain this political intent I will draw again on Lumley’s ideas where
he is writing about understanding influence in terms of a ‘semiconductor’
that can shut down the flow of current in one direction while permitting it
in another. The connection I am making from Lumley’s writing to my own
political intent is in influencing the education of social formations. In
this education I want to open up the flow of values from ourselves as ‘assertive
agents’ that carry hope for the future of humanity and I want to understand
how to close down the flow of the values that do not carry such hope:
“….it makes much more sense to make the flip on influence that
opened the door to semiconduction technology (material that both 'conducts'
and 'resists' at the same time). That is, a medium 'accommodates' an assertive
intrusion at the same time the assertive agent intrudes, but the accommodation,
as in the 'togetherness' descriptions above, is a bigger concept than can
be dealt with by assertion since it is (it can be) purely relational. What
the discovery of the semiconductor effect realized is that instead of describing
the current flow in terms of the movement of charged particles (electrons),
the dynamic could more comprehensively be described in terms of the reconfiguring
of accommodating 'holes' so that one thought of positively charged hole-flow.
When a voltage is applied across a semiconductor, it can shut down the flow
of current in one direction (as in a 'diode') which is hard to explain in
terms of behaviour based on the movements of electrons. That is, while the
holes can open up for electrons that want to move in one direction, they will
not open up for electrons moving in the opposite direction so in the case
of a potential field that is alternating, the current, rather than being alternating
is 'rectified' and only goes in pulses in one direction.
The point is, that while the asserting of a material constituent cannot embody
in itself 'direction' (a reference frame is required for that), the accommodating
quality of relational space can have directionality and therefore it can 'channel'
the flow of assertive constituents. in fact, a collective can co-creatively
shape accommodational channels for its own constituents, a self-referential
organizational ability that minorities argue is being used all the time, but
which propositional logic, the underpinning of our justice system, is innately
incapable of addressing”
My political intent is in developing these web-based communications as a contribution
to interconnecting and branching networks of global communication. I am thinking
of communications that send pulses of values and understandings that carry
hope for the future of humanity and work to prevent the flow of the values
that negate this hope.
Perhaps I can communicate some of the meanings of this political intent by
comparing the pleasure and hope in the inclusional ways of being and communicating
in the video-clips, with Alon Serper’s response to the deaths in Jerusalem
of the 29th January 2004:
I am very isolated for some of my Israeli friends will be very upset that
I
mention the Palestinian casualties [mostly gunmen] here and would regard it
as very offensive and unsafe. Some of my Palestinian [and some in the
radical left] friends will feel the same for mentioning my disgust and
hatred of suicide bombings.
And I feel like telling and screaming to all of you here - You talk about
safe and enriching, love and compassion, communication, inclusionary,
humanity, ubuntu, beautiful word of harmony and love etc etc, where there
is a whole world out there where infants, children and elderly are blown up
into undefined pieces which are hanged and splattered on trees, on cars, on
balconies and on windows - and children and adolescents are driven on by
tanks I have seen it all myself in my own eyes. But, then, I shall be
pretentious, preacher, pompous and a pedagogue. And you may be upset and
feel I am offensive, not safe and enriching
In contributing to the education of social formations I am thinking of enhancing
the flow of values such as those being expressed in the inclusional ways of
being shown in the video-clips. I am thinking of closing down the flow of
values that constitute a whole world out there where infants, children
and elderly are blown up into undefined pieces which are hanged and splattered
on trees, on cars, on balconies and on windows - and children and adolescents
are driven on by tanks.
I believe the availability of the interconnecting and branching networks of
this web-based communication with its visual narrative is contributing to
the flow of values that carry hope for the future of humanity. The visual
narrative also shows that it is possible to live these values in a particular
context. From this possibility I am seeking to develop the probability that
such values can be lived more widely in those contexts that at present are
not carrying enough hope for the future of humanity. Hence my desire to see
the visual narratives of living educational theories that carry such hope,
extend their influence into the education of social formations within which
such hope is needed.
As I develop a living inclusional logic of education I am also using a living
dialectical logic (Naidoo, 2003) as well as a propositional logic.
A Living Dialectical Logic of Educational Enquiry
In my understanding, contradiction is the nucleus of dialectics. Acceptance
of contradictions in the dialectical logic of living theories, contrasts with
the propositional logic described below with its law of contradiction that
eliminates the possibility that mutually exclusive statements can be true
simultaneously. My understanding of contradiction in dialectics is grounded
in the experience of contradictions that are embodied in who I am and what
I do. I am thinking of experiences in which I see myself as a living contradiction
in that I hold certain values, while at the same time I can see myself, with
the help of video, negating them in my practice. At these moments, when I
experience myself as a living contradiction, I hold together mutually exclusive
statements such as ‘I am free’ ; I am not free’; ‘I value
enquiry learning’; ‘I am negating enquiry learning’. As I experience
myself as a living contradiction I often feel a desire to improve what I am
doing in the sense of living my values more fully in my practice. Questions
form of the kind, ‘How do I do this better?’ My imagination creates
possibilities that could enable this to happen. I chose a course of action
and act. As I act I gather data that I can use to make a judgement on the
effectiveness of my actions in living my values more fully in what I am doing.
I evaluate the effectiveness of my action and modify my concerns, ideas and
actions in the light of my evaluations (McNiff, Lomax & Whitehead, 2003).
My use of dialectical logic in explanations of my educational influence is
focused on living contradictions and the process of transforming the experience
of embodied values into communicable, living standards of judgement for testing
the validity of my explanations of my educational influence. As I ask, research
and answer questions of the kind, ‘how do I improve what I am doing?’
I clarify the meanings of my embodied values in the course of their emergence
in my practice. In an earlier work on the growth of educational knowledge
(Whitehead, 1993) I clarified the meanings of my embodied value of academic
freedom in the course of its emergence in the face of pressure to constrain
it in my workplace.
My living educational theories are constituted by the descriptions and explanations
I construct for my own learning in my educational enquiries. My understanding
of dialectical logic goes back to the dialogues of Plato on poetic inspiration,
particularly Phaedrus, where Socrates and Phaedrus are talking about the meaning
of love. Socrates explains his idea that there are two ways in which we come
to know. We break things down into particulars (he says that this should be
in a manner which nature directs rather than in the manner of a bungling carver!)
and that we can hold things together in general ideas. Socrates says that
those who can hold both the one and the many together he follows as if in
the path of a God and he refers to the art of holding them together as the
art of a dialectician. The tension between dialectical and propositional logics
can be seen in contrasting this notion of dialectics with Aristotle’s
ideas from his work ‘On Interpretation’ in which he expresses his
law of contradiction that we have to chose whether a person has a characteristic
or not. In Aristotle’s Logic we cannot hold two mutually exclusive statements
as being true simultaneously. This logic has dominated the logic of theory
in Western Academies over more than 2000 years. It may be time to extend the
logics available to theory creators! Boyer (1997) has already made the case
for extending our understandings of scholarship so that they include the scholarships
of application, integration and teaching. My own work is intended as a contribution
to a scholarship of educational enquiry.
Naidoo (2004) in her living dialectic logic engages with the dialectics of
Ralph Stacey. Stacey draws on similar historical developments in dialectics
to my own but then stays within the Hegelian dialectic. I think Ilyenkov is
correct in accepting Marx’s critique of Hegelian dialectic as he asks
‘if an object exists as a living contradiction what must the thought
(statement about the object) be that expresses it?’. My own view (Whitehead
1999) is that Ilyenkov failed to answer his question before he died because
he saw the answer resting in his ‘writing logic’ rather than seeing
the significance of living logics in answering his question about living contradictions.
As well as using a living dialectical logic in my explanations of educational
influence, I also value the integration, into these explanations, of insights
from theories from disciplines other than educational enquiry that exclude
contradictions between statements. I am thinking of insights from the disciplines
of philosophy, psychology, sociology, history, economics, politics, management
and theology. In valuing such insights I do not want to be understood as accepting
the explicit exclusion of contradiction in the Aristotelean form of rationality,
so eloquently expressed by Karl Popper, that rejects the validity of dialectical
theories on the grounds that because they contain contradictions then they
are completely useless as theories.
Using propositional logic and understanding its use in rejecting dialectical
theories.
One of the tensions in my use of propositional logic in explanations of my
educational influence is that it explicitly excludes the legitimacy of dialectical
theories because they contain contradictions between statements. Popper supports
this exclusion in his use of two laws of logical inference to demonstrate
that any theory that contains a contradiction is entirely useless as a theory.
This demonstration shows how the acceptance of contradiction can lead to the
acceptance of any statement as true. My intention in presenting this reasoning
in the Appendix is to show that I value both my capacities to be able to think
within this form of arguments, while recognising that its rejection of contradictions
between statements leads it to reject the possibility of including in theory
the embodied living contradictions of practice. Hence it is not the most useful
logic to use in making sense of living educational theories and a scholarship
of educational enquiry.
In my communications above I think that I have been using inclusional, dialectical
and propositional logics. I value propositional logic with its law of contradiction
that refuses to accept that two mutually exclusive statements can be true
simultaneously. This logic structures every theory I have encountered in each
discipline of education such as the philosophy, psychology, sociology, history,
economics, politics management and theology of education. My education has
benefited from insights from each of these disciplines. This logic does not
however structure the discipline of my own educational enquiry and life in
education. It contributes to, without dominating, the discipline of my educational
enquiry from the ground of my inclusional and dialectical ways of being.
In my use of propositional logic also I bear in mind Karl Popper’s rejection
of dialectical claims to knowledge. Popper believes that such claims are,
‘without the slightest foundation. Indeed, they are based on nothing
better than a loose and woolly way of speaking’ (Popper, 1963, p.316).
As there are many adherents to this view in the Academy and beyond it is well
worth understanding the logic of the argument that leads to this conclusion.
As such arguments could be used to support the form of intellectual terrorism
described by Lyotard it is well worth understanding both the argument and
its limitation in the development of living inclusional logic of education.
Lyotard writes about ‘terror’ in relation to repression of ideas
by institutions of knowledge. I have certainly felt the disciplinary power
of my university in ways which resonate with Lyotard’s analysis:
“Countless scientists have seen their ‘move’ ignored or
repressed, sometimes for decades, because it too abruptly destabilized the
accepted positions, not only in the university and scientific hierarchy, but
also in the problematic. The stronger the ‘move’ the more likely
it is to be denied the minimum consensus, precisely because it changes the
rules of the game upon which the consensus has been based. But when the institution
of knowledge functions in this manner, it is acting like an ordinary power
center whose behaviour is governed by a principle of homeostasis.
Such behaviour is terrorist…. By terror I mean the efficiency gained
by eliminating, or threatening to eliminate a player from the language game
one shares with him. He is silenced or consents, not because he has been refuted,
but because his ability to participate has been threatened (there are many
ways to prevent someone from playing). The decision makers’ arrogance,
which in principle has no equivalent in the sciences, consists of the exercise
of terror. It says: “Adapt your aspirations to our ends – or else”.
(Lyotard, p. 64. 1984)
While my writings tend to focus on the importance of exploring living contradictions,
it is sometimes important to understand dead contradictions. Popper wrote
extensively about the open society and its enemies. Given my use of living
inclusional, dialectical and propositional logics of education, my own belief
is that Popper can be seen as a dead contradiction in that he believed himself
to be supporting a logic of an open society, while at the same time the logic
was supporting a closed academic society that excluded both dialectical and
inclusional logics. Because others are using Popper’s reasoning to reject
dialectical theorising it is wise to understand his reasons, using two laws
of inference for claiming that ‘A Theory which involves a contradiction
is therefore entirely useless as a theory ‘(Popper, 1963, p.317) I have
set out the form of his argument in the Appendix so that you can see its internal
consistency.
My reason for being clear about Popper’s argument is because I value
my use of propositional logic in arguments and other forms of thinking where
the meanings of statements are clear, shared and unambiguous. Such understandings
are also useful in responding to criticisms that exclude the validity of the
experience of living contradictions in developing dialectical and inclusional
understandings and explanations of educational influence. It often helps to
show that one understands the assumptions in the others’ criticism. My
education has also benefited greatly from insights I have understood from
propositional theories and I acknowledge this as I draw on such insights in
my other publications.
I feel sure that I am going to learn more from your responses about the validity
of the logics I use as well as about the nature of my educational influence
and how it might be extended and improved. Having only recently started to
clarify my understanding of living inclusional logics it is too early to make
judgements on their educational influence in the learning of others, in the
creation of their living educational theories and in the education of social
formations. Yet, I hope that your originalities of mind and critical judgement
will engage with this contribution in ways that you find helpful in your own
enquiries.
In relation to the contemporary politics of Educational Research I see the
highest five * ratings in the last Research Assessment Exercise going to two
Departments of Education whose Education Research is dominated by social science
methodologies and the Aristotelean logic of publications in text-based refereed
journals. One implication of a visual narrative is that the education of the
social formation of the Academy could be transformed through its educational
judgements. I am thinking of a transformation from the Aristotelean logic
of domination, as it is represented in present judgements on the quality of
educational research, to the living inclusional logic in the visual narratives
of living educational theories that are being created from educational enquiries
into inclusional ways of being. I am using the African way of being of Ubuntu,
as an inclusional way of being, to emphasise the postcolonial nature of my
educational project (Murray, 2004).
Using propositional logic to exclude dialectical theorising
Logical inference proceeds according to rules. An inference is valid if the
rule of inference to which it appeals is valid. A rule of inference is valid
if, and only if, it can never lead from true premises to a false conclusion.In
his demonstration that theories that contain contradictions between statements
are entirely useless as theories Popper uses two rules of inference. To explain
the first rule he introduces the idea of a compound statement. Compound statements
such as: ‘Paul is white and Jack is black’, ‘Either Paul is
white or Jack is black (but not both)’,
‘Paul is white and/or Jack is black’, are composed of the component
statements ‘Paul is white’; and ‘Jack is black’.
The uselessness of dialectical theories (theories that contain contradictory statements) is, according to Popper, demonstrated with the help of compound statements that are true if and only if at least one of its two components is true.
For example the assertion ‘Paul is White and/or Jack is Black’ is one which will be true if and only if one or both of its component statements are true; and it will be false only if both of its component statements are false.
As Popper says it is customary in logic to replace the expression ‘and/or’ by the symbol ‘v’ (to be pronounced ‘vel’) and to use such letters as ‘p’ and ‘q’ to represent any statement we like. Hence, in relation to the above assertion we can then say that a statement of the form ‘p v q’ will be true if one at least of its two components, p and q, is true.
The first rule of inference
The first rule of inference for demonstrating that a theory which is constituted by compound statements that contain a contradiction is entirely useless as a theory is:
1) From a premise p, such as ‘Paul
is White’ any conclusion of the form ‘p v q’ such as Paul is
White v Jack is Black’ may be validly deduced.
That this rule must be valid can be seen at once if we remember the meaning
of ‘v’. This symbol makes a compound statement true whenever at
least one of the components is true. Accordingly, if p is true, p v q must
also be true. Thus our rule can never lead from a true premise to a false
conclusion, which means that it is valid. So, our first rule which is stated
‘from the premise p we obtain the conclusion p v q can also be written
as:
p
p v q
The second rule of inference
If we denote the negation of p by ‘non-p’ (p = Jack is Black; non-p = Jack is not Black) then the second rule can be stated as:
‘From the two premises non-p, and p v q, we obtain the conclusion q.’
This statement of the rule can be represented by the symbols:
non-p
p v q
q
The validity of this rule can be established if we consider that non-p is
a statement which is true if and only if p is false. Hence, if the first premise
non-p, is true, then the first component p of the second premise is false;
Thus:
if both premises are true, the second component of the second premise must be true; that is to say, q must be true whenever the two premises are true.
In reasoning that, if non-p is true, p must be false, Popper makes implicit use of the ‘law of contradiction’ which asserts that non-p and p cannot be true together.
Using our two rules in the following argument we can infer from a couple of contradictory premises any conclusion we like and hence demonstrate the uselessness of any theory that contains contradictory statements:
Assume we have the two contradictory premises – say
a) Paul is white
b) Paul is not white
From these two premises using the two rules of influence any statement –
for example, ‘Jack is Black’ can be inferred as follows
From the first premise (a) we can infer, in accordance with rule (1) , the following conclusion:
c) Paul is White v Jack is black.
Taking now (b) and (c) as premises, we can ultimately deduce, in accordance with rule (2).
d) Jack is black.
It is clear that by the same method we might have inferred any other statement we wanted to infer; for example, ‘Jack is not black’, ‘Jack is good’, ‘Jack is not good’. We may thus infer not only every statement we like, but also its negation, which we may not like.
Popper’s conclusion is that “We see from this that if a theory contains a contradiction, then it entails everything, and therefore, indeed, nothing. A theory which adds to every information which it asserts also the negation of this information can give us no information at all. A theory which involves a contradiction is therefore entirely useless as a theory.” (Popper, 1963, p. 317)
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