Andy,
It was certainly not my intention to merge inference in the philosophical sense and statistical inference. In fact, in the paper, we tried to warn the reader for possible confusion, but apparently not clear enough.
I asked Jan Derry about how Brandom is influenced by Hegel. She wrote to me:
"Brandom argues that Hegel developed a non-psychological conception of the conceptual in the Phenomenology where conceptual content is articulated by determinate negation. He sees himself as following this line in his own work e.g. when the parrot says red it only reacts to the stimuli, the human utterance of red already entails not green, not blue etc. - the inferential relations are prior to the designation. Of course, many Hegel scholars resist any argument that Brandom is following Hegel."
See further Derry's paper on rationality, a draft is here; http://eprints.ioe.ac.uk/1138/1/Derry2008Abstract49.pdf
You are right that an educational focus on inferences is not sufficient; it is about the type of inferences. As you write, there are inferences from "the mean is 6" that are very boring, schoolish etc. What I should perhaps have emphasized more is that we were after inferences that statisticians and knowers of statistics make with airthmetic means, such as judging the difference between two groups - something that receives little attention in middle school and which students are often not inclined to do. So we stimulated students to engage in more authentic problems in which they can see the need to use the mean (and other statistical concepts) in fruitful ways and linked to contextual meaning. I don't see the dressage here! In fact, the standard approach of addressing all concepts and representations one by one and testing them with some simple calculations is much more drill-and-practice.
I agree that there is no judgement without concept and vice versa. But we noticed that if we stimualted students to make observations/judgements that their concepts developed, whereas the prior focus on drilling computations seemed to lead to inert knowledge, forgetting how they should be done.
I do have one point of critique on Brandom's inferentialism, and that is what Bakhurst more eloquently articulates than I can (chapter 5 of his Formation of Reason book). It is Brandom's decision to reverse the order of explanation; instead of the Descartian/representationalist route from representation to inference, he starts with inference in particular practices and methodologically explains how representations get their meaning. Like Bakhurst, I actually think (and my experience in classrooms supports this) that representation and ifnerence go hand in hand. Brandom's methodological explanation of starting with inference can therefore not be transferred to how learning develops in this extreme form, I think. But, as an antidote to how many teachers and even some researchers seem to think about knowing and learning, I find Brandom's idea pretty useful.
Arthur
________________________________________
From: xmca-bounces@weber.ucsd.edu [xmca-bounces@weber.ucsd.edu] on behalf of Andy Blunden [ablunden@mira.net]
Sent: Saturday, August 20, 2011 5:51 PM
To: eXtended Mind, Culture, Activity
Subject: Re: [xmca] Representationalism, as a way of knowing, has a history
Arthur,
I have had a chance to read the paper you did with Jan Derry, but
unfortunately Robert Brandom is still a closed book to me. I understood
from friends that he was some kind of Hegelian, but I can't see this in
your quotations. I may get the wrong end of the stick in my comments due
to not knowing Brandom. Also, my positive response to the idea of
Vygotsky as an "inferentialist" as opposed to a "representationalist"
was probably premature, as in your paper "inference" is merged with
"statistical inference." So I may be confused. Please excuse me if I get
things mixed up.
Firstly, I think I agree with the recommendations you are making to
teachers of statistics. This is because a concept can only be grasped
(and Vygotsky agrees) as a situation, or as a problem and its solution.
I gather you propose confronting students with problems, and then
offering them some statistical tools to use to solve the problem. This
approach is of course straight out of the Vygotsky handbook. It also
reflects a certain concept of concept ... but this is not what I gather
an "inferentialist" concept of concept is according to Brandom (judging
from your quotes only), and I can anticipate a line of argument basing
itself on statistical inference which manages to reconcile empiricism to
the obvious fact that human beings can reason. (It is an idea which is
popular among the neuroscientists as well, being a variation on the idea
of conditioned reflex.) If this is what Brandom argues, then my interest
in him declines apace. I think Hegel and Vygotsky have a far superior
approach. :)
You quote Brandom as follows: "The concept _concept_ is not intelligible
apart from the possibility of such application in judging. ...To grasp
or understand (...) a concept is to have practical mastery over the
inferences it is involved in - to know, in the practical sense of being
able to distinguish, what follows from the applicability of a concept,
and what follows from it."
I really don't see the Big Leap Forward from "representationalism" here.
How is this reflected in the concept of "mean"? Presumably when a
student can recognise when a number such as 6 is the mean of 3, 6 and 9?
and reason with it, eg the mean of x + y = the mean of x plus the mean
of y. This is not how I think you are suggesting teachers teach statistics.
The quote from Vygotsky: "we must seek the psychological equivalent of
the conceptnot in general representations ... [but] in a system of
judgments in which the concept is disclosed." NB "*disclosed*", i.e., we
can observe that a concept has been grasped when correct judgments are
made based on the concept. But I think it is wrong to deduce from this
that judgment is prior to concept in analysis, in structure or in
learning. You can't make a judgment on a concept unless you know the
concept. Agreed, learning the concept, in practice, transforms error
into understanding. But this really proves nothing. Judgments get better
as you get a better and better grasp of the concept. But what is the
concept? The only sense I cana make of this is some kind of dressage.
So I am a little bemused.
Andy
Bakker, A. (Arthur) wrote:
Interesting discussion! Here is my penny on representationalism.
Robert Brandom puts forward his inferentialism as an alternative to representationalism. Inferentialism in my view is a significant development in contemporary philosophy, which places inference rather than representation at the heart of human knowing, and which also has implications for education. Brandom explains the meaning of representations from people's participation in the game of giving and asking for reasons (inference).
Brandom, R. B. (2000). Articulating reasons: An introduction to inferentialism. Cambridge, MA: Harvard University Press.
See also the recent book by David Bakhurst - The formation of reason - on this topic. He argues that Brandom is perhaps too drastic in reversing the order of explanation.
With Jan Derry I have written a more educationally oriented paper on inferentialism as an alternative to representationalism (quite common in statistics education, e.g.):
Bakker, A. & Derry, J. (2011). Lessons from inferentialism for statistics education. Mathematical Thinking and Learning, 13, 5-26. http://dx.doi.org/10.1080/10986065.2011.538293
I cite a small part from this article:
+++++
Representationalism refers to the position that representations are the basic theoretical construct of knowledge. In common with several philosophers (e.g., Dewey, Heidegger, Rorty,
Wittgenstein) and educators (e.g., Cobb, Yackel, & Wood, 1992), Brandom (2000) takes issue with this approach noting the dominance of the representational paradigm since Descartes:
Awareness was understood in representational terms. . . . Typically, specifically conceptual representations were taken to be just one kind of representation of which and by means of which we can be aware. (p. 7)
Representationalism is based on the assumption that the use of concepts was explained by what they refer to (i.e., where conceptual content is primarily understood atomistically rather than relationally). Knowing what individual concepts mean is then the basis for being able to make sentences and claims, which in turn can be connected to make inferences. Assuming that a definition of a concept fully conveys its meaning is a possible consequence of such a view.
Brandom reverses the representationalist order of explanation, which leads to an account that he refers to as inferentialism. Taking judgments as the primary units of knowledge rather than representations, he reminds us that:
One of [Kant's] cardinal innovations is the claim that the fundamental unit of awareness or cognition, the minimum graspable, is the judgment. Judgments are fundamental, since they are the minimal unit one can take responsibility for on the cognitive side, just as actions are the corresponding unit of responsibility on the practical side. . . . Applying a concept is to be understood in terms of making a claim or expressing a belief. The concept concept is not intelligible apart from the possibility of such application in judging. (Brandom, 2000, pp. 159-160, emphases in the original)
This entails giving priority to inference in accounts of what it is to grasp a concept:
To grasp or understand (. . .) a concept is to have practical mastery over the inferences it is involved in-to know, in the practical sense of being able to distinguish, what follows from the applicability of a concept, and what it follows from. (Brandom, 2000, p. 48) This clarifies his definition of concepts as "broadly inferential norms that implicitly govern practices of giving and asking for reasons" (Brandom, 2009, p. 120). Any inference leading to a claim is made within such a normative context.
Claims both serve as and stand in need of reasons or justifications. They have the contents they have in part in virtue of the role they play in a network of inferences. (Brandom, 2000, p. 162)
++++
We also cite Vygotsky on this issue:
We must seek the psychological equivalent of the concept not in general representations, . . . not even in concrete verbal images that replace the general representations-we must seek it in a system of judgments in which the concept is disclosed. (Vygotsky, 1998, p. 55)
and think Vygotsky can be interpreted from an inferentialist rather than a representationalist perspective.
See further
Derry, J. (2008). Abstract rationality in education: From Vygotsky to Brandom. Studies in Philosophy and Education, 27, 49-62.
Arthur
-----Original Message-----
From: xmca-bounces@weber.ucsd.edu [mailto:xmca-bounces@weber.ucsd.edu] On Behalf Of Larry Purss
Sent: dinsdag 16 augustus 2011 3:36
To: eXtended Mind, Culture, Activity
Subject: Re: [xmca] Representationalism, as a way of knowing, has a history
Tony,
The point that Karen Barad is making is that there is a long historical line
of viewing the world through a particular set of lenses.
Representationalism and its basic metaphysical premises that "entities",
"things", "relata", PRE-EXIST phenomena and it is through the INTER-activity
of pre-existing "atoms" that relationships form. Karen's INTRA-activity
perspective argues the opposite position, that phenomena pre-exist the
agential "cutting" or scientific "scissors" that are applied to phenomena.
WithIN this phenomenal intra-activity of cutting fuzzy boundaries emerge and
BECOME more distinct and "structured" within the phenomena. Karen always
puts in scare quotes terms such as "components" "parts" and other terms
that attempt to explain "things" withIN phenomena. From her perspective
"relata" or "entties" do not exist prior to intra-activity but are emerging
aspects OF this situated intra-activity.
Her perspective emerges from an elaboration of Neils Bohrs work in
theoretical physics. Karen received her doctorate in theoretical physics and
then moved into philosophy. I'm going to quote a key section of her article.
"Bohr rejects the atomistic metaphysics that takes "things" as ontologically
basic entities. For Bohr, things do not have inherently determinate
meanings. Bohr also calls into question the related Cartesian belief in the
inherent distinction between subject and object, and knower and known.... It
[Bohr's epistemological framework] rejects the presupposition that language
and measurement perform mediating functions. Language does not represent
states of affairs, and measurements do not represent measurement-independent
states of being."
For Bohr the uncertainty principle is not a matter of "uncertainty" at all
but rather of INDETERMINANCY of phenomena. For Bohr THEORETICAL CONCEPTS
[e.g., "position" and "momentum"] are NOT ideational in character but rather
are SPECIFIC PHYSICAL ARRANGEMENTS which are not inherent attributes of
independently existing objects. Any measurement of "position" must use a
RIGID apparatus [such as a ruler] and the "position" is NOT attributed to
the abstract independently existing "object" but rather is a property of the
PHENOMENON - the inseparability of "observed object" and "agencies of
observation". This relational phenomena BETWEEN the apparatuses of
production and the phenomena produced is a process of "agential
intra-action"
Karen then states,
"Therefore, according to Bohr, the PRIMARY epistemological unit is NOT
independent objects with inherent boundaries and properties but rather
PHENOMENA. On my agential realist elaboration, [of Bohr's uncertainty
principle] phenomena do not merely mark the epistemological inseparability
of "observer" and "observed"; rather, PHENOMENA ARE THE ONTOLOGICAL
INSEPARABILITY OF AGENTIALLY INTRA-ACTING "COMPONENTS" That is, phenomena
are ontologically primitive relations - relations without pre-existing
relata."
>From Karen's perspective there is always a mutual ontological dependence of
"relata" withIN the relation. Phenomena is the ontological primitive. Relata
only exist withIN phenomena as a result of specific intra-actions. There is
only relata-withIN-relations.
To make this perspective concrete Karen gives this example. When light
passes through a two-slit diffraction apparatus the light forms a wavelike
diffraction pattern. BUT light also exhibits PARTICLElike characteristics
called PHOTONS. The apparatus can be modified to allow only one slit and
THIS modification allows a DETERMINATION of a given photon's position as
particles only go through a single slit at a time. However in this
intra-activity the wavelike diffraction pattern is destroyed. Bohr explains
this wave-particle paradox as follows: "the objective referent is not some
abstract independently existing entity but rather the PHENOMENON of light
intra-acting with the apparatus. The FIRST apparatus gives DETERMINATE
MEANING to the notion of "wave". The second apparatus gives DETERMINATE
MEANING to the notion of "particle" The notions of "wave" and "particle" do
NOT refer to inherent characteristics of an object that PRECEDES its
intra-action. THERE ARE NO SUCH INDEPENDENTLY EXISTING OBJECTS WITH INHERENT
CHARACTERISTICS. As Karen emphasizes, the two DIFFERENT APPARATUSES effect
DIFFERENT CUTS [measures]. That is draw different distinctions delineating
the "measured object" FROM the "measuring instrument". In other words Karen
believes the two phenomena DIFFER in their local MATERIAL resolutions OF the
inherent ontological INDETERMINANCY withIN phenomena.
Tony, this is certainly a shift of "perspective" but one that is "grist for
the mill" It does emphasize phenomena as inherently relational and objects
[relata] as derivative. Not sure where this fits into CHAT or
phenomenology. John Shotter has diffracted Karen Barad's perspective THROUGH
his elaboration of speech acts from a perspective that diffracts Bakhtin.
He also brings in Merleau-Ponty's perspectives. Tim Ingold's articles also
point in this direction. Certainly challenges the representationalist
epistemology/ontology.
Larry
On Mon, Aug 15, 2011 at 8:59 AM, Tony Whitson <twhitson@udel.edu> wrote:
I think what Larry says is right about the Cartesian legacy, but I think
the legacy in the Anglophone world might owe as much to Hobbes and Locke. I
see all three as sources of the common legacy of modernism.
Descartes is more rationalist while Hobbes and Locke are more empiricist,
but representationalism is what's common to them all.
On Sun, 14 Aug 2011, Larry Purss wrote:
Hi Martin
The other post had 18 entries so thought I would begin a new post.
Karen Barad, in 2003, wrote an article, "Posthumanist Performativity:
Toward
an nderstanding of how Matter Comes to Matter" in the journal "Signs:
Journal of Women in Culture and Society, 2003, Vol.28, no. 3 pp. 801-831"
She has a provocative quote that speaks to Vygotsky's historical
methodology
or way of seeing. She is pointing to the fact that both scientific
realism
and social constructivism share common ground in how they view scientific
knowledge IS the multiple representational forms which MEDIATE our access
to
the material world. Where they differ is on the question of referent.
Whether scientific knowledge represents things in the world as they really
are or "objects" that are the PRODUCTS of social activities, but Karen
points out BOTH groups subscribe to representationalism.
Karen points out,
"Representationalism is so deeply entrenched withIN Western culture that
it
has taken on a common sense appeal. It seems inescapable, if not
downright
natural. But representationalism (like "nature itself," not merly our
representations of it!) HAS A HISTORY" [p. 806]
She references Ian Hacking who traced this notion of knowledge back to
Ancient Greece and the Democritean dream of atoms and the void that
posited
a gap between representations and represented and the concept of
"appearance" makes its first appearance. Karen's perspective is that the
problem of realism in philosophy is a PRODUCT of THIS atomistic worldview.
And from this moment in history the consequence of this product isthe
DIVISION between "internal" and "external" that breaks the line of the
knowing subject.
Joseph Rouse is quoted in Karen's article. He states,
"The presumption that we can know what we mean, or what our verbal
performances say, more readily than we can know the objects those sayings
are about is a Cartesian legacy, a LINQUISTIC variation on Descartes'
insistence that we have a direct and privileged access to the contents of
our thoughts that we lack towards the "external" world."
Karen summarizes this section of her article by saying,
"In other words, the ASYMMETRICAL FAITH in our access to representations
over things is a contingent fact of HISTORY and not a logical necessity;
that is, it is simply a Cartesian habit of mind. It takes a healthy
skepticism toward Cartesian doubt to begin to be able to see an
alternative"
(p. 807)
Karen ends with a concrete example of this perspective which she borrows
from Foucault. In sixteenth century Europe, language was not thought of as
a
MEDIUM; rather, it was simply "one of the figurations of the world".
(Foucault, 1970, p.56). Today the notion of "con-figurations" or
gestalten
point in the same direction of a shift away from representative notions of
knowledge formation. This shift allows us to use our "scissors"
differently
as we make "agential CUTS" in coming to dwell in the world.
Larry
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*Andy Blunden*
Joint Editor MCA:
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Home Page: http://home.mira.net/~andy/
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