Please find a more recent version at:
http://www.prism.gatech.edu/~mh327/argument-mapping_111.ppt
Logical Argument Mapping (LAM):
A tool for problem solving, argumentation,
deliberation, and conflict management
Michael H.G. Hoffmann
March 31, 2007
michael.hoffmann@pubpolicy.gatech.edu
Overview
• Foundational Problems: Ontology and epistemology
• Tools for a solution: Semiotics, pragmatism, and boundary
critique
• Problems of boundary critique
• Problems of problems
• What can we do? Logical Argument Mapping (LAM)
-
LAM: Its functions
LAM: Theoretical background
LAM: The procedure
LAM: Three essential ideas
LAM: Other logical forms
LAM: Summary of important, valid argument forms
LAM: Notation for its ontology
LAM: Evaluation criteria
LAM: Examples on the web
• References
michael.hoffmann@pubpolicy.gatech.edu
Foundational Problems I: Ontology
•
•
Whatever we are talking or thinking about, it is
about something (to on = “the being” in Greek)
Two fundamental problems of ontology:
1. how to grasp a world in flux that is full of complexity,
interdependencies, and without clear boundaries and
structure?
2. how “to bridge the gap between what exists and the
languages, both natural and artificial, for talking and
reasoning about what exists”? (Sowa 2001)
•
Since we can comprehend what exists only so far
as our cognitive abilities go, there is no ontology
without epistemology
Foundational Problems II: Epistemology
•
Epistemology focuses on three
questions:
1. How to justify knowledge claims?
2. How to explain the creation of knowledge?
3. What are the conditions for the possibility of
knowledge and the creation of knowledge?
•
Its fundamental problem is: Since
everything can be represented in an
infinite number of different ways, what
is an adequate representation?
Tools for a solution I: Semiotics
• Semiotics is the theory of signs and
representation systems
• Since there is no knowledge, no
thinking, no communication without
signs and representation systems,
there is no ontology and epistemology
without a semiotic foundation
Tools for a solution II: Pragmatism
•
•
Pragmatism is, first of all, a theory of
meaning
While traditional approaches to
meaning define the meaning of a sign
either by
1. its “extension” (the set of objects signified by a
sign) or
2. by its “intension” (i.e. a definition that refers to
other signs),
pragmatism defines it by its usage
Tools for a solution III: Semiotic pragmatism
• Semiotic pragmatism in the tradition of
Charles S. Peirce claims that defining the
meaning of a sign by its usage depends
on interpretation
• The set of acceptable interpretations is
constrained by a community of sign users
• Therefore,
1. the meaning of signs is relative to social and
cultural communities, and evolves over time
2. also epistemology and ontology are always
relative to time and “lifeworlds” (Habermas)
Tools for a solution IV: Boundary critique
• “Boundary critique” is a concept
developed by Werner Ulrich
• It refers to the epistemological relevance
of “boundary judgments”:
1. “The idea is that both the meaning and the validity
of practical propositions (eg solution proposals or
evaluations) depend on assumptions about what
‘facts’ (observations) and ‘norms’ (valuations) are
to be considered relevant and what others are to
be ignored or considered less important. I call
these assumptions ‘boundary judgements’, for
they define the boundaries of the reference
system to which a proposition refers and for which
it is valid.” (Ulrich 2003, p. 333)
Tools for a solution IV: Boundary critique
2. “No argument can be completely rational in the sense of
justifying all the assumptions on which it depends as well
as all the consequences it may have. What ought to count
as knowledge, that is, as relevant circumstances, ‘facts’
and ‘evidence’ that should be considered? And what
counts as relevant concerns, that is, value judgments
concerning purposes, measures of success and other
criteria of evaluation (‘norms’)? Whose facts and whose
concerns should they represent? Ultimately, there is no
single right way to decide such questions. Yet at some
point argumentation has to end and practical action has to
begin. Boundary judgments define the boundaries of
argumentation” (Ulrich 2001, p. 91)
Tools for a solution IV: Boundary critique
• analyzes how any claim about facts or
values is conditioned by boundary
judgments
• shows how facts and values change when
boundary judgments are modified
• assumes that observations, evaluations,
and boundary judgments form an
interdependent system of selectivity
• analyzes the practical implications of
selectivity: how it may affect all the
parties concerned (Ulrich 2003, p. 333f.)
Problems of boundary critique
• Boundary judgments are not always explicit
• From an epistemological point of view,
boundary judgments are mostly implicit
judgments, i.e. they are invisible and
unconscious
• From a cognitive point of view, “bounding”
is—like “framing,” or “sensemaking”—a basic
cognitive process: it determines how we
interpret the world around us
• All this means: Any attempt to “critique”
boundary judgments is itself determined by the
same mechanisms it analyzes
• This leads to an infinite regress—there is no
way to look at systems of selectivity from the
outside
Problems of problems
•
Remember: Whenever we are talking about
something, we are facing the two ontological
problems:
1. how to capture a world in flux that is full of
complexity, interdependencies, and without clear
boundaries and structure?
2. how “to bridge the gap between what exists and the
languages … for talking and reasoning about what
exists”? (Sowa 2001)
•
Since any talk about something is additionally
constrained by the selectivity of boundary
setting, we get problems of problems
What can we do? Logical Argument Mapping (LAM)
• The infinite regress, and the fact that
bounding determines our thinking on each
level of analysis, is problematic only if we
try to describe what is going on in these
processes
• Any description carries with it a pretense
of objectivity that can never be fulfilled—
since bounding selectivity is inevitable
• The solution: Not description, but a stepby-step process of visualizing bounding
conditions that must be performed by the
involved parties themselves
LAM: Its functions
• Heuristic function:
- visualizing boundary judgments and constraints
- clarifying vague thinking and implicit assumptions
- stimulating creativity, the discovery of alternative
perspectives, and experimenting with representations
- visualizing implications and problems of our assumptions
and possible contradictions among them
- challenging critical thinking and self-reflexivity
• Social function:
- coordinating different problem representations and
boundary judgments
- stimulating negotiation of meanings and argumentation
- connecting expertise
- promoting mutual understanding by visualizing implicit
assumptions and boundary constraints (Hoffmann 2005)
LAM: Theoretical background
• Peirce’s concept of “diagrammatic reasoning”
(Hoffmann 2004, in press)
• Vygotsky’s idea of “semiotic mediation”: the main
function of signs is to regulate both social
interaction and our own thinking (Seeger 2005)
• Toulmin-model of argumentation: argumentation
as procedure; working with graphs (Toulmin 2003
<1958>)
• Application-oriented approaches to logic
(e.g. Luckhardt & Bechtel 1994)
• Computer-Supported Argument Visualization
(CSAV; Kirschner, Buckingham Shum, and Carr
2003)
LAM: The procedure
1. Formulate a claim: the central goal of
your argument, a central thesis
All maps are created with
IHMC Cmap tools:
http://cmap.ihmc.us/
The example
is based on
Economist
2006
LAM: The procedure
2. Provide a reason for your claim
LAM: The procedure
3. Justify the relation between reason and claim
by means of a warrant
LAM: The procedure
4. Try to refute your reason and the proposition
by which you justified the relation between
your reason and your claim (= warrant)
5. If necessary,
a) provide further reason(s) for your original reason and/or
the warrant; this way, your argument becomes an
“argumentation”; or
b) provide alternative reasons for your original claim, or
c) reformulate your claim and start again with step 1
LAM: The procedure
5.a) Provide further reasons for your reason
LAM: Three essential ideas
1.
By providing a justification for the relation between reason
and claim in the 3. step, a crucial part of the arguer’s
boundary judgments and constraints becomes visible
•
•
2.
Because: A reason is a reason for a claim only if one
acknowledges—at least implicitly—the justifying statement
Therefore: LAM makes boundary judgments, bounding constraints,
and implicit assumptions visible
LAM motivates an ongoing process of argumentation
•
•
•
The third step transforms the argument into a logically valid
argument (here: modus ponens)
However, it is only a “sound” argument if both the premises are true
That means: you have to defend two very different things:
a)
b)
•
3.
your primary reason
the statement that justifies the relation between reason and claim
Since everything can be doubted, you are challenged to provide
further reasons, or to modify the argument
LAM allows to check the consistency and completeness of
argumentations based on a visualization of all its elements
LAM: Other logical forms: alternative syllogism
LAM: Other logical forms: modus tollens
The whole example is available online. Click here
LAM: Summary of important, valid argument forms
modus ponens
If A, then B
(=A, only if B;
= A implies B)
A
B
modus tollens
If A, then B
(=A, only if B;
= A implies B)
not B
not A
alternative syllogism
Either A or B
not A (not B)
B
(A)
A if and only if B
A (B) (not A) (not B)
B (A) (not B) (not A)
disjunctive syllogism
conditional syllogism
Not both A and B
A
(B)
 not B (not A)
If A, then B
If B, then C
 If A, then C
LAM: Forms of warrants
• The validity of those argument forms depends on
the following truth-table definitions of the warrants
A
B
If A then B
T
T
F
F
T
F
T
F
T
F
T
T
A
B
Either A or B
T
T
F
F
T
F
T
F
T
T
T
F
A B
T
T
F
F
T
F
T
F
Not both A and B
F
T
T
T
A B A if and only if B
T
T
F
F
T
F
T
F
T
F
F
T
LAM: Notation for its ontology
“Ontology” refers to the content that can be represented in
a map. LAM’s ontology contains the following elements:
Ontology
Characteristics
Function: to represent …
can be doubted
claims, data, imperatives, etc.
can be refuted by one
counter-example
what somebody presupposes
in order to justify a certain
reason for a certain claim
LAM: Evaluation criteria
•
•
•
•
any relation between elements must be clearly
specified both by connector terms (“therefore,”
“objects to,” “but,” “refutes,” “includes,” “means,”
“supports,” “e.g.,” “makes unlikely,” “defined as,”
etc.) and by directed arrows
arguments must be logically valid
argumentations must be as complete as possible; if
there is any element that can reasonably be
doubted, it has to be justified by further reasons
argumentations must be consistent (i.e. no
contradictions within your map); if you add an
objection to any part of an argument, you have to
indicate how to deal with it: Are there further
objections to refute the objection? Should the
objection lead to a qualification, or reformulation, of
the argument? Is there a problem you do not know
how to deal with?
LAM: Examples on the web
• Analysis of an argument about the importance
of jihad (October 23, 2007, 877 KB)
• http://tinyurl.com/yuqop7
• Searching for common ground on Hamas
(March 31, 2007; 279 KB)
• Hume on causality
(March 12, 2007; 2.0 MB!)
• Regulating kidney supply
(Feb 27, 2007; 618 KB)
• Middle East conflict. An Argumentation on the
sovereignty over al-Haram al-Sharif/Temple
Mount in Jerusalem (May 30, 2006; 763 KB)
References
Economist. (2006). Organ transplants. Your part or mine? Iran's example, and the broader case for making it worthwhile
to give kidneys. The Economist, Nov 16th.
Habermas, J. (1984, 1987 <1981>). The Theory of Communicative Action. Boston: Beacon Press.
Hoffmann, M. H. G. (2004). How to Get It. Diagrammatic Reasoning as a Tool of Knowledge Development and its
Pragmatic Dimension. Foundations of Science, 9(3), 285-305.
—— (2005). Logical argument mapping: A method for overcoming cognitive problems of conflict management.
International Journal of Conflict Management, 16(4), 305–335.
—— (in press). Cognitive conditions of diagrammatic reasoning. Semiotica (special issue on "Peircean diagrammatical
logic," ed. by J. Queiroz and F. Stjernfelt).
Kirschner, P. A., Shum, S. J. B., & Carr, C. S. (Eds.). (2003). Visualizing Argumentation: Software Tools for Collaborative
and Educational Sense-making. London: Springer.
Klein, M. (2003). The Jerusalem problem. The struggle for permanent status (H. Watzman, Trans.). Gainesville
University Press of Florida.
Luckhardt, C. G., & Bechtel, W. (1994). How to Do Things with Logic. Hillsday, NJ: Lawrence Erlbaum Associates.
Peirce. (CP). Collected Papers of Charles Sanders Peirce. Cambridge, Mass.: Harvard UP.
Seeger, F. (2005). Notes on a semiotically inspired theory of teaching and learning. In M. H. G. Hoffmann, J. Lenhard &
F. Seeger (Eds.), Activity and Sign - Grounding Mathematics Education (pp. 67-76). New York: Springer.
Sowa, J. F. (2001). Signs, Processes, and Language Games. Foundations for Ontology.
http://www.jfsowa.com/pubs/signproc.htm.
Toulmin, S. E. (2003 <1958>). The Layout of Arguments. In The uses of argument (Updated ed., pp. 87-134). Cambridge,
U.K.; New York: Cambridge University Press.
Ulrich, W. (2001). Critically systemic discourse: a discursive approach to reflective practice in ISD (Part 2). JITTA,
Journal of Information Technology Theory and Application, 3(3), 85-106.
——(2003). Beyond methodology choice: critical systems thinking as critically systemic discourse. Journal of the
Operational Research Society, 54(4), 325-342.