Title: Logical Argument Mapping (LAM): A tool for problem solving, argumentation, deliberation, and conflict management
1Logical Argument Mapping (LAM)A tool for
problem solving, argumentation, deliberation, and
conflict management
Please find a more recent version
at http//www.prism.gatech.edu/mh327/argument-ma
pping_111.ppt
michael.hoffmann_at_pubpolicy.gatech.edu
March 31, 2007
2Overview
- 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_at_pubpolicy.gatech.edu
3Foundational 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
- how to grasp a world in flux that is full of
complexity, interdependencies, and without clear
boundaries and structure? - 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
4Foundational Problems II Epistemology
- Epistemology focuses on three questions
- How to justify knowledge claims?
- How to explain the creation of knowledge?
- 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?
5Tools 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
6Tools 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 - its extension (the set of objects signified by
a sign) or - by its intension (i.e. a definition that refers
to other signs), - pragmatism defines it by its usage
7Tools 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,
- the meaning of signs is relative to social and
cultural communities, and evolves over time - also epistemology and ontology are always
relative to time and lifeworlds (Habermas)
8Tools for a solution IV Boundary critique
- Boundary critique is a concept developed by
Werner Ulrich - It refers to the epistemological relevance of
boundary judgments - 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)
9Tools for a solution IV Boundary critique
- 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)
10Tools 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.)
11Problems 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
islike framing, or sensemakinga 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 regressthere is no way
to look at systems of selectivity from the
outside
12Problems of problems
- Remember Whenever we are talking about
something, we are facing the two ontological
problems - how to capture a world in flux that is full of
complexity, interdependencies, and without clear
boundaries and structure? - 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
13What 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 fulfilledsince
bounding selectivity is inevitable - The solution Not description, but a step-by-step
process of visualizing bounding conditions that
must be performed by the involved parties
themselves
14LAM 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)
15LAM Theoretical background
- Peirces concept of diagrammatic reasoning
(Hoffmann 2004, in press) - Vygotskys 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
lt1958gt) - Application-oriented approaches to logic (e.g.
Luckhardt Bechtel 1994) - Computer-Supported Argument Visualization (CSAV
Kirschner, Buckingham Shum, and Carr 2003)
16LAM The procedure
- 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
17LAM The procedure
- Provide a reason for your claim
18LAM The procedure
- Justify the relation between reason and claim by
means of a warrant
19LAM The procedure
- Try to refute your reason and the proposition by
which you justified the relation between your
reason and your claim ( warrant) - If necessary,
- provide further reason(s) for your original
reason and/or the warrant this way, your
argument becomes an argumentation or - provide alternative reasons for your original
claim, or - reformulate your claim and start again with step 1
20LAM The procedure
- 5.a) Provide further reasons for your reason
21LAM Three essential ideas
- By providing a justification for the relation
between reason and claim in the 3. step, a
crucial part of the arguers boundary judgments
and constraints becomes visible - Because A reason is a reason for a claim only if
one acknowledgesat least implicitlythe
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 - 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
22LAM Other logical forms alternative syllogism
23LAM Other logical forms modus tollens
The whole example is available online. Click here
24LAM Summary of important, valid argument forms
alternative syllogism
Either A or B not A (not B) ?B (A)
modus ponens
If A, then B (A, only if B A implies B) A ?B
A if and only if B A (B) (not A) (not B) ?B (A) (not B) (not A)
disjunctive syllogism
Not both A and B A (B) ? not B (not A)
conditional syllogism
If A, then B If B, then C ? If A, then C
modus tollens
If A, then B (A, only if B A implies B) not B ?not A
25LAM 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 Not both A and B
T T F F T F T F F T T T
A B Either A or B
T T F F T F T F T T T F
A B A if and only if B
T T F F T F T F T F F T
26LAM Notation for its ontology
Ontology refers to the content that can be
represented in a map. LAMs ontology contains the
following elements
Ontology Characteristics Function to represent
can be doubted can be refuted by one counter-example claims, data, imperatives, etc. what somebody presupposes in order to justify a certain reason for a certain claim
27LAM 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?
28LAM 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)
29References
- 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 lt1981gt). 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), 305335. - (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 lt1958gt). 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.