Conceptual impressions surrounding this post are yet to be substantiated, corroborated, confirmed or woven into a larger argument or network.
Continuation from Design Metaphysics: An Exercise in Abductive Reasoning
3. Visual abduction
Peirce claimed that all thinking is in signs, and that signs can be icons, indices, or symbols [10, 11]. Icons are signs that resemble what they represent; examples include pictures, photographs, and geometrical diagrams. Peirce placed great emphasis on diagrammatic thinking and even developed a powerful system of predicate logic based on diagrams or ``existential graphs'' [23]. Surprisingly, Peirce does not seem to have connected his two highly original insights: we know of no text in which he discusses abduction as diagrammatic or iconic. But there are instances of abductive thinking that are most plausibly interpreted as pictorial.
Suppose you return to your car at the shopping center and find a big scratch on one door. Naturally, you wonder how it happened and start to generate hypotheses to explain how the scratch came to be. Your abductions may be purely verbal, if you start to apply rules such as ``If a car door is opened and collides with another car door, the latter door is scratched.'' You could then verbally abduce that some other car door was opened and collided with yours. But a mode of thinking that is natural for many people is to perform the same kind of thinking pictorially. You can form a mental image of a car driving up beside yours and then its driver opening a door that scratches yours. Here the explanation is a kind of mental movie in which you imagine your door being scratched. The abductive inference that the accident happened this way involves a mental picture of the other car's door hitting yours. Such pictures provide an iconic representation of the event that you conjecture to have happened, since the picture you form resembles the hypothesized event in a much more direct way than a verbal/sentential representation would. Whenever our knowledge of how things work in the world involves dynamic pictorial representations, these representations can be used to generate iconic explanations of what occurs. Many scientists have reported that images played a crucial role in their most creative thinking: the most eminent include Bohr, Boltzmann, Einstein, Faraday, Feynman, Heisenberg, Helmholtz, Herschel, Kekule, Maxwell, Poincare, Tesla, Watson, and Watt.
Performing abduction visually may have strong cognitive advantages. With verbal representations such as rules, it may be necessary to search through many possible inferences before finding a plausible explanatory hypothesis. But a picture of a situation may immediately suggest a likely cause, if it vividly displays factors that are spatially contiguous and therefore more likely to be causally relevant. Artificial intelligence is still very limited in its ability to use such visuospatial information, although progress is being made in the direction of imagistic representations. Glasgow has argued for the importance of spatial reasoning in AI and proposed a representational scheme based on 3-dimensional arrays [9, 8]. Graphs provide visual representations that are more flexible than arrays [5, 30], so to show how abduction can be visual yet nevertheless amenable to formal treatment, we will now discuss graph grammars.
A simple graph can be thought of as a purely algebraic structure consisting of a set of vertices and edges, but uses of graphs often exploit their visual character. When we draw a graph representing, for example, the paths between various cities, we get a diagram or mental representation of the routes between cities that resembles the actual roads. The mathematical structure of a graph naturally translates into a graphical diagram that resembles what it represents much more directly than a set of sentences would. Graph grammars consist of sets of production rules that differ from standard verbal productions in that the left-hand sides (conditions) and right-hand sides (actions) are represented as graphs rather than as verbal structures [7, 14, 19]. A graphical production can be interpreted as saying that if you have one graphical structure and you apply a transformation to it, then you get another graphical structure. For abduction purposes, we can think of the right-hand side of a graph production as providing a visual representation of something to be explained, and the left-hand side and the transformation as providing a possible visual explanation.
(Graphic not available)
Figure 1. Graph representation of a Lego block.
To be more concrete, consider children's interlocking Lego blocks. We can represent each block as a graph whose vertices are connectors and sockets, where the connectors on one block fit into the sockets on another block. Figure 1 gives a graph for a simple 4-connector block, with 8 vertices and 12 edges. Transformations possible for Lego blocks include stacking one on top of the other, which produces a new structure in which the connectors on the bottom block go into the sockets on the top block. A graphical production representing this would have a left-hand side of two unconnected graphs and a transformation that produced new edges connecting the appropriate sockets and connectors, producing a new connected graph with a total of 16 vertices and 28 edges, including 4 new ones.
Given such a production, we could explain the existence of a tower consisting of two blocks by hypothesizing that there were two independent blocks that had been transformed by joining. Abduction is then visual because the representations of both what gets explained and what does the explaining use structures that resemble what they represent.
Let us now state this more formally.
Let us now state this more formally.
Definition 3.1 A graph G is a tuple {V,E} where:
- V is a set of vertices;
- E subset (V times V) is a set of edges.
Definition 3.2 A graph grammar Gamma is a finite set of productions P, where a production is a tuple {Gl,Gr,T} such that:
- Gl is the left-hand side;
- Gr is the right-hand side;
- T is the embedding transformation that specifies the relations between the vertices and edges of Gl and Gr.
Definition 3.3 A graph-grammatical abductive explanation of a target graph G^t is a hypothesis graph G^h such that there is a set of productions in P whose successive transformations transform G^h into G^t.
Intuitively, the hypothesis graph G^h provides an explanation of the target graph G^t by virtue of a series of transformations that show how the target graph can be produced from the hypothesis graph.
Graph grammars are not the only possible basis for visual abduction. Leyton [17] presented a ``process grammar'' that could be used to infer the causal history of objects from their shapes. This grammar contains such productions as one that can be interpreted: ``If a shape is squashed, it will indent.'' If the shapes and the processes of squashing and indenting are represented pictorially, then the inference that explains a shape's indentation by its having been squashed is an instance of visual abduction.
This paper does not attempt to present a general theory of visual abduction, but rather some instances that show the limitations of current formal models of abductive reasoning. A fully general characterization of abduction would have to allow representations of causes and effects that are pictorial as well as ones that are sentential. It would also have to admit forms of explanation that centrally employ visual transformations as well as ones that employ deduction and other verbal processes. In addition, we should not rule out the possibility of a multimodal theory of abduction that includes non-visual, non-verbal representations involving smell, touch, and emotion. For example, there are some diseases that physicians can diagnose based on a patient having a particular odor. The need for a multimodal theory is illustrated below with an archaeological example.
4. The demise of SK54
Forming hypotheses to explain the unusual macroscopic properties of artifacts and skeletal remains is an important part of archaeology. This kind of abduction often requires the archaeologist to reconstruct the events in the history of an object which caused it to change in shape or structure from some initial form to the final, observed one. Since this kind of evidence for the history of an object is visual in nature, the archaeologist may find visual mental imagery useful in generating an explanation of it. (See [24] for further discussion.
(IMAGE NOT SHOWN)
Figure 2. The skullcap SK54 with notches indicated by white arrows [2, p. 1117]
Figure 3. The abduced fate of SK54 in the jaws of a leopard [2, p. 1118]
For example, in 1949 excavations of a cave at Swartkrans in South Africa yielded, among much other debris, the skullcap of an australopithecine (thereafter designated SK54). The distinctive features of this skullcap consisted of two notches, one on either side of the centerline, which had obviously been driven into the back of the skull by two pointed objects when the creature was still alive [2]. SK54 is pictured in figure 2, with the notches indicated by the two arrows. At first it was supposed that the notches had been inflicted by two separate blows from a weapon wielded by another hominid, because each notch had been made at divergent angles from the centerline [1]. This hypothesis accorded well with the prevailing theory that human evolution had been driven by murder and cannibalism---Dart's [6] ``killer ape'' hypothesis.
However, an alternative explanation has been offered by Brain [2]. Noting that the lower canine teeth of leopards diverge and are about the right distance apart, Brain hypothesized that the notches had been created by a leopard which had taken the australopithecine's head in its mouth, as dramatically illustrated in figure 3. Indeed, a fossil leopard jaw from the same site (SK349) fits the notches fairly well and shows that the hypothesis is a plausible one; see also [3]. This is shown in figure 4.
Figure 4. Fossil leopard jaw SK349 fitted into the notches of SK54 [2, p. 1117]
This explanation of the notches in SK54 also accords with several other facts about the debris in the Swartkrans cave. The entrance to the cave was a vertical shaft when the australopithecine remains were deposited and those remains are mostly comprised of skull fragments. Similar shaft caves in the area today are frequented by leopards which use the trees which grow around the entrances as places to safely consume prey out of the reach of hyenas. Since leopards tend to destroy the skeletal material of their primate prey with the exception of the skulls, the leopard-predator hypothesis would also explain why the australopithecine remains are mostly skull fragments---the skulls would simply have fallen from the trees and into the cave shafts [2]. This scenario, leopard predation of early hominids, is much different from the ``killer ape'' scenario favored by Dart.
Brain's leopard hypothesis exemplifies the use of visual abduction. The target of explanation---the unusual notches in the skullcap SK54---are highly visual in nature, consisting in their placement, depth, and direction. The hypothesis reconstructs the vital moment in the history of an unfortunate hominid, when its head was clenched in the jaws of a leopard to produce the notches. Because the relevant data are spatial, the hypothesis is most parsimoniously captured visually, as in figure 3, and may well have first occurred to Brain as just such a mental picture. The hypothesis thus abduced was then corroborated by further evidence of fossil leopard jaws and the feeding habits of modern leopards. Thus, this example illustrates that visual abduction fits the expanded criteria for abduction discussed in section 2.
5. Coherence
Abduction is often thought of as a kind of reverse deduction; see section 2.1. Whereas modus ponens infers from p right arrow q and p to q, abduction infers from p right arrow q and q to p. This formulation trivializes the point of abduction, which is to form and evaluate hypotheses that make sense of puzzling facts. Making sense is a holistic matter of fitting the puzzling facts into a coherent pattern of representations. The notion of coherence has usually remained vague, but Thagard and Verbeurgt [29] have recently defined coherence in terms of maximization of constraint satisfaction. After briefly stating their definition, we will show how abduction can be reconceptualized as a coherence problem.
Let E be a finite set of elements ei and C be a set of constraints on E understood as a set (ei, ej) of pairs of elements of E. C divides into C+, the positive constraints on E, and C-, the negative constraints on E. With each constraint is associated a number w, which is the weight (strength) of the constraint. The problem is to partition E into two sets, A (accepted) and R (rejected), in a way that maximizes compliance with the following two coherence conditions:
1. if (ei, ej) is in C+, then ei is in A if and only if ej is in A;
2. if (ei, ej) is in C-, then ei is in A if and only if ej is in R.
Let W be the weight of the partition, that is, the sum of the weights of the satisfied constraints. The coherence problem is then to partition E into A and R in a way that maximizes W.
To understand abduction as a coherence problem, we need to specify the elements and the constraints. The elements are representations of causes and effects; in line with our discussion of visual abduction, we will allow the representations to include both sentential and nonsentential representations such as visual ones. The major positive constraint on abduction is that if one element explains another, then there is a symmetric positive constraint between them. In accord with the first of the two coherence constraints above, this will have the effect that if the explaining element and the explained element will tend to be accepted or rejected together. If, as often happens, more than one element is required to explain another element, the weight on the constraint between each explaining element and the explained element can be less than if there were only one explaining element, in keeping with the theory of simplicity of Thagard [28].
Two sorts of negative constraint are possible. If two elements contradict each other, then there is a symmetric negative constraint between them, but there is also a negative constraint if two elements offer competing explanations of the same fact [28]. Deciding which explanatory hypotheses to accept and which to reject is a matter of maximizing compliance with the two coherence conditions. Computationally, this is a very difficult problem and no tractable algorithm for solving it is available, although various approximation algorithms work quite well [29].
Our account of abduction as a coherence problem avoids all the limitations we discussed in section 2. We assume that the relation between elements is explanation, not deduction. Elements can explain other elements which explain other elements, so hypotheses can be layered and give rise to complex chains of constraints. Abduction is not defined in terms of a fixed set of elements but allows the possibility of creation of new elements that produce a new assessment of coherence. New hypotheses need not be consistent with existing ones, nor need the facts be completely explained. Maximizing coherence involves explaining as much as possible (positive constraints) and being as consistent as possible (negative constraints), but perfection is not to be sought in abductive reasoning. We are not urging inconsistency as a general epistemological strategy, only noting that it is sometimes necessary to form hypotheses inconsistent with what is currently accepted in order to provoke a general belief revision that can restore consistency.
Reducing the weights on constraints when explanation is accomplished by multiple hypotheses allows a complex assessment of simplicity. Finally, since elements can be visual or other nonverbal kinds of representation, we have transcended the limitation of abductive reasoning to sentences.
6. Conclusion
The definitions of abduction proposed by Konolige and by Bylander, Allemang, Tanner and Josephson are clearly inadequate as general characterizations of this important type of reasoning. These definitions made possible precise comparisons with other models and derivation of complexity theoretic results, but the results must be viewed as relative to the abstract model of abduction proposed. One might think that all complexity results would carry over to models of abduction more elaborate than the ones offered: if abduction is more complicated than Bylander et al. allow, then the computational complexity should be at least as great, so abduction would still be NP-hard. But the main results of Bylander et al. concern the difficulty of determining whether an explanation exists, where their notion of explanation is, as we saw, unrealistically restricted to cases where all the data are to be explained. In scientific reasoning, in contrast, the task is to explain as much of the data as you can and to come up with a set of explanatory hypotheses that is better than the current set. It is a matter of satisficing (choosing the most coherence set of hypotheses) rather than optimizing. Abduction characterized in terms of coherence is still intractable, but efficient approximation algorithms exist. There is also the possibility that heuristic search made possible by visual representations can greatly improve the computability of abductions, although this remains to be shown.
Thanks to important formal results such as the theory of NP-completeness, formal methods have achieved much well-deserved prestige in computer science and artificial intelligence. But an oversimplified formalization can distract from important aspects of the kinds of reasoning that underlie intelligence. Graph grammars and other techniques for visual representation offer the prospects of developing more general accounts of the nature of abductive reasoning, which should be construed not as a deviant form of deduction, but as a coherence problem.
Acknowledgements
* We are grateful to John Josephson and Don Roberts for comments on an earlier draft. Thanks to John Ching and Andrew Wong for ideas about graphical representations. This research was supported by the National Science and Engineering Research Council of Canada.
Bibliography
[1] R. Ardrey. African genesis: A personal investigation into the animal origins and nature of man. Atheneum, Ney York, N.Y., 1961.
[2] C. K. Brain. New finds at the Swartkrans australopithecine site. Nature, 225:1112-9, 1970.
[3] C. K. Brain. The hunters or the hunted? An introduction to African cave taphonomy. The University of Chicago Press, Chicago, Ill., 1981.
[4] T. Bylander, D. Allemang, M.C. Tanner, and J.R. Josephson. The computational complexity of abduction. Artificial Intelligence, 49:25-60.
[5] J. Y. Ching. Computational imagery: An alternative framework. Ph.D. thesis proposal, Pattern Analysis and Machine Intelligence Lab, University of Waterloo, Waterloo, On., May 1994.
[6] R. A. Dart. The predatory transition from ape to man. International Anthropological Linguistic Review, 1(4):201-18, 1953.
[7] H. Ehrig, H. J. Kreowski, and G. Rozenberg, editors. Graph-grammars and their application to computer science:4th international workshop, number 532 in Lecture notes in computer science, Berlin, Germany, March 1990. European Association for theoretical computer science, Springer Verlag.
[8] J. I. Glasgow. The imagery debate revisited: A computational perspective. Computational Intelligence, 9:309-33, 1993.
[9] J. I. Glasgow and D. Papadias. Computational imagery. Cognitive Science, 17930:355-394, 1992.
[10] T. A. Goudge. The thought of C. S. Peirce. University of Toronto Press, Toronto, On., Canada, 1950.
[11] C. Hartshorne and P. Weiss, editors. Collected papers of Charles Sanders Peirce. Harvard University Press, Cambridge, Mass., U.S.A., 1958. Volumes 7-8 edited by A. Burks.
[12] C. G. Hempel. Aspects of scientific explanation. The Free Press, New York, N.Y., 1965.
[13] J.R. Hobbs, M. Stickel, D. Appelt, and P. Martin. Interpretation as abduction. Technical Note 499, AI Center, SRI International, 333 Ravenswood Ave., Menlo Park, CA 94025, December 1990.
[14] C.V. Jones. An integrated modeling environment base on attributed graphs and graph-grammars. Decision Support Systems: The international journal, 9(10):255-72, 1991.
[15] P. Kitcher and W. Salmon. Scientific explanation. University of Minnesota Press, Minneapolis, M.N., 1989.
[16] K. Konolige. Abduction versus closure in causal theories. Artificial Intelligence, 52:255-72, 1991.
[17] M. Leyton. Inferring causal history from shape. Cognitive Science, 13:357-87, 1989.
[18] D. V. McDermott. A critique of pure reason. Computational Intelligence, 3:151-60,1987.
[19] M. Nagl. Formal languages of labelled graphs. Computing, 16:113-37, 1976.
[20] J. Pearl. Probabilistic reasoning in intelligent systems. Morgan Kaufman, San Mateo, CA, 1988.
[21] Y. Peng and J. Reggia. Abductive inference models for diagnostic problem solving. Springer Verlag, New York, N.Y., 1990.
[22] R. Reiter. A theory of diagnosis from first principles. Artificial Intelligence, 32:57-95, 1987.
[23] D. D. Roberts. The existential graphs of Charles S. Peirce. Mouton, The Hague, 1973.
[24] C. Shelley. Visual abductive reasoning in archaeology. Under review, 1996.
[25] P. Thagard. Computational philosophy of science. MIT Press, Cambridge, Mass., 1988.
[26] P. Thagard. Explanatory coherence. Behavioral and Brain Sciences, 12:435-67, 1989.
[27] P. Thagard. Philosophical and computational models of explanation. Philosophical Studies, 64:87-104, 1991.
[28] P. Thagard. Conceptual revolutions. Princeton University Press, Princeton, N.J., 1992.
[29] P. Thagard and K. Verbeurgt. Coherence. Under review.
[30] A. Wong, S. Lu, and M. Rioux. Recognition and shape synthesis of 3-D objects based on attributed hypergraphs. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(3):279-90, Jun 1989.
FINAL COMMENTARY
Abductive reasoning:
Logic, visual thinking and coherence. Paul Thagard and Cameron Shelley, 1997
I am of the opinion that all
possible descriptions used to bring to reason any event or experience is wholly
dependent upon the categorization of certain pre-defined symbolic relationships
that when together bring a degree of awareness to a particular field of choice,
focus and/or interest. I’m also of the opinion that consciousness per se, is
the product of series of multidimensional relationships made apparent by means
of symbolic correspondence.
Statements listed below are
based upon issues surrounding the concept of design and the design process.
These disclosures are posted in the following blogs:
This remains a work in
progress.
When designing, methods of reason
are dependent upon, 1. the observer/perceiver of the event/experience, 2. the
context/field in which this observation/perception is made, 3. the language, i.e.
system of symbols used to support and assist in the cognition of an event or
experience. Following are quotes from the work of Thagard and Shelley that I
believe support the concept of design and design thinking.
Design
is symbolic in nature and made apparent by means of signs, symbols, analogy and metaphor.
“Peirce claimed that all thinking is in signs, and
that signs can be icons, indices, or symbols.”
“Finally, since elements can be visual or other
nonverbal kinds of representation, we have transcended the limitation of
abductive reasoning to sentences.”
“In addition, we should not rule out the
possibility of a multimodal theory of abduction that includes non-visual,
non-verbal representations involving smell, touch, and emotion.”
“Abduction is not defined in terms of a fixed set of elements but
allows the possibility of creation of new elements that produce a new
assessment of coherence.” “
“Konolige's definition, like
virtually all available accounts of abduction, presumes that explanatory
hypotheses are represented sententially. But we will now show that some
abductive inference is better understood as using pictorial or other iconic
representations.”
“Abduction is then visual because the
representations of both what gets explained and what does the explaining use
structures that resemble what they represent.”
“A fully general characterization of abduction
would have to allow representations of causes and effects that are pictorial as
well as ones that are sentential. It would also have to admit forms of
explanation that centrally employ visual transformations as well as ones that
employ deduction and other verbal processes.”
The ability to visualize a particular
situation is fundamental to design thinking.
“But there are instances of abductive
thinking that are most plausibly interpreted as pictorial.”
“It would also have to admit forms of explanation
that centrally employ visual transformations as well as ones that employ
deduction and other verbal processes.”
“The elements are representations of causes and
effects; in line with our discussion of visual abduction, we will allow the
representations to include both sentential and non-sentential representations
such as visual ones.”
“But a mode of thinking that is natural for many
people is to perform the same kind of thinking pictorially.”
“Such pictures provide an iconic representation of
the event that you conjecture to have happened, since the picture you form
resembles the hypothesized event in a much more direct way than a
verbal/sentential representation would. Whenever our knowledge of how things work in the
world involves dynamic pictorial representations, these representations can be
used to generate iconic explanations of what occurs. Many scientists have reported
that images played a crucial role in their most creative thinking:”
“A fully general characterization of abduction
would have to allow representations of causes and effects that are pictorial as
well as ones that are sentential. It would also have to admit forms of
explanation that centrally employ visual transformations as well as ones that
employ deduction and other verbal processes. In addition, we should not rule
out the possibility of a multimodal theory of abduction that includes
non-visual, non-verbal representations involving smell, touch, and emotion.”
Design thinking/reasoning is both imaginative
and intuitive.
“The abductive inference that the accident happened
this way involves a mental picture of the other car's door hitting yours. Such
pictures provide an iconic representation of the event that you conjecture to
have happened, since the picture you form resembles the hypothesized event in a
much more direct way than a verbal/sentential representation would. Whenever our knowledge of
how things work in the world involves dynamic pictorial representations, these
representations can be used to generate iconic explanations of what occurs.”
“To understand abduction as a coherence problem, we
need to specify the elements and the constraints. The elements are
representations of causes and effects; in line with our discussion of visual
abduction, we will allow the representations to include both sentential and
nonsentential representations such as visual ones.”
The design process is used for both problem
finding and problem solving in addition to creative thinking.
“With verbal representations such as rules, it may
be necessary to search through many possible inferences before finding a
plausible explanatory hypothesis. But a picture of a situation may immediately
suggest a likely cause, if it vividly displays factors that are spatially
contiguous and therefore more likely to be causally relevant.”
“Many scientists have reported that images played a
crucial role in their most creative thinking.”
“Creative abduction often involves the construction
of novel hypotheses involving newly formed concepts such as natural selection
or AIDS. For Charles Peirce, who coined the term ``abduction'' a century ago,
the introduction of unifying conceptions was an important part of abduction
[11, 25], and it would be unfortunate if our understanding of abduction were
limited to more mundane cases where hypotheses are simply assembled. Abduction
does not occur in the context of a fixed language, since the formation of new
hypotheses often goes hand in hand with the development of new theoretical
terms such as ``atom,'' ``electron,'' ``quark,'' ``gene,'' ``neuron'' and
``AIDS.''
“Abduction is not defined in terms of a fixed set of elements but
allows the possibility of creation of new elements that produce a new
assessment of coherence.”
“Elements can explain other elements which explain
other elements, so hypotheses can be layered and give rise to complex chains of
constraints. Abduction is not defined in terms of a fixed set of elements but
allows the possibility of creation of new elements that produce a new
assessment of coherence. New hypotheses need not be consistent with existing
ones, nor need the facts be completely explained. Maximizing coherence involves
explaining as much as possible (positive constraints) and being as consistent
as possible (negative constraints), but perfection is not to be sought in
abductive reasoning.”
Design and the design process include both
inductive and deductive reasoning.
Second, the deductive model of explanation does not
even provide sufficient conditions for explanation, since there are examples
that conform to the model but do not appear to constitute explanations.”
“But other examples such as the flagpole show that
some additional notion of causal
relevance is crucial to many kinds of explanation, and there is little hope of
capturing this notion using logic alone. Contrast Pearl's [20] work on Bayesian
networks and Peng and Reggia's [21] model of abduction, which employ
ineliminably (?) intuitive notions of causality. A general model of abduction
requires an account of explanation that is richer than deduction.”
“The plausibility of the lower-level hypothesis
comes not only from what it explains, but also from it itself being explained.
This kind of hierarchical explanation in which hypotheses explain other
hypotheses that explain data is also found in science and medicine;”
“But as both Bayesian and explanatory coherence
analyses allow, causes are often themselves effects and assessment of overall
acceptability of explanatory hypotheses must take this into account.”
“A fully general characterization of abduction
would have to allow representations of causes and effects that are pictorial as
well as ones that are sentential.”
“It would also have to admit forms of explanation
that centrally employ visual transformations as well as ones that employ
deduction and other verbal processes.
“Abduction is often thought of as a kind of reverse
deduction;”
“A general model of abduction requires an account
of explanation that is richer than deduction.”
Design along with the design process searches
for meaning and purpose.
“In addition, we should not rule out the possibility
of a multimodal theory of abduction that includes non-visual, non-verbal
representations involving smell, touch, and emotion.”
“While this requirement may be acceptable for
mundane applications, it will not do for interesting cases of belief revision
where the introduction of new hypotheses leads to rejection of previously held
theories.”
Design oversees the symbiotic process of
balancing.
“Elements can explain other elements which explain
other elements, so hypotheses can be layered and give rise to complex chains of
constraints. Abduction is not defined in terms of a fixed set of elements but
allows the possibility of creation of new elements that produce a new
assessment of coherence. New hypotheses need not be consistent with existing ones,
nor need the facts be completely explained. Maximizing coherence involves
explaining as much as possible (positive constraints) and being as consistent
as possible (negative constraints), but perfection is not to be sought in
abductive reasoning.”
“We cannot simply delete a belief and then replace
it with one inconsistent with it, because until the new belief comes in
competition with the old one, there is no reason to delete the old one. Belief
revision requires a complex balancing of a large number of beliefs and kinds of
evidence.”
Design links the parts with the whole and the
whole with its parts.
“Making sense is a holistic matter of fitting the
puzzling facts into a coherent pattern of representations.”
“Elements can explain other elements which explain other elements,
so hypotheses can be layered and give rise to complex chains of constraints.
Abduction is not defined in terms of a fixed set of elements but allows the
possibility of creation of new elements that produce a new assessment of
coherence. New hypotheses need not be consistent with existing ones, nor need
the facts be completely explained. Maximizing coherence involves explaining as
much as possible (positive constraints) and being as consistent as possible
(negative constraints), but perfection is not to be sought in abductive
reasoning”
“The requirement of completeness
makes sense only in limited closed domains such as simple circuits where one
can be assured that everything can be explained given the
known causes.”
“This is a laudable goal but does not justify
building completeness into the definition of an explanation, since the goal is
so rarely accomplished in realistic situations. From medicine to science, it is
not typically the case that everything can be explained even by the best of
theories”.
“Making sense is a holistic matter of fitting the
puzzling facts into a coherent pattern of representations. The notion of
coherence has usually remained vague, but Thagard and Verbeurgt [29] have
recently defined coherence in terms of maximization of constraint satisfaction.
After briefly stating their definition, we will show how abduction can be
reconceptualized as a coherence problem.”
“But simplicity is an elusive notion that is not
adequately captured by the relation of subset minimality which deals only with
cases where we can prefer an explanation by a set of hypotheses to an
explanation by a superset of those hypotheses. We need a broader notion of simplicity
to handle cases where the competing explanations are accomplished by sets of
hypotheses that are of different sizes but are not subsets of each other.”
“We cannot simply delete a belief and then replace
it with one inconsistent with it, because until the new belief comes in
competition with the old one, there is no reason to delete the old one. Belief
revision requires a complex balancing of a large number of beliefs and kinds of
evidence. “
”Elements can explain other elements which explain
other elements, so hypotheses can be layered and give rise to complex chains of
constraints. Abduction is not defined in terms of a fixed set of elements but
allows the possibility of creation of new elements that produce a new
assessment of coherence. New hypotheses need not be consistent with existing
ones, nor need the facts be completely explained. Maximizing coherence involves
explaining as much as possible (positive constraints) and being as consistent
as possible (negative constraints), but perfection is not to be sought in
abductive reasoning.”
Design
invites change and is intuitive by nature.
In scientific reasoning, in contrast, the task is
to explain as much of the data as you can and to come up with a set of
explanatory hypotheses that is better than the current set. It is a matter of
satisficing (choosing the most coherence set of hypotheses) rather than
optimizing. Abduction characterized in terms of coherence is still intractable,
but efficient approximation algorithms exist. There is also the possibility
that heuristic search made possible by visual representations can greatly
improve the computability of abductions, although this remains to be shown.
“Elements can explain other elements which explain
other elements, so hypotheses can be layered and give rise to complex chains of
constraints. Abduction is not defined in terms of a fixed set of elements but
allows the possibility of creation of new elements that produce a new
assessment of coherence. New hypotheses need not be consistent with existing
ones, nor need the facts be completely explained. Maximizing coherence involves
explaining as much as possible (positive constraints) and being as consistent
as possible (negative constraints), but perfection is not to be sought in
abductive reasoning.”
“Such pictures provide an iconic representation of
the event that you conjecture to have happened, since the picture you form
resembles the hypothesized event in a much more direct way than a verbal/sentential
representation would. Whenever our knowledge of how things work in the world
involves dynamic pictorial representations, these representations can be used
to generate iconic explanations of what occurs.
Reconceptualization is fundamental to design
and the design process.
“But an oversimplified formalization can distract
from important aspects of the kinds of reasoning that underlie intelligence.
Graph grammars and other techniques for visual representation offer the
prospects of developing more general accounts of the nature of abductive
reasoning, which should be construed
not as a deviant form of deduction, but as a coherence problem.”
Ref:
Conclusion:
Abductive reasoning is
synonymous with the design process. Design by means of symbolic representation is
synonymous with abductive reasoning. Design creates an exploratory fulcrum where
change can be observed within any arrangement of circumstances consisting of two
or more elements. In reference to change, design reveals how abductive
reasoning is symbolic in nature, i.e. visually/mentally/physically and
emotionally, a method of reconceptualization in the form of a coherent
situation or circumstance, especially where creativity is involved.
Neil de Grasse Tyson
"Where wisdom reigns, there is no conflict between thinking and feeling."
Carl Jung
I believe that a fuller understanding of design’s role
in the application of abductive reasoning will meet current and future challenges
confronting the scientific paradigm, and that in cooperation with the
application of a “design template” can bring forward a new understanding of
consciousness itself.
“The intuitive mind is a sacred gift and the rational mind a faithful servant. We have created a society that honors the servant and has forgotten the gift.”
Albert Einstein
"Because of their very nature, science and logical thinking can never decide what is possible or impossible. Their only function is to explain what has been ascertained by experience and observation."
Rudolf Steiner
* * *
To be design conscious you must be more than an observer.
* * *
By virtue of design, AI provides us the opportunity to learn what it means to be human.
* * *
* * *
Edited: 03.14.2020, 11.28.2020, 01.01.2021, 01.20.2021, 04,12,2021, 01.06.2022, 02.07.2022, 03.15.2022, 03.23.2023, 04.16.2023, 02.01.2024, 002.05.2025
Find your truth. Know your mind. Follow your heart. Love eternal will not be denied. Discernment is an integral part of self-mastery. You may share this post as long as author, copyright and URL https://designmetaphysics.blogspot.com/ is included as the resource and shared on a non-commercial no charge basis. Please note … posts are continually being edited over time. Copyright © 2006 - 2023 C.G. Garant. All Rights Reserved. (Fair use notice) AI usage prohibited. You are also invited to visit https://designconsciousness.blogspot.com/ and https://sagariandesignnetwork.blogspot.com and https://www.pinterest.com
