Hasty Generalizers and Hybrid Abducers

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23 Φεβ 2014 (πριν από 3 χρόνια και 3 μήνες)

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Hasty Generalizers and Hybrid Abducers

External Semiotic Anchors and Multimodal Representations


Department of Philosophy and Computational
Philosophy Laboratory, University of Pavia, Italy



Department of Philosophy, Sun Yat
-
sen University,
Canton, China

Workshop on Abduction and Induction in AI and Scientific Modeling (AIAI06),

ECAI2006, Riva del Garda, Italy, August 29, 2006



Integrating Induction and Abduction



Induction in Organic Agents


Mimetic Inductions


Ideal and Computational Inductive Agents


Mimetic Abductions


Ideal and Computational Abductive Agents


Sentential, Model
-
Based and Manipulative
Abduction


A Cognitive Integration:
Samples, Induction, and Abduction



Van Benthem (2000) on
Abduction

and
Induction



Indeed, it is not easy to give a crystal
-
clear
definition of them, either independently or in
their inter
-
relationship. (Of course, this is not
easy for “
Deduction
” either)



Induction in
Organic Agents



Hasty Generalization, Secundum Quid, Biased
Statistics, Other Fallacies


Strategic versus Rational thinking (conscious
but often tacit)


Mill says that institutions rather than
individuals are the embodiment of inductive
logics

Organic Induction

Human beings mess thing up
above the simplest levels of
complexity. This is particularly
true of
inductive inferences
: it
seems there is a tendency for
hasty and unfounded
generalizations.

But not every generalization
from a single case is bad (that
is a fallacy). Hasty
generalization is a
prudent
strategy
, especially when risks
are high: survival skills are
sometimes exercised
successfully but not
rationally
.
We have a cognitive error but
not a strategic error. This fact
always stimulated the
theorists to say something
helpful about the problem of
induction


MILL
-

(and on
abduction
-

PEIRCE) both
fallacious but strong
.


The Human agent is
genetically and culturally
endowed with a kind of
rational survival kit
(Woods, 2004) also
containing some
strategic

uses of fallacies.

For example:

Hasty generalization

1.
Cynthia is a bad driver.

2.
Women are bad drivers.

It is sometimes worse not to
generalize in this way.



The kid on touching the
element on his mother’s
kitchen stove learns in one
case never to do that again
(
primitive induction
)


This is not an offense to
inductive reasoning.

MILL provides “Methods” for
Induction

PEIRCE integrates Abduction and
Induction through the
syllogistic framework where
the two non
-
deductive
inferences can be clearly
distinguished.

Mimetic Induction


Mimetic
Abduction


Ideal Agents




Kid’s performance is a strategic success and a
cognitive failure.


Human beings are hardwired for survival and
for truth alike so best strategies can be built
and made explicit, through self
-
correction and
re
-
consideration (for example Mill’s methods).


Mill’s methods for induction, Peirce’s
syllogistic and inferential models for abduction
Inductive and Abductive Agents


Ideal Logical Inductive and Abductive Agents


Ideal Computational Inductive, Abductive, and
Hybrid Agents


Merely successful strategies are replaced with
successful strategies that also tell the more
precise truth about things.

Agent
-
Based reasoning and

Agent
-
based Logic


We will exploit the framework of
agent
-
based
reasoning

as illustrated by Gabbay and Woods
(Woods 2004; Gabbay, Woods 2005), so
adopting the perspective of a cognitive agent.



In the agent
-
based reasoning above (Gabbay and
Woods, 2001) logic can be considered a
formalization of what is done by a cognitive
agent: logic is
agent
-
based
.

Agent
-
Based reasoning


Agent Based Reasoning consist in describing and analyzing the
reasoning occurring in problem solving situations where the
agent access to cognitive resources encounters limitations such
as


1.
Bounded Information

2.
Lack of Time

3.
Limited Computational Capacity.



Actually Happens Rule: to see what agent should do we should
have to look first to what they actually do. Then, if there is
particular reason to do so, we would have to repair the account

(Woods, 2005).



Agent
-
Based logic and the framework
of Non
-
Monotonic Logic


Classical logic as a complete system


Deduction and
modus ponens (
the “
truth
preserving feature”
)


Non Monotonic Logic:
new
information can
compel us to revise previous generated
hypotheses (Decision
-
Making Process and the

casual truth preserving feature
”)


Not
-
only
-
deductive reasoning



Agent
-
based reasoning and
Actually happens rule


This rule is a particular attractive assumption
about human cognitive behaviour mainly for two
reasons:



beings like us make a lot of
errors




cognition

is something that we are actually very
good at (
strategic rationality

and
cognitive
economies
)



Fallacies I


It is in this framework that fallacious ways of
reasoning are seen as widespread in human
beings’ cognitive performances, and nevertheless
they can in some cases be redefined and
considered as
good ways of reasoning
.



A
fallacy

is a
pattern of
poor

reasoning which
appear to be a pattern of
good

reasoning (
Hansen, 2002).



Fallacies II

Formal fallacy

Informal fallacy

Deductive argument
which has an invalid
form

(not Truth
Preserving
Reasoning)


(expl.
Affirming the
Consequent
)

Any other invalid
mode of reasoning
whose failing is not in
the shape of the
argument



(expl.
Ad hominem, Hasty
Generalization,…)

The Toddler and the Stove


A sample of
Hasty Generalization


X% of all observed A's are B''s:
(The stove
touched

burns)


Therefore X% of all A's are Bs:
(
All

the stoves burn)


THE STOVE
TOUCHED BURNS

HASTY
GENERALIZATION

ALL THE STOVES

BURN

FALLACIES I

(LOGICAL
PERSPECTIVE)

FORMAL

INFORMAL

BAD REASONIGS

DEDUCTIVE INVALID
ARGUMENTS (
NOT TRUTH
PRESERVING


FEATURES)

INDUCTIVE INVALID
ARGUMENTS

FALLACIES II

(AGENT
-
BASED
PERSPECTIVE)

LIMITED COGNITIVE
SETTING

ACTUALLY HAPPENS
RULE

FALLACIES ARE
“BETTER THAN
NOTHING”
(RATIONAL
SURVIVAL KIT)

COGNITIVE ECONOMIES

CASUAL TRUTH PRESERVING
FEATURE OF FALLACIES

GOOD EPISTEMIC
ACTIONS IN PRESENCE OF
“BAD” REASONINGS

ABDUCTION AS A FALLACIOUS
ARGUMENT

BEING
-
LIKE
-
US AS HASTY
GENERALIZERS

Abduction as an example of fallacy
considered in Agent
-
Based
Reasoning

Abduction

Affirming

the Consequent

Abduction

that only


generate plausible

hypotheses

(selective or creative)


Abduction

considered as

“Inference to

the Best Explanation.”



what is abduction?


theoretical abduction


(sentential, model
-
based)





manipulative abduction


(mathematical diagrams, construals)

creative, selective

scientific
discovery

diagnosis


what is abduction?


theoretical abduction


(sentential, model
-
based)





manipulative abduction


(mathematical diagrams, construals)

creative, selective

scientific
discovery

diagnosis

Theoretical Abduction

SENTENTIAL

MODEL
-
BASED

Theoretical Abduction

SENTENTIAL

MODEL
-
BASED

Peirce stated that all thinking is in signs,
and signs can be icons, indices, or
symbols. Moreover, all

inference

is a
form of sign activity, where the word
sign includes “feeling, image,
conception, and other representation”
(
CP

5.283), and, in Kantian words, all
synthetic forms of cognition. That is, a
considerable part of the thinking activity
is

model
-
based
. Of course model
-
based reasoning acquires its peculiar
creative relevance when embedded in
abductive processes


Simulative reasoning


Analogy


Visual
-
iconic reasoning


Spatial thinking


Thought experiment


Perception, sense activities


Visual imagery


Deductive reasoning(
Beth’s


method of semantic tableaux,


Girard’s “geometry” of proofs, etc.)


Emotion


Model
-
based cognition

Manipulative Abduction

Mathematical Diagrams
(also Model
-
Based)

Construals

Thinking through doing

manipulative abduction

nicely
introduces to

hypothesis generation

in active,
distributed, and embodied cognition


The activity of


thinking through
doing

is made possible not simply
by mediating cognitive artifacts and
tools, but by active process of
testing and manipulation.


Manipulative Abduction

Construals

Thinking through doing

Samples, Induction, Abduction

Manipulative abduction

can be considered a kind of
basis for further meaningful
inductive generalizations
.
For example different construals can give rise to
different inductive generalizations. If “an inductive
generalization is an inference that goes from the
characteristics of some observed samples of
individuals to a conclusion about the distribution of
those characteristics in some larger populations”
(Josephson) what characterizes the sample as
“representative” is its effect (sample frequency) by
reference to part of its cause (populations frequency):
this should be considered a conclusion about its cause.



“If we do not think of inductive
generalizations as abductions
we are at a loss to explain why
such inference is made stronger
and more warranted, if in
connecting data we make a
systematic search for counter
-
instances and cannot find any,
than it would be just take the
observation passively. Why is
the generalization made
stronger by making an effort to
examine a wide variety of types
of A’s? The answer is that it is
made stronger because the
failure of the active search of
counter
-
instances tend to rule
out various hypotheses about
ways in which the sample might
be biased, that is, is
strengthens the abductive
conclusion by ruling out
alternative explanations for the
observed frequency (Josephson
2000)”


Samples and Manipulative Abduction


Construals

Manipulative abduction is the correct way for
describing the features of what are called ``smart inductive
generalizations'', as contrasted to the trivial ones. For
example, in science
construals
can shed light on this process
of sample ``production'' and ``appraisal'': through
construals, manipulative
creative

abduction generates
abstract hypotheses but in the meantime can originate
possible bases for further meaningful inductive
generalizations through the identification of new samples
(or of new features of already available sample, for instance
in terms of the detection of relevant circumstances).
Different generated construals can give rise to different
plausible inductive generalizations.

“If we think that a sampling
method is fair and unbiased,
then straight generalization
gives the best explanation of the
sample frequencies. But if the
size is small, alternative
explanations, where the
frequencies differ, may still be
plausible. These alternative
explanations become less and
less plausible as the sample size
grows, because the sample
being unrepresentative due to
chance becomes more and more
improbable. Thus viewing
inductive generalization as
abductions show why sample
size is important. Again, we see
that analyzing inductive
generalizations as abductions
shows us how to evaluate the
strengths of these inferences
(Josephson, p. 42).”

LOGICAL IDEAL ABDUCTIVE and INDUCTIVE SYSTEMS

-

symbolic
: they activate and “anchor”
meanings

in
material
communicative and

intersubjective
mediators

in
the framework of the phylogenetic, ontogenetic, and
cultural reality of the human being and its language. They
originated in embodied cognition and gestures we share
with some mammals but also non mammals animals (cf.
monkey knots and pigeon categorization, Grialou, Longo,
and Okada, 2005);

-

abstract
: they are based on a
maximal

independence
regarding sensory modality; strongly stabilize experience
and common categorization. The maximality is especially
important: it refers to their practical and historical
invariance and stability;

-
rigorous
: the rigor of proof is reached through a difficult
practical experience. For instance, in the case of
mathematics, as the

maximal

place for convincing
reasoning. Rigor lies in the stability of proofs and in the
fact they can be iterated.

Mathematics is the best example of maximal stability and
conceptual invariance.


logical systems are in turn sets of proof invariants,
sets of structures that are preserved from one proof
to another or which are preserved by proof
transformations. They are the result of a distilled
praxis, the praxis of proof: it is made of
maximally
stable regularities
.



cf. the cognitive analysis of
the origin of the
mathematical continuous
line as a pre
-
conceptual
invariant of three cognitive
practices (Theissier, 2005),
and of the numeric line
(Châtelet, 1993; Dehaene,
1997; Butterworth, 1999).



MAXIMIZATION OF MEMORYLESSNESS

characterizes
demonstrative reasoning. Its properties do not yield
information about the past, contrarily for instance to
the narrative and not logical descriptions of non
-
demonstrative processes, which often involve
“historical”, “contextual”, and “heuristic” memories.



Flach and Kakas (2000). A useful
perspective on integration of
abduction

and
induction
:


explanation

(hypothesis does not
refer to observables


selective
abduction [but abduction creates
new hypotheses too])


generalization


genuinely new
(hypothesis can entail additional
observable information on
unobserved individual, extending
the theory
T
)


Imagine we have a new abductive
theory
T
’ =
T



H

constructed by
induction: an inductive extension
of a theory can be viewed as set of
abductive extensions of the
original theory
T
.


controversies on IAI are of course
open and alive

Thanks

lorenzo.magnani@unipv.it