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Hasty Generalizers and Hybrid Abducers External Semiotic Anchors and Multimodal Representations

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

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

Hasty Generalizers and Hybrid Abducers

External Semiotic Anchors and Multimodal Representations

Lorenzo Magnani

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

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

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

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
- Cynthia is a bad driver.
- Women are bad drivers.
- It is sometimes worse not to generalize in this way.

Van Benthem (2000) on Abduction and Induction

- 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.

- 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

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

- Bounded Information
- Lack of Time
- 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).

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)

DEDUCTIVE INVALID ARGUMENTS (NOT TRUTH PRESERVING

FEATURES)

FORMAL

FALLACIES I

(LOGICAL PERSPECTIVE)

INFORMAL

BAD REASONIGS

INDUCTIVE INVALID ARGUMENTS

GOOD EPISTEMIC ACTIONS IN PRESENCE OF “BAD” REASONINGS

ACTUALLY HAPPENS RULE

LIMITED COGNITIVE SETTING

FALLACIES II

(AGENT-BASED PERSPECTIVE)

BEING-LIKE-US AS HASTY GENERALIZERS

ABDUCTION AS A FALLACIOUS ARGUMENT

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

COGNITIVE ECONOMIES

CASUAL TRUTH PRESERVING FEATURE OF FALLACIES

- what is abduction?
- theoretical abduction

(sentential, model-based)

- manipulative abduction

(mathematical diagrams, construals)

scientific discovery

diagnosis

- what is abduction?
- theoretical abduction

(sentential, model-based)

- manipulative abduction

(mathematical diagrams, construals)

scientific discovery

diagnosis

- 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

SENTENTIAL

Peirce stated that all thinking is in signs, and signs can be icons, indices, or symbols. Moreover, allinferenceis 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 ismodel-based. Of course model-based reasoning acquires its peculiar creative relevance when embedded in abductive processes

Theoretical Abduction

MODEL-BASED

Mathematical Diagrams (also Model-Based)

manipulative abductionnicely introduces to

hypothesis generationin 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.

Thinking through doing

Construals

Manipulative Abduction

“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).”

“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)”

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.

- Samples and Manipulative Abduction
- ConstrualsManipulative 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.

LOGICAL IDEAL ABDUCTIVE and INDUCTIVE SYSTEMS

- - symbolic: they activate and “anchor” meanings in material communicative andintersubjective 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.

- 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

- 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).

- 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.

- 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.

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