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Inductive Generalizations and Manipulative Abduction Department of Philosophy and Computational Philosophy Laboratory, University of Pavia, Italy Department.

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Presentation on theme: "Inductive Generalizations and Manipulative Abduction Department of Philosophy and Computational Philosophy Laboratory, University of Pavia, Italy Department."— Presentation transcript:

1 Inductive Generalizations and Manipulative Abduction Department of Philosophy and Computational Philosophy Laboratory, University of Pavia, Italy Department of Philosophy, Sun Yat-sen University, Canton, China Integrating Abduction and Induction in AI, Edinburgh, UK, July 29, 2005

2 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

3 Van Benthem (2000) on Abduction and Induction Van Benthem (2000) on Abduction and Induction DeductionIndeed, 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 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. 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 mothers 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.

4 Mimetic Induction – Mimetic Abduction Ideal Agents Kids 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 Mills methods). Mills methods for induction, Peirces 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.

5 what is abduction? theoretical abduction (sentential, model-based) manipulative abduction (mathematical diagrams, construals) creative, selective scientific discovery diagnosis

6 what is abduction? theoretical abduction (sentential, model-based) manipulative abduction (mathematical diagrams, construals) creative, selective scientific discovery diagnosis

7 Theoretical Abduction SENTENTIAL MODEL-BASED

8 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(Beths method of semantic tableaux, Girards geometry of proofs, etc.) Emotion Model-based cognition

9 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.

10 Manipulative Abduction Construals Thinking through doing

11 curious and anomalous phenomena dynamical aspects artificial apparatus epistemic acting CONJECTURAL TEMPLATES I (they act on external representation and originate epistemic mediators) looking checking the information comparing events re-ordering, changing relationships choosing, discarting, imaging further manipulations apparatus to measure paleomagnetization of samples Ampére frame turbulent dissipation and diffusivity Turing Universal Practical Computing Machine (PCM) Cognitive Mediators and External Models and Representations

12 simplification of the reasoning task treatment of incomplete and inconsistent information control of sense data external artifactual models natural objects and phenomena CONJECTURAL TEMPLATES II

13 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 As? 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).

14 Mimetic Representations and their Non-Deductive Effect - external representations are formed by external materials that express (through reification) concepts and problems that do not have a natural home in the brain. - internalized representations are internal re-projections, a kind of recapitulations, (learning) of external representations in terms of neural patterns of activation in the brain. They can be internally manipulated like external objects and can originate new internal reconstructed representations through the neural activity of transformation and integration. This explains why human beings seem to perform both computations of a connectionist type such as the ones involving representations as - (I LEVEL) patterns of neural activation that arise as the result of the interaction between body and environment (and suitably shaped by the evolution and the individual history): pattern completion or image recognition, and computations that use representations as - (II LEVEL) derived combinatorial syntax and semantics dynamically shaped by the various external representations and reasoning devices found or constructed in the environment (for example geometrical diagrams); they are neurologically represented contingently as pattern of neural activations that sometimes tend to become stabilized structures - stabilized thoughts - and to fix and so to permanently belong to the I LEVEL At this stage the patterns of neural activation no longer need a direct stimulus from the environment for their construction and fixation. In a certain sense they can be viewed as fixed internal records of external structures that can exist also in the absence of such external structures. These patterns of neural activation that constitute the First- Level Representations always keep record of the experience that generated them and, thus, always carry the Second-Level Representation associated to them, even if in a different form, the form of memory and not the form of a vivid sensorial experience. Now, the human agent, via neural mechanisms, can retrieve these Second-Level Representations and use them as internal representations or use parts of them to construct new internal representations very different from the ones stored in memory. the I level originates those sensations (they constitute a kind of face we think the world has), that provide room for the II level to reflect the structure of the environment, and, most important, that can follow the computations suggested by these external structures. the growth of the brain and especially the synaptic and dendritic growth are profoundly determined by the environment mimetic external representations mirror concepts and problems that are already represented in the brain and need to be enhanced, solved, further complicated, etc. MANIPULATIVE ABDUCTION - NON-DEMONSTRATIVE - IS AN ASPECT OF THIS INTERPLAY MIND transcends the boundary of the individual and includes parts of that individuals environment DESCARTES mind-body dualism we no longer need Descartes dualism: we only have brains that make up large, integrated, material cognitive systems like demonstrative systems, non- demonstrative tools, LCMs and PCMs, etc. the only problem is How meat knows (sum ergo cogito?)

15 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 estensions of the original theory T. controversies on IAI are of course open and alive

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