One-Sided Error Probabalistic Inductive Interface and Reliable Frequency Identification

For EX- and BC-type identification, one-sided error probabilistic inference and reliable frequency identification on sets of functions are introduced. In particular, we relate the one to the other and characterize one-sided error probabilistic inference to exactly coincide with reliable frequency identification, on any setM. Moreover, we show that reliable EX and BC-frequency inference forms a new discrete hierarchy having the breakpoints 1, l/2, l/3, ..

One-Sided Error Probabalistic Inductive Interface and Reliable Frequency Identification

For EX- and BC-type identification, one-sided error probabilistic inference and reliable frequency identification on sets of functions are introduced. In particular, we relate the one to the other and characterize one-sided error probabilistic inference to exactly coincide with reliable frequency identification, on any setM. Moreover, we show that reliable EX and BC-frequency inference forms a new discrete hierarchy having the breakpoints 1, l/2, l/3, ..

Learning Recursive Functions Refutably

Learning of recursive functions refutably means that for every recursive function, the learning machine has either to learn this function or to refute it, i.e., to signal that it is not able to learn it. Three modi of making precise the notion of refuting are considered. We show that the corresponding types of learning refutably are of strictly increasing power, where already the most stringent of them turns out to be of remarkable topological and algorithmical richness. All these types are closed under union, though in different strengths. Also, these types are shown to be different with respect to their intrinsic complexity; two of them do not contain function classes that are “most difficult” to learn, while the third one does. Moreover, we present characterizations for these types of learning refutably. Some of these characterizations make clear where the refuting ability of the corresponding learning machines comes from and how it can be realized, in general. For learning with anomalies refutably, we show that several results from standard learning without refutation stand refutably. Then we derive hierarchies for refutable learning. Finally, we show that stricter refutability constraints cannot be traded for more liberal learning criteria

Reflective inductive inference of recursive functions

AbstractIn this paper, we investigate reflective inductive inference of recursive functions. A reflective IIM is a learning machine that is additionally able to assess its own competence.First, we formalize reflective learning from arbitrary, and from canonical, example sequences. Here, we arrive at four different types of reflection: reflection in the limit, optimistic, pessimistic and exact reflection.Then, we compare the learning power of reflective IIMs with each other as well as with the one of standard IIMs for learning in the limit, for consistent learning of three different types, and for finite learning

On Learning of Functions Refutably

Learning of recursive functions refutably informally means that for every recursive function, the learning machine has either to learn this function or to refute it, that is to signal that it is not able to learn it. Three modi of making precise the notion of refuting are considered. We show that the corresponding types of learning refutably are of strictly increasing power, where already the most stringent of them turns out to be of remarkable topological and algorithmical richness. Furthermore, all these types are closed under union, though in different strengths. Also, these types are shown to be different with respect to their intrinsic complexity; two of them do not contain function classes that are “most difficult” to learn, while the third one does. Moreover, we present several characterizations for these types of learning refutably. Some of these characterizations make clear where the refuting ability of the corresponding learning machines comes from and how it can be realized, in general.For learning with anomalies refutably, we show that several results from standard learning without refutation stand refutably. From this we derive some hierarchies for refutable learning. Finally, we prove that in general one cannot trade stricter refutability constraints for more liberal learning criteria

Apperceptive patterning: Artefaction, extensional beliefs and cognitive scaffolding

In “Psychopower and Ordinary Madness” my ambition, as it relates to Bernard Stiegler’s recent literature, was twofold: 1) critiquing Stiegler’s work on exosomatization and artefactual posthumanism—or, more specifically, nonhumanism—to problematize approaches to media archaeology that rely upon technical exteriorization; 2) challenging how Stiegler engages with Giuseppe Longo and Francis Bailly’s conception of negative entropy. These efforts were directed by a prevalent techno-cultural qualifier: the rise of Synthetic Intelligence (including neural nets, deep learning, predictive processing and Bayesian models of cognition). This paper continues this project but first directs a critical analytic lens at the Derridean practice of the ontologization of grammatization from which Stiegler emerges while also distinguishing how metalanguages operate in relation to object-oriented environmental interaction by way of inferentialism. Stalking continental (Kapp, Simondon, Leroi-Gourhan, etc.) and analytic traditions (e.g., Carnap, Chalmers, Clark, Sutton, Novaes, etc.), we move from artefacts to AI and Predictive Processing so as to link theories related to technicity with philosophy of mind. Simultaneously drawing forth Robert Brandom’s conceptualization of the roles that commitments play in retrospectively reconstructing the social experiences that lead to our endorsement(s) of norms, we compliment this account with Reza Negarestani’s deprivatized account of intelligence while analyzing the equipollent role between language and media (both digital and analog)

Modular and cultural factors in biological understanding: an experimental approach to the cognitive basis of science

What follows is a discussion of three sets of experimental results that deal with various aspects of universal biological understanding among American and Maya children and adults. The first set of experiments shows that by the age of four-to-five years (the earliest age tested in this regard) urban American and Yukatek Maya children employ a concept of innate species potential, or underlying essence, as an inferential framework for understanding the affiliation of an organism to a biological species, and for projecting known and unknown biological properties to organisms in the face of uncertainty. The second set of experiments shows that the youngest Maya children do not have an anthropocentric understanding of the biological world. Children do not initially need to reason about non-human living kinds by analogy to human kinds. The third set of results show that the same taxonomic rank is cognitively preferred for biological induction in two diverse populations: people raised in the Mid-western USA and Itza' Maya of the Lowland Meso-american rainforest. This is the generic species the level of oak and robin. These findings cannot be explained by domain-general models of similarity because such models cannot account for why both cultures prefer species-like groups in making inferences about the biological world, although Americans have relatively little actual knowledge or experience at this level. The implication from these experiments is that folk biology may well represent an evolutionary design: universal taxonomic structures, centred on essence-based generic species, are arguably routine products of our ‘habits of mind,' which may be in part naturally selected to grasp relevant and recurrent ‘habits of the world.' The science of biology is built upon these domain-specific cognitive universals: folk biology sets initial cognitive constraints on the development of any possible macro-biological theory, including the initial development of evolutionary theory. Nevertheless, the conditions of relevance under which science operates diverge from those pertinent to folk biology. For natural science, the motivating idea is to understand nature as it is ‘in itself,' independently of the human observer (as far as possible). From this standpoint, the species-concept, like taxonomy and teleology, may arguably be allowed to survive in science as a regulative principle that enables the mind to readily establish stable contact with the surrounding environment, rather than as an epistemic concept that guides the search for truth

Thinking Things Through

A Photcopy of Thinking Things Through, Princeton Univeresity Press, 198