Strong Constructivizations Research Articles

Cultural-Anthropological Basis of Strong Constructivism in Social Cognition

Purpose. This article is aimed at identifying the cultural-anthropological limits of the applicability of strong constructivism in social cognition. Theoretical basis. The study of epistemic cultures, carried out by the modern German philosopher of science Karin Knorr Cetina, gave reasons to rethink the role of cultural anthropology as a methodological basis of strong constructivism not only for scientific cognition, but also for educational practices, and perhaps also for some other social practices. An important role in identifying less successful versions of strong constructivism was played by the concept of fictionalism of the German philosopher Hans Veihinger, the Chilean biologists Humberto Maturán and Francisco Varela, and the German sociologist and philosopher Niklas Luhmann. Originality. Strong constructivism has broad prospects for use within cultural anthropology as an identification of the cultural foundations of human nature. Local research and educational practices are defined as a model for the formation of those social characteristics of their participants, which they themselves change through self-improvement. Strong constructivists involve the individual empirical experience of researchers, and also correct the inherited rules of scientific research as elements of research procedures and practices, thanks to which they achieve the creation of a common epistemic culture and the elimination of myths about the isolation of scientific cognition from the world. Conclusions. False ways of interpreting strong constructivism as fictionalism and as realism have been revealed. Fictionalism, as a methodology focused on the study of the contents of consciousness, loses the empirical experience of the world. Philosophical realism as positivism in the philosophy of science reduces the significance of scientific discoveries to confirmation of the laws of nature. Karin Knorr Cetina’s proposal to consider constructivism "on its own terms" appears not as a moderate compromise between these extremes, but as the only possible way to adequately reconcile the work of nature and the conscious activity of man. Such coordination takes place primarily in the creation of local epistemic cultures as a collective activity of researchers.

Degrees of Autostability Relative to Strong Constructivizations of Graphs

We show that each computably enumerable Turing degree is a degree of autostability relative to strong constructivizations for a decidable directed graph. We construct a decidable undirected graph whose autostability spectrum relative to strong constructivizations is equal to the set of all PA-degrees.

Degrees of Autostability for Prime Boolean Algebras

We look at the concept of algorithmic complexity of isomorphisms between computable copies of Boolean algebras. Degrees of autostability are found for all prime Boolean algebras. It is shown that for any ordinals α and β with the condition 0 ≤ α ≤ β ≤ ω, there is a decidable model for which 0(α) is a degree of autostability relative to strong constructivizations, while 0(β) is a degree of autostability. It is proved that for any nonzero ordinal β ≤ ω, there is a decidable model for which there is no degree of autostability relative to strong constructivizations, while 0(β) is a degree of autostability.

Index Set of Linear Orderings that are Autostable Relative to Strong Constructivizations

We prove that a computable ordinal α is autostable relative to strong constructivizations if and only if α < ω ω+1. We obtain an estimate of the algorithmic complexity for the class of strongly constructivizable linear orderings that are autostable relative to strong constructivizations.

The index set of the groups autostable relative to strong constructivizations

We obtain an exact bound for the algorithmic complexity of the class of strongly constructivizable computable groups that are autostable relative to strong constructivizations.

Autostability spectra for decidable structures

We study autostability spectra relative to strong constructivizations (SC-autostability spectra). For a decidable structure$\mathcal{S}$, the SC-autostability spectrum of$\mathcal{S}$is the set of all Turing degrees capable of computing isomorphisms among arbitrary decidable copies of$\mathcal{S}$. The degree of SC-autostability for$\mathcal{S}$is the least degree in the spectrum (if such a degree exists).We prove that for a computable successor ordinal α, every Turing degree c.e. in and above0(α)is the degree of SC-autostability for some decidable structure. We show that for an infinite computable ordinal β, every Turing degree c.e. in and above0(2β+1)is the degree of SC-autostability for some discrete linear order. We prove that the set of all PA-degrees is an SC-autostability spectrum. We also obtain similar results for autostability spectra relative ton-constructivizations.

Index Set of Structures with Two Equivalence Relations That Are Autostable Relative to Strong Constructivizations

We derive a bound on the algorithmic complexity for the class of computable structures with two equivalence relations that have a strong constructivization and are autostable relative to strong constructivizations. We construct codings of a linear order and of an automorphically nontrivial directed irreflexive graph into a structure with two equivalence relations. It is proved that such codings preserve the degree spectrum and d-computable dimension.

Degrees of Autostability Relative to Strong Constructivizations for Boolean Algebras

It is proved that for every computable ordinal α, the Turing degree 0 (α) is a degree of autostability of some computable Boolean algebra and is also a degree of autostability relative to strong constructivizations for some decidable Boolean algebra. It is shown that a Harrison Boolean algebra has no degree of autostability relative to strong constructivizations. It is stated that the index set of decidable Boolean algebras having degree of autostability relative to strong constuctivizations is ∏ 1 1 -complete.

Index Sets of Constructive Models of Finite and Graph Signatures that are Autostable Relative to Strong Constructivizations

We estimate algorithmic complexity of the class of computable models of finite and graph signatures that have a strong constructivization and are autostable relative to strong constructivizations.

Index sets of autostable relative to strong constructivizations constructive models for familiar classes

This paper calculates, in a precise way, the complexity of the index sets for computable structures that are autostable relative to strong constructivizations and belong to one of the following classes: linear orderings, Boolean algebras, distributive lattices, partial orderings, rings, and commutative semigroups. We also calculate the complexity of the index set for computable structures that have computable dimension n, where n is a fixed natural number greater than 1.

Index Sets of Constructive Models of Bounded Signature that are Autostable Relative to Strong Constructivizations

We evaluate algorithmic complexity of the class of computable models of bounded signature that have a strong constructivization and are autostable relative to strong constructivizations.

Autostability relative to strong constructivizations of Boolean algebras with distinguished ideals

We study Boolean algebras with distinguished ideals (I-algebras). We proved that a local I-algebra is autostable relative to strong constructivizations if and only if it is a direct product of finitely many prime models. We describe complete formulas of elementary theories of local Boolean algebras with distinguished ideals and a finite tuple of distinguished constants. We show that countably categorical I-algebras, finitely axiomatizable I-algebras, superatomic Boolean algebras with one distinguished ideal, and Boolean algebras are autostable relative to strong constructivizations if and only if they are products of finitely many prime models.

The index set of Boolean algebras autostable relative to strong constructivizations

We obtain exact estimates for the algorithmic complexity for the classes of strongly constructivizable computable models autostable relative to strong constructivizations and belonging to the following natural classes: Boolean algebras, distributive lattices, rings, commutative semigroups, and partial orders.

Index sets of constructive models of nontrivial signature autostable relative to strong constructivizations

Index sets of constructive models of nontrivial signature autostable relative to strong constructivizations

Index Sets of Constructive Models that are Autostable Under Strong Constructivizations

We obtain estimates for the algorithmic complexity of index sets for the class of decidable autostable models and the class of computable models that possess strong constructivizations and are autostable under strong constructivizations.

Index Sets of Almost Prime Constructive Models

We study complexity of index sets of strongly constructive almost prime models, almost prime constructive models, and almost prime with strong constructivizations Bibliography: 14 titles.

Autostability Spectra for Boolean Algebras

Autostability spectra for Boolean algebras and their various enrichments are explored. The basic notions and definitions of computable structure theory used in the paper can be found in [1, 2]. As usual, we write “c.e.” as an abbreviation for “computably enumerable.” Recall that a computable structure M is said to be decidable if its full diagram FD(M) is computable. A structure M is strongly constructivizable if M has a decidable copy. Let d be a Turing degree. A constructivizable structure A is said to be d-autostable if, for any computable copies B and C of A, there exists a d-computable isomorphism f : B → C. A strongly constructivizable structure A is d-autostable relative to strong constructivizations if, for any decidable copies B and C for A, there exists a d-computable isomorphism f : B → C. If A is a constructivizable structure, then the autostability spectrum of A is the set of all Turing degrees d for which the structure A is d-autostable. The autostability spectrum relative to strong constructivizations for a strongly constructivizable structure A is the set of all degrees d such that A is d-autostable relative to strong constructivizations. Denote the autostability spectrum of a structure A by AutSpec (A), and the autostability spectrum relative to strong constructivizations for A by SCAutSpec (A). We say that a Turing degree d is the degree of autostability (degree of autostability relative to strong constructivizations) for A if d is least in AutSpec (A) (in SCAutSpec (A)). Note that in ∗Supported by RFBR (project No. 14-01-00376), by the Grants Council (under RF President) for State Aid of Leading Scientific Schools (grant NSh-860.2014.1), and by the Russian Ministry of Education and Science (gov. contract No. 2014/139).

Degrees of autostability relative to strong constructivizations

The spectra of the Turing degrees of autostability of computable models are studied. For almost prime decidable models, it is shown that the autostability spectrum relative to strong constructivizations of such models always contains a certain recursively enumerable Turing degree; moreover, it is shown that for any recursively enumerable Turing degree, there exist prime models in which this degree is the least one in the autostability spectrum relative to strong constructivizations.

Enacting disability: how can science and technology studies inform disability studies?

This paper aims to discuss how science and technology studies (STS) can inform disability studies and challenge dominant approaches, such as the medical and the social models, in the ordering and representation of disability. Disability studies and STS have followed somewhat parallel paths in the history of ideas. From a positivist approach to their research objects to a strong social constructivism, both disciplines have moved to postmodern conceptualisations of science, technology and disability. In the same manner, this paper brings the conceptual vocabulary of actor-network theory (ANT) to the field of disability studies. ANT enables the ordering of disability as a simultaneous biological, material and semiotic phenomenon. The focus of the analysis shifts from merely defining disability as an impairment, handicap, or social construction (epistemology) to how disability is experienced and enacted in everyday practices, in policy-making, in the body, and in the built environment (ontology). This adoption of an ontological approach to disability allows the analysis to not only discuss how disability is done, but also to follow how disability groups and carriers of disability expertise and experience intervene in policy-making by developing ‘research in the wild’ and confronting scientific experts in different fora (ontological politics).

Autostability of prime models under strong constructivizations

We furnish an example of an Ehrenfeucht theory whose prime model is autostable under strong constructivizations and there exists a prime model in a finite expansion by constants that is nonautostable under strong constructivizations of the theory constructed.