Intuitionistic Theory Research Articles

Cognitive Representations of Social Relationships and their Developmental Origins.

In the human mind, what is a social relationship, and what are the developmental origins of this representation? I consider findings from infant psychology and propose that our representations of social relationships are intuitive theories built on core knowledge. I propose three central components of this intuitive theory. The purpose of the first component is to recognize whether a relationship exists, the purpose of the second is to characterize the relationship by categorizing it into a model and to compute its strength (i.e., intensity, pull, or thickness), and the purpose of the third is to understand how to change relationships through explicit or implicit communication. I propose that infants possess core knowledge on which this intuitive theory is built. This paper focuses on the second component and considers evidence that infants characterize relationships. Following Relational Models Theory (A. P. Fiske, 1992, 2004) I propose that from infancy humans recognize relationships that belong to three models: communal sharing (where people are 'one'), authority ranking (where people are ranked), and equality matching (where people are separate, but evenly balanced). I further propose that humans, and potentially infants, recognize a relationship's strength which can be thought of as a continuous representation of obligations (the extent to which certain actions are expected), and commitment (the likelihood that people will continue the relationship). These representations and the assumption that others share them allow us to form, maintain, and change social relationships throughout our lives by informing how we interpret and evaluate the actions of others and plan our own.

Play in Cognitive Development: From Rational Constructivism to Predictive Processing.

It is widely believed that play and curiosity are key ingredients as children develop models of the world. There is also an emerging consensus that children are Bayesian learners who combine their structured prior beliefs with estimations of the likelihood of new evidence to infer the most probable model of the world. An influential school of thought within developmental psychology, rational constructivism, combines these two ideas to propose that children learn intuitive theories of how the world works in part by engaging in play activities that allow them to gather new information for testing their theories. There are still, however, at least two pieces missing from rational constructivist theories of development. First, rational constructivism has so far devoted little attention to explaining why children's preferred form of learning, play, feels so fun, enjoyable, and rewarding. Rational constructivism may suggest that children are curious and like to play because reducing uncertainty and learning better theories of the causal workings of the world is enjoyable. What remains unclear, however, is why reducing uncertainty in play is interesting, fun, and joyful, while doing so in other forms of learning can be frustrating or boring. Second, rational constructivism may have overlooked how children, during play, will take control of and manipulate their environment, sometimes in an effort to create ideal niches for surprise-extraction, sometimes for developing strategies for making the world fit with their predictions. These missing elements from rational constructivism can be provided by understanding the contribution of play to development in terms of predictive processing, an influential framework in cognitive neuroscience that models many of the brain's cognitive functions as processes of model-based, probabilistic prediction.

$\text{TT}^{\Box}_{\mathcal C}$: a Family of Extensional Type Theories with Effectful Realizers of Continuity

$\text{TT}^{\Box}_{{\mathcal C}}$ is a generic family of effectful, extensional type theories with a forcing interpretation parameterized by modalities. This paper identifies a subclass of $\text{TT}^{\Box}_{{\mathcal C}}$ theories that internally realizes continuity principles through stateful computations, such as reference cells. The principle of continuity is a seminal property that holds for a number of intuitionistic theories such as System T. Roughly speaking, it states that functions on real numbers only need approximations of these numbers to compute. Generally, continuity principles have been justified using semantical arguments, but it is known that the modulus of continuity of functions can be computed using effectful computations such as exceptions or reference cells. In this paper, the modulus of continuity of the functionals on the Baire space is directly computed using the stateful computations enabled internally in the theory.

Intuitionistic sets and numbers: small set theory and Heyting arithmetic

AbstractIt has long been known that (classical) Peano arithmetic is, in some strong sense, “equivalent” to the variant of (classical) Zermelo–Fraenkel set theory (including choice) in which the axiom of infinity is replaced by its negation. The intended model of the latter is the set of hereditarily finite sets. The connection between the theories is so tight that they may be taken as notational variants of each other. Our purpose here is to develop and establish a constructive version of this. We present an intuitionistic theory of the hereditarily finite sets, and show that it is definitionally equivalent to Heyting Arithmetic , in a sense to be made precise. Our main target theory, the intuitionistic small set theory is remarkably simple, and intuitive. It has just one non-logical primitive, for membership, and three straightforward axioms plus one axiom scheme. We locate our theory within intuitionistic mathematics generally.

Intuitive Theories and the Cultural Evolution of Morality

We explore the role of intuitive theories in the cultural evolution of moral cognition, integrating recent work across subfields of psychology and suggesting directions for future research. Focusing on intuitive theories in the moral domain concerning how people judge the moral value of actions and make inferences about moral character, we review evidence that the specific forms these theories take vary across individuals and can change via social learning. We propose that cultural selection can operate over the intuitive theories people apply in the moral domain, in which particular variants of intuitive moral theories can be more “successful” to the extent that they are cognitively efficient or provide reputational benefits. Finally, we explore some implications of considering moral cognition as a kind of cultural technology that can be innovated, considering whether intuitive moral theories help or hinder our ability to improve our collective moral norms or practices.

People Have Systematically Different Ownership Intuitions in Seemingly Simple Cases

Our understanding of ownership influences how we interact with objects and with each other. Here, we studied people’s intuitions about ownership transfer using a set of simple, parametrically varied events. We found that people (N = 120 U.S. adults) had similar intuitions about ownership for some events but sharply opposing intuitions for others (Experiment 1). People (N = 120 U.S. adults) were unaware of these conflicts and overestimated ownership consensus (Experiment 2). Moreover, differences in people’s ownership intuitions predicted their intuitions about the acceptability of using, altering, controlling, and destroying the owned object (N = 130 U.S. adults; Experiment 3), even when ownership was not explicitly mentioned (N = 130 U.S. adults; Experiment 4). Subject-level analyses suggest that these disagreements reflect at least two underlying intuitive theories, one in which intentions are central to ownership and another in which physical possession is prioritized.

An unjustly neglected theory of semantic reference

AbstractThere is a simple, intuitive theory of the semantic reference of proper names that has been unjustly neglected. This is the view that semantic reference is conventionalized speakers reference, i.e. the view that a name semantically refers to an object if, and only if, there exists a convention to use the name to speaker-refer to that object. The theory can be found in works dealing primarily with other issues (e.g. Stine in Philos Stud 33:319–337, 1977; Schiffer in Erkenntnis 13:171–206, 1978; Sainsbury in Erkenntnis 80:195–214, 2015; Sainsbury, Thinking about things, Oxford University Press, 2018), yet these authors provide no sustained discussion of it. Devitt (Designation, Columbia University Press, 1981) did formulate a view on which semantic reference is conventionalized speaker’s reference, yet his views are assimilated to causalist views. This is a mistake. While the conventionalized speaker’s reference view captures much of what is plausible in descriptivism and causalism, it remains distinct from both.

Reconceptualizing selective moral disengagement mechanisms as continuums of moral influence: a theoretical expansion

Abstract Mass communication researchers have applied Bandura’s selective moral disengagement (SMD) concept in diverse contexts to explain audiences’ acceptance of moral violations and reduced condemnation. Recent updates to moral psychology—specifically the application of social intuitionist theories—challenge SMD’s underlying assumptions, necessitating a reconceptualization. In this article, we incorporate modern social intuitionist theories of moral judgment into SMD’s underlying assumptions. We further propose a two-stage moral signal detection process consistent with current decision-making theory in order to explain how SMD reflects a modulation of both moral condemnation and moral commendation. Building on these extensions, we reconceptualize SMD’s eight original mechanisms as expanded continuums of moral influence applicable to diverse forms of moral perceptions and moral judgments. This reconceptualization of SMD removes unnecessary boundary conditions, improves the internal consistency of the theory, and can begin to resolve scholarly disagreements. We conclude the article by providing concrete suggestions for future empirical research.

Sentiment Analysis Method of Epidemic-related Microblog Based on Hesitation Theory

The COVID-19 pandemic in 2020 brought an unprecedented global crisis. After two years of control efforts, life gradually returned to the pre-pandemic state, but localized outbreaks continued to occur. Toward the end of 2022, COVID-19 resurged in China, leading to another disruption of people’s lives and work. Many pieces of information on social media reflected people’s views and emotions toward the second outbreak, which showed distinct differences compared to the first outbreak in 2020. To explore people’s emotional attitudes toward the pandemic at different stages and the underlying reasons, this study collected microblog data from November 2022 to January 2023 and from January to June 2020, encompassing Chinese reactions to the COVID-19 pandemic. Based on hesitancy and the Fuzzy Intuition theory, we proposed a hypothesis: hesitancy can be integrated into machine learning models to select suitable corpora for training, which not only improves accuracy but also enhances model efficiency. Based on this hypothesis, we designed a hesitancy-integrated model. The experimental results demonstrated the model’s positive performance on a self-constructed database. By applying this model to analyze people’s attitudes toward the pandemic, we obtained their sentiments in different months. We found that the most negative emotions appeared at the beginning of the pandemic, followed by emotional fluctuations influenced by social events, ultimately showing an overall positive trend. Combining word cloud techniques and the Latent Dirichlet Allocation (LDA) model effectively helped explore the reasons behind the changes in pandemic attitude.

Optimizing competence in the service of collaboration

In order to efficiently divide labor with others, it is important to understand what our collaborators can do (i.e., their competence). However, competence is not static—people get better at particular jobs the more often they perform them. This plasticity of competence creates a challenge for collaboration: For example, is it better to assign tasks to whoever is most competent now, or to the person who can be trained most efficiently “on-the-job”? We conducted four experiments (N=396) that examine how people make decisions about whom to train (Experiments 1 and 3) and whom to recruit (Experiments 2 and 4) to a collaborative task, based on the simulated collaborators’ starting expertise, the training opportunities available, and the goal of the task. We found that participants’ decisions were best captured by a planning model that attempts to maximize the returns from collaboration while minimizing the costs of hiring and training individual collaborators. This planning model outperformed alternative models that based these decisions on the agents’ current competence, or on how much agents stood to improve in a single training step, without considering whether this training would enable agents to succeed at the task in the long run. Our findings suggest that people do not recruit and train collaborators based solely on their current competence, nor solely on the opportunities for their collaborators to improve. Instead, people use an intuitive theory of competence to balance the costs of hiring and training others against the benefits to the collaboration.

A new model construction by making a detour via intuitionistic theories IV: A closer connection between KPω and BI

By combining tree representation of sets with the method introduced in the previous three papers I–III [39,35,37] in the series, we give a new Π21-preserving interpretation of KPωr+(Πn+2-Found)+θ (Kripke–Platek set theory with the foundation schema restricted to Πn+2, and augmented by θ) in Σ11-AC0+(Πn+21-TI)+θ for any Π21 sentence θ, where the language of second order arithmetic is considered as a sublanguage of that of set theory via the standard interpretation. Thus the addition of any Π21 theorem of BI≡Σ11-AC0+(Π∞1-TI) does not increase the consistency strength of KPω. Among such Π21 theorems are several fixed point principles for positive arithmetical operators and ω-model reflection (the cofinal existence of coded ω-models) for theorems of BI. The reader's familiarity to the previous works I–III in the series might help, but is not necessary.

Property and Trusts: A Modern Project to Create Individual and Collective Personae

The concept of trusts, absent from the classical writings of Marx and Weber on capitalism, was introduced by Frederic Maitland and John Locke as an explanatory framework for the central institutions of capitalism. While these two theorists offered compelling arguments, they relied on intuition and utilized the concept primarily to justify the existing social structure. This paper aims to bring analytical rigor to this intuitive theory and proposes that critical theory embraces the idea of trusts as a critical conceptual tool to unravel the nature of capitalist institutions. Examining limited liability corporations, the modern state, and public debt, the incorporation of trusts into critical theory provides key advantages. First, it facilitates analyzing capitalist institutions in terms of rights and responsibilities, unveiling moral dynamics. Second, it highlights the role of personhood in distributing rights and responsibilities. Third, it can help understand why modern society is ensnared by the shackles of debt.

Biological and cognitive mechanisms and the role of culture in theory of mind development: In need of an integrative, biocultural perspective?

The present paper attempts a comprehensive approach to the biological, cognitive, as well as cultural foundations of theory of mind development. A critical analysis and synthesis of contemporary research findings serves as a basis for revisiting key theoretical accounts regarding the nature and development of this valuable sociocognitive faculty. Are the findings best interpreted within frameworks which consider developmental change and individual differences in the domain-general cognitive abilities (executive functions) that may underlie performance on theory of mind tasks (processing account)? Or is it more fruitful to discuss the development of theory of mind based on domain-specific mechanisms or capacities: an innate, modular mechanism that is underpinned by neurological maturation (modularity theories), or an inborn capacity to form naïve, intuitive theories about the mind, which are then subject to conceptual change as a function of experience (theory theory account), or a mechanism that serves simulations of mental states and related attributions (simulation theories)? Where possible, biological and neurocognitive processes, and experiential influences are discussed in combination. A disentanglement of general cultural influences from more proximal, social or familial effects on theory of mind development is also attempted. The aim is to highlight the value of an integrative, interdisciplinary approach to its study: a biocultural perspective could essentially serve this purpose by shifting attention to the interplay of biological, cognitive, and environmental forces shaping the lifespan dynamics of human theory of mind.

Constructive theories through a modal lens

Abstract We present a uniform proof-theoretic proof of the Gödel–McKinsey–Tarski embedding for a class of first-order intuitionistic theories. This is achieved by adapting to the case of modal logic the methods of proof analysis in order to convert axioms into rules of inference of a suitable sequent calculus. The soundness and the faithfulness of the embedding are proved by induction on the height of the derivations in the augmented calculi. Finally, we define an extension of the modal system for which the result holds with respect to geometric intuitionistic.

Tempering the tension between science and intuition

Scientific ideas can be difficult to access if they contradict earlier-developed intuitive theories; counterintuitive scientific statements like “bubbles have weight” are verified more slowly and less accurately than closely-matched intuitive statements like “bricks have weight” (Shtulman & Valcarcel, 2012). Here, we investigate how context and instruction influences this conflict. In Study 1, college undergraduates (n = 100) verified scientific statements interspersed with images intended to prime either a scientific interpretation of the statements or an intuitive one. Participants primed with scientific images verified counterintuitive statements more accurately, but no more quickly, than those primed with intuitive images. In Study 2, college undergraduates (n = 138) received instruction that affirmed the scientific aspects of the target domain and refuted common misconceptions. Instruction increased the accuracy of participants' responses to counterintuitive statements but not the speed of their responses. Collectively, these findings indicate that scientific interpretations of a domain can be prioritized over intuitive ones but the conflict between science and intuition cannot be eliminated altogether.

Constructing the constructible universe constructively

We study the properties of the constructible universe, L, over intuitionistic theories. We give an extended set of fundamental operations which is sufficient to generate the universe over Intuitionistic Kripke-Platek set theory without Infinity. Following this, we investigate when L can fail to be an inner model in the traditional sense. Namely, we show that over Constructive Zermelo-Fraenkel (even with the Power Set axiom) one cannot prove that the Axiom of Exponentiation holds in L.

Praxis, Diagramm, Körper. Die epistemologischen turns und die Rehabilitation von Kants Euklidizitätsthese

Abstract This paper aims to show how Kant’s concept of mathematical intuition and his thesis of the Euclidicity of space have been rehabilitated by recent interpretations that refer to the concepts of practice, diagrams, and the body. This involves criticising the idea of mathematics as a purely logical and axiomatic science, reading Kant’s theory of geometric intuition as a theory of diagrammatic visualizations, and showing how Kant’s idea of the Euclidicity of space can be justified with reference to embodied experience. These readings contradict the critique of Kant voiced by logicism and logical empiricism. They show that Kant’s notion of non-empirical intuition refers to the embeddedness of human cognition in embodied, media-based practices that function as a third epistemological realm alongside the conceptual and the empirical.

Children's Reasoning About Empathy and Social Relationships.

Across the lifespan, empathic and counter-empathic emotions are shaped by social relationships. Here we test the hypothesis that this connection is encoded in children's intuitive theory of psychology, allowing them to predict when others will feel empathy versus counter-empathy and to use vicarious emotion information to infer relationships. We asked 4- to 7-year-old children (N = 79) to make emotion predictions or relationship inferences in response to stories featuring two characters, an experiencer and an observer, and either a positive or negative outcome for the experiencer. In the context of positive outcomes, we found that children engaged in robust joint reasoning about relationships and vicarious emotions. When given information about the characters' relationship, children predicted empathy from a friendly observer and counter-empathy from a rival observer. When given information about the observer's response to the experiencer, children inferred positive and negative relationships from empathic and counter-empathic responses, respectively. In the context of negative outcomes, children predicted that both friendly and rival observers would feel empathy toward the experiencer, but they still used information about empathic versus counter-empathic responses to infer relationship status. Our results suggest that young children in the US have a blanket expectation of empathic concern in response to negative outcomes, but otherwise expect and infer that vicarious emotions are connected to social relationships. Future research should investigate if children use this understanding to select social partners, evaluate their own relationships, or decide when to express empathy toward others.

A Shared Intuitive (Mis)understanding of Psychophysical Law Leads Both Novices and Educated Students to Believe in a Just Noticeable Difference (JND).

Humans are both the scientists who discover psychological laws and the thinkers who behave according to those laws. Oftentimes, when our natural behavior is in accord with those laws, this dual role serves us well: our intuitions about our own behavior can serve to inform our discovery of new laws. But, in cases where the laws that we discover through science do not agree with the intuitions and biases we carry into the lab, we may find it harder to believe in and adopt those laws. Here, we explore one such case. Since the founding of psychophysics, the notion of a Just Noticeable Difference (JND) in perceptual discrimination has been ubiquitous in experimental psychology-even in spite of theoretical advances since the 1950's that argue that there can be no such thing as a threshold in perceiving difference. We find that both novices and psychologically educated students alike misunderstand the JND to mean that, below a certain threshold, humans will be unable to tell which of two quantities is greater (e.g., that humans will be completely at chance when trying to judge which is heavier, a bag with 3000 grains of sand or 3001). This belief in chance performance below a threshold is inconsistent with psychophysical law. We argue that belief in a JND is part of our intuitive theory of psychology and is therefore very difficult to dispel.

Infants expect friends, but not rivals, to be happy for each other when they succeed.

A friend telling you good news earns them a smile while witnessing a rival win an award may make you wrinkle your nose. Emotions arise not just from people's own circumstances, but also from the experiences of friends and rivals. Across three moderated, online looking time studies, we asked if human infants hold expectations about others' vicarious emotions and if they expect those emotions to be guided by social relationships. Ten- and 11-month-old infants (N=154) expected an observer to be happy rather than sad when the observer watched a friend successfully jump over a wall; infants looked longer at the sad response compared to the happy response. In contrast, infants did not expect the observer to be happy when the friend failed, nor when a different, rival jumper succeeded; infants' looking times to the two emotion responses in these conditions were not reliably different. These results suggest that infants are able to integrate knowledge across social contexts to guide expectations about vicarious emotional responses. Here infants connected an understanding of agents' goals and their outcomes with knowledge of social relationships to infer an emotion response. Biased concern for friends but not adversaries is not just a descriptive feature of human relationships, but an expectation about the social world present from early in development. Further, the successful integration of these information types welcomes the possibility that infants can jointly reason about goals, emotions, and social relationships under an intuitive theory of psychology. RESEARCH HIGHLIGHTS: 11-month-old infants use knowledge of relationships to make inferences about others' vicarious emotions. In Experiment 1 infants expected an observer to respond happily to a friend's success but not their failure. Experiments 2 and 3 varied the relationship between the observer and actor and found that infants' expectation of vicarious happiness is strongest for positive relationships and absent for negative relationships. The results may reflect an intuitive psychology in which infants expect friends to adopt concern for one another's goals and to thus experience one another's successes as rewarding.