The road to The General Theory: J. M. Keynes, F. A. Hayek, and the Genealogy of Macroeconomics

ABSTRACT The criticism made by Friedrich A. Hayek to A Treatise on Money by John Maynard Keynes, and the subsequent controversy that followed with the involvement of members of the Cambridge Circus, sustained important elements to Keynes’ abandonment of his earlier ideas and to his way to General Theory. The figure and position of Hayek operated to clarify the underlying differences and the new theoretical routes for Keynes, one that was more explicitly opposite to critical authors drawing from Knut Wicksell. To some degree, the road to General Theory was paved in the famous 1931 controversy - in particular the rejection of the Wicksell connection.

A relational theory of effects and coeffects

Graded modal types systems and coeffects are becoming a standard formalism to deal with context-dependent, usage-sensitive computations, especially when combined with computational effects. From a semantic perspective, effectful and coeffectful languages have been studied mostly by means of denotational semantics and almost nothing has been done from the point of view of relational reasoning. This gap in the literature is quite surprising, since many cornerstone results — such as non-interference , metric preservation , and proof irrelevance — on concrete coeffects are inherently relational. In this paper, we fill this gap by developing a general theory and calculus of program relations for higher-order languages with combined effects and coeffects. The relational calculus builds upon the novel notion of a corelator (or comonadic lax extension ) to handle coeffects relationally. Inside such a calculus, we define three notions of effectful and coeffectful program refinements: contextual approximation , logical preorder , and applicative similarity . These are the first operationally-based notions of program refinement (and, consequently, equivalence) for languages with combined effects and coeffects appearing in the literature. We show that the axiomatics of a corelator (together with the one of a relator) is precisely what is needed to prove all the aforementioned program refinements to be precongruences, this way obtaining compositional relational techniques for reasoning about combined effects and coeffects.

A theory of cortical map formation in the visual brain

The cerebral cortex receives multiple afferents from the thalamus that segregate by stimulus modality forming cortical maps for each sense. In vision, the primary visual cortex also maps the multiple dimensions of the stimulus in patterns that vary across species for reasons unknown. Here we introduce a general theory of cortical map formation, which proposes that map diversity emerges from variations in sampling density of sensory space across species. In the theory, increasing afferent sampling density enlarges the cortical domains representing the same visual point allowing the segregation of afferents and cortical targets by additional stimulus dimensions. We illustrate the theory with a computational model that accurately replicates the maps of different species through afferent segregation followed by thalamocortical convergence pruned by visual experience. Because thalamocortical pathways use similar mechanisms for axon sorting and pruning, the theory may extend to other sensory areas of the mammalian brain.

General Relativity and Causality, Reasoning from Metaphysics, and E. J. Lowe’s Ontology

The paper aims to show the importance of reasoning “from metaphysics” in the course of a consistent interpretation of the “against neoscholasticism” thesis (J. Ladyman). The idea that “the subject of metaphysics is metaphysical possibilities, and science determines which of them are actually achieved” (E. J. Lowe, J. Katz, etc.) reinforces the role of reasoning “from metaphysics” within the field of metaphysics of science. The general theory of relativity violates the common prevailing intuition that “causality is the subject of local physical interaction” (J. Bigelow). Interpretation of causality in terms of “forces” and “coming into” within the framework of E. J. Lowe's ontology makes it possible to talk about causality in terms of “finding” and “going out” of existence of the corresponding modes of objects connected by a formal “causal relationship”. The transition to E. J. Lowe's ontology helps not only to overcome the intuition of the locality of causality, but also reveals in its own way, for example, such seemingly simple common intuitions as the dependence of the truth of propositions on time or the understanding of time as a dimension. All this once again brings us back to the understanding of the importance of the fact that a scientist, constructing or interpreting a scientific theory, as a rule, uses non-trivial philosophical assumptions that should be the subject of its own philosophical analysis.

Infusing Autopoietic and Cognitive Behaviors into Digital Automata to Improve Their Sentience, Resilience, and Intelligence

All living beings use autopoiesis and cognition to manage their “life” processes from birth through death. Autopoiesis enables them to use the specification in their genomes to instantiate themselves using matter and energy transformations. They reproduce, replicate, and manage their stability. Cognition allows them to process information into knowledge and use it to manage its interactions between various constituent parts within the system and its interaction with the environment. Currently, various attempts are underway to make modern computers mimic the resilience and intelligence of living beings using symbolic and sub-symbolic computing. We discuss here the limitations of classical computer science for implementing autopoietic and cognitive behaviors in digital machines. We propose a new architecture applying the general theory of information (GTI) and pave the path to make digital automata mimic living organisms by exhibiting autopoiesis and cognitive behaviors. The new science, based on GTI, asserts that information is a fundamental constituent of the physical world and that living beings convert information into knowledge using physical structures that use matter and energy. Our proposal uses the tools derived from GTI to provide a common knowledge representation from existing symbolic and sub-symbolic computing structures to implement autopoiesis and cognitive behaviors.

A General Theory of Location Based on the Notion of Entire Location

It would be a good thing to have at our disposal a general theory of location that is neutral with respect to (i.e. that does not rule out or entail) (i) the view that some objects have more than one exact location, (ii) the view that some objects are located without having an exact location, and (iii) the view that some objects are “spanners”—where a spanner is an object exactly located at a region that has proper parts but which has no proper part exactly located at a proper part of the region. As far as I know, no theory of location that can be found in the literature has this feature. I put forward a new theory that does—or so I argue. The theory takes as its sole locational primitive the notion of being entirely located at.

General theory of legal design in law and economics framework of commercial contracting

We need law and economics to do the scientific measurement necessary for legal design to be seen as on the stage of science. Law and economics—which is the application of economic theory, especially microeconomic theory, to the analysis and the practice of law--is a valid tool and approach to reflect on what should be empirically investigated in the practice of legal design. The neoclassical (mainstream) theoretical foundation of economic analysis of law is, however, at times far from reality as it often predicts uncooperative and even selfish behaviour. In real life people do cooperate, have empathy, emotions and even behave in an altruistic way. For those reasons, behavioural law and economics and conventional wisdom are needed to complement the teachings from standard theory in the field of commercial contracting.

Optimal Risk Sharing in Society

We consider risk sharing among individuals in a one-period setting under uncertainty that will result in payoffs to be shared among the members. We start with optimal risk sharing in an Arrow–Debreu economy, or equivalently, in a Borch-style reinsurance market. From the results of this model we can infer how risk is optimally distributed between individuals according to their preferences and initial endowments, under some idealized conditions. A main message in this theory is the mutuality principle, of interest related to the economic effects of pandemics. From this we point out some elements of a more general theory of syndicates, where in addition, a group of people are to make a common decision under uncertainty. We extend to a competitive market as a special case of such a syndicate.

De Giorgi’s inequality for the thresholding scheme with arbitrary mobilities and surface tensions

We provide a new convergence proof of the celebrated Merriman–Bence–Osher scheme for multiphase mean curvature flow. Our proof applies to the new variant incorporating a general class of surface tensions and mobilities, including typical choices for modeling grain growth. The basis of the proof are the minimizing movements interpretation of Esedoḡlu and Otto and De Giorgi’s general theory of gradient flows. Under a typical energy convergence assumption we show that the limit satisfies a sharp energy-dissipation relation.