An analysis of the logic of Riesz Spaces with strong unit

We study \L ukasiewicz logic enriched with a scalar multiplication with scalars taken in $[0,1]$. Its algebraic models, called {\em Riesz MV-algebras}, are, up to isomorphism, unit intervals of Riesz spaces with a strong unit endowed with an appropriate structure. When only rational scalars are considered, one gets the class of {\em DMV-algebras} and a corresponding logical system. Our research follows two objectives. The first one is to deepen the connections between functional analysis and the logic of Riesz MV-algebras. The second one is to study the finitely presented MV-algebras, DMV-algebras and Riesz MV-algebras, connecting them from logical, algebraic and geometric perspective

Popper's verisimilitude: The scientific journey from ignorance to truth

The question of truth is a broadly broached subject in Philosophy as it features along the entire historical and polemical growth of the discipline right from the time of the Ancients down to our Post-Modern era. Yet, the delimiting realization of being unable to register general success in our dogged attempts at truth and knowledge, mostly stares us blankly in the face, for matters on which philosophy endeavours to speculate on, are beyond the reach of definite knowledge.1 Our theories of the universe open up to modifications, refutations, and further propositions, evidencing a historical development in philosophical inquiry. This generally is the growth of our science, of our knowledge. This paper critically seeks to examine Popper’s notion of verisimilitude. It takes us through the scientist’s journey from ignorance to truth, and the difference between probability and verisimilitude. It addresses the relevance of the theory of content in understanding verisimilitude, under its distinctions as quantitative and qualitative. Finally, it discusses corroboration and the criteria for theory-choice

Does Meaning Evolove?

A common method of improving how well understood a theory is, is by comparing it to another theory which has been better developed. Radical interpretation is a theory which attempts to explain how communication has meaning. Radical interpretation is treated as another time dependent theory and compared to the time dependent theory of biological evolution. Several similarities and differences are uncovered. Biological evolution can be gradual or punctuated. Whether radical interpretation is gradual or punctuated depends on how the question is framed: on the coarse-grained time scale it proceeds gradually, but on the fine-grained time scale it proceeds by punctuated equilibria. Biological evolution proceeds by natural selection, the counterpart to this is the increase in both correspondence and coherence. Exaption, mutations, and spandrels have counterparts metaphor, speech errors, and puns respectively. Homologous and analogs have direct counterparts in specific words. The most important differences originate from the existence of a unit of inheritance (the traditional gene) occurring in biological evolution - there is no such unit in language

Does Meaning Evolve?

A common method of making a theory more understandable, is by comparing it to another theory which has been better developed. Radical interpretation is a theory which attempts to explain how communication has meaning. Radical interpretation is treated as another time-dependent theory and compared to the time dependent theory of biological evolution. The main reason for doing this is to find the nature of the time dependence; producing analogs between the two theories is a necessary prerequisite to this and brings up many problems. Once the nature of the time dependence is better known it might allow the underlying mechanism to be uncovered. Several similarities and differences are uncovered, there appear to be more differences than similarities.Comment: title changed, completely rewritten, new version 37 pages previous version 28 pages, to appear in Behaviour and Philosoph

Effective Theories for Circuits and Automata

Abstracting an effective theory from a complicated process is central to the study of complexity. Even when the underlying mechanisms are understood, or at least measurable, the presence of dissipation and irreversibility in biological, computational and social systems makes the problem harder. Here we demonstrate the construction of effective theories in the presence of both irreversibility and noise, in a dynamical model with underlying feedback. We use the Krohn-Rhodes theorem to show how the composition of underlying mechanisms can lead to innovations in the emergent effective theory. We show how dissipation and irreversibility fundamentally limit the lifetimes of these emergent structures, even though, on short timescales, the group properties may be enriched compared to their noiseless counterparts.Comment: 11 pages, 9 figure

Contingency, Irony and Morality: A Critical Review of Rorty's. Notion of the Liberal Utopia

This paper introduces Richard Rorty’s notion of the liberal ironist and his vision of a liberal utopia and explores the implications of these for philosophical questions concerning morality, as well as morality in general. Rorty’s assertions of the contingency of language, society and self are explored. Under the contingency of language, the figure of the ironist is defined, and Rorty’s conception of vocabularies is discussed. Under the contingency of society, Rorty’s definition of liberalism, his opposition of literary culture to materialist and metaphysical culture, and his notions concerning utopian politics are discussed. Under the contingency of self, Rorty’s critique of Kantian and his appropriations of Deweyan and Freudian conceptions of morality are presented. Other key factors discussed are Rorty’s theory of the separation of the private and public spheres of life and his ideas concerning cruelty and human solidarity. In this way, a critical analysis of Rorty’s proposed balance between private, ironic doubt and public, liberal social hope is presented and assessed in terms of its merit as a system of thought suited to the needs of post-metaphysical, liberal societies

A machine learning route between band mapping and band structure

The electronic band structure (BS) of solid state materials imprints the multidimensional and multi-valued functional relations between energy and momenta of periodically confined electrons. Photoemission spectroscopy is a powerful tool for its comprehensive characterization. A common task in photoemission band mapping is to recover the underlying quasiparticle dispersion, which we call band structure reconstruction. Traditional methods often focus on specific regions of interests yet require extensive human oversight. To cope with the growing size and scale of photoemission data, we develop a generic machine-learning approach leveraging the information within electronic structure calculations for this task. We demonstrate its capability by reconstructing all fourteen valence bands of tungsten diselenide and validate the accuracy on various synthetic data. The reconstruction uncovers previously inaccessible momentum-space structural information on both global and local scales in conjunction with theory, while realizing a path towards integrating band mapping data into materials science databases