Related papers: Permanence as a Principle of Practice
Despite the 'apparent clarity' of a given legal provision, its application may result in an outcome that does not exactly conform to the semantic level of a statute. The vagueness within a legal text is induced intentionally to accommodate…
The Art of Memory started with Aristotle's questions on memory. During its long evolution, it had important contributions from alchemist, was transformed by Ramon Llull and apparently ended with Giordano Bruno, who was considered the best…
Within classical propositional logic, assigning probabilities to formulas is shown to be equivalent to assigning probabilities to valuations. A novel notion of probabilistic entailment enjoying desirable properties of logical consequence is…
Noether's first theorem does not establish a one-way explanatory arrow from symmetries to conservation laws, but such an arrow is widely assumed in discussions of the theorem in the physics and philosophy literature. It is argued here that…
The chapter advances a reformulation of the classical problem of the nature of mathematical objects (if any), here called "Plato's problem," in line with the program of a philosophy of mathematical practice. It then provides a sketch of a…
We introduce a fragment of continuous first-order logic, analogue of Palyutin formulas (or h-formulas) in classical model theory, which is preserved under reduced products in both directions. We use it to extend classical results on…
The Univalence Principle is the statement that equivalent mathematical structures are indistinguishable. We prove a general version of this principle that applies to all set-based, categorical, and higher-categorical structures defined in a…
This expository paper advocates an approach to physics in which ``typicality" is identified with a suitable form of algorithmic randomness. To this end various theorems from mathematics and physics are reviewed. Their original versions…
Let $F$ be a global field, let $\vp \in \Fx$ be a rational map of degree at least 2, and let $\a \in F$. We say that $\a $ is periodic if $\vpn (\a) = \a$ for some $n \geq 1$. A Hasse principle is the idea, or hope, that a phenomenon which…
In this paper we investigate the evolution of the concept of area in Peano's works, taking into account the main role played by Grassmann's geometric-vector calculus and Peano's theory on derivative of measures. Geometric (1887) and…
We provide a formal, simple and intuitive theory of rational decision making including sequential decisions that affect the environment. The theory has a geometric flavor, which makes the arguments easy to visualize and understand. Our…
The reflection principle is the statement that if a sentence is provable then it is true. Reflection principles have been studied for first-order theories, but they also play an important role in propositional proof complexity. In this…
Mathematics and its relation to the physical universe have been the topic of speculation since the days of Pythagoras. Several different views of the nature of mathematics have been considered: Realism - mathematics exists and is…
We give some sufficient and necessary conditions on a forcing notion Q for preserving the forcing notion ([omega]^{aleph_0},supseteq^*) is proper. They cover many reasonable forcing notions.
The aim of this paper is to show that Frege's argument which concluded that the reference of a sentence is its truth-value, presented in 'On Sense and Reference' (1892), can be reconstructed taking into account the problems of the notion of…
In Itamar Pitowsky's reading of the Gleason and the Kochen-Specker theorems, in particular, his Logical Indeterminacy Principle, the emphasis is on the value indefiniteness of observables which are not within the preparation context. This…
Separation logic is successful for software verification of heap-manipulating programs. Numbers are necessary to be added to separation logic for verification of practical software where numbers are important. However, properties of the…
A fundamental question in causal inference is whether it is possible to reliably infer manipulation effects from observational data. There are a variety of senses of asymptotic reliability in the statistical literature, among which the most…
The comparison type version of the fixed point result in ordered metric spaces established by Nieto and Rodriguez-Lopez [Acta Math. Sinica (English Series), 23 (2007), 2205-2212] is nothing but a particular case of the classical Banach's…
We highlight four points which have been ignored or underestimated before and which allow a better understanding of "Sur la dynamique de l'electron": (i) the use by Poincare of active Lorentz transformations (boosts); (ii) the necessity,…