Related papers: Reichenbach's Transcendental Probability
We will show that Carl Stumpf's interpretation of the concept of probability is best understood as that of an objective Bayesian. First we analyse Stumpf's work in relation to that of his contemporary Johannes von Kries, and after that we…
Classical statistics and Bayesian statistics refer to the frequentist and subjective theories of probability respectively. Von Mises and De Finetti, who authored those conceptualizations, provide interpretations of the probability that…
Various 'optimistic' attempts have been made to reasonably explain the undeniable effectiveness of mathematics in its application to physics. They range over retrospective, historical accounts of mathematical applicability based on…
We characterize, by easily verifiable properties, abstract ternary relations isomorphic to the causal betweenness introduced by Hans Reichenbach.
This work reviews the understanding of the direction of time introduced by Hans Reichenbach, including the fundamental relation of the perceived flow of time to the second law of thermodynamics (i.e. the Boltzmann time hypothesis), and the…
We are interested here in the program of reconstruction of quantum mechanics of the German physicist and philosopher Carl Friedrich von Weizs\"{a}cker, which still has some supporters today. In the major part of this article, we limit…
These notes were written from a series of lectures given in March 2010 at the Universidad Complutense of Madrid and then in Barcelona for the centennial anniversary of the Spanish Mathematical Society (RSME). Our aim is to give an…
This paper addresses the central question of what a coherent concept of probability might look like that would do justice to both classical probability theory, axiomatized by Kolmogorov, and quantum theory. At a time when quanta are…
Quantum mechanics is a fundamentally probabilistic theory (at least so far as the empirical predictions are concerned). It follows that, if one wants to properly understand quantum mechanics, it is essential to clearly understand the…
Bell's 1964 theorem causes a severe problem for the notion that correlations require explanation, encapsulated in Reichenbach's Principle of Common Cause. Despite being a hallmark of scientific thought, dropping the principle has been…
This note is sketching a simple and natural mathematical construction for explaining the probabilistic nature of quantum mechanics. It employs nonstandard analysis and is based on Feynman's interpretation of the Heisenberg uncertainty…
In this article, we present new comments to the article On Kant's First Insight Into The Problem of Space Dimensionality and Its Physical Foundations. In particular, we discuss how the space concept is designed in the first writing of Kant.…
By formulating the axioms of quantum mechanics, von Neumann also laid the foundations of a "quantum probability theory". As such, it is regarded a generalization of the "classical probability theory" due to Kolmogorov. Outside of quantum…
In two respects Ludwig Boltzmann was a pioneer of quantum mechanics. First because in his statistical interpretation of the second law of thermodynamics he introduced the theory of probability into a fundamental law of physics and thus…
Philosophers now seem to agree that frequentism is an untenable strategy to explain the meaning of probabilities. Nevertheless, I want to revive frequentism, and I will do so by grounding probabilities on typicality in the same way as the…
An out of the box intellectual path exploring the foundations of quantum mechanics is discussed in some detail, in order to clarify why a possibly different way to look at the relevant fundamental questions can be identified and can support…
Physicists have, hitherto, mostly adopted a frequentist conception of probability, according to which probability statements apply only to ensembles. It is argued that we should, instead, adopt an epistemic, or Bayesian conception, in which…
It is said that Einstein's conceptual base for the theory of relativity was the philosophy formulated by Immanuel Kant. Then, is it possible to see how Kant played a role in Einstein's thinking without reading Kant's books? This question…
I argue that Immanuel Kant's critical philosophy -- in particular the doctrine of transcendental idealism which grounds it -- is best understood as an `epistemic' or `metaphilosophical' doctrine. As such it aims to show how one may engage…
We survey the development of probability from 1900, starting with Bachelier's theory of speculation. Fisher information appears in the theory of estimation. We touch on Brownian motion, and the Wiener integral. The Ito calculus, and its…