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Philosophy of Science (and Mathematics)

You may jump directly to one of the following topics:
  1. Logicism and logical empirism
  2. Tagungsnachlese, Königsberg 1930
  3. Gödel's incompleteness theorem(s)
  4. A bit on the vienna circle
  5. Einstein and logical empirism
  6. The Jordan story
  7. Carnap and Quine
  8. An intro to Bayesian statistics
  9. Physicalism
  10. Indeterminism (and acausality) in classical physics
  11. Intertheoretical relations
  12. Selected topics in the philosophy of science

Logicism and logical empirism

Mathematics - in particular the question what kind of reality mathematical objects have - plays a key role in many philosophical debates. For example the empirists have/had some trouble to fit mathematical truths within their scheme. In Logicism and logical empirism I annotate and excerpt a paper by Alan Musgrave on that topic.

Tagungsnachlese, Königsberg 1930

In 1930 the city of Königsberg hosted the "Tagung für Erkenntnislehre der exakten Wissenschaften". Some of the most important researchers on the foundation of mathematics and physics were assembled there. Likewise the story of this conference has a surprising twist with respect to Gödel and his incompleteness theorem(s). Many talks and this story are collected here.

Gödel's incompleteness Theorem(s)

In 1931 Kurt Gödel could prove that the consistency of formal systems (e.g. arithmetics) can not be decided within this system. Before that it was even believed, that the consistency of a larger body could (and ought to be) proved to secure the foundation of mathematics ("Hilbert's program"). For this discovery some material is collected here .

The Vienna Circle

Logical empirism or Neopositivism was championed by the so-called Vienna Circle, a group of scientists and/or philosophers who developed their ideas under the informal direction of Moritz Schlick until the 20s. Their manifest "Wissenschaftliche Weltauffassung: Der Wiener Kreis" (Carnap, Hahn und Neurath 1929), which coined the name Vienna Circle ("Wiener Kreis") can be downloaded. here (PDF, German). Some related material is supposed to follow here.

Einstein and logical empirism

I have collected some resources on this relation here.

Jordan and positivism

Ever heard about the "amplifier theory" of Pascual Jordan? Look here.

Carnap and Quine

A very influential attack on (logical) empirism was performed by Quine in his "Two Dogmas of Empirism" (Phil.Rev. 1951, 60(1):20-43). It questions (among other things) the distinction between analytic and synthetic propositions and develops Quines "holistic empirism". I have collected some resources here.

Bayesian statistics

Many people believe that statistics is dull and dry. However, its foundation and especially the question what "probability" actually means is highly interesting. Most important, this insights act back on the practical application. The little piece "Bayes'sche Statistik für Fussgänger" looks at this.


Apparently physicalism (or a folklore version of it) is the most widespread philosophy of our time. It is the monistic belief that there is nothing over and above the physical. It seems to have passed unnoticed (by many) that this doctrine is actually empty! Here I annotate and excerpt a paper by Crane and Mellor on that topic.

Indeterminism (and acausality) in classical physics

Exotic theories like quantum mechanics and general relativity may have compromised determinism and causality but good old classical mechanics is usually regarded as a shelter for these notions. However, to all appearances there is indeterminism and acausality even there.

Intertheoretical relations

Scientific theories can exhibit interesting relations (like reduction, emergence etc.). For example it is often said that "thermodynamics" reduces to "statistical mechanics", i.e. the latter is supposed to be "more fundamental" and allows to derive the laws of thermodynamics. Accordingly this and similar question are closely related to notions like "scientific change", "scientific progress" or "(scientific) explanation". Here I have collected some material on this topic.

Selected topics in the philosophy of science

Here I have collected some reflections and references on selected topics. Among other things I am dealing with the problem of induction, underdetermination, the context of discovery vs. the context of justification and the like.