Skepticism about the Skepticism

Vasil Penchev • Bulgarian Academy of Sciences: Institute for the

Study of Societies and Knowledge • vasildinev@gmail.com ----------------------------------------- • VAF conference 2015 “Skepticism”: Conference of

the Dutch-Flemish Association for Analytic Philosophy hosted by.

• http://www.eur.nl/fw/vaf2015/ • Erasmus University, Rotterdam, The Niederlands,

28-30 January 201, • 15:15—15:45, Wednesday, January 28, 2015

The question is: • How should skepticism refer to itself? • The classical example might be the doubt of

Descartes, which led him to the necessary obviousness of who doubts

• The formal logical structure is the same as the “antinomy of the Liar”

• That new interpretation of it can be called “antinomy of the Skeptic”

• Descartes resolved it by introducing the meta-position and furthermore defining the “Self” just as that meta-position allows of any other position including that of doubt

The skepticism in quantum mechanics

• Rather unexpectedly, one can reveal the sceptic position to itself in Heisenberg’s uncertainty in quantum mechanics

• It generates the necessity of the observer in final analysis as what allows of that fundamental principle of uncertainty

• As the Self of Descartes, the observer in quantum mechanics is necessary logically for one to be able to state certainly the uncertainly of all, which is not the observer

Skepticism in ... incompleteness • Not less unexpectedly, Gödel’s conception of

incompleteness of any infinite logical structure can be interpreted as another logical and mathematical form of skepticism about the skepticism

• He himself revealed the structure of the “Liar” (consequently also that of the “Skeptic”) in that statement stating that it is untrue, which underlies his theorems of incompleteness

• However following the solution of Descartes, that statement should be in a meta-position to the theory

Skepticism ... in infinity

• Infinity, which is necessary for the construction, is what forces incompleteness mixing the meta-position and position

• Consequently, the fundamental result of Gödel can be interpreted as alternative or complementary to the solution of Descartes:

• If the position and meta-position in skepticism are not absolutely divided from each other, skepticism about the skepticism requires infinity and involves incompleteness

The two kinds of solution

• One can abstract those two solutions, which can be ascribed correspondingly to Descartes and to Gödel, as to skepticism about the skepticism at all

• Might some other, i.e. third solution exist? • In other words, can one reproduce the sceptic

position both to skepticism about the skepticism and to the possible solutions of the antinomy, which appears?

A construction

• This seems to be possible utilizing the following construction:

• These two solutions can be considered as two poles

• The one consist in the absolute separation of the position from the meta-position, the other in the absolute convergence of them

• They generate a continuum between them consisting in turn in the gradual transition from the absoluteness of separation to the other, opposite absoluteness of convergence

The productive skepticism

• The skepticism is what generates that continuum for it doubts the absoluteness both of separation and of convergence

• Furthermore, that continuum allows of an interpretation in terms of quantum mechanics and quantum information as “entanglement”

Creative skepticism

• The examples show that the skeptic position at all as well as the skepticism about the skepticism is rather productive in modern philosophy

• It can be revealed in a series of problems and their solutions in physics, mathematics, and logic, some of which are enumerated above

• Skepticism about the skepticism can be investigated furthermore in other branches of science as well as in contemporary art, religion, politics, etc.