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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”

Skepticism about the Skepticism

Vasil Penchev Bulgarian Academy of Sciences: Institute for the

Study of Societies and Knowledge [email protected] ----------------------------------------- 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, 15:1515:45, 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 Heisenbergs 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, Gdels 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 Gdel 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 Gdel, 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.

Skepticism about the SkepticismVasil PenchevThe question is: The skepticism in quantum mechanics Skepticism in ... incompletenessSkepticism ... in infinityThe two kinds of solutionA constructionThe productive skepticismCreative skepticismSlide Number 11Slide Number 12