**Acknowledgements**

Supported by the grant of Ministry of Education of the Czech Republic MSM 6046137307.

Many thanks are to be expressed to my brother Ing. Petr Hejna for his help with English language and formulations of both this and all the previous texts.

## **A. Appendix**

#### **A.1 Summarizing comparison**

♣ **Under the adiabacity**, [d]**QExt** <sup>=</sup> **<sup>0</sup>**, **of the system** <sup>L</sup>**,** *it is not possible to derive* **such a** *CLAIM* **that is stating this adiabatic supposition.** This *CLAIM* is **constructible not adiabatically,** *outside* **the adiabatic** L **only.**

♣ **Under the consistency of the system** <sup>P</sup>**,** *it is not possible to derive* **such a** *CLAIM* **that is stating this consistency supposition.** This *CLAIM* is **constructible** *purely syntactically***,** *outside* **the consistent** <sup>P</sup> **only (in** <sup>P</sup><sup>∗</sup> � P**) (Figure A1).**

♣ **Without** <sup>P</sup> <sup>∗</sup> **we could not know that P is not self-referencing and is consistent.**

*Common Gnoseological Meaning of Gödel and Caratheodory Theorems DOI: http://dx.doi.org/10.5772/intechopen.87975*

**Figure A1.** *Example of not distinguishing the reality and its image.*
