Naslov
Evidence and self-evidence in the foundations of logic

Autori
Kovač, Srećko

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
Handbook of the 6th World Congress and School on Universal Logic / Béziau, Jean-Yves ; Buchsbaum, Arthur ; Rey, Christoph - Vichy : Université Clermont-Vichy, 2018, 255-255

ISBN
978-2-9544948-1-4

Skup
6th World Congress and School on Universal Logic (UNILOG 2018)

Mjesto i datum
Vichy, Francuska, 16.06.2018. - 26.06.2018

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
correctness, proof, Turing machine, justification logic, causality

Sažetak
We relate the question of the correctness of proofs and of a possible foundation of a logical system to a general, computational, concept of a formal system as a mechanical procedure, in the sense of a Turing machine, for producing provable formulas (Gödel 1934/64). By means of justification logic tools, the question about the evidence in a given system is united with the question of an abstract causal structure of a mechanical decision procedure. After introducing a translation procedure of the work of a Turing equivalent register machine into a suitable justification logic language, it is easy to show that, for each translated register program, the reason (evidence and cause, not necessarily by a register routine) could be proved for the program's halting/non-halting. The evidence of justification logic reasons exceeds the limits of a given formal axiomatic system (since not obeying the constrains of the incompleteness theorems, Gödel 1938). Further, justification logic (including its axiomatic description of reason operators) does not satisfy Gödel's (1938) constructivity requirements. Thus, as a foundational question and the question of the criteria of the correctness of reasoning, we discuss a possible ``meta-justification'' of the axioms about reasons by analyzing the work of a register (Turing) machine in causal terms in comparison with general self-evident structures of a human agent's reasoning. This includes a sort of abstract pragmatic considerations of the use of concepts by an abstract reasoner (attention to our own acts in using concepts, Gödel 1961).

Izvorni jezik
Engleski

Znanstvena područja
Filozofija

POVEZANOST RADA