PhilSci Archive

From the four-color theorem to a generalizing “four-letter theorem”: A sketch for “human proof” and the philosophical interpretation

Penchev, Vasil (2020) From the four-color theorem to a generalizing “four-letter theorem”: A sketch for “human proof” and the philosophical interpretation. [Preprint]

[img]
Preview
Text
@FourLetterTheorem.pdf

Download (281kB) | Preview

Abstract

The “four-color” theorem seems to be generalizable as follows. The four-letter alphabet is sufficient to encode unambiguously any set of well-orderings including a geographical map or the “map” of any logic and thus that of all logics or the DNA (RNA) plan(s) of any (all) alive being(s).
Then the corresponding maximally generalizing conjecture would state: anything in the universe or mind can be encoded unambiguously by four letters.
That admits to be formulated as a “four-letter theorem”, and thus one can search for a properly mathematical proof of the statement.
It would imply the “four colour theorem”, the proof of which many philosophers and mathematicians believe not to be entirely satisfactory for it is not a “human proof”, but intermediated by computers unavoidably since the necessary calculations exceed the human capabilities fundamentally. It is furthermore rather unsatisfactory because it consists in enumerating and proving all cases one by one.
Sometimes, a more general theorem turns out to be much easier for proving including a general “human” method, and the particular and too difficult for proving theorem to be implied as a corollary in certain simple conditions.
The same approach will be followed as to the four colour theorem, i.e. to be deduced more or less trivially from the “four-letter theorem” if the latter is proved. References are only classical and thus very well-known papers: their complete bibliographic description is omitted.


Export/Citation: EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL
Social Networking:
Share |

Item Type: Preprint
Creators:
CreatorsEmailORCID
Penchev, Vasilvasildinev@gmail.com
Keywords: alphabet of nature, four-color theorem, four-letter theorem, human proof versus “machine” proof, two-letter vs four-letter alhabet
Subjects: General Issues > Scientific Metaphysics
Specific Sciences > Mathematics
Depositing User: Prof. Vasil Penchev
Date Deposited: 05 May 2020 15:35
Last Modified: 05 May 2020 15:35
Item ID: 17145
Subjects: General Issues > Scientific Metaphysics
Specific Sciences > Mathematics
Date: 5 May 2020
URI: http://philsci-archive.pitt.edu/id/eprint/17145

Monthly Views for the past 3 years

Monthly Downloads for the past 3 years

Plum Analytics

Actions (login required)

View Item View Item