Prehistory and background:
One may demonstrate that the square of opposition shares the least possible structure of the ordering which cannot be well-ordered directly, namely two bits of information, absolutely independent of each other. That minimal possible information structure is a kind of the minimal alphabet of the universe, necessary for anything to be “written” unambiguously. That alphabet consists of four letters corresponding one-to-one to two independent bits and can be found as the four “letters” of human genome as the four “colors” enough to be colored any map as at a few other exemplifications.
The minimal possible alphabet consisting of only two letters, or a single bit of information, used on our contemporary computers, is enough for any well-ordering to be written exactly. However, it is insufficient to be written relevantly anything which is not well-ordered. The record of anything which is not well-ordered by only two letters implies the loss of information necessarily.
A exceptionally important exemplification of that loss of information is quantum measurement reducing a coherent state before measurement unorderable in principle to a statistical and thus well-ordered ensemble after measurement. Any record of something not well-ordered by the alphabet of two letters implies the well-ordering principle equivalent to the axiom of choice. In fact, the sense to that application of the axiom of choice is to add externally by external choices the information lost after recording by that insufficient alphabet of two letters. After assisting by means of the axiom of choice, the information equation before and after recording, respectively before and after measurement, is restored.
The power of the square of opposition proved in logic during millenia can be also utilized to be hinted the concept of God in the framework of logic, particularly the being of infinity.
A reasonable conjecture in the same course of thought is: the concept of infinity admits to be written by the same alphabet of four letters or two independent bits consistently or even that it might be equated to te the same elementary information structure of two independent bits. The talk intends the discussion of that hypothesis:
Thesis:
1. The concept of infinity can be written relevantly by the alphabet of four letters therefore sharing the universal alphabet enough for anything in the universe.
2. Even more, the concept of infinity is equivalent to that fundamental alphabet consisting of four letters or two independent bits.
3. Consequently, on can conclude metaphorically that anything in the universe, or in other words, anything existing is written by the language of infinity, however consisting necessarily of only four letters.
An idea for the proof of the thesis:
The structure of two independent bits is two-dimensional for it implies a gap between the two bits due right to their independence. The gap between any two dimensions both requires and impies the concept of infinity to be described explicitly or “cataphatically”. In other words, the gap between two dimensions such as two independent bits describes the same, however in an implicit, or “apophatic” way.
Thus, the minimal structure of two independent bits or the alphabet of four letters both can describe infinity and coincides with it.
Conclusion:
The power of the square of opposition, proved during milenia, can be explained by the ontological language of infinity for describing anything, by which it supplies logic.
One may demonstrate that the square of opposition shares the least possible structure of the ordering which cannot be well-ordered directly, namely two bits of information, absolutely independent of each other. That minimal possible information structure is a kind of the minimal alphabet of the universe, necessary for anything to be “written” unambiguously. That alphabet consists of four letters corresponding one-to-one to two independent bits and can be found as the four “letters” of human genome as the four “colors” enough to be colored any map as at a few other exemplifications.
The minimal possible alphabet consisting of only two letters, or a single bit of information, used on our contemporary computers, is enough for any well-ordering to be written exactly. However, it is insufficient to be written relevantly anything which is not well-ordered. The record of anything which is not well-ordered by only two letters implies the loss of information necessarily.
A exceptionally important exemplification of that loss of information is quantum measurement reducing a coherent state before measurement unorderable in principle to a statistical and thus well-ordered ensemble after measurement. Any record of something not well-ordered by the alphabet of two letters implies the well-ordering principle equivalent to the axiom of choice. In fact, the sense to that application of the axiom of choice is to add externally by external choices the information lost after recording by that insufficient alphabet of two letters. After assisting by means of the axiom of choice, the information equation before and after recording, respectively before and after measurement, is restored.
The power of the square of opposition proved in logic during millenia can be also utilized to be hinted the concept of God in the framework of logic, particularly the being of infinity.
A reasonable conjecture in the same course of thought is: the concept of infinity admits to be written by the same alphabet of four letters or two independent bits consistently or even that it might be equated to te the same elementary information structure of two independent bits. The talk intends the discussion of that hypothesis:
Thesis:
1. The concept of infinity can be written relevantly by the alphabet of four letters therefore sharing the universal alphabet enough for anything in the universe.
2. Even more, the concept of infinity is equivalent to that fundamental alphabet consisting of four letters or two independent bits.
3. Consequently, on can conclude metaphorically that anything in the universe, or in other words, anything existing is written by the language of infinity, however consisting necessarily of only four letters.
An idea for the proof of the thesis:
The structure of two independent bits is two-dimensional for it implies a gap between the two bits due right to their independence. The gap between any two dimensions both requires and impies the concept of infinity to be described explicitly or “cataphatically”. In other words, the gap between two dimensions such as two independent bits describes the same, however in an implicit, or “apophatic” way.
Thus, the minimal structure of two independent bits or the alphabet of four letters both can describe infinity and coincides with it.
Conclusion:
The power of the square of opposition, proved during milenia, can be explained by the ontological language of infinity for describing anything, by which it supplies logic.
The presentation also as a PDF, a video or as slides @ EasyChair
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