While writing the last published piece and breaking off to "speak" on the Tauchain chat channel it accrued to me that eventually it will be the mathematical axiomatic framework which we will put on the blockchain in order to allow our machines (computers) to carry on a trusted computational task, a complete consistent and decidable result, each block at a time.
The problem with computers is that they are created to care about the truth,
not because of moral issues,
only because that is how the logic of language is constructed. and of course of math
On the other hand
The entire bitcoin decentralized scheme as a distributed messaging system is founded on the notion that truth is a consensusAnd that each consecutive truth don"t have to comply with the one that came before it unless accepted again on that last block.
Let me stop for a moment in order to get us all on the same page regarding the term "logic" itself.
Logic (from the Ancient Greek: λογική, logike)[1] originally meaning the word, or what is spoken, (but coming to mean thought or reason) is generally held to consist of the systematic study of the form of arguments. A valid argument is one where there is a specific relation of logical support between the assumptions of the argument and its conclusion. (In ordinary discourse, the conclusion of such an argument may be signified by words like 'therefore', 'hence', 'ergo' and so on.)
In computers science logic is:
a system or set of principles underlying the arrangements of elements in a computer or electronic device so as to perform a specified task.
Now we need to realize that this definition of the word logic is in fact an incomplete view of logic if we assume that we wish to define all phenomenon as logical or illogical. In fact the above definition of logic only describe one type logic, a form I will name LINER . And it is the structure of linear logic which govern the type of truth we refer to as logical. Consensus in this content of linear logic is thus illogical. However we all can agree that there is a logical structure which guides the decision making of a consensus. In the next few lines I will try argue the validity of his other type of logic I will simply refer to "NONLINEAR" logic. And I will also argue it to be more fundamental then the linear logic as well as the being the foundation to all the tower of trusted we can built based on linear logic.
It is also that type of logic, the nonlinear logic, which governs the existence of a decentralized system and act as the foundation of all centralized ones. This nonlinear logic also is at the foundation of intelligence and life as a whole. While the liner logic is the one which govern the centralized entity logical structure, it is the nonlinear logic that allow us to trust it. The linear logic is extremely officiant in terms of survival, and humans brought it to the highest level of the consciousness of awareness but I believe that we are just about to enter a new era in which we will discover the structure of nonlinear logic and will eventually raze it to the level of our awareness .
basically consensus means to consent to the truth of the majority.
the truth of the majority means that there is an individual truth to each player
This is a very crucial part of the nonlinear truth. "The truth" is a multiple of the number of participants and is infinite if have infinite participants in the framework in which it is defined. The one truth is all these individual truths which you can not compile into one truth unless use some sort of logical framework. and that logical frame work is not looking for the one truth that all can share based on it being making sense in linear logic but rather at a process we name consent. Consent is process in which the individual gives up its complete view of the truth to comply with another truth. Now of course one can give up his view of the truth and comply with another one's truth, however it will eventually be that consensus about the a truth that will serve each individual best. At this point I will refrain from arguing why a consent to the consensus is most beneficial and will just use the bitcoin as example. In the bitcoin scheme you will get more value for you energy expenses if you will comply with the consensus and avoid ruining a fork.
OK, this is way too much for one entry so we call it : Part One of The Blockchain Role In Forming The Foundation of Mathematics And The Logical Structure of Truth As A Consensus