Ali's Journal

Using mathematical logic to express logical arguments is a step toward the universal format for arguments mentioned in the presentation sent to the Guardian ( https://1drv.ms/b/s!AnmqNbk0QgkYgP8gCWXJ1tbzYVEHHA?e=Axj1rk ). The issue is that there is no strategy in math logic. In contrast, in math, true expressions should be true no matter which “strategy” has been deployed to present it. On the other hand, in the real world, as mentioned in the presentation PDF, arguments involve handpicking pieces of evidence and following a certain strategy to present them. That is against the nature of logic in math.

But by the OOP mindset, strategy is added to logic in math as well. In other words, if a mathematician requires expression A to be correct, they can construct a structure where A is indeed correct. But this will have implications. For example, based on that structure expression B might be incorrect as a consequence. Then logic will incorporate strategic processes.

To clarify the distinction with the current mindset, mathematicians currently search for true expressions (theorems) in a math structure. They link true expressions to derive a new true expression. But in the OOP mindset, expressions A, B, and C are required to be true, then a structure is built where those expressions are true and the aim is to see what type of structure will be generated eventually. In OOP A, B and C are classes and can be reshaped like mud to push the structure toward the intended format. This is in total contrast with fixed, unchangeable axioms.

The debate project becomes clearer over time. For example, at first, I didn’t know it would incorporate law and court, but along the way, it became apparent the intersection was inevitable. The project is about the evolution of a process, it makes sense that the people involved are, in different ways, connected to the topic. The project is not about whether previous processes were good or bad, it is about using new technologies to achieve things that were not possible in the past.

The past few days were mainly spent on the article because I thought it was about to finish but there are a few unclear issues. So I decided to work on the platform again this afternoon. I try to complete a brief presentation today and start contacting the Guardian.

UPDATE 1:

Started working on the presentation about the evolution of ideas, but it’s not complete yet. I think it’ll take a few days (I’m travelling tomorrow but try to continue building the presentation).

This project is a type of contest between different viewpoints. So it’s critical that people who are publicly in total disagreement with each other are involved on opposite sides. This is very good for the contest. It’s clear that participating in this contest doesn’t imply that they endorse people on the opposite side. They compete against each other (which is the requirement of any debate). And my job here is to make sure people from all sides are involved.

The project will include ideas from the math article I’m currently working on. It means I can freely discuss it here because the main ingredients are the same as the math article.

According to the article, mathematical structures can be presented by sequences of functions. In axiomatic structures, axioms are things assumed to be “fact”. Then new facts can be derived from those axioms. So each theorem can be traced back to theorems and axioms in previous layers that build up the proof (i.e. path) for the theorem in question.

Arguments are similar. They can be broken down into building blocks. In a simplified example, imagine an argument consisting of 2 sections: A and B. A is the logical conclusion of A1 and A2. A1 is the consequence of A11, A12, A13, A14, etc. and so on (A11 consists of A111, A112, etc). This way one can draw the tree for that argument. Any inconsistency will block that branch. This is a functional approach to reconstructing arguments in a systematic structure. This tree shows the process of reasoning that led to that argument, from the very first step (i.e. axioms) to the construction of the argument. This is comparable to neural networks where different characteristics of something are being extracted. Based on this method, each argument can be presented by a sequence of numbers, each new branch in the tree updates this sequence. Also the sequence (and so the tree) illustrates the evolution path, from axioms to the argument. Kurt Godel used a similar technique and presented each mathematical theorem with a sequence of numbers. A modified version of his technique can be used here.

Everything discussed so far has been based on the traditional functional approach. But according to the math article, new approaches, such as OOP structure, are also possible . The next versions of the project will incorporate those structures. To clarify the difference, note that not all economical/politiacl arguments are built based on axioms. For example some economists might prefer higher inflation over high unemplyment while others prefer lower inflation. There are numerous examples like that. These economical/political ideologies are built based on ideological building blocks which can be presented by classes in OOP structure. It’s not about correctness or incorrectness here (in contrast to axioms), it’s about political/economaica/social ideological blocks that lead to conclusions that for example higher inflation is preferable to higher unemployment. The important thing here is what can be built based on those idealogical blocks and whether those blocks are capable of constructing coherent structures.