Can Mathematics Evolve Beyond Traditional Logic Structures?

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Discussion Overview

The discussion explores the idea of evolving mathematics beyond traditional logical structures, focusing on the implications of using non-traditional dimensions and informal reasoning in mathematical proofs and concepts.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Exploratory

Main Points Raised

  • Some participants suggest that traditional logical structures in mathematics may be limiting, proposing the use of non-traditional dimensions to reach conclusions.
  • Others express confusion about the original post's argument, asking for clarification on the concepts being discussed.
  • One participant argues that informal reasoning is insufficient without formal proof, indicating a need for logical rigor in mathematics.
  • There are claims that the structure of original theorem logic negates certain theorems, which some participants believe could be addressed through informal mathematics.
  • Some participants propose that negating coordinates might validate certain theorems, while others counter that this could lead to invalid logic regarding mathematical structures.
  • Examples are provided to illustrate the difference between must-be-true statements and could-be statements in mathematics, inviting further exploration of these pathways.
  • Participants express interest in using imaginary and infinite-dimensional numbers as alternative approaches to solving mathematical problems.

Areas of Agreement / Disagreement

The discussion features multiple competing views, with no consensus reached on the validity of informal reasoning versus traditional logic in mathematics. Participants express varying degrees of understanding and acceptance of the original post's ideas.

Contextual Notes

Some participants highlight the need for clarity in the discussion, indicating that certain assumptions or definitions may be missing or unclear. The conversation also reflects a tension between informal and formal approaches to mathematical reasoning.

Anachronistic
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Using the formal logical structure of the original theorem, the converse, the curious inverse, and the all important contrapositive, mathematics is at a standstill. I am trying to get to this very particular coordinate without using formal logic.
 
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Anachronistic said:
mathematics is at a standstill.

What? :confused:
 
Anachronistic, I have no idea what you are talking about. Could you clarify??
 
It has to do with using non traditional dimensions to get to a point
 
You might want to read our rules before you get to your point.
 
Informal reasoning is great, but in order to finish the process, in math, you do have to prove it using logic. Or at least convince yourself that all the details could be done if you wanted, in some cases.
 
The problem with the structure of original theorem logic is that it negates the curious theorem in order to get to inverse points in your coordinate logic. This is only valid in informal mathematics logic.

I like words too.
 
I don't understand the OP's question.
 
Pengwuino said:
The problem with the structure of original theorem logic is that it negates the curious theorem in order to get to inverse points in your coordinate logic. This is only valid in informal mathematics logic.

I like words too.

would then, conversely, the negation of the coordinates validate the curious theorem, providing rigor to the original theorem structure? it seems to me you could sketch an informal argument, but advanced rendering might exceed current pixel capacity.
 
  • #10
Deveno said:
would then, conversely, the negation of the coordinates validate the curious theorem, providing rigor to the original theorem structure? it seems to me you could sketch an informal argument, but advanced rendering might exceed current pixel capacity.

Not at all! The curious theorem is a formalization of contrapositive statements pertaining to the formal structure of possibilities! You can't negate coordinates without forming some kind of invalidating logic of the space-time tensor itself!
 
  • #11
Here is a simple example.

If x = 3, then x + 2 = 5 is a must be true statement.

The converse is a could be statement due to several different ways to get to the number 5 using 2 and 5 in the same dimensions.



Would anybody like to elaborate the different pathways to make the converse statement true?
 
  • #12
Anachronistic said:
Here is a simple example.

If x = 3, then x + 2 = 5 is a must be true statement.

The converse is a could be statement due to several different ways to get to the number 5 using 2 and 5 in the same dimensions.



Would anybody like to elaborate the different pathways to make the converse statement true?

If x+2=5, then x+2+(-2)=5+(-2). So x=3.
 
  • #13
I like using imaginary dimensions of the non real numbers to get to my solutions
 
  • #14
More fun to use infinite-dimensional numbers on a zero-dimensional manifold. Trust me, addition is a BLAST.
 
  • #15
OK, this is silly. Anachronistic, I asked you to explain yourself more clearly, you did not do this. Therefore I'm locking the thread.

My apologies to the people who were having fun with this.
 

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