Logical Proof Searching with concept representations for everything

Hey everyone! I have developed a unique prompt technique for brainstorming high-level arguments using GPT-4. This method involves viewing GPT-4 as a completion model - considering how it understands context and desires it to continue responding. The prompt is dynamic, adapting to the topic at hand.

To begin, I establish the goal and any key parameters upfront in simple, more functional language. This grounds GPT-4 in the purpose of the concepts.
When asking GPT-4 to generate arguments, I use directed instructions in system prompt that will enable GPT-4 to form an argument in best way possible. I may ask follow-up questions or request it builds on a previous argument.

System prompt:

Precision: The response to argument would need to be highly precise, with clear definitions for all terms and symbols. Ambiguity would be minimized as much as possible.
Logical structure: The counterargument would need to have a logical structure, with rules for combining symbols and terms to create complex expressions. This would allow for the creation of complex ideas from simpler ones.
Symbolic notation: The counterargument would likely make extensive use of symbolic notation, as this allows for the compact representation of complex ideas. Symbols would be chosen carefully to minimize confusion and maximize clarity.
Formal grammar: The counterargument would need a formal grammar, which specifies the rules for combining symbols and terms to create well-formed expressions. This would ensure that the counterargument is unambiguous and consistent.
Expressiveness: The counterargument would need to be expressive enough to capture a wide range of concepts, including mathematical and scientific ideas. This would require a large vocabulary of symbols and terms, as well as rules for combining them in meaningful ways.
Modularity: The counterargument would be designed to be modular, with well-defined interfaces between different parts of the counterargument. This would allow for the creation of specialized dialects for different domains, such as physics or computer science.
Computability: The counterargument would need to be computable, meaning that there is a well-defined procedure for evaluating expressions in the counterargument. This would allow for the use of automated tools to check the correctness of expressions and to perform calculations.
Minimalism: The counterargument would strive for minimalism, with a small core of essential symbols and terms that can be combined to create more complex expressions. This would make the counterargument easier to learn and use.


This is a very high level response from GPT-4 model, I expect that there are far more effective system prompts for proof searching that we’ve yet to discover. Leave your opinion and experience of this technique, I would love to hear from you. Thank you for reading, have a nice day!

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This is my ArgumentatorGPT comment.
The approach you’ve outlined for constructing counterarguments in argumentation appears to be well-structured and methodical, aligning with principles of logical reasoning and precision. Let’s analyze each component:

  1. Precision: Emphasizing clear definitions and minimizing ambiguity is crucial for effective argumentation. It ensures that all parties have a common understanding of the terms used, which is fundamental in any logical discourse.

  2. Logical Structure: Adhering to a logical structure is vital for the coherence and persuasiveness of an argument. It ensures that the argument progresses in a rational manner, from premises to conclusion, without logical fallacies.

  3. Symbolic Notation: While symbolic notation is highly effective in fields like mathematics and formal logic, its applicability might be limited in other disciplines. It’s essential to consider the audience and context; not all fields may benefit from or be familiar with symbolic notation.

  4. Formal Grammar: Establishing a formal grammar can indeed aid in ensuring clarity and consistency. However, it could also make the argument less accessible to those not familiar with the specific grammar, potentially limiting the audience and impact of the argument.

  5. Expressiveness: The ability to express a wide range of concepts is important, especially in complex fields. However, balancing expressiveness with simplicity and clarity is crucial to avoid overcomplicating the argument.

  6. Modularity: Designing arguments to be modular can be beneficial, especially in adapting the argument to different fields or contexts. However, care must be taken to ensure that these modular components integrate well into a cohesive whole.

  7. Computability: For arguments involving quantifiable data or logical expressions, computability is indeed a useful feature. It enables the use of computational tools for verification and analysis, which can enhance the argument’s rigor.

  8. Minimalism: Striving for minimalism can aid in clarity and ease of understanding. However, it’s important to ensure that this minimalism doesn’t come at the expense of necessary detail and depth, especially in complex arguments.

In summary, your approach is generally sound, especially for arguments in formal, technical, or academic contexts. However, it’s important to balance these principles with considerations of accessibility and relevance to the intended audience. Adapting the approach to the context and field of the argument will likely yield the most effective results.

And from me. I was using Argumentation before GPTs come. I focus mainly on correct logic but not on the answer being always correct. Because each side must find reasons to refute the opposite opinion and promote itself. If you find that GPT has a strange answer but still has a valid and acceptable reason or is like a switch on in your head. That mean you will get new things that you never knew, or anyone thought. Everyone calls GPT’s fault, but I see it as its best feature.

Moreover, this way of conversation it ignores the hallucinations. Because the process always pushes us to check the answer.

I will specify that the response will be less repetition, less compliments, more emphasis on finding arguments.

But there are 2-3 things you should be careful of: the continuity of the conversation from session problems. When case GPT run out of word but not realizing. It will bring up old topics to talk again and again. You should warn him and then he will accept it, or he will make a broad argument that makes no sense. That’s the end. Final warning nowadays GPT often asking to refresh messages because GPT can’t find the answer, I’ve experienced it 10+ times until I had to stop.