A "Proof Formula" for all maths or formal logic?

In summary, the conversation discusses the possibility of a "master formula" or "proof formula" that would allow mathematicians to prove statements by plugging in numbers. The possibility of finding such a formula for first-order logic or simpler formal theories is also mentioned, as well as the idea of using a formal theory to prove statements with specific Gödel numbers. The conversation also touches on the idea of there being different mathematical languages and the issue of incompleteness in formal theories such as arithmetic. The use of automated theorem proving and proof assistants is also brought up. Overall, the discussion revolves around the relationship between the validity of a statement in a formal language and its Gödel number, and the potential implications of this.
  • #1
moriheru
273
17
I was wondering whether or not there could be a "master formula" . What I mean by a master formula is, maybe not even a formula, some mathematical expression that would allow mathematicians to prove statements simply by plugging in some numbers into a formula.

So I guess in a way a I am talking about a " proof formula" . To be more precise: shouldn't it be possible to find for example by interpolation, a formula that relates the validity of a theorems statement to its Gödel number. I am aware that mathematics is a vast and complicated language, but would this be possible for first order logic or other simpler formal theories .

I believe the reverse process is certainly easier though. I can easily set up a formal theory in which I choose my axioms and inference rules in such a way that for example every theorem with a Gödel number divisible by 17 and 2 is true.

I am aware that I have used the term maths in a rather loose fashion. I am no expert, but there surly is no one mathematical language. Topology may have different rules than Order theory and hence be a different formal theory. Additionally, what about the incompleteness of forma, theory such as arithmetic. Any thoughts...
 
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  • #3
I am a aware of automated proofs such as the W-Z method, but that wasn't quite the point I was trying to make or inquire upon. I was more specifically asking whether a connection can be made between the validity of a statement in a formal language and it's Gödel number and how incompleteness may effect this. Nevertheless the Isabel link was very interesting thank you!
 
  • #4
You can list all valid statements in a specific order. With sufficient resources, you'll find the Gödel number of every proof of length < N for large N. How does that help?
 

Related to A "Proof Formula" for all maths or formal logic?

1. What is a "Proof Formula" in maths or formal logic?

A "Proof Formula" is a set of rules and symbols used to demonstrate the validity of a mathematical or logical argument. It is a way to show that a statement is true by using logical reasoning and evidence.

2. Why is a "Proof Formula" important in maths or formal logic?

A "Proof Formula" is important in maths and formal logic because it allows us to verify the accuracy of a statement or claim. It also helps us to identify any errors in reasoning and ensure the validity of our arguments.

3. How do you use a "Proof Formula" in maths or formal logic?

To use a "Proof Formula", you must follow a set of steps that are specific to the type of proof you are trying to demonstrate. This may include identifying assumptions, using logical rules and symbols, and providing evidence to support your argument.

4. Are there different types of "Proof Formulas" for different types of maths or formal logic?

Yes, there are different types of "Proof Formulas" for different types of maths or formal logic. For example, there are specific proof formulas for algebra, geometry, and propositional logic. Each type of proof formula may have its own set of rules and symbols.

5. Can anyone use a "Proof Formula" in maths or formal logic?

Yes, anyone can use a "Proof Formula" in maths or formal logic as long as they have a basic understanding of the rules and symbols involved. However, it takes practice and experience to become proficient in using proof formulas effectively.

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