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

  1. Apr 19, 2017 #1
    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...
     
    Last edited by a moderator: Apr 19, 2017
  2. jcsd
  3. Apr 19, 2017 #2
  4. Apr 20, 2017 #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!
     
  5. Apr 20, 2017 #4

    mfb

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    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?
     
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