Nonetheless, FOL is a very good start to formalizing physics.

  • Context: Graduate 
  • Thread starter Thread starter mun
  • Start date Start date
  • Tags Tags
    Physics
Click For Summary
SUMMARY

First-Order Logic (FOL) is sufficient for formalizing most aspects of physics, as it can effectively handle first-order mathematics, including sets and differentials. The discussion emphasizes that while FOL allows for the construction of proofs, the inherent non-algorithmic nature of many physical systems presents challenges. Despite these challenges, having the correct axioms enables the use of FOL to validate known solutions in physics.

PREREQUISITES
  • Understanding of First-Order Logic (FOL)
  • Familiarity with mathematical concepts such as sets and differentials
  • Knowledge of proof construction in mathematical logic
  • Awareness of algorithmic versus non-algorithmic systems in physics
NEXT STEPS
  • Explore advanced topics in First-Order Logic (FOL) and its applications in physics
  • Research non-algorithmic systems and their implications in physical theories
  • Study proof techniques in mathematical logic to enhance understanding of FOL
  • Investigate alternative logical systems for formalizing complex physical theories
USEFUL FOR

Researchers in theoretical physics, logicians, and mathematicians interested in formalizing physical concepts using logical frameworks.

mun
Messages
10
Reaction score
0
Hi,

If one were to formalise physics, what would be the appropriate logic to use? Is FOL already sufficient, since the mathematics involved are first-order, e.g., sets, differentials. Or, is a more expressive logic needed?
 
Physics news on Phys.org
mun said:
Hi,

If one were to formalise physics, what would be the appropriate logic to use? Is FOL already sufficient, since the mathematics involved are first-order, e.g., sets, differentials. Or, is a more expressive logic needed?

It really depends what you mean by formalizing physics.

FOL is enough to talk about most meaningful mathematics. In FOL, you can construct proofs of equality between complex-valued functions, which should be enough for almost all physics.

However, regardless of the kind of logic you use, you will run into the problem that most physical systems are not algorithmic. You can give the initial conditions and expect to be able to calculate the final conditions. Though if you had your axioms right and you already knew the answer, you could use such a system to prove you were correct.
 

Similar threads

Other Intro Logic Books (differences between Peter Smith, J.J. Smith and P.Teller)
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Computer languages as examples in formal logic
  • · Replies 40 ·
2
Replies
40
Views
8K
High School What is the usefulness of formal logic theory?
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Is Set Theory Based on Circular Reasoning?
  • · Replies 4 ·
Replies
4
Views
4K
Graduate A "Proof Formula" for all maths or formal logic?
  • · Replies 3 ·
Replies
3
Views
2K
Graduate How do I improve my skills in constructing mathematical proofs?
  • · Replies 1 ·
Replies
1
Views
2K
Admissions I Need some advice about my physics undergraduate options
  • · Replies 11 ·
Replies
11
Views
3K
Graduate Numerical implementation of creation and annhilation operators in the SSH model
  • · Replies 0 ·
Replies
0
Views
794
Graduate The Blessings of Dimensionality and Hilbert's 6th Problem
  • · Replies 4 ·
Replies
4
Views
2K
Book recommendations (abstract algebra and number theory)
  • · Replies 5 ·
Replies
5
Views
4K