What Does a Formal Proof in Physics Look Like?

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Discussion Overview

The discussion revolves around the nature of proofs in physics compared to those in mathematics, exploring the concept of formal proofs in physics, the role of experimentation, and the implications of quantification in both fields. Participants examine whether physics can achieve the same level of certainty as mathematics and how theoretical statements are validated.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • Some participants question whether a proof in physics can be equated to a proof in mathematics, noting that physics is inherently tied to experimental validation.
  • One participant argues that physics cannot be expressed in quantifier form like mathematics, citing the blurry nature of reality and measurement uncertainties.
  • Another participant suggests that physics can indeed use quantification, providing examples of how physical laws can be framed in a mathematical context.
  • There is a discussion about the nature of mathematical truths, with some asserting that certain mathematical statements are true by definition, while others challenge this view.
  • Participants express differing opinions on the implications of proofs in physics, with some stating that theories may be superseded and thus cannot be considered definitively proven.
  • One participant emphasizes that all mathematical statements are of the form "If A then B," while others dispute this claim, arguing that some statements are true by definition.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the nature of proofs in physics versus mathematics, with multiple competing views on the validity and structure of proofs, the role of experimentation, and the interpretation of mathematical statements.

Contextual Notes

Limitations include the dependence on definitions of proof and truth in both mathematics and physics, as well as unresolved questions about the implications of quantification in physical theories.

  • #31
"So the statement that: that all statements in mathematics are of the form "If A then B".
is wrong"

As HallsofIvy said, the statement you're making is on the "If A then B" form, do you actually think you're going any further with this?
 
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  • #32
HallsofIvy said:
Notice, by the way, that all statements in mathematics are of the form "If A then B". .


Here are the axioms of propositional calculus in mathematical logic:


......A----->( B------A)............1

......( A----->( B-----C))-------->(( A----->B)------>(A---->C))...2


where A , B , C are statements.


Do you still insist that all statements in mathematics are of the form " If A then B"??



.......yes or no..........
 
  • #33
Mathematics uses deductive logic, science uses inductive logic. Does this help?
 
  • #34
jimmysnyder said:
Mathematics uses deductive logic, science uses inductive logic. Does this help?

You mean for theorems proved in physics we use only inductive procedures and not the rules of inference?
 
  • #35
evagelos said:
is a proof in physics equal in strength with that in mathematics?

in mathematics we have at one end an ordinary proof and at the other end a formal proof.

how would aformal proof in physics look like,an example would help.

I suppose that the validity of a proof in physics could be checked by an experiment but in the case that we have no experiment what happens??

Thanks

Its a bit different in the case of physics. Theoretically outlining things is usually done mathematically...so either way, you're dealing with mathematical proofs...however, there is still the need of confirmation, which suggests an empirical source.
 
  • #36
evagelos said:
You mean for theorems proved in physics we use only inductive procedures and not the rules of inference?
When you prove theorems, you are doing mathematics. Mathematics in the service of physics is still mathematics.
 
  • #37
HallsofIvy said:
Notice, by the way, that all statements in mathematics are of the form "If A then B". .

evagelos said:
Here are the axioms of propositional calculus in mathematical logic:


......A----->( B------A)............1

......( A----->( B-----C))-------->(( A----->B)------>(A---->C))...2


where A , B , C are statements.


Do you still insist that all statements in mathematics are of the form " If A then B"??



.......yes or no..........


HallsofIvy i am still waiting for an answer,also for the formal proof that:nothing contains everything .


.....That is if you wish of course............
 

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