In order to understand the position within the scientific landscape of computational materials modeling at the quantum level , it is helpful to understand a concept from mathematical logic: formal systems.
You can use the forum underneath to share your thoughts on one or more of the following questions:
- Find another example of a formal system in mathematics, preferably somewhat different from the
examples given in the video. Identify symbols, derivation rules and axioms.
- Does an axiom have to be “true”? For instance, is it allowed to build a formal system similar to the
one discussed in the video, but starting from the axiom “1+1=3” ?
- There is well-known story in the history of mathematics about what can happen if you
replace just one of the axioms of a formal system. You might google for the development/discovery
of non-Euclidean geometry out of Euclidean geometry
The concept of a formal system is used to classify the positive sciences. This allows to understand what it means to have an “ab initio theory” for a particular field of physics:
Two students are arguing:
A: “Newton’s laws are axioms, and therefore they cannot be proven.”
B: “No, that’s not true – I have proven Newton’s laws in a physics course when I was 17 years old.”
According to you, which of both students is right, and why?
Post your answer to this optional question into this forum, and comment on the answers of others afterwards.