4 ms·

Right. is "the basic science of what simple rules do" not the same as Formal systems? https://en.wikipedia.org/wiki/Formal_system https://en.wikipedia.org/wiki

Right. is "the basic science of what simple rules do" not the same as Formal systems? https://en.wikipedia.org/wiki/Formal_system https://en.wikipedia.org/wiki/Formal_system

lupire 9mo ago
It's not Formal Systems. Formal Systems is the study of logical systems themselves. Ruliology is a study of what actual systems do. It's doing the arithmetic computations and looking at the results, not the abstract algebra.
- whatever120 9mo ago
  How is an “actual system” distinct from a formal system? What is actual?
  - Supermancho 9mo ago
    I assume it's related to the aphorism: In theory, theory and practice are the same. In practice, they are not.
    - SideburnsOfDoom 9mo ago
      Yes, but in this case, it's all mathematics and computation. The messy analogue real world isn't involved in either.
- lo_zamoyski 9mo ago
  Not quite. A formal system is a system of syntactic rules defined over an alphabet of symbols. They can be mechanized in principle. Peano arithmetic is one example. A „logical” semantics can be assigned to such a formal system, but it is not a necessary entailment of the syntax, even if such systems are typically motivated by particular semantic models. Model theory might examine how the same formal system affords different interpretations. Such syntactic systems have computational properties, and it is how computer science kicked off historically.
- SideburnsOfDoom 9mo ago
  > Formal Systems is the study of logical systems themselves. Ruliology is a study of what actual systems do. Assuming that you mean the same thing by "logical systems" and "actual systems", then Ruliology must fall under Formal Systems as a sub-discipline? Since studying "what these things do" is a subset of studying "these things themselves". And grounded on it. If not, then what's the difference between "logical" and "actual" systems?

Right. is "the basic science of what simple rules do" not the same as Formal systems? https://en.wikipedia.org/wiki/Formal_system https://en.wikipedia.org/wiki/Formal_system

lupire 9mo ago

It's not Formal Systems. Formal Systems is the study of logical systems themselves. Ruliology is a study of what actual systems do. It's doing the arithmetic computations and looking at the results, not the abstract algebra.

whatever120 9mo ago
How is an “actual system” distinct from a formal system? What is actual?
- Supermancho 9mo ago
  I assume it's related to the aphorism: In theory, theory and practice are the same. In practice, they are not.
  - SideburnsOfDoom 9mo ago
    Yes, but in this case, it's all mathematics and computation. The messy analogue real world isn't involved in either.
lo_zamoyski 9mo ago
Not quite. A formal system is a system of syntactic rules defined over an alphabet of symbols. They can be mechanized in principle. Peano arithmetic is one example. A „logical” semantics can be assigned to such a formal system, but it is not a necessary entailment of the syntax, even if such systems are typically motivated by particular semantic models. Model theory might examine how the same formal system affords different interpretations. Such syntactic systems have computational properties, and it is how computer science kicked off historically.
SideburnsOfDoom 9mo ago
> Formal Systems is the study of logical systems themselves. Ruliology is a study of what actual systems do. Assuming that you mean the same thing by "logical systems" and "actual systems", then Ruliology must fall under Formal Systems as a sub-discipline? Since studying "what these things do" is a subset of studying "these things themselves". And grounded on it. If not, then what's the difference between "logical" and "actual" systems?