new | show | ask | jobs Github

SideburnsOfDoom 10 hours ago

Right. is "the basic science of what simple rules do" not the same as Formal systems?

https://en.wikipedia.org/wiki/Formal_system

▲

lupire 5 hours ago | parent [-]

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 4 hours ago | parent | next [-]

How is an “actual system” distinct from a formal system? What is actual?

	▲	Supermancho 3 hours ago \| parent [-]
		I assume it's related to the aphorism: In theory, theory and practice are the same. In practice, they are not.

▲

lo_zamoyski 2 hours ago | parent | prev [-]

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.