# Questions tagged [formal-systems]

A formal system is broadly defined as any well-defined system of abstract thought based on the model of mathematics. (Def: http://en.m.wikipedia.org/wiki/Formal_system)

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### Is formal truth in mathematical logic a generalization of everyday, intuitive truth?

I'm trying to wrap my head around the relationship between truth in formal logic, as the value a formal expression can take on, as opposed to commonplace notions of truth. Personal background: When I ...
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### Formal System and Formal Logical System

I was reading the Wikipedia article for Mathematical_logic. When reaching Formal_logical_systems, I was curious about its definition and clicked into its own article Logical_system, which redirected ...
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### The Power of Lambda Calculi

A simple question here, which likely demands a somewhat complex answer... Or rather, a set of related questions. What are the advantages of typed lambda calculus over untyped lambda calculus in terms ...
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### What makes a context free grammar ambiguous?

What makes a context free grammar ambiguous?
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### Some different versions of completeness of a formal system, of a logic and of a theory

I have seen people talking about Gödel's complete theorems and Gödel's incomplete theorems on math.SE. I am curious what they are really about, so I try to understand the meaning of completeness first....
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### Understanding the syntactical completeness

A formal system is syntactically complete if for each sentence (closed formula) $\varphi$ either $\varphi$ or $\lnot \varphi$ is provable. A formal system is semantically complete if every ...
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### Is it possible to formalize all mathematics in terms of ordinals only?

Our experience shows that all finitary mathematical objects could be encoded using the natural numbers, and all operations on those objects could be expressed in terms of a few basic operations on ...
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### Why is establishing absolute consistency of ZFC impossible?

Why is establishing the absolute consistency of ZFC impossible? What are the fundamental limitations that prohibit us with coming up with a proof? EDIT: This post seems to make the most sense. In ...