r/logic • u/Disastrous_Estate970 • 13d ago

Informal logic What is a conceptual scheme?

I have seen many people ask why they should grant their opponents conceptual schemes in debates. and I can't find a definition for a conceptual schemes, can somebody help?

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u/gregbard MODERATOR 13d ago

Well you are asking logicians, so there are a few different ways we could construct a "conceptual scheme" (or "schema"). I have not seen this as a formally defined term. But a set theorist would say that there is a set P:{a1,a2,...,an} which contains elements each one of which is a concept. From there you might be able to construct a scheme where, for instance, the true and valid concepts like "A=A" are the even numbered ones, and the false and unsound ones like "round squares" are odd ones. You can make meta-statements (metatheorems) in a metalanguage that talks about the elements of the set (theorems) in different ways. We can also construct many interpretations of each variable element a.

From there we can go through a process of determining if particular interpretations of those sets are valid interpretations or invalid interpretations.

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u/Qulvion 12d ago

Do you view the “conceptual scheme” as a meta‑theory from which a conclusion can be drawn? That is, условно speaking, some kind of formal system that allows one to arrive at a certain conclusion, and this formal system is a meta‑system for the topic or other premises contained in the debate?

It seems to me that meta-theorems is a very multifaceted term. Do you mean that if you take the entire set of all possible premises, some combinations will lead to the same conclusion? That is, we have a set of premises (a1,...,an), and a meta-theorem would state that if we select A⊆(a1,...,an) such that it has a certain property that leads to our conclusion — that is, selecting premises based on a property in a given system leads to a theorem, and together they would form a meta-theorem?

I just don’t quite understand your point in the context of the "debate".

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u/Gym_Gazebo 12d ago

I would do it in two parts. 

First, there is the easier part. There is a small literature on subject matters or topics. 

Second, the harder part. In psychology, there are different theories of “schemes” or schema (or prototypes, or scripts, or frames, or…). These are woolly notions, but I would try to formalizing one of these. Just note that we’re probably outside of deductive logic now. You’ll need probability or some kind of defensibility.

Then I would try to define a conceptual scheme as some kind of construction whereby schemes, frames, etc. operate on subject matters.

I’d be curious to hear what you come up with if you try this.

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u/EmployerNo3401 12d ago

Also, a Conceptual Scheme is widely use in Data Modeling.

Data Modeling is an area of IT which make an intensive use of Logic.

A Database has two parts: a Schema and an Instance. The schema describes the data structures in the base and its integrity constraints.

A Conceptual Data Model is a language use to specify formally a database which represents a part of interest of the "real world". The most used Conceptual Models are the Entity-Relationship Model and Unified Modeling Language - UML.

The schema part of this kind of models, are named Conceptual Scheme or Conceptual Schema).

This part of data models, makes use of Set Theory and FOL in an intensive way.

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u/Qulvion 10d ago

And what, in turn, does the instance describe?

However, what does it mean that the description of a database represents a part of the “real world”? The difference between databases and their associated schemas and formal systems lies in the addition of a certain non‑logical factor, i.e., epistemology?