# Definition for “logical difference”?

I'm currently reading "SQL and Relational Theory" by C.J. Date. And although I'm quite far in the book, I've got a few basic questions. I want to know what the term "logical difference" means, The book does try to explain the term with examples, but does not really explain what it means (or maybe I'm understanding it wrong??)

Here is a small part from the book:

I've said that there's a logical difference between a relation and a picture of a relation. The concept of logical difference derives from a dictum of Wittgenstein's:

• All logical differences are big differences.

I know what a logical difference means intuitively, I know what the difference is between a relation and a picture of a relation. What I want is a formal-like definition of the concept of a "logical difference" so I have a good idea of what it means.

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See Date's book:

Date on Database: Writings 2000-2006

Chapter 4: On the Notion of Logical Difference

Salient quote:

you'll be aware that I often appeal in my writings to the notion of logical difference. That notion is one I find extraordinarily useful in my own work; it's a great aid to clear and precise thinking… The intent of what follows [in chapter 4 of this book], then, is to offer a brief introduction to the concept of logical difference.

…bearing in mind this is Chris Date, for whom "brief introduction" actually amounts to 15 pages of closely-typed prose including footnotes and endnotes!

Follow the above link to the Google Books copy of the book, which should open in your browser, where the chapter seem to be available in full. After you've read the chapter, I'm sure you shall have a good understanding of the concept of logical difference.

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A bit sparse ... any narrative to give some hints? – gbn Dec 14 '11 at 18:48
@gbn: any better? – onedaywhen Dec 15 '11 at 8:22
er... yes. I think :-) – gbn Dec 15 '11 at 8:28

I've read the chapter. I think I now have a good idea of what it means. There is no explicit "definition" for a "logical difference", therefore, I will attempt to explicitly define "logical difference".

first, I will explain the terms I will use in my definition.

• Concept: that which is tested for the logical difference.
• Context: The concept is used in a certain way.
• Result: The effects after the Concept has been used in a Certain context.

Definition: A concept is logically the same as another concept if for each possible context in which the concept can be used has the same result for each concept. Conversely if the results are different, then there is a logical difference.

I think this is the right answer.

Note: This is the definition of my current understanding of "logical difference", this does not mean that it is the correct definition.

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