# 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.

## 3 Answers

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.

• 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.

Having read all of C. J. Date's book that I could view at the link provided, and having earlier read large portions of several of his other books (and viewed several of his instructional videos), I believe I can pose a useful definition for the phrase in question:

I believe the phrase "logical difference" as use by Chris Date means simply a difference which has logical implications in the context of the subject under discussion, as contrasted with a difference without relevance to the subject under discussion.

This latter type of difference could be called a "superficial difference," but more likely should just be called "irrelevant."

Example: If we are talking about databases, there is a logical difference between the model and the implementation (as discussed at length by Date.)

Example: If we are talking about databases, and I bring up the difference between a computer and a monitor, you wouldn't call this a "logical difference." However, it's not a "superficial difference" either; it's simply entirely irrelevant (inapplicable) to the discussion.

Personally, I would contend that all differences are logical differences.

The relevance or irrelevance of an observed difference to the subject under discussion does not determine whether or not it is a "logical difference," although that is, I believe, an accurate description of how Chris Date uses the term.

The very essence of logic (or sanity) is being able to recognize the difference between two things, and to recognize when there is no difference.

More precisely:

Sanity is the ability to recognize differences, similarities and identities.

(This is a fundamental originally posed by L. Ron Hubbard in 1938.)

Thus the very concept of a "difference" is fundamental to the notion of "logic," so how could it be possible to have a difference that is not a logical difference?

If you replace all usages of the phrase "logical difference" with either "important difference" or "relevant distinction," I do not believe you will lose any meaning.

To borrow Date's own terminology, the concept of "logical difference" is logically the same as the concept of "relevant, important distinction."

By the way, just in case my opinions came across as critical, I want to make it perfectly clear that I think C. J. Date is a genius. :)