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Throughout our database work in general, Hugh Darwen and I have always tried very hard to follow certain guiding principles (and, of course, this remark is true of our work on the Manifesto in particular). Of those principles, the most important indeed, it underpins all the rest is this: All logical differences are big differences.

This dictum is due to Ludwig Wittgenstein.1 What does it mean Well, the subject matter of the Manifesto is, essentially, the relational model. And the relational model is at heart a formal system: just as a DBMS is, or an operating system, or indeed any computer program, come to that. Formal systems are what computers are (or can be made to be) good at. And, of course, the basis of any formal system is logic. It follows that with respect to formal systems in general, and hence with respect to programming in general, and with respect to database management and the relational model in particular differences that are logical in nature are very important ones, and we need to pay very careful attention to them. To put it another way: Computers are very precise in their operation they don t have much tolerance for error. In the field of computing above all, therefore, clarity, accuracy, and precision are surely paramount. These remarks are true of database management in particular. Thus, any endeavor having to do with database management, if it s confused over issues as basic as (for example) the difference between a value and a variable, or the difference between a type and a relation, is doomed to eventual failure. We also pointed out in the Manifesto (slightly but only slightly! tongue in cheek) that Wittgenstein s dictum had an interesting corollary: namely, that all logical mistakes are big mistakes. Because, of course, a mistake is a difference; it s a difference between what s right and what s wrong. And it s certainly possible to observe a number of logical mistakes that have been made, and still are being made, in the database industry as a whole ... We also went on to conjecture that the inverse of Wittgenstein s maxim was true as well: namely, that all nonlogical differences are small differences by which we meant, not that differences that are (e.g.) merely psychological in nature are unimportant in absolute terms, but that they are unimportant from the point of view of formal systems in particular. We therefore paid little attention in the Manifesto to nonlogical considerations, such as matters of syntax. (Syntax is important from a human factors point of view, of course, and we naturally tried to choose good syntax over bad when we came to design our own language in the Manifesto. But we don t regard differences that are mere differences in syntax as logical differences, nor for present purposes as very important ones.)

As already explained, this chapter is meant to serve as a general introduction to a series on logical differences. The basic idea is that we often encounter a situation in which we have to deal with concepts that truly are distinct, and yet either

1. At this point in the first draft of this chapter, I wrote: At least, I think it is, though, sadly, Hugh and I have never been able to track it down to its source, and we d be grateful to anyone who could help us in that connection. Little did I know that help was on its way at that very moment. The complete quote is: As I once heard Wittgenstein say, all logical differences are big differences; in logic we are not making subtle distinctions, as it were between flavours that pass over into one another by delicate gradations (from a lecture entitled History of the Corruptions of Logic, by P T. Geach, published in his book . Logic Matters, Basil Blackwell, 1972). Thanks to Stephen A. Wilson for passing on this discovery. Though I can t resist pointing out that it really isn t clear how much of the quote is Wittgenstein and how much Geach! Logicians themselves who really ought to know better aren t always as precise as they might be.