Re: Operationalize orthogonality

From: Tony D <>
Date: 8 Jun 2006 07:46:30 -0700
Message-ID: <>

Pickie wrote:
> Booleans don't in themselves convey order.

Indeed not. You could define an ordering of your own for your own purposes. Something like, say,

greater_than(false,false) = false
greater_than(false,true) = false
greater_than(true,false) = true
greater_than(true,true) = false

There you are, an order defined on booleans. It's arbitrary, meaningless, and pretty much pointless, but it's an ordering all the same.

[ snip ]

> Individual bits can represent booleans, but where is the concept of
> order coming from that turns a set of bits into a coded string of bits?

Turn it around. Try "booleans can represent individual bits". Getting anywhere now ? Maybe I haven't been explicit enough for you; I consider a type to be a set of values (or a set of equations defining the values) and the operators for that type. A type generator will have to offer a way to define the operators for a type, as well as a way of describing the acceptable values for that type. By beginning with relations and booleans, the type generator will allow us to describe new types *and the operators upon them*.

[ snip ]

> So, to answer your question. Not only do I not see it, I do not
> acknowledge it is possible. Obviously there are systems that do it,
> but _not_ by building _solely_ on booleans and relations (even
> theoretically).

Fair enough. You're wrong, but to convince you would obviously require me to define a representation of integers using relations of booleans, and then to define the operators of arithmetic on them. It's doable, but will take ages (remember, "frightening degrees of circumlocution") and sorry, but life's too short (and mine too busy) for that. Received on Thu Jun 08 2006 - 16:46:30 CEST

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