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## Re: [ontolog-forum] First-Order Semantics

 To: "[ontolog-forum] " Christopher Menzel Fri, 15 Jun 2007 20:02:06 -0500 <8B7AB56F-2355-4A43-9BB6-80AFF5A28ACA@xxxxxxxx>
 ```On Jun 15, 2007, at 6:39 PM, Waclaw Kusnierczyk wrote: > Christopher Menzel wrote: >>>> There are (as of course John and Pat know) 2^card(D) relations over >>>> any set (taking relations here to be sets of n-tuples). >>> Only if n=1. >> >> Only if D is finite. > > My point was that a relation over a single set is a set of 1-tuples;    (01) I am not following you. In standard, classical logic and set theory, an n-place relation over a set is a set of n-tuples of members of S. So a 1-place relation -- i.e., a property -- is a set of 1-tuples over S (or, more typically, just a subset of S). A 2-place relation is a set of 2-tuples (i.e., ordered pairs) over S, i.e., a subset of SxS; a 3-place relation is a set of 3-tuples, i.e., a subset of SxSxS; and so on.    (02) > ... >> I must admit that, like any good platonist, I was thinking of D as >> infinite, in which case what I say is true for all n. > > A relation over an infinite set is still an (infinite) set of 1- > tuples.    (03) You appear to be using "relation" to mean "property". Is that right?    (04) > (But see above.) > >> To cover the general case of D any size, insert "at least" above >> after "There are". > > At least, unless n=1.    (05) Huh? That's not even true if "relation" is understood to mean "property". The above claim holds for any finite n -- assuming "relation" is understood as it is standardly used in logic and set theory.    (06) -chris    (07) _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/ Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx Shared Files: http://ontolog.cim3.net/file/ Community Wiki: http://ontolog.cim3.net/wiki/ To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx    (08) ```
 Current Thread Re: [ontolog-forum] First-Order Semantics, Kathryn Blackmond Laskey Re: [ontolog-forum] First-Order Semantics, Pat Hayes Re: [ontolog-forum] First-Order Semantics, John F. Sowa Re: [ontolog-forum] First-Order Semantics, Pat Hayes Re: [ontolog-forum] First-Order Semantics, Christopher Menzel Re: [ontolog-forum] First-Order Semantics, Waclaw Kusnierczyk Re: [ontolog-forum] First-Order Semantics, Christopher Menzel Re: [ontolog-forum] First-Order Semantics, Waclaw Kusnierczyk Re: [ontolog-forum] First-Order Semantics, John F. Sowa Re: [ontolog-forum] First-Order Semantics, Christopher Menzel <= Re: [ontolog-forum] First-Order Semantics, Christopher Menzel Re: [ontolog-forum] First-Order Semantics, Waclaw Kusnierczyk Re: [ontolog-forum] First-Order Semantics, Waclaw Kusnierczyk