[FOM] Follow-up to Tennant

Dean Buckner Dean.Buckner at btopenworld.com
Thu Feb 20 14:21:03 EST 2003

Ross Finlayson wrote

> >> I approach the logic in a similar way as Dean has professed in
> >> preferring mechanisms that are easily explicable in plain language, in
> >> this case, English.

Neil wrote

> > I'm not so sure. This is an idiolect of English that I've never
> > encountered before. Is anyone else on the list as puzzled as I am?
> >
> > Neil Tennant

I'm not sure, Neil, whether you are puzzled by my previous posting, or
Ross's posting, or both.

Maybe Ross could have been clearer (he admits he could) but I think he means
this.  We say

    This set contains the numbers 1-100

Then (I was arguing) the expression "this set" refers to something different
from "the numbers 1-10".  Otherwise if it refers to the same thing, then by
Leibniz' principle (or by elementary common sense), we are saying "This set
contains this set", which I assume we are not.  I think that's pretty clear.
Or if I say

      This box contains 100 pins

"this box" does not refer to 100 pins, nor am I saying "this box contains
this box".  Plain sailing so far, I hope.

Then Ross says

"For calling the two nouns A and B, then the element with the highest
value of both A and B is 100"

Meaning I think that we can say "the highest number in this set is 100", but
can also say "the highest one of these numbers is 100".  That's pretty clear
to me.

Ross goes on

"A and B each have an element of operator  with the for-any-element,
for-each-element, and for-all-elements.  They  almost exactly refer to the
same thing, and may be considered to be the  same thing.  Each describes the
collection of any and all numbers where  the value of the number is between
one and a hundred."

I lost the plot a bit here, but does Ross mean that there are two
semantically different terms for expressing "element of".  When we use set
language, we say "is in" or "is a member of" meaning the element bears the
membership relation to a single object (the set).  Or we can say "is one of"
or "is among the number of" meaning the individual object is a part of a
colleciton of things.

This is a perfectly respectable idea.  Peter van Inwagen mentions it, but
it's much older.  Lesniewski proposed something similar which Prior
discusses in the last chapter of his seminal work "objects of thought".
J.S.Mill also criticises a similar idea as advocated by Hobbes, in the
chapter of _System of Logic_ called "The Import of Propositions" (or
something like that, I don't have the reference with me).

I don't agree with the last bit Ross writes, you need to distinguish a set
(a single object containing its members) from a collection or aggregate of
things, which consist of their members.

Simple enough, Neil?  Ross, maybe wait for half an hour and read what you've
written to see if it makes complete sense, before you hit that tempting
"send" button.

Thanks btw to Nino Cocchiarella for reminding me about Lesniewski.  Hartley
Slater has a v. good paper on "Aggregates" which traces the history of
aggregate theory back to the 1970's.  Also I just remembered the Scottish
logician Sr William Hamilton proposed such a theory back in the 18th
century, which Mill tore to shreds (unfairly) in his book on Hamilton.


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