FOM: Re: isomorphism; annoyment

Jaap van Oosten jvoosten at
Fri Mar 13 08:29:46 EST 1998

> Date: Thu, 12 Mar 1998 15:53:52 -0500 (EST)
> From: Stephen G Simpson <simpson at>
> Jaap van Oosten writes:
>  > I looked it up for you: Graetzer (p.34) defines the notion of
>  > isomorphism for algebras of the same similarity class, not for
>  > algebras of possibly different classes.  O! But what about model
>  > theory? Well, also Chang & Keisler define isomorphisms only for
>  > models of the same language.
> Thanks for looking it up for me.  But I don't get your point.  Isn't
> your reading of Graetzer, Chang/Keisler etc equivalent to, or at least
> consistent with, the view that I expressed earlier?  I.e. that
> algebras of different similarity class, or models of different
> languages, are defined to be non-isomorphic?  Or, at least, not
> defined to be isomorphic?

Which is not the same thing. Let me repeat what you wrote:

  But what about universal algebra books, e.g. books by
  P.M.Cohen, Graetzer, etc.?  In there I think they define isomorphism
  in general, and part of the definition is that isomorphic structures
  have the same signature.  Sorry, I don't have any of those books handy
  right now to pull out a reference, but -- dare I ask -- do you agree?
I think I gave a satisfactory answer to this. It is nowhere "part of the
definition of an isomorphism" that structures have the same signature.

> What are you so upset about?  Please answer this, I'm genuinely
> concerned.

I do this with hesitation, since it really is an emotional matter; but your
genuine concern has softened my heart and I'll tell you what is on my mind.

[WARNING to fom-list readers: what follows does not contain anything of 
mathematical interest]

It's your style, Steve. Already your tone versus McLarty was extremely
unpleasant; here, from your last message:

>  > since "all Boolean algebras" and "all Boolean rings"
>  > are categories. And these two categories are isomorphic.
> No, you misunderstood me.  "All Boolean algebras" does not refer to a
> category.  "All" is a universal quantifier.  It is a standard
> construct in the predicate calculus, going back to Frege.  I assume
> you are familiar with it.  If not, please let me know and I'll try to
> explain it, or you can read up on it in textbooks of mathematical
> logic.  It is sometimes denoted by an upside-down A.

Now who do you think you are fooling, Steve?

But let me explain in some more detail why I get so annoyed at your
messages. I assume most contributors to this list have their private
motives: one of Harvey Friedman is, for example, to establish himself
in that exalted position where people will agree with him on the basis
that it is he who said it. This is a selfish motive that I can respect.
For others (and I suspect Riis and also Pratt to be among those), this
debate is a game they enjoy. 
But you are different from these people. In you, I recognize the type
of revolutionary idealists I used to meet when I was 17. These people
had a CAUSE to fight for (your cause is to exterminate the germ of
category theory), which was of overriding importance in their minds. It
certainly prevailed over ideas of elementary courtesy, or style (and in 
the worst cases, it prevailed over the very life of others). This was,
as I discovered, not merely a phenomenon on the side. It was very essential
to these people to fight with all the rudeness they could muster, because
only that would prove to them, time and again, how dedicated they were to
the ultimate goal.
And I came to realize that the intense satisfaction that these people derived
from their self-proclaimed moral superiority, was highly addictive; many
had become emotionally dependent on it. But like any drug, it needs
refreshment every day, and from time to time you have to raise the dosage.

When I see you relish in dishing it out to people even for minor
grammatical errors like the example above (sometimes even errors in English,
where another might observe that we're not all native English speakers) and
indulge in extremely condescending and patronizing language, for pages and
pages on end, I feel you are satisfying a personal need of the sort just described.
You are entering your dream world, where you are so superior to everyone
(except Harvey Friedman).

I find it revolting.

Jaap van Oosten

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