Correction of a remark on R. Goldblatt "Topoi"

Correction of a remark on R. Goldblatt "Topoi"

[Alberto Peruzzi]

  There is an incorrect statement on pag. 303 of my paper ³Logic in category
theory² appeared in the volume Logic, Mathematics, Philosophy (DeVidi,
Hallett, Clark eds, 2011), where it is said that in 1979

  <<Robert Goldblatt¹s lattice-theoretically oriented introduction, [22],
allowed
logicians to learn of semantics for first-order theories in toposes;
unfortunately,
adjoints only appear in Ch. 16 which was added to the 2nd (1984) edition,
and
play no role before this.>>.

My reference was to Goldblatt¹s  Topoi. The Categorial Analysis of Logic and
what I meant was that this book, which as a graduate I found helpful indeed,
made substantial use of adjoints within a categorical formulation of logic
in chapter 16 (added in the 1984 edition), whereas I knew that they were
already defined  in chapter 15 (which is the last chapter in the first
edition of the book, published in 1979) and used in the same chapter for the
analysis of quantifiers. The need to be brief led me to a statement which
erroneously says that adjoints ³appear², i.e. are introduced in chapter 16:
adjoints were already introduced in chapter 15 where they obviously played a
role.  Thus the claim they ³play no role before this² is wrong at face
value, although their presence simply shifts to what was the <last> chapter
of the previous edition. As for what I referred to for ³role² , I intended
the role of adjoints in a fully axiomatic presentation of logic, which
actually is not made explicit until chapter 16.

Alberto Peruzzi


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Re: Correction of a remark on R. Goldblatt "Topoi"

[Robert Seely]

On Wed, 28 Sep 2011, Alberto Peruzzi wrote:

> My reference was to Goldblatt¹s  Topoi. The Categorial Analysis of Logic and

Those interested might like to revisit the review of this book in the
Journal of Symbolic Logic, Vol 47 (1982), pp 445-448.  If you have
access to the JSL via JStor, this link will get you there:

    http://www.jstor.org/stable/pdfplus/2273159.pdf

Of course, this was written before Chp 16 was added, which reduces to
some extent one critical remark made in the review.

-= rags =-


-- 
<rags@math.mcgill.ca>
<www.math.mcgill.ca/rags>


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