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Re: [ontolog-forum] Truth

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: John F Sowa <sowa@xxxxxxxxxxx>
Date: Fri, 29 Jun 2012 10:30:39 -0400
Message-id: <4FEDBC0F.5010706@xxxxxxxxxxx>
Avril and Chris,    (01)

I am writing a short book entitled _Principles of Logic and Ontology_,
which I promised the publisher that I would finish by December.  The
intended audience is the kind of people who subscribe to Ontolog Forum,
attend Semantic Technology conferences, develop software that uses basic
ideas of logic and ontology, and professors who teach courses to them.    (02)

The tutorial I presented at SemTech in San Francisco a few weeks ago
has a large overlap with what I'm writing for that book:    (03)

    http://www.jfsowa.com/talks/kdptut.pdf    (04)

As you may notice, there is a lot of historical material.  I include it
for background and for showing how the basic ideas appear and reappear
in different guises.  But the principles I want to emphasize are ones
that are easy to explain, easy to learn, and mostly foolproof -- i.e.,
they minimize the amount of confusing and distracting detail, and they 
don't depend on fine distinctions that generate endless debate.    (05)

> There are many different 1kg particulars which all share the identical
> property 1kg. Alternatively, one can say that there are several unidentical
> 1kg properties, where a property is thought to include its constituents
> in the fashion of tropes. Then again, instead of 'constituents', one can
> use 'particular'. That is, some form of property-particular or property-
> constituent dichotomy is needed.    (06)

I would never write anything like that in my book.  I admit abstract
things like measures in the ontology, and I introduce triadic relations,
such as hasMeasure(x, y, kg).  I also define the measure kg by saying
that one can choose some object whose mass is defined to be 1 kg.    (07)

Then the relation hasMeasure(x, y, kg) can be determined by comparing
the object x to the object that defines the standard measure of 1 kg
by using some appropriate mechanism that computes the ratio y to 1.    (08)

This explanation avoids the terms 'universal', 'particular', 'property',
'trope', 'property-particular', and 'property-constituent dichotomy'.
The only place where such terms would occur in my book is in a glossary
of obsolete terms that one might accidentally bump into.    (09)

I'd also like to go back to an earlier point Chris mentioned:    (010)

>> ... the observation that
>>   "p is true" if and only if p.    (011)

> Misplaced right quote there; should be:
>    "p" is true if and only if p.    (012)

I would prefer to use the following punctuation:    (013)

    "'p' is true" if and only if p.    (014)

As you know, I prefer to use a Tarski-style stratified hierarchy
of metalevels:    (015)

    Object level statement:  p.    (016)

    Metalevel statement:  'p' is true.    (017)

    Meta-metalevel statement:  "'p' is true" if and only if p.    (018)

I'll admit that it's possible to have a logic that talks about
truth values without having a strict hierarchy of metalevels.    (019)

But I want to use a formalism that is easy to teach to students and
easy to apply to a large number of practical problems.  A hierarchy
with clearly marked metalevels is much easier for me to explain and
much, much easier for the readers to learn and use without getting
into trouble.    (020)

Note:  As in Tarski's hierarchy, I would allow metalevel N to include
every statement in level N-1 plus the truth values for level N-1.  But
it would not include the truth values for level N itself.    (021)

For simplicity, I allow the words 'true' and 'false' to be indexicals
so that the qualifiers about the level can be omitted.  For example,
If 'p' is at the object level N, a statement "'p' is true" is at
level N+1 and 'true' specifies truth for level N.  when multiple
levels occur in the same statement, the words 'true' and 'false'
can have subscripts to indicate the level.    (022)

John    (023)

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