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Re: [ontolog-forum] What is logic?

To: "John F. Sowa" <sowa@xxxxxxxxxxx>
Cc: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Patrick Durusau <patrick@xxxxxxxxxxx>
Date: Fri, 09 Mar 2007 11:14:07 -0500
Message-id: <45F187CF.5040905@xxxxxxxxxxx>
John, Till,    (01)

John F. Sowa wrote:    (02)

> Patrick,
> I changed the subject line of this thread.
OK.    (03)

> JFS>> Ontology and logic are different subjects.  But I
> >> would add that *every* precise declarative notation that is
> >> capable of making statements that are judged true or false
> >> *is* a version of logic.
> >>
> >> UML diagrams, for example, are a version of logic.  The
> >> declarative subset of natural languages forms a version of
> >> logic -- and in fact, NL (actually Greek) was Aristotle's
> >> inspiration for the first formal logic.  And *every*
> >> statement in *every* version of logic that anyone has
> >> ever invented can be translated into natural language.
> >>
> >> So anyone who is doing any work on ontology is stating
> >> their results in some version of logic (but possibly in
> >> a rather imprecise and insufficiently understood version).
> PD> My, what a large definition of logic you have.
> That's the traditional definition, which goes back to Aristotle.
> Historically, logic evolved from language.  Its name comes from
> the Greek logos, which means word or reason and includes any
> language or method of reasoning used in any of the -ology fields
> of science and engineering.  Aristotle developed formal logic as
> a systematized method for reasoning about the meanings expressed
> in ordinary language.
> In modern terms, a logic may be defined as any precise notation
> for expressing statements that can be judged true or false.  To
> clarify the notion of "judging," Tarski defined a model as a set
> of entities and a set of relationships among those entities.
> Model theory is a systematic method for evaluating the truth
> of a statement in terms of a model.
> But Tarski quoted Aristotle as a basis for his approach, and
> he claimed that he was formalizing the informal methods.
> John the Evangelist had an even larger definition:
>    "In the beginning was the logos, and the logos was with God,
>    and God was the logos.  It was in the beginning with God.
>    All things (panta) came into being through it, and without it
>    nothing that has come to be came into being."
> In short, being (to on) depends on the logos.  Therefore, the
> study of being (ontology) must depend on logic (the study
> of the logos).
>    (04)

Hmmm, true, the many -ologies were derived from the word logos but it 
hardly meant "logic" when used by John the Evangelist.    (05)

For example, in the Septuagint (translation of the Hebrew Bible into 
Greek), which dates to fairly close to that time period, logos was used 
to translate dabar, or 'word' as it is loosely translated into English. 
Logos has a fairly wide range of meanings depending upon the writer, 
time period, etc.    (06)

Thanks to Till for the recent paper citation, it merits a close read but 
I note from the conclusion:    (07)

> The notion of \a
> logic" should depend on the purpose at; in particular, proof theory 
> and model
> theory sometimes treat essentially the same issue in diŽerent ways.    (08)

I sense in the claims that all is logic some universal proof theory and 
model theory. Perhaps that is the source of my uneasiness with that claim.    (09)

Well, that and if we define logic as broadly as John suggests, then it 
becomes as vacuous as "Semantic" is in current usage.    (010)

Hope you are having a great day!    (011)

Patrick    (012)

> John
>    (013)

Patrick Durusau
Chair, V1 - Text Processing: Office and Publishing Systems Interface
Co-Editor, ISO 13250, Topic Maps -- Reference Model
Member, Text Encoding Initiative Board of Directors, 2003-2005    (014)

Topic Maps: Human, not artificial, intelligence at work!     (015)

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