John, (01)
I have no particular argument with your comments below. (02)
I also appreciate the point you are making. But .... (03)
You have only partially described my point - I also said in a post made at
the same time:
CP>Also, I was not arguing for there being no relationship between ontology
and logic. A hundred years ago people like Russell and Husserl saw logic as
being the language that could be used to describe an ontology. However, over
the last 100 years or so, the notion of logic has been refined to the study
of inference. I suspect there is a relationship, but have not managed to
find much material describing it, so if anyone knows of some ..." (04)
So the Aristotelian/Kantian tradition you describe below carries on into the
early 20th century. (05)
However, it seems to me that in the late 20th century this tradition was
abandoned. That logicians (like mathematicians) wanted to develop systems
with little or no ontological commitment. It would be embarrassing if a
scientific discovery were to overturn mathematics or logic. (06)
So, if I look through the philosophy - ontology textbooks on my bookcase,
for example, Lowe's 'The Possibility of Metaphysics: Substance, Identity and
Time', I find only a brief mention of logic, typically where it is
distinguished from metaphysics. If logic were the tool to do ontology, then
one would expect to find more than a paragraph or two in a couple of hundred
pages. (07)
So it seems to me that as a historical comment my original point stands -
where 'tradition' is understood as current mainstream, rather than
historical mainstream. (08)
On the more substantial point as to whether there is a relationship between
logic (as inference) and ontology - I must confess that this in unclear to
me. I have not found much literature on this and colleagues I have asked do
not know of much (apart from some texts in Polish). If there is anything,
I'd be very interested. I have found bits and pieces. For example, Armstrong
characterises the Aristotelian transitivity found in syllogisms as
supervenience. I realise that a lot depends on how you choose to
characterise logic (and ontology). (09)
It does seem to me that if there is relationship, then it is something to do
with Husserl and Russell's notion that logic can be a tool to describe
ontologies - rather than logic IS ontology (in the philosophical sense).
(And that one must be careful not to sink into a use-mention confusion.) In
this case, as PatH noted in a recent email, modern work on logic may become
relevant - for example the delayering that allows subjects to range over
predicates, as predicates range over subjects. (010)
Regards,
Chris (011)
> -----Original Message-----
> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-
> bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F. Sowa
> Sent: 25 January 2009 14:06
> To: [ontolog-forum]
> Subject: Re: [ontolog-forum] Next steps in using ontologies as
> standards
>
> Chris,
>
> I just wanted to address one point:
>
> CP> Traditionally logic studies inference and ontology existence.
>
> Whenever anyone uses the word 'traditionally' with regard to logic
> and ontology, that immediately triggers a historical response.
>
> Aristotle founded both traditions -- ontology and formal logic.
> His method of defining the categories by genus and differentiae
> automatically produces a hierarchy (partial ordering). Porphyry
> started the tradition of drawing the hierarchy as a tree, and
> Leibniz extended the tree to a complete lattice.
>
> But from the very beginning, Aristotle used formal logic (i.e.,
> syllogisms) to reason about the hierarchy. In fact, Aristotle's
> syllogisms are often called 'categorial syllogisms' to distinguish
> them from conditional reasoning by if-then rules, which were
> developed in detail by later Greek and medieval Latin logicians.
> (And in fact, Aristotle's subset of logic is still the most widely
> used core of the description logics, such as OWL. Many ontologies
> expressed in OWL use *only* the Aristotelian subset.)
>
> The first major challenge to Aristotle's upper level (his ten
> top categories) was by Kant, who proposed 12 categories. But
> Kant reinforced the connection between logic and ontology by
> using Aristotle's logic as a basis for deriving his categories.
>
> The relationship between logic and ontology has been very clear
> from the beginning. Aristotle's first six books, which present
> his logic, are called the _organon_ (tool or instrument) because
> the logic they present is intended as a tool for doing philosophy
> in general, of which ontology is called the *first philosophy*.
>
> For a very brief summary of Aristotle and Porphyry in relation
> to the more modern work, see
>
> http://www.jfsowa.com/ontology/ontoshar.htm
> Building, Sharing, and Merging Ontologies
>
> In short, logic is a tool for doing ontology.
>
> John
>
>
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