> On Mar 24, 5:51 pm, John Jones aol.com> wrote:

>> Jerry Kraus wrote:

>>> On Mar 24, 3:03 pm, John Jones aol.com> wrote:

>>>> Jerry Kraus wrote:

>>>>> Here are some simple, straightforward examples illustrating the
>>>>> operation of the Predicate Calculus, developed by Cantor and Zermelo
>>>>> in the late nineteenth and early twentieth century. They are
>>>>> considered the basis for much of modern mathematics and science.
>>>>> http://en.wikipedia.org/wiki/Set_theory
>>>>> Predicate Calculus
>>>>> 1. Subset, Union:
>>>>> {whitecolor} union {horseshape} = {whitecolor,horseshape} not=
>>>>> {horseshape}
>>>>> 2. Cartesian Product:
>>>>> {yellowcolor,blackcolor,whitecolor}
>>>>> *Product*
>>>>> {horseshape}
>>>>> =
>>>>> {(yellowcolor,horseshape),(blackcolor,horseshape),
>>>>> (whitecolor,horseshape)}
>>>>> 3. Complementation:
>>>>> A = {(whitecolor,horseshape)}
>>>>> U = {(yellowcolor,horseshape),(blackcolor,horseshape),
>>>>> (whitecolor,horseshape)}
>>>>> U \ A = {(yellowcolor,horseshape),(blackcolor,horseshape)}
>>>>> 4. Symmetric Difference:
>>>>> A = {(whitecolor,horseshape)}
>>>>> U = {(yellowcolor,horseshape),(blackcolor,horseshape),
>>>>> (whitecolor,horseshape)}
>>>>> Difference =
>>>>> {(yellowcolor,horseshape),(blackcolor,horseshape)}
>>>>> The Problem with them is, they are all quite explicitly stated in the
>>>>> Classic Chinese Dialogue, the "White Horse Dialogue", by Gongsun
>>>>> Longzi, circa 300 B.C. !!!
>>>>> http://faculty.vassar.edu/brvannor/Reader/whitehorse.html
>>>>> The Chinese Logicians, including Gongsun Longzi, were the last
>>>>> exponents of the Mohist School of Philosophy, the only ancient Chinese
>>>>> Philosophical sect to disappear completely, which I have examined in
>>>>> another article, below:
>>>>> http://groups.google.com/group/fr.sci.philo/browse_thread/thread/84f4...
>>>>> The question is, why did they disappear? Why was their work not
>>>>> pursued? What would have been the consequences if it had been
>>>>> pursued? Why is their work not even referenced by modern logicians?
>>>>> What are the relationships between technology, science and social
>>>>> development that lead to some ideas being recognized and developed,
>>>>> while others are not, at a particular time?

>>>> Your post annoyed me. THIS:
>>>> "Subset, Union: {whitecolor} union {horseshape} =
>>>> {whitecolor,horseshape} not= {horseshape}"
>>>> is only a sign, and hence gibberish, like "$£$%%".
>>>> Please write your post again and say what you mean, without opting for
>>>> obscure truncations.- Hide quoted text -
>>>> - Show quoted text -

>>> Sorry if I annoyed you, John. Well, if you read the dialogue, it says
>>> that a white horse is not a horse, because a "horse" is a shape, while
>>> a "white horse" is a combination of a color and a shape, and a shape
>>> alone is not the same as the combination of a color and a shape. That
>>> is, the union of a color and a shape into a single set, is not
>>> identical to a set consisting of a shape alone. Clearer?

>> White and horse are not different or the same, they are incommensurable.
>> They come from unique frameworks. Any ill-inspired 'combination' of them
>> produces a paradigmatic hybrid that appears to support a new object
>> 'white horse'(a hybrid of colour and shape) which only consensus can
>> pardon.
>>
>> To expand a little, if we erronously view a white horse as a combination
>> object then we create a paradigmatic or framework hybrid, created from
>> the interaction of the frameworks of white and horse, seemingly to bring
>> us the framework of white horse whose objects are white horses. But
>> there is no function or process for making such a synthesis of
>> frameworks, frameworks do not interact, they are incommensurable, so
>> only consensus can pardon or allow that combination-framework and its
>> 'combination-objects'- these being the 'combination-white horses'. If we
>> don't view a white horse as a combination then, and to view it
>> correctly, a white horse is a new object, because it comes from a new
>> framework, not a 'combined' framework. To continue, as a horse also
>> comes from a framework - the framework 'horse', then by virtue of coming
>> from unique frameworks the white horse and horse are incommensurable
>> objects, and not the same or different.
>>
>> Thus, it is only our pleasure that judges the incommensurable objects
>> white horse and horse as 'the same', or the chinese philosopher as
>> 'different', but neither are correct.
>>
>> Also, you are saying that an object is a set of properties. That is, an
>> 'unknown X' is the ground for 'combination' or 'union' of properties.
>> But again there can be no union or combination for incommensurable
>> objects like white and horse into a fictional hybrid entity
>> 'combination-white horse'. No, a white horse is an entirely new object.
>> It isn't created by combination. Viewed erronously as a
>> 'combination-white horse', it isn't really an object at all, nor even a
>> framework for instantiating objects, but an obscure hybrid of an object
>> and a framework.
>>
>> OK. Apart from all that, 'sets' aren't functions that can 'combine'
>> things ontologically. A set of cows doesn't create a herd by virtue of
>> being a set. A set might be conceived as a function mapping (set-ing)
>> between either commensurable or incommensurable objects. In the former
>> case a set is not a function because no new properties emerge. In the
>> latter case, new properties seem to emerge (a white horse from white and
>> horse)from the mapping between the incommensurables of white and horse.
>> But they don't in actuality. We need to create a new set, not simply
>> 'combine' old sets. A combination of a knife, fork and spoon doesn't
>> necessarily make a set of cutlery, a set of flowers isn't necessarily a
>> bouquet. We are dealing with incommensurable objects here, even if, for
>> example, the cutlery, and the knives, forks etc are both found in the
>> same place in the same kitchen draw. So in neither case of commensurable
>> and incommensurable objects, is a set operative as a function.
>>
>> Finally, regarding your complaint about the failure of logic to doff its
>> hat where it oughta', technical logic, in the best stereotypical
>> analytic tradition, routinely ignores both historical context and
>> contempory 'continentalist' thought on logic, even ignoring their own
>> natural language philosophical roots. So don't be surprised at the
>> absence of historical echo or comment.- Hide quoted text -
>>
>> - Show quoted text -

>
> NIce analysis, John.
>
> Sure, I'm oversimplifying, not just reality, but, to some extent, also
> the dialogue.
>
> It is astonishingly sophisticated, ontologically, logically, for 300
> B.C. Nothing even close to it in Plato or Aristotle, that I'm aware
> of, anyway. And it does imply most of the basic principles of modern
> logic. Curious how, although the Chinese retained it as a "Classic"
> it tended, along with the other contemporary logical works, to be
> viewed as "trivial" and "frivolous". Did they really think it was
> trivial, or, did they just want to make sure the average person didn't
> pay too much attention to its implications, leaving it to the
> Mandarins to employ it? Ridicule is a very powerful control strategy
> for ideas. Look at what professional academics do to ideas they don't
> like! And, like you say, they just tend to ignore anything that
> doesn't make them look good, or original, in any case.
>
>
>