On Wed, July 4, 2012 23:39, ravi sharma wrote:
> Doug
> Your reply is consistent and has helped me. I was wondering why the whole
> number and truth are not related (01)
Truth, as we have been discussing it, is a feature of a statement/assertion
not of an arbitrary object. (02)
> and as to why the the issue of numbers being true or false,
> does not come up? (03)
Same answer. (04)
> Similarly how many combinations of fractions make up a whole number
> say 1? (05)
There are an uncountable infinity of equations whose answer is the number
1. I'm not sure what you mean by "make up". (06)
> To mathematician 2 is a concept but
> to engineers and physicists at best asymptotic approximations such as
> 1.99999....and degrees of accuracies? (07)
This is the difference between whole numbers, which are counting numbers
and measurements, calculations, or rational/real numbers. An engineer or
physicist can count to two as easily as a mathematician can. A measurement
of a physical quantity will have an uncertainty. (08)
Approximations appear when using computers for division with floating
point results or fractional powers of a number because they are not infinite
precision machines. A computer that stores fractions in a fractional
representation instead of in a binary or digital system needs not approximate
the result of division. (09)
An ontology can model a fraction, logarithm, trigonometric function, or
fractional power without approximation as mathematicians do -- by
referencing the function or simplification thereof. It need not convert
to a non-terminating binary or decimal representation. (010)
I would not relate measurement accuracy or computer calculation
approximations to "truth". (011)
-- doug (012)
> Thanks.
> Ravi
> On Tue, Jul 3, 2012 at 2:23 AM, doug foxvog <doug@xxxxxxxxxx> wrote:
>
>> On Fri, June 29, 2012 19:10, ravi sharma wrote:
>> >...
>> > Doug
>> > Your explanation is logical, however, I do not have to explain (other
>> than
>> > those who believe that 2 is True)
>>
>> Unless we are discussing a computer language in which 0 is FALSE and
>> any non-zero bit/byte/word/doubleword is TRUE, the issue of numbers
>> being true or false, does not come up. The words, as i am used to them
>> being used in the present context apply to statements, and whether they
>> correspond to "reality".
>>
>> > to any one outside as to what 2 is even as a concept?
>>
>>
>>
>> > Then only we ca say 2+2 and then there have to be those who
>> > believe that 4 is True.
>>
>> I'm confused. Do you mean that those who understand what 2 is
>> as a concept and who also understand addition, believe that the
>> statement "2+2 equals 4" is True? If so, i agree.
>>
>> > What I was coming to was that 0, 1, whole number
>> > and infinite as well as innumerable as concepts do these have to be
>> > understood
>>
>> I agree with this regarding the first 3. I wouldn't expect most people
>> to understand infinite and innumerable as concepts.
>>
>> > as language or culture related concepts.
>>
>> I'd disagree that any of your set of concepts are language or culture
>> related. I'd expect an extra-terrestrial intelligence to have the same
>> concepts, but to use different symbols to represent them.
>>
>> > ... as
>> > progression to numbers or whole and fractional numbers, what are the
>> > founding concepts that must be True in languages before we advance to
>> > relationship between these concepts such as equality or absence as
>> 'zero'
>> > although it is not the same as either void or vacuum?
>>
>> The founding concepts that must be true are:
>> * Whole numbers are sequential; there is exactly one "next" number after
>> any given whole number.
>> * Whole numbers can thus be arranged in a unique order in a "number
>> line".
>> * One can count along the number line, counting one sequential number
>> for each number one reaches consecutively.
>> * The first whole number is labeled 0.
>> * The second whole number is labeled 1.
>> * The result of the addition of two numbers is defined as the number
>> reached when counting to the first number from 0, and then counting
>> by the second number from the number reached.
>> * A whole number is equal to itself and to no other number.
>> * The result of adding two whole numbers is always the same whole
>> number.
>> [Given this, one can prove that 0 + n = n.]
>> * Addition is commutative.
>>
>> > John
>> > I read a bit of what you wrote for me and Avril and my inquiry is as
>> to
>> > what should we understand in language that would then help us
>> understand
>> > 2+2=4. Is it necessary to know 0 or 1 prior to mechanics of math or
>> deeper
>> > understanding?
>>
>> Mathematics is based on 0, 1, and counting. One can memorize addition
>> and multiplication tables without understanding what one is doing. But,
>> one should know something about 0, 1, and counting in order to
>> understand
>> additional math.
>>
>> -- doug
>>
>> > Regards.
>> > Ravi
>> >
>> > On Fri, Jun 29, 2012 at 5:55 PM, Obrst, Leo J. <lobrst@xxxxxxxxx>
>> wrote:
>> >
>> >> John,
>> >>
>> >> One issue with this approach is that you thereby reduce ontology to
>> >> logic.
>> >> I think there is reason (and value) to consider both of these subject
>> >> areas
>> >> distinct, if related.
>> >>
>> >> Ontologists use "universal" and "particular" because these technical
>> >> terms
>> >> are important to their exposition of what ontology is. Cf. the "Logic
>> >> and
>> >> Ontology" entry at http://plato.stanford.edu/entries/logic-ontology/.
>> >>
>> >> Similarly, I would oppose a reduction of formal semantics (natural
>> >> language and otherwise) to logic or ontology, though they are
>> related.
>> >>
>> >> Thanks,
>> >> Leo
>> >>
>> >> -----Original Message-----
>> >> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:
>> >> ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F Sowa
>> >> Sent: Friday, June 29, 2012 1:09 PM
>> >> To: Avril Styrman
>> >> Cc: [ontolog-forum]
>> >> Subject: Re: [ontolog-forum] Truth
>> >>
>> >> On 6/29/2012 12:34 PM, Avril Styrman wrote:
>> >> > Then again, properties and particulars are needed in ontologies
>> which
>> >> > directly concern the measurable reality.
>> >>
>> >> I agree. My point, though, is that you don't need the words
>> >> 'property' or 'particular' when you develop or use an ontology.
>> >>
>> >> Those words are useful when you compare the theories of different
>> >> philosophers. But when you are developing a formal ontology, you use
>> >> some formal logic to express it. To discuss the ontology, you never
>> >> need to use any terms other than the words for the syntactic units
>> >> of the logic you use.
>> >>
>> >> If you're using FOL, the only words you need are 'function',
>> relation',
>> >> 'variable', and 'value' (of a variable). If you're using Common
>> Logic,
>> >> the values of a variable can include functions and relations.
>> >>
>> >> I disagree with Quine's attempt to eliminate abstract entities, but I
>> >> am willing to accept his famous dictum:
>> >>
>> >> To be is to be the value of a quantified variable.
>> >>
>> >> In other words, the entities that exist in your ontology are
>> identical
>> >> to the things you can refer to by variables in the logic you used to
>> >> express the ontology.
>> >>
>> >> My recommendation is to use the same terms to talk about the things
>> >> in your ontology that you would use to refer to whatever your logic
>> >> is able to express.
>> >>
>> >> This convention drastically simplifies the verbiage you use to talk
>> >> about your ontology, and it clarifies talk about what exists.
>> >>
>> >> John
>> >>
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>> >
>> >
>> > --
>> > Thanks.
>> > Ravi
>> > (Dr. Ravi Sharma)
>> > 313 204 1740 Mobile
>> >
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>
>
> --
> Thanks.
> Ravi
> (Dr. Ravi Sharma)
> 313 204 1740 Mobile
> (013)
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