Re: On Formal IS-A definition
From: Bob Badour <bbadour_at_pei.sympatico.ca>
Date: Sun, 09 May 2010 00:38:24 -0300
Message-ID: <4be62e32$0$26722$9a566e8b_at_news.aliant.net>
>>David BL wrote:
>>
>>>On May 7, 9:36 pm, Bob Badour <bbad..._at_pei.sympatico.ca> wrote:
>>
>>>>David BL wrote:
>>
>>>>>On May 7, 9:20 am, Bob Badour <bbad..._at_pei.sympatico.ca> wrote:
>>
>>>>>>David BL wrote:
>>
>>>>>>>On May 6, 9:10 pm, Bob Badour <bbad..._at_pei.sympatico.ca> wrote:
>>
>>>>>>>>If one is interested specifically in subtypes of supertypes, a proper
>>>>>>>>subset of a type with a proper superset of operations is a proper
>>>>>>>>subtype of that type. Thus, circle values are a subtype of ellipse
>>>>>>>>values and ellipse variables are a subtype of circle variables.
>>
>>>>>>>There is no subtype relationship between ellipse variables and circle
>>>>>>>variables (in either direction).
>>
>>>>>>>Consider a procedure in an imperative language that is passed a
>>>>>>>reference to a circle variable. Most generally the variable can be
>>>>>>>used as an "in-out" parameter, meaning that the variable is both read
>>>>>>>and written by the procedure. An ellipse variable can only be
>>>>>>>substituted for out-parameters.
>>
>>>>>>Ellipse variables are a proper subset of the variables where one might
>>>>>>store a circle,
>>
>>>>>Elements of sets are values, never variables.
>>
>>>>I am unfamiliar with any restrictions on what goes in sets.
>>
>>>Values are immutable. Variables accessed by imperative programs are
>>>usually mutable.
>>
>>None of which has anything to do with what one may compose a set with.
>>
>><irrelevent philosophical dead-ends snipped>
>>
>>>>>You cannot talk about
>>>>>subset relationships between sets of variables because there is no
>>>>>such thing as a set of variables.
>>
>>>>Of course there is. Suppose I have a set of 3 variables and a dog { a,
>>>>b, c, Rosie } ...
>>
>>>No, that is not allowed. A dog is not a value.
>>
>>You must have some set telling me what I may or may not have a set of.
>>My set of three variables and a dog is a perfectly valid set just as
>>Socrates is a perfectly valid element of a set of men.
Date: Sun, 09 May 2010 00:38:24 -0300
Message-ID: <4be62e32$0$26722$9a566e8b_at_news.aliant.net>
David BL wrote:
> On May 9, 1:09 am, Bob Badour <bbad..._at_pei.sympatico.ca> wrote: >
>>David BL wrote:
>>
>>>On May 7, 9:36 pm, Bob Badour <bbad..._at_pei.sympatico.ca> wrote:
>>
>>>>David BL wrote:
>>
>>>>>On May 7, 9:20 am, Bob Badour <bbad..._at_pei.sympatico.ca> wrote:
>>
>>>>>>David BL wrote:
>>
>>>>>>>On May 6, 9:10 pm, Bob Badour <bbad..._at_pei.sympatico.ca> wrote:
>>
>>>>>>>>If one is interested specifically in subtypes of supertypes, a proper
>>>>>>>>subset of a type with a proper superset of operations is a proper
>>>>>>>>subtype of that type. Thus, circle values are a subtype of ellipse
>>>>>>>>values and ellipse variables are a subtype of circle variables.
>>
>>>>>>>There is no subtype relationship between ellipse variables and circle
>>>>>>>variables (in either direction).
>>
>>>>>>>Consider a procedure in an imperative language that is passed a
>>>>>>>reference to a circle variable. Most generally the variable can be
>>>>>>>used as an "in-out" parameter, meaning that the variable is both read
>>>>>>>and written by the procedure. An ellipse variable can only be
>>>>>>>substituted for out-parameters.
>>
>>>>>>Ellipse variables are a proper subset of the variables where one might
>>>>>>store a circle,
>>
>>>>>Elements of sets are values, never variables.
>>
>>>>I am unfamiliar with any restrictions on what goes in sets.
>>
>>>Values are immutable. Variables accessed by imperative programs are
>>>usually mutable.
>>
>>None of which has anything to do with what one may compose a set with.
>>
>><irrelevent philosophical dead-ends snipped>
>>
>>>>>You cannot talk about
>>>>>subset relationships between sets of variables because there is no
>>>>>such thing as a set of variables.
>>
>>>>Of course there is. Suppose I have a set of 3 variables and a dog { a,
>>>>b, c, Rosie } ...
>>
>>>No, that is not allowed. A dog is not a value.
>>
>>You must have some set telling me what I may or may not have a set of.
> > No there is no axiom in set theory for that. There is however, an > axiom of comprehension which allows any predicate to be used to define > a subset of a given set. > > >
>>My set of three variables and a dog is a perfectly valid set just as
>>Socrates is a perfectly valid element of a set of men.
> > Only in Naive Set Theory. Here are some relevant quotes from > Wikipedia (http://en.wikipedia.org/wiki/Naive_set_theory): > > "It is useful to study sets naively at an early stage of mathematics > in order to develop facility for working with them" > > "Today, when mathematicians talk about "set theory" as a field, they > usually mean axiomatic set theory."
Nothing I wrote has anything to do with ZFC or unrestricted comprehension or naive set theory. My set of three variables and a dog fully complies with ZFC.
You are an idiot. Received on Sun May 09 2010 - 05:38:24 CEST