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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.logic,sci.math
Subject: Re: Replacement of Cardinality (ubiquitous ordinals)
Date: Fri, 02 Aug 2024 06:39:26 -0400
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Ross Finlayson explained on 8/1/2024 :
> On 08/01/2024 05:36 PM, Jim Burns wrote:
>> On 8/1/2024 3:28 PM, Ross Finlayson wrote:
>>> On 08/01/2024 04:23 AM, Jim Burns wrote:
>>>> On 7/31/2024 8:30 PM, Ross Finlayson wrote:
>>>>> On 07/31/2024 01:21 PM, Jim Burns wrote:
>>
>>>>>> If I remember correctly,  your (RF's) name for
>>>>>> not.talking about
>>>>>> what's outside the domain of discussion
>>>>>> is hypocrisyᴿꟳ.
>>>>>>
>>>>>> That sounds like you're delivering a value.judgment:
>>>>>> that we _should not_ not.talk about
>>>>>> what's outside the domain of discussion,
>>>>>> that we _should not_ for example, not.talk about
>>>>>> _all_ triangles when we discuss whether
>>>>>> the square of its longest side equals
>>>>>> the sum of the squares of the two remaining sides.
>>
>>>>> Yeah, my mathematical conscience demands that
>>>>> hypocrisy is bad.
>>>>
>>>> Bad why?
>>>
>>> "Wrong", ....
>>
>> It is wrong to treat claims about right triangles
>> as though they are claims about more than right triangles.
>>
>>> Definition usually expands,
>>
>> The hypocrisyᴿꟳ of NOT expanding
>>   the definition of right triangle ABC
>>   to encompass triangles without right angles
>> leaves it NOT wrong that
>> a segment CH from right angle C
>>   perpendicular to and meeting side AB at H
>> makes two more triangles ACH BCH,
>>   which are both similar to ABC
>>   which, as similar triangles,
>>   have corresponding sides in the same ratio
>> so that
>> A͞H/A͞C = A͞C/A͞B
>> H͞B/B͞C = B͞C/A͞B
>> (A͞H+H͞B)⋅A͞B = A͞C² +B͞C²
>> and
>>   A͞B² = A͞C² + B͞C²  is NOT wrong.
>>
>>>>> hypocrisy is bad.
>>
>> If it is, then it isn't for making things wrong,
>>   which is something hypocrisyᴿꟳ
>>   (not.talking about outside the domain)
>> doesn't do.
>>
>>
>
> There is no "outside" the universe.

Then what *is* restricted comprehension?