Re: how (Aristotle says "potential is actual and actual is potential")

From	Jim Burns <james.g.burns@att.net>
Newsgroups	sci.math
Subject	Re: how (Aristotle says "potential is actual and actual is potential")
Date	2024-06-15 14:49 -0400
Organization	A noiseless patient Spider
Message-ID	<c0feb237-0111-4d0e-a091-3ef97dd45ce0@att.net> (permalink)
References	(16 earlier) <J-2dnWIW34FHY_H7nZ2dnZfqn_adnZ2d@giganews.com> <059b1b30-b12a-4d8f-9c17-0f101285b212@att.net> <tladnSK4ybJ9UvD7nZ2dnZfqn_adnZ2d@giganews.com> <df1fc6f6-57d5-400f-a43e-e64412459cad@att.net> <iRCdneqTcNPzRPD7nZ2dnZfqn_idnZ2d@giganews.com>

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On 6/15/2024 2:12 PM, Ross Finlayson wrote:
> On 06/15/2024 10:53 AM, Jim Burns wrote:
>> On 6/15/2024 1:31 PM, Ross Finlayson wrote:
>>> On 06/15/2024 09:57 AM, Jim Burns wrote:
>>>> On 6/14/2024 10:37 PM, Ross Finlayson wrote:

>>>>> Because iota-values are contiguous, for [0,A]
>>>>> and (A,1], and [0,A) and [A,1], they're
>>>>> "complete" both ways, also they're well-ordered.
>>>>
>>>> That's not Dedekind.completeness.
>>>>
>>>> Note that, for each j/k e {n/d ∈ ℚ: 0≤n/d≤1}
>>>> splits [0,j/k],(j/k,1] and [0,j/k),[j/k,1] exist.
>>>>
>>>> {n/d ∈ ℚ: 0≤n/d≤1} is not Dedekind.complete.
>>>>
>>>> NOT completeness:
>>>> for each point,  exists a split the point is between
>>>>
>>>> Completeness:
>>>> For each split, exists a point between the split.
>>>
>>> It reminds me of physics today and
>>> "between relativity and the quantum, where's gravity?"
>>>
>>> "Euh..., its mechanism is un-defined."
>>>
>>> In mathematics where's continuity?
>>>
>>> "Euh...."
>>
>> NOT completeness:
>> for each point,  exists a split the point is between
>>
>> Completeness:
>> For each split, exists a point between the split.
>
> Induction:
> case 1: not complete, case next: see case 1.

Completeness:
Lines which cross must intersect.
Completeness supplies the intersections.

Cisfinite induction:
⎛ If P(i) changes truth.value from 0 to any k
⎝ then P(i) changes truth.value from some j to j⁺¹
⎛ ∃⟨0,…,k⟩: P(0)∧¬P(k)  ⟹
⎝ ∃⟨0,…,j⁺¹⟩: P(j)∧¬P(j⁺¹)

That is more familiar.looking when written as
⎛ P(0) ∧ ∀⟨0,…,j⁺¹⟩: P(j)⇒P(j⁺¹)  ⟹
⎝ ∀⟨0,…,k⟩: P(k)

Getting to infinity is not
what cisfinite induction does.
Being true for all finites,
of which there happen to be infinitely.many, is
what cisfinite induction does.

By the way,
Completeness:
Lines which cross must intersect.
Completeness supplies the intersections.

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Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-05-28 12:56 -0700
  Re: how (Aristotle says "potential is actual and actual is potential") Jim Burns <james.g.burns@att.net> - 2024-05-28 17:23 -0400
    Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-05-29 02:59 -0700
      Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-05-29 03:36 -0700
      Re: how (Aristotle says "potential is actual and actual is potential") Jim Burns <james.g.burns@att.net> - 2024-05-29 13:07 -0400
        Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-05-29 12:50 -0700
          Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-05-29 12:54 -0700
          Re: how (Aristotle says "potential is actual and actual is potential") Jim Burns <james.g.burns@att.net> - 2024-05-29 18:26 -0400
            Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-05-29 17:31 -0700
              Re: how (Aristotle says "potential is actual and actual is potential") Jim Burns <james.g.burns@att.net> - 2024-05-30 12:44 -0400
                Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-05-30 19:52 -0700
                Re: how (Aristotle says "potential is actual and actual is potential") Jim Burns <james.g.burns@att.net> - 2024-05-31 14:32 -0400
                Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-05-31 18:37 -0700
                Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-01 07:21 -0700
                Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-01 09:24 -0700
                Re: how (Aristotle says "potential is actual and actual is potential") Jim Burns <james.g.burns@att.net> - 2024-06-02 15:23 -0400
                Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-02 13:43 -0700
                Re: how (Aristotle says "potential is actual and actual is potential") Jim Burns <james.g.burns@att.net> - 2024-06-02 23:51 -0400
                Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-02 21:32 -0700
                Re: how (Aristotle says "potential is actual and actual is potential") Jim Burns <james.g.burns@att.net> - 2024-06-03 06:52 -0400
                Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-04 00:23 -0700
                Re: how (Aristotle says "potential is actual and actual is potential") Jim Burns <james.g.burns@att.net> - 2024-06-04 15:04 -0400
                Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-04 15:22 -0700
                Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-04 16:46 -0700
                Re: how (Aristotle says "potential is actual and actual is potential") Jim Burns <james.g.burns@att.net> - 2024-06-04 20:43 -0400
                Re: how (Aristotle says "potential is actual and actual is potential") Jim Burns <james.g.burns@att.net> - 2024-06-04 23:39 -0400
                Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-05 17:26 -0700
                Re: how (Aristotle says "potential is actual and actual is potential") Jim Burns <james.g.burns@att.net> - 2024-06-06 13:10 -0400
                Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-06 17:19 -0700
                Re: how (Aristotle says "potential is actual and actual is potential") Jim Burns <james.g.burns@att.net> - 2024-06-07 00:41 -0400
                Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-07 13:24 -0700
                Re: how (Aristotle says "potential is actual and actual is potential") Jim Burns <james.g.burns@att.net> - 2024-06-07 17:15 -0400
                Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-07 17:29 -0700
                Re: how (Aristotle says "potential is actual and actual is potential") Jim Burns <james.g.burns@att.net> - 2024-06-08 01:35 -0400
                Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-08 08:28 -0700
                Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-08 08:47 -0700
                Re: how (Aristotle says "potential is actual and actual is potential") Jim Burns <james.g.burns@att.net> - 2024-06-08 13:47 -0400
                Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-09 17:11 -0700
                Re: how (Aristotle says "potential is actual and actual is potential") Jim Burns <james.g.burns@att.net> - 2024-06-10 00:46 -0400
                Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-10 13:48 -0700
                Re: how (Aristotle says "potential is actual and actual is potential") Jim Burns <james.g.burns@att.net> - 2024-06-10 23:36 -0400
                Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-10 20:46 -0700
                Re: how (Aristotle says "potential is actual and actual is potential") Jim Burns <james.g.burns@att.net> - 2024-06-11 06:25 -0400
                Re: how (Aristotle says "potential is actual and actual is potential") Jim Burns <james.g.burns@att.net> - 2024-06-11 14:37 -0400
                Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-11 11:49 -0700
                Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-13 12:04 -0700
                Re: how (Aristotle says "potential is actual and actual is potential") Jim Burns <james.g.burns@att.net> - 2024-06-13 23:40 -0400
                Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-14 13:12 -0700
                Re: how (Aristotle says "potential is actual and actual is potential") Jim Burns <james.g.burns@att.net> - 2024-06-14 20:31 -0400
                Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-14 19:37 -0700
                Re: how (Aristotle says "potential is actual and actual is potential") Jim Burns <james.g.burns@att.net> - 2024-06-15 12:57 -0400
                Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-15 10:31 -0700
                Re: how (Aristotle says "potential is actual and actual is potential") Jim Burns <james.g.burns@att.net> - 2024-06-15 13:53 -0400
                Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-15 11:12 -0700
                Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-15 11:29 -0700
                Re: how (Aristotle says "potential is actual and actual is potential") Jim Burns <james.g.burns@att.net> - 2024-06-15 15:14 -0400
                Re: how (Aristotle says "potential is actual and actual is potential") Jim Burns <james.g.burns@att.net> - 2024-06-15 14:49 -0400
                Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-15 12:13 -0700
                Re: how (Aristotle says "potential is actual and actual is potential") Jim Burns <james.g.burns@att.net> - 2024-06-15 16:20 -0400
                Re: how (Aristotle says "potential is actual and actual is potential") "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-11 13:49 -0700
                Re: how (Aristotle says "potential is actual and actual is potential") Moebius <invalid@example.invalid> - 2024-06-11 22:59 +0200
                Re: how (Aristotle says "potential is actual and actual is potential") "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-11 14:14 -0700
                Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-11 16:13 -0700
                Re: how (Aristotle says "potential is actual and actual is potential") Moebius <invalid@example.invalid> - 2024-06-12 01:17 +0200
                Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-12 04:14 -0700
                Re: how (Aristotle says "potential is actual and actual is potential") FromTheRafters <FTR@nomail.afraid.org> - 2024-06-12 12:49 -0400
                Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-12 12:30 -0700
                Re: how (Aristotle says "potential is actual and actual is potential") "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-12 14:18 -0700
                Re: how (Aristotle says "potential is actual and actual is potential") "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-12 14:13 -0700
                Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-12 20:05 -0700
                Re: how (Aristotle says "potential is actual and actual is potential") "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-13 12:22 -0700
                Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-13 15:51 -0700
                Re: how (Aristotle says "potential is actual and actual is potential") Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-06-13 16:34 -0700
                Re: how (Aristotle says "potential is actual and actual is potential") "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-14 11:34 -0700
                Re: how (Aristotle says "potential is actual and actual is potential") "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-06-07 22:30 -0700
                Re: how (Aristotle says "potential is actual and actual is potential") Jim Burns <james.g.burns@att.net> - 2024-06-04 16:04 -0400

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