] Isomorphism between computation and philosophy
Owen is right that there are N! ways to map a set of N objects 1-1, onto
another set of N objects. The first object can go to 1 of N objects, the
next to 1 of N-1, etc. That's pretty standard.
As to the Halting Problem, Why not start with the first few
Another result (the unsolvability of the halting problem) may be
interpreted as implying the impossibility of constructing a program for
determining whether or not an arbitrary given program is free of 'loops'.
Martin Davis, Computability and Unsolvability, 1958
--Joe
On 4/17/13 10:43
Applied Complexity Coffee Group
Subject: Re: [FRIAM] Isomorphism between computation and philosophy
Owen is right that there are N! ways to map a set of N objects 1-1, onto
another set of N objects. The first object can go to 1 of N objects, the
next to 1 of N-1, etc. That's pretty standard
On 4/18/13 7:57 AM, Joseph Spinden wrote:
Another result (the unsolvability of the halting problem) may be
interpreted as implying the impossibility of constructing a program
for determining whether or not an arbitrary given program is free of
'loops'.
Well, compilers can't reason about all
Joseph Spinden wrote at 04/17/2013 07:21 PM:
Owen is right that there are N! ways to map a set of N objects 1-1, onto
another set of N objects. The first object can go to 1 of N objects, the
next to 1 of N-1, etc. That's pretty standard.
Well, saying there are N! maps is different from saying
18, 2013 8:06 AM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Isomorphism between computation and philosophy
I was suggesting the contributors to this chat could go read the Wikipedia
article to give them something useful to say to the beautiful woman about
Subject: Re: [FRIAM] Isomorphism between computation and philosophy
On Thu, Apr 18, 2013 at 10:08 AM, Nicholas Thompson
nickthomp...@earthlink.net wrote:
And I am trying to get folks here to confront the problem of putting in
their own words things they think are obvious for other folks for whom
On Tue, Apr 16, 2013 at 11:10 AM, Nicholas Thompson
nickthomp...@earthlink.net wrote:
snip
Translatability has been a crucial issue in modern analytical philosophy.
Translation implies that you and I have the same piano and that, while we
may call the keys by different names, there is a
Applied Complexity Coffee Group
Subject: Re: [FRIAM] Isomorphism between computation and philosophy
On Tue, Apr 16, 2013 at 11:10 AM, Nicholas Thompson
nickthomp...@earthlink.net wrote:
snip
Translatability has been a crucial issue in modern analytical philosophy.
Translation implies that you
On a tangential note, I was told in 1961 of a project to prove (on a computer)
the theorems in Principia Mathematica. It went well through the first section,
and then they hit the brick wall when they encountered statements like there
exists and for every. When dealing with infinite sets, these
Well said, Steve! Mostly, what's kept me from commenting on the
isomorphism thread is ... well, the word isomorphism. [grin]
I spend _all_ my time... seriously ... arguing against the Grand
Unified Model (GUM). For some reason, everyone seems so certain,
convicted, that there exists the One
Er,, of course there are many, right? With two finite sets of size N there
are N! 1-1, onto unique mappings, I believe.
But relax. I went off the deep end with examples of things like
decidability.
All I'm curious about is whether or not it is possible to somehow make
philosophy, or simply
On Wed, Apr 17, 2013 at 10:27 AM, Nicholas Thompson
nickthomp...@earthlink.net wrote:
snip
So, Owen, you meet a beautiful woman at a cocktail party. She seems
intelligent, not a person to be fobbed off, but has no experience with
either Maths or Computer Science. She looks deep into your
Owen Densmore wrote at 04/17/2013 01:53 PM:
Er,, of course there are many, right? With two finite sets of size N there
are N! 1-1, onto unique mappings, I believe.
Heh, there are way more than that! What I meant was that there exist
more than 1 morphism that results in the same snapshot of
Coffee Group
Cc: Frank Wimberly
Subject: Re: [FRIAM] Isomorphism between computation and philosophy
On Wed, Apr 17, 2013 at 10:27 AM, Nicholas Thompson
nickthomp...@earthlink.net wrote:
snip
So, Owen, you meet a beautiful woman at a cocktail party. She seems
intelligent, not a person
, April 17, 2013 3:03 PM
*To:* The Friday Morning Applied Complexity Coffee Group
*Cc:* Frank Wimberly
*Subject:* Re: [FRIAM] Isomorphism between computation and philosophy
On Wed, Apr 17, 2013 at 10:27 AM, Nicholas Thompson
nickthomp...@earthlink.net mailto:nickthomp...@earthlink.net wrote
:* Re: [FRIAM] Isomorphism between computation and philosophy
** **
On Wed, Apr 17, 2013 at 10:27 AM, Nicholas Thompson
nickthomp...@earthlink.net wrote:
snip
** **
So, Owen, you meet a beautiful woman at a cocktail party. She seems
intelligent, not a person
Of *Owen Densmore
*Sent:* Wednesday, April 17, 2013 3:03 PM
*To:* The Friday Morning Applied Complexity Coffee Group
*Cc:* Frank Wimberly
*Subject:* Re: [FRIAM] Isomorphism between computation and philosophy
** **
On Wed, Apr 17, 2013 at 10:27 AM, Nicholas Thompson
nickthomp
Owen -
Its starting to get lonely here!
It is kind of a dogpile here... with Doug now perched on top! grin
I am *sympathetic* with your desire to have the (mostly formal) language
you are most familiar/comfortable with to apply more *directly* to one
you may merely have romantic ideas
Nick asks Owen:
So, Owen, you meet a beautiful woman at a cocktail party. She seems
intelligent, not a person to be fobbed off, but has no experience with
either Maths or Computer Science. She looks deep into your eyes, and asks
And what, Mr. Densmore, is the halting problem? You find
Lee -
I feel a bit like Beavis (or is it Butthead?) in the light of Doug's
abstruse comment and my introspections on abstract v obtuse.
Heh Heh Heh... he said 'Hauptvermutung' !
I appreciate your use of MathGerman and MathEng which I think
reinforces my point (for anyone who had to learn
Complexity Coffee Group
Subject: Re: [FRIAM] Isomorphism between computation and philosophy
Owen -
Its starting to get lonely here!
It is kind of a dogpile here... with Doug now perched on top! grin
I am *sympathetic* with your desire to have the (mostly formal) language you
are most familiar
Nick: its simple. I married her. Just after explaining Godel to the
philosophy department, and to her Ex who promptly left philosophy and
became a cardio doctor. True.
In terms of the Halting problem, is Wikipedia too formal? The first two
paragraphs:
In computability theory, the halting
You can state it pretty simply: There is no algorithm that can decide
whether an arbitrary computer program will ever stop (Halt), or will
loop endlessly..
Definitely a problem for software testing..
Joe
On 4/17/13 10:15 PM, Owen Densmore wrote:
Nick: its simple. I married her. Just
The problem isn't really looping vs stopping; it's searching vs. finding.
Searching might be expressed iteratively (as a loop) or recursively. But
what the program is really doing is looking for an element that satisfies
some criterion. In many cases, it's not known in advance whether one
exists.
Subject: Re: [FRIAM] Isomorphism between computation and philosophy
Owen is right that there are N! ways to map a set of N objects 1-1, onto
another set of N objects. The first object can go to 1 of N objects, the
next to 1 of N-1, etc. That's pretty standard.
As to the Halting Problem, Why not start
Subject: Re: [FRIAM] Isomorphism between computation and philosophy
In summary, Nick: the problem appears to be two-fold:
1. The real day job is taking up every spare minute of my time, and
2. you guys clearly love to discuss abstraction for the seemingly sole
sake of discussion way, way
Owen,
Ask Dede to provide a translation, would you?
Nick
From: Friam [mailto:friam-boun...@redfish.com] On Behalf Of Owen Densmore
Sent: Wednesday, April 17, 2013 10:16 PM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Isomorphism between computation
: Friam [mailto:friam-boun...@redfish.com] On Behalf Of Joseph Spinden
Sent: Wednesday, April 17, 2013 8:21 PM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Isomorphism between computation and philosophy
Owen is right that there are N! ways to map a set of N objects 1
Philosophy is very broad and includes many things like ethics and anesthetics.
A good test case would be not logic, but poetry.
Blessings,
Doug
http://dougcarmichael.com
http://gardenworldpolitics.com
On Apr 16, 2013, at 9:25 AM, Owen Densmore o...@backspaces.net wrote:
On Sat, Apr 13, 2013
Nick:
It's probably a good thing that I retired before I got wise.
I think I hear the sound of the Arrow of Causality twanging in the bullseye.
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's
Curious. Isn't the proof of Godel's theorem a special case of this?
As I understand it, the proof is this:
Consider the statement: This theorem is not provable. If it is false, the
theorem is provable. Since 'provable' implies true, this is a contradiction.
Therefore the theorem is true,
From: Friam [mailto:friam-boun...@redfish.com] On Behalf Of Owen Densmore
Sent: Tuesday, April 16, 2013 3:50 PM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Isomorphism between computation and philosophy
One has to be careful with nearly all the impossibility theorems
I should correct myself. The mapping is not necessarily an isomorphism.
--Barry
On Apr 16, 2013, at 3:39 PM, Barry MacKichan barry.mackic...@mackichan.com
wrote:
Curious. Isn't the proof of Godel's theorem a special case of this?
As I understand it, the proof is this:
Consider the
Actually, Godel said that the axioms [have to]-[can't] be very carefully
chosen. The theorem says that any mathematical system that contains the
integers cannot be both complete and self-consistent. It is unique in the list
of 'impossibility' theorems in that it has a mathematical proof. The
*Subject:* Re: [FRIAM] Isomorphism between computation and philosophy
** **
One has to be careful with nearly all the impossibility theorems:
Arrow's voting, the speed of light, Godel, Heisenberg, decidability,
NoFreeLunch, ... and so on.
** **
To tell the truth, Godel .. it seems to me
Arrow's impossibility theorem is provable, basically social choice is
impossible given several fairly sound requirements: 3 or more things to
choose between and transitivity of choice.
C isn't a proof, agreed. Although its acceptance is well seen by
observation. And physics hasn't theorems in
.
N
From: Friam [mailto:friam-boun...@redfish.com] On Behalf Of Owen Densmore
Sent: Tuesday, April 16, 2013 5:12 PM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Isomorphism between computation and philosophy
No, I think we can make a mapping from
On Tue, Apr 16, 2013 at 6:10 PM, Nicholas Thompson
nickthomp...@earthlink.net wrote:
I don’t think I said that math couldn’t be mapped onto things. I only
said that such mappings are not essential to math and, further, that when
such mappings occur, the door is opened for confusion that is
between computation and philosophy
On Tue, Apr 16, 2013 at 6:10 PM, Nicholas Thompson
nickthomp...@earthlink.net wrote:
I don't think I said that math couldn't be mapped onto things. I only said
that such mappings are not essential to math and, further, that when such
mappings occur, the door
Doug -
Thanks for weighing in here... as an aside, I skimmed Garden World and
found it compelling... I hope others here will take the time!
On the thread topic, it would be rather convenient in many ways if
there were such an isomorphism as Owen seeks (postulates), but I find it
to reflect
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