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#26 2016-01-08 20:11:04

Relentless
Member
Registered: 2015-12-15
Posts: 624

Re: The Achilles diary paradox

Hello Solvitur,

Which part do you think is unresolved? For your example, it is evident that Achilles can never break his word so long as it is possible for him to perform the task; therefore his promise is almost meaningless (it is equivalent to a statement that he will always be capable of performing the task once).

The advantage of understanding what you earlier called Conclusion 2 is that these kinds of consequences are associated with infinity, usually without confusion (:

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#27 2016-01-08 20:25:29

Solvitur ambulando
Member
Registered: 2015-12-06
Posts: 28

Re: The Achilles diary paradox

Hi Relentless,

I was stuck on the apparent contradiction between statements 4 and 6, but I feel I have now resolved that at least in my own mind. A long-winded way of arriving at the conclusion that you have just concisely summarised!

Last edited by Solvitur ambulando (2016-01-08 20:28:34)

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#28 2016-01-08 20:43:17

Solvitur ambulando
Member
Registered: 2015-12-06
Posts: 28

Re: The Achilles diary paradox

I have now revised the Diary Paradox to avoid the 'Paradox of Permanent Postponement'. The former hinges on the ordering of infinite series whereas the latter highlights the potential pitfalls of conceptualising infinite time.

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#29 2016-01-09 12:26:37

Calligar
Member
Registered: 2011-09-24
Posts: 272

Re: The Achilles diary paradox

Relentless wrote:

Calligar,

Hahaha, you have basically made a duplicate of the first paragraph of post #3 smile Post #4 is a good response to this query - in short, you (and I) are right!

Lol, sorry about that.  I read everything, but since it took me longer to understand everything, so I guess I figured that out after you and forgot you said anything about that.

Solvitur ambulando wrote:

I have now revised the Diary Paradox to avoid the 'Paradox of Permanent Postponement'. The former hinges on the ordering of infinite series whereas the latter highlights the potential pitfalls of conceptualising infinite time.

Lol, interesting how you specifically wanted to avoid what Relentless and I found tongue.


There are always other variables.  -[unknown]
But Nature flies from the infinite, for the infinite is unending or imperfect, and Nature ever seeks an end.  -Aristotle
Everything makes sense, one only needs to figure out how.  -[unknown]

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#30 2016-01-09 23:37:48

Solvitur ambulando
Member
Registered: 2015-12-06
Posts: 28

Re: The Achilles diary paradox

Calligar wrote:

Lol, interesting how you specifically wanted to avoid what Relentless and I found.

I found the point that you and Relentless brought up intriguing and I have engaged with it at considerable length - see my entry at 2016-01-08 17:51:00. But there are two paradoxes here, both of them interesting and each highlighting different aspects of infinite series. If you leave the diary paradox in its original form, the statement that the gods required Achilles to 'eventually take all the pages' allows Achilles to postpone taking non-birthdays indefinitely. This is an interesting observation, but it obscures my original point that the subset of birthday pages is equinumerous with its complement (i.e. countably infinite).

I've been toying with the idea of starting a separate thread to highlight the 'permanent postponement paradox'...what do you think?

Last edited by Solvitur ambulando (2016-01-10 09:10:44)

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#31 2016-03-26 08:59:10

Calligar
Member
Registered: 2011-09-24
Posts: 272

Re: The Achilles diary paradox

What is it you mean more specifically when you say the 'permanent postponement paradox' and how is that related?  Like I guess I'm asking, is that explaining how this whole paradox works, or... (Sorry, I guess I'm asking for more details as I'm just not very sure what you mean).


There are always other variables.  -[unknown]
But Nature flies from the infinite, for the infinite is unending or imperfect, and Nature ever seeks an end.  -Aristotle
Everything makes sense, one only needs to figure out how.  -[unknown]

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#32 2016-03-28 23:55:08

Relentless
Member
Registered: 2015-12-15
Posts: 624

Re: The Achilles diary paradox

I think Solvitur means the paradox that an immortal being can do all of:
1. Make a promise
2. Never fulfill that promise, and
3. Never break that promise either.

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#33 2016-04-10 12:36:38

Calligar
Member
Registered: 2011-09-24
Posts: 272

Re: The Achilles diary paradox

Relentless wrote:

I think Solvitur means the paradox that an immortal being can do all of:
1. Make a promise
2. Never fulfill that promise, and
3. Never break that promise either.

Tis one of many fun things playing around with anything infinite can get you. tongue


There are always other variables.  -[unknown]
But Nature flies from the infinite, for the infinite is unending or imperfect, and Nature ever seeks an end.  -Aristotle
Everything makes sense, one only needs to figure out how.  -[unknown]

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