Eliminating Undecidability and Incompleteness in Formal Systems

What is the basis for reason? And mathematics?

Moderators: AMod, iMod

wtf
Posts: 827
Joined: Tue Sep 08, 2015 11:36 pm

Re: Eliminating Undecidability and Incompleteness in Formal Systems

Post by wtf » Sun Apr 21, 2019 1:23 am

Logik wrote:
Sun Apr 21, 2019 12:43 am
The trivial counter-example is the married bachelor of sciences.
LOL. Good one!

But then again I don't believe natural language can be axiomatized. PeteOlcott does, if I understand him correctly.

ps -- How about this guy?

http://johnbatchelorshow.com/

How critical is the exact spelling of a word? This guy is a Batchelor if not a bachelor.

Logik
Posts: 4041
Joined: Tue Dec 04, 2018 12:48 pm

Re: Eliminating Undecidability and Incompleteness in Formal Systems

Post by Logik » Sun Apr 21, 2019 2:08 am

wtf wrote:
Sun Apr 21, 2019 1:23 am
ps -- How about this guy?

http://johnbatchelorshow.com/

How critical is the exact spelling of a word? This guy is a Batchelor if not a bachelor.
So now you are demonstrating that my is_bachelor() function is incomplete? Nice!

There. Now it checks surname also.

Code: Select all

def is_bachelor(person):
  if person.sex.lower() == 'male' and not person.marital_status:
    return True
  elif person.bachelor_degree:
    return True
  elif person.surname.lower() == "bachelor":
    return True
  else:
    return False
Of course, it is still incomplete because....
bachelor, noun, historical.
a young knight serving under another's banner

wtf
Posts: 827
Joined: Tue Sep 08, 2015 11:36 pm

Re: Eliminating Undecidability and Incompleteness in Formal Systems

Post by wtf » Sun Apr 21, 2019 2:37 am

Logik wrote:
Sun Apr 21, 2019 2:08 am
elif person.surname.lower() == "bachelor":
You have to check all possible alternate spellings too, like "batchelor".
Logik wrote:
Sun Apr 21, 2019 2:08 am
a young knight serving under another's banner
Which illustrates my point that you can't axiomatize natural language. And when Carl Sandburg wrote that the fog creeps in on little cat feet, how would a computer parse that? Poets stretch the bounds of natural language every day. And language changes over time.

Skepdick
Posts: 1493
Joined: Fri Jun 14, 2019 11:16 am

Re: Eliminating Undecidability and Incompleteness in Formal Systems

Post by Skepdick » Sun Jul 28, 2019 2:26 pm

wtf wrote:
Sun Apr 21, 2019 1:23 am
But then again I don't believe natural language can be axiomatized.
wtf wrote:
Sun Apr 21, 2019 2:37 am
Which illustrates my point that you can't axiomatize natural language. And when Carl Sandburg wrote that the fog creeps in on little cat feet, how would a computer parse that? Poets stretch the bounds of natural language every day.
Have you heard of Pāṇini and Aṣṭādhyāyī and how it relates to modern-day natural language processing? Pāṇini's formalised grammar is equivalent to a Type 0 formal grammar in the Chomsky's hierarchy, only it predates it by 2500 years.

Sanskrit is basically a formalised (axiomatised?) natural language by virtue of Sanskrit speakers voluntarily adhering to Pāṇini's grammar rules as best as possible. Or would that make Sanskrit a naturalised axiomatic language?

Some still consider Sanskrit to be sufficiently concise and unambiguous to suffice as a scientific language. And you can write poetry in it.
wtf wrote:
Sun Apr 21, 2019 1:23 am
And language changes over time.
Precisely the problem all formal notations attempt to solve, no? Linguistic (and therefore semantic) non-determinism.

wtf
Posts: 827
Joined: Tue Sep 08, 2015 11:36 pm

Re: Eliminating Undecidability and Incompleteness in Formal Systems

Post by wtf » Sun Jul 28, 2019 11:39 pm

Skepdick wrote:
Sun Jul 28, 2019 2:26 pm
Sanskrit is basically a formalised (axiomatised?) natural language by virtue of Sanskrit speakers voluntarily adhering to Pāṇini's grammar rules as best as possible. Or would that make Sanskrit a naturalised axiomatic language?
I read the Wikipedia article on Sanskrit and I did not discern any connection to formal axiomatic systems. I confess to not understanding the intent of your remark. It may well be true (I have no way of knowing) that Sanskrit operates according to specific rules that can be called axiomatic. If so, I'm wrong in saying that we can't axiomatize natural language.

In fact I may be entirely wrong in my own premise. ZFC is a rigid formal mathematical system, yet within that structure, amazing feats of creative thinking can take place. Perhaps it depends on what level the formal system is. What I mean is, if the axioms declare a specific meaning for each word, or lists all the allowable words, that's too rigid for a language to grow. In natural language, the meaning of words changes all the time, and new words get added to the language.

On the other hand Chomsky talks about the deep structures common to all natural languages.

So perhaps I was being too literal or simplistic when I say you can't axiomatize natural language. If the axiomatic structure allows for creativity and change, then a language can be axiomatized while still allowing for creativity.
Last edited by wtf on Sun Jul 28, 2019 11:45 pm, edited 1 time in total.

Skepdick
Posts: 1493
Joined: Fri Jun 14, 2019 11:16 am

Re: Eliminating Undecidability and Incompleteness in Formal Systems

Post by Skepdick » Sun Jul 28, 2019 11:44 pm

wtf wrote:
Sun Jul 28, 2019 11:39 pm
Skepdick wrote:
Sun Jul 28, 2019 2:26 pm
Sanskrit is basically a formalised (axiomatised?) natural language by virtue of Sanskrit speakers voluntarily adhering to Pāṇini's grammar rules as best as possible. Or would that make Sanskrit a naturalised axiomatic language?
I read the Wikipedia article on Sanskrit and I did not discern any connection to formal axiomatic systems. I confess to not understanding the intent of your remark. It may well be true (I have no way of knowing) that Sanskrit operates according to specific rules that can be called axiomatic. If so, I'm wrong in saying that we can't axiomatize natural language.
The Sanskrit page doesn't cover the technical aspect. Starti with Panini grammar.

https://en.wikipedia.org/wiki/P%C4%81%E ... %81y%C4%AB
https://en.wikipedia.org/wiki/P%C4%81%E ... al_systems

wtf
Posts: 827
Joined: Tue Sep 08, 2015 11:36 pm

Re: Eliminating Undecidability and Incompleteness in Formal Systems

Post by wtf » Sun Jul 28, 2019 11:49 pm

Skepdick wrote:
Sun Jul 28, 2019 11:44 pm
The Sanskrit page doesn't cover the technical aspect. Starti with Panini grammar.
I believe I already acknowledged your general point; but I can't understand the specific reference to such a narrow technical area, what some ancient writer said about an ancient language. I am afraid I can't dive into the arcana with you on this particular topic. But I've already conceded your general point. Perhaps there's something about your posts that still eludes me. You asked if I am familiar with this particular 5th century BCE Sanskrit philologist.

Well no, as it happens. Would I be expected to be?

Skepdick
Posts: 1493
Joined: Fri Jun 14, 2019 11:16 am

Re: Eliminating Undecidability and Incompleteness in Formal Systems

Post by Skepdick » Sun Jul 28, 2019 11:53 pm

wtf wrote:
Sun Jul 28, 2019 11:49 pm
I believe I already acknowledged your general point; but I can't understand the specific reference to such a narrow technical area, what some ancient writer said about an ancient language. I am afraid I can't dive into the arcana with you on this particular topic. But I've already conceded your general point. Perhaps there's something about your posts that still eludes me. You asked if I am familiar with this particular 5th century BCE Sanskrit philologist.

Well no, as it happens. Would I be expected to be?
You made the comment that natural languages are not axiomatizable.
I offered you Sanskrit as the counter-example as an FYI. No deep analysis or engagement or experitse is expected.

2500 years ago, in India a Turing-complete grammar was invented (Panini grammar). It's used as a natural language to this day.

I don't care if you are 'right' or 'wrong' - I am not in this to win arguments. At most I expect an 'Oh! Cool!"

wtf
Posts: 827
Joined: Tue Sep 08, 2015 11:36 pm

Re: Eliminating Undecidability and Incompleteness in Formal Systems

Post by wtf » Mon Jul 29, 2019 1:09 am

Skepdick wrote:
Sun Jul 28, 2019 11:53 pm

I don't care if you are 'right' or 'wrong' - I am not in this to win arguments. At most I expect an 'Oh! Cool!"
Oh! Cool.

User avatar
Speakpigeon
Posts: 957
Joined: Sat Nov 11, 2017 3:20 pm
Location: Paris, France, EU

Re: Eliminating Undecidability and Incompleteness in Formal Systems

Post by Speakpigeon » Sun Aug 04, 2019 5:43 pm

wtf wrote:
Sun Apr 21, 2019 1:23 am
Logik wrote:
Sun Apr 21, 2019 12:43 am
The trivial counter-example is the married bachelor of sciences.
LOL. Good one!

But then again I don't believe natural language can be axiomatized. PeteOlcott does, if I understand him correctly.

ps -- How about this guy?

http://johnbatchelorshow.com/

How critical is the exact spelling of a word? This guy is a Batchelor if not a bachelor.
It's essentially irrelevant. "Informal" arguments are assessed as we assess what other people say, by interpreting what they say in light of what we understand the context is. Sure, we may make mistakes in doing so but anything we do is subject to mistakes and error and failures. No big deal.

There is as you know the "principle of charity", whereby you try your best to interpret what people say in the most favourable light. People stop doing it whenever they have some reason to dislike the speaker. Disagreements are more usually proof of bad tempter and malicious intent.

Informal arguments are not rigorous because they don't need to be. Trying to make hay out of this simple fact of life is just pathetic.

If you want to claim you don't understand an argument, just imagine it's a big guy making it in your face and see if you would keep pretending you don't understand it.

I guess the Internet makes words even cheaper than ever before.
EB

Skepdick
Posts: 1493
Joined: Fri Jun 14, 2019 11:16 am

Re: Eliminating Undecidability and Incompleteness in Formal Systems

Post by Skepdick » Tue Aug 06, 2019 4:34 pm

Speakpigeon wrote:
Sun Aug 04, 2019 5:43 pm
There is as you know the "principle of charity", whereby you try your best to interpret what people say in the most favourable light.
People stop doing it whenever they have some reason to dislike the speaker.
I haven't seen an ounce of charity from you on this forum.

Does that mean you dislike everybody (but yourself)?

Grumpy Frenchie...

User avatar
Eodnhoj7
Posts: 4699
Joined: Mon Mar 13, 2017 3:18 am

Re: Eliminating Undecidability and Incompleteness in Formal Systems

Post by Eodnhoj7 » Tue Aug 06, 2019 11:58 pm

Undecidability and incompleteness are assumptions that if defined would require the same logical systems they serve to define them.

The end.

Post Reply

Who is online

Users browsing this forum: No registered users and 1 guest