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 Godel & Cantor

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youngbuck



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PostSubject: Godel & Cantor   Sun 27 Feb 2011, 4:19 am

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C1 wrote:
Trying to live the life that Kurt Godel scientifically uncovered.

Where can I learn about this?

I see that Godel has a book on Amazon.com called "On Formally Undecidable Propositions of Principia Mathematica and Related Systems"
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Ben Steigmann

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PostSubject: Re: Godel & Cantor   Sat 21 May 2011, 5:07 am

C1 wrote:
Where's Blissentia on this one, as he/she should eat this stuff up.... Take that circle avatar that he/she uses and put 2 dots inside the circle. Both dots represent the same condition, the same reality. What Godel shows us is that one of these dots can be true while the other dot is false. Or, one could make the same case with just one dot, where all systems could show that the dot simultaneously represents a true condition AND a false condition. This is why all deliberately contrived systems are incomplete (see Godel's Incompleteness Theorem), for they can possess mulitple "truths".


That is so creepy - I posted before here as inquirer, though I post elsewhere as Blissentia. How did you know about the "Blissentia" online "identity"?
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Clairvoyant



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PostSubject: Re: Godel & Cantor   Mon 23 May 2011, 4:28 pm

Blissentia wrote:
C1 wrote:
Where's Blissentia on this one, as he/she should eat this stuff up.... Take that circle avatar that he/she uses and put 2 dots inside the circle. Both dots represent the same condition, the same reality. What Godel shows us is that one of these dots can be true while the other dot is false. Or, one could make the same case with just one dot, where all systems could show that the dot simultaneously represents a true condition AND a false condition. This is why all deliberately contrived systems are incomplete (see Godel's Incompleteness Theorem), for they can possess mulitple "truths".


That is so creepy - I posted before here as inquirer, though I post elsewhere as Blissentia. How did you know about the "Blissentia" online "identity"?

...are you saying he wrote that before you changed your name here?
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Ben Steigmann

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PostSubject: Re: Godel & Cantor   Mon 23 May 2011, 10:27 pm

Yep - I changed my name here as soon as I saw that post.
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Silent Wind



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PostSubject: Re: Godel & Cantor   Thu 09 Jun 2011, 1:16 am

C1 wrote:
Georg Cantor and Kurt Godel (pronounced 'girdle') blow our entire system of math and science out of the water. What a crock of bullshit it all is. Just systems of control for men over other men.



Wittgenstein whom I brought up before also says basically the same thing with languages-english, latin, italian etc.. (formal language-Godel) which is why he is also important to study. Your thoughts are controlled by your language just the same as they are with arithmetic or science, math-another language only in numbers. I think the below write up in one of my philosophy books touches on similar stuff as Godel. Your world is limited by your language. 2+2=4. This is a dog. Both are formal languages (man made and fallable) with established sets of rules but neither can be proven outside of themselves as Godel's therom states and Wittgensteins obsrevations shows. 2=4+2, A is dog this. Both with implied/given sets of rules that neither follows therefore unusable. I hope this makes sense to the readers or if you disagree or wish to discuss please do.




In Tractus Logico-Philosophicus, Wittgenstein challenges the study of philosophy. He argues that philosophical problems are mostly Psuedo-problems. They are problems arrived at in an attempt to push thought beyond the limits imposed upon it by language. For Wittgenstein, the world of facts, which is reality, is contained within, rather than beyond, or below the logical structure of language. There is no world of truth which language represents, because all possibilities for truthful propositions are contained within the logical structure of everyday language. Any attempt to step outside the logical confines of language and establish a'priori' philosophical certainties is futile because it assumes that language can be pushed beyond its limits.

In philosophical investigations, Wittgenstein resisted his earlier attempts in Tractus Logico-Philosophicus to push philosophy to the ends of language and understand the limits of factual discourse. He rejected the idea that meaning in language could be accounted for beyond the often multiple nature of its empirical usage. For Wittgenstein, the meaning of words and sentences cannot be understood through a higher logic. Rather words, sentences and their meaning are relational. That is , their meaning is only verified by the nature of their relationship to other words and sentences, which take the shape of familiar language patterns. This means that language can be understood as a complex network of overlapping games played by the interlocutors.

For Wittgenstein, claims to truth can only be assessed by the relative degree of agreement that exists about the rules used to verify them. That is, it is this level of agreement rather than the 'objective' truth itself that counts. 'It is what human beings say that is true and false; and they agree in the language they use. That is not agreement in opinions but in forms of life'. In other words, to say that the propositions or statements made by human beings are initially opinions is to say that they can be verified by their actual meanings. Statements and propositions are, in fact, moves in a game which are verified by the rules of the game. So that the question "What is a word really?" is analogues to "What is a chess piece".


Last edited by Silent Wind on Thu 09 Jun 2011, 1:24 am; edited 1 time in total (Reason for editing : added video)
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PostSubject: Re: Godel & Cantor   Thu 09 Jun 2011, 1:21 am

Imagine the posters on here getting together for months and creating our own language and not being limited by english but instead creating our own language and discussing on this blog in our new language. This would drive the monitors (CIA/NSA/FBI) insane as then they would have to go into overdrive to decipher what it was that we were talking about. Imagine that!!! It would drive them nuts. I imagine there would be tremendous amounts of CPU cycles eating that up.
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Silent Wind



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PostSubject: Re: Godel & Cantor   Thu 09 Jun 2011, 1:27 am

http://www.amazon.com/Philosophical-Investigations-3rd-Ludwig-Wittgenstein/dp/0024288101

Philosophical Investigations is a classical work in the history of philosophy. It is a book which holds a position similar to that of Kant's Critique of Pure Reason, Plato's Meno and Heidegger's Sein und Zeit.

Let's take a look at Wittgenstein's investigations. I have presented Wittgenstein's life in my review of Ray Monk's Wittgenstein biography, let me here focus more on his philosophy.

Wittgenstein starts with a quote from St Augustine. Augustine belived that the principal function of language is to refer to external reality, he believed that all words function similar to names and according to Wittgenstein he seems to have held the view language is learned through ostensive defintions. Wittgenstein, however, rejects this referentialist view of language, believing that language is far more complex than what Augustine thought. Language is an activity, or connected to a number of activitites, which Wittgenstein called language-games. Language-games have different puprposes, not all of them are centered around refering. There are many contexts for using words and many kinds of speach acts. While the logical positivists believed that the meaning of a statement was its method of verification, and Frege believed in two different entities (Sinn and Bedeutung), Wittgenstein rejects these views. According to this thinker from Vienna, meaning is use, and to understand a linguistic expression is to master how to use it and the accompanying techniques, not mereley to understand the verification principle, grasping some Platonic/Fregian entity or have some sense impression in one's head (Locke).

Language is behaviour, practive give the words their sense according to Wittgenstein. This also relates to the private language argument, presented in paragraphs 199ff. Wittgenstein argues that the rules of language must be public and behavioral. It is not, as some like Peter Winch or Kripke have thought, an argument for the principle social nature of language, but for the behavioral aspect of rule-following. Mental terms, according to LW, cannot enter into the language without intimately being connected to overt behavioral patterns. Thus the mentalism of Hume and Locke is rejected, and Wittgenstein shows how knowledge must be more than just access to private sense data. There goes Russell, the British aristocratic sensualists and the Cartesian idea of priveleged access. Sometimes Wittgenstein may seem like a Marxist: it is the practical part of human life that provides that basis for our thoughts and rationality. Being a rational creature, according to Wittgenstein, is not what the rationalist Descartes thought or the empiricists thought; you cannot isolate the intellect or private sensations, because human rationality is based on practical and concrete, physical behavioral patterns.

Througout the investigations Wittgenstein tries to challenge many of the positions held by previous philosophers. He once said that he didn't write for philosophers, but I do think that knowledge of the history of philosophy sheds light over his investigations. he said that WHAT he said would be simple, but understanding WHY he said it, would be difficult.

But even though you are not a professional philosopher, you may receive vital inputs from Wittgenstein. If you can grasp the essence of his ideas of language-games, rule-following, form of life, anti-mentalism and conceptual therapy, you will have knowledge of some of his key ideas ideas.

If you supply your reading of Philosophical Investigations with Ray Monk's marvellous "Ludwig Wittgenstein. The Duty of Genius" you can understand the horizon of this great thinker. Also important, are Baker and Hacker's books on Wittgenstein.

Finally, a word on interpretation. Burton Dreben once had a seminar at the University of Oslo, where he said that if you don't know Frege and Russell, you won't understand Wittgenstein. I completely agree with Dreben that Wittgenstein was much inspired by the philosophers and logicians Frege and Russell. However, one should understand that Wittgenstein was deeply fascinated by poetry, religion and existential questions. Among his favourite writers were Dostoyevsky, Tolstoy and Kierkegaard. When this is taken into account, one can understand Wittgenstein in depth. Wittgenstein was a thinker with great analytical abilities, but never forget that he had a poetic soul. "I am not a religious man, but I cannot help seeing everything from a religious point of view" he once said to one of his friends. The ideas he had on language-games, forms of life and rule-following should be seen in light of some of the profound and important questions a religious man or an existentialist may ask himself.
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Silent Wind



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PostSubject: Re: Godel & Cantor   Thu 09 Jun 2011, 1:32 am

One aspect of this book that makes it important for simply that contribution is the notion of "language games." If language produces reality, different languages produce different realities. In this book, German philosopher Ludwig Wittgenstein developed the related notion of "language games," islands of language, unique each to itself, not wholly translatable one into another. Each of us inhabits a particular language game, he claims, which channels how we see things and understand the world and our places within it. Again, language shapes meaning and understanding and interpretation. The world is disclosed to us through our specific language game. If we live in different language games, we see different worlds. This concept entails, as philosopher Chantal Mouffe says, ". . . a critique of the rationalist conception of the subject [i.e., the knowing, reasoning human mind] that indicates that the latter cannot be the source of linguistic meanings since it is through participation in different language games that the world is disclosed to us."

This is a serious attack on the Modern conception of the human as a reasoning being who can affect change in desired directions through the exercise of that reason. Thus, reason does NOT allow us to see the world as it is and to change it as we wish in a manner leading to progress. The concept of language games is key for many postmodern thinkers.

If we think through language and the use of language is thought itself, what is perceived is indistinct from language use. The two cannot be separated, since language governs interpretation and perception and thought. To revisit the phrase from Wittgenstein, different people play and live in different "language games," that is, their languages lead them to see the world differently, to conceptualize things differently from those in different language games. So what for the person interested in politics?

In the final analysis, this means that whenever we try to understand the world, it is through language, through interpretation, since we cannot directly perceive reality outside of our language. This begins to suggest the likelihood that one's own culture or society or polity does not have universally "true" answers to key questions of human existence; our culture develops answers within its language game that make sense at that particular time for that culture. All is interpretation of uncertain texts within different language games.

Certainly, this is a strong argument. Many disagree that language per se shapes our views of reality. And that argument needs to be taken seriously. Nonetheless, the argument about "language games," although only a small part of this book, is a provocative concept, well worth thinking about.
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PostSubject: Re: Godel & Cantor   Wed 15 Jun 2011, 1:30 am

All of our inputs are open to attack for the purpose of control. This includes language. very good post.

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PostSubject: Re: Godel & Cantor   Wed 15 Jun 2011, 11:36 pm

Silent Wind wrote:
Imagine the posters on here getting together for months and creating our own language and not being limited by english but instead creating our own language and discussing on this blog in our new language. This would drive the monitors (CIA/NSA/FBI) insane as then they would have to go into overdrive to decipher what it was that we were talking about. Imagine that!!! It would drive them nuts. I imagine there would be tremendous amounts of CPU cycles eating that up.

Now this is an idea worth attention - let's do it! After all, Internet 2 keeps threatening to arrive, and what the heck are we gonna do then, hmmmm??? Evil or Very Mad

I personally believe that a really simple code would be the best idea (BUT I don't really know anything about encrypting)- I just am a big fan of simplicity. Lol.Smile

Seriously, I think this is a TERRIFIC idea (and then I could stop feeling so sad about being cut off from all you guys too...) So, if you come up with any ideas on how to start on this, SW, let me know and I'd be glad to help get something going, *hopefully*.

later,
pirat Cool
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PostSubject: Re: Godel & Cantor   Thu 23 Jun 2011, 1:42 am

I wonder why Latin is a dead language? Perhaps it had value for the masses?

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PostSubject: Re: Godel & Cantor   Thu 23 Jun 2011, 12:28 pm

C1 wrote:
I wonder why Latin is a dead language? Perhaps it had value for the masses?

Hmmmm!
Something very interesting may lie here. I have always been very attracted to Latin; it almost seems as if just using it made one a little more intelligent...and it seems to have the power to encapsulate wisdom in a very few words, i;e.
"carpe Diem", for example. Worth exploring, for sure. Smile
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