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Archive for 'Truth'

Kremlin Minutes at Spiegel

Wednesday, November 22nd, 2006

Spiegel Online has a series of Kremlin Minutes posted on their web site, such as this one: The Kremlin Minutes: “We Should Demolish the Wall Ourselves”.

Visit Spiegel Online for more. I am sure we won’t see much of this in US press since as Spiegel points out (last sentence):

In the fall of 1990, as Germany celebrated reunification, an enormous tragedy was taking shape in Moscow. The historical turning point can be reconstructed from previously undisclosed minutes of Politburo meetings published in Russia this month. And Mikhail Gorbachev may finally get the historical recognition he deserves.

We wouldn’t want to give up on the myth that a B-grade actor who couldn’t differentiate between his movie roles and reality was rather The Great Communicator who single-handedly brought the “cold war” to an end.

[ Link ]

Serving a ray of truth?

Thursday, September 28th, 2006

Australian media personality Steve Irwin’s widow Terri offers this, regarding the video footage of the event that led to his death:

BBC | Irwin death film ‘will never air’

Footage of Australian naturalist Steve Irwin’s death will never be broadcast, his widow Terri has said in her first interview since his 4 September death.

“What purpose would that serve?” she asked presenter Barbara Walters in an interview with US programme 20/20.

She goes on to say:

… his death was just a “stupid” accident - “like running with a pencil”.

Well, it looks like she has answered her own question. The video would serve the purpose of establishing whether the event was similar to “running with a pencil” or to poking a pencil into your eye.

[ Link ]

The emperor’s new inadequacy

Wednesday, January 25th, 2006

In a well-reasoned piece titled:

Can humans escape Goedel?:A review of "Shadows of the Mind" by Roger Penrose

Daryl McCollough provides a non-paradoxical version of the Liar's Paradox to illustrate inconsistency in human thinking. In doing so, he addresses a particular aspect of the interpretations of belief and truth with regard to debate on Gödel's incompleteness theorem (the first, for the picky). That issue is a better understanding of human fallibility (and its relationship to the phrase "there are some sentences we know to be true"). Perhaps Wittgenstein can be interpreted to also explore this in his [in]famous commentary on Gödel's Theorem but more on that later.
McCollough writes:

6. How Could Inconsistency Creep Into Human Reasoning?

6.1 As I discussed in the last section, Penrose's arguments, if taken to their logical conclusion, show us not that the human mind is noncomputable, but that either the human mind is beyond all mathematics, or else we cannot be sure that it is consistent. If we reject the "mysterian" position that mind is beyond science, we are left with the conclusion that we can't know that we are consistent. This seems very counter-intuitive. If we are very careful, and only reason in justified steps, why can't we be certain that we are being consistent?

6.2 Let me illustrate with a thought experiment. Suppose that an experimental subject is given two buttons, marked "yes" and "no", and is asked by the experimenter to push the appropriate button in response to a series of yes-no questions. What happens if the experimenter, on a lark, asks the question "Will you push the 'no' button?". It is clear that whatever answer the subject gives will be wrong. So, if the subject is committed to answering truthfully, then he can never hit the "no" button, even though "no" would be the correct answer. There is an intrinsic incompleteness in the subject's answers, in the sense that there are questions that he cannot truthfully answer.

6.3 Now, there is no real paradox in this thought experiment. The subject knows that the answer to the experimenter's question is "no", but he cannot convey this knowledge. Thus there is a split between the public and private knowledge of the subject. But now, let's extend the thought experiment.

6.4 Someday, as science marches on, we will understand the brain well enough that we can dispense with the "yes" and "no" buttons (which are susceptible to lying on the part of the subject). Instead of these buttons, we assume that the experimenter implants probes directly into the subject's brain, and we assume that these probes are capable of directly reading the beliefs of this subject. If the probes detect that the subject's brain is in the "yes" belief state, it flashes a light labeled "yes", and if it detects a "no" belief state, it flashes a light labeled "no". Now, in this improved experiment, the subject is asked the question "Will the 'no' light flash?"

6.5 In this improved set-up, there is no possibility of the subject having knowledge that he can't convey; the probe immediately conveys any belief the subject has. If the subject believes the "no" light will flash, then the answer to the question would be "yes", and the subject's beliefs would be wrong. Therefore, if the subject's beliefs are sound then the answer to the question is "no". Therefore, since the subject cannot correctly believe the answer to be "no", he similarly cannot correctly believe that he is sound. If the subject reasons from the assumption of his own soundness, he is led into making an error.

6.6 As can be seen from this thought experiment, the inability to be certain of one's own soundness is not a deficiency of intelligence. There is no way that the subject in the experiment can correctly answer the question by just "thinking harder" about it.

And provides this conclusion:

8. Conclusion

8.1 Penrose's arguments that our reasoning can't be formalized is in some sense correct. There is no way to formalize our own reasoning and be absolutely certain that the resulting theory is sound and consistent. However, this turns out not to be a limitation on what computers or formal systems can accomplish relative to humans. Instead, it is an intrinsic limitation in our abilities to reason about our own reasoning process. To the extent that we understand our own reasoning, we can't be certain that it is sound, and to the extent that we know we are sound, we don't understand our reasoning well enough to formalize it. This limitation is not due to lack of intelligence on our part, but is inherent in any reasoning system that is capable of reasoning about itself.

I think its a refreshing angle to the old debate, one that does not get as much attention.

P.S: When talking about truth above I am hopefully not mystifying it in a way that ignores the deflationary theory of truth.

You might be a (mathematical) Platonist?

Wednesday, January 25th, 2006

[with apologies to Jeff Foxworthy]

Among other eminent bits, Karlis Podnieks has an interesting test you can use to see if you are a Platonist. As psychologists like to say, denial is more than just a river in Egypt and the first step to recovery is accepting the problem. So, take the test… its for your health! ;-)

Foundations of Mathematics. Mathematical Logic. By K.Podnieks

Suppose, someone has proved that the twin prime conjecture is unprovable in set theory. Do you believe that, still, the twin prime conjecture possesses an “objective truth value”? Imagine, you are moving along the natural number system:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, …

And you meet twin pairs in it from time to time: (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71,73), … It seems there are only two possibilities:

a) We meet the last pair and after that moving forward we do not meet any twin pairs (i.e. the twin prime conjecture is false),

b) Twin pairs appear over and again (i.e. the twin prime conjecture is true).

It seems impossible to imagine a third possibility…

If you think so, you are, in fact, a Platonist.

L’Affaire Sokal: The lowest form of humour

Tuesday, January 10th, 2006

Doron Zeilberger at Rutgers publishes a page of opinions that is a wonderful read, even if you are not a mathematician. In opinion 11 he points out better than I can exactly what was wrong with Sokal’s prank on the pomo philosophers:

Opinion 11 of Doron Zeilberger:
Great Scientists, Lousy Philosophers

The intersection of the sets of great mathematicians or scientists and great philosophers is a rapidly decreasing function of time.

[…]

Nowadays, Traditional God has been replaced, in part, by another God: `Absolute Truth’. Practicing scientists get really annoyed when they are reminded that after all they are also human, and their view of science is time- and fashion- dependent. So Alan Sokal had a good laugh at the expense of post-modern cultural-relativists. But he used the same cheap trick of Euler, intimidation by jargon. He went one step farther: making fun of the sociologists’ jargon. He had the advantage that their jargon is closer to spoken English than his, so he could master it superficially.

Making fun of other people’s language is the lowest form of humor. Like Euler, Sokal did not prove anything, except that physical scientists and mathematicians are arrogant and look down on everybody else. They are also religious fanatics, for whatever religion they may have. Social science has probably lots of rubbish, but so does regular science, and in either case it is not the content that matters so much as the act of expressing oneself’s.

For more info on the Sokal Prank see the Wikipedia.




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