Liar's Paradox

This is a Facebook conversation a friend of mine and I had about the Liar's Paradox.

Let's assume False is 0 and True is 1

Pat's point in the discussion is that if the sentence is true, then it must be false- and then, because it is then false, it is not true. This creates an endless logical spiral where the sentence = 0 and that situation = 1, thereby making the sentence = 1 and the situation now equaling 0, which means the sentence = 0...throwing us into a clear paradox.

My point is that because we have no actual "thing" to judge as true or false to begin with, we have no paradox at all. If you turn the phrase into an equation, we don't have a simple x = y like "sun = hot". If we assumed (this sentence) = (false) is our equation, we must ask ourselves "what is 'this sentence' "? The answer is the four words "this sentence is false". Therefore, (this sentence is false) = (false), which means
((this sentence is false) is false) = (false). This can, and will, go on indefinitely. If you used the words "this sentence" (negating what sentence exactly is being discussed) as X, then we have (X(n+1) = 0) = 0, or
0 = 0- which is no paradox at all.

BUT, in order to have an illogical conclusion to logical reasoning, we must have a logical item of comparison; and reflexive sentences can be tricky. If I said "This sentence is English", we have points for validity; we have English (Latin) letters, English words, English syntax, English sounds, etc. But if I said to you "This sentence is true", what points do we have for validity? For "this sentence" is indeed "this sentence is true" therefore making "this sentence is true" true. We have no "thing" in the sentence, or referred to us BY the sentence, to make true or false. And because we have no basis in our quest for validity, we have no logical quest at all...

...and therefore no paradox.

But don't take my word for it. Enjoy!

Pat- must.. resist.. liar's paradox...

Me- everything i say is a lie?

Pat- something like that, yes

Me- this sentence is false?

Pat- indeed

Me- hhmm

is that even a legitimate sentence?

architecturally, not grammatically

Pat- not sure what you mean by "architecturally"

Me- it's grammatically correct

subject, verb, object

but "this sentence" = "false"

assuming you have true or false, it's a binary subject

1 or 0

so "this sentence" = 0

but "this sentence" can't be "x" by itself

no x = 0

because x (the sentence) encompasses 0

if 0 = false, and 1 = true, then the paradox basically says 0 = 1

and since "this sentence" is both a subject AND a qualifier, can you really have a sentence?

besides...there's no subject being verified

it's not like you're saying "all i say are lies"

but i suppose that's why it's paradoxical

Pat- you have successfully demonstrated that it is a paradox

I'm not sure why it wouldn't qualify as a sentence

Me- if i said "every word i say is a lie" we have something to judge

ie, the words i say

"my words" = "lies"

but with the liar's paradox we don't have that

"this sentence" = "false"

but "this sentence" is nothing. there's no substance here to test for validity

it's not like "my words".

BUT

if you take the string of words "this sentence is false" as what the sentence IS

then the paradox becomes hollow

Pat- hollow?

Me- i can't really think of a good term...

um...

not real? it's not really paradoxical because there's no substance to deal with initially?

i'm seeing it as a mathematical sentence

Pat- so "this sentence is grammatically correct" is not a sentence either?

Me- if you look at the word "sentence" as a stand alone non-variable, then TECHNICALLY it is correct

because "is" qualifies as a verb so long as you have an object to compare the subject too

but because "this sentence" conceptually encompasses every word from capitalization to punctuation, it's hard to make  

qualifier statements

Pat- it seems as though you are suggesting that we cannot talk about sentences

Me- this is, of course, unless you're saying "this sentence" with regards to ANOTHER sentence being examined

Pat- so is it the reflexive nature of it that is the problem?

Me- that's what i'm seeing

i see no "x"

it's more "x = 0" = "0"

but if that's the case then logically we have a 1

for if the sentence is false, then we have a truth

Pat- that is what a paradox is

Me- but we have no substance to make false to begin with

Pat- sure we do

Me- ?

Pat- unless you are suggesting that sentences can't be true or false

Me- ...something i never said

Pat- I didn't think you had

thus "unless"

Me- haha

Pat- but if sentences can be true or false, then that sentence can be true or false

it certainly seems to be making a truth claim

Me- but what have we to prove true?

"this sentence is false" is the sentence itself

Pat- yes

Me- so those four words must be false

and i can't parsel out a variable

so "this sentence is false" = "false" because "this sentence" = "this sentence is false"

Pat- yes

you're essentially demonstrating that it is a paradox. but I don't think that demonstrates your asserted solution

Me- your view of paradox lies in the 1 or 0 argument

mine lies in the fact that there is nothing concrete to be proven either true or false

because every time you try to make "this sentence" into an X, you have to take into account the entire line

Pat- are you asserting that reflexive statements never are true or false?

Me- no

hold on...

you could say "this sentence is not a latin sentence"

and that would be correct

because you would have substance for comparison (ie, the language in which it was written)

but to make an assertion about a sentence that has no real conceptual material FOR comparison makes the comparison  

invalid

besides, assuming we don't use the X(n+1) for every time we use "this sentence"...

"this sentence is false" = "false"
"x = 0" = "0"
"0" = "0"

is true

and 0 = 0 being true does not invalidate either 0 or (x = 0)=0 because they've just been proven to be equal

Pat- invalidate?

Me- "this sentence is not latin"
"this sentence" = "not latin"

this is a valid comparison because we have something to compare

ie, english to latin

"this sentence is not true"
"this sentence"= "not true"

this is an invalid comparison because we have nothing to validate

because "this sentence" encompasses its own validity

in the latin case, the sentence encompassed its own language (so to speak)

in order to prove a truth true, you must have some item or thought or fact to prove true

"this sentence is false" has no "thing" to prove false

the only "thing" we have is false

and false = false is no paradox

Pat- would you agree that "this sentence is true" is neither true nor false?

Me- yes- for, inversely, we have nothing to validate. the problem with the paradox is that we're attempting to compare or  

validate something, and our logical conclusion is an illogical one

my point is that we have nothing to compare or validate to begin with, and therefore cannot have a paradox

Pat- but sentences Are things. if "this sentence is in english" is both a sentence and true, then it is not immediately obvious to  

me that "this sentence is true" is not both of those things as well.

Me- yes- sentences are things. i agree with that.

but the english example gives us something to work with- we have an agreeable example of english writing. it's something  

that can be agreed upon outside of the concept of the sentence itself.

Pat- we don't have an agreeable concept of truth?

11:46pm

Me- we do, but truth is not as concrete as english

let's ignore pidgin and L337 and all that for now

if i asked you "why is the sentence english?" you'll point out that the words are in english, and the structure is english, and  

the letters are latin

but if i asked you "why is the sentence false?", what would you tell me?

what points in or about or of the sentence do we have to judge as false?

we don't. we have no points.

the only point we could have, in a way, is an equation to falsehood

thus the x = 0 argument i made earlier

and if x = 0 = 0, then 0 = 0

and that is true

but 0 being 0 isn't really a paradox

Pat- so, at base, you are asserting that "this sentence is true" or "this sentence is false" do not actually have truth values

yes?

Me- yes, but because it has no values to begin with

i'm disputing existence, not validity

or rather the inability to determine validity on the basis on non-existent values for comparison

Pat- those are different things. are you making an epistemic or an ontologic claim?

Me- i don't know- let me pull out my dictionary here...

nm. give me the cliff's notes.

Pat- are you making a claim about what we can know, or about what is?

Me- what is, in that the sentence "is" not one containing material for validity

i suppose we "can know" what is false but only if we have some"thing" to prove false

"this sentence is false" gives us no"thing" except the term "false"

Pat- if we substitute the variables in your equation, does the outcome differ? where true = 0 and false = 1?

Me- it shouldn't

Pat- what would it look like?

Me- this sentence is false

this sentence = 1

(this sentence = 1) = 1

(X(n+1) = 1) = 1

or, not using X, 1 =1

Pat- what is N?

Me- the sentence itself

every time you use the term "this sentence" you have to use all four words

Pat- and X is?

Me- the words "this sentence"

so ((this sentence is false) is false) = false

it's not a big n as in X(n+1) = Xn + X

it's supposed to be a subscript n+1

to show that everytime you use the phrase "this sentence" you must muse the words "this sentence is false"

since "this sentence" is what we're declaring is false

Pat- gotcha

assuming that the sentence is true, you derive that it is false

(at least, I am pretty sure that is an accurate summary of what you've done)

Me- lol

sounds about right

been a long time since i've done math

Pat- it's akin to symbolic logic, which I haven't done in a while I think you've taken a more convoluted route than  

is necessary, but that's ok

if you assume that the sentence is false, what would your equation look like?

Me- what do you mean?

as in false is 0?

12:32am

Pat- no. however you set your variables, you've assumed the truth of the statement (that the statement is in fact  

false), and derived not not false -> true.

American Exceptionalism

And remember: We cannot rest on our laurels. Our world, and our times, change too fast to sit back and coast on our accomplishments. We must, if not for the strength of our standing then for the security of our descendants, keep going forward.

Chris Christie in 20-never

I greatly respect Gov. Christie for what he knows. He knows how to be effective, he knows how to speak, he knows how to work with people, and most importantly he knows how to lead.

See, there are few people in our country that have that ability to lead. There is a difference between leaders, managers, and figureheads. If you don't believe me, go read a couple decades' of Dilbert. Can you call the Pointy Haired Boss a leader? On the contrary; he's nothing but a manager. Gov. Christie doesn't manage his state. He doesn't just oversee his state. He doesn't sit back and field the underhanded pitches, playing some abstract figurehead in NJ. He leads. And that quality, coupled with the strength of conviction and effective realism is why he'd make a presidential candidate I would be proud to support...

...which is why I don't think he should run in 2012. Do we need him? Oh, more than ever. But Gov. Christie, when asked about a run in '12, said very plainly "No". And I believe him. I believe that he will first and foremost uphold his promise to the residents of New Jersey to lead them well, and he will fulfill that promise. He won't pull a Sarah Palin and eject from office before the first term is up. He won't be like Obama and leave his post to seek higher fame and fortune. His sense of duty, and his sense of honor, will keep him in the place where he can do the most good for the people who need him. That place, for the time being, is Trenton.

I'll be honest with you- if he does decide to run in '12, I would be overjoyed. But that feeling of hope for positive change will be joined by a sense of sadness and some respect lost for the Governor- because he backed down on his word. It's that bittersweet promise to see his term through that hamstrings those of us not in NJ, but a man who keeps his word is rare enough these days.

A man in his position willing to care for his state at the expense of the idol polticians call higher office isn't a member of the rarity these days- he's a member of a class almost extinct.

Poem of the Day

"The Journey"


One day you finally knew
what you had to do, and began,
though the voices around you
kept shouting
their bad advice--
though the whole house
began to tremble
and you felt the old tug
at your ankles.
"Mend my life!"
each voice cried.
But you didn't stop.
You knew what you had to do,
though the wind pried
with its stiff fingers
at the very foundations,
though their melancholy
was terrible.
It was already late
enough, and a wild night,
and the road full of fallen
branches and stones.
But little by little,
as you left their voices behind,
the stars began to burn
through the sheets of clouds,
and there was a new voice
which you slowly
recognized as your own,
that kept you company
as you strode deeper and deeper
into the world,
determined to do
the only thing you could do--
determined to save
the only life you could save.


-Mary Oliver

Student, Write Thyself

I'm a procrastinator. A terrible procrastinator. I'm probably one of the best people at procrastinating that I'll ever meet...and I'll probably meet very few other people who have the problem I do because I'll wait until tomorrow to start looking.

The irony in this is that my best papers were all written at the last minute. For my sophomore English Lit class, I waited until the weekend before to write a 10 page paper on racism and Shakespeare's Tempest. My sources? The Tempest, a paragraph from the complete Cliff's Notes (the one with the notes written on the sides of the page next to the actual play), and one line from a half-page commentary on racism and great literature. For this wonderful work of writing I earned a B+.

I wrote my 10 page paper on the plausibility of a subordinate Space Corps to the Air Force (mirroring the command, logistical, and financial relationship the USMC has to the Navy) 2 hours before class started for the day. I got another B+ on that one.

For my senior thesis, the one on Daoist/Confucian and Christian influences on Chinese and European imperialism (mentioned in "Part 1: Thoughts on God") I started at midnight and finished, all 25 pages and 15 slides later, at 7am. That one earned me a solid A.

While I may put off writing until the last minute, often paying homage to the adage that "If you wait until the last minute, it only takes a minute", I have never, ever, EVER, plagiarized a paper. If I had I wouldn't have graduated with a 2.3.

A (former) friend of mine was the second most powerful student on campus during senior year. Our school had an intolerance policy for cheating, suspected cheating, and suspected suspected cheating that bordered on religious zeal. Virtually everything done there was individual effort; and, sadly, many students received lower grades than they could have earned because they were too afraid to ask more knowledgeable students for help. This friend of mine, on his senior thesis, plagiarized ~80% of his paper. After four years of living under the academic ethic code he chose to ignore it, and leadership chose to look the other way. He was allowed to graduate late, and that was that.

People make mistakes. People get in over their heads. People miss deadlines. People are human. People who lie about authorship, people who cheat themselves out of education and their teachers out of requested work, and people who steal credit are people I owe no respect too. I don't care why you did it- if you pay someone else to write your paper, you have no honor.

This is why I disagree with Mr. "Ed Dante", professional shadow writer.

The problem isn't in the emphasis of evaluation over education. Evaluation pushes people to educate themselves, to learn to perform under pressure, and to prepare for demand responsive situations. Education, to a degree, is subjective. Evaluating education based on pre-set criteria is objective. This is why classes have tests, papers, quizzes, exams, and finals. The more is evaluated, the more as student will be forced to learn and prepare themselves for the field they have chosen to study.

I don't think in this instance "the system" has failed anybody. I think parents have failed their children and students have failed themselves.

Before anyone rushes to the defense of the obviously poor, disadvantaged students, put yourselves in the teachers' shoes. Imagine dedicating your time, if not your life, to teaching younger generations a subject you care about. Now see if you're comfortable knowing someone else is being paid so a student can fake his or her way to a degree.

Or a nursing license.

Or a chaplaincy.

Or into pharmaceutical research.

Or into the military.

Or any other of dozens of fields this shadow author is given money to plagiarize for.

If you yourself are a teacher, or you know someone who is, ask yourself this: if this man and others like him have never worked in or with the field that cheating graduates are going into, are you comfortable not knowing whether your students are truly worth of the degree they've "earned"?

"Thanx so much for uhelp ican going to graduate to now."

Or Else What?

"Those who abjure violence can only do so because others are committing violence on their behalf."
-George Orwell
  From Notes on Nationalism


Here's an interesting take on the necessity of violence to guarantee peace and force to guarantee order. The underlying principle is that without the credible threat of violence laws are just suggestions and rules are just words. It's another look at the "sheep, sheep dogs, and wolves" analogy with an emphasis on the concept of violence from the system rather than the types of individuals within such a system.

Jack Donovan: Violence is Golden

The opposite of such a system would be one without any threat of force at all, which would be sustained by a moralistic, example-setting leader who guides a people strengthened by internal discipline. This type of governance is outlined by Laotze (and embraced by pacifists and hippies alike):

"The more rules you have, the more unhappy people are:
And the more weapons there are, the worse things happen.
The more we want luxuries, the more we abandon simplicity-
And the more laws you pass, the more we will break them.

So the sage says: I do nothing, and the people come together;
By leaving them alone, I let them be on the path-
Bu not using my power, they become rich in themselves.
And if I want nothing, they will return to the essence of their being."
-Daodejing Chapter 57, trans. by Man-Ho Kwok

While almost altruistic to a fault, this is the type of governance I wouldn't be hesitant to support...if it were practical. But it's not. Like the Haight Street experiment in effective socialist communalism, Laotze's vision could only work on a small scale. This brand of governance would be both impractical and ineffective on a nation as large as ours. Why?  Because in America there are too many people and, in a way, we are too fractured culturally to have the societal cohesion necessary for something like this to work. Say what you will, but for the time being that's just the way it is.

On a lighter note, here's an interesting article on a new addition to the Norwegian prison system. Maybe a hybridization of their system and ours would work better than the one we have now.

No Sepukku Here

http://www.politico.com/news/stories/1110/45285.html

When you're the leader of a party that was essentially thrown out of Congress, fighting to stay in command says more about your selfishness than your desire to serve.

Where are the days when a leader would take responsibility for such a large political failure and honorably resign?

Le réseau d'origine

I'd love to say I stumbled across this, but I can't. I'm copying it off of a friend of mine's blog. If you haven't checked it out already, please stop by and give it a peak.

The saddest thing about Olet's predicament was that he was hamstrung by the technology of his day. To realize that someone envisioned (though not necessarily invented) the internet a full 60 years before it became practical is simply amazing. One wonders what technological advances fellow members of our generation are dreaming up that only future generations will see...



From the NY Times: The Web That Time Forgot

"Historians typically trace the origins of the World Wide Web through a lineage of Anglo-American inventors like Vannevar Bush, Doug Engelbart and Ted Nelson. But more than half a century before Tim Berners-Lee released the first Web browser in 1991, Otlet (pronounced ot-LAY) described a networked world where "anyone in his armchair would be able to contemplate the whole of creation."

Although Otlet's proto-Web relied on a patchwork of analog technologies like index cards and telegraph machines, it nonetheless anticipated the hyperlinked structure of today's Web. "This was a Steampunk version of hypertext," said Kevin Kelly, former editor of Wired, who is writing a book about the future of technology.

Otlet's vision hinged on the idea of a networked machine that joined documents using symbolic links. While that notion may seem obvious today, in 1934 it marked a conceptual breakthrough. "The hyperlink is one of the most underappreciated inventions of the last century," Kelly said. "It will go down with radio in the pantheon of great inventions." "

via www.nytimes.com

A Slice of Technological Perspective

He's right. When I was a kid, a cell phone was twice the size of a 2TB hard drive. Today we have cell phones with more computing power than some computers...and we have 2 TERRABYTE hard drives.

The evolution from 8in floppies to the cloud has completely shifted the way data is used, transferred, and stored. The leap from vinyls to SD memory cards completely changed how music was stored on physical media, and the music transition to wireless did away with physical media entirely. It's simply amazing.

I try to keep my ears open for news from the holographic industry. With HD a commonplace occurrence, our transition to and through 3D tv is just an awkward step towards losing the need for a screen altogether.

One of the setbacks to holographic technology is that projections need a way to be seen. When do you see a rainbow? After it rains, when there's still enough water in the air to refract the light waves. If you've ever done laser experiments you know it's easy to see the point where a beam hits an object, but in order to see the beam you need the light to pass through a medium (namely smoke or fog). Normal screens don't have this problem; the image is projected onto the glass from behind and an image is visible. But, like with 3D tv without glasses, I'm sure this is a hurdle and not a show stopper.

When S1M0NE came out, I dismissed the idea of a computer generated holographic woman addressing an audience as something that's possible, but not probable. It could happen, but it wouldn't happen for a few decades.

But if you wanted to reduce those decades to eight years, where would you go?

Japan, of course.

I'll save you the witty wrap-up and encourage you to do your own research.

Rise of the (Droid)Machine?

http://money.cnn.com/2010/11/12/technology/quadroid/index.htm?source=cnn_bin&hpt=Sbin

Apparently, Quandroid is the new Wintel, which makes perfect sense- if you know what it means.

While I can understand and appreciate the comparison, I'm more interested in the Android v Apple battle. I don't forsee the third contender, RIM's Blackberry, going anywhere for the time being. RIM set the standard for smartphones, but that standard is evolving. While government and corporate employees will almost certainly be issued company Blackberries for the next several years, the rest of the cell market is moving in different directions.

The link above made an interesting statement about how Android phones hold 27% of the smart cell market while Apple holds 23%. That figure must ring true to the ears of Droid users as a sign of Apple's impending disenthronement, but here are two things Droid addicts don't realize:

1) The figure compares operating systems, not individual platforms

2) For Droid phones it's a flood of quantity over quality

The iPhone is 100% fruit: it's an Apple mobile operating system (iOS), with Apple software (like iTunes and Safari), on an Apple hardware platform. Droid, on the other hand, is just an operating system (Chrome OS). Google had to pair with six companies (Samsung, LG, Sanyo, Motorola, HTC, and Nokia) to make the phone happen. And considering that fact, you have to look at how many phones can call themselves Droids.

Sprint has 8 phones.
AT&T also has 8.
Verizon, leader of the pack, has 14.
T-Mobile, bringing up the rear, has 3.

Apple, on the other hand, technically has two. But because the 3GS can upgrade to the iOS that runs on the iPhone 4, it's really only one phone.

If we were comparing operating systems' market slices alone, my hat would certainly be off to Android; but we're not. We have THIRTY THREE Android phones against Apple's ONE iPhone. 33:1. Imagine how the market demographics would change if Apple made even 3 or 4 iPhones? Imagine an iPhone 4, an iPhone mini, or an iPhone shuffle. Rather than a couple of Apple phones, we have only one- and Apple is holding 23% of the current market with it. If each Droid phone was given a market percentage as a hardware platform alone, it would be an average of 0.82% per device.

Granted, as a credible OS Android is certainly on the rise, and neither Google nor Apple show any signs of slowing. While Android does have the advantage of being an open platform, we have 7 companies' 33 phones barely doing better than 1 company's 1 phone. When you look at it that way, Jobs is leaving Google in the dust.

How 'bout that Apple?