Descartes' Second Rule vs. Uncertainty

[Lifegazer]

This isn't an example of a paradox. It's like the guy who never speaks saying "I never speak.". It just means that the guy is being contrary to his own nature, because he obviously does speak. Similarly; the guy who says "I always tell lies." must speak the truth to make the statement. So he just contradicts his own nature. There is no paradox.

 

[Greg Bernhardt]

So he just contradicts his own nature.

By definition that's what a paradox is.

 

[Mentat]

Originally posted by drag
But, that's not fair ! I'm not certain of
my existence like I am of math !
Oh... NO ! I'm turning into a shadow !
Oh... Yes ! This is the perfect cloacking
device - just tell people to doubt their
existence - I'm going to be a rich shadow !

Live long and prosper. [/B]

Very funny. I wasn't saying that you stop existing, by doubting it. I'm saying that anything you learn about your existence will be rather worthless (according to Descartes' reasoning), because you doubt your own existence (and your existence is required for you to take in knowledge). It's like saying that doubting the premise makes all other assertions, that are based on that premise, doubtful - and, according to Descartes, doubt makes any new knowledge worthless.

 

[Mentat]

Originally posted by Lifegazer
This isn't an example of a paradox. It's like the guy who never speaks saying "I never speak.". It just means that the guy is being contrary to his own nature, because he obviously does speak. Similarly; the guy who says "I always tell lies." must speak the truth to make the statement. So he just contradicts his own nature. There is no paradox.

Saying "I never speak" is just lying.

Let me try and explain the Liar's paradox another way. Let's take another statement, that is a derivative of the Liar's Paradox: This statement is false. You have two choices, either the statement is false, or it is true. However, if it is true, then the statement really is false (as that's what the statement is stating - "This statement is false"). And, if it is false, then the statement must be true (because that's what it states - "This statement is false"). Thus, in being true, it must be false; and in being false, it must be true. Thus, paradox - as it cannot be true or false, but most be both and neither.

Personally, I don't think that the Liar's Paradox really works exactly the same way. In fact, I think that it is a resolvable paradox. However, the one above ("This statement is false") is not resolvable.

I guess people relate the two, because by saying "everything I say is a lie", I am including that statement, and thus saying that that statement is false. But, I could be lying, when I say "everything I say is a lie", and thus it doesn't have to result in the "This statement is false" paradox.

 

[wuliheron]

Originally posted by Mentat

... by saying "everything I say is a lie", I am including that statement, and thus saying that that statement is false. But, I could be lying, when I say "everything I say is a lie", and thus it doesn't have to result in the "This statement is false" paradox. [/B]

If you are lying about lying, then you are telling the truth which contradicts the fact that you were lying.

 

[Lifegazer]

Originally posted by Greg Bernhardt
By definition that's what a paradox is.

I thought a paradox was when there was no explanation for a specific event/phenomenon?
I don't see how somebody telling lies fits into this category.

 

[Iacchus32]

Originally posted by wuliheron
If you are lying about lying, then you are telling the truth which contradicts the fact that you were lying.

-6 x -6 = 36 ... Is that a paradox?

 

[Mentat]

Originally posted by wuliheron
If you are lying about lying, then you are telling the truth which contradicts the fact that you were lying.

Ah, I see. However, it still seems that "Everything I say is a Lie" is much too general. "This statement is false" is specific, and is thus an obvious paradox. "Everything I say is a lie" could just as easily be a lie, and there is thus no need to ponder the statement, because I wasn't telling the truth when I said it, but could just as well have told the truth many other times in my life.

 

[Mentat]

Originally posted by Iacchus32
-6 x -6 = 36 ... Is that a paradox?

No. Why would it be? It's as obvious as 6 x 6 = 36, isn't it?

 

[Greg Bernhardt]

I thought a paradox was when there was no explanation for a specific event/phenomenon?

http://dictionary.reference.com/search?q=paradox

 

[Iacchus32]

Originally posted by Mentat
No. Why would it be? It's as obvious as 6 x 6 = 36, isn't it?

If you are lying (-6) about (x) lying (-6), then you are telling (=) the truth (36) which contradicts the fact that you were lying.

Why doesn't -6 x -6 = -36 then?

 

[wuliheron]

Originally posted by Iacchus32
-6 x -6 = 36 ... Is that a paradox?

Without context there is no way to decide if this statement is a paradox or not. What we were discussing is a qualitative paradox where numerical values cannot be assigned to the qualities. What you have created is a quantitative statement that only applies in certain circumstances. Not every system of mathematics is the same and in some systems of mathematics it most certainly Is a paradox while in others it is not.

Likewise, you are assigning multiplication as the function in the place of a lie about a lie which is not a multiplication function. In other words, you could write this out in the context of lies and saying:

Six lies times six lies equals thirty six truths, which is most definitely a paradox.

When the statement is more correctly written out as:

A lie plus a lie equals a truth.

 

[Mentat]

Originally posted by Iacchus32
If you are lying (-6) about (x) lying (-6), then you are telling (=) the truth (36) which contradicts the fact that you were lying.

Say what? I don't know how you related -6 to lying, or the truth to 36, or "about" to x, but the reasoning is based on these assumptions (that -6 = lying, and such), and is thus very strange, from my perspective.

Why doesn't -6 x -6 = -36 then?

It's a basic principle of math. Do you honestly not understand this?

 

[wuliheron]

Originally posted by Mentat
Ah, I see. However, it still seems that "Everything I say is a Lie" is much too general. "This statement is false" is specific, and is thus an obvious paradox. "Everything I say is a lie" could just as easily be a lie, and there is thus no need to ponder the statement, because I wasn't telling the truth when I said it, but could just as well have told the truth many other times in my life.

Of course any paradox can be resolved if you make assumptions about it, the issue is that without making those assumptions it remains a paradox. For example, I could assume that This statement is false is actually referring to another statement that really is false.

 

[Mentat]

Originally posted by wuliheron
Of course any paradox can be resolved if you make assumptions about it, the issue is that without making those assumptions it remains a paradox. For example, I could assume that This statement is false is actually referring to another statement that really is false.

If a statement is supposed to refer to another statement, it would use the word "that", not "this". Besides, I wasn't making any assumptions. The person could really be lying, when stating the statemtent of the Liar's paradox.

 

[Iacchus32]

Originally posted by wuliheron
Without context there is no way to decide if this statement is a paradox or not. What we were discussing is a qualitative paradox where numerical values cannot be assigned to the qualities. What you have created is a quantitative statement that only applies in certain circumstances. Not every system of mathematics is the same and in some systems of mathematics it most certainly Is a paradox while in others it is not.

Likewise, you are assigning multiplication as the function in the place of a lie about a lie which is not a multiplication function. In other words, you could write this out in the context of lies and saying:

Six lies times six lies equals thirty six truths, which is most definitely a paradox.

When the statement is more correctly written out as:

A lie plus a lie equals a truth.

Oh, I guess I was thinking about your previous example of the "liar's paradox" where he states he "always lies." Does that add any more clarification? Of course your example of the "six lies times six lies equals thirty six truths" does seem to speak of paradox ... whereas in the mathematical sense (according to Mentat) it makes perfect sense. Or does it?

 

[Mentat]

Originally posted by wuliheron
Six lies times six lies equals thirty six truths, which is most definitely a paradox.

No it's not. It's simply undoable. You can't multiply the one amount of lies by another amount of lies. The very idea lacks meaning.

 

[ahrkron]

Originally posted by wuliheron
To speak of existence in anything other than ambiguous terms is to express bias.

Everybody is free to decide to use ambiguous descriptions, as long as s/he is aware that no valid conclusions can be drawn from them.

Just as humanity once believed the Earth was flat, we may find that our perception of existence is entirely invalid or that existence presents a much more muddled a connundrum than we perceive.

Again, it is apparent that you keep jumping from "validity of existence" to the "validity of perception". As I said before, I'm convinced that most of the apparently paradoxical statements in your posts come from such an abuse of language.

It appears to me it is You who are stretching the meaning of words entirely out of context and merely making communication difficult.

It may seem that way to you, but my intent is not making exchange difficult. Rather, It is my intent to show how many statements you have made in support of your thesis (that "paradox is everywhere") come from ambiguities in your use of language. Of course you don't agree, but I think you are (enormously) overstating the role of paradox, and that it is only fair to present the opposite view in the forum (especially since it is my honest opinion).

you insist on imposing your own biased view of existence on any discussion of the concept.

This is a gross misrepresentation (misunderstanding?). I'm not imposing any view about existence. Rather, I'm saying that, if it has any merit, any view should be able to be presented using, at the very least, clear statements.

The idea that all paradoxes are merely semantic difficulties of language is nothing new, but logicians and other serious scholars disagree.

I disagree as well. I never said that ALL paradoxes are due to incorrect descriptions. What I keep saying is that you construct "paradoxical" statements way too often based on such ambiguous/incorrect descriptions.

Real paradoxes do exist, and they can only be identified and studied by being as accurate as possible in their description. Otherwise, we would just accumulate a huge number of "might-be" paradoxes, most of which would be just a result of mixing scientific and new-age notions of frequencies, energies, dispositions, dimensions and what not.

In particular, the paradox that constitutes the gist of Goedel's theorem was meticulously built and studied using formal logic. It is a beautiful piece of math, and an extremely rigorous account of the limits of decidability.

your arguments are just so much biased garbage.

You are entitled to your opinions.

 

[DrChinese]

Referring to the question posed earlier - how to determine the level of certainty that is "healthy"...

I am a utilitarian, a pragmatist. Knowledge may be incomplete but nonetheless useful. If I waited to know subjects with greater certainty, I would miss most of life.

At one time, I was a student of math because it was so pure and satisfying. I believe this is what Descartes is referring to. But how useless is math when applied to human behavior? We understand so little about the human mind, yet it is something we must deal with every day.

So my conclusion is that working with imperfect knowledge is the norm, and is always "healthy" if it is useful. Many times, even wrong ideas have predictive value. But they lose out to yet better ideas which have greater predictive value, even if the predictive value is still not perfect (or even optimal).

 

[wuliheron]

Originally posted by Iacchus32
Oh, I guess I was thinking about your previous example of the "liar's paradox" where he states he "always lies." Does that add any more clarification? Of course your example of the "six lies times six lies equals thirty six truths" does seem to speak of paradox ... whereas in the mathematical sense (according to Mentat) it makes perfect sense. Or does it?

Yes, its an imperfect analogy I just made up on the spot. Mentat is quite right that the functions of mathematics do not translate exactly.

Originally posted by Mentat
No it's not. It's simply undoable. You can't multiply the one amount of lies by another amount of lies. The very idea lacks meaning.

Yes, it lacks linear logical meaning, but somehow conveyed a message as Iacchus indicated. Jazz is not an exact science, but more a matter of the heart and soul than anything else.

Originally posted by ahrkron
Everybody is free to decide to use ambiguous descriptions, as long as s/he is aware that no valid conclusions can be drawn from them.

This seems to be just about all you have to say, your entire argument. Conservative fundamentalism. If it makes you happy, I'm happy for you. However, I feel no need whatsoever to keep answering what are essentially the same questions over and over again. If you don't get it, don't trust it, etc. that's just too bad. A lot of people don't appreciate jazz. It can be an acquired taste.

Of course, as many critics of early jazz said, you could do anything. The avant-garde can be so much meaningless garbage. The issue is not so much whether it is meaningless issure more or less often, but do serious works emerge from it that can leap ahead of more ploding conservative efforts. The answer, of course, is yes.

Quantitative science can do a great deal, but it has yet to duplicate the human mind and especially creativity. When it does, then I may take your redundant and ignorant criticism to heart.

 

[drag]

Greetings !

ahrkron, I'd appreciate it if you'll also
answer what I said. I'm trying (as ussual) the
direct approach, but for some reason you
seem content to keep discussing ambigous
stuff and small points of semantics with wuli.
Thanks.

Mentat, from what you mentioned so far this
Descartes guy doesn't seem that wise to me.
If he said, for example, we have to be as certain
of stuff as of math - which is an abstract
theory, and if he said doubt is destructive
while doubt is the basis for any exploration
of any kind - well, he just doesn't earn many
points from me.

Live long and prosper.

 

[ahrkron]

Originally posted by wuliheron
If you don't get it, don't trust it, etc. that's just too bad. A lot of people don't appreciate jazz. It can be an acquired taste.

As I said, I didn't expect you to agree.

I do appreciate Jazz and are well aware of the ambiguity and contradiction present in human motivations and behavior. I just don't think poetry makes good arguments and, as I said, I think it is not small stuff that people support arguments and world views with only such half-built logic.

 

[wuliheron]

Originally posted by ahrkron
As I said, I didn't expect you to agree.

I do appreciate Jazz and are well aware of the ambiguity and contradiction present in human motivations and behavior. I just don't think poetry makes good arguments and, as I said, I think it is not small stuff that people support arguments and world views with only such half-built logic.

It is not "half-built" logic, quite the contrary, it is the cutting edge just as Jazz is the cutting edge in music. It is also the basis for how half of humanity views the world.

Science is not always the perfectly symmetrical and harmonious music of the spheres, but often improvisational. If science rejected every theory with loose ends we would not be using Newtonian Mechanics due to its etherial treatment of spacetime and its almost magical vision of the action at a distance of gravity--not to mention the use of paradoxical infinities in calculus.

The two best examples of extremely useful scientific theories built around paradox that I know of are Quantum Mechanics and Relational Frame Theory.

http://www.relationalframetheory.com/forum/index.html

If anything, your objections to such theories and philosophies is half-baked. Before you start attacking the slippery semantics of such theories I suggest you learn more about them.

 

[ahrkron]

Originally posted by drag
ahrkron, I'd appreciate it if you'll also
answer what I said.

I will.

for some reason you seem content to keep discussing ambigous stuff and small points of semantics with wuli.

I don't think they're small stuff. Neither are they big issues, but I just got hooked on them because of the kind of replies he made.

Point well taken though.

 

[ahrkron]

Originally posted by wuliheron
If science rejected every theory with loose ends [...]

It is not the loose ends I contend with, but your way of "inserting paradoxes" via word games/misuse.

If anything, your objections to such theories and philosophies is half-baked. Before you start attacking the slippery semantics of such theories I suggest you learn more about them. [/B]

So, I say
"I think many of the paradoxes you mention are misunderstandings on your part"
and you reply
"so you are attacking these theories, that in my opinion are paradoxical".

Not in the least bit.

Anyway, I think we've both made our points in this respect, and the original intent of the thread was more interesting than this.

 

[wuliheron]

Originally posted by ahrkron

It is not the loose ends I contend with, but your way of "inserting paradoxes" via word games/misuse.

And I contend that you obviously are deliberately refusing to acknowledge even the simplest context I use, contesting the simplest definitions of words, and in general just making a pain-in-the-butt of yourself. You are not seriously debating the issue, but instead, merely attacking the concept like a lot of ethnocentric bigots are prone to do.

So, I say
"I think many of the paradoxes you mention are misunderstandings on your part"
and you reply
"so you are attacking these theories, that in my opinion are paradoxical".

Not in the least bit.

Anyway, I think we've both made our points in this respect, and the original intent of the thread was more interesting than this.

I certainly hope I've made my point, it was squarely aimed at you. Stop being so cententious over paradoxical viewpoints. If you have a serious argument to make, I welcome it. If all you are going to do is take everything I say out of context and split hairs, please keep it to yourself.

 

[Mentat]

Originally posted by drag
Mentat, from what you mentioned so far this
Descartes guy doesn't seem that wise to me.
If he said, for example, we have to be as certain
of stuff as of math - which is an abstract
theory, and if he said doubt is destructive
while doubt is the basis for any exploration
of any kind - well, he just doesn't earn many
points from me.

Live long and prosper. [/B]

In defense of Descartes: He didn't say that we have to be a certain of things as we are of math, but as certain as we are of Arithmetic and Geometry. These things are obvious, and readily demonstrable, and thus do not fit the category of "abstract theory" as you said. Also, he didn't really say that doubt was destructive, so much as he was saying that to doubt everything that you learn is to make you no better than someone who has yet to learn whatever it is you learned, because you will not make good application of it.

 

[drag]

Greetings !

Originally posted by Mentat
to doubt everything that you learn is to
make you no better than someone who has yet
to learn whatever it is you learned, because
you will not make good application of it.

And what's the point in that statement ?
Sounds just like one of those wise-ass
slogans that sometimes fit the situation.

For ahrkron (a reminder about the PoE stuff) :
"What DOES pose a paradox is the apparent inability
of providing a clear explanation according
to all reasoning capabilities we have so far.
So, it's not something that hasn't been
explained yet, it is something that so
far isn't supposed to have an explanation.
(Of course, we can't prove our current
reasoning capabilities will not change and
improve to accommodate existence in the future -
but because of the many faces that characterize
the PoE - the possibility of such new reasoning
is one of the most uncertain things ever.)"


Live long and prosper.

 

[ahrkron]

Originally posted by drag
For ahrkron (a reminder about the PoE stuff) :
"What DOES pose a paradox is the apparent inability of providing a clear explanation according to all reasoning capabilities we have so far.

(Thanks for the reminder )

Why does that pose a paradox? There is no reason to expect that reasoning should produce a "clear explanation" for every problem.

Think of it as a bunch of chemicals on a huge petri dish. After a big while, lots of small formations can reproduce, and they develop behaviors they pass on to their successors. Among such behaviors there are "reasoning" (whatever that is), and a name for the sensation they have when such "resoning capability" produces some sort of pleasure. They classify as a "clear explanation" the sequence of thoughts they have when such pleasure is felt.

Why would they expect their "reasoning" behavior to produce such a sequence for every possible problem?

So, it's not something that hasn't been
explained yet, it is something that so far isn't supposed to have an explanation.

Even if that was the case, why would that pose a paradox?

(Of course, we can't prove our current
reasoning capabilities will not change and
improve to accommodate existence in the future -
but because of the many faces that characterize
the PoE - the possibility of such new reasoning
is one of the most uncertain things ever.)

But in order to have a paradox, you need more than uncertainty; there should be a contradictory statement that, at least apparently, has a similarly solid logical support.

 

[Royce]

I think Descartes had it wrong when he said "I think; therefore, I am."
In my opinion it should be 'I am; therefore, I think.'
I have no idea who first said; "The more I learn the less I know."
Which, of course, means the the better educated we are, the more we learn, the more we know that there is so much more to learn and that very little is known for certain. I have said in other threads that I know nothing. It is one of my favorite lines and is meant to be taken literally.
I can only perceive the world, reality, through my senses and I know my senses are limited and fallable. I can only read what others have written and hear what others say and judge for myself if it is logical, correct, true, probable, impobable or wrong.
If we were to take Descartes literally we could and would study and learn nothing for I believe that we can know very little for certain.
Even Arithemtic and Math have theories, assumptions not always true and are lifetime studies even though there are those who believe that math is a purely mental construction and have no real basis.