- #36
Lifegazer
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.
Descartes' Second Rule vs. Uncertainty
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In summary, Descartes' Second Rule of the Direction of the Mind states that only those objects that our mental powers seem adequate to understand should engage our attention. He believes that science, specifically Arithmetic and Geometry, provide certain and indubitable knowledge. He argues that it is better not to study at all than to occupy ourselves with difficult objects that we are unable to distinguish between true and false. He rejects the idea of embracing complete uncertainty and instead suggests trusting only what is completely known and incapable of being doubted. He concludes that in our search for truth, we should focus on objects with the same level of certainty as Arithmetic and Geometry.
I don't see how somebody telling lies fits into this category.
- #37
Iacchus32
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-6 x -6 = 36 ... Is that a paradox?
- #38
Mentat
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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.
- #39
Mentat
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No. Why would it be? It's as obvious as 6 x 6 = 36, isn't it?
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- #41
Iacchus32
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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?
- #42
wuliheron
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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.
- #43
Mentat
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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.
It's a basic principle of math. Do you honestly not understand this?
- #44
wuliheron
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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.
- #45
Mentat
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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.
- #46
Iacchus32
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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?
- #47
Mentat
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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.
- #48
ahrkron
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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.
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 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).
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.
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.
You are entitled to your opinions.
- #49
DrChinese
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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).
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).
- #50
wuliheron
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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.
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.
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.
- #51
drag
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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, 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.
- #52
ahrkron
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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.
- #53
wuliheron
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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.
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- #54
ahrkron
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I will.
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.
- #55
ahrkron
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It is not the loose ends I contend with, but your way of "inserting paradoxes" via word games/misuse.
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.
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- #56
wuliheron
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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.
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.
- #57
Mentat
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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.
- #58
drag
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Greetings !
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.
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.
- #59
ahrkron
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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?
Even if that was the case, why would that pose a paradox?
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.
- #60
Royce
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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.
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.
- #61
wuliheron
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"The more I know, the more sure I am I know so little.
The eternal paradox."
James Clavell
The Zen and Taoists like to say they are just a beginner. :0)
In the beginner's mind there are many possibilities,
but in the expert's mind there are few.
- Shunryu Suzuki
- #62
Lifegazer
The point is that your existence is confirmed via thought. You cannot confirm your existence without your thoughts. Therefore, there is no logical-legitimacy in your statement.
You know *nothing*? I find it ironical that people who adhere to such philsophy often have a lot to say. No offense intended.
Our sensations are the basis of the known laws of physics. And our physicists are knocking at creation's door. So are our philosophers. You do an injustice to the majesty of our sensations - and I'm not speaking aesthetically here.
- #63
heusdens
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Let:
p : The fact that I exist
q : The fact that I think
Logical assertion:
~p -> ~q (If I don't exist, I don't think)
Which implies:
q -> p (If I think, I exist)
Fact: q
p (I think: therefore I exist)
So, Descartes first tested q, and stated affirmitive that "I think", and then concludes that "I am" (I exist).
The statement "I am, therefore I think" is not following from this, nor directly nor indirectly. While it is true that when I am not, neither I think, it is not the case that when I don't think, therefore I am not.
A stone 'IS', but it does not think. So for a stone the following is true : 'I am'. Being doesn't require thinking. Thinking on the other hand requires Being.
So, Descartes was right in that, and made the logical conclusion that from the fact that he was thinking it can be concluded that he exists/is.
This is just based on the premise that thinking requires being.
Nowhere it says however that being requires thinking. A stone is, but does not think. A river is, but does not think. The universe is, but does not think (#)
(#) although it can be argued that we are a part of the universe, and we think, it follows then also that the universe thinks...
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- #64
drag
Science Advisor
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Greetings !
)
?
this type of sensations (like humans
who can think and invent). Anyway, I'm not
sure this methaphor is really helpfull here.
think about has entities and relations (between
these entities). Now, when you apply any such
reasoning to the Universe you're expecting
everything to have some sort of relation
to anything else. If something apparently should
have no such relations (like the origin of
existence/Universe when considered as a single
total entity - the Universe/existence), then you
can't reason with it. And the rest of the
explanation is in the question above.
(The above is just one of the PoE's many "faces".)
answer - question of mine above should fit.
Also, the recent stuff that comes to mind -
the rules of the game can't explain the game.
Plenty of basicly totally unsolvable (so far
at least) contradictions.
Today, for example, GR and QM appear to disagree.
Why don't we go shouting it's a paradox ?
Because while it may be one, we believe it's
temporary due to its rather limmited and
complicated nature. The PoE poses so many
of the most basic and fundumental questions
and has been recognized for phousands of years,
so we truly accept it (some of us, at least)
as a true(nothing is certain, of course) paradox.
Live long and prosper.
(Thanks for answeringOriginally posted by ahrkron
(Thanks for the reminder
)There isn't
?Because they can have an infinite amount of
this type of sensations (like humans
who can think and invent). Anyway, I'm not
sure this methaphor is really helpfull here.
Because any reasoning we're aware of or can
think about has entities and relations (between
these entities). Now, when you apply any such
reasoning to the Universe you're expecting
everything to have some sort of relation
to anything else. If something apparently should
have no such relations (like the origin of
existence/Universe when considered as a single
total entity - the Universe/existence), then you
can't reason with it. And the rest of the
explanation is in the question above.
(The above is just one of the PoE's many "faces".)
The above explanation should fit. Also, the
answer - question of mine above should fit.
Also, the recent stuff that comes to mind -
the rules of the game can't explain the game.
Plenty of basicly totally unsolvable (so far
at least) contradictions.
Today, for example, GR and QM appear to disagree.
Why don't we go shouting it's a paradox ?
Because while it may be one, we believe it's
temporary due to its rather limmited and
complicated nature. The PoE poses so many
of the most basic and fundumental questions
and has been recognized for phousands of years,
so we truly accept it (some of us, at least
)as a true(nothing is certain, of course) paradox.
Live long and prosper.
- #65
heusdens
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I don't believe that. If ALL we had were our perceptions and sensations, we would have never been able to discover most of the physical laws. How could electro-magnetism, the nuclear weak and strong forces have been discovered without instruments?
Can you imagine that?
Physics does NOT describe our perceptions and sensations of reality, but describe the ACTUAL PHYISICAL world.
I can repeat that 10 MILLIONS TIMES, but you still keep denying that.
Physics decribes the world OUTSIDE OF OUR SENSATIONS, PERCEPTIONS and THOUGHTS, or the MATERIAL WORLD which exists INDEPENDEND of our MIND.
- #66
Lifegazer
All knowledge is derived from the reasoned analysis of sensation. Of course, it can be argued that mathematics and certain 'concepts' are derived from reason alone. But all scientific knowledge is formulated through sensation.
All physical-law is formulated upon, and confirmed by, sensation. Primarily the sensation of 'sight'.
- #67
Mentat
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The point is that too many people think they look smarter by doubting everything they learn. They think that to doubt what you learn is to have true knowledge. This is not true (according to Descartes), and really makes you just as good as a person who never learned it (because what good is taking in knowledge, if you're not going to do so with any kind of certainty? People who have never learned that bit of knowledge also don't have certainty on the matter, so you're no more knowledgeable than them), and perhaps worse, because you have given yourself the opportunity to know more, and have not taken advantage of it.
- #68
drag
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I've been wondering for some time LG - how
did you arrive at this general "conclusion"
in the first place ?
Live long and prosper.
- #69
Mentat
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How is that a paradox? It just means that you are progressing in knowledge. I've heard this before, and just disagree because learning that there is much more to learn is a positive thing. It shows that you have acquired some wisdom, and is not to be looked on as contradictory to learning.
I've heard this one too, and while I agree, I don't see the point. If someone is an expert, why do they need possibilities? They've already accomplished one (or perhaps more) of the possibilities that they had before them, and that is true accomplishment - while the one with just possibilities has yet to accomplish anything.
Oh well, I guess this isn't the thread to discuss old philosophies in.
- #70
Mentat
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Well, if I may speak for lifegazer, he's shown before that that which we reason on is first "sensed/percieved" and then reasoned on. IOW, if I were to reason on why a comet's tail points away from the sun (for example), I would have to have already perceived the existence, both of the comet, and of the comet's "tail".