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If I tell you that every claim I make is exaggerated by 10%--and you suspect I'm telling the truth--then by how much should you assume I'm exaggerating?


If by "claim" I meant literally quoted figures, then the answer is (sqrt(1+4*0.1)-1)*50% = 9.1608% (since 9.1608% plus 9.1608% of 9.1608% = 10%).

But the truth of this statement cannot be assessed unless all its implications are compounded. If I'm saying 10%, then I'm implying that I exaggerate by only 9.1608%, which is then the "real" claim I'm making.

Therefore, I must only be exaggerating by (sqrt(1+4*0.091608)-1)*50% = 8.4472%. But the fun doesn't stop there, because then since I'm really implying that I'm only exaggerating by 8.4472%, I must be exaggerating by even less.

Unfortunately, the infinite sequence here approaches 0% (I was hoping it would approach some finite value). So does this mean I'm not exaggerating at all? But then in what sense is my original claim true? Surely I'm lying! So my answer is that there is no answer that makes full sense to this riddle. Unless you stick with claim meaning literally quoted figures. I could have rephrased it to say that, which would make the riddle have an answer. But sometimes I prefer riddles with no answer, since they can teach you more in struggling to find one.

I find this riddle amusing because I've been thinking a lot lately about the nature of truth: to what extent should we marry truth to language and literal statements, and to what extent does it refer to the meaning behind the statements? I tend to prefer the latter, but I can see why sometimes it leads to confusion and absurdities which is possibly why logicians prefer to deal with truth more literally. However, once you do that you open a whole new can of absurdities. In both cases, I think the problem stems from considering truth to be a binary function... there are usually an infinite number of ways in which any given statement could be (and is) not-quite-right, but that doesn't mean we should say the statement is wrong. We should treat truth more as a measure of how well the structure of the concepts related by the statement corresponds with the structure of the world... and to what degree the person expressing the statement understands what he means by it and to what degree (s)he knows what part of the world it corresponds to (which always depends on context and surrounding structure). It's never going to line up perfectly, but you can still learn things and express things by making statements, even though you know they are never going to be quite right. But now I'm getting off topic from my riddle. I think I have a lot to say on the nature of truth, but I've said it somewhat poorly and disorganized here. I'll try and clean it up a bit sometime and say it better.

Comments

( 21 comments — Leave a comment )
billings
Jul. 14th, 2005 05:23 am (UTC)
Read much philosophy? I'm starting off St. Thomas Aquinas' Summa Theologica right now, and while it's slow going so far, you would probably find the perspective interesting. The proof of the existence of God is about what you'd expect it to be - a good narrowing of assumptions for a believer, rubbish to anyone else - but I think his arguments on the absolute goodness of God, the nature of goodness, etc. apply to what you're talking about.

The idea is that we as beings, existing through God, strive towards the infinite goodness of God. All material things are finite, however, including such material things as solid information. If we hold that truth is good, then clearly our material conception of truth must be flawed in some way, as an absolute truth would be absolutely good, which only lies in one place.

Not that I think you'd necessarily buy into all that, but it's certainly a question that's been investigated. And I've probably screwed up my explanation a whole lot and someone better read will correct my naive extrapolation from the 50 pages I've read. :)
spoonless
Jul. 14th, 2005 08:59 am (UTC)

Read much philosophy? I'm starting off St. Thomas Aquinas' Summa Theologica right now

I do a lot more thinking about philosophy, and discussing it online, rather than reading--which is arguably not the best route--but I'd like to read more if I had the time. I definitely consider it a worthwhile subject.

Although I'd suspect my tastes in philosophers would be pretty far from yours. I don't read theists for a good reason. I'd like to understand what they're trying to say, but the fact is... I have no clue what they're referring to when they use words like "God" or "divine" which are just gibberish to me. So the effort it takes for me to get even a small bit of meaning out of their writings is incredibly large with little to no payoff. Ultimately and ideally, I'd like to understand how everyone thinks... because I believe everyone says the things they say for a reason... but comprehending theist thought will have to be at the far end of my quest, if I ever get to that point.

The idea is that we as beings, existing through God, strive towards the infinite goodness of God. All material things are finite, however, including such material things as solid information.

Sorry, I don't know what "existing through God" or "infinite goodness" means at all. And I doubt you could say anything which would give them meaning to me.

If we hold that truth is good,

Truth is a more powerful word to me than good. Good is an opinion, a desire; truth exists without opinion or desire.

then clearly our material conception of truth must be flawed in some way, as an absolute truth would be absolutely good, which only lies in one place.

I don't see how truth could lie in a place. It doesn't exist at a point in time or in a location... any more than love or the internet does. I'm a representational realist which means I believe a Reality external to the mind exists but we experience it indirectly and we represent it with our mental concepts. I capitalized Reality because it's one of the things I think people might be personifying when the use the word God, but that's just a tiny hunch because there's a whole lot of other contradictory things they say they mean by it at different times. I see truth as a relation between our concepts and Reality... it's an assessment of how accurate our representations are. I don't think this definition of truth fits very well with the way you (or Aquinas) is using it. But maybe if you map your "absolute truth" to my Reality and your "material conception of truth" to my truth then it makes sense. Sort of. But the problem is "material conception of truth" also makes me think of belief, which is a separate thing (and far more subjective) from truth.
billings
Jul. 14th, 2005 02:52 pm (UTC)
I do a lot more thinking about philosophy, and discussing it online, rather than reading--which is arguably not the best route--but I'd like to read more if I had the time. I definitely consider it a worthwhile subject.
I did and have done a lot of the same - I'm frequently accused of thinking too much after all - and while discussion is obviously helpful, I'm pretty certain that serious book learnin' has to be the primary resource for anything if you want to know anything about a topic. Withdrawing into online culture can make you into a bit of a cyberhick. (sounds like an LCC class or something)

If you've never read plato's account of socrates' defense, that's a pretty good place to start on the subject of truth. Plato has a distinctly different idea of truth which has its own problems, but it fits in with your concept of "Reality".

Sorry, I don't know what "existing through God" or "infinite goodness" means at all. And I doubt you could say anything which would give them meaning to me.
Aquinas' definition (possibly other philosophers as well) is that good is that which we all desire, and inasmuch as we understand anything to be desirable to us, we understand it to be good. With our being distinctive and imperfect individuals in reality, however, goodness as we perceive it is still subjective to us. E.g., say that two men are stuck on an island and one of them may survive through cannibalism, but if they refrain they both will die. We may for now assume that being is better than non-being for both the men, so perhaps it is acceptable to slay the other in the night - but if a ship rescues them, it is better to its captain to take on a man who is not capable of betraying his friend in such a manner.

As for "existing through God"... well, there's nothing fancy about that, except the idea that we do not exist through ourselves. We exist due to some other cause which, at its root, is totally unknown to us. Catholics and other monotheists hold that cause to be an essential "I am", "God", the nature of which is learned through divine revelation. Which of course could be a euphemism for chicanery of some sort or another, or it could be something else, depending on your perspective.

Truth is a more powerful word to me than good. Good is an opinion, a desire; truth exists without opinion or desire.
Good is an opinion when others wish to tell you what is good and what is not; likewise for truth. Why should you seek truth and not lies, though? Truth is thus in some way desirable; if we can say that other things besides truth are desirable to the rational mind, then we may describe the desirable as being "good" and the undesirable as being "bad".

I don't see how truth could lie in a place. It doesn't exist at a point in time or in a location... any more than love or the internet does. I'm a representational realist which means I believe a Reality external to the mind exists but we experience it indirectly and we represent it with our mental concepts.
This is why philosophical discussions are still hard for me... words really do have strict meanings in this context, and when I say that "truth resides in a place that is God", that's just totally wrong. :)

I agree with you on the representational realist perspective. I don't think that constitutes a philosophy, however.

I capitalized Reality because it's one of the things I think people might be personifying when the use the word God, but that's just a tiny hunch because there's a whole lot of other contradictory things they say they mean by it at different times.

In your search for truth and reality in the physical realm, have you ever come across a seeming contradiction or inconsistency that was subsequently made clear or otherwise eliminated?
billings
Jul. 14th, 2005 04:07 pm (UTC)
I'm pretty certain that serious book learnin' has to be the primary resource for anything if you want to know anything about a topic. Withdrawing into online culture can make you into a bit of a cyberhick. (sounds like an LCC class or something)
These pronouns are terrible! Ain't no judgement on you, my friend - I make the above claims based on personal experience/mistakes.
spoonless
Jul. 18th, 2005 02:17 am (UTC)
Sorry for the delay, I've been distracted by other things.

If you've never read plato's account of socrates' defense, that's a pretty good place to start on the subject of truth. Plato has a distinctly different idea of truth which has its own problems, but it fits in with your concept of "Reality".

I have it on my bookshelf, actually... at the end of a collection of Plato's works. But I never finished reading through them, got a bit bored during some of his ethics discussions. Maybe I'll read through apology soon, since epistemology is something I'm much more interested in.

Aquinas' definition (possibly other philosophers as well) is that good is that which we all desire, and inasmuch as we understand anything to be desirable to us, we understand it to be good. With our being distinctive and imperfect individuals in reality, however, goodness as we perceive it is still subjective to us. E.g., say that two men are stuck on an island and one of them may survive through cannibalism, but if they refrain they both will die. We may for now assume that being is better than non-being for both the men, so perhaps it is acceptable to slay the other in the night - but if a ship rescues them, it is better to its captain to take on a man who is not capable of betraying his friend in such a manner.

My view is that all good is relative. Something can be good for a particular purpose, but it can't just be intrinsically "good". I think your example of the island illustrates this well. At the very least, even the most universal good is still relative to humankind, and could be different for an alien species with different biological needs. This is why "infinite good" makes no sense to me... and if I'm guessing right at the meaning, a better term for it would be "absolute good" or "universal good" (although neither would be something I'd believe in.)

I agree with you on the representational realist perspective. I don't think that constitutes a philosophy, however.

Well, there are many philosophers who believe in alternatives. In fact, I get the impression that realism is not all that popular in philosophy these days. It's a bit more popular among physicists, but nowhere near universal. I often find myself debating it with others in real_philosophy and other communities. Other alternatives to representational realism are direct realism, transcendental realism, phenomenalism, idealism, transcendental idealism, dualism... and probably a lot more that I'm not as familiar with. Although maybe the way I expressed what I take representational realism to be made it sound a bit more general than it is... for instance, implications of it which seem somewhat obvious to me but you or others might find to be an additional leap.
spoonless
Jul. 18th, 2005 02:51 am (UTC)

In your search for truth and reality in the physical realm, have you ever come across a seeming contradiction or inconsistency that was subsequently made clear or otherwise eliminated?

Yes, we call them "paradoxes". Happens all the time. If I see two things that I know to be true which appear to conflict, then I know there must be something wrong with the way I'm thinking about one (or both) of them.

But in this case, I see one system of thought (atheism) which appears entirely consistant, and another system of thought (theism) which is riddled with contradictions which I don't understand. So the choice seems pretty clear to me. But I guess it depends on a lot of different assumptions which I take for granted which you may not.
billings
Jul. 14th, 2005 02:56 pm (UTC)
I see truth as a relation between our concepts and Reality... it's an assessment of how accurate our representations are. I don't think this definition of truth fits very well with the way you (or Aquinas) is using it. But maybe if you map your "absolute truth" to my Reality and your "material conception of truth" to my truth then it makes sense. Sort of.

Reality as you describe it is what I am referring to when I say absolute truth, and the "material conception of truth" is that truth which you and I understand through the representational patterns in our brains.

But the problem is "material conception of truth" also makes me think of belief, which is a separate thing (and far more subjective) from truth.

The truth in Reality, which we assume exists although we do not know it perfectly, is the only truth which is separate from belief. While your belief in the truth you know is founded upon the backs of giants, a story retold and verified countless numbers of times, it is still a belief.

Of course the difference you're talking about is the difference between my belief in the validity of the material in my genetics text this semester and my belief in God. I can explain a whole lot about how the genetic code is transferred from person to person, how it is transcribed and translated in a general sense, and so on and so forth, and I know that you can go out and perform experiments and say "Yes, that is true." All they really have to believe is that what they see is true, and all the rest can be built up by personal experimentation if such is desired. Yet my belief in God requires a further assumption which I can provide no basis for, the validity of which I have only been able to come to through a subjective experience that is entirely individual. In fact, I cannot even definitively prove to someone else that I believe in God.
spoonless
Jul. 18th, 2005 02:38 am (UTC)

The truth in Reality, which we assume exists although we do not know it perfectly, is the only truth which is separate from belief. While your belief in the truth you know is founded upon the backs of giants, a story retold and verified countless numbers of times, it is still a belief.

I think that all belief is separate from truth--in that, given any truth you are capable of believing or not believing it. Unless there is some truth so obvious we're incapable of not believing it. But if that's ever the case, it's a rare exception.

Of course the difference you're talking about is the difference between my belief in the validity of the material in my genetics text this semester and my belief in God.

I think this may be a misinterpretation of what I was getting at. I wouldn't say there's a huge difference between the type of belief you have in your genetics material and the type of belief you have in God. The main difference, from my perspective, is that you just happen to be wrong about the latter. Either way, your beliefs should all be founded on your experience (and those you've learned through experience are trustworthy and knowledable). Whether or not that experience is verifiable by others does not play a huge role in belief, I don't think. If God has spoken to you directly, and shown you things you can't explain otherwise (after giving it an honest effort), then I could hardly blame you for believing in God. But it wouldn't help convince me or anyone who has not had such an experience. It's a lot easier for me to believe that psychology plays a role in generating such perceived experiences rather than divine intervention.
sid_icarus
Jul. 14th, 2005 06:45 am (UTC)
You could say both:
"every claim I make is exaggerated by 10%"
-AND-
"91.608% of the claims I make are exaggerated by 9.1608%"
and be telling the truth. I think.

(I was gonna say 90.9090...% (10/11) till I read your answer.)
gustavolacerda
Jul. 14th, 2005 10:06 am (UTC)
This reminds me of this paradox.

The standard solution here uses epistemic logic and is analogous to your "9.1608%" answer... they explain why you can't apply it again.
nibot
Jul. 16th, 2005 07:59 pm (UTC)
hey, I'm going to be down in Santa Cruz tonight/tomorrow.. give me a call 510-520-9697.
nibot
Jul. 25th, 2005 05:57 pm (UTC)
apologies for the false alarm
thanks for the call! i was indeed in santa cruz! i got tied up in this whole "family" and "wedding" thing and unfortunately wasn't able to escape for various escapades. (sadness!) perhaps next time.
spoonless
Jul. 25th, 2005 06:55 pm (UTC)
Re: apologies for the false alarm
ahh, was wondering what happened there. So you have family in santa cruz?

Oh yeah, did I ever mention that I almost moved in with Kathy Cooksey a couple months ago? My other roommates and I were at the time looking around at places to move to, and she had just the right number of bedrooms free. For at least a week, we were pretty sure that's what was going to happen, but it fell through at the last minute and we ended up staying in our current place. I mentioned that I read your livejournal and she asked something like "OMG Tobin, what's he doing? crawling through the jungles of [] by now?" (can't remember what country or continent the [] was!)
go4thnx
Jul. 18th, 2005 12:59 pm (UTC)
to what extent should we marry truth to language and literal statements, and to what extent does it refer to the meaning behind the statements

I loath the word 'should', it has too many implications that are too subjective... perhaps it is previous english teachers 'use the active voice'. Although I haven't the breadth or depth in any of the readings billings seems to have, I believe that language is a fundamental barrier to truth. To answer your question directly, never.

The very word truth is laden with denotations and connotations that are not easily 'whisked away' - Perhaps we should start with your accepted definition of truth, which is...?

I believe that truth is experienced, that you cannot rely on the input of one sense alone to convey truth. I further believe that language, which arguably relies on more than one sense, is by itself insufficient. Have you sat through a lecture leaving with only a modicum of understanding, and then later had a lab exercise reveal the whole picture to you?

But it wouldn't help convince me or anyone who has not had such an experience.

I think this hits the nail on the head Jeff. Experience is one of the hardest things there is to relate. How do you distill the combined input of all your senses, emotions, and perceptions into a meaningful expression of language? I believe that the short answer is: you don't, that's why it's called experience. I further believe that experience is the only reliable path to truth; language, love it as I do, is but a crutch.

Now here is where you tell me, no, no, no - I meant math (as a language) not english which certainly seems like it must be less malleable, but I think that's just inexperience talking there ;)
spoonless
Jul. 19th, 2005 04:01 am (UTC)

The very word truth is laden with denotations and connotations that are not easily 'whisked away' - Perhaps we should start with your accepted definition of truth, which is...?

I stated my working definition in a post above here:

"I see truth as a relation between our concepts and Reality... it's an assessment of how accurate our representations are."

I agree that (as with any word) there are many different denotations and connotations people use when they toss around the word "truth". Which is why I bothered to state my assumptions and my preferred meaning for it. Although I'm sure it got buried amongst everything else.

I believe that truth is experienced

You're probably using a somewhat different definition of truth from mine... which is fine. But I have my reasons for preferring mine. The way I like to say it: Reality exists without being true or false, whatever is is, and whatever isn't isn't. Truth comes when you try to understand reality... it's a check on how good a job you're doing. But that understanding doesn't always come in the form of symbolic language... it can sometimes be better understood in terms of internal non-verbal concepts, or "truth" could refer to the subjective reality we each live in and how well it matches up to the objective one outside. Coming to realizations and conclusions which do not involve language (as in, symbols) is one type of truth... which I think is the one you're emphasizing here. Often, it can be the most potent kind of truth... because it's closer to raw experience itself rather than one layer removed.

Have you sat through a lecture leaving with only a modicum of understanding, and then later had a lab exercise reveal the whole picture to you?

While I agree with the point you're making... you unfortunately asked the wrong question to the wrong guy :) I did very poorly in all my labs at Tech and very well in all my lecture classes... most of the lab exercises I found horribly confusing and made me want to tear my hair out. I'm particularly bad at following certain types of written instructions... perhaps this is why I don't cook either. At any rate, I see what you're saying and I agree. There have been many times when relating something back to a personal experience I've had helped me understand an abstract concept better.

Now here is where you tell me, no, no, no - I meant math (as a language) not english which certainly seems like it must be less malleable, but I think that's just inexperience talking there ;)

I wasn't thinking specifically of math when I said "language" but I think it has the same issue of truth... how literally should we define truth? But there's that word again, "should". The reason I use it is because I think this is an issue where there are two (or more) different ways of using truth and the question is which one serves our purposes the best. The purpose here being clarity and communication. But you're right, without me stating what the purpose is, "should" becomes meaningless.
go4thnx
Jul. 19th, 2005 03:45 pm (UTC)
I stated my working definition in a post above here:

"I see truth as a relation between our concepts and Reality... it's an assessment of how accurate our representations are."

Ah, I didn't look very hard did I.

You're probably using a somewhat different definition of truth from mine...

You're right, I am. In my mind, the relation between our concepts and Reality is always changing, many people like yourself set out to do just that; to better understand some facet of, and thereby change, our (currently) accepted definition of Reality. Again, in my mind, truth is (for better or for worse) more of a binary operand than an real number, which makes its usefulness as a measure less than that of a declaration. For that reason I find it sometimes difficult to use the word truth.

I think it is compliment to be called concise in either verbal or written communication. 'Occam's razor', 'the salient argument', 'simpleness is a measure of creativity', how do you Jeff Jones recognize Truth? Is there a set of tests or do you have some intrinsic understanding that is more difficult to articulate?
spoonless
Jul. 19th, 2005 11:54 pm (UTC)

In my mind, the relation between our concepts and Reality is always changing, many people like yourself set out to do just that; to better understand some facet of, and thereby change, our (currently) accepted definition of Reality.

Right. But the thing we're changing is our representation of reality.. our subjective reality, or our concept of reality. My point in using capitalized "Reality" is to indicate that there is something which we cannot directly know (and will never fully know in any finite number of steps) beyond our subjective concepts. So by Reality I mean objective (or external) reality and by "reality" I mean subjective (or internal) reality... the end of the limit process of grokking which we will never complete.

Again, in my mind, truth is (for better or for worse) more of a binary operand than an real number

I would say even treating it as a real number is an oversimplification. Because assigning a real number to truth would imply that truth is only 1-dimensional. Truth is multidimensional in that any idea we have or statement we express can be wrong in many different ways and on many different levels. No statement we make about the world is ever exactly true, because in order for that to be the case we would need to pin down the definitions of all the concepts involved exactly. And since defining concepts is an ongoing interactive process, and depends on the surrounding structure of our representation of the rest of reality, it's something that won't be exact until the whole of Reality is understood... which will probably never happen, and even if it does there will be no way to be certain we're really done.

That said, binary truth is useful for a variety of applications... particularly, where we are working within an understood framework of axioms (such as mathematics, or a particular culture's morality) where we're pretty sure the starting axioms are good enough that we don't need to worry too much about in what ways they might be not-quite-right. You can talk about truth within such a system as relative to how much you trust the axioms, but in the end the statements you make can only be true in the absolute sense to the extent that the axioms are right... and that gets us right back to my more complex multidimensional idea of truth.

how do you Jeff Jones recognize Truth?

I recognize truth when I see concepts I've formed from past experience matching up with all new experiences, and being consistant with each other. I didn't follow the rest of your question (what does "the salient argument" or "simpleness is a measure of creativity" mean?).
(Anonymous)
Jul. 20th, 2005 01:04 am (UTC)
... which will probably never happen, and even if it does there will be no way to be certain we're really done.

I couldn't agree more.

... and that gets us right back to my more complex multidimensional idea of truth.

An obvious extension really, I can accept this.

I recognize truth when I see concepts I've formed from past experience matching up with all new experiences, and being consistent with each other. I didn't follow the rest of your question (what does "the salient argument" or "simpleness is a measure of creativity" mean?).

I follow the identical method, though I get frustrated when I don't have enough experiences to form a concrete[1] truth, the multiple dimensions you point to provide an convenient excuse for the difficulty therein. In times of forced decision making, in the absence of sufficient experience, sometimes one of the truth's contending for the label 'concrete' must be chosen. The criteria I use to select that truth is my gut (intuition), my question to you was what is yours?

[1]By concrete I mean an understanding accurate enough to predict (with some degree of accuracy) the outcome of a similar experience in the future.
spoonless
Jul. 22nd, 2005 12:13 am (UTC)

In times of forced decision making, in the absence of sufficient experience, sometimes one of the truth's contending for the label 'concrete' must be chosen. The criteria I use to select that truth is my gut (intuition), my question to you was what is yours?

Sure, I would call it intuition too. I think all concepts are open and only partially formed and malleable. But some more than others. For the more rigid concepts I use careful reason and good judgement. For the more slushy ones, particularly when I don't have time to make them any more "concrete" (if that fits with your usage of the word), I use intuition or gut feeling. I think these are both really two forms of the same thing, though... intuition is just a faster form of reasoning where you cut a few corners and don't spend quite as much time worrying about the details.
mr_joe_baker
Jul. 21st, 2005 08:33 am (UTC)
Hey what about Lao Tzu you fuckin dicks
Oh and it's about time we start making our own truths. It is the the 21st century after all.


Truth=efficiency.
spoonless
Jul. 22nd, 2005 12:07 am (UTC)
Re: Hey what about Lao Tzu you fuckin dicks
Troll much?
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