Bet You Can't Define "Truth"

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Truth:


[/smartass]

Bet you can't define "Double Post"

From Merriam-Webster,

n: noun
Inflected Form(s): plural truths /'tr�[th]z, 'tr�ths/
Etymology: Middle English trewthe, from Old English trEowth fidelity; akin to Old English trEowe faithful -- more at TRUE
Date: before 12th century
1 a archaic : FIDELITY, CONSTANCY b : sincerity in action, character, and utterance
2 a (1) : the state of being the case : FACT (2) : the body of real things, events, and facts : ACTUALITY (3) often capitalized : a transcendent fundamental or spiritual reality b : a judgment, proposition, or idea that is true or accepted as true <truths of thermodynamics> c : the body of true statements and propositions
3 a : the property (as of a statement) of being in accord with fact or reality b chiefly British : TRUE 2 c : fidelity to an original or to a standard
4 capitalized, Christian Science : GOD
- in truth : in accordance with fact : ACTUALLY

Actually, you can define truth and I just did. Now the question should be, "I bet you can't explain your understanding of the term truth to the extent that it adheres to it's definition."

maybe he means truck, not truth:

truck


1. Any of various heavy motor vehicles designed for carrying or pulling loads.

2. A hand truck.

3. A wheeled platform, sometimes equipped with a motor, for conveying loads in a warehouse or freight yard.

4. One of the swiveling frames of wheels under each end of a railroad car or trolley car.

5. A set of bookshelves mounted on four wheels or casters, used in libraries.

6. Nautical. A small piece of wood placed at the top of a mast or flagpole, usually having holes through which halyards can be passed.

7. Chiefly British. A railroad freight car without a top.

Exactly. Thats what i meant, you just worded it better.

I think some of the definitions from urban dictionary might help a little bit more ( http://www.urbandictionary.com/defi...?term=truth&f=1 ) Examples:

Something that can be proved as beneficial or relavent. But nothing is true on this earth.

Everything is a lie, no matter what Wal*mart tells you.

And if you do know the truth, you are either..

A.) God

B.) George W Bush

or C.) Yo momma.

The truth is out there, but I forgot the URL.

-----------

The thing you're least likely to encounter all day

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the only real anti drug program thats actually going against smoking.

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ANDTHE BEST ONE:

What you can't handle.

MICROSOFT WINDOWS ERROR:
I'm sorry.You can't handle the truth.
Would you like some nice lies
instead?

You were 5 years old. You believed in Santa. Tragically you passed away. Was santa true?


Response: no because everyone else knows santa isn't real


Well if everyone believes the same thing isn't that what truth is?

Is truth our human perception of reality? If it is then wouldn't it be true that the earth was flat if you lived in the 13th century. Or that Greek Gods exist. If it was true for these societies when they existed is that not what truth is? millions of people have lived and died believing in things like these over time.

Only our perception of truth has changed in our time. So is what we percieve today really true?

I do not believe in a perception based truth. There are some instances that regardless the amount of perception you put into it, you cannot refute certain truths. You are either unaware of it or lying to yourself.

Take gravity. Believe in it or not, it exists and it is True that gravity will pull you to ground when you jump from a 60 story building trying to fly becaues your "perception" was that you could fly by pure will.

Just so, there is no Santa Claus, regardless if you die as a little girl not knowing the truth. Even if everybody else in the entire world believed in the Santa Claus tale, it still wouldn't make it true that there was a man who lived in the north pole with an army of Elfes to make toys which he would deliver to them on Christmas eve/Christmas morning. Believing doesn't make it so.

You were practicing this... wern't you?!!

Sort of. We had a debate in a class "critical & logical thinking" on this subject. The debate came up again with a few friends a few months ago.

I've read a bunch of encyclopedia defintions and looked into other resources. It seems like the more I research truth the further I get from comming to a conclusion thats acceptable.

It depends on what you mean by truth. Two people can look at a picture from different angles and see something different. Both of them are seeing "the truth", but from a different angle.

In fact, perception has a way of making things true. For example, assume that the stock market is not crashing. Now let's say a news caster breaks in and says that the stock market is crashing (his perception). What is everyone watching probably going to do? Pull out their stock of course. That could start a run on the stock market and then it really would start crashing. So, perception made reality (truth) in its own image.

Now, I'm a staunch believer that there is some objective truth out there - unfortunately, I also believe you are unable to fully see it unless you take yourself outside the reality you are observing (impossible unless your God). So, although it exists, and we can strive for it all we want (and we should), we will never actually know absolute truth.

Ahhhh... a discussion of philosophy always warms the heart

Matt Fahrenbacher

Whatever the mass agrees on...

The truth is anything you're not too terribly conflicted about when you're trying to figure out if you were misled or are misleading people.

*insert picture of Jimmy Page morphing ages as 'The Seeker" in that Led Zep album gatefold*

Truth is all about perception, if you were going based on the "truth" of the society you lived in and it believed the world was flat, then that would technically be the truth until proven otherwise. To the religious, God is the truth until proven otherwise. To the atheist, God is not true until proven otherwise.

The catch is trying to differentiate between "perceptive truth" and "absolute truth". The two are completely different and yet we use them interchangably.

Fantastic point - in fact, I think absolute truth (for technical reasons) has a capital T. So if we mean perceptive, it's "truth," if we mean absolute, then "Truth."

Matt Fahrenbacher

But isn't absolute truth subject to ones perception and interpretation?

No, that's perceptive truth.

How can one say there is an "absolute truth" other than that it would be the overall perception of humans once they see it for themselves, mathematically, scientifically or physically? Everything is up for individual interpretation. Everything is individual truth, it's what you believe (with as little doubt as possible) and what neither you not someone else could convince you of otherwise.

EDIT: I'm generalizing of course, because many things we see physically are not necessarily the truth to all. There are some things that are seen as absolute by the vast majority of people, especially mathematically and scientifically, but scientific fact is especially subject to change over time.

Exactly. The problem is we all talk about truth as if it is absolute. But none of us can ever know the absolute truth. All we ever know is the perceptive truth. As far as I am concerned, absolute truth as human understanding is a fallacy, but a fallacy that we must strive toward nevertheless.

Truth - that which is, irrespective of belief or disbelief of the observer.

BlackGriffen

Sure, in fact that's what perceptive truth is. It's like I said that I'm a man-whore... wait, that's patently false. Er...

The trick is being able to define something in an absolute setting - everything we know is through our perceptions.

If I close my eyes, does everything go away around me because I do not percieve it anymore? Actually, there is a philosophical line of thought (I forget the philosopher's name) that believes that all reality was perception.

Think if we were in a computer program - it would be possible that nothing that we percieved existed to begin with, just electronic pulses between synopsis in our brain. That doesn't change the fact that there is something that exists, namely the perceiver.

Now, think about this: let's assume that there is no such thing as absolute truth. Therefore, the statement that "I am holding a rock" cannot be true or false, as there is no such thing as absolute truth. But that logically doesn't make any sense! I'm either holding the rock or I'm not- it's a tautology. Depending on your reference point, it may appear that I am or am not holding the rock, but that doesn't change the fact that I am or am not holding the rock.

Another fun statement: "There are no absolutes." Well, that's an absolute statement, so that's a contradiction. Therefore, there must be some absolute truth... perhaps just that the statement that "there is absolute truth" is true, but absolute truth must exist nonetheless.

Game on

Matt Fahrenbacher

There is also a difference between scientific fact and truth. Scientific fact is what science to that point has determined to be true. It may be patently false, and it would fall under the category of perceptive trith for the time being.

Like someone else brought up: just because people in the past thought the world was flat did not make the world flat. People behaved as if the world was flat (boating patterns), and so that percieved truth effectly reality, but that didn't make the earth flat in any absolute sense.

Matt Fahrenbacher

Another problem is that we always try to explain "truths" through language, whether it be written, oral, or other. Language is an imperfect medium. There's always ambiguity in language, making it neigh impossible to determine meanings and truths of even the most simple conjectures.

Truth is truth until a better truth comes along.

Think of scientific theories and how they change: From Newton's gravity to Einstein's warpings of space-time.

Of course, technically, the original truth was never part of what truth absolutely came to be.

There is no absolute truth that any human can grasp, although there may be brief snippets we perceive, here-and-there.

Is math ambiguous?

I guess this is the best definition of "absolute truth" that we'll come across. We can define it, but doubtful if we'll ever truly grasp it on the whole.

Well, that question sure is.

But seriously, certain areas of math are quite ambiguous. The Banach-Tarski paradox describes how, using current mathematical practices, one can prove that it is possible to take a sphere with volume x, cut it up into a finite number of pieces, and reassemble those pieces into two spheres, both with a volume of x.

Right... What kind of "truth" is that?

To be fair, though, when I made my comment about language being ambiguous, I wasn't really referring to the language of mathematics.

I'm not familiar with the banach-tarski paradox, strange (link please?)...but this reminds me of the simple proof in which 2=1, but the problem was that there was a divide-by-zero, I wonder if certain mathematical rules are broken in the example you mention, but perhaps not.

No, in the aformentioned paradox, the "trick" lies in the usage of a certain step that has been used to "prove" many other mathematical ideas that most mathematicians hold to be "true". We have not yet been able to prove many of these ideas without that step, and people continue to use it as if it were "true". Banach and Tarski were trying to show the mathematic community just how ridiculous they were being by continuing to use this step in their proofs. However, it didn't stop them.

As far as linking the paradox, I haven't found the ideal link, so I'll just point you to Google. There are a ton of pages out there on the subject as it is a fairly popular paradox.

Interesting. In the paradox, it looks like the "Axiom of Choice" isn't known to be absolutely true (or at least certain exceptions remain to be absolutely defined).

Exactly, which just goes to show how even mathematics and "truth" can not go hand-in-hand. For how can an axiom (a self-evident or universally recognized truth) not be true?

Well, infinite divisibility can make strange things occur that can't happen in the "real world". An atom, for example, can be moved, but being sliced into small pieces and moved about how we like isn't a feature I know of.

You can get other rather unintuitive ideas from fractals, for example the Cantor middle-thirds set. http://www.math.buffalo.edu/~sww/cl...T/COMPACT2.html

If you ignore the compactness stuff for a moment, essentially you have a subset of [0,1] that has measure 0 but there exists a bijection from it to [0,1] i.e. it has length 1! That seems highly unintuitive, and in fact it should be impossible to construct such a set in the "real world" because matter is not infinitely divisible... at least not smoothly.

Matt Fahrenbacher

Well, an Axiom (a given) is always true. The question is if under the mathematical system they have developed, are they assuming that the axiom of choice is really true? Depending on what axioms you hold to be true to begin with, axioms that are held to be true in different mathematicaly systems need not hold.

Matt Fahrenbacher

1. I'm pretty sure it was FINITE divisibility.

2. Axiom of Choice

1. I'm pretty sure it was FINITE divisibility.

Actually it was infinite divisibility. Sure, you were breaking up the circle into 5 (or four) sections, but the edges weren't exactly your everyday cuts. They were ragged, and probably impossible in terms of real world matter.


2. Axiom of Choice

beh, typed too fast, you know what I meant I'm just not sure they assumed the axiom of choice to be true when presenting the problem. If the axiom of choice turns out to not be true in the given situation, then the paradox is invalid in any system where the axiom of choice is valid.

Matt Fahrenbacher

This is what I was questioning, but it apparently hasn't been figured out yet.

Of course it is impossible in terms of real world matter. That's not the point. The point is that given our system of mathematics and the axioms we hold "true", it is possible.




They did assume the Axiom of Choice to be true. They were then (basically) attempting to disprove it by contradiction.



I'm not really sure what you mean by "given situation". An axiom, by definition, is always true. If it isn't, it isn't an axiom. If the Axiom of Choice turns out to not really be an axiom, then we are going to have to go back and re-prove a lot of things...

Gah, I had a response, and then iTunes and safari started freaking out together and hogging as much processor as they could

Of course it is impossible in terms of real world matter. That's not the point. The point is that given our system of mathematics and the axioms we hold "true", it is possible.

Sure, but you get all kinds of wacky things that don't make any sense in the real world with infinite divisibility - the only reason they seem wacky is because in the real world you don't have infinite divisibility for matter (although you do for time and such, or so we think). Case in point was the set with length 1 but measure 0 - the Cantor middle third set.

What this paradox shows us is that with infinite divisibility, area and volume and the like are not necessarily as nicely defined and easy to think about as in the "real world." It only seems paradoxical from an intuitive stand point, because it does seem to imply that 2 equals 1, but the cantor set seems to imply that 1 equals 0 and that's not really paradoxical - it just assumes infinite divisibility.


They did assume the Axiom of Choice to be true. They were then (basically) attempting to disprove it by contradiction.

Sounds good to me.



I'm not really sure what you mean by "given situation". An axiom, by definition, is always true. If it isn't, it isn't an axiom. If the Axiom of Choice turns out to not really be an axiom, then we are going to have to go back and re-prove a lot of things...

In any given situation, you can assume whatever axioms you want to be true. Like you can assume that the shortest distance between two points is a circle - then instead of talking about Euclidean geometry, you're talking about Spherical geometry. Essentially, based on what axioms you assume to be true, you get different results. So, all I was saying is an axiom is only true if we assume it to be so. There's plenty of different mathematical structures that are created where certain field, group, etc axioms are assumed to be true or false.

Matt Fahrenbacher

Truth is what you believe in.

I agree that there are a ton of strange things you can do with infinity. There's the Cantor set, the cone which can hold a finite amount of paint but would take an infinite amount of paint to cover, etc, etc. But these are in a completely different set than the Banach-Tarski paradox.

The thing is, the Banach-Tarski paradox doesn't involve infinity and lives in a completely different realm of mathematics. Plus, it's a paradox meant to prove something false, unlike the others.

The ones you mention are indeed interesting, but they are fundamentally different than the B-T.



Don't you mean "arc" instead of "circle"? Anyway, what you say is not entirely true. I think you are talking about transcending different coordinate systems and realities. The B-T paradox does neither. An axiom is an axiom and is always true. If you are talking about coordinate system A, then the axiom must say as much. An axiom can't be true in some situations and false in others. The B-T paradox is the same. It can't be true sometimes and false other times. It either is, or isn't.


I think we've done a pretty good job of derailing this thread from "truth" to mathematics. It's all your fault, Stradlater!

I agree that there are a ton of strange things you can do with infinity. There's the Cantor set, the cone which can hold a finite amount of paint but would take an infinite amount of paint to cover, etc, etc. But these are in a completely different set than the Banach-Tarski paradox.

Are you so sure?

From http://www.kuro5hin.org/story/2003/5/23/134430/275



The thing is, the Banach-Tarski paradox doesn't involve infinity and lives in a completely different realm of mathematics. Plus, it's a paradox meant to prove something false, unlike the others.

The ones you mention are indeed interesting, but they are fundamentally different than the B-T.

They might be fundamentally different, I do not know. But here is another quote from the article that I think helps my point:



I really think this article is a good read


Don't you mean "arc" instead of "circle"? Anyway, what you say is not entirely true. I think you are talking about transcending different coordinate systems and realities. The B-T paradox does neither. An axiom is an axiom and is always true. If you are talking about coordinate system A, then the axiom must say as much. An axiom can't be true in some situations and false in others. The B-T paradox is the same. It can't be true sometimes and false other times. It either is, or isn't.

"Great Circle" is the technical term for a straight line on a sphere. Considering we're not really talking about the Sphere in free space, but instead as THE space, a circle is an okay word to use.

An axion is not always true. An axiom is only true if you assume it to be true. Here's an axiom:

"All men are pigs"

This axiom could be true in general, I don't know. But we only know it to be true if we assume it to be so.

Now. once you've assumed your axiom, it can only be false if you're mathematicaly system is inconsitent (you've made two contrary assumptions, something that happens a lot in proofs by contradiction).

You can develop different mathematical systems (groups, fields, etc) based on what axioms you assume to be true. The common field axioms doesn't apply to the set of all 3X3 matricies (no multiplicative commutitivity) for example.

Matt Fahrenbacher

Ok, What is "Truth"


... whatever I agree with.

Defining 'Truth' is easy. Identifying it is another matter entirely.

Of course there is "Truth" (or absolute truth). Whether or not anybody ever sees or understands it is doubtful.

We all have our perspectives of the "Truth". Something must exist to have a perspective of it, correct? So doesn't it follow that there must be a Truth for us to have a perspective of?