Can we perfectly define ANYTHING?

[Dymanic]

Maybe it depends on how you define "define"

I often see discussions on various topics grade off into border skirmishes over the proper placement of some definition boundary. Never mind such quagmires as life, intelligence, randomness, atheist, art or species; I can't think of any concept (outside of pure mathematics) that is perfectly definable.

Is rigorous as good as it gets?

Perhaps if, as it has been suggested, mathematics is crucial to understanding, it is because mathematics is one (I'm thinking the only) system of thought that features terms which are absolutely exempt from ambiguity?

You never hear anyone say, "well, it depends a lot on what you mean by Prime...".

Outside the realm of mathematics though, it seems to me that it is possible to take any word in the language, find some deviant example that clearly deserves exclusion from the category, then demonstrate the hopelessness of locating an exact point of divergence from the central meaning of the term. Attempting to solve the problem by creating endless stacks of sub-categories seems to serve only to provide a richer environment in which to play this game.

Is it really a hammer if it's made out of chocolate?

Nothing is clear cut and defined that includes mathematics. Everything is subjective.

[Kiri]

As far as I know, a perfect definition would require perfect knowlege, which is fated to always be in short supply.

I'd say no, then, because all our representations of reality are more-or-less accurate approximations.

[Dymanic]

Nothing is clear cut and defined that includes mathematics. Everything is subjective.

Mathematics may be subjective for some, but for me it's not.

[Akots]

Originally posted by Dymanic


Mathematics may be subjective for some, but for me it's not.

if your viewpoint of mathematics is unique to you, that MAKES it subjective.

Or am i mixing up my 'bjectives again?

Dictionaries are circular, so I doubt we can define anything perfectly.

I mean, we need words to define words, but those first words are defined by words which are defined by words, etc., ... ... ... which are defined by those first words we are trying to define in the first place.

[Dymanic]

if your viewpoint of mathematics is unique to you, that MAKES it subjective.

Yeah, that was a joke.

[Michael Redman]

I can give anything I want a perfect definition. I just can't convey that definition to others perfectly.

I guess I'm not exactly sure what you mean by "define". :D

[Akots]

Originally posted by Dymanic


Yeah, that was a joke.

Subjectively, so was my response. :p

[ScottDYelich]

defining things perfectly? sure...
explaining them perfectly, probably not.


example of defining something perfectly:

point a a rock... for rock.


If you want to do it with words

point at a rock, say "rock" ...

if both parties *agree* that this respective
object is "rock" .. then that defines *THAT*
rock.

That is, you could just point to something
and say "that" ... etc.

Scott
yes, it is as simple as... that.

[Akots]

Hm... i thought "Rock" meant "Grey and bumpy"...?

I mean, that rock is grey... and it sure is bumpy.

Just look at it!

[ScottDYelich]

Originally posted by Akots
Hm... i thought "Rock" meant "Grey and bumpy"...?

I mean, that rock is grey... and it sure is bumpy.

Just look at it!

heheh, nice word game.

Actually, rock means the thing. If you are saying you thought that rock meant something that you pick out as part of the thing ... then your agreement that rock stood for the thing wasn't true.

If there was a misundertanding as to my example, that is perfectly ok... we can come back to address it.

I will point to something... say, that "rock" ... the agreement that we need to make, using our other "words" .... is that we are agreeing to reference the object -- itself.... not a component of it -- or a feeling about it, etc.

Scott

[Underemployed]

Ceci n'est pas une pipe

[Dymanic]

example of defining something perfectly:
point to a rock... for rock.

Man, I'm sorry, I mean, nice try, but I can't come anywhere near finding that acceptable.

The definition of definition is probably as undefineable as anything else, but that doesn't seem to meet even the grossest minimum requirement.

What if I break your rock into pieces? Is it still a rock?

[Franko]

Definition = the Expression of a Perception
Expression = an Output (result of MPB)
Perception = an Input (result of an Entanglement)
Logical = Comprehensible = Observable (Imaginable, Conceivable) = (met.) Same in your mind as in mine.

You aren’t going to get very far in Logic or Science unless you can precisely define your terms. Mathematics is nothing more than a language with very precise and consistent definitions of it’s terms. Modern computer languages are really no different fundamentally.

[Dymanic]

Franko,

I certainly agree that you aren't going to get very far in a discussion about logic or science unless you can precisely define your terms. In fact, that was really my original point -- discussions about logic or science (or whatever) often seem to consist of little more than negotiation of definitions. The assumption I'm challenging is that for each term, some ideal definition actually exists. The word "definition" is as good a subject term as any to start with.

Your example:

Definition = the Expression of a Perception

seems prone to attack. In about fifty different ways.

[Franko]

Dynamic,

Existence … Reality … is like a giant computer program. It only looks “complicated” when you try and look at the whole thing, but if you sit down, and look at one line of code at a time … the whole thing is very simply, very logical, and very easy to follow along.

Now here’s the thing … Let’s say that you and I are looking at an algorithm – a long program. We are both trying to figure out what the program does (ultimately), and one of us has a “theory” about it. So we both sit down, and we start looking at the code line by line. Now if we both agree on a single line of code (our definitions of the terms match), then we can proceed to the next line of code in the program, but if we disagree about what a particular line of code is going to do, then we have to hash it out and come to an agreement before we can move on.

We can’t just skip a line of code that we disagree on and keep looking at the rest of the program, because EVERY line of code depends on the lines of code that came before it. In other words, if we skipped a couple of lines of code, and then started looking at the program farther down, it is possible that we could have a large disagreement regarding what processing will occur there, because we both have different assumptions about what the preceding lines of codes were doing.

Each line of code is like a definition of a term, and that term is going to be used in subsequent lines of the program. So we can’t disagree on a single line in the middle of the program, and assume that we will agree about an ultimate conclusion regarding the exact ultimate nature of the program.

Your Individual terms are like the keywords in a computer program, and they have to be defined in the same way as a computer language is defined. They have to be concise, and precise, or to put that another way your keywords (terms/vocabulary) needs to be logically consistent (doesn’t self contradict), and parsimonious (not redundant, and not requiring lines not yet accessed).

Definition = the Expression of a Perception

All this means is that the description (expression) of a “thing” you perceive in your mind’s eye is the definition of that “thing” in your terms.

[Dymanic]

Franko,

I am very fond of the computer program model myself. In fact, almost certainly, to a fault. I have to constantly curb my instinct to try to use it to understand things for which it is probably not a particularly useful tool.

A compiler is without question the most rigid, pedantic, unable-to-be-reasoned-with, unable-to-be-bargained-with structure in existence (well, except maybe for a LISP compiler, but anyway). A definition of a thing in your terms is not meaninful to a compiler. You speak in its terms, or you listen to what it has to say (in its terms) about why it does not understand. Period. No discussion, ever. Keywords in a computer language are precise because they are inflexible, and this inflexibility derives from the mathematical substrate on which they are built.

So, again, my point (my tentative conclusion): Only in mathematics are perfectly definable terms possible.

It's actually a question: Is this really the case?

You see, I am not particularly comfortable with this conclusion, and would happily abandon it in the face of a single example of a perfectly definable (non-mathematical) term.

Earlier, I said that the term "definition" itself is probably as good a place as any to start. I realize now that, of course it is exactly the right place to start. If we can't define that--and, not to be argumentative or anything, but I'm going to claim that we still are not quite there--then the only answer seems to be the short answer (no).

(I guess we'll have to do "perfectly" too).

[Shroud of Akron]

Originally posted by ScottDYelich


heheh, nice word game.

Actually, rock means the thing. If you are saying you thought that rock meant something that you pick out as part of the thing ... then your agreement that rock stood for the thing wasn't true.

If there was a misundertanding as to my example, that is perfectly ok... we can come back to address it.

I will point to something... say, that "rock" ... the agreement that we need to make, using our other "words" .... is that we are agreeing to reference the object -- itself.... not a component of it -- or a feeling about it, etc.

Scott but isn't the "thing" gray and bumpy?

[ScottDYelich]

Originally posted by Dymanic


Man, I'm sorry, I mean, nice try, but I can't come anywhere near finding that acceptable.

The definition of definition is probably as undefineable as anything else, but that doesn't seem to meet even the grossest minimum requirement.

What if I break your rock into pieces? Is it still a rock?


you're playing word games.

question: have you changed what we agreed was a rock? it was 1 solid piece, now it is many... so, seems the answer is yes.

If you have changed what we agreed on was a rock, wouldn't you also allow that possibly now you may need a new word to define what
you have?

don't play word games.

we have a rock. we agree it is a rock.
if I pick up the rock. have I changed it? perhaps... I have moved it.
if we still agree it's a rock, then we agree. if not, then we will have to
re-identify it and re-agree on what to call it.

you broke the rock. are the pieces still rocks? sure... maybe.. does it
matter? thing is, you broke the rock -- you might also have broken
the definition!


Scott
difference

[ScottDYelich]

Originally posted by Shroud of Akron
but isn't the "thing" gray and bumpy?

well, sure... the thing has qualities.

we can agree that the thing I pointed to was a rock.
if I point to another thing, I could say rock.

this might confuse you, then am I talking about a
specific rock? no... then I"m talking about things that
have the quality of being a "rock" ..


this is where the religious people go wrong. they
flow from one definition to another when it suits them.

if I point to another rock, and we both agree that it is A rock..
we're not talking about the first thing which was identified (ie: defined) exactly, but now we're talking abut a CLASS... which, we are starting to
try to define... exactly.

one example was, are smaller rocks rocks. ok, perhaps.
are they also pebbles? maybe. are they stones? ok, maybe.
when does a pebble become a rock, or is it both?

interesting questions, but the question was... can we ever define
anything exactly. the answer is yes.

When two people agree to reference something by an agreed upon
method, that defines something. There may ALWAYS be differences
and variations, but if you're saying that because the rock will never
be the same (quantum, etc) ... you're now playing games again.

if you can't tell there's a difference readily, there may not be a need
to pretend there is a difference to call attention to the difference.

hence, if I have two dice and I point to one and go "Fred" and then
put both behind my back and shuffle them and redisplay them,
can we Identify Fred? Well, that's not the point... the point was
that we DID define Fred, if we're not able to tell Fred from something
else -- then we need to add more to the definition, but until that
point, we have defined something EXACTLY as much as is needed...

is that definition the penultimate definition of everything concerning the item? to annoy you, I'd say that the universe/reality is the definition.
if franko says that this is the TLOP goddess, then the goddess is the definition of the rock in it's completeness, that same same definition works for anything and everything, therefore, it can't be used to tell the difference between two things, so it's not a very USEFUL definition -- however exact and correct it might be.

Scott
difference

[Dymanic]

ScottD,

The fact that so many here seem to have so little to say about this may say something in itself, and I appreciate your vigorous effort. Maybe everybody else got past this so long ago it seems too trivial to merit attention. (The enthusiasm with which I often see definition boundaries defended makes me wonder though). I myself have the sinking feeling that looking for perfect definitions is a fool's errand, but I was hoping maybe there was one that I just haven't thought of. If someone could come up with even one perfect definition of a term--any term--I actually think I'd feel a lot better.

I share the objection you have raised to the playing of "word games" in order to avoid dealing directly with a question. That is a frequently used, and quite cheap stunt. But is that really a valid objection in this context? After all, a word game is precisely what this is, and precisely the point is that the objectionable practice of "playing word games" derives from the fact that definition boundaries are fuzzy.

This surely is the reason for the bulkiness and incomprehensibility of the language in which legal documents are written--it is an attempt to minimize the opportunity to exploit the fuzziness inherent in the language. In legalese, it is permitted to continue to add more and more detail to your definition for as long as you want, and many professional careers are devoted to perfecting the skill. Despite this, countless hours and countless sums are spent litigating cases that turn on the precise meaning of some significant term.

Now I think the problem the Shroud had with your "specific instance" example (and the same problem I have with it) is that it isn't very clear what exactly it is that you are referencing by pointing to your rock. Is it the "rockness" of it, or the greyness, or bumpiness, or hardness, or inelasticity, or any one of countless properties it must have? How many of these properties must your rock (or any rock) have in order for it to possess "rockness"? All of them? Or is "rockness" a property somehow independent of these qualities?

Is there any such thing as a rock?

[ScottDYelich]

Dynamic --

I agree...

I'd only add, I think you can define things exactly, when the
things you are aiming to define are SMALL and SIMPLE.

The more you tack onto or into the definition, the further
you get. However, it's also that you get more powerful.

I'm not interesting in defining anything exactly, because I know there's no (or little?) need for such. I am more interesting in defining anyhthing sufficiently!

ie: computed reality. But, see, I've already answered my quesetion.
I'm only interested to see if anyone can punch any holes in it.
So far, there hasn't been any punched.


So, I want to write a program that will learn how to learn.
ok, now, not to get tangled up in the hows, and whys...
lets say I take a snapshot of the mechanism and duplicate it.
now there are two.

ok, now I put THESE two in communication or in shared existence
with each other.

these two things may agree to form their own language and/or agree
on things regardless if they're true or not and they may also decide
to form a language that only THEY (the two of them) understand
because it suits their purpose! we wouldn't be able to understand
it, but they could, mabe, translate it to us.

if their language defined something exactly, and it was translated for us, would the translated definition still have exact meaning? probably not.

ok, now here's where I'm gonna trry to blow your mind.

remember above, I took a snapshot. That's like duplicating the entire
"brain" for one of these things. Yes, from the instant the snapshot is made, there will be divergent paths, but the history before that
would be 100% shared and identical.

So, lets say that machine #1 tells machine #2 to check and verify that definition "ABC" has not been modified since the split. If that checks out, then when #1 tells #2 to refer to the definition, #2 will know
EXACTLY (completely, 100%) what #1 means. Why? It's as if it were part of #2's reality.. and, there are no missed nuances (social influence, connotations, NOTHING) because it is 100% the same.

Granted, *since* the split, #2 could reflect differently on the definition
of ABC because what ABC is definition could rely on other definitions...
but I think you see my point.

Now, the flip side of this coin is.. is this definition the 100% "complete"
definition of the term in question? I don't know. Are we looking to compete with god in terms of omniscience? or are only looking to
convey 100% meaning to another being/entity?

For me, I only care that when I say rock, you know generally what I'm referring to.

Of course, people think I'm a bit weird.

My father asked me if I wanted a beer out of the bottle...
I said yes.. but then was upset when he brought it to me
to drink and it was in a glass. To both of us, it was out of
the bottle.

Sting wants to ask the girl to marry him, in some old fashoned way.
Is he going to ask in an old fashioned way, or is he going to marry
her in some old fashioned way?

If I say rock, is it really a pebble? stone? boulder? If there are
three things on a table, a donut, a cd and a pebble.. and I say please
hand me the stone.. which will you hand me? if I asked you
to please hand me the rock, which would you hand me ?

yet, merriam webster doesn't have ANYTHING in its thesaurus for
"pebble" (or rock, or stone) ...


bah, my memory is failing me... I looked up a word at m-w.com
that meant something like "overlook/mistake" and the word was listed,
but when you followed the link, it said that the word that you put
in was not spelled correctly, and then gave a list of the proper
spellings -- WHICH INCLUDED the spelling that you just used.

I thought that was far too ironic to forget. I guess I thought wrong.

Scott

[c4ts]

Originally posted by Dymanic
Maybe it depends on how you define "define"

I often see discussions on various topics grade off into border skirmishes over the proper placement of some definition boundary. Never mind such quagmires as life, intelligence, randomness, atheist, art or species; I can't think of [b]any concept (outside of pure mathematics) that is perfectly definable.

Is rigorous as good as it gets?
No. "Understood" is as good as it gets. And it's a lot harder to understand something than simply define it. Often, definition comes from understanding, but understanding doesn't always come from definitions. Rigorous definition just clears up semantics.

Perhaps if, as it has been suggested, mathematics is crucial to understanding, it is because mathematics is one (I'm thinking the only) system of thought that features terms which are absolutely exempt from ambiguity?
Mathematics is ambiguous as hell! What is number, anyway?

You never hear anyone say, "well, it depends a lot on what you mean by Prime...".

Outside the realm of mathematics though, it seems to me that it is possible to take any word in the language, find some deviant example that clearly deserves exclusion from the category, then demonstrate the hopelessness of locating an exact point of divergence from the central meaning of the term. Attempting to solve the problem by creating endless stacks of sub-categories seems to serve only to provide a richer environment in which to play this game.
Well, language is meaningless anyway. Pillory's posts can prove that.

Is it really a hammer if it's made out of chocolate?
Yes, it's a chocolate hammer, in the same way a rabbit made out of chocolate is a chocolate bunny. Mmmmm... chocolate. Glaaaaaaaaallll...

[Dymanic]

Mathematics is ambiguous as hell! What is number, anyway?
I'm not saying that there is no ambiguity in mathematics, simply that there are terms in mathematics that are not ambiguous; Prime being a good example.

I'd be interested to see an ambiguous example of primeness.

[c4ts]

Originally posted by Dymanic

I'm not saying that there is no ambiguity in mathematics, simply that there are terms in mathematics that are not ambiguous; Prime being a good example.

I'd be interested to see an ambiguous example of primeness.

Very well, why is a number prime?

Can you think of numbers in terms of something other than numerals?

[Dymanic]

Can you think of numbers in terms of something other than numerals?
Yes.

But my ability to do that seems to be independent of any mathematical property, such as primeness, that they may have.

[c4ts]

Originally posted by Dymanic

Yes.

But my ability to do that seems to be independent of any mathematical property, such as primeness, that they may have.

So what about geometry, the bare foundation of math? Can't you express number in simple geometric terms, without the need for things that involve numerals such as units of measurement? What is primeness anyway?

[Dymanic]

Can't you express number in simple geometric terms
You can express numbers in countless ways that don't involve numerals. But then, it isn't numerals that have properties like primeness.
What is primeness anyway?
Ok, I'll bite.

"An integer not evenly divisible by any whole number other than itself and 1."

[c4ts]

Originally posted by Dymanic

You can express numbers in countless ways that don't involve numerals. But then, it isn't numerals that have properties like primeness.

Ok, I'll bite.

"An integer not evenly divisible by any whole number other than itself and 1."

I'll bite back:

"A prime number is that which is measured by a unit alone."
- Euclid

[Dymanic]

"A prime number is that which is measured by a unit alone."
-Euclid

I can't imagine any circumstances under which I would be inclined to contradict anything Euclid said about primes, but I wonder if he intended that statement to serve as a replacement for the standard definition?

[c4ts]

Originally posted by Dymanic

I can't imagine any circumstances under which I would be inclined to contradict anything Euclid said about primes, but I wonder if he intended that statement to serve as a replacement for the standard definition?

Replacement? Back when Euclid wrote it, there was no standard definition. Have you seen the rest of the definitions in book 7?

[Dymanic]

"Have you seen the rest of the definitions in book 7?
You mean like:

"A unit is that by virtue of which each of the things that exist is called one.

Some of those have been firmed up a little, but Euclid's still da bomb.

I was hoping you were going to attack the definition I provided.

[Ceinwyn]

Well, I thought that's why we developed dictionaries. So far as I know, they were created so that we could agree on basic terms of language.

Oops, sorry Franko.

[c4ts]

Originally posted by Dymanic
"
You mean like:

"A unit is that by virtue of which each of the things that exist is called one.

Some of those have been firmed up a little, but Euclid's still da bomb.

I was hoping you were going to attack the definition I provided.

Unless attacking you means pointing out how math wasn't always so clearly defined, no. There's a whole lot of math that hasn't been clearly defined, and some that doesn't even need to be. And that clearly defining something is no reason to stop thinking about it. For example, you can clearly define a prime number or modular form without necessarily understing what it is. That way you can know things, such as why 2 is considered prime without reiterating the definition of a prime number.

[UserGoogol]

Mmm... probably not. English has too much cruft. Its a pretty good language though.

[DrChinese]

The whole idea of language - any language - is to provide a shorthand for transmission of descriptive terms which are understood my both parties (speaker and listener). In all cases, the description must be contain less content than the maximum descriptive content (i.e. it is the shorthand version). The act of representing the descriptive content is for utilitarian purposes.

My example would be pi. What would happen if you didn't use a shorthand to describe it? You would spend an infinite amount of time describing its infinite number of decimal places. That wouldn't be practical.

So the answer is NO - a complete description of anything is not possible. I am not certain that complete knowledge about anything is even possible, either. But that is another post.

Korzybski said "the map is not the territory" and the full significance of that is still dawning upon us 70 years later. Language is useful approximation.

[Peter Soderqvist]

Soderqvist1: A definition is only an approximation, and every proposition is thus incomplete, its consistency cannot be formalized in the system, some consistency must be taken for granted without formalization!

Kurt Godel's Incompleteness theorem from his Biography
He proved fundamental results about axiomatic systems showing in any axiomatic mathematical system there are propositions that cannot be proved or disproved within the axioms of the system. In particular the consistency of the axioms cannot be proved. Godel's results were a landmark in 20th-century mathematics, showing that mathematics is not a finished object, as had been believed.

It also implies that a computer can never be programmed to answer all mathematical questions. Either mathematics is too big for the human mind or the human mind is more than a machine. ...a consistency proof for [any] system ... can be carried out only by means of modes of inference that are not formalized in the system ... itself.
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Godel.html

"You will know that no doctrine can, without committing the unpardonable sin of circularity, undertake to define all of the terms it employs but that every doctrine must employ one or more terms regarded as being, without definition of them, sufficiently intelligible for the purposes of clear discourse. You will know that for a like reason no doctrine can furnish proof of all its propositions but that every doctrine must contain one or more propositions which it takes for granted, using them without demonstrating them. And you will know that a doctrine can have maximum clarity and cogency when and only when it has the minimum of undefined terms and undemonstrated propositions."
— Cassius J. Keyser, TAT
http://www.esgs.org/uk/und.htm

Soderqvist1: If you add something to the system in order to give it consistency, what you have added will also end up incomplete, the same it is with more adding, and so on in an infinite regress! This "takes for granted" by Professor Keyser from Korzybskian institute for General Semantics, is not formalized in the system, therefore; a human mind is something more than a computational system! :)

[BillyTK]

Originally posted by Underemployed
Ceci n'est pas une pipe

Yeah, 'cos it's a painting! ;) :D

[BillyTK]

Originally posted by buki
Well, I thought that's why we developed dictionaries. So far as I know, they were created so that we could agree on basic terms of language.

Oops, sorry Franko.

Well, as Whodini mentioned, it gets circular WRT dictionaries. Each revision surveys popular usage of a word and takes that as the definition, which everyone uses as the popular definition until a different usage becomes common and is picked up by dictionary publishers, and so on and so on...

So dictionaries create language as much as reflect it!