What is Real?

[Antone]

...I hope you continue to spread intelligence here amoung the mushrooms. Just ignore the mushrooms.

Thank you for the kind words and the encouragement. I still have important things that I need to be doing other than blogging, but I will try to continue to find the time to respond--if at a more leisurely rate.

[altonhare]

Antone replied in PM and I'm gonna post my response here.

Since a though is an object to you--apparently no different from something physical--there's nothing I can say.

The image you're imagining has shape, it's an object by definition. However your description/conception of that object is not physical. This is the difference between imagining an apple and conceptualizing the apple. A concept inherently involves comparison between objects (hence why a concept is *always* defined in terms of objects). When you conceptualize the apple you may describe it as round and fits in your palm. But what does round mean? In order to conceptualize the apple you must compare it to what it is not. You compare it to a block, it's not like a block, it's round. You compare it to a watermelon. You can't fit a watermelon in your palm, it's big compared to the apple. These are conceptualizations, they are not objects, they are relationships among objects. But the static image of the apple in your head has shape and is an object by definition.

You can't define "object" in a non circular, objective way without defining it as shape. Touch is circular because it invokes ANOTHER object to do the touching. This is the definition of a circular definition! Shape does not demand another object. An object has shape all by itself.

An inch on a ruler is part of an object. The inch unit itself, however, is not.

The distance between two has marks on your ruler is the distance between two objects (hash marks). They have shape. This cannot be avoided. All concepts are defined in terms of objects and objects all have shape. It's the only way to avoid contradiction and circularity.

up with two loves? An inch on a ruler is part of an object. The inch unit itself, however, is not. Why not add loves. I had one great love in my youth and one in old age... that's two great loves.

You are not distinguishing between a casual/conversational definition and a scientific definition. A scientific definition is one we can use consistently. Either love is a dynamic concept or an entity. You either point to a woman/heart/cupid and define that as love, or you describe an interaction between entities as love. If you say "I have had two great loves" you either mean you have possessed two objects you label "love" or you mean "I have loved two great people". The people are the entities involved. In the former case "love" is an entity because it has shape. You cannot construct a sensible sentence without an object/entity.

The concept [nothing] has no meaning? It doesn't refer to a specific object or entity.

Exactly, the concept "nothing" by itself has no meaning. It indicates the absence of something. To know what someone means when they use the concept "nothing" they must indicate what something or set of somethings is/are absent. If I say I have "nothing in my pocket" I mean that no object in the universe is in my pocket. I am taking, as my "set of somethings", every object that exists.

No concept has meaning without reference to objects.

But according to you there can't be any categories--because a category is a concept. So again you're creating a paradox for you're self.

I described it as taxonomy. We're just illustrating/conceptualizing what characteristics entities share and which they don't share. This is the definition of categorization. There is no "multiple referent". If I define an object X way it's always defined X way. I may describe it by comparing it to other objects, this is conceptualization. I may categorize it multiple ways. But it is still defined in a single way. It is not relative, it just is.

What does distance have to do with this. Absolutely nothing. Are two close apples different from two far away apples? No. If I make apple sauce out of two apples, is there not a sense in which the sauce is still two apples? Yes.

If you're not using distance criteria for the objects in your equation than you're just doing taxonomy.

You define the two apples in a single way. Once the criteria you stated that define them as apples is/are violated, the apples no longer exist. They are now "sauce". This is Identity, which you haven't quite grasped yet.

So you're a purple man--because that's how I feel like defining you at the moment. Interesting.

I get the feeling you're intentionally missing my points. If you would like to use the symbols "altonhare" and point to a purple man, then that is what the symbols refer to. Always. There is no multiple referent. When you describe the entity you pointed at as purple, a man, tall, etc. these are conceptualizations and involve comparisons of what you pointed at to other entities/objects.

[Antone]

If one does not refer to an object and +/- does not refer to the motion of one or more object(s) and/or the distance between objects, what do they refer to? What do your numbers refer to, if not to objects? Are they just markings on a screen that obey arbitrary rules?

I can somewhat agree with you about [1] referring to an object--but the way I see it, there isn't a single thing which we call a number. Instead there are various "types" of numbers, which are constructed from various aspects--and which are reciprocal in many ways.

The ordinal numbers do not refer to objects, but rather to order: that's why they're called ordinal numbers. When we use the ordinal number [1], we generally are refers to the [first given thing]. But the idea, [first] does not need an object to give it meaning. Suppose there's a group of people who are racing their pets (dogs, cats, turtles, pigs, etc.) And the judge says:
The winner of the game will be the first animal to finish.
Because there are all sorts of differnt shaped animals (this would be true if they were all dogs too, but I wanted to exaggerate the obvious) there isn't any shape that this [first] refers to.

The cardinal numbers place the [elements in a set] into a one-to-one correspondence with the ordinal numbers. The cardinal number of a set is the set's unit of measure and the ordinal number that corresponds with the last element in the set.

My DS theory of Numbers differs from traditional Foundations of Mathematics theories, but I believe the natural numbers are created by combining [the cardinal numbers and the idea of addition].

To understand how that works, we might think of a [set of 10 marbles] as [ten marbles inside a marble sack]. Notice that (according to my DS theory) the cardinal number is not [10], but rather [10 marbles]. By contrast, the natural number [10] is like having a stack of marbles and an empty [marble sack] and adding ten marbles to that sack. The first object that we put into the set/sack, defines the unit of measure for the natural number. That is why the number [1] has such unique properties, and is called the identity element.

We don't have to add marbles to our set/sack... but whatever is the first thing to be placed into the set--all subsequent elements must have the same [unit of measure]--otherwise, we are "adding apples and oranges" as they say. Notice that, if we wanted to, we could put the ordinal numbers into our set--in which case, the unit of measure would literally be [nothing].

If we think in terms of a number line, the natural number [10] is a line segment that is [10 units] long. This line segment starts at the [geometric point noted as 0] on the number line and ends at the [geometric point noted as 10]. Notice vital to think in terms of the [line segment 10] being conceputally separated from the [rest of the number line] by [geometric point] because the [geometric point] has no dimension. Thus, while it separates [10] from the rest of the number line, there isn't any   separating [10] from the rest of the line... that's why it is a conceputal separation. If the [point] had any dimension at all, there would necessarily be space, creating a literal [line segment] that was physically separate from the [number line]. Also, the absolute precision of the [geometric point] means that there isn't any ambiguity as to the length of the line--it is exactly [10 units long]. We cannot possibly measure accurately enough to create such a line in reality--which is why the nubmer line is also a conceputal entity. The image we draw is just there to help us visualize it. Also notice that [0] is the [geometric point] that is immediately to the left of the number line. Again, because the [0 point] is dimensionless, there is no space between the numberline and the [0 point] so in a sense it is part of the number line. But because it is dimensionless, we can say that [0] is literally the [absence of a line segment].

Another (obvious) observation is that [number lines] come in all different scales. So the natural number [10] can literally be a line segment of any arbitrary length--as long as it is divided into 10 units of equal size. This goes back to our set analogy. The number line can have any unit of measure, just as we could put any object into our set--but once the first unit is defined, all subsequent units must be identical.

There are several more different kinds of numbers, including the fraction--which might be said to be a relationship between two different numbers. Traditional number theories also have the irrational numbers. My DS theory does not consider the [irrational numbers] to be significant. Instead, they are held to be nothing but a subset of the infinite numbers which are essentially numbers that--using the number line analogy--have no magnitude but only dimension. The [geometric point 1], which I mentioned earlier, is an example of such an infinite number. But to distinguish it from all the other numbers that are close to it--but not it--
we must follow the [1] with infinitely many zeros, written [1.000...]--where the elipsis indicates that we keep adding the last three numbers indefinitely.

Infinite numbers get their name from the fact that they continue forever, without end; and the fact that they are infinitely precise.

This is a radically different understanding from traditional number theory--for the [finite and infinite] numbers are understood to be defined by the reciprocal properties [magnitude and precision] respectively. I've presented this material very quickly here. My actual theory covers nearly 100 pages--so a log of important stuff has been left out. But defining these numbers in this way allows me to accomplish a great many important things. For example, I believe I have developed counter-proofs that demonstrate that virtually everything Cantor ever said about [infinite sets] was the exact opposite of correct. And this obviously does away with the continuum hypothesis, for example.

A very simple way to demonstrate that the continuum hypotesis is erroneous
The continuum hypothesis is based on the notion that there are infinitely many more irrational numbers than there are counting numbers--to the point where if you were to arbitrarily pick a [geometric point] on the number line, you would theoretically have a 100% chance of chosing an irrational numbers--ACCORDING to traditional theory, that is.

The [irrational numbers], however, are only a subset of the [infinite numbers]--because there are infinitely many series of numbers that we can create that are [infinite] but not [irrational]. For example, if we consider only the [numbers between 0 and 1], then we can create the following infinite series of [infinite numbers] that are not [irrational]:

[.1000...], [.2000...], [.3000...], ...
[.11000...], [.21000...], [.31000...], ...
[.10100...], [.20100...], [.30100...], ...

The first series is simply every counting number followed by infinitely many zeros. The second series is the same as the first but after each number we put a [1]. We could also do a similar series using [2], [3], [4], and so forth. The third series I demonstrate above is the same as the second--except that we place a [0] between the natural numbers and the following [1]. Again, we can create new series using numbers other than [1], or a different number of zeros.

The second step in our proof is to find a way to turn the [infinite numbers] into a well-ordered set--because, according to Cantor, any two sets that can be placed into a one-to-one correspondence must be considered to be the same size.

It is simple to turn the [infinite numbers] into a well-ordered set. Since the [infinite numbers] are reciprocal with the [finite numbers] all we have to do is create a mirror image of the natural number sequence on the opposite side of the decimal point.

.1.1
.2.2
.3.3
.4.4
.5.5
.6.6
.7.7
.8.8
.9.9
10.01
11.11
12.21
13.31
14.41

The number on the left of the decimal is the corresponding [counting number]. And the number on the right is the correspoinding [infinite number]. Tecnically, the infinite number should have infinitely many zeros behing it, but I left them off for ease of viewing.

As we can see, there is an exact one-to-one correspondence between the counting numbers and the [infinite numbers beytween 0 and 1]. Because they are reciprocal, this is exactly what we would expect to see.

Just as kneading bread dough turns the simple elements of flower and water into something more complex than flower and water, so too the convoluted folding and unfolding of ideas has the ability to turn the simple numbers from the ordinal series into more and more complex numbers, each with distinctly unique characteristics and properties.

~Antone

[Antone]

A circular definition is one that states or implies the word it's defining. If you define an object as "touchable" or "perceivable" this implies another OBJECT doing the touching/perceiving. Shape, on the other hand, does not require another object. This is why your definition is circular and mine is not.

I obviously understand what you're saying, but it is wrong for a number of reasons.

First, every [defintion] is [by definition] circular. If it wasn't [circular in at least some way] then it wouldn't tell us anything meaningful about what we're talking about. Consider the following analytical definition for a circle:

a circle is df= x : x is a continuous, closed plain arc that is equidistant at all points form a center point

But we can reverse the definition as follows:

a [continuous, closed plain arc that is equidistant at all points form a center point] is df= x : x is a circle

In a sentence, we can use the word [circle] or the defintion interchangeably. The single word is preferable because it is shorter and more concise. But the fact that we can use them interchangeably clearly indicates that they are the same in some way. And the reason they are the same is because they circle back on one another--and thus are circular.

Isolated from other objects, (and perspectives) every point on a circle is identical to every other point. This is an analogy for the definitional equation--where both sides are semantically identical. If they are not, then it isn't a completely accurate definition.

Traditionally, we call the longer portion of the "equation" the [definition] and the shorter portion [that which is defined]. But that is only convention. If we know what a [circle] is, but do not know what the longer portion means, then the longer portion is [what needs to be defined]--and [circle] is it's definition.

The general purpose of a defintion is to provide known concepts to explain what an unknown concept means; so we can define what we mean by the number [2] by saying it is [1 + 1]. But [1 + 1] can also be defined by [2]. Now, if we are unfamiliar with what [1] is, then [1 + 1] does nothing to define [2]. So it is possible that we may need to define [1] as well.

The fact that [1 + 1] and [2] are both contain numbers does not invalidate them as definitions for the other--because [1], [2], and [+] are all different things. If we don't understand the [oncept of a number], then we can define that separately, in such a way that the [concept of a number] is not used in the definition--as I did in a previous post.

Back to objects
The fact that [one object] touches [another] has nothing to do with circularity unless you take the [perspective of one object] and define [another object] in relation to [that first one]. If you word your definition in such a way that you are taking a general perspective then you might define an objects as [things that can interfer with one another.]
By contrast, concepts are [things that cannot interfere with one another.]

Using this definition--whichsemantically is virtually identical to the one you objected to--there isn't any object that is touching or perceiving the other.

So again, I say you're objection is unwarranted.

Every truth is circular in nature. If it wasn’t circular it couldn’t be true. In fact, paradoxes occur precisely when we break the chain of circularity.

The difference between a truth and a paradox is that with a truth the circularity is so intuitively obvious that we simply ignore the circularity; whereas with a paradox the circularity is so obvious to our rational minds that we simply ignore the truth.

~Antone

[Antone]

Again, I never ever EVER stated a "geometric point" was an object. I stated that a point is an object. ...

Fair enough... but you were responding to what I said... and I think it was pretty obviously that I had to be referring to a [geometric point]. I didn't explicitly specify that, so I'll give you the benefit of the doubt--but what else could I be referring to. There aren't any non-geometric points floating around in space. And I was referring to a specific location. Otherwise, the line stretching between the (geometric) points couldn't have a specific length. After all, an non-geometric point has dimension and thus you have to choose whether to start the measurement from the far side of the point or the near side of the point. The difference may be small, but it will necessarily be different.

Now, you might object that we obviously have to start from the [side of the point nearest to the other point], but then what you are measuring from is still a dimensionless location on the point--so why not just specify that the point is dimensionless to begin with and avoid all the double-talk?

Only a measurement between two [exact locations] can give an absolutely precise measurement--although, since we cannot actually perceive the exact location of the [geometric pionts] the measurement is only conceptually precise. In actual practice, it is necessarily a vague approximation--as all measurements are.

Again, the reciprocal nature of reality reveals itself.

...If you're talking about a "geometric point" in the sense that it has 0 dimensions then you need to think about what you're saying here. Something that has 0 dimensions has no length, width, or height. It is "nothing". Are you measuring the distance between two points or between two nothings? Distance only has meaning as the separation between two objects....

A geometric point is not [nothing]. It is a location. And every measurement is a measurement between two location.

Now, defining an object as a shape (as you do)... I can see what you mean by saying we always measure between two shapes. After all, the tickmarks on a ruler (or other measuring device) are shapes. And we must use them to take a measurement--even if we are dealing with locations.

Two problems with this interpretation. Firstly, you are criticizing my ideas. Therefore, you must use my definitions. And I do not define an object as a shape. Now, if present your theory, and I want to criticize it--I must use your defintions. When we both use our own defintions to discuss things--we might as well be two foreigners that only speak one language, but not the same one. And secondly, even though a physical ruler necessarily relies on shapes--doesn't mean that length ceases to have meaning in the absence of objects. It simply means that we can't measure what that length is without using a physical object--and a physical object that can measure will always rely on various shapes.

. .

The separation between these two points is distance.

No... the separation between the two locations that you are identifying (approximately) by the dots on the screen represent a distance. And the meaning of that distance is necessarily vague, because it is uncertain how we should interpret your representation of those locations. Have you centered the dot on the location? If so that would give us a measurement that is differerent from our earlier suggestion of measuring from the near-side of each dot. But if we are supposed to measure from the near side--then the dots aren't really AT the location where we are measuring from. They are just to the outside of it. So once again, your dots are a misrepresenation of the actual location from which you are measuring.

Just because you reduce the dots down to a [geometric point]--that has only location but no dimension--doesn't mean that they aren't still there, in exactly the same place that they were when the dots that you drew to show their location was there.

Such dots are a visulal aid to measuring the specified locations, but neither [they] nor the [distance between them] is what is being measured.

[Antone]

"Something" is predicated on "thing" which means "object".

For your information only, I define the term [thing] to mean either an [object] or an [entity]. Object being something that is [physically real] and entity being something that is [conceputally real]. That's why we can say, "I just thought of something." When someone says that, they don't necessarily mean that they [just thought of something that has shape]. For example, "I just thought of something. The meeting starts at ten."

This post, however, is dealing with your theory. So for this post I will try to keep my comments grounded in the framework of your ideas as much as I can. This is, admittedly, a difficult thing to do because the mind keeps wanting to fall back into familiar ways of thinking, but I will try.

Object: That which has shape, meaning it has a border, i.e. it is finite, it cannot blend with its surroundings.

This is an objective definition because it does not demand observation.... An object has shape all on its own, even if it were the only object in the universe.

I strongly disagree. Defining an object as a shape not only demands an observation, it also demands an evaluation. My bath/shower is made with several overlapping parts, which are caulked to prevent water getting between them. Is this arrangement a single object, or is it many. A gravel driveway is made of many peices of aggregate. Is it a single driveway or is it many peices of stone. These examples are fairly easy, because the part aspects are obvious--and your definition of [entity] allows you to explain them fairly easily--although you seem to fail to realize that this implies that everything is both an object and an entity--which is almost exactly the same idea that I was saying when I suggested that everything is both a [part] and a [whole]. And you objected to that notion--so how can you not object to your own definition of [object] and [entity]?

But moving one, there are many things that do not have such obvious divisions as you are suggesting. Consider the sun, for example. Is the sun a single object? What shape does it have? Is it round or does it include the prominences. More difficult, where do we end it's boundary? Do we perhaps consider the end of it to be the [chromosphere] or should we consider it to be the [photosphere], etc. And how do we decide where the arbitrary boundary for those things are. And if we can count these "things" as "part" of the sun, then why isn't it appropriate to include the solor winds? But what "shape" does the solar winds have?

For another example, consider the fact that many things have a [smell]. Now, the nose smells things by being able to recognize the various chemical signatures floataing around in the air. These floating chemicals clearly "belong" to a certain thing--which is why we say we are [smelling our cat], or [smellling a roast]. There are parts of the object that have detached and are now floating around in the air. So again, we have the vague boundary... At what point is the smell still a part of the object? And when (if ever) does it become a completely separate thing? And should we call the chemicals floating in the air an object?

Shape simply does not have the flexibility to accurately define all the possible things which might be considered an [object]--because (to some degree or another) all objects have vague boundaries. Given this fact, there are many things which are not inherently shapes based simply on what they are. Instead, they are shapes based on our definitions--which clearly indicates that we are making evaluatioins about what is and isn't a shape. We cannot make these evaluations with out observing the potential shape.

The "touch" definition of object demands another object to do the touching.
An object that exists has shape and location. Again it has location whether we touch/feel/perceive it or not. This is objective and non-circular. We don't prove that an object exists, it either has shape and location or it doesn't. On the other hand the "touch" definition is subjective. I claim I can touch this or that, but you claim I can't.
Other definitions are similarly circular/subjective.

I'm not sure why you insist on attributing this touch definition to my version of a [physical object]. It is an extremely strange notion to think that a physical object must be touched/felt/perceived to be physical. This would imply that things disappears when we aren't looking at them and reappear when we are.

Again, for your information, for me something is a [physical object] if it meets criterion like the following:

(1) it has spatial dimension.
(2) it is publicly accessible, and
(3) it can be physically divided (but not conceputally divided).

I believe that these [distinguishing characteristics of an object] exemplify the inherent quality what you were trying to capture by defining an object as a shape. There is usually very little question about whether something has dimension or not--and where there is a question, those "things" exhibit the qualities of both a [physical object] and a [conceptual entity]. Sub-atomic particles, for instance. (2 and 3) are only a little more vague--and only because their definitions are a little more tricky to clearly define. An ameoba is publicly accessible because (even though not every one can see it) anyone who wants to could put an ameoba under a slide and observe it under a microscope. And for the most part, many different people would all see exactly the same thing if they looked at exactly the same time. There is very little ambiguity about this fact.

Now, in my theory, a [physical object] also has location, obviously, but that's not an essential part of what defines it as uniquely physical--as opposed to conceptual--because a concept can also have a location, as I suggested with the talk about a measurement between [geometric points]. A concept, however, does not have spatial dimension. And a concept is not something that others can share in, so it is not publicly accessible. What I mean by that is two fold. First, the idea resides inside my head, so to speak. So you cannot be privy to it--whereas a rock resides out there where anyone can examine it. Not all objects are easy to access--and not all of them will look the same to different people. But those are variation created by differences in the person, or the perspective--not in the [physical object] itself.

And finally, a [physical object] can be [physically divided]. I have a body. If I cut off my arm, there are now two parts of what used to be my body. Conceptually, however, [body minus arm] is a different concept from [body]. Every physical thing can be divided into two (or more) physical parts. Concepts have no [actual physical aspect]. The concept of my body includes that it is physical--but the concept itself is not physical.

BACK TO YOUR THEORY

Therefore, existents are objects with location or relationships among objects with location. We identify three classes of existent:

1) Object with location. It is continuous i.e. made of a single piece. These are the fundamental constituents of the universe.

2) Entities and static concepts. A specific spatial arrangement of objects with location is an entity. A lion is a specific arrangement of certain atoms. The comparison of the arrangements of objects with location is a static concept such as distance.

3) Dynamic concepts. Consecutive spatial arrangements of class 1 or 2 existents. Examples include velocity, motion, jumping, love, justice, etc. Sometimes "love" and "justice" are used as static concepts, but typically when we use these words we are talking about something dynamic. Usually when we say "justice" we're not just referring to a static, still image of a judge in a courtroom. Instead we imagine the judge pronouncing sentence, banging his gavel, weighing criteria to determine guilt. Love is similar. A still image of a woman usually is not called "love". Typically love refers to something dynamic like a date, conversation, sex, etc.

One of the things I notice about all of this is that... for all your complaining that there shouldn't be reciprocal aspects in my theory--you yourself use reciprocal aspects.

You have [objects and entities]... which is very similar to my [element and sets] or [parts and wholes], etc. Because your [entities] are a collection (set) of obects (elements).

Similarly, you have [objects] and [comparisons between objects], which you call concepts. Aside from the fact that not all concepts are a comparison of objects--this is a reciprocal structure. [objects] are totally independent of [comparisons], as you stated earlier. But [comparisons] are not objects either. They both have something to do with [objects] but one IS a [single object], and one is [what is "between" two objects]. notice that each of these definitions contains two aspects. [single + object] and [two + not object].

This is the same structure that I've been suggesting in my posts--and even in your denials, you tend to demonstrate that it is the appropriate structure.

Again, you have [static] and [dynamic]--again, obvious reciprocals.

Now, I can work in your theoretical structure. But I believe that mine is preferably for a number of reasons.
(1) my structure is more intuitive. For the most part, words like [object], [entity], [concept], etc. are used in exactly the same way that we use them in common everyday speech. Your words are not, (as I believe I've demonstrated on several occasions). Sometimes, your words fit into intuitive, common, everyday speech... but not all of the time.
By contrast, I believe that my terms always do. I define certain terms differently than traditional theories do--such as [empty set]. But [empty set] isn't an every day word anyway. Among the commonly used words, my definition allows all of them to mean what they already mean--instead of having to change the usage in order to satisfy a technical definition within the theory.
(2) My structure is more symetrical, and I believe this gives my DS theory several advantages. For example, it allows me to very easily set up equivalencies that serve as definitions. And because they are reciprocal, I can convert back and forth between various perspectives--while keeping the whole the same. This allows me to resolve logical problems and paradoxes that non-symetrical theories tend to struggle with much more. Also, because myb definitions are reciprocal, I can manipulate the definitions using the rules and structure of the theory to reach conclusions that are unknown. I belive this allows me to speculate on unknown topics with a greater degree of logical certainty than is available to other theories.

So, it isn't that your theory isn't workable. But, the way I see it, it suffers from the same shortcomings that every other theory suffers from--and that is that it isn't consistent and complete. Eventually, if you follow a chain of logic far enough, it will lead you into a problem that can't be resolved.

In my opinion, I've already mentioned quite a few of those.

[altonhare]

Fair enough... but you were responding to what I said... and I think it was pretty obviously that I had to be referring to a [geometric point]. I didn't explicitly specify that, so I'll give you the benefit of the doubt--but what else could I be referring to. There aren't any non-geometric points floating around in space.

Check out "What's the point":

http://www.youtube.com/watch?v=PSJjs4l_FHU

If you think there are a bunch of 0D shapeless nothings floating around... just watch the video.

Otherwise, the line stretching between the (geometric) points couldn't have a specific length.

Really?

. .

There's not a specific distance between those two?

______

That doesn't have a specific length?

Eheh.

After all, an non-geometric point has dimension and thus you have to choose whether to start the measurement from the far side of the point or the near side of the point.

Because, in physics, we distinguish between length and distance. Length is the extent of a shape in a direction. Distance is the separation between TWO shapes. Check out "A Line is Not a Distance:

http://www.youtube.com/watch?v=TrD8a1_PcG4

Even if we did not define it this way (and so choose ambiguity), we simply make the choice and state it. We still have a specific distance. In fact stating our choice tells another person more information about what we're doing than not doing so.


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. .
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Figure one.
The distance from the right side of the right point to the left side of the left point is greater than the distance from the left side of the right point to the right side of the left point. Both distances are specific, just tell me which one you are reporting.

so why not just specify that the point is dimensionless to begin with and avoid all the double-talk?

Because a dimensionless "point" looks like this:

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Figure two. Dimensionless "point".

Can we define distance like this:

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Figure three. Two dimensionless "points" separated by a "distance"

Or like this:

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. .
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Figure four. Two physical points. The separation between them is distance. The extent each has in a direction mutually perpendicular to every other direction is length.

oblems with this interpretation. Firstly, you are criticizing my ideas.

But your definition of object is circular, as I've clearly illustrated. "Touch" invokes another object to do the touching. Is an object not an object until we confirm it is so by touching? Even under this circular definition, you cannot "touch" a geometric "point".

And secondly, even though a physical ruler necessarily relies on shapes--doesn't mean that length ceases to have meaning in the absence of objects.

Really?

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Figure five. The "length" of an absent object.

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__
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FIgure six. An object called a line. Its length is its extent in a direction perpendicular to each other direction

It simply means that we can't measure what that length is without using a physical object--and a physical object that can measure will always rely on various shapes.

We are not talking about measurement. We're talking about a definition. Can we define length by pointing at figure 5?

Just because you reduce the dots down to a [geometric point]--that has only location but no dimension--doesn't mean that they aren't still there, in exactly the same place that they were when the dots that you drew to show their location was there.

See figure one and figure two.

[altonhare]

I strongly disagree. Defining an object as a shape not only demands an observation, it also demands an evaluation.

Stunning! My table doesn't have shape unless I look at it!

[Antone]

Since a though is an object to you--apparently no different from something physical--there's nothing I can say.

The image you're imagining has shape, it's an object by definition.

First, there are a great many thoughts that do not have a shape--as I've demonstrated before. You complained that all of the examples I used were a relationship betwen objects--as if that were significant--but there are concepts that do not fit that either. For example, the [square circle] is not a shape; nor is it a relationship between shapes, in my opinion. And the concept of [nothing] is another example. But these examples arent' necessary, because a [single shape] is something distinctly different from a [relationship]--even if it is a [relationship] between [multiple shapes].

Second, even if we allow only thoughts that are shapes to be considered. You still have a problem. Lets assume that the concept [apple] defines a [shape]--okay, I'll grant you that for the moment. But not all apples are the same. Even in the same variety... even off the same tree... each apple is a little different from the other--so how can you call [all of those different shapes]--a [conceputal shape]. Maybe you could get away with this for something like a square or a circle that becomes larger or smaller. But the differences in the shape of an apple inclues the actual outline. Some are [smooth], others are [lumpy], some are [rounder] others are more [oblong], etc.

At best, a [concept] is most definitely not a [shape] in the same sense that a [physical object] is a [shape]. Instead, such general concepts are a [range of shapes]--or in other words it is a [vague shape]. While a [physical object] is a [specific shape].

A concept inherently involves comparison between objects (hence why a concept is *always* defined in terms of objects).

This is true, but objects are also always defined in terms of concepts. For instance, a [physical apple] is a [physical object] that exemplifies the following concepts--among others: it originally has a [stem], a [peal], and[seeds]. It is a [fruit]. Iit can generally be used as [food]. It [grows on a tree] and is [part of a plant]... etc. Each [physical object] is defined by a [series of concepts] that categorize [what it is] and [what it must have] conceptually speaking. When an apple is growing on a tree--it always has a stem. But some stems stay with the apple when it is picked and some do not. The fact that the [shape of a stem] is optional for a [conceptual apple] clearly seems to indicate that that shape is not a specific part of the concept of apple. It can only be a part of the concept because the concept is vague and covers a wide range of shapes.

BTW, what is the [shape] that represents the [concept fruit] or the [concept food]?

[Antone]

Exactly, the concept "nothing" by itself has no meaning. It indicates the absence of something. To know what someone means when they use the concept "nothing" they must indicate what something or set of somethings is/are absent. If I say I have "nothing in my pocket" I mean that no object in the universe is in my pocket. I am taking, as my "set of somethings", every object that exists.

No... the concept [nothing] has a very specific meaning which you just (almost) stated.

nothing is the absence of every physical thing

This obviously means that the only place where [nothing] can truely exist is in the conceptual realm, because by definition all [physical things] are necessarily [physical].

Now, when the person says, "I have nothing in my pocket," they are not exactly telling the truth. For instance, there is [air] in their pocket. There are probably dust particles in their pocket, etc. When we say such a thing, we are assuming certain things. For example, we are assuming that we're talking to a person who isn't a vegetable--and therefore has an intuitive understanding of what the word nothing means. And so they know all of the above (at least intuitively) and so they also know that [nothing] has no physical meaning unless we allow certain limitations on what it refers to. Thus, it is understood that what we really mean when we say such a thing is that there is nothing of any significance in my pocket.

Compare this to the question and answer...

"What did you get?"
"Nothing?"

In this case, you would be correct... the set that the speaker is dealing with is [every object that exists]. And what he "got" clearly has no shape.

Terms like [0] and [none]... are not the same thing as [nothing], because these are counting terms--and what we are counting must be something that has some identifiable structure--else the numbers we use to count with have no meaning. Thus, when we say we have [0], it is meaningless unless we know what it is we have [0] of. But [0] is not the same thing as [nothing] unless the set we are counting is [every physical thing]. And in that case, we might still have conceptual things that we can count.

[Antone]

... But [0] is not the same thing as [nothing]

Actually, the way I see it, [0] is the physical aspect of nothing.

Because we are now referring to things that physically exists--the only way to express the [concept of nothing in physical terms] is to invert some aspect of the concept. Instead of defining that [nothing is there], we define [what physical things are not there].

Once again, this is the difference between the whole set, which is [every physical thing] and certain elements of that same set. Because sets and elements are reciprocal, this is again exactly what we would expect.

[altonhare]

For example, the [square circle] is not a shape; nor is it a relationship between shapes,

What is it then? Define the word "square" and then define the word "circle" so we can know what this is. If you mean these words the way I think you do then you have simply placed two contradictory words next to each other, nobody can conceive of a square circle. It is neither because it is inconceivable i.e. meaningless. Just because you can utter some words doesn't make them mean anything. It's an "invalid concept". It's not something, it's not nothing, it's not a relationship among somethings. It's two sets of symbols that each individually refer to a set of criteria. When you try to integrate these criteria you cannot. Square circle can only mean the shape square and the shape circle. It means "A square and a circle".

Your problem is that you try to integrate contradictions. This is extremely illogical and always leads to paradox.

And the concept of [nothing] is another example.

Again, nothing is a relationship between every object in the universe! It means that [all of the objects in the universe] are not at location X.

You repeatedly claim "nothing" as an example and have repeatedly failed to refute this point I have repeatedly made.

Maybe you could get away with this for something like a square or a circle that becomes larger or smaller. But the differences in the shape of an apple inclues the actual outline. Some are [smooth], others are [lumpy], some are [rounder] others are more [oblong], etc.

So we make new names for each one. Smooth_apple, Lumpy_apple, round_apple, etc. No matter how many distinguishing features there are, we can identify them and uniquely specify a single apple.

So no problem here.

At best, a [concept] is most definitely not a [shape] in the same sense that a [physical object] is a [shape]. Instead, such general concepts are a [range of shapes]--or in other words it is a [vague shape]. While a [physical object] is a [specific shape].

---------
___
---------

Figure one. Something with shape.

----------

----------

Figure two. "Something" without shape.

You will have to explain "vague shape". There is either shape or there isn't.

This is true, but objects are also always defined in terms of concepts.

When you define something1 as something2 and define something2 as something1 this is called circularity. Circular means these definitions don't actually say *anything at all*.

You are confusing the conceptual description of an object with the object itself. We can describe objects in terms of concepts. But the object is just itself, it is not defined by some relationship.

While up is the opposite of down and right is the opposite of left (concepts), apple is not the opposite of "no apple". Objects are not reciprocal.

BTW, what is the [shape] that represents the [concept fruit] or the [concept food]?

You can define these concepts in terms of objects in a number of ways. The concept "fruit" could be defined simply by showing someone a series of fruits and saying "fruit", then showing them a series of vegetables/meats/etc. and saying "not fruit". This is what it means to define a concept, you understand the concept ultimately by comparing objects. In this case the concept "fruit" is just a collection of shapes you pointed at that expressly forbids some other shapes you pointed at. This same method applies to "food".

Other methods are more general. A fruit may be defined as any object composed of >X% fructose. This boils down to counting the number of fructose molecules (objects). Therefore, the concept "fruit" is defined in terms of the object "fructose molecule". A food may be defined as something containing >X% carbon atoms and >Y% water molecules. The concept "food" is defined in terms of the objects "carbon atom" and "water molecule".

No matter how you do it, a concept can only be understood as a relationship among objects.

http://www.youtube.com/watch?v=P9kA6dbaer4

This obviously means that the only place where [nothing] can truely exist is in the conceptual realm, because by definition all [physical things] are necessarily [physical].

Obviously, I've stated repeatedly that the word "nothing" is a concept. Of course.

Thus, it is understood that what we really mean when we say such a thing is that there is nothing of any significance in my pocket.

Exactly, where "nothing of significance" is defined as some set of objects that the person considers insignificant. This is why I said:

To know what someone means when they use the concept "nothing" they must indicate what something or set of somethings is/are absent.

So every time someone says "nothing" you are assuming what set of objects they consider insignificant. Again, the concept is defined in terms of objects.

Actually, the way I see it, [0] is the physical aspect of nothing.

Physical: shape

The shape of nothing?

---------

---------

Figure three. The "shape" of nothing.

[Antone]

For example, the [square circle] is not a shape; nor is it a relationship between shapes

... nobody can conceive of a square circle. It is neither because it is inconceivable i.e. meaningless.

There are plenty of ways to conceputalize a [square circle]. And each person is likely to select a different way. Here are a few examples: (1) as a [sphere]--in which case we are thinking of the word [square] in terms of dimension and [circle] in terms of shape. (2) if we think of the sphere as [the object that is outlined when we spin a circle one full turn], then we can invert it and thing of a [square circle] as [the object that is outlined when we spin a square one full turn]. (3) Or we might think of the relationship between a [Riemann sphere projecting onto a cartesian graph]

These three definitions, of course, are (more or less) based on shapes--a cartesian graph has no boundaries and so it has no outer shape--but each person has a different idea of what we're talking about when we refer to a [square circle], so the concept is not based on a singular complex of [shapes and/or relationships between shapes]. Moreover, there are some ideas that are not be based on shapes and there is no reason to assume that the [square cirlce] can't be one of them.

For example, in the DS theory, I define infinity as [endless]. What is the shape of [endlessness]? Yet surely [endlessness] is a concept that has meaning. Another example of a [concept that has no shape] is the concept of a [four dimensional square], or a [ten dimensional square]. There are pictures that can help one to visualize (inaccurately) what a [four dimensional square] would be like--but there isn't any physical object that truely reflects this concept because the fourth dimension is being drawn on a page that is only 2-dimensional, and even if we built a 3-dimensional model of it, it would still be a dimension short. We can conceputalize what such a thing might mean, but we can't point to a physical object that reflects that concept physical.

In addition to being something that people can imagine--these multi-dimensional concepts can be manipulated mathematically to produce consistent results in much the same way that mathematics that models 3-dimensional space can produce consistent results.

So once again, I would suggest that there are all sorts of concepts that do not fit your defintions--and yet are real concepts and not just concatenations of concepts--the way a [unicorn] is or the way you apparently believe a [square circle] is.

...you try to integrate contradictions. [You find] This is extremely illogical and always leads to paradox.

The whole foundation of my theory is to integrate contradictions in a logical way that does not lead to paradox--so in that much, at least, you are correct. I can't help you with seeing the logic though--if you refuse to see it.

And the concept of [nothing] is another example.
Again, nothing is a relationship between every object in the universe! It means that [all of the objects in the universe] are not at location X.

You repeatedly claim "nothing" as an example and have repeatedly failed to refute this point I have repeatedly made.

Wrong. I have repeatedly refuted your point in numerous ways. For example: (1) [All the objects in the universe] is not a shape--so the relationship between this shapeless thing, [All the objects in the universe], does not satisfy your definition. (2) the claim that [nothing is a relationship between every object in the universe] does not satisfy the claim that a [concept] is a [relationship between two or more shapes]. Rather it is a relationship between [All the objects in the universe] and the concept [absence of]... what shape does [absence of] have?
I suppose you could claim that [absence of] is like [nothing] in that it is again defined by [all of the objects in the universe]--but then you clearly have a circular definition, which becomes virtually meaningless.

Maybe you could get away with this for something like a square or a circle that becomes larger or smaller. But the differences in the shape of an apple inclues the actual outline. Some are [smooth], others are [lumpy], some are [rounder] others are more [oblong], etc.
So we make new names for each one. Smooth_apple, Lumpy_apple, round_apple, etc. No matter how many distinguishing features there are, we can identify them and uniquely specify a single apple.

Yes, you can use this technique to uniquely specify a single apple...but not to specify the concept [apple], because that isn't JUST a [smooth apple] or a [lumpy apple], ect. it is all of those things at the same time. Which implies that none of those things is a significant aspect of what [apple] is.

In essence, these are the [concatenation of two distinct concepts], for just as [apple] is not defined by [smooth] or [lumpy]--the concept [lumpy] has very little to do with [apples], except to be a very small sampling of the [things that can be lumpy]. Creating the [union of two concepts] creates a [new and unique idea]--but it does so by having each concept limit the range of the other. [Lumpy apples] is a very small subset of [apples], and it is also a very small subset of [lumpy things].

But all of this misses the point anyway... the fact is that for every [limiting conceputal modifier] that you can come up with, I can show you two examples of things that are still [different in shape]. My conceptual modifiers must become more and more exacting in nature--but until you are referring to two instances of the [exact same shape at exactly the same time], I can demonstrate that the shapes of the two things] you're referring to are unique and different from one another in at least some miniscule way.

At best, a [concept] is most definitely not a [shape] in the same sense that a [physical object] is a [shape]. Instead, such general concepts are a [range of shapes]--or in other words it is a [vague shape]. While a [physical object] is a [specific shape].
You will have to explain "vague shape". There is either shape or there isn't.

The concept [line] is exemplified by all of the following objects:
________
____
_
____________________
___________
___________________________
What is the shape that [all of these lines], (and all of the possible lines that I haven't included) have?

Each of these [individual lines] has a [specific shape]. But collectively, they only have a [vague shape]. It isn't a technically accurate defintion, because it's somewhat circular--but the type of line I'm referring to can be defined as:

A [line] is such that [two parallel lines] will be the [same distance appart] at all points that are perpendicular to each other

Using this "definition" the following shapes are not [lines].
[, ), 0,

They do not belong in the collective group of things that exemplify the [concept line]. But by the same token
[____________________]does not define this concept either. It is one example of a thing that exemplifies the concept, but it is not the concept itself, because that concept includes all sorts of things that are [not____________________]. As demonstrated by all of the other examples of lines that we can think of.

This is true, but objects are also always defined in terms of concepts. When you define [something 1] as [something 2] and define [something 2] as [something 1] this is called circularity. Circular means these definitions don't actually say *anything at all*.

That's why my DS theory never, ever does that.

On the other hand, things that are reciprocal are not the same thing. That is why I can use [A] to define [1/B] and to define [1/A].

We can define a [pit] as a [hole], but it is also acceptable to define a [hole] as a [pit]. We define both in terms of the other. Obviously, unless we know what at least one of them means, the defintion doesn't tell us anything--but that is true of every defintions, it's just that most definitions contain more words.

I'll post more on this later...

You are confusing the conceptual description of an object with the object itself.

How can I be the one who is confusing the two--when I'm the only one (of us two) who is distinguishing between them. I am keeping them meticulously separated in meaning precisely so that I don't confuse them, and blur them into one singular thing.

We can describe objects in terms of concepts. But the object is just itself, it is not defined by some relationship.

This is a bit like saying that a [hole] is just a [hole]... it's not defined by some [pit].
Of course a [hole] is a [hole]!
Of course a [specific physical hole] isn't the same thing as the [concept hole]... That's what I keep trying to explain to you. But the [range of possible holes, which is the concept] does indeed define whether or not a [specific thing] is a [hole] or [not a hole]. If the specific thing is an [element of the conceputal set] then it is a [hole] because it [exemplifies the conceptual quality of being a hole]. If the [specific thing] isn't an [element of that conceputal set], then it isn't a [hole].

This is exactly why two different people can look at the same physical thing, and one can call it a [hole] and the other can call it [not a hole]. That is because each person has a different [conceptual set] that contains different [elements] for that concept. And the way that we accumulate the [elements in our conceputal sets] is by observing a specific object and being told what it is.

Observe the way a child learns. They see a [four-legged, fury animal, with a tail, and whiskers] and they say [ball] because that's the word they know. And their mother says, "No, that's a cat." So they lear to call this new object a [cat]. Then they go next door where they see a small dog that has [four legs, fur, a tail, whiskers] and the child calls it a [cat]. Over time, the child builds up a set of objects that do and do not exemplify the various concepts that it has learned. And the more examples of the concept the child sees the better they become at distinguishing between what is and isn't a cat.

They also learn to create conceputal subgroupings... For intance, they may go to the zoo and see a [tiger] and call it a [dog], even though they've gotten pretty good at telling the difference between cats and dogs. One of the qualities they were using may have been the relative size differnce between [cats and dogs]. The [tiger] is bigger, so they figure it must be a [dog]. But no, they are told that it is a [tiger] which is a type of [big cat]. Each time they learn something they are building the sets and elements that define their understanding of the world.

While up is the opposite of down and right is the opposite of left (concepts), apple is not the opposite of "no apple". Objects are not reciprocal.

Of course the [characteristics s that define objects] have reciprocal qualities. A [physical apple] is physical, a [conceputal apple] is not physical. [not x] is always the reciprocal of [x]. So a [physical apple] is the reciprocal of a [conceputal apple].
Simlarly, [being an apple] is the reciprocal of [not being an apple]. But both the [conceptual and the physical apple] exemplify [being an apple], so [being a conceptual or a physical apple] is the reciprocal of [not being a conceptual or a physical apple]. And the [union of all the reciprocal qualities that either do or do not apply to an object] define that object with meticulous conceputal accuracy.

In [absolutely physical terms], we have not defined the [physical apple] using these conceputal terms--because the apple is physical, and is thus not conceputal in nature. But in such [absolute physical terms] all we can say is that they apple is what it is. We cannot measure it with absolute accuracy. We cannot taste it with absolute accuracy.

This should be obvious since, for example, food tastes differently when we have a cold. In addition, what we eat tastes the way it does based on the particular configuration of our tastebuds--and the way wev interprets the signals coming from those tastebuds into our brain. Even if two people had exactly the same tastebuds and signal processing, they could not eat the [same part of the same apple]. And each part of an apple tastes just a tiny little bit different.

More over, any of the ways that we would go about describing the physical apple are themselves concepts. For example, what is [red] without a concept. The color [red] covers a range of colors--which may well be seen quite differently by different people.

What this all means is that there is no way to precisely define the [physical aspect of the apple] in [strictly physical terms]. But using conceptual terms, it becomes quite easy (by comparison) to define the apple with a very high degree of conceptual accuracy.

The concept "fruit" could be defined simply by showing someone a series of fruits and saying "fruit"

In other words, you're admitting that you think it should be defined in the same way that I do. As a [set]. As a vague conceputal concept. You just prefer to avoid certain common sense terms and thus you define the terms of your theory in non-intuitive ways--at least for me.

[altonhare]

There are plenty of ways to conceputalize a [square circle]. And each person is likely to select a different way. Here are a few examples: (1) as a [sphere]--in which case we are thinking of the word [square] in terms of dimension and [circle] in terms of shape. (2) if we think of the sphere as [the object that is outlined when we spin a circle one full turn], then we can invert it and thing of a [square circle] as [the object that is outlined when we spin a square one full turn]. (3) Or we might think of the relationship between a [Riemann sphere projecting onto a cartesian graph]

Great, all your definitions are shapes or relationships among shapes. My point is corroborated.

but each person has a different idea of what we're talking about when we refer to a [square circle], so the concept is not based on a singular complex of [shapes and/or relationships between shapes].

It doesn't matter in the slightest if you use the symbol "square circle" to refer to a different shape or relationship among shapes than me! It does not change the fact that we are each referring to either a shape or a relationship among shapes. Again my point is corroborated.

Moreover, there are some ideas that are not be based on shapes and there is no reason to assume that the [square cirlce] can't be one of them.

Not only have you failed to support this claim, you have only given credence to the opposite.

Another example of a [concept that has no shape] is the concept of a [four dimensional square], or a [ten dimensional square].

You cannot use this claim to support your argument until you define dimension.

Besides that, you cannot conceive of anything with 4 physical dimensions. No person in the universe can visualize anything in 1, 4, or more dimensions. A four dimensional "object" is again a contradiction by the physical definition of "dimension". Simply because you place two words next to each other with conflicting definitions/criteria does not a disembodied concept make.

To make the claim "a four dimensional square exists" you have to define dimension and define square. Then the object "four dimension square" either fulfills the criteria of your definitions or it does not. I assert that you will be incapable of defining dimension, square, and object in such a way as to conceive of a four-dimensional object without self-contradiction. Of course, you agree that we must avoid self-contradiction. Therefore if you contradict yourself then your proposed concept "four dimensional square" is an invalid concept and again all concepts are relationships among shapes.

For example, in the DS theory, I define infinity as [endless]. What is the shape of [endlessness]? Yet surely [endlessness] is a concept that has meaning.

No concept has shape. Infinity does indeed refer to "something" without shape/bound. "X is infinite" simply means that "X does not have shape" which means that "X is a concept and not an object". This is counter intuitive but that's because casual conversation is not based on consistency. In science we demand consistency, scientific communication demands more than casual chats in bars.

Infinity is a concept that has meaning, it means X is a concept and not an object i.e. X is a relationship among shapes and not a shape itself.

In addition to being something that people can imagine--these multi-dimensional concepts can be manipulated mathematically to produce consistent results in much the same way that mathematics that models 3-dimensional space can produce consistent results.

You must distinguish between physical dimensions and mathematical dimensions. I can assign an arbitrary number of parameters to some region of my room. I can assign it three coordinates and thus say it is mathematically three dimensional. Then I can assign it a time, a temperature, a density of air, a density of benzene... etc. and assign it an arbitrarily large number of mathematical dimensions. All these parameters I assign are relationships among shapes. The region of space in my room did not suddenly take on 4, 5, etc. physical dimensions because I assigned more parameters. The region of space did not suddenly become inconceivable or self-contradictory.

Just because we model something with an equation involving 4 or more parameters/coordinates/independent equations does not make it physically 4 dimensional. The object/entity itself is still a relationship among shapes. The parameters we assigned are relationships among shapes. All these are conceivable.

So once again, I would suggest that there are all sorts of concepts that do not fit your defintions--and yet are real concepts and not just concatenations of concepts--the way a [unicorn] is or the way you apparently believe a [square circle] is.

I have shown why there are no concepts that do not fit my definitions. You cannot define the words in your claim in such a way to define a concept that is not a relationship among objects without contradicting yourself.

The whole foundation of my theory is to integrate contradictions in a logical way that does not lead to paradox--so in that much, at least, you are correct. I can't help you with seeing the logic though--if you refuse to see it.

Apparently this is our problem. I accept Identity and you do not. You try to integrate contradictions. This will always lead to paradox.

Wrong. I have repeatedly refuted your point in numerous ways. For example: (1) [All the objects in the universe] is not a shape--so the relationship between this shapeless thing, [All the objects in the universe], does not satisfy your definition.

Each object in the universe has shape! Of course the concept "all the objects in the universe" does not have shape. You cannot have actually read and understood my definitions. Each shape in the universe is some distance from your pocket, you define this set of criteria as "nothing". It's a relationship among shapes.

(2) the claim that [nothing is a relationship between every object in the universe] does not satisfy the claim that a [concept] is a [relationship between two or more shapes]. Rather it is a relationship between [All the objects in the universe] and the concept [absence of]... what shape does [absence of] have?

Umm, the distance of every object in the universe from each other is a relationship among shapes... Are you intentionally missing this? I have repeatedly stated that concepts do not have shapes but are relationships among shapes. You just stated exactly that as a "refutation"...

No concept has shape. Only the objects/entities have shape. Some relationship among them is a concept. The concept "nothing" indicates that every object (shape) in the universe fulfills some specific set of spatial criteria. This set of criteria may end up specifying that no object/entity is within an inch of your pocket (besides the entities comprising your pocket).

Are you really not understanding this?

I suppose you could claim that [absence of] is like [nothing] in that it is again defined by [all of the objects in the universe]--but then you clearly have a circular definition, which becomes virtually meaningless.

"absence of" is just a synonym for "nothing". There is no circular definition...

Yes, you can use this technique to uniquely specify a single apple...but not to specify the concept [apple], because that isn't JUST a [smooth apple] or a [lumpy apple], ect. it is all of those things at the same time. Which implies that none of those things is a significant aspect of what [apple] is.

The concept "apple" is anything that fulfills some specific criteria i.e. is a relationship among objects/entities. I don't see the problem.

My conceptual modifiers must become more and more exacting in nature--but until you are referring to two instances of the [exact same shape at exactly the same time], I can demonstrate that the shapes of the two things] you're referring to are unique and different from one another in at least some miniscule way

I don't see the problem. If one entity is different from another in some miniscule way we use a different word for it.

Each of these [individual lines] has a [specific shape]. But collectively, they only have a [vague shape]. It isn't a technically accurate defintion, because it's somewhat circular--but the type of line I'm referring to can be defined as:

Right, it's not technically accurate because it's wrong. Each object you showed had a shape. That which doesn't have shape is a concept. They all fulfill the set of criteria specified by the word "line". In what you have presented the symbol "line" does not refer to a shape because it is a concept. There is no such thing as a "vague shape" unless, as you said, you want to use circular/wrong definitions.

But by the same token
[____________________]does not define this concept either.

Obviously. What you showed is a single object. A concept is always a relationship between two objects.

That's why my DS theory never, ever does that.

Defining object as touchable is circular because it demands another object to do the touching, your definition of "object" implies the word "object" itself! This is your problem. Touch is dynamic, it requires an action. What if an object is the only one in the universe? Is it then not an object because it's not touchable? Your definition results in a paradox. Shape is static. An object has shape even if it is the only object in the universe. You will need to define this most basic word "object" in a non-circular observer-free way before the rest of your theory can have meaning.

This is exactly why two different people can look at the same physical thing, and one can call it a [hole] and the other can call it [not a hole]. That is because each person has a different [conceptual set] that contains different [elements] for that concept. And the way that we accumulate the [elements in our conceputal sets] is by observing a specific object and being told what it is.

Agreed! We observe an object and name it.

In [absolutely physical terms], we have not defined the [physical apple] using these conceputal terms--because the apple is physical, and is thus not conceputal in nature. But in such [absolute physical terms] all we can say is that they apple is what it is. We cannot measure it with absolute accuracy. We cannot taste it with absolute accuracy.

Exactly! The physical apple isn't reciprocal in any way because it is an entity!

Nature doesn't care if we can measure or taste it with "100% accuracy". The apple is, regardless of our observations/measurements. Objects/entities are not reciprocal. Only concepts are.

In other words, you're admitting that you think it should be defined in the same way that I do. As a [set]. As a vague conceputal concept. You just prefer to avoid certain common sense terms and thus you define the terms of your theory in non-intuitive ways--at least for me.

We're not quite on the same page yet. There's nothing vague here. I avoid some common sense terms for consistency, casual conversation does not because we don't care about consistency at the bar.

I maintain that your definition of "object" undermines your entire theory. Additionally I maintain that objects are not reciprocal, as you pointed out. Finally I maintain that all concepts are relationships among shapes. Your examples are invalid. If you actually analyze your claims about higher dimensional "objects" you will come to the same conclusions with regards to the "square circle", that they are either invalid concepts (demand contradiction) or are relationships among shapes.

[altonhare]

Obviously. What you showed is a single object. A concept is always a relationship between two objects.

I should modify this to say "at least two objects".