altonhare

In response to criticisms of my denial of "instantaneous velocity" or in general "instantaneous change", especially as it relates to calculus, this person has written well on the topic and reflects a lot of my own thought: http://milesmathis.com/are.html

"Why" questions are leading questions. "Why" presupposes purpose, i.e. the result of a conscious act toward a goal. So the question "why do entities exist?" presupposes that a conscious entity had a reason to make entities exist. To avoid "what made the original conscious entity exist" question we might declare the original conscious entity to be "eternal". Then we are stuck asking why other entities need to be brought into existence whereas the original conscious entity does not. We realize that this is an arbitrary distinction, there is no reason to think that entities were suddenly brought into existence by the act of a conscious will. Not only is it an arbitrary assertion, but it asserts that something can be created from 'nothing', an explicit contradiction. So we avoid the arbitrary and the contradictory by stating that entities exist. In general, we should avoid "why" questions except in the context of consciousness. Why did she go to the store? Because she wanted milk. Why did the rock fall down the hill? Because it wanted to get to the bottom? In the context of inanimate objects we generally (not always) replace "why" with "how". HOW did the rock fall down the hill? A gust of wind came along and pushed it. Why did the rock fall down the hill? Because Jim decided to kick it down the hill. Why is the sky blue? I donno, because the sky wants to be blue? Because God wants the sky to be blue? The better question is, HOW does air interact with light in such a way as to make the sky appear blue? Why do objects fall to earth? Again, do they want to fall to earth? Does TFSM push them toward the earth? Instead, HOW do objects fall to the earth? i.e. how does the mechanism called "gravity" work? I realize that in most daily conversation "why" questions are used in the context of the inanimate, with no problems, because it is usually assumed that the person means "how". What I mean is, we usually don't assume the person thinks a rock, or other inanimate object, has a purpose (a why). However this doesn't always get across, and it is important to remember the underlying, implicit assumption in "why?"

Understood. Hopefully this discussion got us both to think a little harder and possibly even learn something, even if neither of us is any closer to agreement. I'll close by making a statement based on my limited reading and knowledge of Oism. Rand seems to have said, on a number of occasions, that an entity is that which is "bounded" or "finite" or many other such synonyms. This would rule out "groups", since each unit in a group is bounded. However I believe it is also true that she never formally laid this down as part of Oism. I would also point out that, in addition to Euclid, Aristotle's Metaphysics speaks of "form" and other such synonyms for shape in reference to what an entity is: from Aristotle's Metaphysics Also, in general, substance ontologists focus on "that which is common to all". Shape, form, boundedness, etc. is common to all entities. This is exactly the criterion by which we distinguish physical objects from conceptualizations and avoids ambiguity, circularity, or individual opinion.

What will you refer to, if not something that exists? How will you refer to it before you observe it? How will you communicate with the ET? An entity is an entity. There is no "strong sense". When we're being rigorous it's either an entity or not. If it has shape, it's an object. It may not exist because it lacks location. I am visualizing a unicorn. The unicorn I am visualizing has shape, it is an object, but it lacks location. I am visualizing a spot, it has shape, but it also lacks location. The lake you "see" at the desert has shape, it's an object, but it lacks location (assuming the lack is not actually there). The distinction between objects that exist and objects that do not is location. The distinction between that which is something and that which isn't, i.e. what we can refer to as the subject of a sentence, is shape. I said earlier that of course we can describe this entity as being made of this or that. But we cannot define the word "entity" nor define "music box" as "made of parts". This begs the question, what are the parts? The entity itself is the shape you see before you, a single discrete unit. I never even said this. Whether you call a ball that's been squeezed "Ball2" and the original unsqueezed ball "Ball1" or you call them both "ball" is a personal choice. A person is justified in classifying them separately on the basis that one is oblong and the other is spherical. Another person is justified in classifying them together based on being round. They have shape *and* location. What's color to a blind man? What's color to Nature, when no humans have ever been born? What's duration or mass? What's sound to a deaf man? Or again to Nature? Nature doesn't recognize these. It's important to distinguish between two definitions of "sound", the vibration of entities and the human act of perceiving and identifying "sound". If a tree falls it vibrates the atoms of air around it. If there is a human present they perceive "sound". Now apply this to "color". An atom by itself may emit light. If there is a human present they may compare their perception of it to their perception of another atom emitting light differently and call the difference "color". In general when people say sound or color I interpret this as the human experience of hearing and sight. If I'm not referring to these human experiences I usually talk simply about motion and light. But there is no *guarantee* that every single entity that exist emits light, so light emission cannot be a fundamental, primitive aspect of all entities. As far as motion is concerned, we cannot even conceptualize or talk about motion without talking about *that* which is moving. So again motion cannot be a primitive aspect because it begs the question of what is moving? What distinguishes it? I never said this either. Shape is *primitive*. By this I mean that, in order to perceive, identify, conceptualize, and talk about any of the other properties we first need a shape before us. We cannot conceptualize motion without *that* which is moving. We cannot conceptualize light emission without *that* which is emitting light, or without visualizing light. What is doing all these things, what is vibrating, emitting, etc.? To answer this question you will irrevocably have to point at a shape. The property that is intrinsic to ALL entities is shape. An entity may have more characteristics, but shape is the bare minimum to qualify as an entity. Additionally entities that exist have location. What typically happens is the person listening has an association with the words you're using. The imbue your statement with their own meaning. When talking about mundane or everyday things we all tend to imagine or mean the same things and this works fine. In other kinds of discourse it is catastrophic. The person listening takes your statements to mean what THEY would mean if THEY said it. The end result is that you neither conveyed any meaning to them and they did not learn anything from you. The only way around this is to point at the entities that serve as the subject of your statements. At a bare minimum, what you point at will have shape. It will have to. You offer a lot of criticism, although it's clear you don't yet fully understand. But I have not seen anyone provide a definition of "entity" other than as a "self evident primary". But this is unacceptable, this means that what qualifies as an entity is a matter of personal opinion. X is something for me but not for you, and that's okay cuz everyone's different and special. Nature doesn't care about your personal opinion. Shape does not make provisions for opinion, it restricts the word "entity" to that which you can point at. This leaves it clear, rigorous, and non-circular. Other definitions, such as that which you can see/touch, are circular because they invoke another entity to do the seeing/touching. It's not a definition, it's a proof. An entity was an entity before you saw it or touched it, what qualified it as an entity before then? Another definition, an entity is "made of X", is also circular because it says an entity is that which is made of entities. So, can you offer better the circular see/touch and made off criteria or the useless "self evident primary"?

None of what you said addresses the incident issue. What is the attribute which is intrinsic to all entities? Do all entities emit light? Do they all have inertial mass? When we strip away these attributes, what is left? What is the last attribute which, if we strip it away, we no longer have an entity?

If you have never perceived Barack, then when you say "the current president of the United States", you are using a floating abstraction. You have no idea what you're referring to. On the other hand, if I perceive this keyboard on my desk, *then* talk about it, then I am dealing with *this* keyboard on my desk. It's the opposite of absurdity, to deny what you see right before you is absurd! There is absolutely no doubt whatsoever that you are perceiving an object. If you see a shape, you are obviously perceiving that shape. Now, whether you conclude that there is an object *there* (at some location), that it is wet (like a lake), or any other of a number of characteristics about it is up to your prior experiences with similar shapes. Your prior experience being limited, you could be wrong. However, obviously if there is a shape there, there is a shape there. If you see a shape, you see a shape. That you deny this is beyond me. All irrelevant. An object is not what it does, which is all I said, and which you did not argue against. Okay now we're moving from color to interaction with light. Does an entity have to interact with light to be considered an entity? The argument here is that there is only a single criterion for entity-hood: shape. An entity doesn't have to emit or absorb light to be considered an entity. All it needs is shape. Of course not. Shape doesn't refer to a specific shape. It simply refers to the quality of having shape. This quality is static. Unlike color/light, which is dynamic, i.e. 'a' photon must be emitted or absorbed. Also unlike "mass", which involves acceleration. Also unlike "tangible", which involves the action of touching. An object doesn't have to move, make a sound, emit light, etc. to be an object. Do you agree? Does the apple have to emit red light to be an entity? Does it have to fall off the tree? An entity would still be an entity, even if it never did anything. What makes it an entity in the absence of conscious observation and actions? The fact that it has shape. Without shape, there is nothing. We are not visualizing an entity anymore. In our minds we can strip away photon emission, inertia, etc. and there is still shape. The shape is what you point to and name. Its ALL the ET sees. Everything that comes after is treating the word as a concept. It's an entity before you ever pointed to it and named it. It was an entity not because it had color or weight, but because it had shape. By shape I don't mean it was triangular or pyramidal or whatever. By shape I mean it does not spontaneously spread out and become infinite, i.e. shapeless. It remains a finite, discrete thing. Intelligible, usually. Meaningful, almost never. Flawed logic. Let me translate: (1) Either there is something outside of a bounded space/shape x, or there is nothing outside of a bounded shape x. As: (1) Either there is an object outside another object x, or there is not an object outside another object x. This is all "nothing" means, it means "no object". When you say "there is no nothing" it is implied that you are saying "there is no nothing that exists". This just means "there is no no object that exists" which means "there is an object that exists". This is the only way to make this statement meaningful, avoiding contradiction. 3 does not follow from 1 and 2. There's either a 2nd object or not. Either way, an object is that which has shape. Surely an object doesn't spontaneously acquire shape only by virtue of rubbing shoulders with another object. Let's take this a different route. An object does not have to have taste, color, etc. to qualify as an object. It needs shape as a minimum. Without shape, how will you see it, touch it, taste it, visualize it, etc.? Without shape none of the others are possible. Without shape, what is coming up against your tongue? What hits your eyeball? Obviously a puddle is not a candle and they are not the same object.

You're the one who is not understanding. The purpose is to step back and ask what the universe would be like if we were omniscient. Then we draw deductions about what humans will observe in such a universe. If what we observe is consistent, this is support for the universe as we imagined it. Replace the word "space" with any other word. If you claim X is "suffused" then I have a right to ask you what IS X? Then it is your responsibility to point to X. If unable to point to the actual X, you will at least have to show a picture or model. If you cannot fulfill this simple minimum condition, then "X" is a wildcard, a floating abstraction. What's 'a' field? I'm not asking for a description or a quantification, I'm asking you what IS it, paleface? I'm an ET. Impossible. Motion cannot be transferred like an entity itself. Transfer itself involves motion. You're talking about the motion of motion. We still need to see 'a' field/EM wave, so we can even know what's moving. Then they are most certainly not entities. Empty: nothing Are you saying space is nothing or that it is an enclosure, inside of which there is no entity present? Is space like a box? transferring motion? Moving motion? You've gotta be kidding me. Point. Space is an attribute? And all this time I thought you were saying it was an entity! This is insane. This summarily converts all attributes into entities, a completely absurd notion.

I shouldn't have stated that the "friend" was moving at 0.5*c. What I said wasn't meant to be taken quantitatively but rather qualitatively. When you move faster relative to your friend you both calculate the same speed of light, although you both perceive different distances-traveled and different "times". So if you're moving toward the light source at .5*c and your friend is "stationary" s/he sees light going at a speed of 1/1. You see it going at 0.577/0.577 = 1. You will of course observe a doppler blue shift but a relativistic red shift. To know which way it goes you'll just have to calc it, wikipedia has lots of great articles on rel, here's the one on the relativistic doppler shift: http://en.wikipedia.org/wiki/Relativistic_Doppler_effect

You need to distinguish between the concept of a keyboard, something this long, this color, this shape, etc. and *this* keyboard on my desk. When you simply utter "the keyboard on altonhare's desk", unless you perceive it, you're not referring to *this* keyboard on my desk. You never verified its existence because you never identified it in the first place. You may have verified a claim i.e. there is something this long, this shape, etc. at this location. You verify whether this statement is true or not. Since 2 and 3 contradict 1, we must discard 1. It is not possible to doubt if a particular object exists since I am perceiving it. First of all, color is an awful counterexample. Color is a dynamic concept, it requires motion to observe and conceptualize color. Since no object IS what it DOES, we immediately discard all dynamic attributes as primitive, intrinsic characteristics common to all objects. How is there color without a consciousness to name something yellow and another thing blue? How is there color without a consciousness to conceptualize "color"? Certainly you don't propose that one atom identifies another as blue. Shape does not require a consious observer. Shape, in the primitive sense, has nothing to do with conscious identification or comparison. Objects have shape whether you're looking or not, even if all humans (or life for that matter) die off. With no life, no consciousness, there is no "color" or "rough". There are only shapes at locations. The concept "group of entities" does not consist of any entities because... it's conceptual. Entities may be described as consisting of entities, but not concepts. Also, since "made of" is a description by a conscious observer, entity in the primary sense refers to a single, discrete unit. In the moment where you point to it and name it, it is just itself. You have not begun to describe it in any way. This thing you are pointing at is associated with this sound you utter. So yes, at that moment, entity in the primary sense is referring to a single unit. The distinction is not artificial in the least. People make this equivocation all the time and it's the source of a lot of confusion and absurdity. You can certainly kick a table or a chair. Technically you cannot say that you kicked a piece of furniture, but we know what you mean. In everyday casual language this distinction is generally unimportant because we all have similar ideas about furniture and baseballs. But in deeper discussions, especially in science, the distinction is absolutely crucial. So no, no absurdity is present except insofar as one feels comfortable in using loose, casual speech and uncomfortable otherwise. You're used to saying that you can kick concepts because everyday concepts are widely agreed upon and well understood. You've become so used to it that you think it's absurd not to be able to speak this way. What you mean by "I kicked a piece of furniture" is "I kicked an object that is either a chair, a table, a cabinet, .... etc." In casual speech we don't have time for this kind of precision and it's just not necessary. But scientific language demands more precision than everyday speech. And indeed everyday speech is riddled with imprecision! That's why we call it "casual" instead of "scientific". In casual language we can speak of actions as causal primaries! i.e. her jumping caused the boat to rock. But we know only entities are causal primaries, not actions or attributes. In casual speech we can say completely ridiculous things like "anger took him over" or "love brought them together" or "parliament voted". All of these casual sentences speak of action, but what's acting? An entity? Do you really propose everday, casual speech as the standard by which we should decide the matters we are debating? If it leads to an absurdity in everyday speech, no good, not allowed? In more rigorous terms we say she hit the boat repeatedly then the boat rocked. Here "she" is the subject of the sentence, which must be an entity with shape (unlike love and jumping). "Hit" is the action she performs, boat is the entity she performs the action on, and "repeatedly" is an adverb that qualifies her action. "She" is the causal primary, boat is the entity being acted upon, and rocking is the resulting action. If you want to communicate with the ET, what will you say? A concept caused the boat to rock? An action? If an action, an action of what? You will have to point at the entity and illustrate the action. "Jumping caused the boat to rock" absolutely will not do it for the ET. You can't show the ET 'a' jumping. Groups seem to be where we're having the most friction. Mental groupings are concepts though, just as love and anger are. Therefore it is just as irrational to say that 'a' group hit you as it is to say that anger hit you. No group of objects is an object. "Group" is summarily conceptual. And exactly, in both your examples you are naming TWO entities. TWO entities is not ONE entity. No GROUP of objects is ONE object. You already said it, they are "physical characteristics". They are comparisons/conceptualizations that humans have made. An object, all by itself, just "sees" shape. An atom does not recognize mass or frequency. You absolutely need a human being to make observations and take measurements and then conceptualize "mass" and "frequency". I did not say they are "less objective". I am identifying the most primitive characteristic intrinsic to *all* objects. The table has shape *before* you point to it and name it. It is not brown, mahogony, hard, flat, etc. until you compare it to something else. The table doesn't have shape only when you're looking at it. edge, boundary, those are synonyms. boundary, as a synonym of shape, has nothing to do with an interface between two objects. With shape, there is no comparison taking place. Certainly an object doesn't spring into being when another object comes along. You're saying an object has no shape, no extent, unless we're looking at it!? Does my infamous keyboard disintegrate when I leave then reform when I come back? Right, you said it, human standards. Now again I'm not saying these characteristics can't be objective. However I am identifying that characteristic of an object that it had before humans ever came about. Even when nobody is around with a tape measurer, a camera, a retina, etc. This characteristic is absolutely critical to identify and maintain rigorously in scientific discussion. Again only because you're comfortable with loose, casual speech and uncomfortable with the opposite. Your level of comfort with using almost any term in the capacity of "object" is bizarre to me. Object means something very specific. Its this loose language, especially with regards to objects, that leads to huge meaningless debates, circular reasoning, absurd questions, and lots of wasted time. The question of "Is X an object? is not a matter of anyone's opnion, it is not up for debate. If it has shape, it's an object. If someone wants to propose that X is an object, they can point. Whether you name the object before you with the same name that you used before is irrelevant. How narrow (or wide) you decide to make your criteria for categories such as "chicken" or "candle" is entirely up to you. As far as I'm concerned it's a candle, then it's a puddle. They are not the same. You may decide that it's a candle, then it's still a candle. Perhaps your criteria for naming something "candle" is "whatever is made of wax". My proposal is not without precedent. Euclid more or less said this, but ultimately failed to actually implement the shape criterion:

Hey cmd, I appreciate you reiterating where the whole discussion came from to keep everything in the right context and to keep us on track. I was discussing this with another objectivist. I'll give some examples to illustrate the point. You tell me there is something round and hard in my front yard at home you call X. I'm at work. I come home and see a baseball in my front yard. Did I verify that it exists? Or did I verify that you were telling the truth? I contend that I verified if you were telling the truth or not. I observe the baseball, consistent with what you said, therefore you were telling the truth. How could I verify if *it* existed if I did not even know what *it* was before I observed it? I did not know what it was, because I had not yet perceived it. I form a mental conception of something that is round and hard. I visualize it, imagine feeling it in my hands. I see no reason something that is both round and hard cannot exist. Now, you propose that I can "verify whether it exists". Here, "it" immediately refers to something particular, my mental conception. I already know my mental conception exists in my mind. So I cannot verify whether my mental conception exists. If "it" is referring to "something out there that is both round and hard" then, upon discovering a baseball, you did not verify whether the baseball exists or not! You *discovered* something with characteristics you have already observed in the past. Before you discovered the baseball, you were never referring to the baseball itself. You were referring to a mental conception. So you could not verify whether the baseball existed, because you were never referring to it in the first place. You never referred to the baseball itself until you observed it. It does change. Determination is different than observation. Very different. I observe that which exists. I do not determine that what I am observing exists. This is wrong, I admit. I didn't think this through enough, what I should have said is that whatever I conceptualize or observe is, of course, something particular. So X is always something particular. However X is either something I observe or something I conceptualize. I don't verify whether each of these exists. One I am conceptualizing already and the other I am observing already. Objects move. What's the big deal? I explain the event/observation by saying that some fundamental object sticks to others. When these fundamental constituents move they shake loose from each other. This is a theory to explain the event. I still disagree with (2). I observe objects that exist. I do not grasp, determine, conceptualize, etc. their existence. If you refer to something like a television, computer, etc. as an object you are treating it as a single thing. As soon as you talk about how it was made, what it is made of, etc. you are dealing with the concept of a TV or computer. What you pointed at was the object. Your description of it is a conceptualization. I am not saying entities are only things that are grasped directly by perception. I am saying an entity is that which has shape. I am also not saying that you cannot describe an entity as being made of entities. Any definition besides "shape" for entity qua entity cannot be used consistently. An object has shape all on its own. Other properties such as color, sharpness, roundness, roughness, etc. require the comparison/conceptualization of a conscious observer. An object in the primary sense just has shape, it is intrinsic. I am not saying that an entity such as a music box is not made of entities. I am distinguishing in what context we can use a word to refer to an object and in what context we cannot. We can only use the word "music box" to refer to an object if we are referring to the shape which we point to. We cannot refer to conceptualizations and groups as if they were objects because, quite simply, they are conceptualizations and not objects. The music box is not 'a' group of gears. The music box is itself, it is what I pointed to. "Group of gears" is a conceptualization of the spatial proximity of entities. This avoids the absurdity of asserting that the Eiffel Tower and my left toe is an object. That kind of nonsense is right out. It identifies the most primitive, intrinsic quality common to all objects. It makes the word "object" unambiguous. It prevents absurdity like asserting that the Eiffel Tower and my left toe are 'a' object. Groups are not objects. A music box is NOT a group of gears. A music box is a music box is a music box. It is what I point to. It may be made of gears, this is a description of it, not a definition of it. We cannot haphazardly replace the word "music box" with the phrase "group of gears" wherever we want because one refers to an object, a shape, and the other refers to a conceptualization, the mental association of entities under some criteria. The shape criterion It is free of observers, other objects and "proof". Whether an object is big, heavy, red, soft, smooth, rough, etc. is a matter of a person's perception and comparison. An object is not identified as rough unless there is another object to compare it to that is not rough. An object is not colored unless there is at least one more object of a different color. An object is not big unless there is at least one object that is small. Shape, on the other hand, an object has shape even if it is the only object in the universe. The only alternative to shape is shapeless, i.e. nothing. There is no nothing. What I am presenting is not as bizarre as it sounds.

Concepts can indeed refer to attributes. The problem we have here is that "collection of entities" refers to some attribute of entities such as proximity. Since attributes cannot perform actions we cannot logically use concepts such as groups/collections in a sentence as if they were entities. Often we do this anyway as a convenient shorthand and, if the terminology and the abstraction is familiar enough, no meaning is lost. On the other hand, the entity itself is what you see before you, something you take at face value. Your understanding of the entity (how it was made, how it was put together, what it is used for...) is in your mind. The abstraction/conceptualization in your mind cannot perform actions or be acted upon. You cannot kick "it". It makes no sense to. You can kick the entity, the man or the bee or the dog. You cannot kick your mental association between entities, no matter how strong your mental association may be.

Hey cmd, before I respond I want to say I appreciate your constructive criticism and commentary. You are not, in this case, talking about a particular thing. You conceptualizing based on particular things you have already observed. You're guessing that you may observe in the future something that is hard, round, etc. Can a thing be both hard like wood and round like a balloon? You're not talking about verifying the existence of a particular thing.Then you stumble across a baseball. Did you verify the baseball existed? No, you just observed it and it happens to share conceptual characteristics with things you have already observed. The baseball is a particular thing that exists. Your concepts of round and hard are just characteristics of things you have observed before. I am simply arguing that you do not and cannot verify whether a particular thing exists. I'm making the distinction between verifying the existence of a particular thing and simply observing that which happens to share conceptual characteristics with things you have already observed. You may have verified that there is an entity with such and such characteristics, but you didn't verify whether *a particular thing* exists. First off, I don't really understand the distinction you're trying to draw between us. I take in direct percepts that define my ontology and then draw deductions/conclusions from that. You construct your ontology from percepts. So we both build our ontologies from percepts. Second off, I agree that existence is not a perceptual determination. I've been pounding on that, in fact. I observe that which exists. I don't determine, verify, etc. if *this* thing exists. I observe it. That's my whole argument against people talking about verifying whether X exists. If they have not observed X then X is not something particular and since everything that exists is something particular, they are not verifying whether X exists. You might say that the mental conceptualization represented by X exists. But when you stumble upon the baseball you cannot make the leap to saying you verified *it* (qua it) exists. I have observed a balloon and a block. I felt and saw sharp edges on the block but not on the balloon. I refer to this comparison as "round" versus "blocky". I also felt that the balloon was squishy/soft, I could push in on it. The block I could not. I refer to this comparison by describing the balloon as "soft" and the block as "hard". I wonder if there is an object that is both round and hard. I don't think there's any reason not, so I guess there is one. I discover a baseball. It is both round and hard. I did not verify whether *the* baseball existed. I simply discovered something which I could describe via previous conceptualizations. The fact that I guessed right is good luck or good intuition. 2 is absolutely not my claim. Entities exist whether we perceive them or not. I observe that which exists doesn't mean that which I don't observe doesn't exist. Your first statement is misconceived. You are misusing the word "consist". 'A' group is a concept, a mental construct, and cannot be said to "consist" of anything. This is why it contradicts your correct statement (4). Concepts, by definition, do not "consist of" entities. "Groups of entities" do not consist of entities. Its a concept, a mental association of entities. The problem here is the way you're using the word "object" or synonymously "entity". When we point at something and name it (treat it as an object) it is taken at face value. It is a single standalone thing. When you start talking about *how* it was made, *what* it is made of, etc. you are describing and conceptualizing. You point at a table and say "table". The ET just sees one standalone thing. The table is an object. The ET knows nothing about what it is made of, how it was made, what it's used for, etc. When you talk about what the table is made of you are conceptualizing it, i.e. you are using the word "table" to refer to the concept of cutting wood into specific shapes and putting it together so people can eat off it... etc. When talking about table qua table, or any entity qua entity, it is not "made of parts". In the primary sense an entity is simply that which you point at and has shape. There is no caveat for being a "sum of its parts". As soon as you talk about it being a sum of other entities you are dealing with a concept and not an object. You are dealing with the concept of atoms bonding or chopping trees etc. No entity, in the primary sense, is a "sum of parts". In the primary sense "entity" encompasses a single distinguishing characteristic, shape. The problem here is in (3). You went from music box qua music box in (1) to music box that was made by putting these entities (gears) together in this specific way in (3), which is explicitly a concept. The act of putting together the music box with gears is conceptual. This is an equivocation between music box the object and music box the concept.

If atoms could move faster than light then yes, you could be hit in the head with one before seeing it with your eyes. The supersonic bullet is a good analogy. The reason you and your friend both calculate the same speed of light is very simple. Your friend, travling at 0.5*c relative to you, has a clock that physically ticks slower than yours. So you see the light beam traverse a meter in a single tick of your clock, your friend sees it traverse half a meter but also only sees half a tick of his clock. You both get c=1. This is a bit patronizing and heavy-handed. Frisky is trying to visualize and understand the situation from a rational, intuitive approach in hopes of reconciling it with observations. No, light does not "seem to have a different speed" for the person moving. Light's speed is calculated exactly the same. Yeah, I've heard the "light is instantaneous" argument before and I can't conceive of any way it could possibly be true. Not only do I have issues with "true instantaneity" but every experiment ever done summarily falsifies it. In particular, a very simple setup (done in high vacuum 10^-10 mbar): Source S and detector D are separated by 1 unit distance. Turn on the source and a timer, D detects and turns off the timer. The time for this is t and the speed of light is 1/t. If light is "instantaneous" then t is the time for us to detect the change in D, which is essentially constant. Now S and D are separated by 100 unit distances. Repeat the experiment. If light is "instantaneous" but only appears to have a finite velocity because it takes some time for us to detect it, then we will get the speed of light has 100/t, where t is essentially a constant temporal offset. Thus, if light were "instantaneous" we would expect its calc'd speed to increase with the separation of source and detector. We do not observe this effect. Until the proponents of "instant light" can surmount this seemingly invincible empirical barrier, I do not know how anyone can take such an idea seriously.

What can it even mean for a dimension to be "small"? An object can be small, but a concept? Brian Greene's analogies all fail. All the analogies in the world ultimately fail. In the "relativity of simultaneity" two observers come to contradictory conclusions. This is unacceptable. While observers in rel agree on if A is longer than B or if A has greater velocity than B, they disagree on the simultaneity of AB and CD. As we know there are no contradictions in reality. This indicates that time, at least as measured, is not fundamental to reality. But relativity is based on the idea that time IS fundamental. How will you "prove" that my table is 4, 5, or more dimensional? In which direction will you move it? Will you show that the inverse square "law" of gravity is different on tiny scales? But here you have just shown that the inverse square "law" is not a law but just a macroscopic correlation, a good heuristic formula. You'll have a new quantitative relationship for the attraction between bodies. Will you throw the table into a collider and tell me you pumped in more "energy" than you got out? What is this "energy", can you point to it? Show me a picture of it? Space is not "real". Space is nothing, and there is no nothing. I like your ideas on time and movement. Nope. The leprechaun I am visualizing in my mind doesn't exist. The keyboard I am visualizing in my mind doesn't exist. It exists if it has shape and location. Concepts exist although they lack shape and location if they are perceptually derived from shapes with location.

How is pi() a standalone, completed "number"? i.e. a finished result? Mathematically pi() represents, as you said, a series. Not just any series, but one for which we can always write an additional term. So pi() represents an operation, something that hasn't been done yet. Specifically what hasn't been done yet is adding in the nth term in the series. So we work with the symbol pi() until we're ready to get a finished result, at which point we finally calculate a number and replace pi() with it. You cannot manipulate that which is indefinite, undetermined, or neverending. Manipulations of pi() in algebraic equations and so forth are founded on the tacit assumption that pi will be converted into a number at the end, so we can say that we were just dealing with that number all along.

Just define the word "dimension" and you're all set. Dimension: Quality of an object indicating it has extent in one of three mutually perpendicular directions. With this definition, "time" is not a dimension. You cannot move in the direction of time. If you go with a more mathematical definition then you can justify as many "dimensions" as you want by constructing independent vector bases. But then one must ask what this has to do with real objects. I disagree very strongly. In fact, there is no reason to insert "time" into equations of motion at all. Motion is relational, i.e. the relationship between the locations of objects. When mathematicians say an object "is moving with respect to time" they are eschewing the physical nature of the situation in exchange for a mathematical convenience. They cannot say A is moving with respect to B until they point to A and B. time: motion + observer Sounds very good. In physics, i.e. the study of objects that exist (*this* keyboard), all objects are three dimensional. What do you mean by "exist in reality"? There is a fundamental difference between an object's dimensionality (its length, width, and height) and my experience of getting older, of before/after, etc. "Time" is dependent upon the conscious observer. When we remove the conscious observer there is no "time" thing lying around, there are only 3D objects at locations. Only when the conscious observer looks and says "A is moving twice as fast as B" or something similar, does the concept of "time" even arise. Not just any word we utter or anything we can measure qualifies as a dimension. Dimension, at least in physics, has a very specific and unambiguous meaning. It refers to the quality of an object having extent in one of three mutually perpendicular directions. When we introduce the conscious observer s/he may conceptualize temperature, time, weight, etc. but these are in his/her head. Nature didn't "know" about them. Exactly. It takes a conscious observer, with memory, to conceptualize "time". When we remove him/her there are only 3D objects changing location. Movement does not require the human mind. Motion is just two or more locations of an object. A human doesn't have to observe the object or measure the locations. If it was at two or more locations, it moved. Space is "nothing", a 0. Matter is a shorthand term humans use for the sum total of all objects that exist. Very well said . All the experiments in the world cannot change the definition of "dimension". Whether time is a dimension or not is not a matter of experiment or verification. I propose time is a dimension. My pendulum swung fewer times when I was running than when I was standing. Therefore time is a dimension. How will you "verify" if time is a dimension, if you do not even know what a dimension is!? You have to settle the definition first so we know what you're actually going to prove. Length, width, and height are ubiquitous and self-evident attributes of every object we observe. Where is time? Can you point in its direction? Can you point at it? A picture of it? When you think about the issue critically you realize that "time" is a mental conception of the relative motion of objects. We pick a standard mover and say everything else is moving X much faster or slower than it. We can then say something takes 1/X "time units" to go a unit distance. If the physicist cannot even imagine or illustrate a muon, let alone point to it, then s/he has nothing. All the measurements in the world do not make up for an arbitrary and/or nonexistent hypothesis. Without this crucial step the word "muon" remains a Joker and all statements based on it are arbitrary. Assuming the physicist can get past this hurdle, now s/he will have to explain the physical process of muon decay, since his/her theory is based on it. What causes the decay? If s/he cannot explain this process then s/he cannot possibly draw meaningful scientific conclusions from experiments based on it. Assuming the physicist can get past this , at best s/he has shown that the physical processes governing muon decay are altered at high velocity. As long as decay processes are treated as random physicists cannot even begin to base conclusions so fundamental as "time is a dimension" on decay experiments. The reason the concept "dimension" does (or does not) apply to time depends solely on the definition of "dimension". There is the physics definition, which I stated, and there is the mathematical definition. In mathematics "dimensions" are essentially anything you can measure but can't equate mathematically to another measurable. This seems highly arbitrary and rationalistic to me. It also seems a little dishonest since those reading mathspeak outside the field are generally thinking about physical dimensions. Distance doesn't change with perspective. Distance-traveled changes with perspective. Distance is a static concept. In relativity and most measurements you are NOT measuring the static concept "distance" between the floor and ceiling of the train but the dynamic concept "distance-traveled by a photon" from the floor to the train. It seems this misconception is nearly universal and inevitably leads to misunderstanding. An object can, of course, expand or contract under various circumstances for a variety of reasons. I measure a brick and a block of metal, concluding the metal is longer than the brick. You measure them and conclude the brick is longer than the metal. I measured on a summer afternoon and you measured on a January night. Do we suddenly conclude that time or temperature are dimensions? Of course not! We formulate a hypothesis (atoms perhaps) and a theory that atoms stick together, some more than others. When the atoms are moving fast they loosen from their stickiness and have a greater distance between each other. Metal atoms bind less rigidly so, when they move faster (are heated), they slip and slide away from each other more than in the rigid binding of brick. So if a pendulum seems to swing fewer times when you're running you don't conclude time is a dimension. This is at best a restatement of what happened, not an explanation! That the clock swung fewer times is just an observation. What's the scientific theory/explanation? Time dilated? If you cannot point to time this "theory" is a non-starter. No amount of experimentation in the world will suddenly make my keyboard 4D. It is clearly and unambiguously 3D. The product of momentum and mass is just m^2*v, so not sure what this means. Time is a convenient paramter to use when dealing with the motion of many objects. If we have only three objects A, B, and C we can just describe their relative motion directly, using only their relative location: AC = 2*BC i.e. A is moving twice as fast as B. If we have many objects this becomes more difficult, so we let everything move "with respect to time". This is essentially laying down a universal standard for everything's motion, so that we don't have to deal with purely relational motion anymore. Since physics has never found a "preferred frame" i.e. a preferred standard in Nature, the correct physical representation is purely relative motion with no "respect to time" while inserting "time" is a mathematical convenience. This is not to deny everyone's everyday experience/conceptualization of "time". However this is more a subject of philosophy than physics. Physics seeks to understand purely the physical situation, i.e. the objects. Philosophy seeks to study concepts like consciousness and the mind.

But this is exactly what I'm doing. I have never pointed at a thing without shape. I have never imagined a thing without shape. In fact, I can neither induce nor rationalize 'a' shapeless "thing". I didn't say "most important". I'm saying the most essential, primitive attribute. Just try to imagine an entity without shape. Visualize it. Or try pointing to one. It cannot be done. You point and say "swarm" and the alien just sees bees (individual entities, shapes). Shape, in fact, seems axiomatic. How will you argue for 'a' shapeless "thing"? First you will have to visualize or point to a thing, which will already have shape. You try to talk about or imagine things for the purposes of discussing if it can be shapeless, but you already see its shape. I don't see the difficulty with a quest to name "mental entities". They're called concepts. Up is a concept. Love is a concept. The leprechaun I'm imagining is a nonexistent entity. This keyboard is an existent entity. Like I said, it's impossible to point at that which lacks shape. Shape is axiomatic. When does the swarm suddenly not qualify as an entity then? When the bees are each an average of an inch apart? A foot? A meter? A light year? What if I bring a banana peel and slap it against the Eiffel Tower so it sticks and point at them? Everything is causally related to some degree. When do you draw the line? Looking forward to seeing that. What do you even mean by an entity having "range and domain"? Could you show me an example of a number actually expressed as an infinite sequence? What's this "infinity" and how will I know when I've reached it? Did you count them? Measurement is always limited by one's reference standard, which is given 1. If a ruler is a little shorter than your reference standard all you can say is that its length is <1. If its a little longer than it's >1. You can guess at values in between, but all we can *know* from a measurement are statements of the form "A is longer than B". Any quantitative information, such as A and B are around the same length, or A is twice as long as B, are guesses. Irrationals such as pi are not actually numbers, but processes (operators). Pi expresses an operation such as making successively high order polygons. The term "irrational number" is a misnomer. Pi invokes the *concept* of a circle, i.e. the concept of incessantly making a higher and higher order polygon. This is different than O, which is an object many would call a circle.

A mental entity is just any object I imagine, a square, a leprechaun, etc. The distinction from an existent entity (Eiffel Tower) is that existent entities have presence i.e. location. The leprechaun is not located anywhere, I am just visualizing it. This is circular, an entity is a thing, these are synonyms. When you say "out there" I think you're invoking presence/location. I don't know what you mean by "in isolation from its surroundings"? A portion of your yard is conceptual in the sense that you draw an imaginary line in your yard. There is no independently existing entity "portion of yard" lying there. You had to perform an imaginary operation (drawing a boundary) and then identify the result of this operation. At best I can think of this as an entity you imagine, that has shape but not location. I must strongly disagree with this. Concepts lack shape and cannot qualify as entities in any sense. What is the shape of up? Right. Essentially anything that can serve as the subject of a sentence, whatever we can utter that we have a mental association with, somehow qualifies as an entity. However entities are causal primaries. This means there are concepts which we understand that are not causal primaries, which means not everything we understand and think about qualifies as an entity. I think having more than one "sense" of using the word entity just muddles communication and leads to confusion at best, while at worst it can lead to paradox, misintegration, and a logical breakdown. We need a single way to use this word, and I propose shape. When you look you just see bee. The "acting together" is a mental criterion by which you group multiple entities. Allowing groupings of entities to qualify as an entity leads to absurdity. But you decided a bunch of bees could be an entity. So there is no reason a priori to say other groupings of entities can't be entities. This is avoided if we just stick to the shape definition. A psychological association is an entity? Why? What qualifies as an entity? It sounds like you are just saying that whatever seems significant to a person is an entity. However, irrespective of our identification, entities just have shape.

It's not a matter of "following". It's a simple matter of logic. "I will verify whether X exists" Since X is a specific entity, i.e. *this* keyboard, it makes no sense to say I will "verify" its existence. It's this keyboard. I don't see how this can be debated with Oists, since existence is the first axiom, and Ayn Rand makes it clear that we don't "verify" or "prove" the axioms. Maybe I imagine something in my head, and think (for whatever reason, insanity, delusion, religion, prior experience with something similar to it) that something like it exists. One day I stumble upon something that resembles what I imagined. Did I "verify" that the entity *in my head* exists? The entity in my mind is mental, it doesn't exist, it lacks location. I cannot "verify" if it exists because it doesn't exist by definition. I didn't "verify" whether the entity I stumbled upon existed either, I just observed it. Nobody has ever verified an entity's existence, we just discover entities that exist. This shows you do not understand the difference between a product of the mind, a concept, and an entity. If you point to it and name it, you are treating it as if it were a single entity. However most people will take your implied meaning by the common definition of swarm: a group of... Now you are defining a concept "swarm" as the grouping of all these little bees. Let's remove linguistic connotation. You point and say "X". I look and I see a bunch of buzzing dots. I'm not sure if you are pointing at the dot and naming it X or if you are telling me that you will you "X" as a convenient shorthand to mean "a bunch of buzzing things close together". The issue is that I have already identified the entity "dot" because each one has shape. Perhaps your vision is poor or whatever and you see a single shape, a blob. You look and see "buzzing blob". You do not identify the entity "dot" (or bee). You point and say "X!". I am not sure what you mean so I catch a bee and show it to you, or I bring you closer to the bees. Now you understand. You point at a bee and say "bee", then step away and hold out your arms and say "X". Now I understand that "X" is a conceptual grouping of bee entities, and I assume the grouping criteria (the relationship) is proximity/distance. If you look at the bees and see individual bees then "swarm" is a concept, a relationship amongst entities (bees). If you look and do not identify the individual bees *at all*, then you are identifying it as a single entity. As long as what you point to has shape, it is identified as an entity. To everyone, I think, the collection of symbols "swarm" does indeed refer to a conceptual grouping of individual bees by proximity (perhaps a biologist would have more criteria but the common man probably not). Who said anything about existence being "impugned"? I'm talking about logical communication. You have not understood my argument. Concepts (such as mental groupings) exist as products of the Mind IF that concept is based on perceptually identified entities (such as bees). So when you point at a bee and say "bee" then point at a collection and say "swarm", the conceptual grouping "swarm" exists as a mental grouping of bee entities. However, only entities themselves can logically perform actions or be acted upon. Therefore it makes no sense, logically, to talk about kicking 'a' swarm. Swarm just refers to a mental grouping! Are you kicking someone's mental processes? Whatever you're kicking, it has shape, it's an entity (a bee). Easily. Entities have shape. Concepts do not. Concepts are mental relationships between entities. An entity is a single, independent existent. Concepts are plural in that we need at least two entities to form a concept and dependent in the sense that they depend upon the Mind. No, it only shows your lack of understand the difference between objects and concepts. When you point to blood and name it, without identifying any other parts, you are treating it as a single independent entity not comprised of parts. As soon as you point to cells and define "blood" as "group of these entities" then "blood" is referring to a conceptual grouping. This is a matter of logic. When you identify individual entities and then mentally group them together, the word you use to refer to this mental grouping refers to a concept. If they cannot even imagine it, let alone point to it, they have no idea what they're even searching for. This reminds me: "It is not possible to put forward a strict definition of... existence." "Catholic teaching virtually asserts that God's existence can be proved." "Existence is at once familiar and rather elusive. There is more than a little difficulty in saying just what existence is. from the Catholic encyclopedia. The idea is similar. How can they even begin to "prove" that God exists if they don't even know what it means to exist? What the hell are they proving? Likewise, how can a physicist "verify" a black hole exists if s/he cannot even imagine it, let alone point to it? If you claim X exists, your first step is to point to it. If you want us to assume X exists, you at least have to show us what it looks like. Predict that a thing exists? This is highly illogical language. Predict means to guess something about the future. You're predicting that a entity will exist at some time in the future? Verify its existence? Before you can verify it, you have to know what you're looking for. An atom is a hypothesis, an entity that is assumed to exist for the purposes of a theory to explain a phenomenon of Nature. "Let us assume atoms exist, and they look like tiny little balls" *point to a ball*. You don't "verify" that atoms exist. At best you provide evidence and argument to convince someone to believe your theory. The hypothesis is just an unjustified, unverified assumption for the purposes of explaining the theory (by definition of hypothesis). lol, of course, no object IS two objects, much less the "sum" of two objects (whatever that means). That would be a contradiction. An object is an object is an object. "The sum of" objects is a conceptual grouping of objects. I'm sorry you see it this way. Skepticism is fine, but not skepticism for skepticism's sake. If you disagree you need to provide an alternate version or say why what I said is wrong. Agreed. A key word you use is "random". I think you use this to distinguish between collections of entities which you have already mentally grouped via your experiences thus far in life and those which you have not mentally grouped. The ones you have not grouped (such as a toe and Harvard) you describe as "random". Someone else, however, may have stubbed their toe repeatedly while at Harvard and thus have formed the mental grouping "Harvard and toe" because s/he associates his/her toe with Harvard. Aleph will probably argue similarly, that your use of "random" is more an indication of your personal groupings than a reason to discount 'a' group as "an object". This is why we need to distinguish clearly between object and concept. An object is that which has shape. We point to it and name it. You cannot point to 'a' group. You point to what you have identified as "swarm" and the alien from another planet just sees bees (individual shapes). It is when you make clear that you are referring to their spatial relationship when you say "swarm" that the alien understands the concept "swarm". When we look, independently of conceptualization, we just see individual entities, bees. This summarily precludes all groupings from qualifying as objects, be it "toe and Harvard" or "arm and leg". Human the entity is of course, an entity you point to and name "human". Human the concept may be referring to a spatial relationship amongst 3 trillion cell entities, although I think it is considerably more complicated than that.

The reason you're having difficulty is because you're not thinking logically. Or perhaps you are, I don't know what's in your brain, but what you're expressing isn't logical. "boundary" is a concept and not an object. Things can't "contain" concepts the way a box contains a rock. What kind of sense can it make to ask if the box contains up, love, or insanity? This is not a trivial semantic issue. In science and philosophy we demand rigorous, unambiguous communication. Nobody can entertain a question or claim which invokes such irrational ideas as a box containing wideness (i.e. an entity containing a concept). This is one way we distinguish our discipline from religion. You do not verify whether an entity exists. You observe an entity that exists. The chair was already there, you're just observing it now. Did it not exist before you observed it or after? Obviously an entity exists even when we're "not looking", therefore we never really "verify" the existence of an entity. We just happen to observe one. A big difference with the caloric theory of heat is that you're simply verifying a *theory*. Theories we may provide evidence for or against because they're just that, theories. An explanation is neither Right nor Wrong, it's just an explanation. One's believe in an explanation is either Right or Wrong, but the theory itself is just a theory. You provide evidence for (i.e. verify) a theory empirically and attempt to convince your audience to believe the theory. If they believe it they may be Right, but they may also be Wrong in their belief. New specific empirical observation may repudiate it, of course, and may even resuscitate a theory that nobody has believed for a long time. There's a big, BIG difference between verifying if *this* keyboard exists, and verifying if *this* keyboard is hard because it's made of tightly bound atoms. In the former case I am attempting to "verify" that which is axiomatic and self-evident. This is a circularity and defies the meaning of "axiom". In the latter case I am posing a hypothesis (i.e. an unjustified assumption) and using it to explain a phenomenon, then trying to find empirical evidence that will convince an audience that my explanation is True. The hypothesis you ask the audience to take at face value for the purposes of your theory. You don't prove a hypothesis, it makes no sense, because a hypothesis is an unjustified assumption by definition. It is the first step, so it must be unjustified (the empirical evidence comes last). Your thoughts aren't entities, of course they don't have shape. Thinking is an action, "thought" is convenient shorthand term referring to some specific sequence of thinking. i.e. when you say "I had a thought" you're not saying you suddenly acquired an entity called a thought. You mean you performed some action called thinking, the aggregate of which you refer to as 'a' thought. Obviously actions such as thinking or "having a thought" are not entities. Can 'a' thought run, jump, swim, or play? If your "subatomic particle" has no shape then its chances of being an entity die right there. I thought we just completed the lesson on groups/sets. "The set of X" is not an entity itself, so it of course lacks shape. X itself may be an entity, though. Your comment shows your lack of understanding, not mine. The biggest problem with "infinite" is that it is used in so many different ways and, even in the individual ways it is used, it is misused. Infinite as an adjective is unacceptable because adjectives describe entities, which have shape, and that which is infinite in extent does not have shape. The other way it is used is as an adverb, when someone says something like "there are an infinite number of objects that exist". Since number is a concept, specifically an action (to count), infinite objects can only mean "to count incessantly". What this is essentially saying is that we could count entities and never stop, if we so desired. But when will we stop and decide that there are now an "infinite number"? Again you are being illogical and contradictory. You say I may never "find" a "smallest unit of matter" (fundamental constituent) and yet I can "observe" it. How do you find something without observing it? Additionally, you are again talking about "space" as if it were an existent. You say that one might see the space that contains an entity. This contains two instances of treating space as an existent. First you say that one might see it. Second you say that it may contain an entity. A concept (such as nothing) cannot contain a rock like a box (entity) contains a rock. Does Objectivism surround a rock? This is just as absurd as talking about space surrounding/containing an entity. Wrong. When you tell someone "there are 2 rabbits in the field" this is a shorthand way of saying "I counted a rabbit in the field then I counted a rabbit in the field". How else do you know there are two rabbits, except by performing a process/action? Equations like 1+1=2 do indeed express actions except in the trivial case where it is a restatement of Identity "A=A, 2=2". Therefore some criteria must distinguish the LHS and RHS. One criteria is distance. On the LHS we have an object at a distance >X from another object. On the RHS we have the same two objects at a distance <X. The equation, then, states that two objects moved closer. It expresses an action. When you talk with objectivists it will be the most productive for everyone involved, including you, to strive to speak in the most essential language. I mention this because, here, I do not know what precisely you mean by "negative" or "essence". I'll try to answer, but it may be irrelevant because I have to assume your meaning. Essentially, no existent's "essence" (its identity) is "negative" (the lack of an identity). A IS A as opposed to A is not B A is not C A is not D . . . ad nauseum The former is identity, the latter is, at best, a description of A to someone that has never observed A, but has observed B, C, and D. No existent IS what it IS NOT. This is an explicit contradiction. You may be able to describe an entity to someone in terms of what it is not, but they will never know what A IS until they observe A. Then they know what A IS (rather than just knowing how it compares to other entities). I donno, how would you define negation? I don't use terms like space, negation, annihilation, etc. nor make claims about them. The burden is on you to define what you mean by the symbols "negation". In physics "matter" just means "all objects that exist" and an object is that which has shape. Shape is a necessary but insufficient condition for existence. Not only must A be something, it must also be somewhere. So an entity that exists has shape and location. The elephant I picture in my head has shape, but it is not present, it lacks location. *This* keyboard has both shape and location, it exists. The whole discussion of whether entity X exists is irrelevant and arbitrary, as Nate pointed out. Can a unicorn exist? Can a *)08ds80S)h exist? I have some equations, now can *)08ds80S exist? The relevant question is whether reality can be accurately described by a particular method, such as with a particular geometry. Because you are not thinking in essentials. What is an entity/object? Is it anything that can serve as the subject of a sentence? Certainly not, because then even "nothing" could be something! This would turn "entity" into a God word, a Joker in the card deck. An entity is that which has shape. Does a GROUP of X's have shape? What kind of absurdity is that? X is an entity. X X X is an X, an X, and an X. Three entities. Each one is an entity. Mentally you group them together and think about a "group of X's". This is not an entity itself, this is entirely in your mind. Entities are what we visualize or point at. Concepts are what we *understand*. We *understand* that there are three X's a small distance from each other, and we refer to this understanding as "group". Concepts are products of the Mind. However all concepts are some relationship amongst 2 or more entities, i.e. concepts are first predicated on entities. So, to express your concept to another (to make someone else understand what you understand) you will first have to present them with some entities with which you will demonstrate your concept. To understand above" you will *first* need two entities, such as a table and a coconut. Sit the coconut on the table and utter "above". Put the coconut below the table and utter "below". Put an apple on the table, then put another apple on the table. Utter "two apples". Put an apple on the table. Utter "three apples". Etc. "One" refers to something. "Two" refers to the act of bringing something and something else close together, and so on. So far, "open sphere" remains a concept disconnected from entities. First you will have to show us the relevant entities, then we may begin to understand the concept "open sphere". If "open sphere" is an entity itself, you have but to point to it. So groups, which are stuff, are things you can "kick and feel". If you can kick or feel 'a' group, then you are some kind of being far beyond me. I can kick a boat, but I cannot kick a group of boats! I can kick a boat and kick a boat. I can kick a boat, then kick a boat. I have never kicked a group, personally. If you have kicked a group sometime aleph, could you relate this experience? What's it like for your foot to come up against a concept? Could you show me (at least a picture) of this "group" that your foot came up against, so I can go try it?

What precisely is the distinction between "matter" and "objects"? Could you define exactly what you mean by "matter"? So, then, why are you talking about the properties of space at all, i.e. how it is related to matter/objects/whatever? If space is a term indicating 0, nothing, a placeholder, i.e. nonexistent, what sense can it make to talk about its relationship or properties? That which exists may have properties and a relationship to other existents. Ah, you mean is there a fundamental constituent, i.e. an object that is just itself, it is not made of other objects (it cannot be broken). It seems that Identity demands it. If A is made of B is made of C... ad infinitum this would seem to preclude A from having identity, since its identity is dependent upon a neverending chain of identities. So it seems there must be some "smallest entity", which is a single piece, and cannot be broken. At some point, we must have an entity that is not made of other entities, an entity with its own identity that is not a result of the relationship of other entities. Mathematics can, at best, tell us if one or more entity(ies) can be accurately described in a specific way we refer to as an "open sphere" or not. Mathematics has no power to answer the question of what an entity IS. Math can only describe. Correct. What's "stuff"? The latter part of your sentence is meaningless unless we know what "stuff" means.

I agree. An equation, set of equations, or a word are themselves just symbols without referents to reality. In order to avoid rationalism and absurdity we must start with observation as our first premise. Every entity we observe has shape, i.e. a boundary. We can, then, point at it or at least visualize it. It is irrational to talk about whether this or that entity exists, or to "verify" it. What kind of sense can it make to verify whether this chair exists? On the other hand, if you are asking how best to describe an entity, this is a reasonable question. An entity may be best described as round, flat, open, etc. for the purposes of quantitative accuracy or comparison. The entity exists or not. Just because you decide to describe it in a different way does not verify (or fail to verify) its existence. Agreed. Shape is the most primitive and essential quality of an entity. Without shape we have... nothing. Shape is primitive (i.e. undefinable and self-evident). Similar to how there is no alternative to existence, there is no alternative to shape. To talk about shapeless is to talk about nothing, yet talking about X (or performing any action on X) implies X is a thing, thus invoking a contradiction. Just as talking about non-existence is pointless and absurd, because talking about anything demands existence. This is a restatement of identity. Saying something is itself i.e. A=A is an axiom. You are using it to prove that A can have an existent referent. This is a meaningless tautology. Infinity violates identity and rationality. An object cannot be infinite because then it would lose its most essential attribute, shape. 'An' infinite object is not an object. Shape is not defined. At best it is described. Furthermore, shape is a static concept. Equations all express dynamic concepts, i.e. they describe motion. The equation of a mathematical line is not the same as the physical entity called a line. It is an itinerary describing the motion of a physical entity. Objects are what we visualize and/or point to. Equations are a way of describing the motion of objects. Yes it is! Touch is a "touchy" issue so to speak. When two fundamental entities come together, close enough so that they are no longer separate, do they remain distinct entities? They appear to, now, have a single surface. i.e. two objects appear to have become one. I've more to say on the topic, hopefully I'll remember to return to it. Well said. I can visualize entities, but they do not exist (the ones I'm visualizing). They are entities because they have shape, but they do not exist because they lack location. Right, of course we do. The repulsive forces can be interpreted as the blending of the electron shells of atoms, i.e. the surfaces of these shells come so close that they become indistinguishable and now possess a single surface. I do not "verify" that this keyboard has a boundary. What kind of sense can it make to prove that *this* keyboard is an object, or to "verify" that it has (or doesn't have) a boundary? Again, what do physical measurements have to do with whether *this* keyboard exists? If someone says "X exists" s/he simply has to point at it. If s/he cannot then s/he can show us what they are visualizing, and we must assume it exists for the purposes of the ensuing discussion. So the more serious issue is that this entity "open sphere" has not been pointed to or illustrated. The entire discussion is non sequitur because "open sphere" is still a placeholder, an arbitrary set of symbols that refer to a set of equations. These equations do not describe objects but rather the motion of objects, they tell us the relative location of one or more object(s) as they traverse a defined path. Fallacy, X cannot be defined as "not Y". A dog is not "not a tree". The issue here is that finite is the only term with relevance to reality. Infinite, as an adjective, is supposed to describe objects (and is often incorrectly used as such), but again 'an' infinite object would lack the most essential quality that makes a thing a thing, shape. So the only interpretation of defining infinite as "not finite" is "shapeless" which, at best, means "infinite" is mean to describe a concept and not an object. Since a concept is a relationship amongst entities the word "infinite" is predicated upon some entities, which must be pointed at or at least visualized first, before "infinite" can take on any meaning. Ted: A is perfectly defined. Bill: What is it? Ted: It is not B. Bill: d'oh, but what IS it? Or what's B? Ted: B is not A. Bill: What are they though? Ted: They're not each other... Things are not what we define. Things are what we point at and/or visualize. After that we may describe them with an equation or by comparing them to other things. But before we can describe or compare, first we must have the thing before us or firmly visualized in our mind.

Science will not answer this question because it is fallacious to attempt to verify whether this or that entity exists. An entity exists independent of your belief or attempt at verification. Additionally groups, groupings, and group hierarchies are conceptual, and concepts are not objects. Each object is an object, you might point to each one, but the association you have between them is entirely conceptual. A grouping or listing of objects is not an object (except trivially insofar as the symbols on the page which refer to those objects and the page itself are, themselves, objects). It is irrational to talk about combinations of objects "existing". An object is an object is an object. Each entity exists. A combination, group, or listing objects is a list of symbols enumerating entities that exist. You might, conceptually, associate one with another but this concept is of course not an entity. It also makes no sense to talk about "what can be said to legitimately exist". Existence is self-evident and axiomatic. There is no provision for proof, verification, or testimony. I point at something, I recognize that it exists. The problem is you went from simply pointing at the quarter and naming it to describing it. A description is a conceptualization. The moment you point at it and say "quarter" it is an object. Then when you say it is shiny, round, etc. you are conceptualizing it. You're dealing with the *concept* "quarter". When you say it is made of atoms this is a description, and you must first tell us what an atom is, i.e. you will have to point at an atom or a model of an atom. If you can point at an actual atom then now we realize that the quarter was a concept integrated by our brain by the perception of multiple entities, which our brain automatically subconsciously grouped. The atom is an entity, the quarter is a concept. If you cannot point at what you're talking about (an atom), but only a model of it, you're now asking us to assume something like what you're pointing at exists in reality. You will not, and indeed cannot, verify this assumption. This is a hypothesis, an assumption you ask us to take at face value in order for you to explain some phenomenon involving the quarter. At the hypothesis you do not describe the object. You just point to it and name it. Why does it break, bend, etc? When you're done we can choose to believe your explanation, thus believing in the existence of atoms, or we can choose to disbelieve it.

I'm going to assume by "matter" you mean "objects", if not please correct. Space cannot be the same as objects because space is conceptually the antithesis of an object, of a thing. Space is an absence, a 0. 0 is not a number, it is strictly a placeholder. An object is a something, a 1. Putting "time" next to the word space does not change this, since time can only be the observation of relative motion, not a thing itself. Are the fundamental constituents discrete or continuous? Are you asking if the universe is composed of disconnected, separate entities or of interconnected ones? In this regard it seems the empirical evidence is pretty clear that entities are continuously connected to each other. In particular I have not heard of a rational explanation for most phenomena of light in terms of the discrete corpuscular hypothesis. In this regard it seems that Nature has indicated the affirmative. Whatever entity is responsible for light does not seem to interact with itself, even if it is colocal. Whatever entity is responsible for magnetism seems also to pass right through other entities, although it does seem to interact with them at least. The most compelling phenomenon of Nature is, I think, that light does not seem to interact with itself. What do you mean?