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aleph_0

Objectivist Mereology

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How can it be the standard of what is possible? What does that even mean? It was possible that the caloric theory could have been true, it does not contradict any concept of existence, it just turns out to be physically impossible.

It means observation is the standard because it is the final authority on what is possible. Caloric theory could have been true only before the contradicting experiments and observations were made. After the observations have been made, we know that caloric theory does contradict the concept of existence and always has. The concept of existence refers to existence, this particular existence. There are not multiple existences and therefore not multiple concepts of existence. The concept of existence has a unique referent is not about some hypothetical construct(s) rationalistically derived from alleged first principles or axioms.

"Could have been true" refers to the theory's epistemological status at the time. Caloric theory was never metaphysically possible, but that was not known until after experiment eliminated the possibility.

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I've been reading this thread with some interest, trying to figure out how in the world anyone could assign logical statements to the relationship between parts and wholes without looking at what the relationship is between parts and wholes. I also don't understand the need for some people to come up with "a more rigorous presentation of Objectivist principles" in the sense of coming up with modal logic components. I mean, who is it going to convince, for one thing? I bet there are not that many people who can even read that modal logic "mathematical" language. Is it going to convince people like the Maverick Philosopher and his ilk who use modal logic exclusively without looking at reality? I don't think so because as soon as you say, now look at the facts, they will think that you are a primitive savage, as they have said that about Objectivists, including Ayn Rand.

The equation E=mc^2 is a very compact way of presenting some of Einstein's thoughts, but without knowing anything about what the terms refer to or how to do addition and powers, it doesn't mean anything to that person. Besides, even though it is compact does not mean that it is right, one has to look at the facts of reality and see if it is right or not.

Objectivism is verified inductively, and can only be verified inductively. Rationalistic schema centered around its key terms won't do anybody any good. Rationalism is part of the problem we are having, especially rationalism based on false premises, and that can only be fought rationally -- by presenting the facts.

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@aleph_0:

I do accept the distinction, and it probably does ultimately hinge on it, but you presumably take the distinction between metaphysics and physics to be a genuine one (otherwise you would be in the position of thinking that the metaphysics forum should be full of physics formulae and experimental data, which I doubt you want).

In the context of this discussion we are taking about a physically existing object, the study of the properties of which is the science of physics. If a material object exists metaphysically, it exists physically, and you want to talk about a perfect "Platonic" boundary of a physical object you must explain what you mean by it.

Again, the contest between the caloric theory and the mechanical theory of heat was won not by proving what was metaphysically impossible, but by experimentation, and so caloric theory is still metaphysically possible. It is for this reason that scientists were ever able to describe the caloric theory, and to make predictions about what would be true if heat were caloric rather than mechanical. And it is through knowledge of what caloric theory implies (even though the theory describes, as you call it, the null set) that we were able to disprove its reality.

Yes, treating heat as a fluid contradicts the facts of how heat is known to behave, and so the caloric theory was discarded; this is because we knew enough about how both heat and fluids behave. If one were to treat atoms, say, as open spheres, one would need to give a reason why one would suspect that atoms should be modeled in this way, just as scientists observed some of the properties of heat and concluded that it behaved somewhat like a fluid. But this would require you to know how open spheres behave when they interact, and I thought we agreed before that deriving physical behavior from pure mathematical models is inappropriate. So I still think that using open spheres to model physical objects is inappropriate in a way that the caloric or the ether is not.

I don’t see why you insist on this. You don’t need to see each atom of a thing to know that it’s made up of atoms. In fact, it is impossible to see an atom, regardless of the technology you use to visualize it. You must deduce their existence through a theory which implies them.

The fact that we can't see atoms doesn't matter-- it still wouldn't make sense to talk about a literal metaphysically existing boundary of an atom, in the mathematical sense.

@altonhare:

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.

I agree; this is why I object to defining perceptually evident entities using abstract topological descriptions. The notion of an "open sphere" as a literally existing object is arbitrary, much as God is because of his supposed property of omniscience. Someone talking about an object in the shape of a sphere with no boundary is making the positive claim that it has such a property, which as I mentioned before would require infinitely precise measurements to check. So because the property of being "open" is arbitrary I would go further and ask why talking about objects with open boundaries is useful at all.

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Incorrect your confusing existent with entity.

I don't see why that's so, but it seems like not a terribly important point.

When one defines sphere he finds that "open" would contradict its essential charachteristic shape. Unbounded object is the same as saying a= non a

I don't see why. Open sphere is just as much a shape as closed sphere.

It means observation is the standard because it is the final authority on what is possible. Caloric theory could have been true only before the contradicting experiments and observations were made. After the observations have been made, we know that caloric theory does contradict the concept of existence and always has.

It doesn't contradict the concept of existence--if so, then one could have found out that the caloric theory of heat was wrong by pure conceptual analysis, and needed no experimental data. The concept of existence refers to existence, but they're not the same, and analysis of one is not the analysis of the other. The concept of existence doesn't contain within it the implication that heat must be mechanical. Were experiments to have turned out differently, we could still intelligibly talk about heat being caloric and science could have moved on from there. If you don't take this to be a genuine difference, I don't see how you can think that metaphysics should be a study independent of physics.

I've been reading this thread with some interest, trying to figure out how in the world anyone could assign logical statements to the relationship between parts and wholes without looking at what the relationship is between parts and wholes.

Who has done this? There's a huge debate about the relationship between parts and wholes, and it seems to me they're looking at that relationship.

I also don't understand the need for some people to come up with "a more rigorous presentation of Objectivist principles" in the sense of coming up with modal logic components. I mean, who is it going to convince, for one thing?

It's not designed to convince but to accommodate understanding.

If a material object exists metaphysically, it exists physically, and you want to talk about a perfect "Platonic" boundary of a physical object you must explain what you mean by it.

I'm willing to stipulate that, if something exists metaphysically, then it exists physically. That doesn't rule out a difference between metaphysical possibility and physical possibility, nor does the distinction imply Platonism.

If one were to treat atoms, say, as open spheres, one would need to give a reason why one would suspect that atoms should be modeled in this way, just as scientists observed some of the properties of heat and concluded that it behaved somewhat like a fluid. But this would require you to know how open spheres behave when they interact, and I thought we agreed before that deriving physical behavior from pure mathematical models is inappropriate. So I still think that using open spheres to model physical objects is inappropriate in a way that the caloric or the ether is not.

I don't see why you couldn't use previous observations about matter to then come up with different predictions based on whether matter were continuous or discrete. We know matter exerts gravitational force, it bounces of of other matter, etc. That behavior might be different under the different hypotheses of continuity and discrete boundaries.

The fact that we can't see atoms doesn't matter-- it still wouldn't make sense to talk about a literal metaphysically existing boundary of an atom, in the mathematical sense.

The fact that you can't see an atom matters, since it's an example of something you don't have to investigate each microscopic detail to then conclude a fact about the whole--like in continuity and discrete boundary questions. But we seem to have laid that issue to rest now.

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I'm willing to stipulate that, if something exists metaphysically, then it exists physically. That doesn't rule out a difference between metaphysical possibility and physical possibility, nor does the distinction imply Platonism.

Then what is the distinction between a metaphysical possibility and a physical possibility? Why not just stick with the idea of possibility if you have evidence that a certain kind of entity may exist?

I don't see why you couldn't use previous observations about matter to then come up with different predictions based on whether matter were continuous or discrete. We know matter exerts gravitational force, it bounces of of other matter, etc. That behavior might be different under the different hypotheses of continuity and discrete boundaries.

What does it mean for matter to be continuous-- infinitely divisible? Also I still don't know what you mean by discrete vs. continuous boundary.

The fact that you can't see an atom matters, since it's an example of something you don't have to investigate each microscopic detail to then conclude a fact about the whole--like in continuity and discrete boundary questions. But we seem to have laid that issue to rest now.

What do you mean by atom here? Do you mean a literal point particle, or just "that which cannot be divided further"?

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Then what is the distinction between a metaphysical possibility and a physical possibility? Why not just stick with the idea of possibility if you have evidence that a certain kind of entity may exist?

The difference is that we could live in a universe where there is a class of things which are physically possible, which would be a subclass of the metaphysically possible things. Metaphysics studies the general principles of existence, while physics studies the principles of things that happen to exist. One is a matter of conceptual analysis and the other is not, though it depends on conceptual analysis (as does everything else, since all studies depend on concepts). So while there is nothing in the concept of existence that precludes the caloric theory of heat--nor does it contradict the concept of existence today, when we know that heat is actually mechanical--and so it is metaphysically possible.

What does it mean for matter to be continuous-- infinitely divisible?

Not exactly (or at least, that's not precise enough to communicate the meaning). It would mean that the boundary of any given material object should be described by a continuous function [or functions] (i.e., be described by a function [or functions] which is identical to its limit at all points).

Something is discrete if it, at some point, can no longer be sub-divided--that is, if it has some unit of smallest dimensions. (So a smallest length, area, perimeter, etc.) The reason I use continuity and discrete boundary is because you could have an infinity of points in-between any two points and they would not necessarily be continuous (the ordered field of the rationals is like this). I don’t suppose this would be metaphysically impossible, but I don’t find it terribly interesting, while continuity and discrete boundary do seem interesting.

What do you mean by atom here? Do you mean a literal point particle, or just "that which cannot be divided further"?

Here I’m just talking about the atom we know about through physics.

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QUOTE (Plasmatic @ Apr 10 2009, 07:37 PM)

Incorrect your confusing existent with entity.

I don't see why that's so, but it seems like not a terribly important point.

QUOTE

When one defines sphere he finds that "open" would contradict its essential characteristic shape. Unbounded object is the same as saying a= non a

I don't see why. Open sphere is just as much a shape as closed sphere.

To the first read ITOE.

To the second round-cube is a shape? You need to understand what essential characteristics are in relation to the law of identity.

Ive been working on something that is related to this entire thread and will post it when I'm done...

Edited by Plasmatic

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Is there unrestricted compositionality?

Objectivism qua philosophy does not address this directly, and there is no authoritative way of judging whether something is implied by Objectivism, but I'll tell you what I think: I hold that the Universe is inexhaustible, which means that you can never say things like "I have discovered the end of the Universe. There exists no entity past this point, and no entity will ever get past it." All you can say is: "Within the context of my current knowledge, I have not identified any entity past this point." With respect to mereology, this means that you can never say "This is an elementary entity not composed of any parts" ; you can only say "Within the context of my current knowledge, I am not aware of what, if any, parts this entity is made of."

Is parthood a transitive relationship, and is it extensional?

Transitivity is quite trivial.

Now, if by "extensional," you mean "an entity is identical to the sum of its parts," then my answer (again, I am not speaking for Objectivism) is a definite NO. In fact, that is one of the greatest, most entrenched philosophical fallacies that still go unchallenged today. The most obvious counter-example is the entity you see when you look into the mirror--or any counscious organism, for that matter. No single cell of a conscious organism has consciousness as an attribute, yet the whole organism does have consciousness as an attribute. This means that there is more to it than just the cells it is made of.

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Objectivism qua philosophy does not address this directly, and there is no authoritative way of judging whether something is implied by Objectivism, but I'll tell you what I think: I hold that the Universe is inexhaustible, which means that you can never say things like "I have discovered the end of the Universe. There exists no entity past this point, and no entity will ever get past it." All you can say is: "Within the context of my current knowledge, I have not identified any entity past this point." With respect to mereology, this means that you can never say "This is an elementary entity not composed of any parts" ; you can only say "Within the context of my current knowledge, I am not aware of what, if any, parts this entity is made of."

That's not quite the question of unrestricted compositionality. The principle of unrestricted compositionality states that, for any two objects, there is a third which composes them. So there is an object which is my left fingernail and the north half of the Eiffel Tower between 1960 and 1965. Let's call it Dribke.

Just as you may point to one ship in a fleet of ships and say, "This is a fleet of ships," without pointing to all of the fleet of ships, you can also point to my left fingernail and say "This is Dribke."

Transitivity is quite trivial.

Actually, my girlfriend has a very clever argument that proper parthood is not, if you accept three-dimensionalism. (And so, it's actually a bit of an argument against three-dimensionalism.)

Now, if by "extensional," you mean "an entity is identical to the sum of its parts," then my answer (again, I am not speaking for Objectivism) is a definite NO. In fact, that is one of the greatest, most entrenched philosophical fallacies that still go unchallenged today. The most obvious counter-example is the entity you see when you look into the mirror--or any counscious organism, for that matter. No single cell of a conscious organism has consciousness as an attribute, yet the whole organism does have consciousness as an attribute. This means that there is more to it than just the cells it is made of.

Good point. I'll have to think about it.

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The difference is that we could live in a universe where there is a class of things which are physically possible, which would be a subclass of the metaphysically possible things. Metaphysics studies the general principles of existence, while physics studies the principles of things that happen to exist. One is a matter of conceptual analysis and the other is not, though it depends on conceptual analysis (as does everything else, since all studies depend on concepts). So while there is nothing in the concept of existence that precludes the caloric theory of heat--nor does it contradict the concept of existence today, when we know that heat is actually mechanical--and so it is metaphysically possible.

This is very much analytic/synthetic flavor-- you want to tease out the implications of "existence" via pure conceptual analysis without the "messy" details of what the physical facts happen to be. You want to discover what is true in all possible words, so to speak? That which precludes the caloric theory of heat from the concept of existence is simply that caloric has not been shown to exist. The fact that such was not known at one point in time merely means that we as humans are able to imagine materials having properties which contradict each other in certain circumstances (where the contradiction is not explicit either due to ignorance or context-dropping), not that the imagined substance in question is "metaphysically possible."

Not exactly. It would mean that the boundary of any given material object should be described by a continuous function [or functions] (i.e., be described by a function [or functions] which is identical to its limit at all points).

Does such a conception not run against the same objection I've been raising in this thread? An appeal to an object "containing all of its limit points" is a positive claim that such an object can be known to exist, which it cannot due to the impossibility of infinitely precise measurement.

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This is very much analytic/synthetic flavor-- you want to tease out the implications of "existence" via pure conceptual analysis without the "messy" details of what the physical facts happen to be.

Not at all. I love facts. Empiracle facts, however, don't tell you what's metaphysically possible. They're different subjects.

You want to discover what is true in all possible words, so to speak? That which precludes the caloric theory of heat from the concept of existence is simply that caloric has not been shown to exist.

That doesn't preclude it from the concept of existence. Just from physical existence.

The fact that such was not known at one point in time merely means that we as humans are able to imagine materials having properties which contradict each other in certain circumstances (where the contradiction is not explicit either due to ignorance or context-dropping), not that the imagined substance in question is "metaphysically possible."

There was never a contradiction in the caloric theory of heat.

Does such a conception not run against the same objection I've been raising in this thread? An appeal to an object "containing all of its limit points" is a positive claim that such an object can be known to exist, which it cannot due to the impossibility of infinitely precise measurement.

It's not that mathematical points exist in the supposed entity, but that a function describes the physical points in the entity. That is, there is an isomorphism. For every mathematical point, there is a physical point; for every ordering of the mathematical points there is an equivalent ordering of the physical points. Again, there is no need for infinitely precise measurement, as has been established above.

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That doesn't preclude it from the concept of existence. Just from physical existence.

We're talking about the possibility of a material object existing. In what sense other than physical existence would a material object exist?

There was never a contradiction in the caloric theory of heat.

Doesn't it contradict conservation of mass (friction created large amounts of heat that didn't flow in from elsewhere)? Certainly not something an actual fluid ought to do. I know its abandoned nowadays since it has no predictive power and the kinetic theory gives a causal account of heat.

In any case, even if caloric theory was discarded as being arbitrary instead of contradictory, that doesn't change my objection against a material open sphere. Before the kinetic theory was developed caloric was a perfectly reasonable assumption, since we knew a lot about how heat and fluids both behaved. I've never seen anything with an "open boundary" running around, and it's impossible to tell whether a material object even has one, let alone the properties differentiating it from objects with "closed boundary".

It's not that mathematical points exist in the supposed entity, but that a function describes the physical points in the entity. That is, there is an isomorphism. For every mathematical point, there is a physical point; for every ordering of the mathematical points there is an equivalent ordering of the physical points. Again, there is no need for infinitely precise measurement, as has been established above.

I don't know what you mean by "physical points." But granting them for the moment, you can't just have a bijection of mathematical points and physical points, since that would run up against all kinds of paradoxes involving cardinality being ill-behaved with regard to other measures of size and shape, as I'm sure someone with your screen name is familiar. You'd need at least the continuity of your isomorphism in order to capture what you're getting at, and then you have the same infinite precision problem that you did before.

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Doesn't it contradict conservation of mass (friction created large amounts of heat that didn't flow in from elsewhere)?

If it did, conservation was a discovered law.

I've never seen anything with an "open boundary" running around, and it's impossible to tell whether a material object even has one, let alone the properties differentiating it from objects with "closed boundary".

Strictly speaking, the boundary is never open or closed--the figure is open or closed. But anyway, you don't have evidence that the objects around you right now are not open, and I don't see any reason to suppose that it's impossible to tell.

I don't know what you mean by "physical points."

Just point-sized objects. That is, having no extension.

But granting them for the moment, you can't just have a bijection of mathematical points and physical points, since that would run up against all kinds of paradoxes involving cardinality being ill-behaved with regard to other measures of size and shape, as I'm sure someone with your screen name is familiar.

What would be the problem? I've had conversations with people more mathematically educated than I am, and they've never expressed knowledge of such problems.

You'd need at least the continuity of your isomorphism in order to capture what you're getting at, and then you have the same infinite precision problem that you did before.

What infinite precision problem do I have? I just need verifiability, like with atoms.

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It doesn't contradict the concept of existence--if so, then one could have found out that the caloric theory of heat was wrong by pure conceptual analysis, and needed no experimental data. The concept of existence refers to existence, but they're not the same, and analysis of one is not the analysis of the other. The concept of existence doesn't contain within it the implication that heat must be mechanical. Were experiments to have turned out differently, we could still intelligibly talk about heat being caloric and science could have moved on from there. If you don't take this to be a genuine difference, I don't see how you can think that metaphysics should be a study independent of physics.

The rationalist understanding of a contradiction is an internal inconsistency. External inconsistency is a different matter, and is contingent upon particularities that could have been different. This internal versus external dichotomy is yet another instance of the analytic-synthetic dichotomy.

The concept of existence refers to existence and all of its properties known and unknown. Existence is identity and a contradiction is a statement contrary to that identity. All contradictions are contradictory for the same reason. Internal vs. external consistency is a distinction based upon a nonessential because there are not two kinds of identities, the known and unknown.

Metaphysics and physics both refer to the same existence and have the same concept of existence. The difference is the method used to study the subject. Physics is about measurements, metaphysics omits all measurements. No amount of metaphysical reasoning can substitute for a measurement, but all actual values of measurements are metaphysically necessary because they are measurements of existence, the same existence that metaphysics studies.

The concept of existence does contain within it the implication that heat must be mechanical. That is the identity of existence, the same invariant identity studied in different ways by physics and metaphysics.

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Strictly speaking, the boundary is never open or closed--the figure is open or closed. But anyway, you don't have evidence that the objects around you right now are not open, and I don't see any reason to suppose that it's impossible to tell.

It's impossible to tell since it requires infinitely precise measurements to tell. Since we can't measure infinitely precisely we probably shouldn't worry about classifying objects this way.

Just point-sized objects. That is, having no extension.

Similar problem here-- smaller than any positive volume. Can't really show this one exists either-- here you can say a material object has some nontrivial extension. I think the closest result in this direction for elementary particles is the electron, and that they only have to within 10^-22 meters or so.

What would be the problem? I've had conversations with people more mathematically educated than I am, and they've never expressed knowledge of such problems.

Well a representation of an object wouldn't be unique in any meaningful sense if you allow general homeomorphisms, for one. If you just have bijections you could "represent" a three dimensional object by a line segment, for another. Point being your correspondence can't just be a bijection, you need some fairly strong degree of continuity.

What infinite precision problem do I have? I just need verifiability, like with atoms.

Such a verification would presuppose infinitely precise measurement; you'd need to show that the map sends convergence sequences to convergent sequences.

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If mereology is a legitimate field of research, it would be a special science and not an aspect of philosophy. I say this because of the special characters used to set up the axioms and such in the Wikipedia article. I have a math background and have done differential vector calculus, but that stuff under mereology doesn't mean anything to me at all. So, it is a specialization, and it evidently uses a specialized notation for compactness, which means it is not a part of philosophy, despite the fact that Aristotle and other philosophers ventured into it. Ancient philosophers were into all sorts of special sciences, but it wasn't philosophy they were doing at that time. Philosophy deals with generalized abstractions from observations, and there terms must be available and understandable by any man who can read the language of the philosopher -- i.e. it must be clearly stated in English, or Greek, or Spanish, or French, without specialized notations that in and of themselves requires having had a specialized study in order to comprehend.

I was wondering about the earlier example of the top half of the Eiffel Tower and one's left toenail, and I don't see why anyone would think of that as an entity. Sure, your imagination can put together whatever it wants to, but that doesn't mean that it is an entity, except in the conceptual realm, and even there it breaks down because your toenail is not apart of the Eiffel Tower. The only way doing this might make sense that I can ascertain is something like a computer program variable where one puts together strings from different fields to make a new field -- i.e. one has the field "Credit Card" and the field "Master Card", and one can put those strings together to form the field (or string) "creditcard+mastercard". But still, that is not an entity in the sense of a basketball being an entity comprised of actual rubber parts glued together, but maybe this requires discussion.

In other words, yes the study of the relationship of the parts to the whole can be a legitimate field of study, but if you are going to be arbitrary about what you are combining together, I don't see how that will serve your mind well.

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I don't see why a thing loses shape when it doesn't contain its boundary.

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.

I don't understand the point. I can talk about whether a chair exists, and I can verify it by observing a chair. I can also talk about whether there are heat calories (in the sense of caloric theory of heat) and then verify or deny.

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).

My thoughts have no shape. Sub-atomic particles may have no shape.

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.

This makes no sense, and either contradicts itself or demonstrates a lack of understanding. The set of points on a sphere defined by x2 + y2 + z2 = 1 is infinite yet has shape.

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 idea of something being “infinitely infinite”, or “infinite in every way,” makes no sense. But infinity itself does not mean indefinite, or indefinable, or without boundary. It means that, in one respect, there is no limit. The universe may have infinite matter, and this would not be self-contradictory.

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"?

Matter may be infinitely decomposable and this would not be a contradiction. You may never find a smallest unit of matter, and yet you can observe it, see (or know) space that contains it, and space that doesn’t, it can interact with things in a determinate way, and so on.

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.

That’s patently false. 1 + 1 = 2 describes no motion when you’re telling someone how many rabbits are in a field.

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.

Why can’t you define something negatively, if its essence is negative?

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).

How do you define negation? Sure, you can use examples of things which are not defined by negation—but that doesn’t prove that it is, in principle, forbidden. (Hey, “forbidden”! That which you are not allowed to do!)

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".

I take it “matter” is a loaded technical term in physics, while “object” is just anything that exists.

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.

I’m not. I’m asking about the metaphysical possibility of the reality of an open sphere.

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.

I find it simply ridiculous to say that a group of pencils is not an object, or a fleet of ships, or a lamp (which is just a grouping and configuration of plastic, metal, cloth, glass, etc.).

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.

It’s a technical term meaning “junk”. It’s the things you can kick and feel.

Sure, the formation of groups as a mental act may be conceptual, but the groups themselves are just stuff.

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?

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That's not quite the question of unrestricted compositionality. The principle of unrestricted compositionality states that, for any two objects, there is a third which composes them.

I see. In that case, my answer is no. While you can conceptually group objects together into sets, that is not composition, just mental grouping. You can say "Let S be a two-element set containing my left fingernail and the Eiffel Tower" ; S is a valid way of referring to two objects together, but it is not a composite entity existing in outside reality, it is just a mental concrete that you have chosen to symbolize both of the two entities.

my left fingernail and the north half of the Eiffel Tower between 1960 and 1965

As a side note, I don't think "X between 1960 and 1965" is a valid way of referring to an object. X may be an object, and it may have existed between 1960 and 1965, but if it did, the X that existed between 1960 and 1965 is the same object that exists now.

Actually, my girlfriend has a very clever argument that proper parthood is not, if you accept three-dimensionalism.

LOL, I'd be curious to hear that argument!

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If mereology is a legitimate field of research, it would be a special science and not an aspect of philosophy. I say this because of the special characters used to set up the axioms and such in the Wikipedia article. I have a math background and have done differential vector calculus, but that stuff under mereology doesn't mean anything to me at all. So, it is a specialization, and it evidently uses a specialized notation for compactness, which means it is not a part of philosophy, despite the fact that Aristotle and other philosophers ventured into it. Ancient philosophers were into all sorts of special sciences, but it wasn't philosophy they were doing at that time. Philosophy deals with generalized abstractions from observations, and there terms must be available and understandable by any man who can read the language of the philosopher -- i.e. it must be clearly stated in English, or Greek, or Spanish, or French, without specialized notations that in and of themselves requires having had a specialized study in order to comprehend.

This is simply ridiculous. The only symbolic formalisms used in the wiki page are sentences from first order predicate logic. The characters you didn't recognize are shorthand for propositions used for the sake of brevity and rigor. Instead of writing "For any object x, for any object y and for any object z, if x is a part of y and y is a part of z then x is a part of z", you can just write Pxy & Pyz -> Pxz. Predicate logic is a language contemporary anglo-american philosophers frequently employ in all areas of investigation, not just mereology.

And even if this is somehow too much for your notation averse sensibilities to handle, how does your argument follow? Why does the particular notational expression of the same set of facts affect whether or not they are philosophical in content? That's like saying that a testimony recorded word for word in stenographer's shorthand has different content then the words of the original speech because shorthand is a specialized notation. Serious category error.

In other words, yes the study of the relationship of the parts to the whole can be a legitimate field of study, but if you are going to be arbitrary about what you are combining together, I don't see how that will serve your mind well.

The point is to find out what makes one combination arbitrary and another rational, not to justify absurdities.

Edited by cmdownes

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And even if this is somehow too much for your notation averse sensibilities to handle, how does your argument follow? Why does the particular notational expression of the same set of facts affect whether or not they are philosophical in content?

I wasn't trying to refer just to the symbolism, but like higher mathematics, the symbolism shows that it is a special science. Neither mathematics nor mereology are aspects of philosophy. Just because you are using logic, that doesn't make it an aspect of philosophy. Besides, logic is non-contradictory identification of the facts of existence as given by observation. In order to validate any of those claims of mereology, you would have to observe what the relationship of the parts to the whole are. "Logic" apart from confirming it with observation is rationalism, not rationality. And I think the example given of one's left toe nail and the top of the Eiffel Tower is pretty well evident that it is rationalism.You can't just go around arbitrarily clumping things together and say it is now a whole of which the things clumped in together are its parts.

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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.

Huh? Objects exist independently of belief THEREFORE one cannot verify whether or not an entity exists? That doesn't follow in the least. I don't see how you get total epistemic agnosticism about the existence of objects on the basis there being an objective reality.

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).

This just seems pigheadedly silly. I can point to a swarm of bees and say "swarm". Oh look, an entity, an object. But the swarm is composed of parts, namely individual bees. Lots of objects are like this - in fact, almost every object you interact with on a day to day basis from pizza to particle accelerators. The objective existence of an object isn't impugned by saying that it is composed of parts. Your argument seems to be that somehow bees "really" exist but swarms don't. I invite you to give a warrant for thinking that our understanding of swarm is "conceptual" whereas our understanding of bee is "ostentive". Or the same trick for leg and table.

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.

As above, I don't see how you can meaningfully distinguish between entities and "conceptual associations". Which is the cloud of atoms I call my body? The group of cells I call my blood? Which is the association of gears I call my grandfather clock? Which is the association of letters I call a word, or words I call a sentence? I think these kind of cases show why the retreat into the self-evident existence of some limited class of objects is problematic.

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.

This seems the most obviously false thing you write. The first counterexample that comes to mind is the search of physicists for black holes. We have some entity we think exists, that our working model of the universe predicts exists, so we go out and look to verify its existence. The second is, well, the everyday experience of accepting through testimony the existence of things that aren't self-evidently obvious, like atoms or Somalia. And third, you've inadvertently answered the question in arguing that its incoherent. Your answer is that only self-evidently existent objects exist, and that there do not exist any objects such that they are the sum of two or more distinct objects.

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.

We live in a radically impoverished universe if this is accurate. But more to the point, you don't actually argue for why any of this is so. You just assert it.

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I wasn't trying to refer just to the symbolism, but like higher mathematics, the symbolism shows that it is a special science. Neither mathematics nor mereology are aspects of philosophy. Just because you are using logic, that doesn't make it an aspect of philosophy. Besides, logic is non-contradictory identification of the facts of existence as given by observation. In order to validate any of those claims of mereology, you would have to observe what the relationship of the parts to the whole are. "Logic" apart from confirming it with observation is rationalism, not rationality. And I think the example given of one's left toe nail and the top of the Eiffel Tower is pretty well evident that it is rationalism.You can't just go around arbitrarily clumping things together and say it is now a whole of which the things clumped in together are its parts.

How is mereology neccessarily logic without observation? "Mereology" is part of the class of terms that includes "ethics" or "metaphysics". It's an area of inquiry with different approaches, some "rationalist" in your sense of the word, some more empirically oriented. To say "you can't go around arbitrarily clumping things" shows that unrestricted composition is false, not that mereology is rationalist.

Also, warrant the argument. Why does having a symbolism show that it is a special science? This is an unsupplied premise of your argument that you haven't justified. Taking time and effort to understand or having a technical language doesn't neccessarily mean that its subject matter isn't philosophy.

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I've changed my mind about mereology. The subject matter is such a source of confusion that the positions on the topic can be brought together under a name. For example, there is a fallacy of composition and a fallacy of decomposition. One cannot logically deduce any of the attributes of the whole are attributes of the parts. But denying that deduction is an applicable method is not the same as denying causality. It must be the field for induction, I don't know of any other methods.

Philosophers don't know how induction can be reliable, so its a stumbling block for them.

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Perhaps we are talking past one another re entities, so I will refer you to the entry under "entity" in the Ayn Rand Lexicon. Especially this entry from Dr. Peikoff:

"This term [entity] may be used in several senses. If you speak in the primary sense, “entity” has to be defined ostensively—that is to say, by pointing. I can, however, give you three descriptive characteristics essential to the primary, philosophic use of the term, according to Objectivism."

A random mental collection of things or even a real random collection of real things, is not an entity. I was going by Aleph-O's presentation of mereology re one's left toe nail and the Eiffel Tower as an example of a mereological entity when I was arguing against mereology as a legitimate field of research. By the way, a human being qua entity is not a collection of three trillion cells; a human being is an entity -- one thing.

Regarding using specialized symbols: Philosophy has to be available to every man, since every man needs to have a philosophy, so it has to be written in a common language. It is not necessarily not philosophy if it is written in a highly technical and symbolic language, but if it is written that way then it is for a specialized class of men who have studied the highly technical symbolism in order to understand it; that is something like vector calculus is not a part of philosophy.

I would say the study of the relationship of the parts to the whole is too specialized for it to be philosophy, just as geometry or physics is too specialized to be apart of philosophy. It is not something every man needs to know (in the kind of mereological details) in order to live his life rationally. Mereology, done properly, would be a specialization -- a special science. So, to answer the original inquiry of this thread, there is no Objectivist mereology just as there is not an Objectivist physics or an Objectivist calculus or an Objectivist geometry.

I had never heard of mereology until this thread, which indicates just how specialized it is, since I have a lot of general knowledge.

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