Physical infinity

[NameYourAxioms]

SL, let's examine the validity of your anti-Objectivist rejection of the Law of Identity. When you claim that there are an "infinite number of 'speeds' between 0 MPH and 55 MPH", what you are really saying is that an object can travel somewhere between 0 miles and 55 miles (no more, no less) in one hour.  55 miles is a finite range, not infinite.

Edited August 15, 2016 by NameYourAxioms

[DonAthos]

1 hour ago, NameYourAxioms said:

SL, let's examine the validity of your anti-Objectivist rejection of the Law of Identity. When you claim that there are an "infinite number of 'speeds' between 0 MPH and 55 MPH", what you are really saying is that an object can travel somewhere between 0 miles and 55 miles (no more, no less) in one hour.  55 miles is a finite range, not infinite.

This is disappointing. StrictlyLogical obviously invested significant time and energy in composing his last reply to you -- and this reductive response of yours hardly repays him for it. It is unjust.

Furthermore, whether what you say is "pro- or anti-Objectivist," or in concord with the Law of Identity, is (in part) the nature of what you're discussing -- it will be borne out (or refuted) by your arguments. I only need your arguments, not your opinion of your own correctness (presumably, SL would consider you to be the one out of step with the Law of Identity; as for myself, I'm as yet undecided).

As for the content, I take SL's contention to be that between 0 and 55mph, there are an infinite number of speeds that one could travel. You say that the range is finite... but in your apparent rejection of the "infinite," do you mean it in the same sense he does? (I.e. is this a genuine disagreement, or some form of equivocation or misunderstanding?)

For instance, let us say that between 0 and 55mph, there are 55 possible speeds: 1mph, 2mph, 3mph, ...

But then we recognize that a person may travel at 1.5mph, which makes 56 possible speeds. Or at 1.1 mph -- so there are 57. Or at 1.05, so there are 58.

If we continue in this manner, can you tell me -- what will be the final number representing the finite number of possible speeds between 0 and 55mph?

Edited August 15, 2016 by DonAthos

[NameYourAxioms]

MPH is a man-made mathematical ratio.  Mathematical division is epistemological.  Numerators (miles) are infinitely divisible by denominators (hour) but you mustn’t forget that mathematics is only a tool devised by men to help answer questions about matter.  A number system, to be manageable, must be open-ended.  Mathematical infinities (that do not exist in the world) are an indispensable part of mathematics.  An arithmetical sequence extends into infinity without implying that infinity actually exists.
 
Is your car traveling 33 MPH or is it traveling 33.333333333333333333333333333333333333333333333 MPH?  The standard of precision that a given man chooses is an epistemological matter (man chooses whether to round the infinite mathematical sequence at 40 digits or 0 digits).  You have mistakenly taken the infinite mathematical precision possibilities afforded by our man-made decimal number notation system (epistemology) as proof for the existence of actual infinity (metaphysics).  The distinction between rational numbers and irrational numbers is not a metaphysical distinction pertaining to magnitudes.  It is rather, a mathematical distinction pertaining to the means of identification of quantitative relationships.  You are confusing the means of measurement (which are dependent on man's consciousness) with the objects of measurement (objects are what they are independent of man's consciousness).  The need for irrational numbers arises from a difference between mathematics and engineering.  In engineering (applied physics) with a concrete application in mind, one can always identify the required precision in advance.  But the application of mathematics is open-ended.  There is simply no way to anticipate the level of precision that may, someday be required for some reason. Geometric propositions have infinite precision but all of our measurements have finite precision.

Don't believe that our decimal number notation system is man-made?  Try expressing an irrational number to the precision of 40 decimal places using Roman numerals. 

 

 

 

[New Buddha]

The above post by NameYourAxioms is exquisite, well stated, cogent,and completely in line with Objectivist Epistemology.

My only nit (isn't there always one?) is that I would use the word "ontological" in lieu of "metaphysical".

Edit: Upon further reading, I need to add that the following statement:

"Mathematical infinities (that do not exist in the world)...."

Is neither true, nor false.  The claim that the Universe is "finite" is no more justified than a claim that the Universe is "infinite".  However, Rand does hold that the Universe is (ontologically) "finite", so the position is in line with Objectivism.

 

Edited August 16, 2016 by New Buddha

[NameYourAxioms]

The universe is EVERYTHING THAT EXISTS.  There can be NOTHING outside of the universe (including "other universes") since nothing is excluded from the concept "universe".

Existence, the universe, is a self-sufficient primary.  There is nothing that causes there to be something rather than nothing; there is nothing prior to existence, beneath existence, or outside of existence.  To grasp the axiom that existence exists, means to grasp the fact that nature, i.e., the universe as a whole cannot be created or annihilated.  Matter is indestructible, it changes forms, but it cannot cease to exist.  The universe- the entirety of that which is- neither came into being nor it can go out of existence.  There is no time at which nothing existed; the universe is not in time or space; time and space are relationships among things in the universe.

Philosophers are the guardians of scientific epistemology.  Philosophy, in identifying the nature of existence (metaphysics) and the rules of cognition (epistemology), is the base of physics.  Scientists work from a philosophic base and much research that scientists have done has been distorted by wrong philosophical premises.

“String theory” is an arbitrary construct based on playing with mathematics rather than supported by observational data and its concepts including “11-dimensional space” are invalid.

 

 

 

Edited August 16, 2016 by NameYourAxioms

[New Buddha]

See my Friday, 7:55pm post and my reference to Russell's Paradox.

Edit:  The term "Metaphysics" in Objectivism is rarely used, and it is use in an entirely different way than traditional philosophy.  And, in fact, traditional philosophy doesn't even use the term in a consistent way.  The Metaphysics of Plato are not those of Aristotle.  The Metaphysics of Hegel are not those of Marx, etc.

In Objectivism, Rand pretty much limits the use of the term Metaphysics to distinguish between the Natural and the Man Made.

 

Edit:  Your following statement is completely consistent with Objectivism, but is, none the less, tautological and has no scientific meaning:

"Existence, the universe, is a self-sufficient primary.  There is nothing that causes there to be something rather than nothing; there is nothing prior to existence, beneath existence, or outside of existence.  To grasp the axiom that existence exists, means to grasp the fact that nature, i.e., the universe as a whole cannot be created or annihilated.  Matter is indestructible, it changes forms, but it cannot cease to exist.  The universe- the entirety of that which is- neither came into being nor it can go out of existence.  There is no time at which nothing existed; the universe is not in time or space; time and space are relationships among things in the universe."

While I'm not a theoretical physicist, I do have an engineering background.  If I disagree with your above paragraph, how exactly would I need to change the way I view/use Mechanics?

Edited August 16, 2016 by New Buddha

[NameYourAxioms]

Go to page 88 of Introduction to Objectivist Epistemology and read the chapter entitled "The Analytic-Synthetic Dichotomy" where the claim you are making is thoroughly destroyed.

According to Kantian believers of the analytic-synthetic dichotomy, tautologies are propositions that repeat the same thing.  To them, Ayn Rand's oft-repeated proposition (that she borrowed from Aristotle) “Man is a rational animal” means nothing more than “A rational animal is a rational animal”.  Objectivism rejects the analytic-synthetic dichotomy as false.

 

Edited August 16, 2016 by NameYourAxioms

[New Buddha]

I can see that you have been treated like crap on the forum - being peppered by endless questions, to no end.  I'm trying to engage you in a discussion.  And, in fact, I largely agree with you on  most points that you have made (at least I think I do).  But not all of them.

I agree with you that the concept "infinity" and/or "irrational" numbers are tools.  And I agree that they say nothing about the ontological nature of the Universe, in toto.  I prefer to use the term "ontological", while you prefer to use the term "metaphysical", and I spelled the reasons why I choose to do so.  I'm not sure that this really matters.

However, where we differ, is that I hold the position that "finite" is ALSO a tool - in the exact same way that "infinite" is.  And I hold that position that the Universe is - ontologically - neither finite nor infinite.  And, in fact, this is a meaningless question/statement.

This does go against some of Rand's writings, but Rand's knowledge of science was pretty much non-existent.

 Our scientific understanding of the Universe is, at it's most basic, comprised of Newtonian Mechanics, Relativity, and Quantum Mechanics.  There is also work being done in Cosmology, which studies large scale structures in the Universe.  These disciplines mathematize the degrees of freedom in subsystems of the Universe.  Russell's Paradox explains why we cannot create a single Mechanics of the entire Universe.

This has nothing to do with Kant's Transcendental Epistemology or a priori /a posteriori, noumena/phenomena dialectics.

I posted a link to a lecture by Carlo Rovelli, who's work (especially on RQM) has shaped my position on such matters, and there is also an interesting book by Lee Smolin, The Singular Universe, that addresses some of the same issues.

Edited August 16, 2016 by New Buddha

[NameYourAxioms]

In regard to tautologies, nominalists don't get it that concepts refer to metaphysical referents, not definitions.  It is an error to think that a concept is equal to its definition (nominalism).  The Russellian paradoxes arise because philosophers have attempted to treat truth as if it were a matter of correspondence between words and facts.  The word is not the object of cognition, but its form.

According to Wittgenstein "To say that John and Paul are both men is to say nothing more than we apply the word “man” to each."  The word is not what the units have in common; what they have in common is the distinguishing characteristics.  A concept represents knowledge, not a social practice in the use of words.  The metaphysical component of concepts is regarded as their content. The available context of knowledge determines the referents of the concepts. 

A definition of “man” as “a two-legged animal” is too broad because that definition would include birds.  But how are we to know prior to defining “man” that birds aren’t men?  We do not begin with a definition.  We do not begin with a concept.  We begin with perception, including perceived similarities and differences.  Concept-formation precedes definition.  We start from observation of reality, not from definitions.  The definition is the final step in the process, not the first.

 

 

 

Edited August 16, 2016 by NameYourAxioms

[New Buddha]

You and I are obviously just talking past each other.  So I'll bow out of the post.

[NameYourAxioms]

Hopefully this is sufficient proof that your comment that Ayn Rand rarely used the term “metaphysics" is way off.  Has anyone in this forum actually read anything that Ayn Rand wrote?

From "Philosophy: Who Needs It?" by Ayn Rand:  

    Concepts serve as units and are treated epistemologically as if each were a single mental concrete- always remembering that metaphysically each unit stands for an unlimited number of actual concretes of a certain kind.

    Aristotle held that definitions refer to metaphysical essences, which exist in concretes  

    Aristotle regarded essences as metaphysical; Objectivists regard essences as epistemological.

    The metaphysical referent of man’s concepts is not a special, separate metaphysical essence, but the total of facts of reality he has observed.

    Although axiomatic concepts designate fundamental metaphysical facts, they are products of an epistemological need.

    Metaphysically, the referents of “5” are any 5 existents of a specified kind; epistemologically, they are represented by a single symbol, “5”.

    Each of an existent’s characteristics has the same metaphysical status.

    The characteristics designated as “essential”- and the definitions which express them- may alter as one’s cognitive context expands.  Thus essences are not intrinsic to entities in the Platonic or Aristotelian manner; they are epistemological, not metaphysical.  A definition is a device of man’s method of cognition.

    Metaphysically, all facts are inherent in the identities of the entities that exist, i.e., all facts are necessary.  The concept of “necessity” in a metaphysical context, is superfluous.

    A major source of confusion is the failure to distinguish metaphysical facts from man-made facts.

    Metaphysical facts are unalterable by man and limit the alternatives open to his choice.

    “Infinity” in the metaphysical sense, as something existing in reality, is an invalid concept.  The concept “infinity” in that sense, means something without identity, something not limited by anything, not definable; Therefore, the measurements omitted here are all measurements and all reality.

    Furniture exists on the same metaphysical level as tables and chairs; the hierarchy is epistemological.

    In asking yourself whether any concept is of a metaphysical primary, you have to ask yourself: to what does that concept refer?

    Locke, Berkeley, and Hume didn’t have a concept of existence as a metaphysical fact.

    If anything is metaphysical, attributes are.

    The only thing that concerns philosophy is that we can say: whatever it is, it will have to be what it is, it will be and no contradictions claimed about it will be valid-as for instance, the current theories about a particle that goes from one place to another without crossing the places in between (quantum entanglement?).  That is metaphysically impossible, and you don’t have to be a scientist to know that.

    The alternative of what “had to be” versus what “didn’t have to be” doesn’t apply metaphysically.  It applies only to the realm of human action and human choice.

From "The Virtue of Selfishness" by Ayn Rand:

    Most philosophers are not concerned with discovering the metaphysical cause or objective validation of ethics.

    Ethics is a metaphysical necessity of man's survival.

    Men do not live in lifeboats so a lifeboat is not the place on which to base one's metaphysics.

[StrictlyLogical]

20 hours ago, NameYourAxioms said:

SL, let's examine the validity of your anti-Objectivist rejection of the Law of Identity. When you claim that there are an "infinite number of 'speeds' between 0 MPH and 55 MPH", what you are really saying is that an object can travel somewhere between 0 miles and 55 miles (no more, no less) in one hour.  55 miles is a finite range, not infinite.

 

14 hours ago, NameYourAxioms said:

MPH is a man-made mathematical ratio.  Mathematical division is epistemological.  Numerators (miles) are infinitely divisible by denominators (hour) but you mustn’t forget that mathematics is only a tool devised by men to help answer questions about matter.  A number system, to be manageable, must be open-ended.  Mathematical infinities (that do not exist in the world) are an indispensable part of mathematics.  An arithmetical sequence extends into infinity without implying that infinity actually exists.

Since you seem to equate "relative speed" with math rather than identify it as a metaphysical aspect of a system, let us investigate distance.

Consider a system in reality of object A and object B, moving relative to one another such at time 1 they are at a distance of 1 foot relative to one another and after constant velocity at a later time 2 they are at a distance of 10 feet relative to one another. 

1.  The metaphysical "aspect" of the system which is distance between A and B at any time between time 1 and time 2, has metaphysical identity, i.e. it exists, is particular and everything else metaphysical identity of some aspect of entities implies. 

2.  At every time between time 1 and time 2 in respect of the distance between A and B, the metaphysical identity of the system, is different and distinct from the metaphysical identity of the system at every other time between time 1 and time 2.

3.  One can identify and count a number of various metaphysical states of the system, e.g. "the number of all the times the system is such that object A and object B are an even multiple of 1inch apart from each other".  "the number" is a valid concept and it is ascribable because it is finite.

3.  If one were to attempt to characterize "the number" of ALL of the different metaphysical states between time 1 and time 2 one would be in error as there is no number.  Put a different way you would not be able to count all the different metaphysical states, or no matter what number you choose (any arbitrary large integer number) there are "more" distinct metaphysical states which actually occurred between time 1 and time 2.  i.e. there are "more" metaphysical states than any finite integer quantity.

4.  In an attempt to characterize, i.e. extend the concept of the "the number" of states from particular specific kinds of finite cases (multiples of 1 inch, etc.) which can be counted, to enable one to label, in terms of quantity, "all" of the metaphysical states actually occurring between time 1 and time 2, one refers to the "the number" of all the states as "infinite".  Although this technically is an error as "infinity" is not "a number", it is more like progressively adjusting the sentence

A "The number of metaphysical states" is meaningless when referring to "all" the states of the system between time 1 and time 2 -> "the number" does not exist.  "All" the distinct states, while being progressively enumerated, is always larger than any finite number.

B "The number of metaphysical states" is undefined, but also "larger" than any number.

C "The number" of metaphysical states that actually occurred is infinite.

 

In this way "infinite" or "infinity" are relevant concepts when referring to objective metaphysical reality, at least in this particular instance.

 

[New Buddha]

1 hour ago, StrictlyLogical said:

Since you seem to equate "relative speed" with math rather than identify it as a metaphysical aspect of a system, let us investigate distance.

Discussions of Mechanics without math IS meaningless.

[Eiuol]

1 hour ago, StrictlyLogical said:

3.  If one were to attempt to characterize "the number" of ALL of the different metaphysical states between time 1 and time 2 one would be in error as there is no number.  Put a different way you would not be able to count all the different metaphysical states, or no matter what number you choose (any arbitrary large integer number) there are "more" distinct metaphysical states which actually occurred between time 1 and time 2.  i.e. there are "more" metaphysical states than any finite integer quantity.

This makes no sense. Are you saying there are an INFINITE number of states an entity can be in? Or are you saying there are an infinite number of MEASUREMENTS you can perform? The first is impossible given the law of identity and an example of an invalid concept (the "metaphysical infinity" that Rand denies), the second is an epistemic issue.

[GrandMinnow]

On 8/14/2016 at 0:33 AM, New Buddha said:

I introduced [an example of] Russell's Paradox into a post about infinity.   [...]  Russell came across this paradox when he a Whitehead were writing the Principia [...] I saw that Gran Minnow also made a similar post regarding Set Theory.

 

I don't see an example of Russell's paradox in your post. 

Russell wrote of the paradox in 1901; as far as I know, this was well before he and Whitehead began Principia Mathematica.

I don't know what post of mine you have in mind in this context.

[NameYourAxioms]

Motion is an action (verb) of an entity relative to other entities. Motions are not attributes (adjective) of entities. This is like not understanding the difference between a verb and adjective.

An object's identity doesn't change as it moves. According to the Law of Causality, which is a corollary of the Law of Identity, a thing can only act in accordance with its nature. A man cannot fly to the moon by flapping his arms like a bird but he can walk, run, swim, dance, etc. His identity doesn't change with every step he takes.

A particular object in motion at a particular time relative to another object is not a separate distinct entity with its own unique identity from that exact same object a millisecond or nanosecond later.  

On one hand you talk about this as a singular system with changing identities which is invalid since to be something is to have a specific identity.

On the other hand you describe your system as an infinite number of separate systems with their own identities which is also invalid.

Time is a measurement and measurements are infinitely divisible. We can choose to divide time into microseconds or nanoseconds, etc.  You are projecting a quality of something epistemological (the infinite divisibility capabilities of math) onto reality itself.

[StrictlyLogical]

21 minutes ago, NameYourAxioms said:

A particular object in motion at a particular time relative to another object is not a separate distinct entity with its own unique identity from that exact same object a millisecond or nanosecond later.  

On one hand you talk about this as a singular system with changing identities which is invalid since to be something is to have a specific identity.

On the other hand you describe your system as an infinite number of separate systems with their own identities which is also invalid.

Please clarify whether you hold statement 1 or 2 as false.

2 hours ago, StrictlyLogical said:

1.  The metaphysical "aspect" of the system which is distance between A and B at any time between time 1 and time 2, has metaphysical identity, i.e. it exists, is particular and everything else metaphysical identity of some aspect of entities implies. 

2.  At every time between time 1 and time 2 in respect of the distance between A and B, the metaphysical identity of the system, is different and distinct from the metaphysical identity of the system at every other time between time 1 and time 2.

 

[StrictlyLogical]

1 hour ago, Eiuol said:

This makes no sense. Are you saying there are an INFINITE number of states an entity can be in? Or are you saying there are an infinite number of MEASUREMENTS you can perform? The first is impossible given the law of identity and an example of an invalid concept (the "metaphysical infinity" that Rand denies), the second is an epistemic issue.

Careful.  You need to pay attention to what I have said.

 

In layman's terms how many different distances between A and B EXIST, between time 1 and time 2?

No evasion.  Answer directly.  Before you answer think about whether you hold 1 or 2 as false and why and think about the consequences of holding either to be false:

2 hours ago, StrictlyLogical said:

1.  The metaphysical "aspect" of the system which is distance between A and B at any time between time 1 and time 2, has metaphysical identity, i.e. it exists, is particular and everything else metaphysical identity of some aspect of entities implies. 

2.  At every time between time 1 and time 2 in respect of the distance between A and B, the metaphysical identity of the system, is different and distinct from the metaphysical identity of the system at every other time between time 1 and time 2.

 

My answer is ALL distances between and including 1 foot and 10 feet precisely because relative distance in the system of A and B is an aspect of metaphysical reality (not the number or the measurement but the actual physical reality of the system which is the referent of any measurement) which is distinct and has identity. 

Care to share your answer?

[StrictlyLogical]

35 minutes ago, NameYourAxioms said:

Time is a measurement and measurements are infinitely divisible. We can choose to divide time into microseconds or nanoseconds, etc.  You are projecting a quality of something epistemological (the infinite divisibility capabilities of math) onto reality itself.

An issue directly related to this discussion:

Is the past something which "exists"? (notice the tense) Does the future "exist"? (Again notice the tense) Do you hold that the metaphysical identity of an object extends into the past or into the future?  If existence is identity, what is the status of something that existed or something that will (but does not yet) exist?

[NameYourAxioms]

Both are equally invalid since both refer to a nameless system with multiple identities. 

Distance is a relationship between objects.

Your so-called metaphysical entity that you call a system is an arbitrary construct.

The only entities is your scenario are the 2 objects. There is no third object known as a system with multiple identities.

[Eiuol]

26 minutes ago, StrictlyLogical said:

In layman's terms how many different distances between A and B EXIST, between time 1 and time 2?

Infinite.

But, you see, the question as framed is a bit loaded. There are an infinite number of distances really, on top of how it is now an epistemic question. There are a definite number of states, or else it'd lack identity. As for measuring these states, there are an infinite number of ways to measure. The facts of reality are definite and limited. To be sure, you would be measuring reality and objectively, but of course measuring reality and any abstractions are epistemic. But there are additional problems, and I think NameYourAxioms has the right idea. I don't think there's an issue to talk about systems, though.

Either way, whatever singular distance relationship between two entities exists, there's exactly and only one distance between any two entities. As for measuring that distance, there are an infinite number of ways to measure that single distance relationship. If E1 and E2 share distance relationship d, that relationship is always d. d may be measured by any standard, and with rational numbers even. Extrapolate that to the possible relationships over time. It may be hard to measure this, and arguably impossible. The fact remains that a range of possibilities is also a single aspect of identity, so that's not really an infinite number of states. It's just a larger scale relationship than a single moment in time.

The part I quoted before, I did read the prior stuff. It didn't make sense, or more specifically, I don't see how it followed from your chain of reasoning.

Infinite is a valid concept, I don't think anyone disagrees. I can't tell though if you are also saying "infinite" is valid and a perceptual level concept?

[DonAthos]

On 8/15/2016 at 5:43 PM, NameYourAxioms said:

MPH is a man-made mathematical ratio.

NameYourAxioms,

With this post, were you responding to mine? I will proceed as though that were so, due to the proximity of your post to mine, but in the future you may wish to consider using some sort of an address or the forum-provided quote feature (both of which I'm demonstrating here, for your edification). That will help to avoid confusion.

On 8/15/2016 at 5:43 PM, NameYourAxioms said:

 Mathematical division is epistemological.  Numerators (miles) are infinitely divisible by denominators (hour) but you mustn’t forget that mathematics is only a tool devised by men to help answer questions about matter.  A number system, to be manageable, must be open-ended.  Mathematical infinities (that do not exist in the world) are an indispensable part of mathematics.  An arithmetical sequence extends into infinity without implying that infinity actually exists.

I don't believe I've yet made any claims regarding the nature of mathematics, or that "infinity actually exists." (About that: I don't know what it would mean for "infinity to actually exist"; can you provide an example? I'd like to know what we're saying is impossible.)

I did ask you whether there were an infinite range of speeds between 0mph and 55mph. Should I expect a direct reply to that question?

On the nature of mathematics, I see that you say that "mathematical infinities...do not exist in the world" -- because "mathematics is only a tool devised by men." Is it the case that being a tool devised by men implies metaphysical non-existence? I grant that mathematics does not exist as a rock does: it is not physical. But don't mathematics exist in the world as a "mental entity" or something similar? Love does not exist as a rock does, either, but I would say that love exists in some fashion. Am I wrong there, too?

On 8/15/2016 at 5:43 PM, NameYourAxioms said:

Is your car traveling 33 MPH or is it traveling 33.333333333333333333333333333333333333333333333 MPH?

I agree that this is down to mere measurement -- and also that, given certain standards of precision, one might regard 33 or 33.3...mph as the same. But I don't think this speaks to the question I'd asked you.

Given that we do have the need for such precision -- and the technological know-how -- to regard 33 and 33.3mph as different, then is there any difference, in reality or "metaphysically," between a car driving at 33mph and one driving at 33.3mph? Is there anything actually different which we are denoting with our comparison of those speeds, and which is captured by our concepts and measurements and reflected in our language?

On 8/15/2016 at 5:43 PM, NameYourAxioms said:

You have mistakenly taken the infinite mathematical precision possibilities afforded by our man-made decimal number notation system (epistemology) as proof for the existence of actual infinity (metaphysics).

If this is indeed meant for me, then I disagree that I've done any such thing. Or at least, I have not done so awares, because I'm still unclear as to what "actual infinity (metaphysics)" might entail (apart from my suggestion, above, that mathematics, as other concepts, may exist as a "mental entity") -- so I don't know how I've made any claim for having a proof for it.

I have made a case that there are an infinite number of speeds between 0mph and 55mph, which I think is true and defensible, whatever implication others might draw from that fact. Otherwise, I'm trying to probe and better understand both your and SL's position.

20 hours ago, New Buddha said:

I can see that you have been treated like crap on the forum - being peppered by endless questions, to no end.

I absolutely disagree that NameYourAxioms "has been treated like crap," and equally with the characterization of his/her "being peppered by endless questions."

Philosophical discussion involves being questioned -- that's the nature of the beast -- and except for the emergence of "too many questions" as a talking point (and arguably a deflection), I don't see that there's been anything untoward or out of the ordinary about this thread.

19 hours ago, NameYourAxioms said:

Has anyone in this forum actually read anything that Ayn Rand wrote?

Ayn who??

[StrictlyLogical]

19 hours ago, NameYourAxioms said:

Both are equally invalid since both refer to a nameless system with multiple identities. 

Distance is a relationship between objects.

Your so-called metaphysical entity that you call a system is an arbitrary construct.

The only entities is your scenario are the 2 objects. There is no third object known as a system with multiple identities.

When you identify "A and B are 5 feet apart and are NOT 10 feet apart" are you identifying anything about metaphysical existence?

YES or NO?

 

If NO is distance all in your mind?  A delusion?  An irrelevancy disconnected from the facts of reality?  Are you stating perception is invalid?...

[NameYourAxioms]

You don't "identify" A and B as 5 feet apart. Being 5 feet apart is not part of either object's identity any more than you standing next to a fire hydrant is part of your identity. Your identity doesn't change when you walk away from the fire hydrant.

Distance is a measurable relationship between metaphysical entities.

The measurement is infinitely divisible. Measurement must be performed by man. Measurement is an epistemological tool we use to understand metaphysical reality. Division is a mental action.

[StrictlyLogical]

45 minutes ago, NameYourAxioms said:

You don't "identify" A and B as 5 feet apart. Being 5 feet apart is not part of either object's identity any more than you standing next to a fire hydrant is part of your identity. Your identity doesn't change when you walk away from the fire hydrant.

Distance is a measurable relationship between metaphysical entities.

The measurement is infinitely divisible. Measurement must be performed by man. Measurement is an epistemological tool we use to understand metaphysical reality. Division is a mental action.

Is the distance between your eyes part of your metaphysical identity? 

Please note I am NOT referring to a measurement of the distance... but actual distance itself which is capable of being measured. (the OBJECT of the measurement, not the product or expression of it)

(Here I assume, contrary to your previous submissions, that even though you are made of a great number of particles ... the system which is you has metaphysical identity.)