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Javelin Argument for Infinity

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Its not a direct quote, (as you know), but his work in metphysics got the philosophic ball rolling toward what we know as the law of identity. If it were a direct quote I would have cited a reference. Did you ask because youre genuinely interested, or as a feeble attempt to make me look like I dont know what Im talking about?
No, I didn't know that it was not a direct quote. I was genuinely interested in whatever passages by Aristotle (whether or not the words "A is A") you consider to mean what Ayn Rand means by "existence exists". (When you wrote "Ayn Rand said it best "existence exists", or Aristotle if you like "A is A".", I did understood you to mean that Aristotle had said "A is A" and by that he means what Ayn Rand means by "existence exists", but as you have clarified I recognize that you did not intend a direct quote of Aristotle; yet still I genuinely wish to know what passages in Aristotle are to be construed as saying what Ayn Rand means by "existence exists".) Edited by Schmarksvillian
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No, I didn't know that it was not a direct quote. I was genuinely interested in whatever passages by Aristotle (whether or not the words "A is A") you consider to mean what Ayn Rand means by "existence exists". (When you wrote "Ayn Rand said it best "existence exists", or Aristotle if you like "A is A".", I did understood you to mean that Aristotle had said "A is A" and by that he means what Ayn Rand means by "existence exists", but as you have clarified I recognize that you did not intend a direct quote of Aristotle; yet still I genuinely wish to know what passages in Aristotle are to be construed as saying what Ayn Rand means by "existence exists".)

That was presumptuous on my part, and sorry if I came off in a snide manner. To clarify, I wasnt implying that "A is A" and "existence exists" mean the same thing, what I was getting at was that the questions being posed about "who/what decided gravity/speed of light....."etc. are best examined by first realizing that existence is primary, independent of consciousness. Simply speaking, primacy of existence metaphysics once understood, really makes such questions seem silly. Furthermore, identity, and causality are certainly deemed topics of "philosophy", but when we delve into "gravity, the speed of light" etc. were talking about the special sciences. "Infinity" as a concept is certainly a philosophic discussion, but the inquiries presented were going in another direction. Who was it that first coined "A is A", I really dont know?...

j..

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Who was it that first coined "A is A", I really dont know?...

Taken as the formula ‘Every A is A’, the principle of identity was being used by logicians at least by the time of Albert the Great (13th cent.). They used it, for example, to prove the convertibility of "No B is A" to "No A is B". They added "Every A is A" to "No B is A" to infer "No A is B", relying on one of Aristotle’s forms of syllogism (first mood of the second figure):

No L is M

Every S is M

No S is L

No B is A

Every A is A

No A is B

(See Kneale and Kneale’s The Development of Logic, 235–36.)

The logical formula of identity ‘A is A’ was expressed first by Leibniz. He was the first to capitalize the law of identity in logic, in mathematics, and in metaphysics.

Leibniz knew that not all valid forms of deductive argument can be reduced to syllogistic form, but he maintained that the principle common to a properly enlarged theory of deduction is the substitution of equivalents, which is a logical license of identity.

Identity and contradiction are two opposites of the same fundamental law for Leibniz. “An identity corresponds to a proposition which implies a contradiction. For the primary impossibility in propositions is this: A is not A; just as the primary necessity in propositions is this: A is A (Ltr. to H. Conring, 19 March 1678).

~~~~~~~~~~~~~~~~

Said of any existent, “A is A” can mean either “A is being A, specifically, A is predicatively being A the way it is and not in other ways” (Metaph. 1041a10–26) or it can mean “A is the same as A”. The latter can be divided into the merely verbal, as when we say “a belly is a tummy” or it can be more than merely verbal interchangeability, as when we say “a triangle is a trilateral” or “the morning star is the evening star.”

It is because identity has various bearings in the real that it has various bearings in logic. These would include the license of substituting like for like and the proscription of equivocation. Truth is preserved under the former, spoiled under the latter.

Another bearing of identity in logic is the logical relation of identity, which is usually denoted by the equals-sign in the texts (Copi’s Symbolic Logic, 158–68; Quine’s Methods of Logic, 268–73). Logic assimilates this relation by adding two axioms to those sufficient for the logic of (logical) quantification. One of those additional axioms is: for any a, a = a.

The workings of identity in logic can sometimes look like a barren exercise. But these workings are for true thinking about the way the world is.

~~~~~~~~~~~~~~~~

Oops! I was supposed to put this under a certain one of the existing branches of the root, rather than on a new branch. I'll get it right next time.

Edited by Boydstun
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questions being posed about "who/what decided gravity/speed of light....."etc. are best examined by first realizing that existence is primary, independent of consciousness.
Without commenting on the notion of existence as primary, I do at least agree with you to the extent that such questions couched as "who or what decided ..." do seem silly.
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  • 2 months later...

There are actually galaxies in every direction in the sky which are mostly blocked by gas and other objects. The reason we're not blinded by looking up at the sky is that in the farthest distances we can see objects are moving away from us at nearly the speed of light (Doppler effect). The Hubble law which holds approximately across the sky says that other galaxies are moving away from us at a speed proportional to their distance away from us so that the observable universe is really only a small piece of a whole we will can NEVER see. The moral of the story is we have no idea how much matter exists within the universe and how far the universe extends.

Tensorman's point is the only point that really matters for the javelin thought experiment. Consider the real numbers, every two real numbers x & y have a definite distance between them given by d(x,y) = |x - y| and the set of real numbers is unbounded. The javelin argument suggests that the universe is without end - but that does not mean that its necessarily infinite. We may live in a 4-dimensional plane or on the surface of a 4-dimensional sphere or a combination of the two (a torus).

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Tensorman's point is the only point that really matters for the javelin thought experiment. Consider the real numbers, every two real numbers x & y have a definite distance between them given by d(x,y) = |x - y| and the set of real numbers is unbounded. The javelin argument suggests that the universe is without end - but that does not mean that its necessarily infinite. We may live in a 4-dimensional plane or on the surface of a 4-dimensional sphere or a combination of the two (a torus).

After nearly 20 years of working with geometric shapes, granted, within a three dimensional framework of reference - this solution seems to suggest trying to envision a 'shape' for the universe, which is paramont to stepping 'outside of the universe' to describe it. This does not integrate with 'there is no outside of the universe'.

If the universe is not in time, rather time is in the universe - it would seem that the universe is not a shape, rather shape is within the universe as well. Just as man observes and concludes temporalness to much of what he sees, and desires to apply it to existence as well, the familiarity with the observable existents possessing shape, trying to apply shape to something which has been stated as "there is no outside of the universe, or, there is no 'there' there".

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  • 4 months later...

Here's a point: gravity won't let you escape. The javelin doesn't have unlimited energy, so cannot expand the boundary. As for a volitional being standing on the boundary, that is absurd. How did he/she get there, given the huge gravitational potential pulling back to the center? Context dropping is the only way this is a puzzle.

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  • 4 years later...

Two javelins, traveling in opposite directions. One of the notions behind travel, is heading toward a destination. To apply the mathematical concept of infinity to the universe, is to sidestep inquiring about what is the destination toward which the javelins are transversing?

Edited by dream_weaver
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  • 2 weeks later...

Two javelins, traveling in opposite directions. One of the notions behind travel, is heading toward a destination. To apply the mathematical concept of infinity to the universe, is to sidestep inquiring about what is the destination toward which the javelins are transversing?

The universe is not infinite. 

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Two javelins, traveling in opposite directions. One of the notions behind travel, is heading toward a destination. To apply the mathematical concept of infinity to the universe, is to sidestep inquiring about what is the destination toward which the javelins are transversing?

 

You can easily define travel based on "the origin" from which it is coming...

 

Here some things to think about in the context of the "Javelin" argument:

 

Suppose space is only a relationship between existents not a thing itself.  If the relationships are not "limited" in magnitude, then things could in theory be removed from each to any length, but at any one time they must be separated by some specific (and finite) length.  The magnitude of the length is unbounded but the actual space is, dare I say, FOREVER, finite. (If for  time t it is finite, then for time t+1 it is finite, At time t = 1, it is finite therefore for all times t it is finite) .

 

The J argument also relies on the premise that only two possibilities exist.  It is perfectly conceivable that space is finite but curves back onto itself so that going in one direction brings you back to your starting point.

 

Physics based arguments are good for sobering up an opponent but are not philosophical in nature.

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After nearly 20 years of working with geometric shapes, granted, within a three dimensional framework of reference - this solution seems to suggest trying to envision a 'shape' for the universe, which is paramont to stepping 'outside of the universe' to describe it. This does not integrate with 'there is no outside of the universe'.

This comment presumes there can only be geometry from an extrinsic point of view. This ignores whole sections of libraries devoted to intrinsic geometry-that which is discoverable from within.

Dream weaver's comment about destination is unnecessary. Objects do not have to have a destination. Shine a flashlight into the night sky at a random angle and ask yourself if the light has a destination. It will have a relative motion but there is no objective destination.

Andie's assertion that the universe is finite is is not meaningful since there is no objective way to validate such an assertion. Reduce this to perception. Until then I will take Andie's assertion as meaningless gibberish.

Whether the universe is infinite or finite is not currently reducible to anything perceivable. Therefore, such questions are like debating how many angels can dance on the head of a pin. Rand's razor leads us to shun such speculations as not meaningful.

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You can easily define travel based on "the origin" from which it is coming...

 

Here some things to think about in the context of the "Javelin" argument:

 

Suppose space is only a relationship between existents not a thing itself.  If the relationships are not "limited" in magnitude, then things could in theory be removed from each to any length, but at any one time they must be separated by some specific (and finite) length.  The magnitude of the length is unbounded but the actual space is, dare I say, FOREVER, finite. (If for  time t it is finite, then for time t+1 it is finite, At time t = 1, it is finite therefore for all times t it is finite) .

 

The J argument also relies on the premise that only two possibilities exist.  It is perfectly conceivable that space is finite but curves back onto itself so that going in one direction brings you back to your starting point.

 

Physics based arguments are good for sobering up an opponent but are not philosophical in nature.

SL, I do not find curved space conceivable. Curvature is a concept derived from entities which are curved, be they the more abstract trajectories or the more concrete compound curvature embodied in an automobile. Harriman uses the example of moving the space inside of a living room out into the back yard to make room for some furniture. In this sense, I find it a rather absurd notion.

 

Euclid's theorems dealing with lines and circles were planar in nature. The notion of extending the line, as I grasp it, is akin to the intersection of two planes, that can be extended along the axis of intersection as required, much as number can be extended in a similar vein. The concept of curvature is distinct from the concept of straight. To conflate the two is an epistemological error from this standpoint, without disregarding the euclidean framework from which it is derived.

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This comment presumes there can only be geometry from an extrinsic point of view. This ignores whole sections of libraries devoted to intrinsic geometry-that which is discoverable from within.

Dream weaver's comment about destination is unnecessary. Objects do not have to have a destination. Shine a flashlight into the night sky at a random angle and ask yourself if the light has a destination. It will have a relative motion but there is no objective destination.

Andie's assertion that the universe is finite is is not meaningful since there is no objective way to validate such an assertion. Reduce this to perception. Until then I will take Andie's assertion as meaningless gibberish.

Whether the universe is infinite or finite is not currently reducible to anything perceivable. Therefore, such questions are like debating how many angels can dance on the head of a pin. Rand's razor leads us to shun such speculations as not meaningful.

I brought destination in as an aspect from the notion of travel. To travel is go from where one is, to where one wants to be. Travel to the store, to the moon, or in the case of the Voyager missions, currently in progress, to interstellar space beyond the heliosphere of the Milky Way Galaxy, the natural question to someone who states they intend to travel is: Where to?

 

Even without a destination in mind, a traveler desiring to see the world, is always someplace during the course of their travels.

 

The example of a flashlight being shone at a random angle is a bit problematic, at least from the standpoint of a straight line. The earth revolves on it's axis and is orbiting the sun, which has also a trajectory of it's own, or so I'm led to believe. In that sense, the kinematics involved simply complicate the matter.

 

Intrinsic geometry harkens back to a point I made elsewhere regarding the development of curvature being described using an extension of euclidean geometry in conjunction with methods of relating, via orthographic projection, multiple views to describe complex curvature of surface development.

 

The finer point this apparently is not being made fully clear here, is that "travel" is an abstraction from abstractions, where "destination" is one presupposed aspect.

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. The concept of curvature is distinct from the concept of straight. To conflate the two is an epistemological error from this standpoint, without disregarding the euclidean framework from which it is derived.

This statement disregards 150 years of research into the subject. Perhaps it is better for you to think in terms of "unaccelerated" paths (many of which are manifestly curved) versus the curvature that results from certain potentials that arise through mass, energy and momentum. Perhaps you should not talk about "straight" paths and instead speak of unaccelerated paths since that seems to be the source of your confusion. The curvature you speak of results from the way mass, energy, and momentum affect measurement. This curvature has certain physical consequences that have been observed. That mass-energy-momentum potentials affect measurement is far removed from an epistemological error. Any Euclidean framework is irrelevant and assuming it's existence is an epistemological error.

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.

The finer point this apparently is not being made fully clear here, is that "travel" is an abstraction from abstractions, where "destination" is one presupposed aspect.

The problem I have with "destination" is that it seems to presuppose a will that things like asteroids do not have, and for all we know some things may depart from us and never arrive anywhere. In this case there is no objective basis for a discussion of destination.

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This statement disregards 150 years of research into the subject. Perhaps it is better for you to think in terms of "unaccelerated" paths (many of which are manifestly curved) versus the curvature that results from certain potentials that arise through mass, energy and momentum. Perhaps you should not talk about "straight" paths and instead speak of unaccelerated paths since that seems to be the source of your confusion. The curvature you speak of results from the way mass, energy, and momentum affect measurement. This curvature has certain physical consequences that have been observed. That mass-energy-momentum potentials affect measurement is far removed from an epistemological error. Any Euclidean framework is irrelevant and assuming it's existence is an epistemological error.

As I grasp the J argument, it remains with us from ancient Greek times, and serves as a thought experiment. In this context is where notion of straight line is applied As we add the other observations from physics, these are additional considerations that have been discovered since then.

 

Measurement, too, is a process. The ongoing issues that arise where the act of measurement has adverse implications with regard to the certainty that can be arrived at indicates that something paradoxical remains to be resolved. Isolating the philosophic considerations is sometimes easier said than done.

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The problem I have with "destination" is that it seems to presuppose a will that things like asteroids do not have, and for all we know some things may depart from us and never arrive anywhere. In this case there is no objective basis for a discussion of destination.

Good point.

This would indicate travel of a cyclical nature, such as the moon about the earth, or the earth about the sun, where trying to integrate "destination" with "travel" fails. Back to the drawing board. :)

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SL, I do not find curved space conceivable. Curvature is a concept derived from entities which are curved, be they the more abstract trajectories or the more concrete compound curvature embodied in an automobile. Harriman uses the example of moving the space inside of a living room out into the back yard to make room for some furniture. In this sense, I find it a rather absurd notion.

 

Euclid's theorems dealing with lines and circles were planar in nature. The notion of extending the line, as I grasp it, is akin to the intersection of two planes, that can be extended along the axis of intersection as required, much as number can be extended in a similar vein. The concept of curvature is distinct from the concept of straight. To conflate the two is an epistemological error from this standpoint, without disregarding the euclidean framework from which it is derived.

Without curved space you cannot understand General Relativity. This curvature predicts that javelins will always return to the source from which it was thrown.

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Without curved space you cannot understand General Relativity. This curvature predicts that javelins will always return to the source from which it was thrown.

That presumes I'm trying to understand General Relativity here. I am not.

 

In my years of describing the compound curvature of various surfaces, it has always been accomplished by multiple views in conjunction with strategic sectional analysis, The only general relativity I've needed to deal with,  is the general relativity between corresponding views permitting addition views to be generated or projected from the information laid out from their corresponding views. The J argument was presented long before Newton put forth his magnum opus, thus, as a thought experiment, did not include, i.e., disregarded General Relativity as a mitigating factor extrapolated from said framework. 

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This comment presumes there can only be geometry from an extrinsic point of view. This ignores whole sections of libraries devoted to intrinsic geometry-that which is discoverable from within.

Dream weaver's comment about destination is unnecessary. Objects do not have to have a destination. Shine a flashlight into the night sky at a random angle and ask yourself if the light has a destination. It will have a relative motion but there is no objective destination.

Andie's assertion that the universe is finite is is not meaningful since there is no objective way to validate such an assertion. Reduce this to perception. Until then I will take Andie's assertion as meaningless gibberish.

Whether the universe is infinite or finite is not currently reducible to anything perceivable. Therefore, such questions are like debating how many angels can dance on the head of a pin. Rand's razor leads us to shun such speculations as not meaningful.

The objective way we validate the finite-ness of the universe is through basic astronomy.

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That presumes I'm trying to understand General Relativity here. I am not.

 

In my years of describing the compound curvature of various surfaces, it has always been accomplished by multiple views in conjunction with strategic sectional analysis, The only general relativity I've needed to deal with,  is the general relativity between corresponding views permitting addition views to be generated or projected from the information laid out from their corresponding views. The J argument was presented long before Newton put forth his magnum opus, thus, as a thought experiment, did not include, i.e., disregarded General Relativity as a mitigating factor extrapolated from said framework. 

Whether you're 'trying' to understand GR is beside the point, because it's not about you. Rather it's about Gr being the explanation of record of movement on a cosmological scale.

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This curvature predicts that javelins will always return to the source from which it was thrown.

General relativity necessitates no such thing. More generally, gravitational theories involving curvature do not necessitate such an outcome. There are many such cosmological models where said javelins part and never return to the "source from which it was thrown", as if that phrase has any true meaning.

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General relativity necessitates no such thing. More generally, gravitational theories involving curvature do not necessitate such an outcome. There are many such cosmological models where said javelins part and never return to the "source from which it was thrown", as if that phrase has any true meaning.

You write as if there's more than one 'gravitational model ("many such cosmological models"!!!)...hilarious.

 

So please, tell me about them because my poor college courses only taught one,the  Newtionian, which was proven false by GR.

 

As for the equation, it's the 'R' (Ricci) on the left side which describes the natural curvature of space with respect to several other coefficients. To this extent, the trajectory of said arrow in real space will never be straight--ostensibly the only state in which it would not return.

 

Think about walking on the earth's surface. Now make the assumption that the surface is flat....

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