My point is that if you consider just the effect, just the broken glass, for example, you observe change. Change is more simple than a whole cause-and-effect series. If you stand on the beach and watch the tide rise, you see only the effect of certain gravitational causes. But just in that "effect," you see change.

As soon as we are able to note change, and that is going to be long before we are so sophisticated as to be ascribing causes to effects, we are able to see two (or more) states that mark the relation of before and after, or of succession. In changes alone, we can perceive the simplest manifestation of what we come to know as "time." That's the idea I'm promoting. So the broader, better definition of time would be the ordering of which all changes admit, rather than the measure of relative motion.

As to its originality, Stephen's references (I haven't looked into them) seem to show that Aristotle urged such a view. It might seem a piddling issue, but I think, on the contrary, such things are critical. Only the broadest, precise definition will serve to foster understanding and lead us to accurate, related theoretical positions.

=Mindy

Leonid,

To lift a heavy body using a lever and fulcrum, the force one must apply to the lever varies with the ratio of lever lengths to either side of the fulcrum. To lift a heavy body more easily, one moves the fulcrum more towards the heavy body, changing that ratio of lengths.

When one senses by touch that an object is cool or warm, one’s sensation reflects the time rate of heat transfer between one’s body and the object. The direction of heat flow (energy flow) will be from the warmer entity to the cooler. It is not the flow direction and amount of heat transferred that this sensory system reports. Rather, it is the flow direction and time rate of heat transfer that is reported. The instantaneous ratio of heat transfer to time passage determines the intensity of warmth or coolness. (I’m just speaking of the sensory system that deals with moderate differences in temperature; the sensations of burning or freezing involve different receptors, and I don’t know those functional response relationships.)

Some physical magnitudes are ratios of others and have physical results as ratios.

I don't understand your example. Why it isn't a cause -effect relation? There are three entities have been involved: baseball transfered the energy to the window frame and window frame to the glass.Glass underwent change as result of interaction with baseball which had energy-that is capacity to act.Moving of baseball is not a cause, kinetic energy, which baseball posseses is.

"The power (energy per unit of time) flowing through my lamp is a ratio, specifically 50 watts (50 x 10exp7 ergs per second).

Definition of second: "The time needed for a cesium-133 atom to perform 9,192,631,770 complete oscillations."

Your ratio is a combination of two unrelated processes-namely flow of energy through your lamp and oscillations of cesium-133 atom.These two processes exist in Nature, but ratio between them not,this ratio has no physical meaning whatsoever and obviously doesn't exist in Nature. We just performed arbitrary mental connection between two unrelated processes for the sake of convenience.You could also use the rate of water flow (water clock),sand (sand clock) or any other process.Your example proves that "time" is simply tool to measure one process of change by using another , and as such , time is mental concept, not the fact of existence.Suppose, you want to reconstruct the history of Universe and claim that Universe exists 13 billion years. That means, Earth orbited Sun 13 billion times. But Solar system exists only 4,5 billion years which makes such a statement meaningless-Earth orbited Sun before Earth and Sun came to existence!

Thanks for the added information. I appreciate your detail.

in your case - chutzpah?

Greg,

When the book came out, I surmised that Leonard Peikoff was either Prof. E or Prof. B from their roles in the conversation with Rand. Some months later, Allan Gotthelf remarked, in a thoughtful letter to me concerning an essay in the initial issue of Objectivity, that he was Prof. B.

Several years later, I learned that Larry Gould, who had attended the seminar, had reported in an interview in Full Context that he was Prof. M and that E was Peikoff, B was Gotthelf, and A was Harry Binswanger.

(LG is personally known to me. His seminar connection is related here [first paragraph] by his partner in life.)

How many other non-existing aspects of things are we able to measure?

= Mindy

While all changes must have causes, the difference which is the change, is not at all the same thing as the cause and its effect!

A baseball breaks a window. The baseball's mass and trajectory require it to pass through the window frame. The glass in the window frame can't absorb the energy of the ball, so it is forced to splinter. Moving baseball-stationary window glass. That's the causal pair. The change in question is the whole versus the broken window glass. Whole versus broken. Two states of the glass itself. The change doesn't involve the baseball, because it isn't a cause-effect relation. It is changes that cause-effect set out to explain. We mustn't confuse them. So, Leonid, your statement, "change is a result of [sic] interaction of two or more entities," is a mistake. (It is true that interactions of entities imply change, of course.)

On the other hand, when you say that "time" is a frame of reference we create in order to describe changes, you are in agreement with my proposal. I elaborate a bit on how and why we conceptualize "time" from observing changes.

-Mindy 

How do you know Peikoff asked these questions of Rand? In my copy it's Prof E at one of the workshops.

Is there such a thing as momentum?

What is the difference between an object with momentum and one without?

Note: The words "motion", "change", "before", "after" and "action" all assume time. The suffix "-ing" usually denotes time too. Even "exist" contains the concept of "now".

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Magnitudes, also called quantities, are determinate relations in the world. Our measurements reveal magnitudes to us as they are, at least once we understand our scales and what about them is conventional. (The implicit measurements by our perceptual and motor systems also reveal magnitudes, but not in conceptual, linguistic form.)

Ratios are ratios of magnitudes, and ratios are themselves magnitudes in the world, independent of our measurement or computation of them. The power (energy per unit of time) flowing through my lamp is a ratio, specifically 50 watts (50 x 10exp7 ergs per second). The speed of the locomotive is a ratio, measurable in a variety of ways. A strain gage reflects the ratio of the extension of a solid under load to its extension without load.

All of our sophisticated instruments—such as wattmeter, tachometer, or strain gage—are contrived by conceptual animals. But these instruments are physical devices, having the outputs they have, outputs related to inputs in determinant ways, whether or not anyone is comprehending those relations.

Quantities do exist independently, but without measurement they can be expressed only in qualitative terms (exists or not). Even if one uses such an expression as “a lot" or "a little" that presupposes estimation which is epistemological process, pertained to human consciousness. Established quantity presupposes such epistemological process. But we are talking about unestablished quantities. Ratio is relation between quantity A and B: A/B-the process which can be performed only by humans. The concept of duration presupposes establishing of the ratio between two processes-in your example A-geological change; B-number of rotations of Earth around Sun. Can this ratio be established independently from human mind? Without established ratio one cannot speak about duration, one only can establish that change took place.

Ratios between unmeasured magnitudes of the attributes of existents are facts of reality independently of any consciousness. Magnitudes are in the world independently of our measurement of them. Rand and Peikoff got this right in the following exchange. (They were using the term quantity for what I call magnitude.)

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

PEIKOFF: Is it correct to say that quantity is a metaphysical concept and measurement an epistemological one, in the sense that if human beings and consciousness were erased, there would still be quantities, but there would no longer be such a thing as measurement. Measurement involves a human act of establishing relationships.

RAND: Of establishing quantity, that’s right.

PEIKOFF: And is that why you formulate the nature of concept-formation in terms of omitting measurements rather than omitting quantities?

RAND: Right.

PEIKOFF: Because you omit the relationships that you could establish?

RAND: Yes. But the quantities continue to exist whether you measure them or not.

(ITOE App. 199–200)

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

Ratios between magnitudes in the world are uniquely what they are independently of which measurement scales we use to ascertain those ratios (provided the scale we select is of the type known as ratio scale). All appropriate measurement scales will yield the same ratio between my height and yours.

The epochs of the geological history of the earth have the durations they have independently of our discovery of those durations, independently of our measurements of those magnitudes.

Here are resources on the topic of time in Objectivity, as compiled in the Subject Index:

Time V1N6 38–39, V2N3 50, 63, V2N4 185–86,  V2N6 152, 154–62, 184–85; Causal Inertness of V1N3 39; as Complement of Energy V1N3 39, V1N4 79, V2N6 171; and Consciousness V1N1 11, V1N2 10–11, V1N3 19–20, 64, V1N4 24, V2N1 111, 118, V2N2 88–89, V2N4 155, V2N6 12–18, 184–85; Contingency in Future V1N3 35, 37–39, 86–87, V1N4 26–28, V1N5 74–75, V2N2 82, 114–16, V2N4 23–24, 186–87, V2N5 155–56; Discrete V1N3 18–20, 48; Development of Concept of V2N2 82–85, V2N6 109; and Existence V2N3 50, 61; Finitude of Future V1N3 37–38, V1N5 4, 17–18; Fixity of Past V1N3 33, 82, V2N5 159; as Form of Intuition V2N4 103, V2N5 13–14, 16–18, V2N6 162–63; Homogeneity of V1N3 39, V1N6 38, V2N3 62; and Identity V1N3 8, 18–20, 33, 43, 47–49, V1N4 65–66, V1N5 7–8, V2N6 45, 185; and Life V1N3 19, V1N5 25, V1N6 146–47; Preference V1N5 10–12, V2N2 56; and Succession V2N2 77, 82–85, V2N3 52, V2N5 23; and Tensed Beliefs V1N1 24, V1N4 6, 66

... as a metaphysical entity. There's just stuff doing things and things doing stuff. "Time" is a concept by which we humans make the process intelligible and sequential to ourselves. It's epistemological, not metaphysical. It's not inherent *in* reality but is a conceptual tool by which we make sense *of* reality. Remove humans from this earth and there's no "time" - just stuff doing things and things doing stuff.

kkulak

I think that concepts "before and after" cannot define time. These concepts presuppose time, to use them one has first to define what time is, otherwise that would be circular argument. Only change exists as independent event which is pertains to reality.Change is a result of interaction of two or more entities.(Law of Causality) Duration of change is a relative concept. If your car is running 100km/h is it fast or slow? If change happened instantly-there is no duration. If not-how do you know that this particular change related to the given interaction. I think that time is a frame of refference which we created in order to describe changes.Stephen said "the ratios of their durations to the duration of an earth revolution about the sun are facts independent of the existence of consciousness or life. " Ratios don't exist in Nature. They are creation of human mind, integration of independent events, which gives to us the concept of time. This is an act of consciousness.

"ratios of their durations"

Stephen, I think I now understand what Greg and Leonid are getting at.

Duration is a construct created by human beings. This construct is valid, reliable and pertains to reality and luckily is sensitive enough (milli-seconds) to any movement. "before/after" would happen independent of consciousness/observer – true. But the ‘ratio’ or any measurement would have to be devised and arbitrarily created.

Leonid, do you disagree that ‘before/after’ events can be independent of consciousness? I don’t think you were but just clarify please.

My question to you guys is this.
If a constructed concept such as time or any other measurement were created by an observer and it pertains to reality in its reliability and sensitivity (i.e. it is objective and can be quantified) – is it still arbitrary?

kkulak

Leonid,

Even where there is no causal connection between two particular events, it can still be a fact independent of consciousness that one of those events was before the other. We reconstruct the geohistory of the earth. That requires abstraction and it requires selection of our units of time measure, but the sequences of the eras and the ratios of their durations to the duration of an earth revolution about the sun are facts independent of the existence of consciousness or life.

"I see no reason why this requires human conciousness as it happens with and without it."
because time is not an entity, and represents an act of mental connection between two events which is in the realm of human consciousness. It means, that it's not enough,that two events happened,for these events may or may not have casual connection (like dry weather and full Moon,or my physical age and number of times Earth orbited Sun). To introduce concept of time one has to make integration of these two events and this is an act of consciousness. Obviously, different events are happening simultaniously without any intervention of human consciousness,but only consciousness can put them together to create concept of time,which is an expression of relation between them.Consider-what exactly do you mean when you say that you car's velocity is 100km/h? 1km=1000m, 1 metre is some arbitrary chosen measure and 1 h is 3600 seconds.1 second is defined as time during which certain numbers of certain atoms decay. What all this has to do with your car? Nothing whatsoever.

Like gods, it doesn't exist without being constructed by sentient creatures.

Mindy, "something that is true of all changes." - other than that, they have nothing in common. (Some people could, I suspect, write theses on the drying of paint.)

"In other words the introduction of time refference is only possible by comparison one event with another-which is conceptual action-meaning that outside of the realm of human consciousness time doesn't exist."

If existence exists outside human conciousness, then two entities exist alone and their relationship (distance) between them must also exist outside of human conciousness.
I am sure you agree on this one.

But the concept of "before" and "after" is the measurement of time that it may take for an object in motion to pass relative to another object. I see no reason why this requires human conciousness as it happens with and without it.

kkulak

"What do all of these have in common besides two contrasting states, one replacing the other, a "before" and an "after?" Before or after what? That presuposes certain frame of refference-like dry weather became rainy after 30.November 2001, or before Christmass, or after full Moon etc...In other words the introduction of time refference is only possible by comparison one event with another-which is conceptual action-meaning that outside of the realm of human consciousness time doesn't exist.

Regarding whether or not there is something other than "before" and "after" that all changes have in common, consider just these few: growth: two inches high becomes ten inches high; emotion: calm turns to panic; weather: dry becomes rainy. What do all of these have in common besides two contrasting states, one replacing the other, a "before" and an "after?" I think it takes only a little effort to conclude there aren't other commonalities, as we are talking about something that is true of all changes.

"Successives" might turn out to be equivalent to "change;" it seems to embody the idea of "after" and "after that," except "successive" doesn't differentiate between changes in a thing and replacements of one thing by another. In the latter case, a location or some other index is necessary to relate the two things. Being neighbors is not being replacements.

If I'm right, "successive" applies the notion of time. Notice that "replacement" has the same complication; "re-" and "place" preceed its use, and "re-" implies a judgment of time, making it also an application of the idea of time.

= Mindy

Constancies don't give us a "before" and "after."

I don't know how pure your constancies would be, but, as I assume you know, steady-state stimulation disappears from sense-perception.

If you are saying that to describe something as constant, one must compare it to some changing thing, I think "constancy" still doesn't add anything. What about a flash of light or a brief sound? They are unchanging, but are they constant?

Perhaps you don't mean to make "change" and "constancy" exhaustive...

As to other ways changes are ordered, a review of some instances might satisfy you that there isn't. The very breadth of the term works against it. Is there any character, besides, perhaps, "identity," that a thing can possess, that doesn't, under some circumstances, change? And if that is correct, what commonality is even a candidate to describe all those characteristics' changes, except "before" and "after?"

Perhaps "change" doesn't seem to be fundamental. How do we define "change" without using synonyms such as "alteration," etc.? I like this formulation: a change is a difference a thing has to itself. Of course, the only way a thing can be different than what it is is to be one way at one moment, and another at a later time.

I don't see why "existence" needs to be stated. A change is a change in an entity, just like motion is motion of an entity, etc.

"An order of successions" might run into problems of fundamentality, for to define "successive" you may need to refer to time.

Grasping "Existence exists," implies all kinds of things, including sexual reproduction. From a genetic epistemological point of view, I don't think it implies time or change, that is, it doesn't reveal time or change. I don't think we can legitimately read into "exists," duration.

Perhaps the value of the "change" formulation of time is in its genetic epistemology. It is there, at least, that the satisfaction of answering Kant can be found.

= Mindy

Your definition is pretty good: “Time is the ordering of which all changes admit.”

I would add something that you probably also mean: “Time is the ordering of which all changes or constancies admit.”

I have two reservations. The first concerns the definite article. I wonder if there are other ways in which changes are ordered besides the distinctly temporal ordering. So it might be better to say: “Time is an ordering of which all changes or constancies admit.” Then we need to collect those other ways of ordering changes, if any, so we can mention the distinction of the temporal ordering among them. That would get us back our definite article.

My second reservation is that there is no reference to existence in the definition, and I’m not sure the right way to add it. There is a long tradition of latching time to change (and a minority who argue that there could be time without change), but there is also a long tradition of latching time to existence.

In his third letter to Clarke (1716), Leibniz writes:

“I have said more than once that I hold space to be something purely relative, as time is—that I hold it to be an order of coexistences, as time is an order of successions.”

“[Time is not] anything distinct from things existing in time.”

J.H. Lambert writes in a letter to Kant (13 Oct. 1770): “Duration appears to be inseparable from existence.” He brings forth a number of true basic propositions about time, he concludes that time is a primitive concept of something real that cannot be given a definition ultimately noncircular, and he rests content with “time is time.”

Philosophical characterizations of time are worthwhile and need to dovetail at all joins with what standard modern physics learns about time (time as parameter v. as dynamic variable; time in thermodynamics, in quantum mechanics, in special and general relativity; etc.). Grasping “existence exists” patently (w/o further premise) entails grasping that “existence endures.” The grasping itself is a change available for direct grasp. The act of grasping the statement “existence exists” implies that one exists as a perceiver of existence, that one is an existent and an activity.

Further: a, b

Thanks, Stephen. I imagine I had read that at some point, but didn't realize its antecedents when I re-formulated it later. I'm not sure about "universal order within which all changes  are related;" my thought was that the one thing all changes have in common is a before and an after. Reiterate "before" and "after," or, "after" and "after that..." and you get the continuum of time. I can urge this view with more authority now. You didn't say whether you find it convincing...?

= Mindy

Mindy recommended here that time be defined as “the ordering of which all changes admit.” In Time for Aristotle, Ursula Coope argues that Aristotle’s conception of time is that one.

From the back cover:

"Aristotle claims that time is not a kind of change, but that it is something dependent on change; he defines it as a kind of 'number of change'. Ursula Coope argues that what this means is that time is a kind of order (not, as is commonly supposed, a kind of measure). It is universal order within which all changes are related to each other. This interpretation enables Coope to explain two puzzling claims that Aristotle makes: that the now is like a moving thing, and that time depends for its existence on the mind."

From the Table of Contents:

1.   The introductory puzzles

2.   Time is not change but something of change

3.   Time follows change and change follows magnitude

4.   The before and after

5.   The definition of time as a kind of number

6.   Time as a measure of change

7.   All simultaneous time is the same

8.   The sameness of earlier and later times and nows

9.   Being in time

10. Time and the soul   

Issues tackled in the posts upward from this good thought by Reed have been carefully examined in this illuminating book:

Time, Creation, and the Continuum

Richard Sorabji

The Boston Colloquium on the Philosophy of Science will have, in the afternoon of 3 November, a session on The Philosophy of Infinity. Among the papers to be presented:

“The Many Types of Infinity in Ancient Philosophy and in Late Antiquity”

Emilie Kutash

I don't think that's a quote from my posts, are you sure I said that? I was urging change as the basis of the concept of time.

Motion is change of location. It doesn't presuppose the concept, "time."

Why do you say the fallacy of a stolen concept is not a fallacy?

= Mindy

“Time is either infinite (in the past) or it has a beginning."

The concept of time is not irreducible primary as concept
Of existence. Time is ontologically connected to the concept of change which is connected to the concept of identity which is connected to the concept of entity. Existence doesn't have beginning. It simply exists. Does it means that time was always part of existence? Not necessarily. Suppose in some stage existence was one single unchanging entity. To such existence the concept of time is inapplicable. If such a proposition sounds crazy then compare it with superstring theory of N-dimensional universe.
"The concept of motion is dependent on the concept of time”
Not, if one is not interested in the rate of motion, velocity. One may observe the fact of motion or change without to compare it with any other process of change. One may say “I’m getting old"-meaning that he notes physiological change of one's body. But if one says “I’m fifty years old"-one simply means that since he's born earth has orbited sun fifty times. This astronomical fact as such doesn't indicate any physiological changes in one's body. But if one connects these two events together, that is-if one uses astronomical event to measure rate of physiological change, then and only then one employs the concept of time. Therefore the concept of time presupposes an observer, conscious intelligent being which is able to do this kind of integration. In other words, if you postulate infinity of time you postulate primacy of consciousness which is contradiction in terms. Since time is abstract integrated concept, its beginning is human conceptual thinking. There is no time outside of human mind.
BWT, ancient Greeks hadn't had any concept of time and did well without it.

Mindy -
"Time is a measurement of motion"

The concept of motion is dependent on the concept of time so this is an example of the Stolen Concept Fallacy. However, the Stolen Concept Fallacy is not really a fallacy and nothing has been stolen.

Thanks for bringing this to my attention. I was accused of "smuggling" a concept in another discussion and now I understand where the idea came from.

Cheers,

Reed

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I don't believe time exists except as a construct for our convenience. It is relative and differs for each observer depending on most usefully a reference point such as a regular orbit. Infinity is a human construct too

You can assume your own definition of "time" (eg. "Time is a measurement of motion") for the sake of argument. If we consider all time and it is without a beginning (or first motion) then it is infinite. Relativity and irregularity of "time" make no difference to the conclusion either.

I realised from Leonid's post that objectivists deny time (as normal people understand it), that is why I included the second example...

A count of events is either infinite or there was a first event.
To believe that events are finite and that there was no first event is to willingly believe something untrue.

[like time,] Infinity is a human construct too
Are count and measure also human constructs?

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When you say, Reed, that "Time is either infinite or it has a beginning," your premise is like asking what is outside the universe...what came before time, when did it begin? 

The terms, "beginning," "before," "after," "start," and "stop," etc. only make sense within time. Your view is that time in its entirety is somehow within "time." Like having the universe being within "space." If you understand why it's senseless to ask, "What's outside the universe?" you should appreciate why it's meaningless to ask "When did time begin?" "Begin," as you are using it is a stolen concept; "begin" and "beginning" are ways of marking time, they require time, to have any meaning.

= Mindy

Gregster Grasshopper.

time exists except as a construct for our convenience.

It is relative and differs for each observer depending on most usefully a reference point such as a regular orbit.

Infinity is a human construct too

Leonid and Gregster -
Time is either infinite (in the past) or it has a beginning.
To believe that time is finite and that time has no beginning is to willingly believe something untrue.

The same is true if we discuss events instead of time...

A count of events is either infinite or there was a first event.
To believe that events are finite and that there was no first event is to willingly believe something untrue.

Something can not be both not finite and not infinite.

Gregster -
I don't get the relevance of the non sequiturs from Peikoff.

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Gregster,

Would it be fair to suggest she was proving atheism rather than entertaining the possibility in the leap of faith?

I was told the prototype super-collider offered numerous scientific advancements eg. an improved cappuccino machine resulted. (True)

My bet is they will learn much but won't create more mass from less. Of course I could be proved wrong but I don't think so.

Reed, from http://www.solopassion.com/node/5088#comment-58339 I say finite because infinity is a concept which doesn't physically exist. It's a mathematical device.

“Nature is existence regarded as a system of interconnected entities governed by law; it is the universe of entities acting and interacting in accordance with their identities. What then is a “super-nature”? It would have to be a form of existence beyond existence; a thing beyond entities; a something beyond identity.

The idea of the “supernatural “ is an assault on everything man knows about reality. It is a contradiction of every essential of a rational metaphysics. It represents a rejection of the basic axioms of philosophy (or, in the case of primitive men, a failure to grasp them).

[..]

Is God the creator of the universe? Not if existence has primacy over consciousness.

Is God the designer of the universe? Not if A is A. The alternative to “design” is not “chance.” It is causality.

Is God omnipotent? Nothing and no one can alter the metaphysically given.

Is God infinite? “Infinite” does not mean large; it means larger than any specific quantity, i.e., of no specific quantity. An infinite quantity would be a quantity without identity. But A is A. Every entity, accordingly, is finite; it is limited in the number of its qualities and in their extent; this applies to the universe as well. As Aristotle was the first to observe, the concept of “infinity” denotes merely a potentiality of indefinite addition or subdivision. For example, one can continually subdivide a line; but however many segments one has reached at a given point, there are only that many and no more. The actual is always finite.”

Pg 31,32 “Objectivism; The Philosophy of Ayn Rand” Leonard Peikoff.

That applies to the exercise from Mr Boydstun http://scidiv.bcc.ctc.edu/math/Infinity.html
http://www.solopassion.com/node/5088#comment-57197

And from this page http://scidiv.bcc.ctc.edu/math/diag.html Listing the counting numbers is impossible too. Cantor's statement ”the infinity of decimal numbers is greater than the infinity of counting numbers.” is wrong.

...and had the good sense to contribute it elsewhere.

=Mind-y

There may be movements, electrons changing orbits, molecules forming, etc. underlying a leaf's change of color, but that's irrelevant. You might as well say that there is no such thing as being at rest, since all atomic and sub-atomic particles are in motion. Then, of course, as nothing can be said to be at rest, at least relatively, there is no frame of reference to note movement, so there's no motion!

The change of green to yellow is locally static. This gives us evidence of change, or "becoming," that doesn't involve evidence of change of location. So "change" is the more basic idea on which to base the concept, "time."

It's natural that physics uses a special, limited concept. It has a limited perspective on the world.

=Mindy 

"What about the count of collisions?"

Since the number of electrons is finite,number of collisions also should be finite. BTW, this is not very common event. Usualy each electron located on its energetic level and if it not exited it doesn't collide with other particles.But suppose that number of collisions is potentially endless.By counting them you always reach some finite number Nx+1. Eventually you will run out of material tools of counting and storage of this information-even if you turn all Existence to huge computer,since Existence is also finite.You may reach very big number but it will be finite number.

Leonid -
What about the count of collisions?

I'm hoping you consider collisions happen and have always happened.

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I take it that the thread you refer to was removed by your good self after you re-evaluated its contribution to good sense.

Yes,change is more broad concept,then motion. You also can use "becoming" . In general, change means that A becomes B (like green leaf becomes yellow) ,child becomes adult , iron becomes rust etc...But in all processes of change motion is involved (motion as change of place,of molecules,atoms,electrons). So motion is basic concept.

...is that time is the ordering of which all changes admit. Motion is change of place, so it is included, and in some ancient philosophies "motion" is used more broadly than change of place. But growth, and all changes of quality that take place without motion are assumed under my definition. It has, I think, better face validity.

If this sounds strange, think of all the kinds of changes you can. What do they all have in common? There is a "before" and an "after," and that difference, I believe, grounds our idea of time in the most general way possible.

I don't know if this is more useful as genetic espistemology, or as the definition itself; I think it is both. Note that it answers Kant in his bold claim that there is no way to derive the idea of time from experience.

By the way, Gregstir, this is part of what I was talking about in the cognitive invariance thread you so scorned, remember?

=Mindy

Electrons don't orbit nucleus of atom as planets orbit sun.It is more proper to describe it as electron cloud. If you ask about total numbers of electrons,then this number is finite, as total mass of Universe.
" The density of matter in the universe is about 3 x 10-30 g/cm3, which means that it is 300 billion billion billion times less dense than water. Note that this includes the contribution of dark matter and so the density of luminous matter (that we see as stars and galaxies) is only about one-tenth of the figure given above.

Now, the size of the observable universe is about 14 billion light years, and using the above value of density gives you a mass (dark and luminous matter) of about 3 x 10 power 55 g, which is roughly 25 billion galaxies the size of the Milky Way.", which is finite number. From this number one can calculate numbers of electrons. If the power of our observation will increase in the future we may have bigger number which also will be finite. BTW, I don't think that objectivist definition of time as relation is incoherent.

Gregster -
I thought your pre edited answer was better.

Even if I assume only one atom without beginning that has moving electrons I end up with an infinite number of orbits.

Why did you decide the orbit count would be finite?

BTW: I read the book you sent some time ago. I'm just procrastinating about writing my opinion of it.

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Checked & edited: As put here;
http://www.solopassion.com/node/5088#comment-56754 , and if I'm correct and matter is non-destructible (has always been around in one form or other), then the number of electrons is finite. Their orbits would be "finite" but damned hard to pin down.

Leonid -
I see, with that definition of time it would be impossible to give coherent answers about time.

Would the total count of all electrons' orbits that have ever happened be a finite number.
If so, why?

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Objectivism's position is that whatever exists is finite.
"Time is a measurement of motion; as such, it is a type of relationship. Time applies only within the universe, when you define a standard—such as the motion of the earth around the sun.
The universe is eternal in the literal sense: non-temporal, out of time.

Leonard Peikoff, “The Philosophy of Objectivism”
lecture series (1976), question period, Lecture 2.

It is possible to imagine Universe in which no change takes place. Such Universe would be timeless. Time starts with change.

Leonid -
You apparently subscribe to the notion that time as we know it doesn't have starting point

I was under the impression that objectivists believe that existence is without beginning.

Am I incorrect to think objectivists believe that, or do you disagree with objectivism on this point?

Cheers,

Reed.

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Inf/inf would be=1 if infinity had numerical value. But it hasn't! Let examine your example. These are your premises:
1. A=inf.
2. A+10=B
3. B=inf

If A=inf and B=inf than, according to mathematical rules, A=B. Therefore A-B=0. What happened,then, to 10 minutes? They just disappeared in the thin air. Meaning, you cannot do any mathematical operations with infinite numbers. In mathematics any number divided on itself equals 1. If ,as you claim, "Infinity/infinity does not necessarily equal 1",
then what we are dealing with, are not numbers.

"The error in step 7 prevented any proof that... "if you perform such an operation then every number is equal to any other number".-that's not an error. That what high school algebra proves.

The error in step 7 is an error. Infinity/infinity does not necessarily equal 1, as demonstrated here.

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You apparently subscribe to the notion that time as we know it doesn't have starting point, but it is the same as to say that Universe is infinite, as you mentioned in your early post "If the size of the universe is larger than all finite sizes then the universe's size is infinite."

You argument simply bring us to initial premises of this thread and therefore is circular. Besides, " larger than" implies finite. Infinite number cannot be larger or smaller than any other number since it doesn't have numerical value, as I've demonstrated in my small algebraic exercise. For the same reason infinite number cannot be bigger that another infinite number. That would be contradiction in terms. You example actualy proves the absurdity of the notion that infinite numbers exist.

B is not the number of minutes from now to 10 munutes in the future.

B is the number of minutes that will have ever passed at a time 10 minutes in the future - infinite.

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"The error in step 7 prevented any proof that... "if you perform such an operation then every number is equal to any other number".-that's not an error. That what high school algebra proves. If you divide A/0 you get infinite number, as you yourself demonstrated. Any infinite number is equal to any other infinite number. That why in my example you get 1=2 and that why such an operation is prohibited by mathematical rules.

"A = total number of minutes that have ever passed up to now. (Infinite)
B = total number of minutes that will have ever passed 10 minutes from now. (Infinite)

B - A = 10

I don't get it. B is 10, A is also finite . And in any case A>B so B-A is <0, negative number. How did you get 10?

Leonid -
The error in step 7 prevented any proof that... "if you perform such an operation then every number is equal to any other number".

Now you have to explain how the operation with two infinite numbers gives you finite number?

A = total number of minutes that have ever passed up to now. (Infinite)
B = total number of minutes that will have ever passed 10 minutes from now. (Infinite)

B - A = 10

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I don't think there is an error in Leonid's step 7. You do realize he is making an argument to absurdity?

--Mindy

I don't disagree. The whole exercise demonstrates why mathematics forbid this operation-namely division to 0-exactly because by doing so one gets infinite and therefore undefine number. So the error in my example wasn't in step 7 as you indicated.You allowed to reduced "a" in both sides of the equision( and it can be specified that a>0).However you not allowed to reduce (a-a) in step 3 since this reduction is amount to division on 0.Any number divided on itself gives you 1. Even if A=infinite A/A=1. Now you have to explain how the operation with two infinite numbers gives you finite number? I don't think it can be done. It is much easier to accept that in fact actual infinite numbers don't exist.

Leonid -
I have explained the error as well as I can (which I think you misunderstand) but your disagreement is not really with me, your disagreement is with mathematics.

From Wikipedia - The Indeterminate Forms include 0/0, ∞ - ∞, ∞/∞, 0×∞ [and some others that won't display properly here].

Cheers,

Reed.

You presupose that infinite number has actual value(0) which is wrong- infinite means number without value. But even if you are right and A is infinite A/A=1, not zero and therefore 1=0 which is absurd again.

Leonid -

A x 0 = 0

What is "A"? "A" can be anything and the equation will still be true. The equation can be rearranged as follows.

A = 0/0
This equation is true for all values of "A".

For simplicity assume 1/0 is infinity.

infinity/infinity = (1/0) / (1/0) = (1 x 0) / (0 x 1) = 0/0
Therefore "B = infinity/infinity" would be true for all values of "B".

Your step 7 was a mathematical error.

No, Kevin, I'm not Nazi, far from it. Neither I’m ethical relativist. I see nothing wrong in calling a spade a spade Marxist a scum and scientologist a cheat. Chris Wolf said "For example, we are told that an academic Marxist is not merely mistaken, but is 'evil,' and is guilty of practicing 'evasion.' People who are the victims of such attacks frequently come away baffled. They cannot understand how their character and honesty can be judged solely by the ideas they have proposed or defended. "

So, by what I suppose to judge the character of Nazi or dictator or Marxist or mystic if not by their ideas? By their dress? Hitler appreciated Chopin and very much loved his dogs. Kant was great host and liked to invite people for dinner. Nevertheless his philosophy was evil and eventually begoted Marxism and Nazism. How and by what should I judge him?

"How would you call academic Nazi, Kevin?"

Wiilam Sceek wrote

"Kevin, you are stupid, socially retarded, ignorant and grievously misinformed -- Leonid is neither psychiatrist or nor psychologist. He is a cardiologist, you fucking moron."

A cardiologist is a physician who is certified to treat problems of the cardiovascular system—the heart, arteries, and veins. Cardiology is classified as an internal medicine subspecialty. Knowledge of internal medicine and other specialties is required to obtain certification.

What's REALLY Wrong With Objectivism?
http://www.jeffcomp.com/faq/wrong.html

by Chris Wolf

Why do so many Objectivists insist on attacking the honesty, integrity, and character of their opponents? Are such attacks an aberration, or is this sort of behavior actually advocated by Objectivism?

Such attack behavior, so prevalent among Objectivists, is not supported and advocated by the fundamental principles of the philosophy of Objectivism. However such behavior is personally supported and advocated by Ayn Rand, Leonard Peikoff, and many of their supporters. Such behavior is a clear case of misapplication of the fundamental principles of Objectivism. (If you think it's impossible for the originator of a philosophy to misapply it; think again.)

Anyone who has had much exposure to the philosophy of Objectivism, or the Objectivist movement, has observed the endless moralizing and condemnation which seems to characterize the philosophy of Objectivism and many of its adherents. People who oppose the philosophy of Objectivism, or who simply espouse ideas at odds with Objectivism, frequently find their character, honesty, and integrity under vicious attack.

Infinite number doesn't mean very big number, it means that such a number has no identity and therefore meaningless.
In mathematics you get infinite number if you divide any number to 0 : X=A/0 X is infinite. But if you perform such an operation then every number is equal to any other number.

For example : 1. (a2-a2)=(a+a)(a-a)
2. a(a-a)=(a+a)(a-a)
3. a(a-a)/(a-a)=(a+a)(a-a)/(a-a)
4. a=a+a
5. a=2a
6. a/a=2a/a
7. 1=2 which is absurd. I've got this result since I divided to (a-a) which is zero ( reduction (a-a)step 3) and I ended up with infinite number without identity which is equal to any other number. Such a number doesn't have any meaning and that why mathematical rules prohibit to divide to zero.So infinite numbers don't exist. Potential endless series of numbers do exist but last actual number is always finite. Consider (N1,N2, N3....Nx+1).Nx could be as big as you whish and you always can add 1 to it, but the last number will be finite untill next addition. Absolutely infinite God of Spinoza as absolute infinite number has no identity and therefore doesn't exist. " To be"-as Rand observed-" is to be something."

How would you call academic Nazi, Kevin?

Addendum to More Infinity

I should state Spinoza’s definition, which was the sort of metaphysical infinity in the center of Rand’s target. From the first part of Ethics, sixth Definition:

“By God I understand a being absolutely infinite, i.e., a substance consisting of an infinity of attributes, of which each one expresses an eternal and infinite essence.”

“Exposition: I say absolutely infinite, not infinite in its own kind; for if something is only infinite in its own kind, we can deny infinite attributes of it . . . .” (Compare with Existence-Is-Identity Axioms.)

Concerning Newton’s triangle with the hypotenuse sweeping to vertical, to parallel the vertical side of the triangle, one should ask: At the “last point,” is the ratio of triangle’s base to its hypotenuse a rational number or an irrational number? What kind of number is neither? These questions could not be correctly answered until further advances in mathematics, such as the development of projective geometry and the work of Cantor. (Not, I say not, to make small of Newton.)

this long

Anyone -

How long is now?

"The ability to conceptualise an entity does not prove it's existence."

This man is severely demented

What's REALLY Wrong With Objectivism?
http://www.jeffcomp.com/faq/wrong.html

by Chris Wolf

Why do so many Objectivists insist on attacking the honesty, integrity, and character of their opponents? Are such attacks an aberration, or is this sort of behavior actually advocated by Objectivism?

Such attack behavior, so prevalent among Objectivists, is not supported and advocated by the fundamental principles of the philosophy of Objectivism. However such behavior is personally supported and advocated by Ayn Rand, Leonard Peikoff, and many of their supporters. Such behavior is a clear case of misapplication of the fundamental principles of Objectivism. (If you think it's impossible for the originator of a philosophy to misapply it; think again.)

Anyone who has had much exposure to the philosophy of Objectivism, or the Objectivist movement, has observed the endless moralizing and condemnation which seems to characterize the philosophy of Objectivism and many of its adherents. People who oppose the philosophy of Objectivism, or who simply espouse ideas at odds with Objectivism, frequently find their character, honesty, and integrity under vicious attack.

Space is not an entity but measure of separateness between entities. Therefore space cannot explode, wrap, bend, melt boil etc...Observe that such a theory also contradict universal constant C which is light speed. What would be velocity of light if space suddenly exploded? Obviously more than C.
"new galaxies were continually forming in the gaps in between... I think you’d agree this is unlikely - forming from what?"-frankly, I don't know. I'm only doctor, not astrophysicist. But some of them entertain idea of "white holes" which instead to absorb matter, as black holes do, produce new matter to fill up the gap.