Originally Posted by

**Sig**
Who is Hilbert in this case? So far as I know Craig is the one who argues about the infinite library as an illustration as to why actual infinities are logically contradictory or irrational if realized.

I was referring to David Hilbert, the mathematician. The argument you are referencing is Hilbert’s, not Craig’s originally.

Originally Posted by

**Sig**
Yes, all temporal points are essentially the same, and yes the "dimensionality" of time is just a mental construct, not an actual thing. Just like the number 1 has meaning but it doesn't exist in and of itself. Time is a measure not a thing.

You’d have to offer support as to why this would be the case, modern physics uses time as an actual thing not some kind of abstract object.

Time has the same dimensional qualities as any point in space. The location of an object is displayed by giving its X,Y,Z, and T coordinates. Time is an essential part of both quantum mechanics and relativity. Neither field treats it like a mental construct. Time is affected by gravity and by velocity, both of which indicate it isn’t just a mental construct.

As loathe as I am to reference Wiki, they do have a good explanation of this concept here:

Spacetimes are the arenas in which all physical events take place—an event is a point in spacetime specified by its time and place. For example, the motion of planets around the sun may be described in a particular type of spacetime, or the motion of light around a rotating star may be described in another type of spacetime. The basic elements of spacetime are events. In any given spacetime, an event is a unique position at a unique time. Because events are spacetime points, an example of an event in classical relativistic physics is , the location of an elementary (point-like) particle at a particular time. A spacetime itself can be viewed as the union of all events in the same way that a line is the union of all of its points, formally organized into a manifold, a space which can be described at small scales using coordinate systems.

A spacetime is independent of any observer. However, in describing physical phenomena (which occur at certain moments of time in a given region of space), each observer chooses a convenient metrical coordinate system. Events are specified by four real numbers in any such coordinate system. The trajectories of elementary (point-like) particles through space and time are thus a continuum of events called the world line of the particle. Extended or composite objects (consisting of many elementary particles) are thus a union of many world lines twisted together by virtue of their interactions through spacetime into a "world-braid".

However, in physics, it is common to treat an extended object as a "particle" or "field" with its own unique (e.g., center of mass) position at any given time, so that the world line of a particle or light beam is the path that this particle or beam takes in the spacetime and represents the history of the particle or beam. The world line of the orbit of the Earth (in such a description) is depicted in two spatial dimensions x and y (the plane of the Earth's orbit) and a time dimension orthogonal to x and y. The orbit of the Earth is an ellipse in space alone, but its world line is a helix in spacetime.[13]

The unification of space and time is exemplified by the common practice of selecting a metric (the measure that specifies the interval between two events in spacetime) such that all four dimensions are measured in terms of units of distance: representing an event as (in the Lorentz metric) or (in the original Minkowski metric) where is the speed of light.[14] The metrical descriptions of Minkowski Space and spacelike, lightlike, and timelike intervals given below follow this convention, as do the conventional formulations of the Lorentz transformation.

http://en.wikipedia.org/wiki/Spacetime

I would strongly recommend the following page as a good introduction to this: http://www.pitt.edu/~jdnorton/teachi...ime/index.html

Originally Posted by

**Sig**
Not placed and removed, just placed over and over again, the same golf-ball in each member of the set.

In what sense can you place the same physical golf ball into a set repeatedly without removing it? How do you put an item in a box twice without having removed it from the box? That would seem to make your analogy nonsensical.

Originally Posted by

**Sig**
And yes now, now is put into this infinite set over and over and over again. It is one thing, the universe. Not a whole bunch of different universes stacked on top of one another in a temporal set.

No one argued that it is a whole bunch of different universes stacked on top of one another. Think of time more like we think of a physical dimension. Think of a plane. If I were to draw a line on that plane at Y=5, I wouldn’t say that that is just a bunch of Y’s stacked on top of each other. I would say the line represents Y at different relations to X. The same is true of time. Now is the universe at one relation to t, yesterday is the same universe at a different relation to t.

Originally Posted by

**Sig**
Take the golf ball and spin it. Then put put a snapshot in the set every second. Its still the same golf ball over and over again. An infinite set of it is still just the one golf ball not an infinite number of books in a library that you can take one out and then wow, there are still just as many books there, crazy. Well if its all just representations of the same book that isn't at all contradictory.

But you’ve stumbled onto Craig’s other objection. Your set of pictures, is it ever infinite? Can it be actually infinite?

There are two answers. 1) No, of course not, you can’t count to infinity. This answer is the one I would hold and is Craig’s second objection to that idea.

2) Sure somehow, then the set of pictures you have is an actual infinite. That actual infinite displays some logically incoherent properties as described by Hilbert.

It doesn’t matter that it is the same golf ball, what matters is whether the number of pictures is infinite or not.

Originally Posted by

**Sig**
Effectively yes, otherwise you could put 7 in every position in the set.

That makes them ordered, it doesn’t make them causally prior, right?

Originally Posted by

**Sig**
Look, it doesn't even work with finite sets. Take your own life. Lets make all the moments of your life and put them in a library. Now take one squatch out of the library, that means a moment of your life doesn't exist anymore.

Having read more of your response now I think my point above about how physics treats time as a dimension is even more relevant. You seem to be confusing the objects described by a dimension with the dimension itself.

Here you conflate the term “moments” of my life with “Squatch” as if I were the same thing as the moments of my life. Clearly those are two separate concepts. A moment is a relational phrase concerning physical dimensionality’s relationship to a specific point in a temporal dimension. It is the Ys in relationship to a single X if we were thinking of our plane above.

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