How does one find True Knowledge?

[Tamminen]

It's more appropriate to use the phrase "boundary of time", and to ask: Does time (the temporal dimension) have a boundary in the past/future?

But if there is a singularity in the past, there may be a "boundary" from our perspective but no boundary from the perspective of someone "approaching" the singularity. I think this is what general relativity is about. Great masses can "bend" time, make it slower or faster depending on where the observer happens to be - and perhaps even stop it from someone's point of view.

[RJG]

An infinite number of 'segments' on a 1" ruler DO NOT have a "0" dimension, and therefore are NOT "UNDEFINED". ALL segments have a length greater than 0".

That's a matter of opinion.

Math has no "opinions".

X=number of segments. We can't say what value X has. So it seems reasonable to say X is UNDEFINED.

A denominator of "0" = UNDEFINED value.

What would you call an unknown and unknowable quantity X if it is not UNDEFINED?

"Infinite" ...in this case.

[devans99]

Math has no "opinions".

Mathematics does not prove anything about the existence or well definedness of actual infinity. It all comes down the ‘axiom of infinity’ - that just declares actually infinite sets exist - nothing is proved one way or the other. So it is everyone’s right to either believe or not believe in that axiom. As a finitist, I don’t believe in it. And maths is quite possible without actual infinity - potential infinity is enough for calculus - calculus was invented and worked fine long before the axiom of infinity was adopted as part of the foundations of mathematics.

X=number of segments. We can't say what value X has. So it seems reasonable to say X is UNDEFINED.

A denominator of "0" = UNDEFINED value.

But UNDEFINED is not just divide by zero, it means something with a poorly defined value, for example ∞/∞ is also undefined (because of different possible types of infinity). Actual infinity has a poorly defined value so I think it qualifies.

[Felix]

Tamminen: But if there is a singularity in the past, there may be a "boundary" from our perspective but no boundary from the perspective of someone "approaching" the singularity.

The boundary is a product of human mentality, it's not possible to approach it physically.

Tamminen: I think this is what general relativity is about. Great masses can "bend" time, make it slower or faster depending on where the observer happens to be - and perhaps even stop it from someone's point of view.

No, gravity bends light and energy, not time, you're confusing the external "objective" passage of time with the internal subjective perception of the passage of time, they are not coterminous.

[Tamminen]

The boundary is a product of human mentality, it's not possible to approach it physically.

The "boundary" is what we call the Big Bang, or the initial singularity, and it is true that we cannot approach it because we cannot make time trips to the past, but the geometry of spacetime near the singularity is different than ours. This can be compared with black holes that bend spacetime in a similar way.

No, gravity bends light and energy, not time, you're confusing the external "objective" passage of time with the internal subjective perception of the passage of time, they are not coterminous.

Matter and energy, including light, bend spacetime, meaning they bend both space and time, which means that time gets slower or faster near matter and energy, depending on where the observer stands. Matter and energy are the origin of the bending of spacetime. That light "bends" near a big mass is because space is curved there. Light proceeds along a straight line, but the geometry of spacetime is not Euclidean near big masses.

[Felix]

Tamminen said: the geometry of spacetime near the singularity is different than ours.

You're not making sense, there is no "near the singularity," it happened billions of years ago, we can only theorize as to the nature of spacetime at that moment, and no, it can't be compared to black holes, since we can observe them, they are not merely theoretical like the Big Bang.

Tamminen said: Matter and energy, including light, bend spacetime, meaning they bend both space and time, which means that time gets slower or faster near matter and energy, depending on where the observer stands.

Again, you're confusing empirical observations with subjective perception, the passage of time is only faster or slower relative to the speed and momentum of separate human observers, i.e., the position and speed of one observer versus that of another, subjectively their experience of the passage of time would be similar.

[Tamminen]

You're not making sense, there is no "near the singularity," it happened billions of years ago, we can only theorize as to the nature of spacetime at that moment, and no, it can't be compared to black holes, since we can observe them, they are not merely theoretical like the Big Bang.

Cosmologists can make rational calculations about what spacetime was like just "after" the singularity, and I think it is something like inside or near black holes.

Again, you're confusing empirical observations with subjective perception, the passage of time is only faster or slower relative to the speed and momentum of separate human observers, i.e., the position and speed of one observer versus that of another, subjectively their experience of the passage of time would be similar.

Of course subjectively their experience of the passage of time would be similar. But that was not the point. It is a measured fact that spacetime bends near big masses. This has no effect on how things behave inside each frame, seen from that frame. Seen from another frame things look different. So we speak about different things.

[Felix]

Tamminen said: Cosmologists can make rational calculations about what spacetime was like just "after" the singularity, and I think it is something like inside or near black holes.

Well, I don't see how such a comparison would be valid. We know how black holes are formed, their structure is not incompatible with the known physical properties of our universe. But we do not know what caused the Big Bang or what material conditions were like when it occurred. They may have been much different than they are now, and space-time may not have been integrally linked as they are now, post Big Bang.

[Tamminen]

But we do not know what caused the Big Bang or what material conditions were like when it occurred.

According to modern scientific cosmology the initial singularity is the temporal limit of spacetime. So there cannot be anything "before" it. Nothing has caused the universe because there was nothing to cause it. The world is a cause of itself. This last sentence is my opinion, not a scientific fact.

[RJG]

Nothing has caused the universe because there was nothing to cause it.

Sound Logic!

The world is a cause of itself.

Not-sound logic. -- Both X<X and X>X are logical impossibilities.

Whether we personally like it or not, the only logically sound explanation is that the universe has "never not existed".

But if we prefer to discard logic as our means of reasoning, then, have at it folks, ANYTHING is possible!

[Tamminen]

Not-sound logic. -- Both X<X and X>X are logical impossibilities.

This has nothing to do with the world being causa sui. Also the world with infinite past needs a cause of being. 'Finite' and 'infinite' describe the geometry of spacetime. The cause of the being of spacetime, if any, does not depend on its geometry. But its geometry may depend on its cause of being. And its cause of being, in my metaphysics, is the subject and its self-evidence. But I know this kind of thinking is foreign to you, so let's leave it for now.

[Tamminen]

Whether we personally like it or not, the only logically sound explanation is that the universe has "never not existed".

On this I can agree, if you have not noticed.

[Consul]

The world is a cause of itself.

Not-sound logic. -- Both X<X and X>X are logical impossibilities.

Self-causation is impossible indeed.

Whether we personally like it or not, the only logically sound explanation is that the universe has "never not existed".

This is trivially true—since there cannot be any time when there is no time—, no matter whether or not time has a boundary in the past.

[RJG]

Whether we personally like it or not, the only logically sound explanation is that the universe has "never not existed".

This is trivially true—since there cannot be any time when there is no time—, no matter whether or not time has a boundary in the past.

Since there cannot be a time when there is no time, there cannot be a "boundary" to the past. A "boundary" implies 'two' sides.

...which means that this is more than "trivially" true, ...it is "absolutely" true.

[Tamminen]

Self-causation is impossible indeed.

Don't you think the universe as a whole needs a cause or reason of being? Maybe not, but if it needs a cause, what else could it be than causa sui, so that its being gets explained from within, so to speak? I have my hypotheses about this, and I refer to some of my longer posts.