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A Logic Paradox

So it is not possible to calculate a half planck?

If a planck has a length, why can't that length be divided by 2?

At that point, all the physics breaks down. you can a number, but when it comes to the actual piece of reality associated with that number, no, you don't.
 
That is Zeno's paradox of motion, which dates back to the 5th Century BCE.

The modern answer is based on calculus, namely that an infinite geometric series can in fact converge. As Wolfram Alpha phrases it, "the infinite number of "half-steps" needed is balanced by the increasingly short amount of time needed to traverse the distances."

There are plenty of other paradoxes, such as the Russell's Paradox:

"R is the set of all sets that do not contain themselves. Is R contained in R?"

(This type of set construction is typically ruled out by ZFC.)


Or, Quine's paradox, which avoids the self-reference underlying many paradoxes:

"yields falsehood when preceded by its quotation" yields falsehood when preceded by its quotation.


Anyway.... Some terminological clarifications are probably required. "Logic" is actually a specific field which is used to determine the validity of inferences. Modern logicians don't see their tools as "measuring everything," and have known for quite some time that there are boundaries to logic. The most critical of these was articulated by Kurt Godel, who proved that any axiomatic logical system capable of constructing arithmetic will either be inconsistent or incomplete, but cannot be both. (I.e. if your logical system is truly complete, then it will allow inconsistencies, and that renders your logical system useless; and if you exclude those inconsistencies, then it can't be complete.)

The person you were talking to may have meant terms like "reason" or "rationality," which is not the same thing. It's a common example of using a technical term according to a non-technical meaning.

You beat me to it. Here's my favorite paradox (mainly because of its simplicity):

This sentence is false.
 
Someone mentioned in another thread "logic" and how all things can be measured through logic.

Here is some logic:

1. Between any two points (A,C), there is a third point exactly halfway between the other two points (B).

2. Between point (B) and point (C) there is yet another point (D) exactly halfway between point (B) and point (C).

3. In fact, there is an infinite number of points exactly halfway between any other two points, based on 1 and 2 above.

4. In order to travel from one point to any other point, one must pass through an infinite number of points that are increasingly "exactly halfway" from where one is and where one is going.

How long will that take?

In other words, can one complete an infinite number of tasks in a finite amount of time?

Put another way:

I hold in my hand a basketball. I drop the ball. It hits the floor and bounces back up. We all see it. Yet, logic says it cannot happen.

It cannot happen because before the basketball falls to the floor, it must fall to a point exactly halfway to the floor. Once there, it must then fall to a point exactly halfway between the halfway point and the floor. This process must repeat itself an infinite number of times before the ball hits the floor. Can the basketball complete an infinite number of tasks in a finite amount of time?

Logic dictates the ball cannot hit the floor.

If you doubt the logic of #4 above, here is the test: Give me any two points, tell me how far apart they are. I will divide that distance by 2 and show you the halfway point. Do it again. I will always show you the halfway point by dividing the distance by two. infinity.

Logic Paradox

If you put point D between B and C, doesn't point D then become point C and point C become point D?

How could D come before C?
 
If you put point D between B and C, doesn't point D then become point C and point C become point D?

How could D come before C?

Once a point is named, it is that point, named.

Now, I may have committed some labeling convention faux pas, but seriously? That is the part of the argument that has you flummoxed?
 
Everyone instinctively realizes that the universe consists of an infinite amount of components.
 
A barber shaves all the men who can't shave themselves. Who shaves the barber?
 
Someone mentioned in another thread "logic" and how all things can be measured through logic.

Here is some logic:

1. Between any two points (A,C), there is a third point exactly halfway between the other two points (B).

2. Between point (B) and point (C) there is yet another point (D) exactly halfway between point (B) and point (C).

3. In fact, there is an infinite number of points exactly halfway between any other two points, based on 1 and 2 above.

4. In order to travel from one point to any other point, one must pass through an infinite number of points that are increasingly "exactly halfway" from where one is and where one is going.

How long will that take?

In other words, can one complete an infinite number of tasks in a finite amount of time?

Put another way:

I hold in my hand a basketball. I drop the ball. It hits the floor and bounces back up. We all see it. Yet, logic says it cannot happen.

It cannot happen because before the basketball falls to the floor, it must fall to a point exactly halfway to the floor. Once there, it must then fall to a point exactly halfway between the halfway point and the floor. This process must repeat itself an infinite number of times before the ball hits the floor. Can the basketball complete an infinite number of tasks in a finite amount of time?

Logic dictates the ball cannot hit the floor.

If you doubt the logic of #4 above, here is the test: Give me any two points, tell me how far apart they are. I will divide that distance by 2 and show you the halfway point. Do it again. I will always show you the halfway point by dividing the distance by two. infinity.

Logic Paradox

Your points are merely external measurements, not physical realities. Neither the ball nor the floor knows they're there. They therefore do nothing to hinder the balls flight to the floor.
 
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