I have a couple of arguments for time being discrete rather than continuous (actually similar arguments can be used for discrete space too). Thanks in advance for any feedback.
1. A point in space cannot have size=0 because it would only exist in our minds and not reality (no width; insubstantial)
2. Similarly, the point in time ’now’ cannot have length=0 (if it exists for 0 seconds, it does not exist)
3. Or if a ‘now’ had length=0, then a second would contain 1/0=UNDEFINED ‘nows’
4. So ‘now’ has length >0
5. Can’t be length = 1/∞ because ∞ does not exist (∞ + 1 > ∞ making a nonsense of ∞. Or if you define ∞ + 1 = ∞, implies 1 = 0)
6. So a ‘now’ has a finite, non-zero length. Time is composed of a chain of ’nows’ so time must be discrete
Or
a) Imagine a second and a year
b) By the definition of continuous, both time period are graduated identically (to infinite precision).
c) So there must be the same information content in both (same number of time frames: ∞)
d) But a year should contain more information than a second
e) Reductio ad absurdum, time must be discrete — Devans99
time is just change/motion — Terrapin Station
If time is just change/motion, why does it run slower when an object travels near the speed of light or is near an intense gravity field? — Devans99
The effects on mass (basically a kind of "pulling" on the mass in both cases) is a counteracting force that make changes/motions relatively slower. — Terrapin Station
So time (in the v term) determines mass. So something in the universe must be aware of time else it could not assign a mass. That suggests time is real? — Devans99
I have a couple of arguments for time being discrete rather than continuous (actually similar arguments can be used for discrete space too). Thanks in advance for any feedback.
1. A point in space cannot have size=0 because it would only exist in our minds and not reality (no width; insubstantial)
2. Similarly, the point in time ’now’ cannot have length=0 (if it exists for 0 seconds, it does not exist)
3. Or if a ‘now’ had length=0, then a second would contain 1/0=UNDEFINED ‘nows’
4. So ‘now’ has length >0
5. Can’t be length = 1/∞ because ∞ does not exist (∞ + 1 > ∞ making a nonsense of ∞. Or if you define ∞ + 1 = ∞, implies 1 = 0)
6. So a ‘now’ has a finite, non-zero length. Time is composed of a chain of ’nows’ so time must be discrete
Or
a) Imagine a second and a year
b) By the definition of continuous, both time period are graduated identically (to infinite precision).
c) So there must be the same information content in both (same number of time frames: ∞)
d) But a year should contain more information than a second
e) Reductio ad absurdum, time must be discrete — Devans99
Who says the temporal continuum needs to contain instants? Likewise who says that the spatial continuum needs to be pointy? Perhaps the continuum has no fundamental level at all, no unit with which all other quantities are multiples of.
If that is the case, then the idea of "now" as a snapshot moment in time is mistaken and the passage of time as a succession of said moments (not unlike a succession of strips on a piece of film) is also confused. This is what you seem to implicitly assume in the your argument. Just as objects may be distant from one another without any fundamental length, events simply come and go continuously without any fundamental duration. — Mr Bee
Who says the temporal continuum needs to contain instants? Likewise who says that the spatial continuum needs to be pointy? Perhaps the continuum has no fundamental level at all, no unit with which all other quantities are multiples of — Mr Bee
events simply come and go continuously without any fundamental duration. — Mr Bee
The concept of 'now' presupposes that time exists; and now separates the past from the future - two more meaningless concepts without that of time itself. — Tim3003
So surely time must exist, but what it's made of must be similar to what space is made of. — Tim3003
What structure does time have if it's not a series of instants? — Devans99
But if an event has no duration it would not exist. 'Now' could not exist if it had zero duration. Think about filming someone for zero seconds - you'd have no film right? — Devans99
Just a series of events without any smallest units — Mr Bee
Problem is that means a second and a year would have the same information content which does not seem right. Clearly more information in a year - the continuum seems paradoxical. Maybe it's one of those concepts that we can conceive of in our minds but never occurs in reality? Reality seems deeply logical and free of paradoxes. — Devans99
We can also tell the difference between past, present and future so there must be something special about 'now' so the concepts of past and future have meaning. Some sort of positional cursor that regular eternalism/relativity does not incorporate must exist. — Devans99
What structure does time have if it's not a series of instants? — Devans99
Who says the temporal continuum needs to contain instants? Likewise who says that the spatial continuum needs to be pointy? Perhaps the continuum has no fundamental level at all, no unit with which all other quantities are multiples of.
If that is the case, then the idea of "now" as a snapshot moment in time is mistaken and the passage of time as a succession of said moments (not unlike a succession of strips on a piece of film) is also confused. — Mr Bee
The analogy is with a mathematical line, which does not consist of individual dimensionless points or tiny finite segments, but instead can always be divided infinitely into shorter and shorter lines. — aletheist
That's paradoxical. It works ok in the mind but not in reality: If I have a real line length 1 mile, it contains more information than a real line length 1 centimetre. But if they are both continuums then they both contain the same amount of information. Which is impossible. Which is proof by contradiction that continuums do not exist in the real world. — Devans99
Just curious what definition of "information" you're using. — Terrapin Station
Why? It begs the question to presuppose discrete units of "information" (i.e., points or finite segments) that comprise a "real line." Again, the "parts" of a true continuum are also true continua.If I have a real line length 1 mile, it contains more information than a real line length 1 centimetre. But if they are both continuums then they both contain the same amount of information. Which is impossible. — Devans99
I repeat: Because space-time is a true continuum, motion/velocity is a more fundamental reality than either position or duration. Marking and measuring the position of a particle at any particular instant imposes an arbitrary discontinuity, like a point on a line.If you imagine a particle in an interval, the position of the particle relative to the beginning of the interval can be regarded as information. In a continuum, that piece of information (particle position) has infinite precision so infinity many bits of information. — Devans99
Because space-time is a true continuum, — aletheist
An argument from incredulity is not persuasive, and alleging "magic" suggests a lack of interest in engaging in serious philosophical discussion. What exactly do you mean by "structurally the same" in this context?Your continuum is just magic - how can 1 light year be structurally the same as 1 millimetre? — Devans99
In what specific sense do you hold that the hypothesis of a real continuum is "logically unsound"? Are you claiming that it is somehow logically impossible, or merely not actual? Either way, why do we nevertheless routinely refer to "the space-time continuum"?I don't believe in magic so I have to take a different view - no continuums in nature; they are logically unsound and nature does not do unsound. — Devans99
A bare assertion is also not persuasive. Even if I grant the premise, the discontinuity of actuality/existence does not, by itself, rule out the reality of true continua.Also it can't be a continuum because actual infinity does not exist. — Devans99
1. A point in space cannot have size=0 because it would only exist in our minds and not reality (no width; insubstantial)
2. Similarly, the point in time ’now’ cannot have length=0 (if it exists for 0 seconds, it does not exist)
3. Or if a ‘now’ had length=0, then a second would contain 1/0=UNDEFINED ‘nows’
4. So ‘now’ has length >0
5. Can’t be length = 1/∞ because ∞ does not exist (∞ + 1 > ∞ making a nonsense of ∞. Or if you define ∞ + 1 = ∞, implies 1 = 0)
6. So a ‘now’ has a finite, non-zero length. Time is composed of a chain of ’nows’ so time must be discrete — Devans99
In what specific sense do you hold that the hypothesis of a real continuum is "logically unsound" — aletheist
A bare assertion is also not persuasive — aletheist
Yet again: Because space-time is a true continuum, motion/velocity is a more fundamental reality than either position or duration. We can construct a continuum as the path that a particle traces (or would trace) over an interval of time--which is not a collection (infinite or otherwise) of discrete positions. Besides, how could merely possible positions constitute an actual infinity?How on earth could you construct a continuum? It requires us to construct an actual infinity of possible positions for particles to occupy. Thats impossible. — Devans99
That definition is incorrect, according to the standard mathematics of infinity; mainly because it begs the question by presupposing the discreteness of quantity. In any case, I am advocating the reality of continua, not the actuality of infinity.Actual infinity, if it existed, would be a quantity greater than all other quantities ... — Devans99
That definition is incorrect, according to the standard mathematics of infinity; mainly because it begs the question by presupposing the discreteness of quantity — aletheist
In any case, I am advocating the reality of continua, not the actuality of infinity — aletheist
All I can suggest at this point is looking into the standard mathematics of infinity. I side with Peirce, rather than Cantor, in denying that the real numbers constitute a true continuum.X in my proof could be real or natural; I made no assumptions. That is a fair proof that actual infinity is not a quantity IMO. — Devans99
No, it does not. That is only one way to model it, which I consider incorrect. Another is that the line is a true continuum that does not consist of discrete points or line segments at all. You can arbitrarily mark any such point or segment, but by doing so you introduce a discontinuity into that which is really continuous in itself.Think about a real-life line segment, say the distance between your eyes and the screen; that HAS to be an actual infinity of points/line segments by the very definition of continuous. — Devans99
No, they did not. That is only one way to model it, which I consider incorrect. Another is that any finite interval of time is a true continuum that does not consist of discrete instants at all. You can arbitrarily mark any such instant, but by doing so you introduce a discontinuity into that which is really continuous in itself.Think about the second that just past; by the definition of continuous; its has to include an actually infinite number of moments/periods of time. They just all happened. — Devans99
I can make sense of that, but it is not the case. A true continuum has a cardinality exceeding that of any infinite set. In Peirce's terminology, a true continuum has a multitude exceeding that of any infinite collection. Between any two points that we mark on a line, there is an inexhaustible continuum of other potential points; between any two instants that we mark in time, there is an inexhaustible continuum of other potential instants.All 'cardinality of the set of natural numbers' moments just happened if you can make sense of that. — Devans99
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