Required Reading: Ontology, Infinity, Existence of God
No two things can be infinite. Therefore whatever is infinite is that thing than which nothing greater can be thought. That is the gist of St. Anselm’s ontological argument; his proof of God. Basically Anselm’s argument is that the thing than which nothing greater can be thought is God. His proof of God is that a god that exists only in the mind is not as great as a god who exists in both the mind and reality. So any thing for which a greater thing can be thought cannot be God.
Most medieval versions of God describe it as being infinitely merciful, or knowing, or powerful. If God is infinite in one respect, then in accordance with Anselm’s argument, God must also be infinite in all other respects. A God which is infinitely merciful, but finitely powerful, is not that than which nothing greater can be thought. Likewise, a thing that is infinitely one thing, but finitely another can not be God if there is some being (which I can think of) who has infinite power, mercifulness, wickedness, penis size, volume, ductility, etc., and is not limited by finitude in any aspect.
Of course, Anselm’s proof has a flaw, which is that it only shows that if god exists, then god exists in both the mind and reality. I don’t intend to prove God’s existence, for reasons that ought to become clearer next week. The important thing is that provided that the “than which nothing greater can be thought” argument is sound - and I feel that it is - even if the proof that follows from it isn’t, the God must be infinite in every aspect. God must be an infinite thing.
Next Week: On the identity of the infinite, in which I fiddle with knobs and twiddle dials until my brain factory can reconcile three infinite things that we normally perceive as distinct.
Thursday, April 29, 2010
Thursday, April 22, 2010
On infinite time and infinite space:
Required Reading: Absolute time and space, psychological arrow of time
I was thinking about merging these two bits in the first place, but then I changed my mind. Then I got sick last week and didn't bother to update, so I'm merging them again. Besides, this first one is terrible. These two arguments are basically the springboard for next week's ridiculous statement.
Time
Time is infinite, infinitely divisible, and absolute. Even if time is given beginning and end points, its infinite divisibility allows for it to progress eternally, on some small level. Those boundaries would face the same asymptotic relationship that faces measurements, as I’ve described previously.
Besides that, it is impossible to ascribe an endpoint for time. Following the endpoint, were there a mind to perceive it, that mind could easily extend time. The statement “It’s been one hour since time stopped” proves the point through the contradiction. (Indeed, the phrase “following the endpoint” ought to prove the point by inference). In this way, time is endless (infinite). So long as there is a conscious mind to experience time, time will be seen to continue its passing. As such, without a conscious mind to experience time, there is certainly no reason to assume that time would not continue to pass in its absence. Provided that we don’t traipse off into idealism, the object permanence we learn as infants ought to apply.
Space
Space is infinite and absolute. There is no such thing as nothing. All physical things occupy space. Space is an infinite medium in which arbitrary divisions are made, separating it into finite parts. The space between two points is occupied by invisible gases and particles, not nothing.
Every object we perceive occupies a space of the same volume. Our arbitrary measurements of volume allow that space to be reinterpreted in any shape. A sphere which has a volume of 72 cubed metres can be rearranged to take the form of a 72 cubed meter replica of the Taj Mahal.
Physical objects do not “push space aside.” They occupy as much space as is required for such objects to exist and retain their volume and mass. I have encountered the criticism that if space is infinite, and all space is occupied, nothing ought to be able to move (because the combined force of an infinite number of objects would absorb any force made by one object in its attempt to move).
Such a criticism implies nothingness, because it requires that there be “room” for space to displace into in order to make more room for objects to move around. In infinite space, there can be no limitation on the movement of anything, because there is infinite space for things to move within. As objects are merely finite divisions within one infinite space, it is hardly unexpected that space would remain space regardless of whether every part of it moves or is immovable.
Perhaps science has not fully been able to explain the way that objects occupy space. Perhaps objects exchange particles at such a rate that form and structure are retained, but particles no longer occupy the same part of space (again, divisions in space are arbitrary).
“Space” in this instance is not to be confused with Outer Space; a construct which is itself an arbitrary division of absolute space.
Next Week: On God as infinite, in which I bring this whole infinity talk thing to its logical conclusion, and tackle some common ideas about the big guy in the sky.
I was thinking about merging these two bits in the first place, but then I changed my mind. Then I got sick last week and didn't bother to update, so I'm merging them again. Besides, this first one is terrible. These two arguments are basically the springboard for next week's ridiculous statement.
Time
Time is infinite, infinitely divisible, and absolute. Even if time is given beginning and end points, its infinite divisibility allows for it to progress eternally, on some small level. Those boundaries would face the same asymptotic relationship that faces measurements, as I’ve described previously.
Besides that, it is impossible to ascribe an endpoint for time. Following the endpoint, were there a mind to perceive it, that mind could easily extend time. The statement “It’s been one hour since time stopped” proves the point through the contradiction. (Indeed, the phrase “following the endpoint” ought to prove the point by inference). In this way, time is endless (infinite). So long as there is a conscious mind to experience time, time will be seen to continue its passing. As such, without a conscious mind to experience time, there is certainly no reason to assume that time would not continue to pass in its absence. Provided that we don’t traipse off into idealism, the object permanence we learn as infants ought to apply.
Space
Space is infinite and absolute. There is no such thing as nothing. All physical things occupy space. Space is an infinite medium in which arbitrary divisions are made, separating it into finite parts. The space between two points is occupied by invisible gases and particles, not nothing.
Every object we perceive occupies a space of the same volume. Our arbitrary measurements of volume allow that space to be reinterpreted in any shape. A sphere which has a volume of 72 cubed metres can be rearranged to take the form of a 72 cubed meter replica of the Taj Mahal.
Physical objects do not “push space aside.” They occupy as much space as is required for such objects to exist and retain their volume and mass. I have encountered the criticism that if space is infinite, and all space is occupied, nothing ought to be able to move (because the combined force of an infinite number of objects would absorb any force made by one object in its attempt to move).
Such a criticism implies nothingness, because it requires that there be “room” for space to displace into in order to make more room for objects to move around. In infinite space, there can be no limitation on the movement of anything, because there is infinite space for things to move within. As objects are merely finite divisions within one infinite space, it is hardly unexpected that space would remain space regardless of whether every part of it moves or is immovable.
Perhaps science has not fully been able to explain the way that objects occupy space. Perhaps objects exchange particles at such a rate that form and structure are retained, but particles no longer occupy the same part of space (again, divisions in space are arbitrary).
“Space” in this instance is not to be confused with Outer Space; a construct which is itself an arbitrary division of absolute space.
Next Week: On God as infinite, in which I bring this whole infinity talk thing to its logical conclusion, and tackle some common ideas about the big guy in the sky.
Friday, April 9, 2010
On the infinite:
Required Reading: Infinite divisibility, the paradox of infinite divisibility, infinity,
Any thing that is infinite can be divided into an infinite number of finite parts an infinite number of times. That is infinite divisibility. For example, measurements take an indeterminate volume and use an arbitrary value or increment to divide that indeterminate volume into smaller and smaller finite values.
Every thing can be divided in that way. There is nothing that is not divisible into smaller and smaller parts; nothing that is not infinitely divisible. This applies to the infinite - which by definition is of indeterminate value - like it does to any other thing.
There can only be one infinite thing. That which is infinite is all that there is by definition. Infinity as a quality is absolute, which means that it refers to limitlessness, endlessness, boundlessness, as opposed to a vaguer incapacity for human measurement, which is inherent in the infinite in the first place. An infinite thing extends forever, in all directions, and in all ways (an infinite thing which is not infinite in every respect is not infinite - more on this later). There can be no infinite object which occupies the same space (or non-spatial plane, if such a thing exists) as another, because the infinite is endless such that any other object/entity would be a part of it necessarily.
Whatever is infinite is the only thing there is. That is a confusing statement because as humans we live in terms of the finite; we see differences between ourselves and other objects and we don't normally think of those objects and ourselves as being one thing. You are not the same as a hammer; you are not the same as a giant robotic badger; you are not the same as your identical twin, even. So the idea of being a small part (a finite division) of something much larger would, to quote the vernacular, “blow your mind.” So, in terms of human experience, there is either no infinite thing (because of our perception of objects/entities as being separate and different), or our ideas about the relations between objects must be changed, and all things must be part of the one infinite thing.
Next Week: On infinite time and space, in which I make a really lame argument for why time is infinite, just for the sake of saying so. Then I make a slightly more convincing argument about space, maybe.
Any thing that is infinite can be divided into an infinite number of finite parts an infinite number of times. That is infinite divisibility. For example, measurements take an indeterminate volume and use an arbitrary value or increment to divide that indeterminate volume into smaller and smaller finite values.
Every thing can be divided in that way. There is nothing that is not divisible into smaller and smaller parts; nothing that is not infinitely divisible. This applies to the infinite - which by definition is of indeterminate value - like it does to any other thing.
There can only be one infinite thing. That which is infinite is all that there is by definition. Infinity as a quality is absolute, which means that it refers to limitlessness, endlessness, boundlessness, as opposed to a vaguer incapacity for human measurement, which is inherent in the infinite in the first place. An infinite thing extends forever, in all directions, and in all ways (an infinite thing which is not infinite in every respect is not infinite - more on this later). There can be no infinite object which occupies the same space (or non-spatial plane, if such a thing exists) as another, because the infinite is endless such that any other object/entity would be a part of it necessarily.
Whatever is infinite is the only thing there is. That is a confusing statement because as humans we live in terms of the finite; we see differences between ourselves and other objects and we don't normally think of those objects and ourselves as being one thing. You are not the same as a hammer; you are not the same as a giant robotic badger; you are not the same as your identical twin, even. So the idea of being a small part (a finite division) of something much larger would, to quote the vernacular, “blow your mind.” So, in terms of human experience, there is either no infinite thing (because of our perception of objects/entities as being separate and different), or our ideas about the relations between objects must be changed, and all things must be part of the one infinite thing.
Next Week: On infinite time and space, in which I make a really lame argument for why time is infinite, just for the sake of saying so. Then I make a slightly more convincing argument about space, maybe.
Thursday, April 1, 2010
On Simultaneity:
Required Reading: Simultaneity, Relativity of simultaneity, the present, the paradox of infinite divisibility
I'd like to note, before I get down to business that the wikipedia page for simultaneity has an interesting point, which is that the root of the word "simultaneous" - simult - is indicative of a supernatural or divine coincidence. Understand, as you read the rest of this entry, just how supernatural a coincidence it would have to be for two events to occur simultaneously. Thought for food.
Simultaneity is improbable for the same reasons that pinpointing “the present” is impossible. I say improbable, because it is possible that two events could occur at the exact same time - no matter how infinitely small the increments of time-measurement are.
However, the smaller the measurements are (and remember, the increments of measurement could become infinitely smaller) the more likely it is that you'll discover that two events that appear to be simultaneous are in fact set apart by such and such an infinitely small duration. So, simultaneous events are extremely rare, to the point that it is likely that they have either never occurred or will never occur.
That said it is possible for events in progress to be happening simultaneously, provided that the "happening" of the event is described in a nonspecific way. For example, “burning” refers to the process of being burnt, but does not refer to any specific part of that process. So, two candles can be burning simultaneously, but it can't be determined by any accurate means whether they were lit simultaneously, or burnt out simultaneously, or put out simultaneously, or reached the middle of the candle simultaneously, or began to melt simultaneously, etc.
Because the occurrence of events is asymptotic (approaching zero or infinity), we have to assume (again) that it is either impossible to determine simultaneity, or it must be the case that simultaneity itself is not possible.
Just like we need relative durations in order to talk about the present, we need to think of occurrences relatively in order to assume that some of them happen simultaneously. Without turning a blind eye to the indeterminacy that's packaged in with these concepts, we would lack the ability to experience or comprehend time in a stable and cohesive sort of way.
Meanwhile simultaneity as an objective concept cannot be considered a true possibility - rather, a theoretical concept.
Next week: On the infinite, in which I tackle infinite divisibility a little more directly and try to explain what it really means for something to be infinite.
I'd like to note, before I get down to business that the wikipedia page for simultaneity has an interesting point, which is that the root of the word "simultaneous" - simult - is indicative of a supernatural or divine coincidence. Understand, as you read the rest of this entry, just how supernatural a coincidence it would have to be for two events to occur simultaneously. Thought for food.
Simultaneity is improbable for the same reasons that pinpointing “the present” is impossible. I say improbable, because it is possible that two events could occur at the exact same time - no matter how infinitely small the increments of time-measurement are.
However, the smaller the measurements are (and remember, the increments of measurement could become infinitely smaller) the more likely it is that you'll discover that two events that appear to be simultaneous are in fact set apart by such and such an infinitely small duration. So, simultaneous events are extremely rare, to the point that it is likely that they have either never occurred or will never occur.
That said it is possible for events in progress to be happening simultaneously, provided that the "happening" of the event is described in a nonspecific way. For example, “burning” refers to the process of being burnt, but does not refer to any specific part of that process. So, two candles can be burning simultaneously, but it can't be determined by any accurate means whether they were lit simultaneously, or burnt out simultaneously, or put out simultaneously, or reached the middle of the candle simultaneously, or began to melt simultaneously, etc.
Because the occurrence of events is asymptotic (approaching zero or infinity), we have to assume (again) that it is either impossible to determine simultaneity, or it must be the case that simultaneity itself is not possible.
Just like we need relative durations in order to talk about the present, we need to think of occurrences relatively in order to assume that some of them happen simultaneously. Without turning a blind eye to the indeterminacy that's packaged in with these concepts, we would lack the ability to experience or comprehend time in a stable and cohesive sort of way.
Meanwhile simultaneity as an objective concept cannot be considered a true possibility - rather, a theoretical concept.
Next week: On the infinite, in which I tackle infinite divisibility a little more directly and try to explain what it really means for something to be infinite.
Subscribe to:
Posts (Atom)
