Roachboy:

finite - Definition from the Merriam-Webster Online Dictionary
infinite - Definition from the Merriam-Webster Online Dictionary

Merriam Webster defines the infinite as the boundless, or endless. I think that's the most standard generic definition.

There are different ones depending on the field in which you delve. Religion, mathematics, etc. have slightly different variations.

So to answer your (possibly rhetorical but whatever) question: endless and infinite seem to be the same, and you don't necessarily have to exhaust all of them since it is mathematically possible to prove that something is infinite. (A universally accepted notion)

a merriam webster dictionary definition doesn't exactly resolve questions of meaning.
if they did, all philosophy would be is putzing about until someone in a conversation got fed up with it and decided to turn to a dictionary.

i would think a finite process could theoretically be endless in the sense that it would repeat it's activities endlessly and produce whatever it produced endlessly, but that seems to me a finite situation, infinite only in the most restricted (mathematical) sense.

infinite has a considerable metaphysical weight to it, a considerable history. to collapse it into it's mathematical definition requires that you define the rules of the game up front such that this is the meaning that we are talking about. the op did it to some extent long ago, but the discussion moved out from under that.

such discussion as there is here at this point is really a conflict over which rules for interpretation obtain.
i've been playing by the rules of philosophy of language; vigilante by something between cosmology and something else (can't remember); you by mathematics. so it's no surprise there'd be a differend. and it's no surprise that the debate would reach a point where someone would try to stipulate the rules by stipulating the genre.

thing with doing that is that it makes discussion circular. you know in advance the meaning that's in question because the rules of the game spell it out for you.

the philo of language is probably the only space that allows for consideration of the relation between such rule sets, words and phenomena in the world that they're made to refer to. but this is also a genre with it's own rules. so by mentioning it, i engage in the same game of trying to stipulate which game we're playing.

we could go in any of these directions.
but no question of any real interest is settled via merriam webster---except in the special case of one or another player in a given game not understanding the word.

I don't think you can consider one without considering them all. In your head you can contemplate whatever, but as soon as it becomes interpersonal we are bound by the rules of language. If we're talking about infinity, we have to adhere to the commonly accepted definition of the word. If you or the OP mean to discuss something else, or your personal conception of infinity, then it has to be explicitly stated.

I am not taking a strictly mathematical approach. I feel like I've taken a few here, and what you just said is more or less what I've been saying. We have to start from a common ground and only use things which are understood and accepted by everyone. This is ancient philosophic theory.

Perhaps, since you seem to be adequately versed in philosophy, you'd care to give us this grounding, and then we can all work together to come to some sort of conclusion. (Most likely not, but hey).

Will you present us with the definition of infinity (that we should discuss) and propose a method we should use to resolve this question? There will be no more debates on what infinity means, and from there on in Infinity will be used to refer to the item defined by you.

i did already. i defined it as a negative concept, one produced through inversion of notions like finitude. it has no particular referent. to generate notions like infinity, all you need is the capacity to negation, which is a formal matter.
within christianity, negative theology came closest to addressing it's meaning: we have no access to the infinite because our understanding is finite. so if god is infinite, human beings can know nothing about this god, not even whether she exists or not, and the name "god" is nothing but a name.
that repeats the act of creating a notion through negation of an existing one. but at least it's consistent.

from that viewpoint, mathematical notions of the infinite are just one of any number of ways to locally define the category, one which produces some interesting effects and is useful within certain games.

what i think makes the category of the infinite interesting is how it gets used and what those usages do, not what putative referent there is in the world/universe. it's interesting as a generator for speculative thinking in some contexts. but these usages are conditioned by rules, so the meta-question (to my way of thinking anyway) has to do with rules usage and phenomena in the world, how relations are established, how they condition processes of meaning generation, and how the results of these processes frame experience of the world.
so i wouldn't go in the same direction as you in pursuing the question of what the infinite is, really.
not that yours isn't interesting...it's just not how i'd approach it.

but this all follows from the premise that the infinite is the product of an act of negation, so is the result if you like of a formal operation. in other words, it is a noun that is not a name.


that's what i think the category is.

Yours is an interesting approach, but perhaps I'm not fully understanding your definition, because it seems a little bit vague to me.

Is the sequence of PI infinite? Does that prove infinity? Or does this miss the point you're trying to make? Are you saying that infinity has to be spatial? (length, weight, duration) or not?

I pondered the idea of infinity all night because I did not sleep.

Perhaps it's just an eternal awakeness of sorts.

I no longer 'suffer' from insomnia.

Now I call it, infinity. It was a fun game, while it lasted...um wait, that means
I finited it. Oh well.

the sequence of pi would be under the rules that are particular to mathematics, so assuming that something infinite is a series that it in principle endless.

my definition is more an explanation: if you assume the term finite, the infinite is simply it's negation. everything that is not finite, then. so it's not a name in the sense that there's nothing to point at. it's an empty signifier that way, a form that delimits. so a pure category.

that's what lead me to the bit about negative theology. if you assume human understanding is finite, then the infinite would not be accessible to it. this follows from strictly applying the same operation i outlined above.

the usual assumption with a noun is that one treats it as a name. there is a phenomenon in the world, you can in principle point to it, this is what that phenomenon is called, how it's referred to. what i'm saying is that this notion of the infinite comes about through another route, through inverting another noun. you could say---and people have (descartes for example)---that because i know the category "the infinite" that it follows that there is such a thing. but that supposes the noun is a name, in the sense the start of this paragraph indicates. if it's not, and it's a negation or inversion of another noun, then it's an empty space. once the category is in place, it functions to point toward this empty space (everything which is not finite). descartes' treatment of it as a name makes little sense outside the particular christian tradition he was part of. it's curious to see it wedged into the meditations on first philosophy, just after the cogito ergo sum business, so just after he attempts to ground philosophy. but there it is. you can see for yourself.

I think infinity is possible and what it does is simply take you to another dimension.

An example:
An infinite number of 1 dimensional lines gives you 2 dimensional plane
An infinite number of 2 dimensional planes yields you in the third dimension
An infinite volume of 3 dimensional models takes you to travel time through parallel worlds
An infinite number of 4 dimensional time lines takes you to deal with another unit called tachyon which recently to have infinite speed(faster than light).
And so forth

Also to create millions of species and atom based precision in movement of planets in an order of 10 to the power who knows what span of the galaxy, you would need infinite super computing wisdom that God only has.

No?

The second dimension does not admit the third. I know what you're trying to say, but no, that's not how it works. Otherwise you could only ever have things with infinite measurements in all dimensions.

Also, please don't bring "God" into the equation, because that's a separate discussion, and it's not an element that everyone agrees on.

I don't see the connection with tachyons either.

Hello ManWithAPlan, sorry if I included the subject of the creator in my reply. I was just trying to be add to the subject of infinity, infinite wisdom.

Here's what I mean about the second dimension. If you have an infinite number of planes with Angstrom width they will add together to a certain definable width which you define depending on the number of planes and the variables in question.

As in:
A = A number going to Angstrom ( I stress going to)
B = A number going to Infinity = 1/A
Hence Width = constant * A * B = k * A * 1/A = K = a certain volume definable

I think the question of whether infinity exists has a lot in common with the question of whether god exists in that there really isn't any proof either way, but folks tend to come down on either side of the fence anyway.

Why would anything tangible be infinite? Why wouldn't it? I challenge anyone to answer either of these questions affirmatively with anything other than a handful of wishes.

Oh regarding Tachyons its a hypothesis of mine about infinity. An infinite number of time lines in the forth dimension yields you in the dimension where you are in comparable speed to the (x where x goes to infinity) speed of the Tachyons which I think in my humble opinion is the 5th dimension.

@cellfactor: No need to apologize. It isn't as though you've offended me. I'm simply trying to keep us on track. There are rules in philosophy. You can't try to explain something in terms other than those that everyone accepts. For instance, I may not accept that god is infinitely wise, or I may not know he is, so it's not a good way to try to prove something.

A two dimensional plane does not have a height. You can theoretically position them (theoretically, read: academically) in 3-space such that the origin of each will have a z-coordinate, but they still won't have a height, so you could not stack them.

If you're talking about an infinite amount of pieces of paper or something that is like a 2d plane but has the height of an angstrom, then the height of the stack is infinite.

I don't know what you mean by "going to". I assume you mean "approaching", as in limits, which is also a theoretical concept, and not something observable.

I also don't understand what your equation is trying to show. Of course if you pick three things, set two of them to be inverses, and multiply them, you'll be left with the third. It doesn't seem to show anything at all.

@filtherton - who says only tangible things can be infinite? The way I see it is you have 3 levels of abstraction: tangible, observable, conceivable.

Let us reserve tangibility to our concrete perceptions. We can see and feel a yardstick. It has an innate spatial length.

Let observable be the set of properties which we can observe though are not innate to an entity. Like a cycle, a planet's orbit, a trajectory, the passage of time, a wheel's rotation

Let conceivable be the set of concepts which we can imagine with our minds but not experience directly for one reason or another.

Seeing as how our lives are limited, we cannot experience infinite time. We also cannot experience breathing underwater without the aid of SCUBA gear... we cannot experience being a bird. But that doesn't mean those things don't exist.

As our senses are limited, we cannot experience infinite length or distance. We also cannot see all the way to china from the usa, but that doesn't mean that china doesn't exist.

We can however talk about these things, including infinity, so it must exist. If there is no example of it in the universe, it exists only conceptually. but if there is no experiential example, then it can still exist on one of the other two levels; we just can't see it.

"Why" implies teleology. Can you prove that things have a purpose? If not, then you can't ask that question. Something might be infinite simply by coincidence.

To revive an old challenge - If the universe is not infinite, then what do we call the thing in which the universe sits? Is that infinite? Does a non-infinite universe imply multiple universes? Are they infinite? If so, does that not mean that the thing that contains them has to be infinite? And ultimately, if the universes are not infinite, what acts as a boundary between them that prevents us from saying that they are really just one universe?


edit:

I've also just thought of something that I think pretty much ends this debate:
Infinity exists. Time is infinite.

Time is always measured from a frame of reference.
If the universe is infinite (in time), and has no end, then time within the universe is infinite and infinity exists.
If the universe is finite, there must be another frame of reference which can admit that*, which seems to me has to be infinite**

* Meaning, can see the beginning and end of the universe.

** Unless that thing also comes to an end, in which case there must be something else, etc.

edit 2:

Can you link me to your Tachyon theory? I could try to find it myself but I want to make sure I get the exact one that you mean.

Right. I don't dispute any of this. All I'm saying is that everything ever conceived of exists (or did), at the very least, on a conceptual level. It's a trivial observation, and we could just as well be talking about invisible elephants.

Philosophy implies teleology. Without an assumption of purpose, all you have is a bunch of untethered statements with no explanatory value at all. So while it is quite possible that something with the property of infiniteness came about as a coincidence, the mere mention of this possibility doesn't make for a compelling case for the existence of infinity.

Here's that teleology thing again. Why would you assume that the universe sits in anything?


Why would there need to be another frame of reference to admit that the universe is finite? To paraphrase: If a universe begins and ends and there's no one around to admit it, does that universe ever exist?

Your argument here depends on some pretty arbitrary notions about what must exist outside of the universe.

It's not teleology to say that the universe must reside in something. It's just logical. If you have something that is not infinite, then what happens when you go outside it? Note: I'm not saying it does reside in something because I'm not saying it's finite. But if we take as given that it's finite, and we can traverse it, then that means there must be such a point where we cease to be in the universe and must be in _something else_.

Note the scenario where all space is bent such that when traveling to the outer reaches of the universe you end up wrapping around. This would be something like a hyper-sphere effect where the dimension is folded up upon itself. To me, that would be infinite, but that's another topic, sort of.


Why do you need a frame of reference? Because that's how time is measured. Theory of relativity?

If time needs a reference in order to be measured, then outside of that reference, time does not exist, therefore applying some notion of infinity to it seems illogical since it can't be measured outside of a reference.

I believe infinity exists simply because I can't see a reason not to believe it exists. However, proving it becomes paradoxical because we would need an infinite existence to prove it.

I opened this subject simply because the universe including planets, species, micro organisms and all creations seem to have an unlimited amount in design in them and putting them all together tends to create a very huge or uncountable amount of data to make them. So this would require a very huge or infinite processing power. This means infinite wisdom. That can only be explained by God. Now you may believe in God or not that is your choice but I think the subject is relevant to infinity.

Angstrom is a distance that goes to zero meaning it will always decrease even if you want to imagine something smaller than it, there will be something smaller. That's what I mean going to, meaning an a number that is infinitely small.

The mathematical line has zero thickness not angstrom thickness however when we talk about reality there is no such thing as zero thickness. No matter how small even if it is smaller than a quark it will have a thickness. Now volume, matter, and time are reality hence their equations are those created by variables that have their extra dimension not being zero hence its the closest number to zero. the closest number to zero is angstrom hence angstrom applies to dimensions in reality.

Imagine it like this. I want to draw two dots A and B on a line. Dot A and Dot B are each on certain centimeters from Zero point.
Dot width: 0.000000000000001cm
Dot A pos: 0.000000000000001cm from Zero
Dot B pos: 0.000000000000001cm from Zero
they will still be on the same spot so i want to make them on different spots
Dot width: 0.00000000000000000000000000000001cm
Dot A pos: 0.00000000000000000000000000000001cm from Zero
Dot B pos: 0.00000000000000000000000000000001cm from Zero
Still on the same spot so:
Dot width: 0.00000000000000000000000000000000000000001cm
Dot A pos: 0.00000000000000000000000000000000000000001cm from Zero
Dot B pos: 0.00000000000000000000000000000000000000001cm from Zero
ok so I do like this
Dot width: 0.0000000000000000000000000000000000000000000000001cm
Dot A pos: 0.0000000000000000000000000000000000000000000000001cm from Zero
Dot B pos: 0.0000000000000000000000000000000000000000000000002cm from Zero
Now they are not on the same spot but
they're: 0.0000000000000000000000000000000000000000000000001cm from each other

So what it means if you have to have 2 points that are distinct from each other and you want to line them up near each other in physical space then the 2 points have to not lie on top of each other. meaning the points should be angstrom apart from each other. this means the closest space between 2 points is angstrom. now if we put an infinite number of angstroms near each other they will get you a certain value as defined earlier. If you have time perhaps you can ask a math teacher about it.

thats how its done in mathematics in formulas taught at schools and universities

I know what an angstrom is. For any number n | n > 0; n * infinity = infinity.

If you have an infinite amount of angstroms, it will give you infinity.


JumpinJesus - I'm not sure I understand what your point is. There are lots of references that we use... such as "time from event A", but there's also relativistic time, as in the theory of relativity. If something has a motion, its trajectory can be plotted with a reference point to something. If something has a duration (a defined beginning or ending), then its being can be plotted with a reference point to SOMETHING. Otherwise it doesn't make sense and that first something must not have an end point.

I apologize here for the misinterpretation. The variable that I am seeking is X where X goes to zero. Its a number so small that there is no number smaller than it. In other words, its an ever decreasing number, that's why in studies we use "goes to". Imagine x where x is an ever decreasing number. Also imagine stacking an ever increasing number of units on top of each other, hence

x where x decreases ever * y where y increases ever = k

why k, its because k is to be a constant since x and y are in the same dimension. You see lengths of 2 units would increase at the same speed in the same dimension if you put them under the same effect, hence linear difference. Its like a car with an engine A and a car with an engine B, the cars maximum speeds are at linear amount from each other because they both use the same combustion technology. Now if you use a car with hybrid technology, thats another dimension.

It's implicitly teleological, a few steps down the road from asking why. Saying something is "logical" doesn't mean anything. It's also perfectly logical to say that the universe must not reside in something. Something that is finite has a boundary, but that doesn't mean that there is anything outside the boundary.

If the universe was finite, it probably wouldn't need its finiteness measured. It's quite possible that it would remain finite without any sort of frame of reference to measure it. Time passes while we sleep, after all.

It isn't a question of NEED to be measured, or measuring as an act. It's potential to be measured we're talking about.

Teleology is concerned with the notion that everything has a reason. I'm not saying that there's a reason for the universe to be finite or infinite. My argument was that regardless, time is infinite. I'm not saying time doesn't exist if we dont' measure it, because we can currently meaure the passage of time back at a place in time before time measurement was invented (By humans).

If we use time not in the human-constructed sense, but in the relativistic sense on which physics rests, then time is relative to a frame, and it has nothing to do with teleology at all, implicitly or otherwise.

The teleology comment was directed solely at your assumption that finite things must be contained.

I'm not quite sure how you can make the claim that time in the "relativistic sense" isn't constructed by humans. All science is a human construct.

Perhaps it has been too long since I took physics, but if I recall correctly, a frame of reference is nothing more than the point from which observations are made. I'm not certain how this concept leads to infinite time.

"Science" is a human construct, but before we discovered what gravity was, assuming we know now, it still existed didn't it? "Science" is simply giving phenomena a name.

WORDS are a human construct. This whole thread is questioning whether or not what HUMANS call INFINITY exists. So I don't see where you're going with this. That goes for your last commend on frame of reference too. Sure, that's just what we call it, but that doesn't change the fact, does it? A rose by any other name, right? How we think of things doesn't change their nature.

Yes, gravity probably existed. No, science isn't simply giving phenomena names. Science is about modeling the interactions between phenomena.

I'm just trying to understand your proof that time is infinite, because it doesn't make sense to me. Your claim is that time must be infinite because if it wasn't then there would have to be some sort of "frame of reference" to "admit" it, and since there are an infinite number of frames of reference, then... ?

It doesn't make sense to me, and it's possible that's because language can be the limiting factor in transmitting ideas. It could also be because your proof doesn't actually make sense, but I'm willing to give you the benefit of the doubt.

It's a question of what happens when we reach the end of the universe. You either have to wrap around because space and time is bent, or breach it. If you breach it, then where are you? What is "non-universe"?

No