An interesting idea

[Lheticus]

I'd like to talk about the concept of infinity. Honestly...I'm not sure what it entails fully, so what I'm about to propose is very likely flawed--but I'd at least like to iron out those flaws.

In my understanding, something that is "infinite" is endless, boundless, going on forever. There are things we understand to be examples of this--outer space for one, at least as far as we know. However, it cannot be said that such things cannot be quantified--the act of stating something is infinite it itself a quantification.

This is almost 100% conjecture, but...I believe there are things greater than infinity in our universe--things that lie outside the realm of quantification itself. Literally impossible to measure, even by the metric of infinity. Most if not all of what could possibly fit this description do not and cannot be physically expressed, but that does not, as perhaps some would have it, cheapen their value; it instead increases it incalculably. I'm thinking in particular of something I heard in the episode of House where he hallucinates the Moriarty character: "You think the only truth that matters is the truth that can be measured." Too often, I believe, we real-world humans place value in things that can be measured (appropriately enough, they are nearly always "things" themselves) and not in things that cannot.

I'm not 100% sure yet how far I'd go with this, but I suspect I will only confirm the validity of going the furthest: It is not what CAN'T be measured in this world that is worthless in the grand scheme, but what CAN. That which can be measured is only fulfilling its ideal purpose when it is used for that which can't. That is what I want to believe, and I suspect it will stand up to scrutiny--which naturally is why I'm presenting it here.

[factotum]

Mathematically, what you're saying doesn't work. For instance, if you multiply infinity by 2 in mathematics, the answer is infinity; you don't somehow get a "bigger" infinity by doing that.

As for the universe being infinite, current theories suggest it isn't. If it all started from a single point (the Big Bang) then it can't possibly be, because it would have had to expand at infinite speed in order for that to happen, and that's physically impossible.

[Lheticus]

Mathematically, what you're saying doesn't work. For instance, if you multiply infinity by 2 in mathematics, the answer is infinity; you don't somehow get a "bigger" infinity by doing that.

As for the universe being infinite, current theories suggest it isn't. If it all started from a single point (the Big Bang) then it can't possibly be, because it would have had to expand at infinite speed in order for that to happen, and that's physically impossible.

I'm not positing that there is a value greater than infinity--I am proposing that there are things/concepts greater than infinity that are outside the realm of value altogether. In a set of all possible values, these are what that set does NOT contain. Thus, mathematics are irrelevant in their cases.

Also, thanks for updating me on the example.

[Anarion]

As a philosophical debate, the point is somewhat irrelevant. We're talking with words, and you have to communicate with words. All the variations on "incalculable" or "unable to assign value" come down to is another way of saying that you're not sure how much human beings are capable of knowing. There's a whole field dedicated to this: It's called Epistemology and it is, at its core, the study of knowledge itself.

Here's the Wikipedia article, you can spend an hour of your life clicking links. http://en.wikipedia.org/wiki/Epistemology

[warty goblin]

I'm not positing that there is a value greater than infinity--I am proposing that there are things/concepts greater than infinity that are outside the realm of value altogether. In a set of all possible values, these are what that set does NOT contain. Thus, mathematics are irrelevant in their cases.

Also, thanks for updating me on the example.

Greater than is a mathematical notion, your definition is explicitly mathematical, and moreover imposes a fairly strong ordering condition on your proposed set of things. By most definitions of sets of all possible values, this is entirely easy to work with. I can define functions that map there, e.g. f(1) = greater than infinity, and so forth. This in turn opens the door to a rigorous study of this new set, if anyone were so inclined.

It's also worth noting that infinity is a sort of overloaded term. We say lim(x ->0) (1/x^2) = infinity because it's unbounded above, but this is definitional. We also say that the cardinality of the natural numbers is countably infinite, in the sense that there isn't a 'last' natural number, but you can count them. There is also such a thing as uncountably infinite, and indeed infinities that are larger than that. In that sense, mathematics already has things that are larger than infinity. It's relatively trivial to prove there's an infinite number of them in fact.

[banthesun]

I'll just leave this here

[Lheticus]

Greater than is a mathematical notion, your definition is explicitly mathematical, and moreover imposes a fairly strong ordering condition on your proposed set of things. By most definitions of sets of all possible values, this is entirely easy to work with. I can define functions that map there, e.g. f(1) = greater than infinity, and so forth. This in turn opens the door to a rigorous study of this new set, if anyone were so inclined.

It's also worth noting that infinity is a sort of overloaded term. We say lim(x ->0) (1/x^2) = infinity because it's unbounded above, but this is definitional. We also say that the cardinality of the natural numbers is countably infinite, in the sense that there isn't a 'last' natural number, but you can count them. There is also such a thing as uncountably infinite, and indeed infinities that are larger than that. In that sense, mathematics already has things that are larger than infinity. It's relatively trivial to prove there's an infinite number of them in fact.

"Greater than" is not an explicitly mathematical concept. To say that it is to say that something cannot be "greater" in any terms except quantity, which I think is absurd. My definition is not explicitly mathematical, its entire purpose is to defy mathematics. The entire point I'm trying to make is that there are real things in this world, essentially all of them in the realm of concept, that defy the concept of quantity itself, and thus mathematics itself--yet people still try to quantify them even if only by vague degree systems, and any attempt to do so results in incomplete answers and sub-optimal conclusions and frames of thinking.

[Icewraith]

"Greater than" is not an explicitly mathematical concept. To say that it is to say that something cannot be "greater" in any terms except quantity, which I think is absurd. My definition is not explicitly mathematical, its entire purpose is to defy mathematics. The entire point I'm trying to make is that there are real things in this world, essentially all of them in the realm of concept, that defy the concept of quantity itself, and thus mathematics itself--yet people still try to quantify them even if only by vague degree systems, and any attempt to do so results in incomplete answers and sub-optimal conclusions and frames of thinking.

Except you appear to be talking about mathematics and infinity on a definitional basis. If you don't want the trappings and associations of mathematics and logic, you probably shouldn't use their terminology. May I suggest "inconceivable"?

[Lheticus]

Except you appear to be talking about mathematics and infinity on a definitional basis. If you don't want the trappings and associations of mathematics and logic, you probably shouldn't use their terminology. May I suggest "inconceivable"?

I DO want those trappings. What I'm trying to prove here is that there are things math can't be applied to. While that may seem like a truism to some, what I'm saying is there are people who still attempt to apply the concept of quantity--which IS a purely mathematical concept--to ideas that lie outside the realm of mathematics, and flaws are created as a result.

I think at this point an example is needed--and what I have in mind is a powerful one: love. Love is totally outside the realm of mathematics, it cannot be quantified, even by the concept of infinity. Yet I doubt there are many here who have never heard the phrase "how much do you love me?" even once, whether in real life or coming from a screen. What I'm trying to do here is fight the kind of thinking that brings people to say that phrase--the tendency to attempt to quantify EVERYTHING, even that which cannot be quantified.

[warty goblin]

"Greater than" is not an explicitly mathematical concept. To say that it is to say that something cannot be "greater" in any terms except quantity, which I think is absurd. My definition is not explicitly mathematical, its entire purpose is to defy mathematics. The entire point I'm trying to make is that there are real things in this world, essentially all of them in the realm of concept, that defy the concept of quantity itself, and thus mathematics itself--yet people still try to quantify them even if only by vague degree systems, and any attempt to do so results in incomplete answers and sub-optimal conclusions and frames of thinking.

Greater than is not explicitly mathematical, no. However you are saying something is greater than a number, which is either mathematics or nonsense. You can say X is greater than Y all you want about all sorts of things, but if Y is a number, X had better be one as well, or you end up with absurdities like the concept of cheese is greater than 1.2321.

I DO want those trappings. What I'm trying to prove here is that there are things math can't be applied to. While that may seem like a truism to some, what I'm saying is there are people who still attempt to apply the concept of quantity--which IS a purely mathematical concept--to ideas that lie outside the realm of mathematics, and flaws are created as a result.

Really, I think the only person applying mathematical concepts to non-mathematical constructs is you.

I think at this point an example is needed--and what I have in mind is a powerful one: love. Love is totally outside the realm of mathematics, it cannot be quantified, even by the concept of infinity. Yet I doubt there are many here who have never heard the phrase "how much do you love me?" even once, whether in real life or coming from a screen. What I'm trying to do here is fight the kind of thinking that brings people to say that phrase--the tendency to attempt to quantify EVERYTHING, even that which cannot be quantified.

In which case it is incorrect to say that love is greater than infinity, because that is an explicit quantification. Which seems a relevant point because being greater than infinity but non-mathematical is how this thread started out. It's totally fine to say you can't quantify some things. But you can't turn around and then quantify them. It's also perfectly fine to quantify things, but you can't then turn around and say they can't be quantified.

[Chen]

I DO want those trappings. What I'm trying to prove here is that there are things math can't be applied to. While that may seem like a truism to some, what I'm saying is there are people who still attempt to apply the concept of quantity--which IS a purely mathematical concept--to ideas that lie outside the realm of mathematics, and flaws are created as a result.

I think at this point an example is needed--and what I have in mind is a powerful one: love. Love is totally outside the realm of mathematics, it cannot be quantified, even by the concept of infinity. Yet I doubt there are many here who have never heard the phrase "how much do you love me?" even once, whether in real life or coming from a screen. What I'm trying to do here is fight the kind of thinking that brings people to say that phrase--the tendency to attempt to quantify EVERYTHING, even that which cannot be quantified.

But quantity can be assigned to love. Perhaps not numerical quantities but I can say I love my wife more than I love my house, for example. I'm not really clear what this has to do with infinity though or why you'd bring it up.

[Lheticus]

Greater than is not explicitly mathematical, no. However you are saying something is greater than a number, which is either mathematics or nonsense. You can say X is greater than Y all you want about all sorts of things, but if Y is a number, X had better be one as well, or you end up with absurdities like the concept of cheese is greater than 1.2321.


Really, I think the only person applying mathematical concepts to non-mathematical constructs is you.


In which case it is incorrect to say that love is greater than infinity, because that is an explicit quantification. Which seems a relevant point because being greater than infinity but non-mathematical is how this thread started out. It's totally fine to say you can't quantify some things. But you can't turn around and then quantify them. It's also perfectly fine to quantify things, but you can't then turn around and say they can't be quantified.

I withdraw the phrasing "greater than infinity", consider it changed to "outside infinity"--which is really a subset of what I'd also said, there are things outside of mathematics that people attempt to quantify. This was the point I'd REALLY been trying to make all along. I apologize for creating confusion--this was indeed a greater semantics error than even I usually make. Any other concerns?

[Lheticus]

But quantity can be assigned to love. Perhaps not numerical quantities but I can say I love my wife more than I love my house, for example. I'm not really clear what this has to do with infinity though or why you'd bring it up.

If you believe you love something "more" than something else, then what you feel isn't actually love, but one of many emotions often confused for it. For example, your house could please you greatly, you could derive great satisfaction and pride from the ownership of it, leading to endorphins and pleasure when thinking of it, you could be physically attracted to your wife to great degree--the hypothetical "you" in this scenario could very well actually love her as well--but you cannot say you love one more than the other, because all that means is you do not actually "love" one or both things. Love is not a thing that can be subjugated by degrees of "more" or "less"--not when it's real. You either love someone/something, or you do not--or you have feelings toward it that feel similar to love but are subtly different to the point where you are not able to distinguish that difference.

[warty goblin]

I withdraw the phrasing "greater than infinity", consider it changed to "outside infinity"--which is really a subset of what I'd also said, there are things outside of mathematics that people attempt to quantify. This was the point I'd REALLY been trying to make all along. I apologize for creating confusion--this was indeed a greater semantics error than even I usually make. Any other concerns?

Why not just say non-quantifiable? There's plenty of quantifiable things that a person would reasonably understand to be outside of infinity; the number of keys on your keyboard for instance is very much a non-infinite quantity.

You seem to be operating under the (perhaps unintentional) belief that infinity is somehow at the edge of what mathematics can do, and therefore anything outside of mathematics is somehow beyond or outside of infinity, like math is a circle and once you move far enough, you are outside its perimeter. As somebody who does a fair amount of mathematics, I feel I should make clear that this is not the case. There are lots of things outside of the infinite that math handles regularly, indeed there's substantial branches of mathematics that don't even care about numbers to any particular degree.

If you believe you love something "more" than something else, then what you feel isn't actually love, but one of many emotions often confused for it. For example, your house could please you greatly, you could derive great satisfaction and pride from the ownership of it, leading to endorphins and pleasure when thinking of it, you could be physically attracted to your wife to great degree--the hypothetical "you" in this scenario could very well actually love her as well--but you cannot say you love one more than the other, because all that means is you do not actually "love" one or both things. Love is not a thing that can be subjugated by degrees of "more" or "less"--not when it's real. You either love someone/something, or you do not--or you have feelings toward it that feel similar to love but are subtly different to the point where you are not able to distinguish that difference.

You just quantified love again, albeit as a binary, to which other emotions can converge.

[Lheticus]

Why not just say non-quantifiable? There's plenty of quantifiable things that a person would reasonably understand to be outside of infinity; the number of keys on your keyboard for instance is very much a non-infinite quantity.

You seem to be operating under the (perhaps unintentional) belief that infinity is somehow at the edge of what mathematics can do, and therefore anything outside of mathematics is somehow beyond or outside of infinity, like math is a circle and once you move far enough, you are outside its perimeter. As somebody who does a fair amount of mathematics, I feel I should make clear that this is not the case. There are lots of things outside of the infinite that math handles regularly, indeed there's substantial branches of mathematics that don't even care about numbers to any particular degree.



You just quantified love again, albeit as a binary, to which other emotions can converge.

Well, you're certainly right that I believed that infinity is the most all encompassing extent to which mathematics can be applied. The number of keys on my keyboard is within the set of the infinite--the infinite CONTAINS the finite--that's what I believe. And I certainly find the idea that there are branches of math that don't focus mainly on numbers, as in my understanding, numbers are what math IS. I also fail to see how the attribute of binary is a quantification. In my view, it is a qualification.

[warty goblin]

Well, you're certainly right that I believed that infinity is the most all encompassing extent to which mathematics can be applied. The number of keys on my keyboard is within the set of the infinite--the infinite CONTAINS the finite--that's what I believe. And I certainly find the idea that there are branches of math that don't focus mainly on numbers, as in my understanding, numbers are what math IS. I also fail to see how the attribute of binary is a quantification. In my view, it is a qualification.

It is fair to say that there are branches of math concerned with numbers. These are certainly the areas one sees in school, through at least the first couple years of undergraduate. However this is an incomplete characterization of the field as a whole. If I had to characterize math as a whole, I would say it is primarily concerned with the rigorous, axiomatic investigation of relations between abstract entities, which in many cases may be represented by numbers.

For instance, whether or not a theorem can be proven true is a mathematical concern. Now you can of course represent provability by the binary pair {0, 1}, but if you are unhappy with saying that this quantifies love, one must be equally discontent with the notion that one has quantified provability in this manner. By this one may see that provability, despite being entirely mathematical, is no more quantifiable than your definition of love - even if any particular study of provability is extremely numeric, the question itself by your logic is not.

[Lheticus]

It is fair to say that there are branches of math concerned with numbers. These are certainly the areas one sees in school, through at least the first couple years of undergraduate. However this is an incomplete characterization of the field as a whole. If I had to characterize math as a whole, I would say it is primarily concerned with the rigorous, axiomatic investigation of relations between abstract entities, which in many cases may be represented by numbers.

For instance, whether or not a theorem can be proven true is a mathematical concern. Now you can of course represent provability by the binary pair {0, 1}, but if you are unhappy with saying that this quantifies love, one must be equally discontent with the notion that one has quantified provability in this manner. By this one may see that provability, despite being entirely mathematical, is no more quantifiable than your definition of love - even if any particular study of provability is extremely numeric, the question itself by your logic is not.

I do not whatsoever your dispute your assertion of my view on the concept of provability--you can either prove something or you can't. I do not view a binary yes/no as a quantitative, but rather a qualitative attribute. In other words, your second paragraph is exactly right, which means that transitively, since proving theorems is under the mathematical purview, your statement about math not necessarily being focused primarily on numbers is true--if I accept proving theorems does not itself emphasize numbers, and honestly a statement to that effect would very much be news to me, since theorems themselves are comprised of numbers, or at the very least numeric variables.

[warty goblin]

I do not whatsoever your dispute your assertion of my view on the concept of provability--you can either prove something or you can't. I do not view a binary yes/no as a quantitative, but rather a qualitative attribute. In other words, your second paragraph is exactly right, which means that transitively, since proving theorems is under the mathematical purview, your statement about math not necessarily being focused primarily on numbers is true--if I accept proving theorems does not itself emphasize numbers, and honestly a statement to that effect would very much be news to me, since theorems themselves are comprised of numbers, or at the very least numeric variables.

But theorems are not necessarily concerned only with numbers. For instance the statement 'if parallel lines are unique, then rectangles exist' is a (true) theorem. It's about numbers in the same way that the statement 'there exists at least one person I love' is about numbers. But the relationship of parallel lines and rectangles is one part of a question that kept mathematicians occupied for literally thousands of years.

A further example; the theorem "the theorem 'if parallel lines are unique, rectangles exist" is provable' is itself a provable statement. The proof in this case being the construction of the proof that Euclidean space is a sufficient condition for the existence of rectangles. There's no numbers at all in that theorem though, and what it's concerned with is the demonstrability of a statement that is itself only concerned with numbers in the most passing of ways.

A lot of math is about numbers. Most of the math one is taught unless pursuing a specialist degree in math is about numbers. But not all math is about numbers.

[Lheticus]

But theorems are not necessarily concerned only with numbers. For instance the statement 'if parallel lines are unique, then rectangles exist' is a (true) theorem. It's about numbers in the same way that the statement 'there exists at least one person I love' is about numbers. But the relationship of parallel lines and rectangles is one part of a question that kept mathematicians occupied for literally thousands of years.

A further example; the theorem "the theorem 'if parallel lines are unique, rectangles exist" is provable' is itself a provable statement. The proof in this case being the construction of the proof that Euclidean space is a sufficient condition for the existence of rectangles. There's no numbers at all in that theorem though, and what it's concerned with is the demonstrability of a statement that is itself only concerned with numbers in the most passing of ways.

A lot of math is about numbers. Most of the math one is taught unless pursuing a specialist degree in math is about numbers. But not all math is about numbers.

I have no issue with any of this.

[warty goblin]

I have no issue with any of this.

Glad I could be somewhat illuminating.

For what it's worth, I tend to agree with the notion that there are things which do not take well to quantification. However if quantification is available, I tend to view it as generally the way to proceed towards understanding.

[Chen]

If you believe you love something "more" than something else, then what you feel isn't actually love, but one of many emotions often confused for it. For example, your house could please you greatly, you could derive great satisfaction and pride from the ownership of it, leading to endorphins and pleasure when thinking of it, you could be physically attracted to your wife to great degree--the hypothetical "you" in this scenario could very well actually love her as well--but you cannot say you love one more than the other, because all that means is you do not actually "love" one or both things. Love is not a thing that can be subjugated by degrees of "more" or "less"--not when it's real. You either love someone/something, or you do not--or you have feelings toward it that feel similar to love but are subtly different to the point where you are not able to distinguish that difference.

Wow that whole paragraph is so massively arrogant I don't even know where to start. I'm curious as to why you are defining love so strictly, and where that definition even comes from. Why is love such an absolute concept? Why can there not be degrees to it? I'm sure you've said you like something more than you like something else. Why would "like" and "love" be so inherently different in that one is absolute and the other isn't? What about hate? Or any other emotion? Is love just the special one here for some reason?

[Lheticus]

Wow that whole paragraph is so massively arrogant I don't even know where to start. I'm curious as to why you are defining love so strictly, and where that definition even comes from. Why is love such an absolute concept? Why can there not be degrees to it? I'm sure you've said you like something more than you like something else. Why would "like" and "love" be so inherently different in that one is absolute and the other isn't? What about hate? Or any other emotion? Is love just the special one here for some reason?

I wish I could explain it better. I really do. Part of why I made this thread in the first place was to see if I could explain it--clearly I can't. That paragraph is my belief on what love is, and I probably did use a few too many "you"s there, sorry. I can hardly push that belief on others any more than any other, and as evidenced, I can't even clarify it worth a damn either.

Sorry. Ugh, I'm starting to think I should request this thread locked. I have plenty more to say, but...no idea HOW to say it! >_< And if I try, I'm just going to attract more hate because I can't for the life of me figure out a way to put it in terms people can readily understand. D:

[MilkMonster]

This was mentioned earlier, but it looks like this is really just a matter of qualitative versus quantitative data.

More specifically, you are looking at different levels of measurement. http://en.m.wikipedia.org/wiki/Level_of_measurement

Looking at the 'nominal' entry it states: Numbers may be used to represent the variables but the numbers do not have numerical value or relationship.

I believe this would satisfy your idea of 'existing outside of' infinity or mathematics.

I understand you are taking a look at this from a more philosophical perspective (I've never been much of a philosophy guy myself), that being said (and I hate to jump on the bandwagon), I just don't see where you are going with this, or what you're trying to say.

[Anarion]

I can't tell if answering someone's "how much do you love me?" with "don't be silly, your application of quantitative values to love is erroneous, my love for you is an unquantifiable aspect of the universe," is a terrible plan or deeply romantic.

[Lheticus]

I can't tell if answering someone's "how much do you love me?" with "don't be silly, your application of quantitative values to love is erroneous, my love for you is an unquantifiable aspect of the universe," is a terrible plan or deeply romantic.

Oh brother. XD How about just "I can't possibly express that"?

[Grinner]

I wish I could explain it better. I really do. Part of why I made this thread in the first place was to see if I could explain it--clearly I can't. That paragraph is my belief on what love is, and I probably did use a few too many "you"s there, sorry. I can hardly push that belief on others any more than any other, and as evidenced, I can't even clarify it worth a damn either.

Sorry. Ugh, I'm starting to think I should request this thread locked. I have plenty more to say, but...no idea HOW to say it! >_< And if I try, I'm just going to attract more hate because I can't for the life of me figure out a way to put it in terms people can readily understand. D:

I want to say I understand your point, but there's just so many ways to interpret it...

Take a look at this, and let me know what you think.

This was mentioned earlier, but it looks like this is really just a matter of qualitative versus quantitative data.

*snip*

I understand you are taking a look at this from a more philosophical perspective (I've never been much of a philosophy guy myself), that being said (and I hate to jump on the bandwagon), I just don't see where you are going with this, or what you're trying to say.

I'm gonna say that's not at all what he meant, but if that's true, it's really not your fault. The OP does seem very vague and rambling.

[Closet_Skeleton]

The entire point I'm trying to make is that there are real things in this world, essentially all of them in the realm of concept, that defy the concept of quantity itself, and thus mathematics itself

Well duh.

Of course, numbers themselves are a concept, as is 'quantity'. Emotions like love are actually far more tangible than numbers are. Mathematics is an abstract simplification. Deceptively, there are things called Real Numbers and Imaginary Numbers but that has a completely different meaning to normal language since all numbers are imaginary.

We have a bowl containing 7 apples. I eat some and now have 5 apples. How much less apple do I have in my bowl? By numbers its 7-x=5, but that's only if I count the apples. If I weighed my 7 apples and found they were 37 ounces and then weigh my 5 apples and find I have 29 ounces then its 37-x=29. Of course, my apples are not all identical, you'd expect one apple to weight 37/7=29/5 ounces, which any calculator can tell you is incorrect. None of my apples are identical and they do not weigh the same, so the number 7 I get by counting them and the number 37 I get by weighing them does not actually represent anything about an individual apple.

This same issue will apply to absolutely anything you want to count. Money is even worse, since the actual value of a currency will not be the same at the start of the transaction as at the end of it. If you can't even really count apples but for practical purposes can do so fine, then there's not reason why you shouldn't for practical purposes be able to quantify anything. This is the whole point of IQ tests, you can't measure intelligence, but you can measure IQ because its an abstraction.

The whole point of infinity is that you cannot count numbers. If you want a 'concept that cannot be quantified' then mathematics, clearly one of our most powerful abstract concepts, should be the first place you look, not emotions.

As for the universe being infinite, current theories suggest it isn't. If it all started from a single point (the Big Bang) then it can't possibly be, because it would have had to expand at infinite speed in order for that to happen, and that's physically impossible.

Current theories that are terrible at actually explaining what an expanding universe means.

From one perspective, an expanding universe is infinite, because you can never reach the end of it unless you can move faster than its expanding. If you can't measure its finiteness then it will appear infinite, we'll never know if the universe is infinite or not, we can only guess based on evidence that points towards expansion.

Of course, an infinity doesn't actually mean big. The coastline problem is an obvious example. The length of a coastline (or any other fractal edge) is determined more by the size of the ruler you use than the coastline you're measuring. You can keep shrinking the size of your ruler and the coastline will keep increasing in measured length. Since measurements are just numbers and numbers are infinite you can keep inventing smaller measurements even if you're measuring things smaller than atoms. A finitely sized planet like our own contains millions of islands each with an infinitely long coastline.

But quantity can be assigned to love. Perhaps not numerical quantities but I can say I love my wife more than I love my house, for example. I'm not really clear what this has to do with infinity though or why you'd bring it up.

I'm not sure, assuming that your house is not a woman and that your wife is not a building, if you love your house with the same kind of love as you love your wife there may be something odd about you. Your affection for a building and your affection for a person are probably different types of love, which is a difference of kind not a difference of scale.

If you were polygamous you could love one wife more than another wife, but that's a different situation.

A further example; the theorem "the theorem 'if parallel lines are unique, rectangles exist" is provable' is itself a provable statement. The proof in this case being the construction of the proof that Euclidean space is a sufficient condition for the existence of rectangles.

Of course, 'proven' only means 'proven relative to postulates that are themselves unprovable'. One could in theory create a bunch of clearly false postulates and attempt to create a geometry of say, 7 dimensional space that is mathematically sound. Inside a particularly bizarrely designed maze you might even be able to navigate using this geometry

[Gravitron5000]

I'll just leave this here

You beat me to it ... also, Proof that some infinities are bigger than others

Except you appear to be talking about mathematics and infinity on a definitional basis. If you don't want the trappings and associations of mathematics and logic, you probably shouldn't use their terminology. May I suggest "inconceivable"?

You keep using that word. I do not think it means what you think it means. I couldn't resist.

I think at this point an example is needed--and what I have in mind is a powerful one: love. Love is totally outside the realm of mathematics, it cannot be quantified, even by the concept of infinity. Yet I doubt there are many here who have never heard the phrase "how much do you love me?" even once, whether in real life or coming from a screen. What I'm trying to do here is fight the kind of thinking that brings people to say that phrase--the tendency to attempt to quantify EVERYTHING, even that which cannot be quantified.

Except that in many of those instances the response to "How much do you love me?" is poetic rather than formulaic. Although the question may have been asked in mathematical terms, it was not fishing for a mathematical answer.

[Asta Kask]

Do we know if there's an infinite number of infinities?

[warty goblin]

Do we know if there's an infinite number of infinities?

Yes, the proof is fairly trivial.
Take the natural numbers, N. They are infinite.

Their power set must have larger cardinality than N.

The power set of the power set of N has larger cardinality again.

In general for any n in N, the nth iterated power set of N will be infinite, of larger cardinality than all kth iterated power sets k < n, and of smaller cardinality than all mth iterated power sets, m > n.

This constructively produces a countably infinite number of distinct infinities.