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Author  Topic: Time and Beginning to Exist  
Straggler Member (Idle past 790 days) Posts: 10332 From: London England Joined: 
Well I don't really disagree with any of that. But to nitpick.
Rahvin writes: I don't think there's any such thing as an "objective concept." A "concept" by definition can exist only within the confines of an intelligent mind. It's an abstract representation of something else, which may or may not actually exist in objective reality. OK. But that doesn't mean that all concepts are equally subjective does it? You can see what is meant when I describe the concept of 4 as having objective existence in a way that my as yet unwritten or unstated idea for a novel does not  Right? The concept of an apple has an objective basis in a way that the concept of the Easter Bunny or Goldilocks doesn't.
Rahvin writes: I would argue that the parts of reality represented by "4" and "Pi" are objective, but that the words and concepts themselves are our own invention. Well obviously the words, symbols and exact conception are human inventions. But let me ask you this: Do you think that reality is innately logical? Do you think that a concept like pi is arguably an aspect of objective reality and thus can meaningfully be said to have been discovered rather than invented? We would presumably agree that any suitably advanced civilisation would be aware of this relationship
The symbols used are indisputably just human conventions. But the relationship being expressed is arguably a property of objective reality. No?


1.61803 Member (Idle past 1325 days) Posts: 2928 From: Lone Star State USA Joined: 
designtheorist writes: "Outside all frames of reference" is an interesting idea. Do you mean like a timeless, immaterial realm? But why can't such a realm have its own frame of reference? Things happen because there is a degree of inequalities in the universe. Thermodynamics is the process that allows systems to achieve homeostasis through the exchange of energy states. If everything was in homeostasis and delta s= zero.how could there be any change? No time and space and matter is for all intensive purposes moot. For there to be a "nothing" there must be NO THING. Subtracting ones existence from the equation at least in this reality is impossible as Quantum mechanics shows a observer/measurement is somehow linked to the outcome. We can try to imagine anything we want. But we can't know without looking into the box.


Rahvin Member (Idle past 209 days) Posts: 3976 Joined: 
Well obviously the words, symbols and exact conception are human inventions. But let me ask you this: Do you think that reality is innately logical? I think that reality appears to be innately selfconsistent. The Universe doesn't make arguments, so the term "logic" doesn't really apply. I also think that the term "logic" when used in a context like yours carries additional meanings that are inaccurate  thanks to Star Trek, many people equate "logic" with "makes intuitive sense," and the Universe flatly does not. Hey, if you can nitpick, so can I
Do you think that a concept like pi is arguably an aspect of objective reality and thus can meaningfully be said to have been discovered rather than invented? I think that a concept like pi can be said to be based on reality, and therefor represents an aspect of objective reality, limited by our understanding of that aspect. I think our understanding of pi is pretty welltested and extremely precise for all practical considerations, but I still think it's important to differentiate our understanding of reality from reality itself. No matter how accurate a map we draw, we are still drawing a map, and the map is not the territory.
We would presumably agree that any suitably advanced civilisation would be aware of this relationship Agreed
The symbols used are indisputably just human conventions. But the relationship being expressed is arguably a property of objective reality. No? The relationship is still a representation of a real relationship. Remember how all science is tentative pending additional evidence? This is why. All of our concepts, from "2" to "Hydrogen" to "2+2=4" and "pi=3.1457..." are merely representations of observed aspects of reality. Because they are representations limited by our own observational capabilities, they are subject to change when new information proves our representations to be inaccurate. Newton described the relationship between heavenly bodies and introduced orbital mechanics. But as it turned out the relationship expressed in his mathematical representation was wrong, on scales outside of normal human experience. Einstein was able to provide a more accurate representation for the real relationship that works at all scales (so far...). Do you see what I mean here? There are times when we can reasonably believe that our maps are indistinguishable from the territory, like with concepts like "4" or "pi." They're well tested, and the probability of us being wrong with those concepts is so slim it's basically beneath consideration. But they're still just maps, not the territory itself. You should know from my posting history that I'm not in any way advocating some sort of idiotic equivocation like "well everything is just subjective anyway." All of our concepts are subjective, but some concepts are more likely to accurately represent reality than others. The human understanding when it has once adopted an opinion (either as being the received opinion or as being agreeable to itself) draws all things else to support and agree with it.  Francis Bacon "There are two novels that can change a bookish fourteenyear old's life: The Lord of the Rings and Atlas Shrugged. One is a childish fantasy that often engenders a lifelong obsession with its unbelievable heroes, leading to an emotionally stunted, socially crippled adulthood, unable to deal with the real world. The other, of course, involves orcs."  John Rogers


Straggler Member (Idle past 790 days) Posts: 10332 From: London England Joined: 
Last questions:
Do apples objectively exist? Does pi objectively exist? Does the Easter Bunny objectively exist? Are mathematical concepts like pi closer in nature to empirical things like apples than they are to wholly subjective notions such as the Easter Bunny?


Rahvin Member (Idle past 209 days) Posts: 3976 Joined: 
Last questions: Do apples objectively exist? The things we call apples certainly appear to exist in objective reality, though we know now that their real nature is significantly different from the limited sensory input we receive about them. What we see as discrete objects of a specific shape and size with a particular taste and texture are actually perturbations in a quantum probability field that interact with other perturbations in quantum probability fields such that at different scales they behave like quarks, protons, atoms, molecules, cells, and apples. That said, there is still a miniscule possibility that we are in the Matrix or some other realitysimulation (a dream, etc) and that apples are fictional.
Does pi objectively exist? The relationship represented by pi certainly seems to exist in objective reality, and it seems to be extremely accurate. The Universe appears to be selfconsistent, and within that framework the diameter and circumference of a circle have a very specific relationship, apparently every time without fail. That said, again, there is a miniscule possibility that the world we experience is in fact fictional, and that real objective reality does not contain the relationship pi, or where that relationship is different. It rather hurts my brain to think of a simple mathematical relationship like pi being different somehow, but my lack of imagination is not necessarily a bar to reality, which already manages to boggle my mind on multiple topics.
Does the Easter Bunny objectively exist? It doesn't appear to. It appears to be an amalgamation of multiple concepts that do base themselves on an understanding of objective reality (bunnies and eggs, for example), but the myth as a whole diverges significantly from any evidence and contradicts several expectations (mammals laying eggs, let alone colored eggs, as an example) based on significantly repeated observations, which points to the hypothesis that the Easter Bunny is, in fact, just a madeup fictional character. There is, of course, a miniscule possibility that we live n the Matrix. Or that the Hare Club for Men actually exists and purposefully distorts the myth of the Easter Bunny into a strawman representation of itself (embellishing fact with fictional nonsense like claiming that the bunny lays eggs) and covers up actual evidence of its existence and true nature. You'll note that, in the case of pi and apples, the chances of either of those concepts not corresponding to aspects of objective reality are miniscule, while the reverse is true of the Easter Bunny, where the larger probability by far is that the Easter Bunny is fiction. All concepts are just our attempts to map the territory of reality, but some maps don;t correspond to any territory, while others are very accurate. We tell the difference by examining evidence based on observing how predictions drawn from our maps are contradicted or verified through additional exploration of reality.
Are mathematical concepts like pi closer in nature to empirical things like apples than they are to wholly subjective notions such as the Easter Bunny? You're taking this as part of the neverending idiocy of "subjectivity vs. objectivity." But I'm not RAZD. Please do remember that.
Even though all human concepts are (and can only ever be) representations within human minds limited by the perception and understanding of human beings, some of those concepts will more accurately represent objective reality than others. "Gravity" is a concept that represents a fundamental force of the Universe, like "electromagnetism" or "the Strong Nuclear force." Our representations could be wrong, but because we've tied their definitions to examinations of reality through testing and evidence, they're far more likely to be accurate than a random madeup guess like pink unicorns made of happiness and sunshine. The map is never the same as the territory in the same way that there is no globe that is actually the planet Earth. But many globes will far more accurately represent the real planet Earth than any map of Middle Earth found in a Tolkien novel. We take linguistic shortcuts and say "apples really exist" when the likelihood of the alternative is so tiny as to be insignificant, and/or where the complexity of the real truth is inclusive of the simplistic answer and doesn't add significant practical meaning to the ideas being exchanged at the time. We just don't need a quantumphysics lesson to ask whether someone likes the flavor of apple pie. Somewhat like how we can use Newton to predict the motion of a pendulum, even if it's not quite as accurate as Einstein. But it's important to remember that our understanding is separate and distinct from what we are trying to understand. Our models of the Universe can always be wrong, while the Universe is the way it is regardless of whether we understand it or even exist to ask the questions in the first place.The human understanding when it has once adopted an opinion (either as being the received opinion or as being agreeable to itself) draws all things else to support and agree with it.  Francis Bacon "There are two novels that can change a bookish fourteenyear old's life: The Lord of the Rings and Atlas Shrugged. One is a childish fantasy that often engenders a lifelong obsession with its unbelievable heroes, leading to an emotionally stunted, socially crippled adulthood, unable to deal with the real world. The other, of course, involves orcs."  John Rogers


Straggler Member (Idle past 790 days) Posts: 10332 From: London England Joined: 
Whatever objectively exists can only ever be experienced and conceived of subjectively. This seems to be your main point. And I couldn’t agree with it more. This much is essentially inarguable. But I still take issue with one key thing that you have said.
Rahvin writes: "Four" is still a subjective concept, it only exists in your head, it's a symbol that represents something in reality. I would suggest that mathematical entities such as 4 and Pi can be said to exist objectively. In fact I would suggest that they arguably have a greater claim to objective existence than things like apples. Now of course there are all sorts of provisos to this. Of course we take linguistic shortcuts regarding the necessarily subjective nature of ALL experience and ALL concepts. But it would be taking things to the absurd to conclude that apples don’t objectively exist because of these limitations wouldn’t it? We can hopefully both agree that apples do indeed exist (aforementioned provisos implicit). So the question is — Does Pi exist? It obviously doesn’t exist in the same physical sense that apples do. But I think you can very meaningfully say it exists as a property of reality. I think to say that 4 or Pi only exist subjectively is no more sensible than saying that my conviction in the existence of apples is a subjective belief.
Straggler writes: We would presumably agree that any suitably advanced civilisation would be aware of this relationship
Rahvin writes: Agreed I put it to you that this relationship is therefore not something that we (or any other suitably advanced alien civilisation that may be out there) have invented. I put it to you that this relationship is instead an aspect of objective reality that we have discovered.In short I put it to you that this relationship objectively exists in some sense that is independent of the minds conceiving it. What do you think? Rahvin writes: You're taking this as part of the neverending idiocy of "subjectivity vs. objectivity." But I'm not RAZD. I think the sort of subjectiveobjective shenanigans we have both engaged in with RAZD elsewhere are different and not overly relevant to anything being discussed here. I think the link between reality and maths as the language of logic is fascinating and very possibly tells us something rather deep about the nature of reality itself.


Rahvin Member (Idle past 209 days) Posts: 3976 Joined:

Whatever objectively exists can only ever be experienced and conceived of subjectively. This seems to be your main point. And I couldn’t agree with it more. This much is essentially inarguable. But I still take issue with one key thing that you have said. I think our "disagreement" is small, and that we probably have something pretty close to the same idea going on here.
I would suggest that mathematical entities such as 4 and Pi can be said to exist objectively. In fact I would suggest that they arguably have a greater claim to objective existence than things like apples. "4" and "pi" represent concepts that do seem to accurately correspond to consistent relationships in objective reality. "4" in particular is a representation of such a basic concept that it's hard to conceive of it being wrong. It's barely conceivable that we live in a simulated Universe like the Matrix where "4" maps to a part of our experience, but while the "real" Universe contains no such thing. But the vastly more probable option is that "4" represents something real  an integer between "3" and "5" that corresponds to particular amount, and where that amount is present in many realworld environments. It's a description of such a basic abstract concept (you can talk about four "real" atoms or four "real" apples or four fictional bowls of porridge) that fits so well with observations of reality (if we line up five apples, we can definitely see that one whole apple exists between apples three and five, so it's not a fraction, it must be an integer) that I would agree that it more accurately reflects something objectively real than the word "apple" does.
But it would be taking things to the absurd to conclude that apples don’t objectively exist because of these limitations wouldn’t it? We can hopefully both agree that apples do indeed exist (aforementioned provisos implicit). Sort of. Basically, yes. The reason the alternative is absurd is simply that the probability of that alternative (that "apples" don't objectively exist, etc) is so low as to be beneath consideration. I think it's important to acknowledge at a basic level that any concept or experience we have is our brains' attempt to map reality (and some of that isn;t even conscious) using the limited information available to our senses, but we don;t seem to disagree on that at all. An "apple" is far more complex than the word actually implies, and it's not what our senses seem to tell us in many respects (we aren't actually "touching" the apple, there is no real contact, it's just the repulsion of electron shells providing the illusion of contact, etc), but for practical everyday purposes the term "apple" represents an objectively real thing with sufficient accuracy that we may as well say "apples are real, objective things."
So the question is — Does Pi exist? It obviously doesn’t exist in the same physical sense that apples do. But I think you can very meaningfully say it exists as a property of reality. I think to say that 4 or Pi only exist subjectively is no more sensible than saying that my conviction in the existence of apples is a subjective belief. "4" and "pi" exist within the selfconsistent Universe we experience, which may or may not be real. We could live in the Matrix, remember, and in the "real" Universe "pi" could be exactly five, or there could be no such thing as circles in the first place. It's an absurdly low probability, but all human knowledge is tentative pending additional evidence, and math carries no exception to that universal truth. In the Universe we do experience though, "4" and "pi" represent relationships that are identical for every observer in a relevant context and which have been accurate regardless of whether the observers were aware of the relationship or not. They're damned accurate representations of what we perceive of as reality by any test you can name. More accurate than "apple," largely because they're such abstract concepts that apply universally at such a basic level. I don't think we're really in disagreement here.
I put it to you that this relationship is therefore not something that we (or any other suitably advanced alien civilisation that may be out there) have invented. I put it to you that this relationship is instead an aspect of objective reality that we have discovered. In short I put it to you that this relationship objectively exists in some sense that is independent of the minds conceiving it. What do you think? We invented the mathematical symbols and even the relationship to represent something we observe that we did not invent. Assuming our measurement of that real relationship is accurate , any independent observer capable of taking similarly accurate measurements would arrive at the same representative relationship expressed in the equation, even if the symbols used were different.
I think the sort of subjectiveobjective shenanigans we have both engaged in with RAZD elsewhere are different and not overly relevant to anything being discussed here. I think the link between reality and maths as the language of logic is fascinating and very possibly tells us something rather deep about the nature of reality itself. Agreed, though I also think it's interesting to see what it tells us about ourselves.The human understanding when it has once adopted an opinion (either as being the received opinion or as being agreeable to itself) draws all things else to support and agree with it.  Francis Bacon "There are two novels that can change a bookish fourteenyear old's life: The Lord of the Rings and Atlas Shrugged. One is a childish fantasy that often engenders a lifelong obsession with its unbelievable heroes, leading to an emotionally stunted, socially crippled adulthood, unable to deal with the real world. The other, of course, involves orcs."  John Rogers


Straggler Member (Idle past 790 days) Posts: 10332 From: London England Joined: 
Good post. The disagreement is getting smaller. But it hasn’t vanished yet
Straggler writes: I put it to you that this relationship is therefore not something that we (or any other suitably advanced alien civilisation that may be out there) have invented. I put it to you that this relationship is instead an aspect of objective reality that we have discovered. In short I put it to you that this relationship objectively exists in some sense that is independent of the minds conceiving it. What do you think? Rahvin writes: We invented the mathematical symbols and even the relationship to represent something we observe that we did not invent. The reason I chose that relationship is that I don’t see how it can possibly be derived from empirical observation. It is a mathematical relationship. So what observations are you suggesting it is based on?
Rahvin writes: Assuming our measurement of that real relationship is accurate , any independent observer capable of taking similarly accurate measurements would arrive at the same representative relationship expressed in the equation, even if the symbols used were different. What accurate measurements are you suggesting are required in order to derive that particular relationship? Whether Pi has been calculated to 10 decimal places or 10 million decimal places doesn’t make any real difference to the truth of this relationship does it?


Percy Member Posts: 21842 From: New Hampshire Joined: Member Rating: 5.5 
Son Soku writes: Please let me know if this is in anyway unclear. It's not exactly unclear, but I'm left wondering why some things should be so. So there are two oceans of fields. One ocean is the electroweak field, the other is the doublet field. Don't these oceans occupy the same space? If so, what makes them two different oceans and why aren't they considered one ocean of 8 liquids? What does "After the doublet field took its value" mean, and why would the fact that it has taken its value cause it to require an infinite amount of energy to make a parcel/particle of just one liquid? So, before the doublet field took its value, in addition to the singleparcel possibilities, weren't combinations of parcels possible? If not, why not? Why do you mention particles at one point, but your list of combinations after the doublet field took its value only includes bosons? Does the name "Spontaneous Symmetry Breaking" imply that the doublet field took its value spontaneously? Thanks for the help, good deeds never go unpunished, as they say. Percy


Son Goku Inactive Member

Don't these oceans occupy the same space?
Yes, they do indeed.
If so, what makes them two different oceans and why aren't they considered one ocean of 8 liquids?
Good point. Something I left out of my previous explanation. Basically the electroweak field is a vector field and the doublet field is a scalar field.An example of a vector field is the wind velocity on the Earth's surface, which requires an vector at each point to describe the wind speed and direction. Similarly the electroweak field has a magnitude and direction at each point, which in some sense would tell you how much it effects the velocities of fields that interact with it. The doublet field on the other hand is just a number at each point, like temperture on the Earth's surface. From the point of view of the oceans of liquids, this doesn't matter, but it's the basic reason they can't be put together. What does "After the doublet field took its value" mean,
When the universe cooled enough, the doublet field assumed a certain strength value, even though it had zero energy. It basically got "locked" into a particular value everywhere, similar to how crystals get locked into a particular shape after you cool them from molten crystal. (In fact the same mathematics describes both)
and why would the fact that it has taken its value cause it to require an infinite amount of energy to make a parcel/particle of just one liquid?
Basically when we want to reshape a crystal, we have to melt it and then cool it again to get another shape. Different crystal shapes will then reflect light differently. Similarly different "locked" values of the doublet field will give different packagings of "field liquid", the only way to change this or to return to the original packaging is to reheat the whole universe, since the doublet field is everywhere. Reheating the whole universe would take infinite/effectively infinite energy.
So, before the doublet field took its value, in addition to the singleparcel possibilities, weren't combinations of parcels possible?
In the way I've given it, no.
If not, why not?
The value of the doublet field is one of the physical quantities that effects what packagings are possible or not. Just as the shape of a crystal determines the strength of light and colour spectrum of the light reflected by it. More directly however for each different combination of colours we can make a "subfield" of those colours, for example I could have a "C + D + G" field, from my previous post. These subfields can only be packaged into particles if they have zero strength at zero energy. The reason being that if a field has some strength at zero energy it has none of the correct properties (doesn't evolve correctly) to make particles. However since all these fields interact with the doublet field, some of their field strength comes from it. If its value is just right, it will cancel against the other things contributing to the fields strength and the "C + D + G" field will have zerostrength and so it can create particles.
Why do you mention particles at one point, but your list of combinations after the doublet field took its value only includes bosons?
I include only the bosons for simplicity. If I used the fermions, things get a little more complicated. For example the colours mix differently for a left spinning electron and a right spinning electron, which would make the presentation a bit more difficult. However the basic mechanism is the same, I just excluded them for technical complexity and length (there's a lot of fermions).
Does the name "Spontaneous Symmetry Breaking" imply that the doublet field took its value spontaneously?
Actually no. The name is historical in origin. Originally the idea was used for crystals and ferromagnets, which do seem to spontaneously pick a shape or direction at random. Since the mathematics is the same we just use the same name. However the doublet field would have settled into its value. Although I guess when the settling occurs over a fraction of a second you could call it spontaneous.


New Cat's Eye Inactive Member 
Thanks for taking the time to type that up. I enjoyed reading it and felt like I learned some stuff


Rahvin Member (Idle past 209 days) Posts: 3976 Joined: 
The reason I chose that relationship is that I don’t see how it can possibly be derived from empirical observation. It is a mathematical relationship. So what observations are you suggesting it is based on? Mathematics is essentially a language of symbols that represent observations in the "real" world. We can observe an apple (an integer) and see how the relationship between integers changes as we add or remove apples; we can observe half or a third of an apple and develop fractions and decimals. We observe exponential and other nonlinear relationships int he real world, too. The language of mathematics takes observations and converts them into abstract concepts with a set of rules governing their relationships with each other based on realworld observation. When we talk about pi, we aren't talking about a theoretical relationship  that symbol was made to represent a real, measured relationship between the circumference and diameter of a circle. Those symbols, though, can be used in a purely abstract sense, even to describe a fictional set of observations. I can talk about four apples that I don't have, or try to calculate the minimum energy required for the Death Star's superlaser to destroy the planet Alderaan. The relationships still have a basis in the real world, just like the word "apple" refers to something real even when I'm talking about an imaginary apple. A specific mathematical expression, like yours, or my four imagined apples, can be a map that corresponds to no territory. That's basically why I mentioned previously that even mathematics is tentative. But we didn't invent "4," or "pi." We invented the symbols, but we based them on real observation. We didn;t invent exponential relationships  you observe one every time you drop an object. We just invented the symbols, and took measurements to see the specific relationship in specific cases to the best of our observational ability. Because the symbols are based on real things, an independent alien observer will likely have developed a basically identical mathematical language that just uses different symbols. 1+1=2 would be a universally agreeable expression once you convert the writing systems...whether you're talking about adding real apples or counting imaginary TIE fighters.
What accurate measurements are you suggesting are required in order to derive that particular relationship? Whether Pi has been calculated to 10 decimal places or 10 million decimal places doesn’t make any real difference to the truth of this relationship does it? That's basically my point. If we can only calculate pi to 10 decimals, we're less accurate than if we can calculate it to 100, or 1000. In the case of pi, we know we can never be perfectly precise because we can't ever calculate an infinite number of decimal places. We know that our map can never exactly match the territory, just that we can attain sufficient accuracy for any and all practical needs. When we talk about pi, we're talking about our understanding of the relationship between the diameter and circumference of a circle to the best of our observational ability, and in this case it's been tested very well such that we have great confidence that pi is not, in fact, "5" or "12.7." An alien intelligence would also be aware of the relationship, and would not likely believe pi to be "5," though they may have calculated pi to a different number of decimal places than we have and therefore be slightly more or less accurate in their understanding. The human understanding when it has once adopted an opinion (either as being the received opinion or as being agreeable to itself) draws all things else to support and agree with it.  Francis Bacon "There are two novels that can change a bookish fourteenyear old's life: The Lord of the Rings and Atlas Shrugged. One is a childish fantasy that often engenders a lifelong obsession with its unbelievable heroes, leading to an emotionally stunted, socially crippled adulthood, unable to deal with the real world. The other, of course, involves orcs."  John Rogers


Straggler Member (Idle past 790 days) Posts: 10332 From: London England Joined: 
Rahvin writes: That's basically my point. If we can only calculate pi to 10 decimals, we're less accurate than if we can calculate it to 100, or 1000. Pi is a geometric entity relating to perfect circles. Perfect circles don't physically exist. The value of pi to 39 decimal places will tell you the radius of the circumference of the known universe to an accuracy of the radius of a hydrogen atom. Try empirically measuring that. The last time I looked we had calculated pi to about 5 trillion decimal places. And yet any similarly advanced alien civilisation unencumbered by human cultural or psychological baggage but with comparable computational power at their disposal could agree this same entity to this same degree of astonishing accuracy (differences in nomenclature implicit) The idea that Pi objectively exists is not limited to what can be physically/empirically observed or measured. In fact it has little to do with physical measurements or observations at all.
Rahvin writes: Mathematics is essentially a language of symbols that represent observations in the "real" world. But that's the question here. Is that true? Both the value of Pi beyond measurable accuracy and the relationship are objectively true. Yet these things cannot be derived empirically from the physical world.
Wiki on philosophy of mathematics writes: Mathematical realism, like realism in general, holds that mathematical entities exist independently of the human mind. Thus humans do not invent mathematics, but rather discover it, and any other intelligent beings in the universe would presumably do the same. You seem to disagree. You seem to be taking a much more empirical approach. But are you simply assuming that anything which can be called "real" (i.e. actually exist) must be exist in some physical sense or is there some definite reason to take the empirical stance that you seem to be advocating?


NoNukes Inactive Member 
When we talk about pi, we're talking about our understanding of the relationship between the diameter and circumference of a circle to the best of our observational ability I think we can do better than that. The circumference of a circle of radius 1/2 can be conceived exactly without reference to a decimal representation of pi. It is however the case that pi is an irrational number that cannot be expressed as the quotient of two rational numbers. Your position is, to my mind, the same as saying that we cannot have an exact conception of sqrt (2). But we can certainly conceive of a 1 by 1 square and its diagonal. As for the rest of your comment, I'm still on the fence about whether numbers exist outside of the mind, but I'm leaning towards believing that they do. Apparently there is not universal agreement about the issue.


Straggler Member (Idle past 790 days) Posts: 10332 From: London England Joined: 
NN writes: As for the rest of your comment, I'm still on the fence about whether numbers exist outside of the mind, but I'm leaning towards believing that they do. I think a lot of people will intuitively go along with the idea that numbers objectively exist in some sense because numbers do relate so well to the physical world. But the notion that the objectivity of mathematical entities is necessarily dependent on aspects of physical reality is rather limiting and leads to some strange conclusions . For example we all seem to agree that 4 can be said to exist independently of conceiving minds. But what about infinity? Many would be less willing to conclude that infinity exists in the same sense that 4 does because it seems to lack any similar physical basis. But if 4 does objectively exist because it has a physical basis but infinity doesn’t then logically there must be some integer that is the largest number to have a physical basis (i.e. the total number of elementary particles in the universe or something like that). But It seems a bit absurd to suggest that some integers do objectively exist whilst others don’t.. Anyway  I am sort of arguing the mathematical realist case in this thread but in truth I don't know what I think either.



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