All mathematical structure exist.

[vectorcube]

Modal realism!

1. All mathematical structure exist necessarily.
2. Our universe/multiverse is a mathematical structure.
-------------------------------------------------------
A) Our universe/multiverse exist necessarily.



Consciousness

1'. All mathematical structure exist necessarily.
2'. Consciousness is a mathematical structure.
-------------------------------------------------------
B) Consciousness exist necessarily.


Premise 1 and 1' is just tagmark` s mathematical universe hypothesis. Nozick called this the principle of fecundity. It is very similar to David Lewis ` s Modal realism.
Premise 2 is plausible given all the evidences from physics.
Premise 2' is thesis of strong AI. Namely, consciousness can be derived by an execution of an algorithm. Any algorithm is itself a mathematical structure. Therefore, 2'.

What is amazing about premise A, B is that they are known to be contingent. The universe\multiverse need not exist, but they just happen to exist. Similarly, Consciousness need not exist. There need not be any subjective feeling of the self, but it just exist without much reason. Premises A, and B are necessary, because they are arrived at deductively via premises. I say the premises are pretty reasonable.


This is confusing to many people, but when i say "all possible mathematical structure exist". I don` t just mean the multiverse exist. If the multiverse exist, then our universe would be a substructure. Our multiverse would be just one out of infinitly many mathematical structures! I am say all those *other* structures exist also. Some would be total weird. Some would be similar to our universe/multiverse.


The set of "all possible mathematical structure exist" is a proper subset of the set of "all logically possible worlds". The fomer is restrictive to realities with a particular mathematical structure, while "all logically possible worlds" are not limited to worlds with a particular mathematical structure. A world could be defined in other ways other than a math structure. Here is an example:

World W: A world rule by magic as in the harry potter movies.

The world W would not be a mathematical structure, but W is a "logically possible world". To see why W is not a math structure. Math deals with stable regular patterns. That can` t happen if harry starts changing the world by the power of his spell to doom the sun, and change subatomic structures to cheese.

Another example:

World W1: is a world defined by an infinite set of propositions.

Imagine an infinite list of propositions that specific W1 in every detail imaginable. There is a proposition that specific how each atom moves in W1. Of course, no propositions can ever contradict one another.

Therefore, we define

World W1: A maximally consistent set of propositions.

[JoeDawg]

I say the premises are pretty reasonable.

On what basis?

I think sometimes when people spend lots of time doing math, they start thinking that math is more real than the physical world. The ancient greeks did this with geometry, and by extension, Plato had his forms. But our understanding of the universe didn't really start taking off until we started making rigorous empirical observations, and adapting mathematics to these observations. Similarly theories are nothing much better than fantasies, unless they actually correspond to observation, and we don't observe math. Math is just a flexible and convenient shortform description of what really exists.

[vectorcube]

On what basis?


Premise 1 and 1' is just tagmark` s mathematical universe hypothesis. Nozick called this the principle of fecundity. It is very similar to David Lewis ` s Modal realism.
Premise 2 is plausible given all the evidences from physics.
Premise 2' is thesis of strong AI. Namely, consciousness can be derived by an execution of an algorithm. Any algorithm is itself a mathematical structure. Therefore, 2'.




On what basis?

I think sometimes when people spend lots of time doing math, they start thinking that math is more real than the physical world. The ancient greeks did this with geometry, and by extension, Plato had his forms. But our understanding of the universe didn't really start taking off until we started making rigorous empirical observations, and adapting mathematics to these observations. Similarly theories are nothing much better than fantasies, unless they actually correspond to observation, and we don't observe math. Math is just a flexible and convenient shortform description of what really exists.

I am not committed to the veiw of modal realism, or ultimate ensamble. I hold it at the back of my mind just like a toy idea. The reason i even take this idea seriously is that this hypothesis give us a nice explanation to some deep philosophical questions.

Here is a list of goods:

1. explaining modality in terms of quantifications over possible worlds.

2. explain why there is something possible, but does not exist, and why something exist. What is the selective rule which dictates what is possible, and what gets to exist.

3. "What breaths fire into the equation, and make a universe for the equation...to describe?" Hawking.

4. Why this particular(fundamental) equation, and not something else entirely different?

I think adopting modal realism( or variation of it) can help us explain 1-4

[apeiron]

Premises A, and B are necessary, because they are arrived at deductively via premises. I say the premises are pretty reasonable.


Actually they could do with a little work.

What is meant by mathematical structure existing? Does it necessarily exist in a "material" way like the universe or consciousness?

Why should math have ontic status rather than merely epistemic? And if it exists ontically, is this in some dualistic platonic sense or what exactly?

So how does the existence of "mathematical structure" actually entail the existence of "physical structure" in practice. Why should we believe in this connection?

Please define.


A world could be defined in other ways other than a math structure. Here is an example:

World W: A world rule by magic as in the harry potter movies.

The world W would not be a mathematical structure, but W is a "logically possible world".

How do we know magic has no mathematical structure as a fact? Perhaps we just haven't discovered the rules. It's possible.

But then also how can it be logically possible in a sense that would not require "logical" to mean crisply self-consistent in some reasonable fashion? Is it logical that worlds can be illogical?

Perhaps you could get away with calling magic worlds just possible worlds. Except it would remain illogical that they lacked a most obvious necessary trait of "a world" - the self-consistency that allows it to be defined as "a world" rather than an unprincipled collection of events.

Please explain.

[vissarion.eu]

All possible and impossible (impossible from NOW reference) exist, but it's comes purely from nothing. If you see in math books many equations so you already get them and they exist in your minds, but you and your body are not from math, it is from nothing and this nothing makes magic. What you seeing, what you hearding can be transformed into frenquencies, those in bits, your memory less or more also in bits with some bluernes, so you consist of some math, but it's only your consciousnes and everything that you hearding or seeing or touching and so on exist only in your minds/counsciousnes, but not in real. So Math tricked that you exist, but your thinking process is not probably from math, but from magic or some tape, which have math bits, your counciousnes is like Turing mashine, but I believe there is somthing than math to made up your counciousnes and that it would run in time. I don't believe, that math making first some quantum mechanic or that quantum mechanic making counciousnes and first physical body/brain. What you fell is what you feel and it's not from math, but more precisly from magic and this magic from nothing, from what more else can come magic? From simulation? Maybe. But what laws then creates this simulation? Again quantum mechanics? Why? Just it's very easy/good visible that everything or more precisly conciousnes comes from nothing. And since physicists is just part of my mind/counssciousnes then philosophs of course was 99% right saying that everything come from nothing or that mind is primaral raver than matter. So idealists was right 99.999999999999% about primarality of minds and matterialists wrong. So because there still not some smart humans made all internet and so on, but it come from nothing/minds so I just need to play this nothing game how humans smart, how monkeys stupid and how idealists quite right, but still hiding that there is minds (which can be interpretated not nessasary like nothing or what comes from nothing), so I must play this game and to say, mind(s)/consciousnes come from nothing.

[vectorcube]

What is meant by mathematical structure existing? Does it necessarily exist in a "material" way like the universe or consciousness?

Modal realism is more closer to principle of fecundity. mathematical universe hypothesis is different to the other two. You need to know that they are different, and the differences matter.

For our purpose, i opt for modal realism.

Why should math have ontic status rather than merely epistemic? And if it exists ontically, is this in some dualistic platonic sense or what exactly?


Why would this question matter regarding modal realism?

So how does the existence of "mathematical structure" actually entail the existence of "physical structure" in practice. Why should we believe in this connection?

The first question ask for why nature choice "this situation", so i don t know.
I already answer the second with reasons on previous post.


How do we know magic has no mathematical structure as a fact? Perhaps we just haven't discovered the rules. It's possible.

math deals with stable regular patterns. That can` t happen if harry starts changing the world by the power of his spell to doom the sun, and change subatomic structures to cheese.

Is it logical that worlds can be illogical?

It is like asking if impossible worlds exist. Perhaps a world with true logical contradiction? I don` t think so.

Perhaps you could get away with calling magic worlds just possible worlds. Except it would remain illogical that they lacked a most obvious necessary trait of "a world" - the self-consistency that allows it to be defined as "a world" rather than an unprincipled collection of events.

You suppose possible world *lack* self-consistency, but this cannot happen, because possible worlds are by their nature, self consistency.

Another example to define a possible world is to called it "A maximally consistent set of propositions".

So for possible w, there are infinite( finite) many propositions that specific W. This infinite string with not be contradictory, and with can defined W completely in all detail.

[vectorcube]

All possible and impossible (impossible from NOW reference) exist, but it's comes purely from nothing. If you see in math books many equations so you already get them and they exist in your minds, but you and your body are not from math, it is from nothing and this nothing makes magic. What you seeing, what you hearding can be transformed into frenquencies, those in bits, your memory less or more also in bits with some bluernes, so you consist of some math, but it's only your consciousnes and everything that you hearding or seeing or touching and so on exist only in your minds/counsciousnes, but not in real. So Math tricked that you exist, but your thinking process is not probably from math, but from magic or some tape, which have math bits, your counciousnes is like Turing mashine, but I believe there is somthing than math to made up your counciousnes and that it would run in time. I don't believe, that math making first some quantum mechanic or that quantum mechanic making counciousnes and first physical body/brain. What you fell is what you feel and it's not from math, but more precisly from magic and this magic from nothing, from what more else can come magic? From simulation? Maybe. But what laws then creates this simulation? Again quantum mechanics? Why? Just it's very easy/good visible that everything or more precisly conciousnes comes from nothing. And since physicists is just part of my mind/counssciousnes then philosophs of course was 99% right saying that everything come from nothing or that mind is primaral raver than matter. So idealists was right 99.999999999999% about primarality of minds and matterialists wrong. So because there still not some smart humans made all internet and so on, but it come from nothing/minds so I just need to play this nothing game how humans smart, how monkeys stupid and how idealists quite right, but still hiding that there is minds (which can be interpretated not nessasary like nothing or what comes from nothing), so I must play this game and to say, mind(s)/consciousnes come from nothing.

If something comes from nothing based on the rules of QM, then i can ask why QM is true. That don` t explain anything.

One can even doubt that there is such a thing as nothing, because nothing is not a thing.

[Redbelly98]

1. All mathematical structure exist necessarily.

I'm not a regular in the Philosophy forum, my background is actually in science, but I'll have to disagree with this premise.

My view is that mathematics is a language, used to describe quantitatively what we observe. So to say that mathematical structures exist is like saying that the words in our spoken language exist. They don't, at least not in a real physical sense.

[vissarion.eu]

If something comes from nothing based on the rules of QM, then i can ask why QM is true. That don` t explain anything.

So what is then in phylosophy mind? I thing that mind comes from nothing like british idealism states that possible everything do not exist, why you denying it? "He argued, for instance, in The Unreality of Time that it was not possible to produce a coherent account of a sequence of events in time, and that therefore time is an illusion. His book The Nature of Experience (1927) contained his arguments that space, time, and matter cannot possibly be real." http://en.wikipedia.org/wiki/Idealism#British_idealism

Okay now why quantum mechanic true IN OUR minds. So QM is true only in this simulation of your minds (but it still can be not true, at least because you don't sow QM experiments personaly, so they can be falsified like any narcotics effect can be placeb or due some over reasons).

But maybe I don't get your point And maybe you don't get my in preious post. Because I didn't say that somthing comes from nothing based on QM. I say that somthing comes from nothing and I believes into it with 99.999999999999% certainty. And over possiblity is that simulation of your conciousnes is not brain effect, but is from some over quantum mechanical tricks - I was meaning this and realy not such strange thing like somthing comes from nothing and this nothing is from quantum mechanic. So If you say there quantum mechanic can't create brain without physical body then I can easily to say to you that then simulation is based on some real laws, but this lows are not from nothing but they are real, but also they are not quantum mechanical laws.

One can even doubt that there is such a thing as nothing, because nothing is not a thing.

So you dissagre with this quate:
"His book The Nature of Experience (1927) contained his arguments that space, time, and matter cannot possibly be real." http://en.wikipedia.org/wiki/Idealism#British_idealism
?

Yes nothing can produce whatever thing you want, nothing is just absolutly empty space, and if it have inside some matterial wall then it is not nothing. Then this walls may form box and it's becomes not nothing. But nothing is purely empty space. And in this empty space apears counciousnes/minds - you or more precisly I because you from my reference point do not exist. Why in empty space can't apear invisible imaginary equation? Yes it can or at least is such possiblity that it can, so if it can then everything can apear imaginary like counciousnes.

I thing just nothingnes in any possible way trying to hide it's existence if possible that to say. Because if you realise that nothing exist. Then QM is fake, your body existance laws is fake, all humans are just iliusion to you to believe that everything have some laws. So then what world should apear to your eyes? So then you realising that nothing exist and you see black and hear silence then you becoming don't see your legs and your and then only memories is for you, so would you like such a live? And now memmories based also on nothing so you itself will dissapear so you just need to play this game that you somthing doing for reason and I would say that this reason is just to exist, because everything still don't have any logic and all humans still are not real, but part of your counciousnes. QM is maximaly maded to fool you to believe that everything exist and can be real, it maximaly maded to almost like looks like very possible laws of nature, no shapes no questions, you also don't thinking too real because you are simulation from nothing so you or I still not real, but raver I want one thing - exist forever because real or not but still somthing felling and seeing.

Now where is flaw in QM? QM saying that wavefunction colapsing from big wave to small area/point, this area is up to 1000 or bilions times smaller than initialy wave. So then all energy is teleportated to small point. But you can say, there flying small gnome in small spaceship and each time he stroking different point according some plan, but then there must be very collective plan of all electrons which shooting measuring device through slits etc. But isn't this story not the same like Earth holds on turtle or elephant and this turtle on over turtle or elephant this on another ant to infinity. So this exactly the same electron have counciousnes or energy is teleportated choose one from those or argue that counciousnes come from nothing and there no matterial, real things, just imaginary ones.

[apeiron]

I'm not a regular in the Philosophy forum, my background is actually in science, but I'll have to disagree with this premise.

My view is that mathematics is a language, used to describe quantitatively what we observe. So to say that mathematical structures exist is like saying that the words in our spoken language exist. They don't, at least not in a real physical sense.

This is the obvious common sense approach - the map is not the territory. So no surprise that philosophical approaches like modal realism give philosophy a bad name.

As is being asked in the conspiracy theory thread, do these guys really believe their own arguments? Or is it just a way to spin out a career?

The natural approach (also described carefully in the branch of philosophy known as semiotics) is that the world would exist. It self-organises in some averaging, regularising, resonance based way. Then humans can come along and describe these regularities in mathematical language. Statements about equivalence (symmetry) and scale (asymmetry).

So does the number 1 exist? No, not like the world. But the essence of what we mean by one-ness can be found all over the place.

One is not "necessarily existent" as lifeforms may have never got round to constructing the kind of languages in which 1 has its contextual meaning (being opposed to the many, for a start).

The one-ness quality would always be out there as a natural regularity of self-organising development. But if say there really was nothingness, then one-ness of that self-organising regularity type also could never have existed as a possibility. Not even in imagination because if nothingness could actually be the case, then self-organising development also gets banned as a consquence. Things (or rather nothings) would have to have that non-feature as well.

But 1, our name for one-ness, is not a thing that has existence except as a human concept and part of our language system, part of mapping of the territory. So it cannot have an existence/non-existence issue except in this very secondary, epistemic, sense.

Really, modal realism, modal logic in general, is schoolboy stuff. But like conspiracy theories, it can be amusing how it plays out, the contortions people go through to "believe".

[qsa]

1,2,3 ..ready set go REALITY. The natural numbers and relations created with them (structure, geometry) constitute the ultimate truth.1,2,3.. Is the basic and the Only truth, everything else is derived notion (from the relations). There is no difference between the mathematical language description of the mathematical objects and the objects themselves. The same would be true for the description of physical stuff with mathematical description; they are one and the same. The first argument is many times stronger than the second. You can define any relation between groups of numbers to your heart’s content, let them produce familiar or unfamiliar, apply to our universe or not, make them as exotic as you like, no problem. But you do have to live with consequences of you definitions; they might produce a really weird existence. You can create a universe out of nothing. Just throw random numbers consider that bunch your space, throw other numbers, and make them represent particles’ positions on the previous numbers. There you go; just a taste of what is possible. Check out a realistic (test) universe created that way.
http://www.qsa.netne.net

[vectorcube]

I'm not a regular in the Philosophy forum, my background is actually in science, but I'll have to disagree with this premise.

My view is that mathematics is a language, used to describe quantitatively what we observe. So to say that mathematical structures exist is like saying that the words in our spoken language exist. They don't, at least not in a real physical sense.

The tradition idea of mathematical propositions is that they are descriptive about numbers. For example: The proposition "13 is prime" is about the number 13. To many, the act of saying 13 has the property of being prime means that 13 really exist. Now, you can ask if i belleve in santa claus, becayse "santa claus is fat" is about santa claus, and the statment seems to be describing santa claus. One distinction is that math propositions are objective, while santa might not be objective. The fact that math propositions seem to describe numbers, and the fact that numbers seems to have an objective existence in their own right independent of minds lead us to think they do exist.

[DaveC426913]

Poinit of order, vectorcube: Why do you consistently use "` " instead of "'"?

i.e. tagmark` s should be tagmark's.

It makes it very difficult you read your posts.

Carry on.

[JoeDawg]

One distinction is that math propositions are objective, while santa might not be objective.

How are math propositions objective?

[apeiron]

Poinit of order, vectorcube: Why do you consistently use "` " instead of "'"?

i.e. tagmark` s should be tagmark's.

It makes it very difficult you read your posts.

Carry on.

Or Tegmark's if we were being picky.

[apeiron]

For example: The proposition "13 is prime" is about the number 13. To many, the act of saying 13 has the property of being prime means that 13 really exist.

Yet properties of objects are always given their meaning by their contexts. So primeness is a fact about a lack of factors. Every other number has to be considered in case divisors might not have been noticed.

So on this semiotic consideration, properties as usual are context-dependent rather than purely inherent in objects.

So objects - even mathematical - only gain their crisp properties, their meaning, from being parts of larger systems. Every event must have a context to be an event.

And what is with this idea that maths is self-evidently objective? Are you saying it is even the majority view within philosophy of maths? The case needs to be argued. I have already argued for the epistemic case and glad to go futher.

[qsa]

after 10000 years of civilization we are questioning if 1,2,3 ... to be a fact. Really. And we hope to discover the secret of existence!

[vectorcube]

Poinit of order, vectorcube: Why do you consistently use "` " instead of "'"?

i.e. tagmark` s should be tagmark's.

It makes it very difficult you read your posts.

Carry on.


Are you sure it is because it is "difficult"?

[vectorcube]

How are math propositions objective?

Example is fermat` s theorm. We now know that the theorm is true( because we have a proof), but conceivably, some alien from outer space would produce a proof that shows that theorm is true. The alien could never show that the theorm is falses even if they want to. Similarly, fermat` s theorm would be true even if fermat never formulated the conjuncture in the first place.

[vectorcube]

Yet properties of objects are always given their meaning by their contexts.

properties as usual are context-dependent rather than purely inherent in objects.

.

properties are represented by predicates, and they are forever tied to their instances.

For predicate P, there is a object m, so that Pm. Is not clear why Pm is context dependent, or what that even mean.

So objects - even mathematical - only gain their crisp properties, their meaning, from being parts of larger systems.




The set of natural numbers is a math structure. Tell me the larger context?


And what is with this idea that maths is self-evidently objective?Are you saying it is even the majority view within philosophy of maths? The case needs to be argued. I have already argued for the epistemic case and glad to go futher

never made any definitive claims at all.

[Redbelly98]

The tradition idea of mathematical propositions is that they are descriptive about numbers. For example: The proposition "13 is prime" is about the number 13. To many, the act of saying 13 has the property of being prime means that 13 really exist. Now, you can ask if i belleve in santa claus, becayse "santa claus is fat" is about santa claus, and the statment seems to be describing santa claus. One distinction is that math propositions are objective, while santa might not be objective. The fact that math propositions seem to describe numbers, and the fact that numbers seems to have an objective existence in their own right independent of minds lead us to think they do exist.

Here is a counterexample to that logic:
I could say, "The purple elephant in the dream I had last night, had a single tusk".
This is an objective statement, yet the purple elephant never existed.

EDIT:
Or more generally, we can imagine anything, even ascribe some objective properties to it, but it still doesn't exist.

"Santa Claus wears a red suit" would be an objective statement about Santa Claus.

[DaveC426913]

Here is a counterexample to that logic:
I could say, "The purple elephant in the dream I had last night, had a single tusk".
This is an objective statement, yet the purple elephant never existed.

EDIT:
Or more generally, we can imagine anything, even ascribe some objective properties to it, but it still doesn't exist.

"Santa Claus wears a red suit" would be an objective statement about Santa Claus.
Not sure I agree.

Re: the elephant. How can there be an objective statement about something only you can see? It is, by definition, subjective. Same with Santa, it is only agreed upon by the general populace that he wears a red suit. That's not objective.

How would you go about falsifying such claims?

[vectorcube]

Here is a counterexample to that logic:
I could say, "The purple elephant in the dream I had last night, had a single tusk".
This is an objective statement, yet the purple elephant never existed.

EDIT:
Or more generally, we can imagine anything, even ascribe some objective properties to it, but it still doesn't exist.

"Santa Claus wears a red suit" would be an objective statement about Santa Claus.

Well, you can invent a character called santa, and ascribe some properties P to santa.

The objectivity comes in in math is when people knowns the rules and axioms of say twin primes, and that two mathematicians separated by long distence, and never had any contact with one another can suddenly discovery some new properties about twin primes. No one seem to ascribe any properties to twin primes at all.

[qsa]

Leopold Kronecker said: "The natural numbers come from God, everything else is man's work."

[vectorcube]

Leopold Kronecker said: "The natural numbers come from God, everything else is man's work."

well, anti-platonism is a completely consistent view.

[qsa]

well, anti-platonism is a completely consistent view.



I was suggesting that, even he, believed in natural numbers are true and given. At least this is my understanding.

[Pagan Harpoon]

I think it's pretty clear what's going on here. If we accept that mathematics transcends us and our universe utterly, the ultimate ensemble, and perhaps also those related ideas, are perfectly reasonable. If we don't, then they are not.

Some people here seem to accept that mathematics transcends us utterly, others don't. I like the idea that it does and I give it as a stipulation before entering into any philosophy where it is likely to be involved. That is not to say that I necessarily "believe" it, that would be dumb, it is clearly impossible to demonstrate something like this.

[qsa]

http://www.fqxi.org/community/forum/category/31416

this place reviews up to date hardcore philosophy of physics.

enjoy, if you had not seen this place already.

[apeiron]

Some people here seem to accept that mathematics transcends us utterly, others don't. I like the idea that it does and I give it as a stipulation before entering into any philosophy where it is likely to be involved. That is not to say that I necessarily "believe" it, that would be dumb, it is clearly impossible to demonstrate something like this.

It is fair enough to take transcendance as an unproveable principle and then to consider what must follow. But why does it seem a plausible one in the first place, compared to the alternative?

To me, I prefer to assume that all is somehow one, all is connected, related. Once some essential aspect of reality is taken to be broken off and floated away, then a causal relationship becomes illogical, or at least paradoxical, mystical.

Why should I give up the notion that reality is a connected whole? The fact that reality is stratified seems obvious. So local instance is different from global principle.

But platonic maths, gods, mind, beauty, truth and goodness, psychic powers - every notion supported by claims of transcendance ends up just causing endless trouble.

Why should it still be anyone's preferred hypothesis?

[Pagan Harpoon]

I don't see the supposition that mathematics transcends our existence as causing any trouble. Moreover, it does not require that a piece of reality be cut loose so as to float away. As I see it, what we call reality, along with all of the other realities of the ultimate ensemble are not cut off from each other, they are all subordinate to mathematics, tied together under that.

It is my preferred hypothesis because I see any alternative as belittling any conclusions that are ever made about anything. If I suppose that logic and mathematics are only as they are for me, now, then maybe someone else could come along and not only work with different starting assumptions and predefined rules, but come up with things such as "Your usually understood rules of addition and the definitions of the real numbers imply that 2+2=5."

The proposal that mathematics is not divorced from our experience and our universe is equally unprovable as the proposal that it is. Also, I think the fact that logic and mathematics as we understand them now work in every situation that has ever been envisaged is strong circumstantial evidence in favour of their universality.

[apeiron]

I don't see the supposition that mathematics transcends our existence as causing any trouble. Moreover, it does not require that a piece of reality be cut loose so as to float away. As I see it, what we call reality, along with all of the other realities of the ultimate ensemble are not cut off from eachother, they are all subordinate to mathematics, tied together under that.

OK, so what is the nature of the connection between ensembles? This is the classic issue of platonism. How do the forms actually shape the chora in practice?

You say things are all "tied together" which implies some action on something's part. How does the transcendant actually achieve such feat?

I'm not saying there is absolutely nothing like the transcendant.

In arguing that "all is relationships", this is an ontology that also requires the "existence" of limits. Reality has its boundaries or event horizons. This seems to raise the question of what lies "beyond". The answer would have to be truly nothing. Or rather, only vagueness.

But this is not the same as a positive claim about things like gods or numbers standing in some abstract place beyond our concrete existence.

[Pagan Harpoon]

They are not tied together in any material way, they can have no interaction with each other. Or more correctly, if ever two worlds have interaction with each other, they should be considered as one world, or mathematical object. The thing that connects them is mathematics and logic as we understand it now, I propose that it is valid everywhere (that applies to the everywhere of every contingency) and at all times.

As for how the ideas come to give form to things, I answer that it happened in the same way that our world was given form, whatever way that may be.

As for boundaries to reality, it depends on what you mean by "reality." The boundaries on our universe are those that are consistent with the initial conditions of the universe that can give rise to us as sentient beings exactly as we are. If you meant it in a broader sense, all possible universes, there are no boundaries, there are an infinite number of mathematical objects that can describe a universe so there are infinitely many universes. Similarly, some of those universes are themselves infinite.

[vectorcube]

I don't see the supposition that mathematics transcends our existence as causing any trouble. Moreover, it does not require that a piece of reality be cut loose so as to float away. As I see it, what we call reality, along with all of the other realities of the ultimate ensemble are not cut off from each other, they are all subordinate to mathematics, tied together under that.


if modal realism is true, then the ultimate ensamble is a proper subset of modal possible worlds.

[apeiron]

As for how the ideas come to give form to things, I answer that it happened in the same way that our world was given form, whatever way that may be.


But you can see that this is unsatisfactory. It is what makes me more interested in alternative approaches which do offer answers.


If you meant it in a broader sense, all possible universes, there are no boundaries, there are an infinite number of mathematical objects that can describe a universe so there are infinitely many universes. Similarly, some of those universes are themselves infinite.

That is a contention and so needs to be supported by some argument. And if you don't even have a speculative story on how maths/form entails physical universes, why should we place too much credence on the possible fruits of this (non)relationship?

Infinite math objects may = infinite actual universes. It is the idea de jour. But I am asking about the robustness of the eqivalence relation being claimed. Apart from the fact you can say it, why would we believe it?

[apeiron]

if modal realism is true, then the ultimate ensamble is a proper subset of modal possible worlds.

Appreciate the fact you are now taking the more careful epistemic approach of qualifying "if X is true". That is really helpful to serious discussion (and I do find the possibility worth discussing simply because it is the extremal position of a particular line of thought).

[vectorcube]

Appreciate the fact you are now taking the more careful epistemic approach of qualifying "if X is true". That is really helpful to serious discussion (and I do find the possibility worth discussing simply because it is the extremal position of a particular line of thought).

" is true" is metaphysics. It is not an epistemic notion.

[JoeDawg]

Example is fermat` s theorm. We now know that the theorm is true( because we have a proof), but conceivably, some alien from outer space would produce a proof that shows that theorm is true. The alien could never show that the theorm is falses even if they want to. Similarly, fermat` s theorm would be true even if fermat never formulated the conjuncture in the first place.

That confuses the theorem, with the evidence for the theorem. Evidence, facts about the world, are what is most often referred to as objective. The theorem describes something that may or may not be supported by evidence.

Proof is a mathematical concept, that generally has to do with logical consistency, not evidence.

Evidence is not 'proof' of anything. Evidence provides a basis for prediction.

[Redbelly98]

Not sure I agree.

Re: the elephant. How can there be an objective statement about something only you can see? It is, by definition, subjective. Same with Santa, it is only agreed upon by the general populace that he wears a red suit. That's not objective.

How would you go about falsifying such claims?

These philosophical arguments are tougher than I thought they would be.

[apeiron]

" is true" is metaphysics. It is not an epistemic notion.

And "if" - the actually relevant qualifying word here?

[vectorcube]

And "if" - the actually relevant qualifying word here?

Does that matter?

[vectorcube]

That confuses the theorem, with the evidence for the theorem. Evidence, facts about the world, are what is most often referred to as objective..


Did i say evidence?


The theorem describes something that may or may not be supported by evidence.

Empirical evidence? It is crazy to me why you would talk about evidence here. Math propositions are necessary true. As such, they cannot be falsified by evidence like any scientific theory.


roof is a mathematical concept, that generally has to do with logical consistency, not evidence.

Evidence is not the right word. What you want is deduction. Theorms are deduced from premises. What you say about logical consistency do little to explicated proof. I would say criterion are much more strict.

[JoeDawg]

Did i say evidence?

If it is objective, it exists independent of mind. Unless you base your mathematical axioms on some type of common existing 'evidence', then your axioms will be completely arbitrary, and so will your alien's axioms. In which case, you would come up with completely different theorems. Your theorems would untrue for your alien, and vice versa.

Empirical evidence? It is crazy to me why you would talk about evidence here. Math propositions are necessary true. As such, they cannot be falsified by evidence like any scientific theory.

Mathemathical axioms are definitions. Those definitions are based on human experience.

Evidence is not the right word. What you want is deduction. Theorms are deduced from premises. What you say about logical consistency do little to explicated proof. I would say criterion are much more strict.
Where do you get your premises and criterion?

[apeiron]

Does that matter?

If something is true does tend to have a different meaning that something is true. So yes, you could say it matters.

[vectorcube]

If it is objective, it exists independent of mind. Unless you base your mathematical axioms on some type of common existing 'evidence',

Again, there is no evidence. Math objects to not have any causal relation to physical matter.

then your axioms will be completely arbitrary, and so will your alien's axioms. In which case, you would come up with completely different theorems. Your theorems would untrue for your alien, and vice versa.

I get what you are saying, but the way you say it is wrong.

Platonism is the view that there are objective mathematical facts. Now, platonism is not without it` s problems. The most problematic( one would say the only problem) problem is the explication of how we come to know these mathematical facts. This is an epistemic problem. If mathematical facts exist, then they have no causal connection with the world, and thus, there is really no evidence.

Mathemathical axioms are definitions. Those definitions are based on human experience.

For platonist, math axioms are not definitions at all. The axioms are used to describe mathematical facts.



Where do you get your premises and criterion?

That is outside the issue. I rather we remain focus. At present, you seem to not know platonism, and i think you ought to read about it before you reply. I suggest you read about it, and ask me questions. That way, you can learn something.

[vectorcube]

If something is true does tend to have a different meaning that something is true. So yes, you could say it matters.

What does that matter for the topic at hand?

[qsa]

wiki quote

"It is a profound puzzle that on the one hand mathematical truths seem to have a compelling inevitability, but on the other hand the source of their "truthfulness" remains elusive. Investigations into this issue are known as the foundations of mathematics program."

I think there is big confusion here between "compelling inevitability" and the "source". I think people get the idea because the source can debated, the "compelling inevitability" is not so compelling. even the "fictional" interpertation does not doubt 2+2=4

no matter what source, these "compelling inevitability" is what existence is made of.Is there any other really "compelling" entities we can count on.

[vectorcube]

wiki articles usually suck. It is good to have a general overview, but for more meat, you ought to read the stanford philosophy site.

[qsa]

wiki articles usually suck. It is good to have a general overview, but for more meat, you ought to read the stanford philosophy site.

I agree, but I was trying to give conclusion type statment to arguments. It would take too
much time to argue every little concept (philosophy does a good job in not closing issues and openning new ones). My interest is finding how reality works in the physics sense, but I use just enough pertinent philosophy(tammed in Einstien's word) to excute my goal. I learned that when I did my Master's Degree in UK; the stress is on research.

I wonder if you have any thought on the articles in fqxi site.

[JoeDawg]

Again, there is no evidence. Math objects to not have any causal relation to physical matter.

Useful mathematical statements like 1+1=2, are abstract representations of the physical observable world. If you are going to claim they exist independently, you need some sort of evidence to show that this is so. The axioms of modern mathematics are not random, they have a solid foundation in the physical, which is why they can describe the physical so well.

Platonism is the view that there are objective mathematical facts.

Plato was wrong. There is no higher reality of forms. Its not necessary, nor is there any evidence for such a thing. The ancient greeks were overly impressed with abstract thinking because their understanding of the physical world was so rudimentary. It was thought that the physical world was chaotic, ruled by the whim of the gods. They could use mathematics and geometry, which was logical and predictable, as a foundation.

But the reason mathematics was logical and predictable is because it is abstract and constructed. It was like the difference between living in a cave, and building a house. The latter was preferable to the greeks because they could design it to fit what they needed. Mathematics was designed and constructed to address certain needs, which is why it appears more solid than say the english language, which is more chaotic.

If mathematical facts exist, then they have no causal connection with the world, and thus, there is really no evidence.

Then they have no relation to this world, and are pure fantasy.

That way, you can learn something.
LOL. whatever.

[JoeDawg]

wiki articles usually suck. It is good to have a general overview, but for more meat, you ought to read the stanford philosophy site.

If you really want to learn something, don't rely on secondary sources.

[vectorcube]

I agree, but I was trying to give conclusion type statment to arguments. It would take too
much time to argue every little concept (philosophy does a good job in not closing issues and openning new ones). My interest is finding how reality works in the physics sense, but I use just enough pertinent philosophy(tammed in Einstien's word) to excute my goal. I learned that when I did my Master's Degree in UK; the stress is on research.

I wonder if you have any thought on the articles in fqxi site.

I don`t have comment, because i did not have time to look over it.

Here is a site that sort of like arxiv for philosophy of science:http://philsci-archive.pitt.edu/

[vectorcube]

Useful mathematical statements like 1+1=2, are abstract representations of the physical observable world. If you are going to claim they exist independently, you need some sort of evidence to show that this is so. The axioms of modern mathematics are not random, they have a solid foundation in the physical, which is why they can describe the physical so well.

Again, mathematical objects do not have any causal relation to physical matter. In philosophy, not many people agree on anything, but this is something everyone agrees if there are mathematical facts.

I see you want to look for a reason that the axioms "are not random". The platonist line of thought is to assume humen have special intuition to know mathematical facts. People can be inspired by nature, but mathematical facts are real.


Plato was wrong. There is no higher reality of forms. Its not necessary, nor is there any evidence for such a thing. The ancient greeks were overly impressed with abstract thinking because their understanding of the physical world was so rudimentary. It was thought that the physical world was chaotic, ruled by the whim of the gods. They could use mathematics and geometry, which was logical and predictable, as a foundation.

But the reason mathematics was logical and predictable is because it is abstract and constructed. It was like the difference between living in a cave, and building a house. The latter was preferable to the greeks because they could design it to fit what they needed. Mathematics was designed and constructed to address certain needs, which is why it appears more solid than say the english language, which is more chaotic.

Well, it is fine if you want to think that way, but platonism( as understood by modern philosophiers) is a coherent view. As with any coherent view in philosophy, there is always problems. I guess you have to make up your own mind.




Then they have no relation to this world, and are pure fantasy


It can `t be pure fantasy. If it is fantasy, the it is pretty easy to deny situations from obtaining, but it is hard to deny "4=2+2". There seems to be an objectivity to "2+2=4" that is independent of sense experience.

[vectorcube]

If you really want to learn something, don't rely on secondary sources.

why can ` t you learn something from secondary sources? When people study relativity, i highly doubt they learn it from reading einstein` s paper. In fact, i don ` t see people learning from primary sources quite that often if they are not experts. For their jobs, they need to know details, and publish papers. I think it is quite acceptable to know the argument as expressed in the from of concise propositions, and conclusions.

[magpies]

Wouldn't it be interesting if one day we found out electrons come in the shape of the number 1.

[vectorcube]

Wouldn't it be interesting if one day we found out electrons come in the shape of the number 1.


i will be surprise if 1 is in the shape of 1.

[magpies]

Hello surprise nice to meet you.

[JoeDawg]

Again, mathematical objects do not have any causal relation to physical matter.

That is your claim. You have yet to show why you think this is so. The fact Plato believed it is not a proof.

In philosophy, not many people agree on anything, but this is something everyone agrees if there are mathematical facts.

Sure their are mathematical facts, there are all kinds of facts, but your claim was that they were objective. Objective facts are independent of mind. Mathematics is something we learn when we are very young, so its not really surprising that we take it for granted.

humen have special intuition to know mathematical facts. People can be inspired by nature, but mathematical facts are real.

Special intuition? Human intuition is about pattern recognition. Its an evolved capacity, that manifests through our accumulated knowledge. When we are babies we learn to distinguish between objects, when we are older we learn to count, then to add...etc... We are taught about numbers and mathematics. We learn all this through examples, through experience. Once we have the basics down, we can creatively mix and adjust these patterns to deal with new situations. There is nothing magical about it.

Plato didn't have our modern understanding of things. You don't need a magical soul, with a priori truths embedded in it.

Well, it is fine if you want to think that way, but platonism( as understood by modern philosophiers) is a coherent view.

If math has no causal relation to experience, then it would be useless to us, because it wouldn't reflect what we experience. One could certainly develop a completely alien form a mathematics, based on random axioms, but that's not the math we use. We have created a mathematics that reflects how our world works.

but it is hard to deny "4=2+2".

Its hard to do so, because our experience shows us how addition works.

There seems to be an objectivity to "2+2=4" that is independent of sense experience.
That's because 2+2=4 is not an axiom. Its a formulation that relies on axioms that were abstracted from exprience, and taught to you when you were young.

All kinds of things seem objectively true... because we are used to them, because we grew up with them and have developed an intuition about them. Intuition is not objective, it is, by definition, subjective.

[JoeDawg]

why can ` t you learn something from secondary sources?
You can learn lots from encyclopedias and wikis. You can learn more from primary sources.

[vectorcube]

That is your claim. You have yet to show why you think this is so. The fact Plato believed it is not a proof.

Actually this is not my claim. This is the standard claim in any philosophy textbook.
No, mathematical facts do not interact in any physical process, or physics interaction.
Are you sure you really want me to prove this?



Sure their are mathematical facts, there are all kinds of facts, but your claim was that they were objective. Objective facts are independent of mind. Mathematics is something we learn when we are very young, so its not really surprising that we take it for granted.

This is for technical reasons. To say that it is a fact implies that it is objective, and mind independent. The word "fact" also means "state of affair" in philosophy in case your are interested.



Special intuition? Human intuition is about pattern recognition. Its an evolved capacity, that manifests through our accumulated knowledge. When we are babies we learn to distinguish between objects, when we are older we learn to count, then to add...etc... We are taught about numbers and mathematics. We learn all this through examples, through experience. Once we have the basics down, we can creatively mix and adjust these patterns to deal with new situations. There is nothing magical about it.

Plato didn't have our modern understanding of things. You don't need a magical soul, with a priori truths embedded in it.


Focus on the topic!

I am not at all trying to argue for platonism. I am tell you that platonism has alot of modern following, and it is a consistent view as any philosophical views can be.

If math has no causal relation to experience, then it would be useless to us, because it wouldn't reflect what we experience. One could certainly develop a completely alien form a mathematics, based on random axioms, but that's not the math we use. We have created a mathematics that reflects how our world works.

Stay focus, please.

I hope you know that to say non causal is really mean to have a priori knowledge.
A priori knowledge is not at all useless. math is a priori necessary. mathematical proposititons are true in all possible worlds, so they obviously work in the actual world.

Its hard to do so, because our experience shows us how addition works.

Perhaps, but platonism is a metaphysical thesis. Perhaps, people learn how math work from experience, but the math is objective.

That's because 2+2=4 is not an axiom. Its a formulation that relies on axioms that were abstracted from exprience, and taught to you when you were young.

All kinds of things seem objectively true... because we are used to them, because we grew up with them and have developed an intuition about them. Intuition is not objective, it is, by definition, subjective.

As in the previous reply. Platonism is a metaphysical thesis. You can come up with as much stories as you want of how people come to know math, but the math is objective( according to platonist).

You can learn lots from encyclopedias and wikis. You can learn more from primary sources.

Textbooks are usually secondary source. They tend to summerize arguments in digestable bits from many primary works in the form of research papers, and books.

To me, you really cannot say primary source are better, because it depends on your purpose. If you are a kant scholar( say), then you get pay to read the original work, and it is your responsibility to read the original work. If you want an overview of the field, i suggest you read textbooks because they focus on what are the essentials for the most recent debate, and what are the arguments for\againist a thesis. I personal think it is better, because it draws on the perspective of many people all at onces, and what separate them are the strength of their arguments.

[Pagan Harpoon]

Old, convetnional mathematics is designed such that it reflects very closely the nature of our universe as we see it. As we progress in science and maths, it gets closer and closer to perfectly describing everything in it. I don't doubt that there exists a system of mathematics that can perfectly describe our universe at every level and I think that most people would agree with me there. I view the fact that there are perfectly consistent and mathematical systems that don't relate to the physical existence of our universe or our experience to be evidence that mathematics is not subordinate to our physical existence. Again, whether or not mathematics is a human thing that we invented to describe the universe that we see or a preexisting code that underlies the operation of everything that we just discover and examine cannot be demonstrated or argued either way, either accept it or refuse it, but you are mistaken if you believe that your view of the matter is necessarily correct.

I would like to make an addition to Vectorcube's mention of mathematical facts. That 2+2=4is not necessarily an objective mathematical fact. However, I think that it is reasonable to suppose that if objectivity exists at all, then that 2+2=4 follows from the definitions and axioms that are usually understood is as objective a fact as there ever can be. Whether or not those definitions and axioms are good ones to take, on the other hand, is subjective.

[apeiron]

That's because 2+2=4 is not an axiom. Its a formulation that relies on axioms that were abstracted from exprience, and taught to you when you were young.


This is an excellent point. All axioms would seem to be statements that could be true, could be false. They don't seem to have an absolute necessity about them.

The consequences that flow from an axiom would be necessary, but not the axioms themselves - the usual Godellian modelling point.

Perhaps if vectorcube really wants to focus, he can suggest some axiom, like axiom of choice, that he believes has necessary truth (no choice but to exist). And prove to us how it is a necessary truth.

[vectorcube]

One more time,

The axioms of math according to the platonists are used for descriptive purposes.

[apeiron]

I am not at all trying to argue for platonism. I am tell you that platonism has alot of modern following, and it is a consistent view as any philosophical views can be.


It is impossible to ever know what you are arguing for as you say this kind of thing every time you find you really have to explain something. Very weak.

But platonism is only consistent in the way ghosts, gods and other things are impossible to disprove because they are treated as being not part of our world. In fact platonism is even worse according to you if the forms have no causal connection with the world.

Plato did try to account for how forms brought organisation to the chora with his flickering shadows on the cave wall allegory. So he did think there had to be a causal connection of some kind.

I suspect the reason quite a few philosophers and mathematicians like platonism is that it gives their disciplines greater weight - science and its observations can again play second fiddle to those employing pure reason.

But I've actually found true platonism to be quite rare even there. Notable exceptions would be people like Roger Penrose and David Chalmers.

I remember asking one philosopher at the first Tuscon consciousness conference why Chalmers was suddenly the big star when he talked such nonsense. Oh, he is bringing back dualism again, said this guy exactly like a naughty schoolboy.

Anyway, once philosophy starts putting its explanations in realms where their being true or false makes no observable difference - well I think we can say internal consistency becomes irrelevant. It is no longer modelling as there are no measurements.

It is the same as religion, psychic powers or any other just-so stories. At any point where an idea ceases to have consequences for observables, then it is no longer part of what I would consider to be the knowlege developing process.

[Pagan Harpoon]

I am inclined to think of a model that makes predictions about the world that can be tested so as to prove them true or false as science rather than philosophy.

Both mathematics and physical existence are there, let's not bother calling that into question. I don't think it's an unreasonable position to suppose that physical existence came before mathematics and gave rise to it, though that view does not appeal to me. It is no less reasonable to propose that mathematics comes before physical existance and is on a higher level than it. This is not equivalent to gods, as that involves creating a new entity that has never been observed and can't ever be.

[apeiron]

I don't think it's an unreasonable position to suppose that physical existence came before mathematics and gave rise to it, though that view does not appeal to me. It is no less reasonable to propose that mathematics comes before physical existance and is on a higher level than it.

It seems pretty easy to make a distinction between ideas with measurable consequences and ideas without. Whether we call it science, metaphysics, philosophy, maths, or whatever, is beside the point. Within all these disciplines (witness the string landscape debacle) it seems a fair dividing line. Those doing modelling without possible consequences are simply doing something else.

And from a hierarchy theory point of view, when you are talking about maths and physical existence, this loses all its angst if we just accept them both as accounts of the world at different levels of generality or abstraction. They are not different in kind, just different in degree.

So we could say we have a naive direct experience of reality, an experience of reality mediated at the level of physical modelling, an experience of reality mediated at the even more rarified level of mathematical modelling.

At no stage do we ever know the world directly. It is always impressions mediated through ideas. But we ascend from a very subjective level of modelling (what it is like for me looking out through my eyes), to increasingly objective - what it is like for me to look with my eyes through these instruments and controlled laboratory situations, then through my eyes employing these philosophical and mathematical concepts. By the time I get to the top level, it seems like I am seeing objective reality.

[vectorcube]

apeiron,


It is impossible to ever know what you are arguing for as you say this kind of thing every time you find you really have to explain something. Very weak.

Explain what? What is difficult? The majority of the mathematics and philosophy community are platonist. Every one knows the pros, and cons of this view( until you don` t know it, and that is pretty weak). The problem is the epistemic problem inherent in the platonist view, and it is the only major problem with this view. If you know anything at all of the other views in the philosophy of math, you know the others are in a much worst situation.


But platonism is only consistent in the way ghosts, gods and other things are impossible to disprove because they are treated as being not part of our world. In fact platonism is even worse according to you if the forms have no causal connection with the world.


You just know this? come on? Do you think i am making this up? Go read about it, and stop claiming that i invented the whole idea. How do you even know i am a platonist anyway?


Plato did try to account for how forms brought organisation to the chora with his flickering shadows on the cave wall allegory. So he did think there had to be a causal connection of some kind.

I suspect the reason quite a few philosophers and mathematicians like platonism is that it gives their disciplines greater weight - science and its observations can again play second fiddle to those employing pure reason

out of topic. Not related to motivation.

Anyway, once philosophy starts putting its explanations in realms where their being true or false makes no observable difference - well I think we can say internal consistency becomes irrelevant. It is no longer modelling as there are no measurements.

This don` t even make sense. Something can be logically consistency, but unfalsifiable.

It is the same as religion, psychic powers or any other just-so stories. At any point where an idea ceases to have consequences for observables, then it is no longer part of what I would consider to be the knowlege developing process.

This is no argument for or againist. Opinion.

[vectorcube]

I am inclined to think of a model that makes predictions about the world that can be tested so as to prove them true or false as science rather than philosophy.

Both mathematics and physical existence are there, let's not bother calling that into question. I don't think it's an unreasonable position to suppose that physical existence came before mathematics and gave rise to it, though that view does not appeal to me. It is no less reasonable to propose that mathematics comes before physical existance and is on a higher level than it. This is not equivalent to gods, as that involves creating a new entity that has never been observed and can't ever be.


You can think whatever you want. I think it is good character to actually know the view you are talking about. You comment about the axioms being subjective is not the platonist line of thought. You ought to know it.

[Pagan Harpoon]

And from a hierarchy theory point of view, when you are talking about maths and physical existence, this loses all its angst if we just accept them both as accounts of the world at different levels of generality or abstraction. They are not different in kind, just different in degree.

To not accept both views as consistent and unfalsifiable is idiotic, regardless of whatever effect it has on the "angst" of the issue. That is the way it is.

To challenge the view that mathematics is above our physical universe in this way challenges not just that particular viewpoint, but the whole basis for this discussion. That criticism can be applied equally to the opposing side, there is no reason to claim that it is derived from physical experience either, that just seems to be the popular take.

If you feel that the issue lacks angst, then you shouldn't have wasted your time talking about it.

You can think whatever you want. I think it is good character to actually know the view you are talking about. You comment about the axioms being subjective is not the platonist line of thought. You ought to know it.

I have never mentioned the words Plato, Platonism or anything similar. I am not necessarily talking about any particular labeled philosophy, just what seems to make sense. To deny that someone else in a different universe might decide that a different set of axioms are better than the ones used most by us is to deny the whole idea of the ultimate ensemble.

[vectorcube]

At no stage do we ever know the world directly. It is always impressions mediated through ideas.

in case you are interest. Your view here has an anti-realist favor, and it will benefit you to read more of this view.

[vectorcube]

I have never mentioned the words Plato, Platonism or anything similar. I am not necessarily talking about any particular labeled philosophy, just what seems to make sense.

Great.

To deny that someone else in a different universe might decide that a different set of axioms are better than the ones used most by us is to deny the whole idea of the ultimate ensemble.

What is this suppose to mean? Someone else in a different universe can do whatever they want.

[Pagan Harpoon]

Precisely, that is why the choice of which axioms are the best is subjective, we choose a certain set, someone else can choose a different one, neither is right, neither is wrong.

More correctly, our universe runs on a certain set of axioms, that is objective because it lives in the universe, but for the purposes of pure mathematics, any set can be taken and said to be better.

[vectorcube]

Precisely, that is why the choice of which axioms are the best is subjective, we choose a certain set, someone else can choose a different one, neither is right, neither is wrong.

More correctly, our universe runs on a certain set of axioms, that is objective because it lives in the universe, but for the purposes of pure mathematics, any set can be taken and said to be better.

Great, but how is this relate to platonism?

[Pagan Harpoon]

The title of this thread does not necessarily refer to Plato in any way, nor do my comments in it.

[vectorcube]

The title of this thread does not necessarily refer to Plato in any way, nor do my comments in it.

Great. Keep up the great work!

[Evo]

Locked pending moderation.