Why does math work in our reality?

[wofsy]

Perhaps you underestimate language. Check out linguistic relativity. The wiki on it has some notes on the empirical research involved.

Also, out of curiosity, what is your academic standing in mathematics?

no academic standing - been reading on my own and sitting in on classes. Great fun.

 

[Pythagorean]

no academic standing

I'm probably not the first to tell you, but as someone who does have an academic standing in physics, I can tell you that mathematics doesn't perfectly describe things in physics. It describes things much better than traditional language does, it's more descriptive in terms of quantification and it's more complex, allowing it to be used to discuss a lot of different situations, but it's still very much a language.

The real universe, however, is very stochastic, and we generally take advantage of the convenience of approximations and where we can, waving our arms about and saying "this mathematical relationship is only good in this situation and only to this accuracy."

Even in quantum mechanics, after the initial groundwork is laid down... it's approximation after approximation after approximation to get to a model of real world applications.

 

[wofsy]

I'm probably not the first to tell you, but as someone who does have an academic standing in physics, I can tell you that mathematics doesn't perfectly describe things in physics. It describes things much better than traditional language does, it's more descriptive in terms of quantification and it's more complex, allowing it to be used to discuss a lot of different situations, but it's still very much a language.

The real universe, however, is very stochastic, and we generally take advantage of the convenience of approximations and where we can, waving our arms about and saying "this mathematical relationship is only good in this situation and only to this accuracy."

Even in quantum mechanics, after the initial groundwork is laid down... it's approximation after approximation after approximation to get to a model of real world applications.

Approximations do not mean that there isn't a mathematical underpinning to the universe. Quite the contrary. By the way, pulling academic rank is in my view inappropriate to this conversation. Do you just want me to stop thinking and take your word for it?

A physicist once told me that rather than physics and mathematics being approximations to observed phenomena, the opposite is true. Observed phenomena and their explanations are approximations to the correct physics/reality.

 

[Pythagorean]

Approximations do not mean that there isn't a mathematical underpinning to the universe. Quite the contrary. By the way, pulling academic rank is in my view inappropriate to this conversation. Do you just want me to stop thinking and take your word for it?

A physicist once told me that rather than physics and mathematics being approximations to observed phenomena, the opposite is true. Observed phenomena and their explanations are approximations to the correct physics/reality.

no, I want you to take some classes and think about it for yourself after you've had some exposure to it.

Your last sentence in your last paragraph, I agree with, by the way. But in my case, it contributes to my point. I don't see it as an "opposite".

 

[wofsy]

no, I want you to take some classes and think about it for yourself after you've had some exposure to it.

Your last sentence in your last paragraph, I agree with, by the way. But in my case, it contributes to my point. I don't see it as an "opposite".

What classes do you suggest. I have taken a course in Quantum Mechanics, General realtivity, have read Feynmann's Lectures on Physics.

BTW On a Riemannian manifold with a potential function the metric can be modified so that the paths of particles in the presence of the potential are geodesics. Why can't this be done with the gravitational potential and give another way to do GR?

 

[arithmetix]

I reply to this message:
[yes - but I do not agree that math is a language - i agree that we can talk about it and think about it - to say that a 4 dimensional projective space is just just a word in a language with some grammar is just like saying that a tree is just part of a language.
Mathematical objects are perceived just as trees or cars.]

My answer:
I think that the 4-dimensional space is an object that may be described in a language about which everything is, in principle, known... whereas the tree is an object about which we know nothing except what we have discovered by experiment.
The 4d object is part of a mental map we have found to be congruent with 'reality', and while the universe of mathematical truths is like the 'real world' in that we may discover things we did not previously know in it, it is not the same as the real world... the map is not the territory.

 

[wofsy]

I reply to this message:
[yes - but I do not agree that math is a language - i agree that we can talk about it and think about it - to say that a 4 dimensional projective space is just just a word in a language with some grammar is just like saying that a tree is just part of a language.
Mathematical objects are perceived just as trees or cars.]

My answer:
I think that the 4-dimensional space is an object that may be described in a language about which everything is, in principle, known... whereas the tree is an object about which we know nothing except what we have discovered by experiment.
The 4d object is part of a mental map we have found to be congruent with 'reality', and while the universe of mathematical truths is like the 'real world' in that we may discover things we did not previously know in it, it is not the same as the real world... the map is not the territory.

Why isn't everything in principle known about the tree? Or why isn't there anything about the tree which is in principle knowable? Or if there is nothing in principal that is knowable about the tree then how can we form a theory about it? Or isn't any theory that successfully predicts new experiments just a theorem and in principal knowable?

 

[vectorcube]

Approximations do not mean that there isn't a mathematical underpinning to the universe. Quite the contrary. By the way, pulling academic rank is in my view inappropriate to this conversation. Do you just want me to stop thinking and take your word for it?

A physicist once told me that rather than physics and mathematics being approximations to observed phenomena, the opposite is true. Observed phenomena and their explanations are approximations to the correct physics/reality.

You should reply to me in what i said on post 138.

 

[vectorcube]

Perhaps you underestimate language. Check out linguistic relativity. The wiki on it has some notes on the empirical research involved.

Also, out of curiosity, what is your academic standing in mathematics?

It is not necessary falses. Mathematical platonism do see mathematical proposition as being descriptive. There is nothing incoherent about this idea.

 

[vectorcube]

My answer:
I think that the 4-dimensional space is an object that may be described in a language about which everything is, in principle, known... whereas the tree is an object about which we know nothing except what we have discovered by experiment.
The 4d object is part of a mental map we have found to be congruent with 'reality', and while the universe of mathematical truths is like the 'real world' in that we may discover things we did not previously know in it, it is not the same as the real world... the map is not the territory.

This makes no sense to me. If math is a map, then it is a composite of many maps of which one correponds to reality. That is to say, our universe is a mathematical structure describle captured by some axioms.

 

[SixNein]

I'm probably not the first to tell you, but as someone who does have an academic standing in physics, I can tell you that mathematics doesn't perfectly describe things in physics. It describes things much better than traditional language does, it's more descriptive in terms of quantification and it's more complex, allowing it to be used to discuss a lot of different situations, but it's still very much a language.

The real universe, however, is very stochastic, and we generally take advantage of the convenience of approximations and where we can, waving our arms about and saying "this mathematical relationship is only good in this situation and only to this accuracy."

Even in quantum mechanics, after the initial groundwork is laid down... it's approximation after approximation after approximation to get to a model of real world applications.

I would like to point out that mathematics is not exact. There is approximations in mathematics and even uncertainty.

Alas, I would ask what is physics? Is physics not the mathematical relationships found in our universe?

 

[vectorcube]

Alas, I would ask what is physics? Is physics not the mathematical relationships found in our universe?

Physics is certainly not some random relationship conjured up because it is "beautiful".

 

[apeiron]

I think that the 4-dimensional space is an object that may be described in a language about which everything is, in principle, known... whereas the tree is an object about which we know nothing except what we have discovered by experiment.
The 4d object is part of a mental map we have found to be congruent with 'reality', and while the universe of mathematical truths is like the 'real world' in that we may discover things we did not previously know in it, it is not the same as the real world... the map is not the territory.

The place to start this debate would be epistemology - acceptance that all knowledge is modelling. Knowledge is always a map (and so embeds a human purpose, representing where we want to go).

Then the question becomes what kind of knowledge of reality is maths?

Clearly it is knowledge of the most general or universal kind. The most general or universal that we find useful *as a map*.

So we can know a tree at many levels of modelling, from memories of particular trees in my garden to what we get taught about plant life in general in botany class. But what kind of mathematical level generalisations can we make about trees?

The fractal nature of tree branching would be one "deep insight". It connects trees to many other phenomenon like river systems and other dissipative structures.

Dissipative structure theory is of course a physical theory about energy flows and entropy degraders. And fractals are the product of mathematical equations. So we can see how there is a path from what some like to call qualitative-to-quantitative description.

A tree is a highly qualitative experience as we know "so many things" about it. But in a stuck together, constructed, componential sort of way. The idea of "tree-ness" is multi-dimensional. Then dissipative structure theory is a much more general description that is also much more constrained in its application. It has qualitative aspects (like energy flow) but also offers "things that must be measured" - such as quantities which get conserved. Then fractals are completely general, so general they no longer appear to refer to any real life instances. There are no qualitative aspects, just the quantitative - variable plugged into equations.

So what I am arguing is that all knowledge is modelling. Qualitative or quantitative. Then modelling does follow a hierarchy of generalisation. You start with "raw experience" (or the kind of natural world modelling that animal brains evolved to do, which also embed purposes of course). Then move away from raw experiences of trees and fish and ponds to increasingly more general, and thus reduced (stripped of qualifying specifics, trimmed of unneccessary phenomenal dimensions) levels of modelling. Physics is our word for the limit of science, the limit of description for what is real. Then maths is the step beyond, into generalities that are not real, that are pure quantity - but which can have qualities like energy or inertia plugged back into their frameworks and so become a tool for doing physics or other reality modelling.

Well, I say maths is pure quantity, but of course the axioms of maths are the vestiges of qualitative description. We boil reality right down to the last irreducibly necessary concepts - like assumptions about continuity~discreteness, stasis~change, chance~necessity.

Maths itself is of course a mix of disciplines.

You have algebra~geometry (the discrete vs the continuous descriptions). Algebra and geometry are in effect the exploration of the world of all possible general objects or general structures.

Then you have logic, which is the generalisation of causality, the generalisation of reality's rules.

And within maths there are levels of generalisation, as made explicit in category theory. So topology is more general than geometry. Arguably, by taking away the quantitative aspects of geometry - distance and angle and curvature - topology becomes a more qualitative level of description. Yes, it does reduce geometry towards the axiomatic nub, the ideas like continuous~discrete dimensionality that are its founding assumptions.

So category theory ends up with a ur-reduced, ur-general, map of reality. Objects and morphisms. Like a map which is a blank sheet of paper with an arrow saying "you are here" and a second saying "everything else is somewhere else".

To sum up, all knowledge is modelling. All modelling is shaped by purpose. Maps have reasons. Maps also want to be as simple as possible - particulars are reduced to leave generalisations.

Then human knowledge starts up where animal knowledge left off. We start off with a highly subjective or qualitative view of reality and work towards an objective or quantitative view. Maths is an almost purely general level of map making, but even here some founding qualitative axioms are required.

 

[SixNein]

Physics is certainly not some random relationship conjured up because it is "beautiful".

I think most people misunderstand the beauty of mathematics. People have to think deeper then symbols and equations in order to see it. The beauty of mathematics is the understanding it imparts to the mathematician. In some cases, a mathematician may be the first human to set foot on a new world, and he maps it so that physicists and engineers may find their way. The world the mathematician sees is described as beautiful.

 

[wofsy]

I am saying that there infinite many ways things could be for the universe, and that is what makes it contingent. There could be a universe described by cellular automata, but we do not happen to live in such a world. Mathematical propositions are true in all possible worlds, and that is what makes it necessary.



I do believe some form of modal realism. You are correct that possibilities only exist if something actually exist. My point that is that there on logical reasons for excluding these worlds based on logic, and logic alone.



Something like every possible world corresponds to a fundamental equation of some specific form. I am sure if you open yourself, you see that the world of "harry potter" is logically possible, but there is no governing dymanical law.




Not so. Suppose for a contradiction that such a law exist that govern the entire ensemble of universes. Say law U. But U and -U is also logically possible. Thus, -U would govern it `s own possible ensenble. contradiction.

Here is the thing you need to know. For a law of nature L, -L is a logically possibility.
For a mathematical proposition P, -P is logically impossible.


You benefit greatly by reading Nozick ` s principle of fecundity.

Logical possibility has nothing to do with what I am saying. You seem to think that I do not understand that one can never prove that the universe must be a certain way. I am saying that what is knowable - must contain mathematical stuctures - and that what is knowable is what is actually real - we can not speak about what is not knowable - to me this is not a question of logic, or formalisms - but a question of what is knowable.

 

[vectorcube]

I think most people misunderstand the beauty of mathematics. People have to think deeper then symbols and equations in order to see it. The beauty of mathematics is the understanding it imparts to the mathematician. In some cases, a mathematician may be the first human to set foot on a new world, and he maps it so that physicists and engineers may find their way. The world the mathematician sees is described as beautiful.

I guess you fail to see the point. The point is that there is difference between math and physics, and most people ignore that difference. People don` t make up equations in physics unless there is a physical motivation, and constrint imposed by physical reality.

 

[vectorcube]

I am saying that what is knowable - must contain mathematical stuctures - and that what is knowable is what is actually real - we can not speak about what is not knowable - to me this is not a question of logic, or formalisms - but a question of what is knowable.

That is still wrong. Take the harry potter universe. This universe cannot be described by math, yet, it is logically possible, and knowable.

 

[Pythagorean]

What classes do you suggest. I have taken a course in Quantum Mechanics, General realtivity, have read Feynmann's Lectures on Physics.

BTW On a Riemannian manifold with a potential function the metric can be modified so that the paths of particles in the presence of the potential are geodesics. Why can't this be done with the gravitational potential and give another way to do GR?

Just out of curiousity:

Did your QM course involve linear algebra with eigenspinors using the pauli matrice and complex operators as observables on a wave function in the schroedinger equations? Did your general relativity class have you solving tensor equations?

I haven't studied general relativity nor Riemannian manifolds. If you really understand the mathematics behind that question, why don't you pose the question mathematically and find out where it breaks down? Is that question even relevant to our discussion?

 

[wofsy]

Just out of curiousity:

Did your QM course involve linear algebra with eigenspinors using the pauli matrice and complex operators as observables on a wave function in the schroedinger equations? Did your general relativity class have you solving tensor equations?

I haven't studied general relativity nor Riemannian manifolds. If you really understand the mathematics behind that question, why don't you pose the question mathematically and find out where it breaks down? Is that question even relevant to our discussion?

the course was a standard first course given by Brian Greene at Columbia University. I also correspond with a Physics Professor on QM. Once a month a group of friends get together to discuss the measurement problem. Currently we are studying Bohm's deterministic theory of QM.

I asked this same question of my GR ( grad course) prof and he referred me to some papers and thought that there are in fact alternatives to GR based on this concept. The mathematics of the question is simple differential geometry and the students in the class were familiar with it. If you would like to learn about this I would be glad to write a different thread for you to read - say in the GR section of PF. I asked the question to you only just out of curiosity thinking that you might have some thoughts on it since you said you have academic credentials.

 

[arithmetix]

well it sounds to me as if what the original questioner, who has taken the name 'perspectives', wants is certainty about knowledge. Absolute, unquestionable certainty, for me, comes out of meditat
ion, and studying Tao, and prayer. Such deep certainty is intransmissible and indescribable, but is very simple to apprehend if you get quiet enough.
I don't personally believe that any absolute truths can be clearly stated in any language. I do think that this whole thread has been contributed to by philosophers however, and I suggest that philosophy would be a good thing to study along with the maths.

please see next post before responding!

 

[arithmetix]

... a bit of a think later, and having reviewed the rules:
I now withdraw from further discussion on some of what I have said, since I have opened an area of this debate which, far from physics, treats of religion. My views are my own and I have the right to them and the right to state what they are, but this is a dangerous area to get into since it may easily lead to heated discussion.
Anyone wishing to respond to the religious aspect of my post is welcome to respond to me personally, and if they have anything interesting to say we could find another venue.
Thank you.

 

[vectorcube]

The place to start this debate would be epistemology - acceptance that all knowledge is modelling. Knowledge is always a map (and so embeds a human purpose, representing where we want to go).

Then the question becomes what kind of knowledge of reality is maths?

Clearly it is knowledge of the most general or universal kind. The most general or universal that we find useful *as a map*.

So we can know a tree at many levels of modelling, from memories of particular trees in my garden to what we get taught about plant life in general in botany class. But what kind of mathematical level generalisations can we make about trees?

The fractal nature of tree branching would be one "deep insight". It connects trees to many other phenomenon like river systems and other dissipative structures.

Dissipative structure theory is of course a physical theory about energy flows and entropy degraders. And fractals are the product of mathematical equations. So we can see how there is a path from what some like to call qualitative-to-quantitative description.

A tree is a highly qualitative experience as we know "so many things" about it. But in a stuck together, constructed, componential sort of way. The idea of "tree-ness" is multi-dimensional. Then dissipative structure theory is a much more general description that is also much more constrained in its application. It has qualitative aspects (like energy flow) but also offers "things that must be measured" - such as quantities which get conserved. Then fractals are completely general, so general they no longer appear to refer to any real life instances. There are no qualitative aspects, just the quantitative - variable plugged into equations.

So what I am arguing is that all knowledge is modelling. Qualitative or quantitative. Then modelling does follow a hierarchy of generalisation. You start with "raw experience" (or the kind of natural world modelling that animal brains evolved to do, which also embed purposes of course). Then move away from raw experiences of trees and fish and ponds to increasingly more general, and thus reduced (stripped of qualifying specifics, trimmed of unneccessary phenomenal dimensions) levels of modelling. Physics is our word for the limit of science, the limit of description for what is real. Then maths is the step beyond, into generalities that are not real, that are pure quantity - but which can have qualities like energy or inertia plugged back into their frameworks and so become a tool for doing physics or other reality modelling.

Well, I say maths is pure quantity, but of course the axioms of maths are the vestiges of qualitative description. We boil reality right down to the last irreducibly necessary concepts - like assumptions about continuity~discreteness, stasis~change, chance~necessity.

Maths itself is of course a mix of disciplines.

You have algebra~geometry (the discrete vs the continuous descriptions). Algebra and geometry are in effect the exploration of the world of all possible general objects or general structures.

Then you have logic, which is the generalisation of causality, the generalisation of reality's rules.

And within maths there are levels of generalisation, as made explicit in category theory. So topology is more general than geometry. Arguably, by taking away the quantitative aspects of geometry - distance and angle and curvature - topology becomes a more qualitative level of description. Yes, it does reduce geometry towards the axiomatic nub, the ideas like continuous~discrete dimensionality that are its founding assumptions.

So category theory ends up with a ur-reduced, ur-general, map of reality. Objects and morphisms. Like a map which is a blank sheet of paper with an arrow saying "you are here" and a second saying "everything else is somewhere else".

To sum up, all knowledge is modelling. All modelling is shaped by purpose. Maps have reasons. Maps also want to be as simple as possible - particulars are reduced to leave generalisations.

Then human knowledge starts up where animal knowledge left off. We start off with a highly subjective or qualitative view of reality and work towards an objective or quantitative view. Maths is an almost purely general level of map making, but even here some founding qualitative axioms are required.

weird. So math is a "map". Why? because people evolved from monkeys?

 

[vectorcube]

Math is :
1. about sturctures( possible or actual).


Physics is:
1. Finding relationships between different quentities( observer, or not).

I think it is very easy to see the similarities/differences between the two.

 

[Pythagorean]

the course was a standard first course given by Brian Greene at Columbia University. I also correspond with a Physics Professor on QM. Once a month a group of friends get together to discuss the measurement problem. Currently we are studying Bohm's deterministic theory of QM.

I asked this same question of my GR ( grad course) prof and he referred me to some papers and thought that there are in fact alternatives to GR based on this concept. The mathematics of the question is simple differential geometry and the students in the class were familiar with it. If you would like to learn about this I would be glad to write a different thread for you to read - say in the GR section of PF. I asked the question to you only just out of curiosity thinking that you might have some thoughts on it since you said you have academic credentials.

Our modern physics class was a two-semester class that involved QM, Nuclear, and a choice between GR or nonlinear dynamics at the end. We unanimously voted for nonlinear dynamics. I have never been interested in GR, personally. Nonlinear dynamics (to me) is more applicable and diverse in terms of the world we experience on a day-to-day basis.

I've read part of a book by Brian Greene, "The Fabric of the Cosmos" (which I own). And I loved his discussion of Newton's bucket in the beginning of it, but I'm fairly turned-off by string theory, so the book didn't hold my interest enough to finish after he got into that.

Anyway, to put us back on topic, my opinion on the matter of mathematics is that it's a core way to quantify human thinking in terms of traditional logic. Not every mathematical abstraction we can think of necessarily pertains to the real world, but every mathematical abstraction we can think of does necessarily pertain to the computational methods of the human brain. In other words, I suspect any mathematical theory you can come up with has a good chance of telling you how the human brain makes abstractions and uses them to make (and check) constant predictions of the world around it, though any particular math theory you come up with won't actually be useful for making predictions about the world.

This is a lot like farting and watching porn. We don't have any evolutionary purpose for farting or watching porn, but we do have evolutionary purposes that farting and watching porn are a byproduct of.

 

[wofsy]

Our modern physics class was a two-semester class that involved QM, Nuclear, and a choice between GR or nonlinear dynamics at the end. We unanimously voted for nonlinear dynamics. I have never been interested in GR, personally. Nonlinear dynamics (to me) is more applicable and diverse in terms of the world we experience on a day-to-day basis.

I've read part of a book by Brian Greene, "The Fabric of the Cosmos" (which I own). And I loved his discussion of Newton's bucket in the beginning of it, but I'm fairly turned-off by string theory, so the book didn't hold my interest enough to finish after he got into that.

Anyway, to put us back on topic, my opinion on the matter of mathematics is that it's a core way to quantify human thinking in terms of traditional logic. Not every mathematical abstraction we can think of necessarily pertains to the real world, but every mathematical abstraction we can think of does necessarily pertain to the computational methods of the human brain. In other words, I suspect any mathematical theory you can come up with has a good chance of telling you how the human brain makes abstractions and uses them to make (and check) constant predictions of the world around it, though any particular math theory you come up with won't actually be useful for making predictions about the world.

This is a lot like farting and watching porn. We don't have any evolutionary purpose for farting or watching porn, but we do have evolutionary purposes that farting and watching porn are a byproduct of.

Interesting idea about the brain. Do you think that if viewed as a physical object rather than experiential (if that is a word) the formation of mathematical ideas in it means anything about Nature?

An interesting historical aside is that Riemann seems to think that idea formation was the true model of the universe and tried to compare finite objects to ideas and continuous space to the mind as a whole. His model for the universe was that it had the same processes as the mind.

I think this philosophical attitude inspired his invention of shocks in non-linear wave equations. The shock is like a "new idea" that lawfully arises in the "mind" to resolve an apparent contradiction, in this case a multi-valued signal. The law is preserved - but the mind/Nature if you will - creates a new object in order to preserve it and also changes the meaning of what a solution to the equation is.

He came up with this idea rather than introducing diffusion terms (changing the law) to prevent a multiple signal. His view I guess was that Nature does not change its laws but rather creates new things if it has to to preserve the laws.

More generally I think that the attitude that unchanging truth is to be discovered behind inexact observation is a guiding koan of modern physics. It can be seen in Einstein,Lorenz, Gallileo, Riemann. This is one reason that I can not accept the view that math is mere modeling. If that were Kepler and Newton's view then the Ptolemaic system would never have been rejected. It was an incredibly accurate model and could be adjusted periodically to preserve its accuracy. It was rejected precisely because it did not present universal law - in fact it contradicted the idea of universal law since it had to be modified from time to time - sort of like putting diffusion terms into the wave equation.

This thread because of its empiricist/positivist bias doesn't even care about this and doesn't care what thoughts inspired the progress of science. In fact I am sure that someone in this thread will write that the Ptolemaic system was perfectly fine and Gallileo and Kepler and Newton and Riemann and Einstein and all of the others were jerks - they just didn't understand anything.

 

[arithmetix]

I am interested in the notion that a consistent structure must underlie all possible worlds.
I quote from post 138, in which vectorcube wrote:

I am saying that there infinite many ways things could be for the universe, and that is what makes it contingent. There could be a universe described by cellular automata, but we do not happen to live in such a world. Mathematical propositions are true in all possible worlds, and that is what makes it necessary.

Also quote from vectorcube in the same post:
"I do believe some form of modal realism. You are correct that possibilities only exist if something actually exist. My point that is that there on logical reasons for excluding these worlds based on logic, and logic alone."


I ask: is it really possible to determine, using logic, whether a universe must be logical? Or even whether this universe is logical? (I have noticed that logic fails us on some kinds of question.)
For instance imagine that a prime cause exists, and imagine that we have a project to dtermine the nature of that cause. Then should one of us stumble on the exact description of that cause there would be no way for him to prove his discovery out, because logic demands that a statement be proven by an alternative analysis which must be shown to lead to the same result.
Of course this is impossible for a sole, prime cause... therefore it is not possible to address this kind of question, using logic.

 

[vectorcube]

I am interested in the notion that a consistent structure must underlie all possible worlds.
I quote from post 138, in which vectorcube wrote:

I am saying that there infinite many ways things could be for the universe, and that is what makes it contingent. There could be a universe described by cellular automata, but we do not happen to live in such a world. Mathematical propositions are true in all possible worlds, and that is what makes it necessary.

Also quote from vectorcube in the same post:
"I do believe some form of modal realism. You are correct that possibilities only exist if something actually exist. My point that is that there on logical reasons for excluding these worlds based on logic, and logic alone."


I ask: is it really possible to determine, using logic, whether a universe must be logical? Or even whether this universe is logical? (I have noticed that logic fails us on some kinds of question.)
For instance imagine that a prime cause exists, and imagine that we have a project to dtermine the nature of that cause. Then should one of us stumble on the exact description of that cause there would be no way for him to prove his discovery out, because logic demands that a statement be proven by an alternative analysis which must be shown to lead to the same result.
Of course this is impossible for a sole, prime cause... therefore it is not possible to address this kind of question, using logic.

I don `t understand your example. Logic by itself cannot tell us anything at all. What it tells use is that for a proposition p, p&-p is impossible.

 

[arithmetix]

Quoting myself:
"... For instance imagine that a prime cause exists, and imagine that we have a project to determine the nature of that cause. Then should one of us stumble on the exact description of that cause there would be no way for him to prove his discovery out, because logic demands that a statement be proven by an alternative analysis which must be shown to lead to the same result.
Of course this is impossible for a sole, prime cause... therefore it is not possible to address this kind of question, using logic. "

Because prime cause contains all results, every result must lead back to prime cause, but because each result does arise in the same way (same cause) no independent demonstration of cause is possible. Hence prime cause cannot be proven to be prime cause, even if we somehow know what prime cause is.
If that helps... (?)

 

[vectorcube]

Quoting myself:
"... For instance imagine that a prime cause exists, and imagine that we have a project to determine the nature of that cause. Then should one of us stumble on the exact description of that cause there would be no way for him to prove his discovery out, because logic demands that a statement be proven by an alternative analysis which must be shown to lead to the same result.
Of course this is impossible for a sole, prime cause... therefore it is not possible to address this kind of question, using logic. "

Because prime cause contains all results, every result must lead back to prime cause, but because each result does arise in the same way (same cause) no independent demonstration of cause is possible. Hence prime cause cannot be proven to be prime cause, even if we somehow know what prime cause is.
If that helps... (?)

I am uncertain what this has to do with logically possibilities.

 

[apeiron]

Quoting myself:
"... For instance imagine that a prime cause exists, and imagine that we have a project to determine the nature of that cause. Then should one of us stumble on the exact description of that cause there would be no way for him to prove his discovery out, because logic demands that a statement be proven by an alternative analysis which must be shown to lead to the same result.
Of course this is impossible for a sole, prime cause... therefore it is not possible to address this kind of question, using logic. "

Because prime cause contains all results, every result must lead back to prime cause, but because each result does arise in the same way (same cause) no independent demonstration of cause is possible. Hence prime cause cannot be proven to be prime cause, even if we somehow know what prime cause is.
If that helps... (?)

Alternatively, thinking in terms of prime causes could be where you go wrong - it is not actually "logical".

The other way to look at it is teleological. Perhaps only some certain outcome is self-consistent. So start from any kind of initial conditions and the system will develop to arrive at the same old place.

Kind of like attractors in dynamics. And that would be how maths developed - the sub-set of patterns that are self-consistent over the total space of potential patterns. Realities would be the same, and thus "mathematical" - or at least ameniable to modelling as patterns.

Syllogistic reasoning is a tool. But it is also useful to understand Aristotle's wider story on causality - his four causes. Purpose or teleology is something we need to bring back into logic modelling. In systems approaches, it is what is called global constraints.

 

[vectorcube]

Alternatively, thinking in terms of prime causes could be where you go wrong - it is not actually "logical".

The other way to look at it is teleological. Perhaps only some certain outcome is self-consistent. So start from any kind of initial conditions and the system will develop to arrive at the same old place.

Kind of like attractors in dynamics. And that would be how maths developed - the sub-set of patterns that are self-consistent over the total space of potential patterns. Realities would be the same, and thus "mathematical" - or at least ameniable to modelling as patterns.

Syllogistic reasoning is a tool. But it is also useful to understand Aristotle's wider story on causality - his four causes. Purpose or teleology is something we need to bring back into logic modelling. In systems approaches, it is what is called global constraints.

what do you mean here?

 

[arithmetix]

In post 170, vectorcube agrees that we are unable to determine whether we are in a logical universe, and offers the notion of a teleological model for consideration.
I think that vectorcube is right (if that is indeed what he means to say) and I wonder whether this will help us with the ostensible subject of our thread. If we are unable to determine whether the universe is or is not logical, we are unable for the same reasons to determine "why" math works, and the question is (regrettably) answered.

 

[vectorcube]

In post 170, vectorcube agrees that we are unable to determine whether we are in a logical universe, and offers the notion of a teleological model for consideration.
I think that vectorcube is right (if that is indeed what he means to say) and I wonder whether this will help us with the ostensible subject of our thread. If we are unable to determine whether the universe is or is not logical, we are unable for the same reasons to determine "why" math works, and the question is (regrettably) answered.

Hold on. I say no such thing!

Look, answer me this:

Do you think there is true contradiction?

 

[arithmetix]

no
i don't

 

[arithmetix]

sorry about that very short post. After I've done the cooking I'll come back and work out exactly what I do think.