Foundations of maths

[david345]

Gödel is wrong because he depended his argument on the idea that the abstract nature that defines the class of a universal to include itself. While I think this is alright too, in such an interpretation, he has no justice to assume that an infinite regress itself is not allowed.

 

A set that is defined as "the set of all sets" is one in which a member of it must also include this set too in an infinite regress. So his argument about such a possible set to be unable to be 'closed' or is "incomplete" falters because with respect to reality because he merely begs that the idea of infinity is not closed. But just because we as humans are locally unable to find closure with respect to totality as a whole, does not mean that totality itself finds this idea "incomplete".

 

For instance, the idea of a verb such as "walk" is infinite in this sense. Yet we still understand it finitely too. We do this when we create the term, "walking" to give it a noun meaning. [a Gerund]

 

The proof by Gödel was merely to show that all logical systems cannot be closed as he presented this type of argument to show that at least one will always exist that is in itself unclosed by his definition. However, we can also argue that the very process of him demonstrating the non-closure of all logics/maths can be closed in 'process' by redefining infinity in those logics generatively to become closed just as a verb can be translated into a noun. Even if another proof can come along to reinstate Gödel's theorem, another theorem can be presented generatively to prove it closed.

 

Another point is that if you accept Gödel's "Incompleteness Theorem" as is, this HAS to apply for all systems including science with it's stance on permanent tentativity in the same incompleteness. Most already default to assume that science does not nor cannot determine 'truth' because of this. Therefore, is science not just as rationally insignificant as logic in the same way? It is for this reason that I find science incomplete without the philosophy respecting logic as its underlying reality.

 

NOTE: You know that while Gödel's theorem is a theorem, what I present about redefining "infinity" can also disprove Gödel's theorem and act as a theorem itself. It makes his theorem itself without closure allowing for all logical systems.

This is completely wrong. You are just making a fool of yourself with this ridiculous nonsense.

[Scott Mayers]

This is completely wrong. You are just making a fool of yourself with this ridiculous nonsense.

Okay?

 

Thanks for your disapproval. But if you know the rules of appropriate dialectic, your first sentence grants you the onus to provide your own justification with proof. Considering that you lack this awareness by default, it tells me you lack even the standards of logic itself to be able to judge one way or the other. Thus, I'm guessing that you don't even know whether Godel's theorem is even valid in the first place. This proves definitively that you have no credibility to your own view and are merely acting to harass.

 

Next.

[david345]

 

 

I'm very familiar with Godel's incompleteness theorem and have contention with it as it allows a set to be defined such that it's universal description can be included within the set. [A Set of all Sets, for instance which requires it to be included in itself]

The principia was written specifically to ensure that the the set of all sets was not included in itself. Godel's proof was written specifically for the principia. Obviously his proof would not have worked had it such a requirement.

 

As to Godel (excuse that I'm not bothering to use the character map for the 'o'), he even had doubts of it later as new set theory ideas came about that limited the dilemmas that lead to Godel's Incompleteness Theorem.

Godel's proof applies to ZFC. I'm sure you could find some crackpot "set theory" Nobody cares about your crackpot "set theory".

 

 

Lets just be honest for a minute. You have no interest in telling the truth. You come on the various science sites with your numerous sockpuppets. Michael12345, md65536, tar, mrintelligentdesign, sillybilly, dadoulous, loislane, etc. You have proven time and time again you are willing to say whatever is necessary to "prove" we live in a ten thousand year old intelligently designed, geocentric, LET universe. When someone corrects you they are met with your standard response. "Your wrong because (insert word salad, lies, strawman, accusations of bullying and corruption, etc.)"

 

YOU came on the internet speaking about the truth. You should not be surprised when someone shows up to tell it. Should I be a liar like you? Should I play along with your games? Should I act like there is meaning to your lies and word salads? Of course not. There are students who come to these sites in hope of finding legitimate information. Instead they get a multi-sockpuppet troll claiming to be a University professor.

 

Perhaps you should consider your other thread before you taddle to the moderators like you did last time.

http://www.scienceforums.net/topic/91433-why-im-here/

[swansont]

Lets just be honest for a minute. You have no interest in telling the truth. You come on the various science sites with your numerous sockpuppets. Michael12345, md65536, tar, mrintelligentdesign, sillybilly, dadoulous, loislane, etc. You have proven time and time again you are willing to say whatever is necessary to "prove" we live in a ten thousand year old intelligently designed, geocentric, LET universe. When someone corrects you they are met with your standard response. "Your wrong because (insert word salad, lies, strawman, accusations of bullying and corruption, etc.)"

 

YOU came on the internet speaking about the truth. You should not be surprised when someone shows up to tell it. Should I be a liar like you? Should I play along with your games? Should I act like there is meaning to your lies and word salads? Of course not. There are students who come to these sites in hope of finding legitimate information. Instead they get a multi-sockpuppet troll claiming to be a University professor.

 

Perhaps you should consider your other thread before you taddle to the moderators like you did last time.

http://www.scienceforums.net/topic/91433-why-im-here/

 

 

!

Moderator Note

Rules violations, including suspected sockpuppetry, should be reported to the staff via the report post button — airing accusations such as you have is out of line (and would also be quite a trick, considering the geographic separation involved). Personal attacks are also not going to fly. If you can't focus on the subject matter, consider passing on discussion altogether.

[PeterJ]

Scott - I see some sense in what you're saying but I have to work hard to do it. Perhaps you don't realise you have a slightly odd way of speaking.

 

David - "The principia was written specifically to ensure that the the set of all sets was not included in itself."

 

I get the impression that it was written without a thought for the set of all sets, and that this problem only came up later to bite the author.

[overtone]

This book may be relevant, to the extent the discussion has content: https://en.wikipedia.org/wiki/Laws_of_Form

[PeterJ]

Wow. Kudos, overtone. The first time I've seen LoF recommended by anyone other than me. Yes, very relevant.

 

For an accompanying text that would be consistent with the description of reality in LoF there would be Hermann Weil's 'Das Kontinuum'.

[BlackSunGod]

In my honest opinion is the other way round. Maths describe reality = eternal truths. Science describes what our senses/devices perceive = contingent truths = empirical truths = mutable truths (and it does it with maths by the way, if we remove maths from science we get Alchemy or divination). As we refine our experiments and experimental devices, our models and results will get closer and closer to pure math (as we are seeing with quantum mechanics, mathematical biology, computational neuroscience, countless fields that seemed detached to maths in the past are almost 100% mathematical today, and the fields that were already mathematical became even more mathematical). We'll probably get to a point where we can unify all of the scientific knowledge under the banner of Maths and then remove the extra layer of Physics and the rest of sciences. I propose we'll just call Physics the Maths of particles, Black Holes and such, Biology the Maths of life, Chemistry we can call it the Maths of bigger particles and its interactions, Psychology Maths of the mind, etc. Sorry for the lack of originality I'm a scientist not a marketing expert ok?

Edited October 31, 2015 by BlackSunGod

[cladking]

In my honest opinion is the other way round. Maths describe reality = eternal truths. Science describes what our senses/devices perceive = contingent truths = empirical truths = mutable truths (and it does it with maths by the way, if we remove maths from science we get Alchemy or divination). As we refine our experiments and experimental devices, our models and results will get closer and closer to pure math (as we are seeing with quantum mechanics, mathematical biology, computational neuroscience, countless fields that seemed detached to maths in the past are almost 100% mathematical today, and the fields that were already mathematical became even more mathematical). We'll probably get to a point where we can unify all of the scientific knowledge under the banner of Maths and then remove the extra layer of Physics and the rest of sciences. I propose we'll just call Physics the Maths of particles, Black Holes and such, Biology the Maths of life, Chemistry we can call it the Maths of bigger particles and its interactions, Psychology Maths of the mind, etc. Sorry for the lack of originality I'm a scientist not a marketing expert ok?

 

I don't so much disagree as I see it from another perspective. Math is quantified logic and reality is most probably completely logical.

 

But it's not math we need to come to understand, it's reality.

[BlackSunGod]

If you really want to understand a computer software do you study only the output of the program or also the language in which is written?

[andrewcellini]

If you really want to understand a computer software do you study only the output of the program or also the language in which is written?

wouldn't it also be important (possibly more important that the two you've listed) to understand how much memory some program requires and how long some program will take? also, is there a more efficient way of achieving similar output?

 

not sure how relevant this is to the topic though. it seems as if this is a poor analogy for understanding reality just because there is more to understanding the behavior of some program that to know what language it was written in and its output.

[studiot]

I usually ask those who maintain that all reality is amenable to description by mathematical formulae the following question.

 

You are going to build an earth embankment, starting (of course) with the bottom layer and ending up with the road/rail/canal formation surface at a prescribed location, elevation and width.

 

The original ground you are starting from is uneven and sloping.

 

Where do you start?

[PeterJ]

BalckSunGod - Nice comment. You might like this.

 

"Although all forms, and thus all universes, are possible, and any particular form is mutable, it becomes evident that the laws relating to such forms are the same in any universe. It is this sameness, the idea that we can find a reality which is independent of how the universe actually appears, that lends such fascination to the study of mathematics. That mathematics, in common with other art forms, can lead us beyond ordinary existence, and can show us something of the structure in which all creation hangs together, is no new idea. But mathematical texts generally begin the story somewhere in the middle, leaving the reader to pick up the thread as best he can. Here the story is traced from the beginning.

Unlike more superficial forms of expertise, mathematics is a way of saying less and less about more and more. A mathematical text is thus not an end in itself, but a key to a world beyond the compass of ordinary description. "

 

George Spencer Brown - Laws of Form

[cladking]

If you really want to understand a computer software do you study only the output of the program or also the language in which is written?

 

 

I'm a hardware guy.

[BlackSunGod]

Even if you are a hardware guy, you could spend 3 years trying to understand how a computer works, but if you don't know the LOGIC behind circuit design, how the parts interact, etc you won't be able to. Actually a good analogy for this is modern biology. Biologists were those hardware guys that dealt with all the experiments and field research, but until the fields of Mathematical Biology, Complex Networks, Bioinformatics took off Biologists couldn't make sense of the data and fully explain the experiments. In my honest opinion this will happen with the rest of sciences but in a more profound level. Even if we keep following the empirical approach, our models will be closer and closer to pure maths until we realise that reality consists of maths (or let's say numbers and their interactions) instead of matter, dark energy, spacetime or whatever. I would say that the reality we perceive is the output of the software, the software and indeed the hardware itself would be maths.

[cladking]

Even if you are a hardware guy, you could spend 3 years trying to understand how a computer works, but if you don't know the LOGIC behind circuit design, how the parts interact, etc you won't be able to. Actually a good analogy for this is modern biology. Biologists were those hardware guys that dealt with all the experiments and field research, but until the fields of Mathematical Biology, Complex Networks, Bioinformatics took off Biologists couldn't make sense of the data and fully explain the experiments. In my honest opinion this will happen with the rest of sciences but in a more profound level. Even if we keep following the empirical approach, our models will be closer and closer to pure maths until we realise that reality consists of maths (or let's say numbers and their interactions) instead of matter, dark energy, spacetime or whatever. I would say that the reality we perceive is the output of the software, the software and indeed the hardware itself would be maths.

 

This just isn't true. I believe it seems true because of two fundamental misunderstandings. First is the nature of math and second is the nature of reality. We have simply defined nature through experimental results and these seem to be mathematical because math is logical and reality is logical. Math is quantified logic so it's a quantification of reality. In a sense you're exactly right probably because eventually we just might know the equation of reality itself but for now all we have are bits and pieces of math that can be used to solve problems when they are applied properly to the real world.

 

I don't know that all knowledge will ever be simplified to an equation or a mathematical construct so for now all that's left is to examine the hardware and the "owner's manual" (metaphysics). I believe a great deal of math is being misapplied and this gets more apparent every day as the world wastes ever more resources and human talent and human life. We're doing ever more work to waste ever more of everything. Need I even mention this is unsustainable? When people start worrying about all the consumption they want to decrease efficiency even more to combat it. We close efficient (relatively) factories in the US and open inefficient ones with even lower quality in China and ship the products from the other side of the world. Products that once lasted for decades now last for weeks or months. So they just shrink the package, pump it up with water, and put it on sale for double what it used to cost. We even ship all this garbage great distances to put it back into the earth.

 

Math is not the solution to our problems nor to understanding reality. Math is a tool and a very useful one at that. But, it must be appropriate for each of its uses and it obviously is not. This is simply the nature of math as quantified logic and the nature of man to use creative accounting, double billing and double books, lying figures, and cheating prosperous. It can occur even in real science (of which less and less seems to exist every year).

[studiot]

 

We're doing ever more work to waste ever more of everything

 

But modern politics has made an amazing leap forward when it was realised that individual citizens no longer have to work hard wasting resources. Their government can do this much more efficiently for them, whilst the citizens take their ease, if they can still afford it.

 

[cladking]

 

But modern politics has made an amazing leap forward when it was realised that individual citizens no longer have to work hard wasting resources. Their government can do this much more efficiently for them, whilst the citizens take their ease, if they can still afford it.

 

 

Indeed. Government can waste more in a second than a village can waste in a lifetime.

 

 

 

 

 

 

 

 

But the system is unsustainable and the nature of its collapse can not be predicted with any kind of math so it can not be controlled.

 

[BlackSunGod]

 

This just isn't true. I believe it seems true because of two fundamental misunderstandings. First is the nature of math and second is the nature of reality. We have simply defined nature through experimental results and these seem to be mathematical because math is logical and reality is logical. Math is quantified logic so it's a quantification of reality. In a sense you're exactly right probably because eventually we just might know the equation of reality itself but for now all we have are bits and pieces of math that can be used to solve problems when they are applied properly to the real world.

 

I don't know that all knowledge will ever be simplified to an equation or a mathematical construct so for now all that's left is to examine the hardware and the "owner's manual" (metaphysics). I believe a great deal of math is being misapplied and this gets more apparent every day as the world wastes ever more resources and human talent and human life. We're doing ever more work to waste ever more of everything. Need I even mention this is unsustainable? When people start worrying about all the consumption they want to decrease efficiency even more to combat it. We close efficient (relatively) factories in the US and open inefficient ones with even lower quality in China and ship the products from the other side of the world. Products that once lasted for decades now last for weeks or months. So they just shrink the package, pump it up with water, and put it on sale for double what it used to cost. We even ship all this garbage great distances to put it back into the earth.

 

Math is not the solution to our problems nor to understanding reality. Math is a tool and a very useful one at that. But, it must be appropriate for each of its uses and it obviously is not. This is simply the nature of math as quantified logic and the nature of man to use creative accounting, double billing and double books, lying figures, and cheating prosperous. It can occur even in real science (of which less and less seems to exist every year).

Maths being misapplied is not a problem of Maths themselves. That's our problem. I can express my point of view in another way with an example: Pythagoras Theorem will hold for any possible Universe that contain a single triangle in any possible sense (a physical triangle made of wood, a triangle of forces, etc). We express that relation with our human symbols but the pattern itself is eternal and necessary. All of reality must be like that. Explaining a Universe half mathematical and half not would suppose a bigger problem (how maths interacts with non-maths?).

 

In my honest opinion, the problems that you talk about are more related to Science (and its relations with Economy and Politics) and not Mathematics.

 

I put it in another way. You wake up tomorrow and you decide it's a good day to build a Universe. What is the better approach, to construct it physically or to program it? Economically it will probably be cheaper to program it, also easier to manipulate, to do trial and error, to correct mistakes, etc. This is just a thought experiment, I know it has no validity as a logical argument lol, but indeed our computer simulations of the Universe and our video games for example are just that: caricature universes programmed using mathematical languages. To think that we little stupid humans have found this solutions in the lifetime of our species and that the Universe itself (of which you and I and all our mathematical devices form part) hasn't found even more mathematically perfect ones... I dunno man, it's up to you what to think but for me the answer is obvious

[cladking]

Maths being misapplied is not a problem of Maths themselves. That's our problem. I can express my point of view in another way with an example: Pythagoras Theorem will hold for any possible Universe that contain a single triangle in any possible sense (a physical triangle made of wood, a triangle of forces, etc). We express that relation with our human symbols but the pattern itself is eternal and necessary. All of reality must be like that. Explaining a Universe half mathematical and half not would suppose a bigger problem (how maths interacts with non-maths?).

 

 

Again, I'm going to have a tough time disagreeing with you because we are in general agreement.

 

However there is only one universe, one possible universe, and a single reality that applies everywhere. In this reality there is a 3: 4: 5 triangle and these proportions can be described mathematically or by other means. The beauty of using math is that physical displacements or distances can be easily and "precisely" communicated.

 

But the triangle doesn't conform or bend to math but rather they both answer to the exact same logic and this logic is everywhere a part of reality. This logic guides a bird's flight and every planet. Nature doesn't perform infinite calculations to keep the stars in orbit but rather the universe can be described by logic.

[Strange]

However there is only one universe,

 

You don't know that.

 

one possible universe

 

That is almost certainly not true.

 

, and a single reality that applies everywhere.

 

Again, you don't know that.

 

In this reality there is a 3: 4: 5 triangle and these proportions can be described mathematically or by other means.

 

Is that true in non-Euclidean space? (That is a genuine question, I don't know the answer...)

[cladking]

 

You don't know that.

 

 

That is almost certainly not true.

 

 

Again, you don't know that.

 

 

Is that true in non-Euclidean space? (That is a genuine question, I don't know the answer...)

 

 

You don't know that.

 

 

That is almost certainly not true.

 

 

Again, you don't know that.

 

 

Is that true in non-Euclidean space? (That is a genuine question, I don't know the answer...)

 

 

Of course I don't know any of that. I don't know you're real or that some consciousness isn't intentionally trying to make me mispercieve reality. I don't even know that the communicative "property of math (ab=ba) applies in every single case. Maybe it only applies when I check it and that consciousness makes it that way. Maybe sometime I'll check it when He's not looking and find out it's all a fraud.

 

Science may never be able to answer the questions. In 500 years so far we still don't know even the tiniest fraction of 1% of everything that is. If there were such a thing as infinity, our knowledge hardly adds up to its reciprocle.

 

In the meantime I will posit that reality is exactly what it appears to be. I will make a conscious effort to see that reality rather than the models created by science. This is much like ancirent science except that it is augmented by modern science and modern math.

[imatfaal]

 

 

 

Of course I don't know any of that. I don't know you're real or that some consciousness isn't intentionally trying to make me mispercieve reality. I don't even know that the communicative "property of math (ab=ba) applies in every single case. Maybe it only applies when I check it and that consciousness makes it that way. Maybe sometime I'll check it when He's not looking and find out it's all a fraud.

 

Science may never be able to answer the questions. In 500 years so far we still don't know even the tiniest fraction of 1% of everything that is. If there were such a thing as infinity, our knowledge hardly adds up to its reciprocle.

 

In the meantime I will posit that reality is exactly what it appears to be. I will make a conscious effort to see that reality rather than the models created by science. This is much like ancirent science except that it is augmented by modern science and modern math.

 

The triangle thing doesn't work in curved space - it is one of the ways we are looking to set bounds on the curvature of our universe; find a known triangle in space and look at the lengths and angles. In general AB doesn't equal BA when dealing with matrices - the lack of application of Commutative (not communicative) Law in Matrices shows up in some interesting ways in quantum mechanics not least that one version of the HUP flows from non-commuting operators. Things are weird enough without positing extra layers of uncheckable gumpf

[DevilSolution]

......urahh for the collective consciousness....this thread is a reflection of reality. There's the nit picking kids, the superiority complex "people", the occasional piece of banter and the people who have an "honest" and open opinion on the OP and hereafter.

 

We are products of logic, the children of truth.

 

It "SEEMS" there are some fundamental questions that are beyond our comprehension, we're confined to what is logically possible although that is infinitely finite.

 

 

B...B..BbbbbBUMP......last one tnight i swear. ()(o.O)()