Case for math antirealism

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My hunch is that mathematics doesn't describe the universe so much as the universe IS mathematics. The entire universe is the expression of a complex formula such as a fractal. Noting is "real" as such; anything we call an object is just a mathematical object consisting of various mathematical properties that make it appear like a separate object within the larger formula; rather like there appear to be objects inside the Mandelbrot fractal. We are discovering various mathematical relationships (laws) about these objects and their interactions with one another, but yet can't see the big picture; the formula that describes the entire universe. I further suspect that this grand formula is "simply" an expression of nothing. i.e. trace the universe right back to the big bang and the very point prior to the big bang there was nothing, zero, zilch. But nothing can also be expressed as +1 + -1 or in ever more complex ways and relationships and I suspect our universe is simply the expression of one of these formula through time.

But you're still thinking in terms of our conceptualised version of mathematics. I would say that our conception is maths is woefully inadequate because its based on a logic system which falls apart at the level of quanta. The really interesting stuff is all going on at the molecular level where our mathematics becomes clumsy. At the macro level where our consciousness tends to reside you have what appear to be discrete packets of matter but this is illusion. I think that the universe is information however and this information is just energy states. Thus when matter is sucked into a black hole some scientists believe that its state data is mapped 2 dimensionally on the surface. Maths is just the language we have invented to decode that. The universe simply is. Maths like language is a means through which we can understand reality on a raw level.

I think humans invented it and it likely does not apply accurately to anything outside this planet.....yet people think they can figure the universe and everything out with mathmatics.... they'll fail obviously.

Math is real

When God set up the Universe he first set up the laws of mathematics.

Then built everything according to those laws.

But he messed up. And he knows it. And soon he is gonna toss it all back into the hopper and melt it all down, and redo it all. And he's gonna redo the laws of mathematics for the next universe. Just start with a whole new rulebook.


For example:next time around the value of Pi ( the circumference of a circle over its diameter) will be exactly "3".

Not the irrational number it is now. Not this "three point one four followed by the endless string of numbers" jive. EXACTLY 3.0.! And everything will be fine. More perfect than it is now.

Most of you are answering only strawmen of the antirealism idea.

They do not claim that 1+1 is not equal to 2. No, they say math is logic and is thus self consistent, but isn't necessarily always consistent or neccessarily correlate to reality (or at least our reality.) Math is the art of expression, it can express that which is real and that which isn't, it only requires that they logically fit.


Additionally, since math is symbolic logic, the numbers are only symbolic for ideas similarly to language, that is why math is sometimes called "the language of math." It is the fallacy of saying that because we can conceive of something it must exist. Example: we have a concept for God therefore God must exist. Any self respecting atheist will refute that and all that Many physicists hold to the antirealist ideas concerning math, and the idea of math realism is considered to be medieval and outdated by many prominent mathematicians. The works of the great Lobachevsky who made an alternative geometry, non-euclidean geometry, that was logically consistent. He created a great and wondrous geometry where triangles can exist having less than 180 degrees and technically could have 0 degrees if the sides were infinite. Maybe it applies to reality, maybe it doesn't, but prior to him it was accepted that Euclidean geometry was absolute truth and therefore real. If you assign meaning to the strings in such a way that the rules of the game become true (i.e., true statements are assigned to the axioms and the rules of inference are truth-preserving), then you have to accept the theorem, or, rather, the interpretation you have given it must be a true statement. The same is held to be true for all other mathematical statements.


Here is an antirealist document from a Math Ph.D. whose research focuses on
diophantine geometry. It is actually a criticism of modern education, but he does talk about math a bit.
www.maa.org/external_archive/devlin/LockhartsLament.pdf

Some math correlates well with reality, and thus it is used as a tool for science and other subjects.

To claim that the universe is math doesn't necessarily conflict with some branches math antirealism. If the universe is logical, then it can be expressed mathematically, however many things that are impossible in the universe can also be expressed mathematically.

Another branch of Math Antirealism is fictionalism.
Also, I suggest the work of Hartry Field who published a book that showed that all science can be done without math, but that math is a useful tool, so that mathematics is a reliable process whose physical applications are all true, even though its own statements are false. For Field, a statement like "2 + 2 = 4" is just as fictitious as "Sherlock Holmes lived at 221B Baker Street"?but both are true according to the relevant fictions.

the notion of perfect as being represented byan integer is flawed. 3 is an odd number for instance. I submit that 12 is more perfect. Why is 3 intrinsically more perfect than 3.457858673839486930586

Yep maths is an internally consistent system but to preserve this inner consistency you have to violate human reason. The quantum vacuum for instance has infinite energy because an inifnite frequency spectrum exists there. This means that a quantum system can draw on photons created from the excitation of waves in the vacuum state.
This necessitates fluctuations within the field which occur about a mean of zero. Our conception of maths as a system for measuring discrete quanta doesnt work in this case because over time the energy fluctuations always equal zero

It started out looking like you were making a pun on the word "perfect" in a mathematical context. But apparently you're not.

There IS such thing as a "perfect number" in mathspeak. Like some numbers are "prime" (USDA Grade A!).

A "perfect" number is one that is the sum of all of its positive divisors other than its self. Its a rare breed of number.

Six is the first one ( its divisors are 1,2, and 3. And its the sum of 1,2, and 3). Twenty eight is the next perfect number, then comes 696, and 8128. And there are even bigger ones.

But I think that it's self evident that life would be simpler if the value of Pi were an integer, and not an irrational number. Even if the integer is a pedestrian one, like three, and isnt a "perfect" number-like six.

And further-that it shows that the creator just wasnt on the ball. And further -that it explains everything-all of the evil and suffering in universe! That God wasnt on the ball! Or thats what came to me one evening many years ago after I had taken a few bong hits!

Exactly. [Rhetorical question] Can identical objects in the physical world can even be identified?

At the atomic level, we see with isotopes that atoms of the same element can have different number of neutrons. So, if we say, 1 atom of carbon + 1 atom of carbon = 2 atoms of carbon, then all we have is 2 atoms of carbon in the abstract, not the physical world because these carbon atoms can be different from each other in the physical world.
http://www.answers.com/Q/Are_all_atoms_ ... _identical
http://en.wikipedia.org/wiki/Isotope

The question was posed on the other thread about whether QM could provide us a definition of what it means to be identical. If not, then math becomes abstract and/or subjective. 1 + 1 = 2 only when a particular human thinks those socks are close enough alike, or a human leaves open to interpretation what it means to be a "sock".

What you are talking about are known as approximations, e.g. Newton's Law of Gravity is now seen as an approximation of the current best, which is Einsteins. In time, Einstein's theories may well prove to also be approximations. That we describe things as being identical is not the fault of mathematics, instead,I would say i is the fault of our innate prejudice for what appears to us as "common sense".

Rather than being the villain here, it will be mathematics which uncovers any flaws in our explanations.

Maths is a descriptive language and a tool all in one. It helps us describe things in nature and it also predicts that which should occur in nature. Therefore, as far as I understand it, maths can be objective. As a recent example; the standard model predicted the presence of the Higgs Mechanism (in fact without this mechanism the standard model would have proven itself wrong). The Higgs mechanism was predicted purely on the basis of mathematical equations, and low and behold, we have discovered empirical evidence for it.

You are using QM to attack Mathematics, yet it is Mathematics which is defining QM, it is mathematics that is making us "follow the evidence". I am treading on thin ice here as I do not have a great grasp on QM, (I am "only" somewhat closing in on E=MC'2) but here goes, I would suggest that without the objective nature of mathematics we would have NO understanding of QM.

Last edited by DentArthurDent on 05 Sep 2014, 5:12 am, edited 1 time in total.

One proton is pretty much like another. The same with electrons, and neutrons. Subatomic particles are identical. So there you have it: identicality ( or identicalness). So you have groups of identical things. Therefore number.

Electrons, neutrons decay thus have different energy states, so they may not be identical.

"One example of this decay is carbon-14 (6 protons, 8 neutrons) that decays to nitrogen-14 (7 protons, 7 neutrons) with a half-life of about 5,730 years" )i.e., 1 neutron decayed into a proton.
http://en.wikipedia.org/wiki/Neutron#Bo ... tron_decay

With regards to protons, I would wonder if all protons are the same, then how can this happen, "Experiments at the Super-Kamiokande detector in Japan gave lower limits for proton mean lifetime of 6.6×10^33 years for decay".
http://en.wikipedia.org/wiki/Proton

It sounds like protons may also decay over time which would mean they may have different energy states.

However, "In particle physics, proton decay is a hypothetical form of radioactive decay in which the proton decays into lighter subatomic particles, such as a neutral pion and a positron. There is currently no experimental evidence that proton decay occurs".
http://en.wikipedia.org/wiki/Proton_decay

Looks like you right per the physical object of a "proton" , unless they prove decay.

Most of what you wrote is venturing into different philsophical ideas. I am simply relating to you the ideas of math realism and math anti-realism. I cited the wikipedia page that shows these are different "schools" of thought.



If you allow math to be determined based on "common sense" then you would be in the math anti-realism camp, because "common sense" is subjective.

If common sense is subjective then how is common sense truthfully common?

Because subjectivity is common.

What's the title of the book? I seem to remember searching for it on Amazon a few years back before giving up.

Can't the whole realism/anti-realism discussion be construed as a discussion about the (un)reality of mathematical entities (e.g. those ostensibly referred to by such terms as "2" and "triangle")?

(Or more specifically, about the (un)reality of numbers? Or sets? (Hasn't it been accepted that numbers are the fundamental entities of all mathematics including geometry; and hasn't it been accepted that numbers are a special kind of set? I might be a bit off on this.))

Mathematical anti-realism - that is, if I'm right, the view that there are no such things as mathematical entities (sets, numbers, figures, what-have-you) - sounds preposterous at first, but once you try to specify what mathematical entities are, then it's easier to appreciate the controversy of the question regarding their reality.

What is 2? It isn't identical to this or that physical object-pair (two apples, two hands, etc.); nor, perhaps, is it just an idea in the mind (though some metaphysicians might disagree) - more generally, it has no spatiotemporal properties (i.e. it doesn't occupy space and time), and it doesn't have any effects in the way that physical events do; therefore (so it's been said), it's eternal and immaterial, and we know it only through a special faculty of rational intuition, or some such.

Now if you're suspicious of what's written in the previous paragraph, then you might actually have some anti-realist sympathies! One of the challenges for anti-realism is to account for what it is that practitioners of mathematics, as such, actually do. (Language-games?)