Mathematics and faith

Fremen

I'm gonna play devil's advocate here and say that mathematics is based on faith. The modern foundation of mathematics is known as ZFC - the Zermelo Fraenkel axioms with the axiom of choice.

There's a theorem which says an axiomatic framework is inconsistent if and only if we can prove that it is consistent. That means it's impossible to demonstrate that you'll never come across a contradiction in your mathematics. Hence, one requires faith.

Any thoughts on that?

gosplan

Fremen wrote: »

There's a theorem which says an axiomatic framework is inconsistent if and only if we can prove that it is consistent.

is this an error?

Fremen

Nope. If you can prove it's consistent, then your whole axiomatic framework is f***ed.

mikhail

Fremen wrote: »

I'm gonna play devil's advocate here and say that mathematics is based on faith. The modern foundation of mathematics is known as ZFC - the Zermelo Fraenkel axioms with the axiom of choice.

You can't start from nothing.

There's a theorem which says an axiomatic framework is inconsistent if and only if we can prove that it is consistent. That means it's impossible to demonstrate that you'll never come across a contradiction in your mathematics. Hence, one requires faith.

Godel's theorem doesn't say what you think it says. See, for example,
http://cscs.umich.edu/~crshalizi/notabene/godels-theorem.html

mikhail

Fremen wrote: »

There's a theorem which says an axiomatic framework is inconsistent if and only if we can prove that it is consistent. That means it's impossible to demonstrate that you'll never come across a contradiction in your mathematics. Hence, one requires faith.

I only skimmed over this before, presuming that it an argument from all the old familiar places. Godel's theorem is extremely different from what you said. Wikipedia saves me from writing it out:

The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an "effective procedure" (essentially, a computer program) is capable of proving all facts about the natural numbers. For any such system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem shows that if such a system is also capable of proving certain basic facts about the natural numbers, then one particular arithmetic truth the system cannot prove is the consistency of the system itself.

Wikipedia also has a short bit on the limitations of the theorem, which must be the most popularly exaggerated result in mathematics.
http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems#Limitations_of_G.C3.B6del.27s_theorems

robindch

Fremen wrote: »

Any thoughts on that?

That you're conflating religious "faith" with axiomatic consistency?

Zillah

Doing anything but instantly going completely and irrevocably catatonic requires axioms.

Yes, mathematics is based on an assumption; everything is. Where we begin to judge whether something is reasonable or not is when we consider how many assumptions are made, or if they go above and beyond neccessary axioms.

Fremen

mikhail wrote: »

I only skimmed over this before, presuming that it an argument from all the old familiar places. Godel's theorem is extremely different from what you said.

The version given on the wikipedia page is, yes. There are other versions...

mikhail

Fremen wrote: »

The version given on the wikipedia page is, yes. There are other versions...

It's a mathematical proof. No, there aren't.

cavedave

Gödel created an ontological proof of the existence of god. It is quite similar to St. Anselm from the 11th century

Bertrand Russell said "The argument does not, to a modern mind, seem very convincing, but it is easier to feel convinced that it must be fallacious than it is to find out precisely where the fallacy lies."

Fremen

mikhail wrote: »

It's a mathematical proof. No, there aren't.

You can prove the same theorem different ways. Pythagoras' theorem has at least twenty different proofs. Distinct statements can be shown to be logically equivalent to each other - there are at least five conditions I know of which are equivalent to the Riemann hypothesis.

Godel's second incompleteness theorem:

For any formal effectively generated theory T including basic arithmetical truths and also certain truths about formal provability, T includes a statement of its own consistency if and only if T is inconsistent.

Many world-class mathematicians have niggling doubts about the consistency of the foundations of mathematics:
http://mathoverflow.net/questions/40920/what-if-current-foundations-of-mathematics-are-inconsistent
(that website has at least three fields medalists who post on it regularly - Tao, Gowers and Thurston).

Quibbling about Godel aside, the point I'm trying to make is that mathematics is the language of scientific reasoning. If mathematics itself is suspect, doesn't that raise philosophical issues with all scientific endeavour?

Edit #2: Russell himself was convinced by the ontological argument for a short time, according to "the god delusion". It really is a very nice argument, though fundamentally flawed.

robindch

Fremen wrote: »

the point I'm trying to make is that mathematics is the language of scientific reasoning. If mathematics itself is suspect, doesn't that raise philosophical issues with all scientific endeavour?

All scientific conclusions are tentative and based up on physical evidence, so I can't see how Godel's Incompleteness Theorems -- which applies to axiomatic systems which deal with natural numbers -- really applies.

If something is demonstrated physically to the point at which it is accepted as "fact", then the mathematics which describe it, if there are any, must be mapped to correspond to the physical process. Ie, it's basically nothing more than convenient that maths describes physics well, but the mapping "means" nothing since it is effectively arbitrary and, like the assumption of the universality of physical law, is simply a simplification which is commonly made in order to reduce the complexity of the world to something that we can deal with.

mikhail

Fremen wrote: »

There's a theorem which says an axiomatic framework is inconsistent if and only if we can prove that it is consistent.

Fremen wrote: »

For any formal effectively generated theory T including basic arithmetical truths and also certain truths about formal provability, T includes a statement of its own consistency if and only if T is inconsistent.

If you don't see that these are different statements, you're not a mathematician. The Peano arithmetic can be proved consistent using Zermelo–Fraenkel set theory (ZFC), among other ways.

Fremen

mikhail wrote: »

If you don't see that these are different statements, you're not a mathematician. The Peano arithmetic can be proved consistent using Zermelo–Fraenkel set theory (ZFC), among other ways.

Ok, so maybe I should have said
"There's a theorem which says an axiomatic framework is inconsistent if and only if a proof of its consistency follows logically from the axioms".

Sure we can prove consistency of Peano arithmetic in ZFC, but how do we then prove consistency of ZFC? Maybe you can extend to some other system which says ZFC is consistent, but how do you prove concistency of that?

You can keep going down that road, but at some point you need to take it on faith, which should be disturbing to any philosopher of science.

robindch

Fremen wrote: »

at some point you need to take it on faith

Er, yes. At some point you have to assert axioms and rules of production. If you don't, then you can't even get going.

You can use the word "faith" to describe how you feel about these axioms and rules, but it's used in a completely different way than the religious use the term -- "faith is the assurance of things hoped for, the conviction of things not seen".

And as I said in the previous post, the mapping between the physical universe and maths is arbitrary, so deciding that the mathematical framework you're using is formally undecidable -- for whatever that term might mean in a context in which Godel's theorem does not apply to start with -- cannot reduce one's already minimal level of philosophical trust in the system.

seamus

Ignoring the mathematical complexities here, there's a difference between having faith that something is correct and assuming that something is correct.

That means it's impossible to demonstrate that you'll never come across a contradiction in your mathematics

Therefore we assume that we will not. We don't have "faith" that we will not. Mathematics and in fact all of science is built on the principle that, "We will assume X is the truth, but we do not assert that it definitely is". That's not faith.

Faith says, "I believe that X is definitely the truth" - it does not provide room for error or correction. You cannot say, "I believe that X is the truth, but I'm open to correction". That's not faith, that doesn't display any confidence in your belief.

Mathematics is only as confident as the next proof. If someone manages to show that the basis of all mathematics is unstable and the proof is in error, then we will reformulate and start again. Religion on the other hand will simply ignore any counter-proof and continue on with the same faith that it has always had.

Improbable

seamus wrote: »

Ignoring the mathematical complexities here, there's a difference between having faith that something is correct and assuming that something is correct.

Therefore we assume that we will not. We don't have "faith" that we will not. Mathematics and in fact all of science is built on the principle that, "We will assume X is the truth, but we do not assert that it definitely is". That's not faith.

Faith says, "I believe that X is definitely the truth" - it does not provide room for error or correction. You cannot say, "I believe that X is the truth, but I'm open to correction". That's not faith, that doesn't display any confidence in your belief.

Mathematics is only as confident as the next proof. If someone manages to show that the basis of all mathematics is unstable and the proof is in error, then we will reformulate and start again. Religion on the other hand will simply ignore any counter-proof and continue on with the same faith that it has always had.

Well religion changes over time as aspects of it are shown to be false à la metaphor blah blah blah. But it's a very good and valid point.

gosplan

So if I break this down into normal language(nerds!!).

1: Axioms are basically assumptions
2: Mathematical systems are built on such assumptions
3: Therefore trust in any mathematical system requires an element of 'faith'

Is the key difference between 'faith' in axioms and 'faith' in religion not the overwhelming evidence that usually precedes mathematical assumptions.

i.e. Euclids first axoim states that a straight line can be drawn between any two points. It doesn't really require too much 'faith' to go along with that.

robindch

gosplan wrote: »

trust in any mathematical system requires an element of 'faith'

No. You write down your axioms, your symbols and your rules for manipulating both and you see where it goes. Your conclusions are inevitable consequences of the position you've started from, and you can start from anywhere you wish. Faith just doesn't come into it.

gosplan wrote: »

Euclids first axoim states that a straight line can be drawn between any two points. It doesn't really require too much 'faith' to go along with that.

And there are many self-consistent mathematical systems in which one or more of Euclid's postulates does not exist, or has been changed.

The most well-known are the non-Euclidean geometries which result from substituting for his fifth axiom, the famous Parallel Postulate.

Non-Euclidean geometries, btw, were first developed (but hushed up) by Gauss at the start of the 19th century, and were considered relatively obscure mathematical constructions until Einstein realized, around 100 years later, they could be applied to space-time.

In summary, we appear to live in a universe in which Euclid's fifth postulate does not apply -- how cool is that

Morbert

Here's a question: Consider theories X and X'. It is not known whether or not X is consistent. If the consistency of X' is provable in X. Can we be sure that the inconsistency of X' is not provable in X?

My hunch is that the answer is yes. Though I don't really know enough about this area of maths.

Pygmalion

I believe that the set {1,2,3} is the same as the set {1,2,3}. (A simple application of the first axiom in ZFC)
I believe that the world was created in 6 days.

Both of the above are simply assumptions we're making about the world without proof, yes.

For some reason though I don't have a problem accepting the first one. :rolleyes:

Ah yes, gosplan said it before me, missed this post:

gosplan wrote: »

Is the key difference between 'faith' in axioms and 'faith' in religion not the overwhelming evidence that usually precedes mathematical assumptions.

i.e. Euclids first axoim states that a straight line can be drawn between any two points. It doesn't really require too much 'faith' to go along with that.

nozzferrahhtoo

I am a little confused. I have more maths qualifications than most people but I have to admit I am not much above the layman on it either.

But from what I know maths is nothing to do with faith, it is entirely defined from the beginning. WE define from the start what 1 means, what 2 means....

(Side note: Pygmalion has it right. 1, 2, 3 or any number is essentially, to be simplistic, what we define as meaning any set of elements that has the same number of elements as any other set of elements.)

There is no faith in this, we are the ones defining it from the very start. The fact that those definitions allow us to make certain tests and predictions is the heart of science. Tests and predictions are exactly what science is about.

So as I am saying, I am confused. I do not see where Faith comes into this at all. Not even a little.

Morbert

nozzferrahhtoo wrote: »

I am a little confused. I have more maths qualifications than most people but I have to admit I am not much above the layman on it either.

But from what I know maths is nothing to do with faith, it is entirely defined from the beginning. WE define from the start what 1 means, what 2 means....

(Side note: Pygmalion has it right. 1, 2, 3 or any number is essentially, to be simplistic, what we define as meaning any set of elements that has the same number of elements as any other set of elements.)

There is no faith in this, we are the ones defining it from the very start. The fact that those definitions allow us to make certain tests and predictions is the heart of science. Tests and predictions are exactly what science is about.

So as I am saying, I am confused. I do not see where Faith comes into this at all. Not even a little.

In a way, that's why I asked the question I did. I think, if the answer is yes, then no faith is required at all. But if the answer is no then the ground isn't quite as firm.

Enkidu

Mathematics is more like chess than a religion. The Zermelo-Fraenkel-Choice axioms are like the rules of a game. When I say that a bishop moves diagonally in chess I am not assuming this is true, I am in fact defining chess. Similarly the axiom of pairing (for example) defines Zermelo-Fraenkel-Choice set theory. There are other set theories just like there are other games.

The point of the axioms of set theory is that we want a foundational game. Take two areas of mathematics, differential geometry and group theory. If we want to use ideas from one in the other we need a rigorous way of applying them. This can only be done if differential geometry and group theory are two "subgames" of some "supergame". Set theory was created to be this supergame.

Enkidu

Morbert wrote: »

Here's a question: Consider theories X and X'. It is not known whether or not X is consistent. If the consistency of X' is provable in X. Can we be sure that the inconsistency of X' is not provable in X?

My hunch is that the answer is yes. Though I don't really know enough about this area of maths.

The answer is yes, if X proves X' is consistent then it can't prove X' is inconsistent.

Morbert

Enkidu wrote: »

The answer is yes, if X proves X' is consistent then it can't prove X' is inconsistent.

Cool, thanks. In other words, even if we don't know X is consistent, we can at least be sure that it is consistent regarding some things?

Enkidu

mikhail wrote: »

I only skimmed over this before, presuming that it an argument from all the old familiar places. Godel's theorem is extremely different from what you said. Wikipedia saves me from writing it out:

I'm fairly certain that Fremen's statement is a correct phrasing of Godel's second incompleteness theorem. If a system is capable of proving that it is consistent then it is in fact inconsistent for, by Godel's second incompleteness theorem, a consistent system cannot prove it is consistent.

All of this comes with the proviso that the system is "large" enough to contain the theory of the natural numbers. For example Euclidean geometry can be shown to be complete and consistent, it is capable of proving it's own consistency without being inconsistent. This is because it cannot simulate the natural numbers.

Enkidu

Morbert wrote: »

Cool, thanks. In other words, even if we don't know X is consistent, we can at least be sure that it is consistent regarding some things?

Yes, it will be consistent regarding its proof of the consistency of its own subsystems.

Of course, even though X is reliable in what it tells you about X', this still doesn't tell you anything about X', since X could be inconsistent.

Morbert

Enkidu wrote: »

Yes, it will be consistent regarding its proof of the consistency of its own subsystems.

Of course, even though X is reliable in what it tells you about X', this still doesn't tell you anything about X', since X could be inconsistent.

Did you mean " this still doesn't tell you anything about X "?

Enkidu

Morbert wrote: »

Did you mean " this still doesn't tell you anything about X "?

No, I mean X'. The proof of the consistency of X' given by X can only be valid if you take X to be consistent itself.

For instance I could use the theory of complex numbers to show the consistency of the real numbers and it will never give me another answer for that. Of course the complex numbers themselves may still be inconsistent and hence the proof of the consistency of the real numbers cannot be trusted as an absolute result but only a result consistent relative to the consistency of the complex numbers.

Morbert

Enkidu wrote: »

No, I mean X'. The proof of the consistency of X' given by X can only be valid if you take X to be consistent itself.

For instance I could use the theory of complex numbers to show the consistency of the real numbers and it will never give me another answer for that. Of course the complex numbers themselves may still be inconsistent and hence the proof of the consistency of the real numbers cannot be trusted as an absolute result but only a result consistent relative to the consistency of the complex numbers.

Ok, I think I get what you're saying. If X' is a subsystem of X and Y, consistency of X' in X does not necessarily imply consistency of X' in Y.

That seems fine by me. Mathematicians would need faith in claiming X' is absolutely consistent, but mathematicians never actually claim things like that for "large" systems.

Zombrex

Fremen wrote: »

I'm gonna play devil's advocate here and say that mathematics is based on faith. The modern foundation of mathematics is known as ZFC - the Zermelo Fraenkel axioms with the axiom of choice.

There's a theorem which says an axiomatic framework is inconsistent if and only if we can prove that it is consistent. That means it's impossible to demonstrate that you'll never come across a contradiction in your mathematics. Hence, one requires faith.

Any thoughts on that?

Faith in what?

I'm not a professional sums person (that is the technical term right?) but do you have to assume you won't come across a contradiction? If you don't then what are you putting faith in?

Enkidu

Morbert wrote: »

Ok, I think I get what you're saying. If X' is a subsystem of X and Y, consistency of X' in X does not necessarily imply consistency of X' in Y.

That seems fine by me. Mathematicians would need faith in claiming X' is absolutely consistent, but mathematicians never actually claim things like that for "large" systems.

Yes precisely, where "large" is "containing the natural numbers as a subsystem".

sponsoredwalk

Considering how basic/elementary the axioms and set theory are I don't
think it's fair to claim faith is involved. I mean do you have faith that a
geometric point exists? As far as I know there is no such thing as a point,
there is no such thing as a 2 dimensional line, it's a fundamental
abstraction that can't be reduced any further. Furthermore you take it on
faith that 2 + 2 = 4 because you're "belief" this occurs is based on a few
axioms and an operation, will it always be? I think it's always best to think
of these things as Enkidu said and think relative to what system. My
thinking is that if some fundamental aspect of set theory was shown to be
wrong it wouldn't invalidate everything about math it would just alter that
which it touches directly & seeing as there is so much consistency above
set theory you could at least argue that there is consistent subsystem.
If we're thinking about the real world a lot of it just doesn't seem to apply,
it seems as if there is a deducable size for this abstract geometric point
in nature & if this is found what does that say about the abstraction we
use? Is math a consistent system within itself but inconsistent with
respect to reality? Is reality is merely a subsystem of math that is
altered from the ideal situation?

Anyway, considering the situation today using the word "faith" is merely
cannon fodder for creationists & once they get hold of any idea, no matter
how foolish, they'll run with it. I think the main reason quantum mechanics
hasn't been exploited to it's full capability by them is simply because it's
too difficult to understand, we don't need them doing it with ZFC too
QM is popping up more and more lately!

https://www.youtube.com/watch?v=Wbiasg2xMIo

Cool Mo D

There is no "faith" in maths.

It doesn't matter if the axioms taken in mathematics are "true" or not in any bigger sense, it just isn't important. Absolutely anything could be taken as an axiom, it can have no relation to any kind of reality at all.

For example, if one of Euclid's postulates about geometry was shownto not describe our world at all, the maths would still be perfectly correct - it would not be an accurate description of geometry as we see it, but it would still be an accurate geometry under the axioms supposed.

Maths is simply a logical framework which illustrates what logically must be true given a set of axioms. If inconsistent axioms are given, contradictory answers will result. This is not "wrong" maths, however, but a logical consequence of inconsistent axioms.

Enkidu

Cool Mo D wrote: »

Maths is simply a logical framework which illustrates what logically must be true given a set of axioms. If inconsistent axioms are given, contradictory answers will result. This is not "wrong" maths, however, but a logical consequence of inconsistent axioms.

You can do even more than that. Not only only are the axioms flexible, but also the rules of logical deduction. For instance I can use ZFC with the standard rules of logic or ZFC with alternate rules of logic.

In general, in modern mathematics, we can move between different toposes. Standard ZFC is one topos, constructivist mathematics is another topos, e.t.c. so we have great freedom.

Enkidu

robindch wrote: »

Non-Euclidean geometries, btw, were first developed (but hushed up) by Gauss at the start of the 19th century, and were considered relatively obscure mathematical constructions until Einstein realized, around 100 years later, they could be applied to space-time.

In summary, we appear to live in a universe in which Euclid's fifth postulate does not apply -- how cool is that

The strange thing about Gauss was that he rarely published his ideas. There are indications that Gauss was on the way to discovering quaternions long before Hamilton did.
However non-Euclidean geometry proper was really developed by Bernhard Riemann.

Newaglish

Sorry, but I don't have a clue what this thread means nor what anyone is saying.

Just to clarify so that I understand, is the OP's post basically the following?
______________________________________

2 + 2 = 4

Does this mean that God exists?
______________________________________

If so, my answer is twofold:

1: No
2: What a ridiculous question

Now, someone may (in normal human people language) explain if I have misunderstood something?!

sponsoredwalk

I'm supposed to be studying one of his books but I'm tired & I thought I'd
finally read the big article online about him. I came across this:

Joseph Gerver, Rutgers University
I met Serge Lang in 1967, my sophomore year at
Columbia, when I took his multivariable calculus
class. This was before the days of unified calculus.
All of us were math majors and many of us were
spoiled by our high school experience of learning
math with very little effort. So Lang would frequently
throw chalk at us, or yell.
I often ate dinner at the Gold Rail with Richard
(now Susan) Bassein and Eli Cohen, and if Lang
was also eating there he would always join us and
usually pick up the tab. Sometimes we would talk
about math. Lang did not think logicians were true
mathematicians, because no real mathematician
would worry about whether a proof made use of
the axiom of choice. Why shouldn’t you use the
axiom of choice? It’s obviously true! Think about
it! How could you not be able to construct a set by
choosing one element from each set in a collection
of sets? Just do it!
http://www.ams.org/notices/200605/fea-lang.pdf

Goduznt Xzst

Newaglish wrote: »

2 + 2 = 4

Does this mean that God exists?

psst! Actually... 2 + 2 = 5 (for extremely large values of 2)

robindch

Enkidu wrote: »

There are indications that Gauss was on the way to discovering quaternions long before Hamilton did.

Just as well he didn't. Wouldn't have had anything to do last Saturday afternoon

nozzferrahhtoo

Newaglish wrote: »

Sorry, but I don't have a clue what this thread means nor what anyone is saying.

Just to clarify so that I understand, is the OP's post basically the following?
______________________________________

2 + 2 = 4

Does this mean that God exists?
______________________________________

If so, my answer is twofold:

1: No
2: What a ridiculous question

Now, someone may (in normal human people language) explain if I have misunderstood something?!

I am not sure it has anything to do with God. The OP is just trying to tell us that if you believe 2+2=4 then you have done this on faith. You are putting your faith in the meaning of the numbers 2 and 4, and in the meaning of the operations + and =.

However what it seems to me that the OP has missed is that there is no faith involved here because we ourselves have defined from the beginning what 2, 4, + and = actually mean. We do not have faith in what they might mean, we DECIDED what they mean.

It makes as much sense as saying that thinking one team gets a goal when a ball goes in the net is an article of faith when in fact it was us who defined the rules of that game.

In other words the OP could do with reading a book on Number Theory and what we actually mean by the numbers we use and how those numbers were defined based on “Sets”.

Amazotheamazing

Interesting documentary about Maths here, touches on both faith in maths and faith in religion.
http://www.youtube.com/watch?v=Cw-zNRNcF90

fergalr

Correct me if I'm wrong here, as I'm not really a mathematician, but...


I might say:
"What if the moon were made of cheese?"

Now, surely that statement doesn't require any 'faith'?
After all, I'm just saying 'what if'. I'm not claiming the moon is actually made of cheese.


Now, if someone came to me and told me 'the moon is made of cheese', then it'd require a lot of faith on my part to believe that person, considering what I already know about cheese, and moons.


But if they said 'What if the moon was made of cheese?' - well, they aren't saying it is - they are just saying 'lets play a game, where we pretend it is, and see what happens next?'

You might say "That's a stupid thing to be thinking about", and not want to play the game. Thats fine, its a matter of preference. But the key thing is that it doesn't require any faith to think about the moon being made of cheese, because we are just saying 'what if'.


We can go on from there.

You might say 'What if the moon was made of cheese? We could use it to feed astronauts!'

You could think about what else might be true, if it was true that the moon was made of cheese.
You might need to introduce other 'what ifs' for the game to be fun.
'What if the moon was made of cheese, and if astronauts could eat cheese, and if they landed on the moon, then they could eat the cheese!'


No one would be claiming that the moon is actually made of cheese, and no faith in this axiom would be required to play the game of figuring out what else might be true.



So it goes with maths.
You start out by defining a system, with a set of definitions that you pluck out of the air.
You make no claim that these definitions are true.
Instead you are saying 'Well, what if these things are true?'
And, like assuming the moon is made of cheese, this requires no faith. Theres nothing to have faith in!


Watch how euclid does it:

1. A point is that of which there is no part.
2. And a line is a length without breadth.
3. And the extremities of a line are points.
4. A straight-line is (any) one which lies evenly with points on itself.

http://farside.ph.utexas.edu/euclid/Elements.pdf

Lots of 'what ifs' - and he eventually gets on to talk about right angled triangles.


Claiming that the real world is similar to the funny game euclid decides to play definitely requires a lot of faith, or evidence, or experiment, or all three. And that's what physicists do.



Now, you have to be careful. And if there's a way of making this argument interesting, its here - its very easy to sneak things in that aren't properly defined, or defined from first principles, without meaning too.

Its also questionable on how solid of ground you can put the rules that you use to move from one true statement to the next.

And its very easy to assume too much, on faith, about how the maths relates to the real world.

Certainly, if the thread was called 'physics and faith' then, at a very low level, there might be questions to answer.

But if anyone is safe from this claim, for better or worse, then I reckon its the mathematicians.

ISAW

nozzferrahhtoo wrote: »

I am not sure it has anything to do with God. The OP is just trying to tell us that if you believe 2+2=4 then you have done this on faith. You are putting your faith in the meaning of the numbers 2 and 4, and in the meaning of the operations + and =.

I think a lot of confusion is about what we mean by "faith" in god and "faith" in science for example. It can be two different uses of the same word. The underlying thinkg might be different. this does not happen in formal languages ike mathematics.

what we actually mean by the numbers we use and how those numbers were defined based on “Sets”.

But even reducing mathematics or numbers to set theory can yield contradictions with basic axioms of set theory . Either that or the basic axioms of set theory aren't enough hence is "either inconsistent or incomplete"

THe OP point smacks of classic scepticism i.e. what do we actually believe exists?