The Australian philosopher colin leslie dean points out that mathematicians cannot tell us what a true statement is.
Truth is a tricky problem
In mathematics the old idea of “true” was that of Hilbert who believed that
a true statement was one proven from axioms
Now since Godel made a distinction between a proven statement and a true statement mathematicians are at a loss to tell us what a true statement is
Godel noted a true statement was independent of provability by his
distinction
Mathematicians now need a definition of a true statement independent of provability but they cant give us that definition of true independent of provability
as mathematician cant tell us what a true statement is
as following Godel there are proven statements and true statement
but they cant tel us what a true statement in mathematics is
they can tell us they can prove
1+1=2
but
they cant tell us why it is true
for since Godel provability is not a criteria for truth
but they cant tell us what this criteria for truth is now with the collapse of the Hilbert idea
THUS THERE IS NO “TRUE” STATEMENTS IN MATHEMATICS ONLY PROVEN ONES
What mathematicians call “true” is always “true, if the axioms upon which it rests are true” - at a minimum. We have known this and been explicitly aware of this at least since Peano. But really, for centuries.
ladyjane, you really need to get out more. This Dean guy is waaaaay behind the curve. If this is news, then so is “Romans invade Palestine”.
ladyjane - your thesis is that there are no true statements in mathematics. That has been known for a long time, since before this Dean guy was born. That’s my point. What the heck is yours?
Maths is a language like english or japanese. The statements truth depends on how well it describes reality.
Maths is just made up we can invent whatever rules we want. In this way we are free to make any statement be true or false within the mathematical language. by within the language I mean its totally abstract we’re just making up rules and using them to prove statements it doesn’t matter its just symbols. The question is can we create a set of rules, a mathematical language that can describe the world to help us do things like build cars, bridges, computers or predict the stock market. If we can then great the maths is useful yay woo! On the other hand if we a mathematical language that has no use then thats ok its not right or wrong its just not useful.
Bottom line maths on its own is meaningless but it can be useful to describe things that do have meaning. “x = a + b” is just a statement its just some symbols its neither true or false because its just an abstract set of 4 symbols. But if we say that
x means number of people in the football stadium
= means equals
a means number of men in the football stadium
means added to
b means number of women in the football stadium
we see that the statement describes reality too atleast a good approximation. Maybe theres some hermaphrodites in the stadium! That is a serious point though using “x= a + b” we may get the answer to the question how many people are in the stadium slightly wrong. But its atleast a useful approximation depending on why you would want to know the answer.
Huh? beacuse I didn’t. Its a perfectly fine equation. I choose x = a + b beacuse it was easy to think of a meaningful example that it could describe. whats your point?
My point is… that truth… necessarily must have SOME part in any rational system.
And, if we’re going to insist on rationality, then I can only hope Mr. Dean has something relevant to say that will help us out of this apparent dilemma!
I wonder if Amazon has any of his writings?
Either that… or I could perhaps… discount him out of hand as being…obsolete, or “behind the curve.”
I’m just a farm boy from NC though… what do I know?
oh really then what does godel mean by true statements in his first incompleteness theorem if there are no true statements in maths
by your account godels theorem then is meaningless as he tells us there are true statements which cant be proven- seeing there are no true statement according to you then his theorem is just babble
sorry there is no way out
rationality ends in meaninglessness
all products of human thinking ie science maths philosophy end in self contradiction or meaninglessness
dean does not publish his books through capitalist enterprises amazon can go fu,k them selves
if you want deans books
go here and download them FREEEE
then can the equation I posited ever be meaningful?
X - X = X
If it cannot ever be meaningful, then you’re admitting that a standard exist by which to judge something as meaningful or meaningless, hence concluding that there are indeed meaningful equations to which it can be compared.
If you say that it CAN be meaningful, then you refute yourself outright.
I’m probably talking out of my hind parts here, so forgive me for my ignorance of proper terminologies. It’s just that, I’m a little confused on this point.
And, thanks for the link to Ms. Jane. I’ll have to take a look at it while I’m working tomorrow (gov. tax dollars at work!)
from
Shotgun
who could have sworn the internet itself was a form of capitalistic enterprise.
Janie - what I am saying is that there are no unqualifiedly true statements and that this has been known for many years. I metnion it only because you are continulally posting about this as if it’s urgent news that the world should hear. Every educated person has already heard it.
It would be much more interesting to hear what ramifications you may draw from this fact. I am curious myself why this is even important to you. Or to me.
Godel was very popular among the populace. I do not know that he shook the earth under actual, mathematicians, qua mathematicians.
I would say that neither statement is true or false but they are inconsistant. And so if we have to except them both as true we cannot give the symbols (x, =, -) their usual meaning.
I think you need to look at this in a slightly different way. But for that you have o understand what a formal system is.
Baically within a system we start with some axioms and then have rules to manipulate the axioms to create statements. Every statement we create has been proven within the system. But at this point we don’t have to give the symbols any kind of meaning. Once we give them meaning however we can then see if their are any inconsistancies.
With statements like x = a + b we automatically interprete this to be a statement about numbers. Hence there is some kind of description that we can think of to give x = a+ b meaning. Ofcourse we could argue that there is meaning in the completely abstract statement “a number X equals a number A plus a number B”. But does it only appear to have meaning because we are so used to seeing how that equation can describe things in reality; beause we are so used to counting things. I guess this is plato vs non-plato. Do numbers themselves have existence and meaning or is it just what they describe that has meaning?
I think I used to be more of a platonist and now I’m more undecided.
!