A new math

[olavisjo]

This topic is for discussing errors in our current understanding of math.

[Divine Insight]

The problem with our current understanding of the concept of number is that it is "ill-defined".

Now, before I continue allow me to put this in the framework of a logical conditional statement:

"IF modern mathematical formalism is supposed to correctly describe the quantitative nature of our physical universe, THEN our current modern mathematical formalism is wrong".

Now let me further break this down for those who may be unfamiliar with how conditional statements like this work.

After the IF statement follows a hypothesis or proposition often denotes symbolically as P.

In this conditional statement P = "modern mathematical formalism is supposed to correctly describe the quantitative nature of our physical universe"

If you believe P to be TRUE, then you have reason to be concerned with what conclusion I am drawing from this in the second half of this conditional statement.

If you believe P to be FALSE, then you have no reason to care what is said in the second half of the conditional statement. In fact, if you believe P to be FALSE, then you have no reason to care about anything I have to say on this subject matter.

However, if you believe P to be TRUE, then we can move forward in a meaningful way to address my proposed conclusion.

~~~~~

The second half of this conditional statement following the THEN statement is the conclusion that I hold to be TRUE. This is called the conclusion traditionally symbolized by the letter Q.

If, and only if, you have accepted P to be TRUE, do you have any reason to be interested in Q.

In my conditional statement Q = "Our current modern mathematical formalism is wrong"

It is my job then to show that IF P THEN Q is true.

Remember if you disagree with P, or believe P to be FALSE, then arguing over whether or not Q is true is superfluous.

So anyone who argues with me concerning the truth value of P already doesn't understand how logic and mathematics works.

All you need to do is simply state, "I don't accept the P is true", and you're done. There is absolutely no point in arguing any further beyond that.

The only people who should be interested in what I have to say are the people who are willing to accept the TRUTH of P as a valid premise, hypothesis, or proposition. Only then should they be concerned with the truth value of Q.

~~~~~
More on P

Now having said the above I would be willing to offer reasons why I believe P should be true. And those are discussions concerning P = "modern mathematical formalism is supposed to correctly describe the quantitative nature of our physical universe"

I can't "prove" that P must be true. On the contrary, P is open to your own subjective opinion and evaluations, based on whether or not you believe mathematics should correctly describe the quantitative nature of our physical universe.

There are many mathematicians (far too many IMHO) who don't accept that P should be true or even needs to be true.

Obviously I disagree with that view. But like I say, that view is basically nothing more than a subjective opinion and cannot be proven one way or the other.

Having said this I am willing to offer my reasons for believing that mathematical formalism should properly describe the quantitative nature of our physical universe. But I can only hope to convince people of this on common sense grounds. It can't be "proven" because there is no law written in the stars of what mathematical formalism has to be. Mathematical formalism is an invention of mankind and therefore we can basically chose to make it into whatever we so choose.

~~~~~

And now on to Q

Once it has been accepted the P should indeed be true, then I can show why Q is necessarily true.

~~~~

Further Related Information

It might also be useful to know how people view the concept of number in general and how they believe it to be defined.

Please check the following thread for discussions on the meaning and definition of number. Thank you.

On the definition of number

[olavisjo]

.

If you believe P to be FALSE, then you have no reason to care what is said in the second half of the conditional statement. In fact, if you believe P to be FALSE, then you have no reason to care about anything I have to say on this subject matter.

I choose this option for the simple reason that reality can do whatever it wants, it does not need to conform to logic, reason, math or anything else. Humans create mathematical relationships that for some strange reason just happen to correspond to reality, the reason for this correlation of math and reality is a great mystery to me.

[micatala]

The problem with our current understanding of the concept of number is that it is "ill-defined".

Now, before I continue allow me to put this in the framework of a logical conditional statement:

"IF modern mathematical formalism is supposed to correctly describe the quantitative nature of our physical universe, THEN our current modern mathematical formalism is wrong".

Now let me further break this down for those who may be unfamiliar with how conditional statements like this work.

After the IF statement follows a hypothesis or proposition often denotes symbolically as P.

In this conditional statement P = "modern mathematical formalism is supposed to correctly describe the quantitative nature of our physical universe"

If you believe P to be TRUE, then you have reason to be concerned with what conclusion I am drawing from this in the second half of this conditional statement.

If you believe P to be FALSE, then you have no reason to care what is said in the second half of the conditional statement. In fact, if you believe P to be FALSE, then you have no reason to care about anything I have to say on this subject matter.

However, if you believe P to be TRUE, then we can move forward in a meaningful way to address my proposed conclusion.

~~~~~

If one believes, or in fact, knows P to be false, then yes, one could consider the entire statement to be irrelevant.


If you really are only interested in the truth of the conditional statement, then yes, you can ignore whether P is really true or not.

However, if you are interested in the truth of the conclusion as a general statement, then the truth of P is relevant. P and (If P then Q) implies the truth of Q.



Are you really saying you are NOT arguing for the truth of Q?



As far as the truth of P goes, well, you may certainly feel free to avoid defending it as long as you make no claim regarding the truth of Q.


But if you are really going to assert the truth of Q, then I will challenge you to provide evidence for P. Frankly, I think it is probably false and could be shown to be false by looking at the history of "modern mathematical formalisms."

In fact, you do not even need to look at modern formalisms. The Greeks engaged in plenty of mathematics without caring the slightest whether it said anything about the real world or not. So did Fermat and Pascal.

[JohnA]

The problem with our current understanding of the concept of number is that it is "ill-defined".

Now, before I continue allow me to put this in the framework of a logical conditional statement:

"IF modern mathematical formalism is supposed to correctly describe the quantitative nature of our physical universe, THEN our current modern mathematical formalism is wrong".

Now let me further break this down for those who may be unfamiliar with how conditional statements like this work.

After the IF statement follows a hypothesis or proposition often denotes symbolically as P.

In this conditional statement P = "modern mathematical formalism is supposed to correctly describe the quantitative nature of our physical universe"

If you believe P to be TRUE, then you have reason to be concerned with what conclusion I am drawing from this in the second half of this conditional statement.

If you believe P to be FALSE, then you have no reason to care what is said in the second half of the conditional statement. In fact, if you believe P to be FALSE, then you have no reason to care about anything I have to say on this subject matter.

However, if you believe P to be TRUE, then we can move forward in a meaningful way to address my proposed conclusion.

~~~~~

The second half of this conditional statement following the THEN statement is the conclusion that I hold to be TRUE. This is called the conclusion traditionally symbolized by the letter Q.

If, and only if, you have accepted P to be TRUE, do you have any reason to be interested in Q.

In my conditional statement Q = "Our current modern mathematical formalism is wrong"

It is my job then to show that IF P THEN Q is true.

Remember if you disagree with P, or believe P to be FALSE, then arguing over whether or not Q is true is superfluous.

So anyone who argues with me concerning the truth value of P already doesn't understand how logic and mathematics works.

All you need to do is simply state, "I don't accept the P is true", and you're done. There is absolutely no point in arguing any further beyond that.

The only people who should be interested in what I have to say are the people who are willing to accept the TRUTH of P as a valid premise, hypothesis, or proposition. Only then should they be concerned with the truth value of Q.

~~~~~
More on P

Now having said the above I would be willing to offer reasons why I believe P should be true. And those are discussions concerning P = "modern mathematical formalism is supposed to correctly describe the quantitative nature of our physical universe"

I can't "prove" that P must be true. On the contrary, P is open to your own subjective opinion and evaluations, based on whether or not you believe mathematics should correctly describe the quantitative nature of our physical universe.

There are many mathematicians (far too many IMHO) who don't accept that P should be true or even needs to be true.

Obviously I disagree with that view. But like I say, that view is basically nothing more than a subjective opinion and cannot be proven one way or the other.

Having said this I am willing to offer my reasons for believing that mathematical formalism should properly describe the quantitative nature of our physical universe. But I can only hope to convince people of this on common sense grounds. It can't be "proven" because there is no law written in the stars of what mathematical formalism has to be. Mathematical formalism is an invention of mankind and therefore we can basically chose to make it into whatever we so choose.

~~~~~

And now on to Q

Once it has been accepted the P should indeed be true, then I can show why Q is necessarily true.

~~~~

Further Related Information

It might also be useful to know how people view the concept of number in general and how they believe it to be defined.

Please check the following thread for discussions on the meaning and definition of number. Thank you.

On the definition of number

If P then Q is not an argument.

You need at least two premises (2 P's), to make a conclusion Q. And you need to show that Q in not a non sequitur.

Since you admitted that you only have one P can not be shown true or false, and you have no other premise, we can reject your claim as a invalid unsound argument, thus not an argument at all.

But this seems to me just your own way of "DI mystical experience" where you want to substitute accepted logic/reasoning for your own system of logic.

There you have it. Philosorcery at its best.

BTW, Wikipedia says a number is:
A number is a mathematical object used to count, label, and measure.

Google says:
number
ˈnʌmbə/
noun
plural noun: numbers

1.
an arithmetical value, expressed by a word, symbol, or figure, representing a particular quantity and used in counting and making calculations.
"think of a number from one to ten and multiply it by three"
synonyms: numeral, integer, figure, digit; More

2.
a quantity or amount.
"the company is seeking to increase the number of women on its staff"
synonyms: amount, quantity; More


Now, what is your issue with this definition? Oh, you reject dictionaries, so you are want your own definition. What is this definition, your definition of 'number', the 'DI number'?

[Divine Insight]

Are you really saying you are NOT arguing for the truth of Q?

Of course I'm arguing for the truth of Q. But only relative to the truth of P.

In other words, it's meaningless to even argue for the truth of Q if you already reject the truth of P.

This is precisely why I have placed this in this conditional statement as I have.

As far as the truth of P goes, well, you may certainly feel free to avoid defending it as long as you make no claim regarding the truth of Q.

I have no need to defend P. If you reject P, then I couldn't care less about your opinions, and you couldn't care less about mine. So if you reject P then there is no point in any further conversation between us on this topic.

This is precisely why I've placed it in this format of a conditional statement. To avoid useless arguments. If you reject P, fine. You are free to do so. However, if you reject P, then you couldn't care less about the truth of Q.

But if you are really going to assert the truth of Q, then I will challenge you to provide evidence for P. Frankly, I think it is probably false and could be shown to be false by looking at the history of "modern mathematical formalisms."

Of course it's false in terms of the history of modern mathematical formalism. That's my whole point. I'm saying that mathematicians have made a "wrong turn", if any only if, you accept the truth of P.

If you reject the truth of P, then you automatically confess that mathematics does not need to correctly describe the quantitative nature of the universe. That's precisely what you have already rejected.

In fact, you do not even need to look at modern formalisms. The Greeks engaged in plenty of mathematics without caring the slightest whether it said anything about the real world or not. So did Fermat and Pascal.

And with respect to my conditional statement then they have already rejected P.

In other words, they have already rejected the idea that mathematics should correctly describe the quantitative nature of the physical universe.

So, fine. They have rejected P.

Anyone who rejects P, has already confessed that they don't care whether mathematics correctly describes the quantitative nature of the universe or not.

This is what P is all about and why I have placed it where it is in this conditional statement.

To argue over P is silly and quite futile. I have no desire to argue with people over the truth of P.

If they conceded that mathematics does not need to correctly describe the quantitative nature of the physical universe, then they have already admitted that they don't care about this.

What surprises me is why any scientist would be comfortable with P.

[Divine Insight]

If P then Q is not an argument.

You need at least two premises (2 P's), to make a conclusion Q. And you need to show that Q in not a non sequitur.

Since you admitted that you only have one P can not be shown true or false, and you have no other premise, we can reject your claim as a invalid unsound argument, thus not an argument at all.

You're right John. If P then Q is NOT an argument.

Where have I ever claimed that it was?

Clearly you are not understanding at all.

I've simply offered you this conditional statement. I suggest that if you accept that P is true, then I can show that Q is also true.

I haven't made any arguments toward that end at all.

If you reject P, then you have no interest in discussing anything with me further, moreover, by rejecting P you also confess that you don't care whether mathematics correctly describes the quantitative nature of physical reality at all.

So, fine. I accept that and I have no more interest in discussing the topic with you any further at that point. This is precisely why I begin with this conditional statement. To weed out those who don't care whether mathematics correctly describes the quantitative nature of the physical universe. If you don't care about that, then I have no interest in conversing with you any further.

That's the very purpose of this conditional statement.

But this seems to me just your own way of "DI mystical experience" where you want to substitute accepted logic/reasoning for your own system of logic.

There you have it. Philosorcery at its best.

This is a perfectly legitimate use of a conditional logic statement. It is totally in accordance with all of the formal rules of logic.

If you reject P, then why are you bothering to continue to argue with me at all?

Don't you even understand the basics of this conditional statement?

BTW, Wikipedia says a number is:
A number is a mathematical object used to count, label, and measure.

Google says:
number
ˈnʌmbə/
noun
plural noun: numbers

1.
an arithmetical value, expressed by a word, symbol, or figure, representing a particular quantity and used in counting and making calculations.
"think of a number from one to ten and multiply it by three"
synonyms: numeral, integer, figure, digit; More

2.
a quantity or amount.
"the company is seeking to increase the number of women on its staff"
synonyms: amount, quantity; More


Now, what is your issue with this definition? Oh, you reject dictionaries, so you are want your own definition. What is this definition, your definition of 'number', the 'DI number'?

Neither of those "definitions" are mathematically rigorous. Moreover, they both use terms like "quantity" and "counting" without having even mentioned what these other terms actually mean.

Look at #2 "a quantity or amount". Well, duh? Is that the definition of number? A quantity or amount? A quantity or amount of what?

Do you even have a clue how number is actually defined within mathematical formalism? And do you have any idea how many different formal definitions there actually are for the concept of number within mathematical formalism?

[JohnA]

If P then Q is not an argument.

You need at least two premises (2 P's), to make a conclusion Q. And you need to show that Q in not a non sequitur.

Since you admitted that you only have one P can not be shown true or false, and you have no other premise, we can reject your claim as a invalid unsound argument, thus not an argument at all.

You're right John. If P then Q is NOT an argument.

Where have I ever claimed that it was?

Clearly you are not understanding at all.

I've simply offered you this conditional statement. I suggest that if you accept that P is true, then I can show that Q is also true.

I haven't made any arguments toward that end at all.

If you reject P, then you have no interest in discussing anything with me further, moreover, by rejecting P you also confess that you don't care whether mathematics correctly describes the quantitative nature of physical reality at all.

So, fine. I accept that and I have no more interest in discussing the topic with you any further at that point. This is precisely why I begin with this conditional statement. To weed out those who don't care whether mathematics correctly describes the quantitative nature of the physical universe. If you don't care about that, then I have no interest in conversing with you any further.

That's the very purpose of this conditional statement.

But this seems to me just your own way of "DI mystical experience" where you want to substitute accepted logic/reasoning for your own system of logic.

There you have it. Philosorcery at its best.

This is a perfectly legitimate use of a conditional logic statement. It is totally in accordance with all of the formal rules of logic.

If you reject P, then why are you bothering to continue to argue with me at all?

Don't you even understand the basics of this conditional statement?

BTW, Wikipedia says a number is:
A number is a mathematical object used to count, label, and measure.

Google says:
number
ˈnʌmbə/
noun
plural noun: numbers

1.
an arithmetical value, expressed by a word, symbol, or figure, representing a particular quantity and used in counting and making calculations.
"think of a number from one to ten and multiply it by three"
synonyms: numeral, integer, figure, digit; More

2.
a quantity or amount.
"the company is seeking to increase the number of women on its staff"
synonyms: amount, quantity; More


Now, what is your issue with this definition? Oh, you reject dictionaries, so you are want your own definition. What is this definition, your definition of 'number', the 'DI number'?

Neither of those "definitions" are mathematically rigorous. Moreover, they both use terms like "quantity" and "counting" without having even mentioned what these other terms actually mean.

Look at #2 "a quantity or amount". Well, duh? Is that the definition of number? A quantity or amount? A quantity or amount of what?

Do you even have a clue how number is actually defined within mathematical formalism? And do you have any idea how many different formal definitions there actually are for the concept of number within mathematical formalism?

Oh, I forgot again, I need to factor in your 'DI obscurantism'.

A conditional logic statement is not an argument. Similar, there are problems with using a math concept in the English language (http://en.wikipedia.org/wiki/Material_c ... onditional). You have an issue with Math, but you use it to formulate "arguments"? How bizarre. There you have it. So, no matter how much you regurgitate your math based conditional statement in English language, it can not and will make make any sound logical conclusions.

As for Math and describing reality:
micatala answered it here, and I agree:
http://debatingchristianity.com/forum/v ... 801#606801
And I want to add:
Math is just a 'tool' used by science, it is one of the languages of science.
"If all of mathematics disappeared, physics would be set back by exactly one week." --- Richard P. Feynman (1918 - 1988)


On the number thing.
You have not answered my question:
Now, what is your issue with this definition? Oh, you reject dictionaries, so you are want your own definition. What is this definition, your definition of 'number', the 'DI number'?

Look at #2 "a quantity or amount". Well, duh? Is that the definition of number? A quantity or amount? A quantity or amount of what?

Did you read it: Here goes again:
"the company is seeking to increase the number of women on its staff"
"they received a large number of complaints"

If you have no definition and you can not show why the definitions provided should not be rejected then your number 'argument' falls flat as well.
Notice the above, it has two premises and one conclusion. It is a valid sound argument.

Now, try to answer the questions without straw man and red herring "DI logical fallacies".

[Divine Insight]

@ JohnA.

I have offered you the following:

P = "modern mathematical formalism is supposed to correctly describe the quantitative nature of our physical universe"

You have rejected this as being irrelevant or false.

I accept your position on this and therefore we have nothing further to discuss.

You concede that modern mathematics does need to correctly describe the quantitative nature of our physical universe.

If that's your position I have no desire to try to convince you otherwise.

I'm more than willing to simply agree to disagree with you at this point.

This is the very purpose of this conditional statement. There is no point in wasting my time arguing with people who have already conceded that mathematics does not need to correctly describe the quantitative nature of the universe.

[keithprosser3]

As I understand it, DI is moaning about the way that mathematics has become abstracted away from any requirement to describe the 'physical world'.

But that is the great strength of maths! For example, when physicists started to realise the world was not Euclidean the mathematicians had already laid the ground work for them. The mathematicians could suggest the solution to the physicists because mathematicians had been playing with curved spaces for ages before any practical application was imagined for them. The same could be said for many of the mathematical tools physicists use.

The problem is we don't yet know what the nature of physical reality is, so we don't know what the best sort of mathematics to describe it will be. If we limit mathematicians to work only within what we think is the case today, we might well have the vision or tools to solve the next problem.

Maths is abstract. That has its plus side and its minus side, but on balance I think DI will have to get to love mathematics as it is, rather than mathematics adapting to DI on this one.