For some reason people here like to stick Roman numerals on their houses, it keeps reminding me.Your mind could do with filling a bit more Flappie.I

oftenwonder how the Romans managed to multiply, but that's a bit offtopic.

# Mathematics

### #21

Posted 20 June 2005 - 10:59 AM

### #22

Posted 20 June 2005 - 11:06 AM

69 92

34 184

17 368

8 736

4 1472

2 2944

1 5888

Having crossed out 184, 736, 1472 and 2944 because they are opposite even values we add up the right-hand column to come to the answer:

92 + 368 + 5888 = 6348 which is 69 x 92.

**Edited by Adanac, 20 June 2005 - 11:07 AM.**

### #23

Posted 20 June 2005 - 11:09 AM

Skeptic could argue that language is not absolutely true, that any word that has ever been defined is not objectively true simply on the basis of the fact that words and their definitions are made up and defined by people, they are themselves axiomatic i.e. the word "apple" when referring to an apple doesn't need any more explanation, when I say "the apple fell to the ground", no one doubts my definition of the word apple, they take it that it is absolutely true by definition.

The whole of science would go belly up if not for mathematics, this computer I am writing to you would have been impossible to design without mathematics, so saying something is not "objectively true" does not mean anything when it has empirical applications. The fact that math works is self-evident truth, we accept a degree of error in our meaurements because in principle 'perfect' measurements are either impossible or there is a point beyond which it becomes useless for us to talk about it in it's application to our lives.

For instance we don't talk about objects in absolute technical terms, i.e. there is an apple, made of substance x, which is made of atoms, which are in turn made of protons, neutrons and electrons, etc, etc. We speak in terms of generalities, contexts and relationships.

**Edited by mordecai, 20 June 2005 - 11:21 AM.**

### #24

Posted 20 June 2005 - 11:24 AM

Are measurements objectively true? And if not, when I buy a bag of chips and it says 255grams and I weigh it and it turns out to be 255g. Then the measured amount of chips in the bag is not objectively true?

**Edited by mordecai, 20 June 2005 - 11:25 AM.**

### #25

Posted 20 June 2005 - 05:29 PM

So, we have established that it is valid to say 1+1=2, right.

Now, what if I were to ask you to say whether this is valid: 1+1=10....?

Of course not! Not if I am using the decimal* system anyway!

But if I was using the binary system it would be completely valid to say 1+1=10...!

Enough said?

But two in binary is denoted by "10" and it means double of one unit not ten times. In binary instead of counting 9 digits and then starting another column one place to the left(as we do in the decimal system) we start a new column after we've counted two digits(or something like that).Its not a case of 1+1 =2 is not absolute truth it still remains true in binary the only difference is the language used. In the same way un +un = deux is the same as one + one = two.

Does anybody agree with that or is philosophy just way above my understanding?

**Edited by medazelim, 20 June 2005 - 05:31 PM.**

### #26

Posted 20 June 2005 - 05:59 PM

I don't know to what extent notation should be considered mathematics.

DJP

### #27

Posted 20 June 2005 - 07:10 PM

What you have done here is committed the fallacy of equivocation. All we have here is an argument from ambiguity, not anything actually factual.So, we have established that it is valid to say 1+1=2, right.

Now, what if I were to ask you to say whether this is valid: 1+1=10....?

Of course not! Not if I am using the decimal* system anyway!

But if I was using the binary system it would be completely valid to say 1+1=10...!

Enough said?

This is actually semantics, not mathematics.

### #28

Posted 20 June 2005 - 07:29 PM

If you want real examples, I consider this easy to get into:

http://en.wikipedia....allel_postulate

(but to get the point of the discussion you have to get to the end and think about non Euclidean geometries which is pretty hard)

This is also not too hard:

http://en.wikipedia....d_(mathematics)

(it's got a steeper learning curve but is actually much easier than talking a whole lot about curved spaces)

Anybody who's done first year maths should be able to get into it.

DJP

### #29

Posted 20 June 2005 - 07:35 PM

### #30

Posted 20 June 2005 - 09:41 PM

What are you talking about?It still doesn't change the fact that the original argument was predicated on a logical fallacy.

Skeptic's given an analogy by way of example, and being an analogy, it wasn't perfect. I imagine Skeptic would agree. You've objected to his analogy, on the same grounds that I did. It doesn't prove that the "original argument was predicated on a logical fallacy." I don't even think that Skeptic has really presented an argument, except perhaps that he doesn't like mathematical realism.

And anyway, who says that semantics isn't mathematics?

DJP

### #31

Posted 20 June 2005 - 09:43 PM

I'm talking about the original argument.What are you talking about?It still doesn't change the fact that the original argument was predicated on a logical fallacy.

And anyway, who says that semantics isn't mathematics?

Oh of course, how could I have missed it?

### #32

Posted 21 June 2005 - 01:04 AM

DJP

### #33

Posted 21 June 2005 - 01:31 AM

What you have done here is committed the fallacy of equivocation. All we have here is an argument from ambiguity, not anything actually factual.So, we have established that it is valid to say 1+1=2, right.

Now, what if I were to ask you to say whether this is valid: 1+1=10....?

Of course not! Not if I am using the decimal* system anyway!

But if I was using the binary system it would be completely valid to say 1+1=10...!

Enough said?

This is actually semantics, not mathematics.

With hindsight, yes: in trying to provide an example that people, who had difficulty with the original argument, could follow, I fell into the trap of using a completely irrelevant example.

I retract that example and thank you, medazalim, for pointing out the problem with it. DJP, thanks for providing links to better examples.

However, I stand by my original argument, which is that

**at the level of axioms, mathematics cannot be said to be "true".**

Fortigurn, do you also disagree with my original argument? It is clear that my original argument isn't based on equivocation or any other fallacy which I can identify, so if you disagree with that, you have to point out why. Remember, I said that at the level of axioms, mathematics cannot be said to be true. Dealing with mathematics at the level of axioms takes us to the Philosophy of Mathematics, which is a meta-perspective. Remember, we know that non-logical axioms refer to a priori propositions that are only valid for a

*given*mathematical theory. They are theory specific. They do not "work" in other, equally valid theories - theories, which, taken togetherm kae up the body of knowledge of mathematics. Non-logical axioms do not satisfy all conditions in all possible universes. Non-logical axioms outnumber logical ones in modern mathematics.

To summarise: mathematics rely on logical and non-logical axioms. Non-logical axioms aren't universally true; they are only "true" within a given theory. Non-logical axioms constitute the majority of axioms in modern mathematical theory. What does that tell you?

Mordecai and others, who keep pointing out that mathematics work, are all correct. But the issue of whether mathematics works or not, was never in dispute.

**At the level of pragmatics**it is abundantly clear that mathematical models that satisfy the requirements of mathematical validity (even if they contradict other equally valid mathematical models) are all "true" (although I prefer the word "valid").

**At the level of axioms,**mathematics cannot be said to be "true".

**Edited by Skeptic, 21 June 2005 - 01:42 AM.**

### #34

Posted 21 June 2005 - 01:44 AM

With that statement? It may be true, it may not be true. It may be true and not true simultaneously. I have no idea.However, I stand by my original argument, which is that

at the level of axioms, mathematics cannot be said to be "true".

Fortigurn, do you also disagree with my original argument?

It is clear that my original argument isn't based on equivocation or any other fallacy which I can identify, so if you disagree with that, you have to point out why.

I was referring to the original hilarious (and incredibly relevant), argument that 1+1 /= 2.

### #35

Posted 21 June 2005 - 01:46 AM

It was the deliberate confusion of these two which constituted the original fallacy of equivocation.

At the level of pragmaticsit is abundantly clear that mathematical models that satisfy the requirements of mathematical validity (even if they contradict other equally valid mathematical models) are all "true" (although I prefer the word "valid").At the level of axioms,mathematics cannot be said to be "true".

### #36

Posted 21 June 2005 - 02:00 AM

With that statement? It may be true, it may not be true. It may be true and not true simultaneously. I have no idea.However, I stand by my original argument, which is that

at the level of axioms, mathematics cannot be said to be "true".

Fortigurn, do you also disagree with my original argument?

OK, that's an honest answer and completely acceptable.

### #37

Posted 21 June 2005 - 02:12 AM

I still don't know what the original argument is. I'm interested to find out.

Here it is:

Dealing with mathematics at the level of axioms takes us to the Philosophy of Mathematics, which is a meta-perspective.

First set of statements:

1) Modern mathematics consist of a collection of theories which together constitute the body of knowledge of mathematics.

2) These mathematical theories can be valid individually, even whilst contradicting other, equally valid theories in mathematics

Second set of statements:

3) Non-logical axioms refer to a priori propositions that are only valid for a given mathematical theory; they are theory specific; they do not "work" in other, equally valid theories

4) Non-logical axioms do not satisfy all conditions in all possible universes.

5) Non-logical axioms outnumber logical ones in modern mathematics.

Based on the the above, the conclusion is: at the level of axioms, mathematics cannot be said to be true.

Anyone who can show any of the statements (propositions) above to be false, or the conclusion to be false, can falsify the argument.

### #38

Posted 21 June 2005 - 02:24 AM

Fortigurn

With that statement? It may be true, it may not be true. It may be true and not true simultaneously. I have no idea.However, I stand by my original argument, which is that

at the level of axioms, mathematics cannot be said to be "true".

Fortigurn, do you also disagree with my original argument?

OK, that's an honest answer and completely acceptable.

### #39

Posted 21 June 2005 - 02:52 AM

Would you consider 2 = 0 to be a hilarious idea?I was referring to the original hilarious (and incredibly relevant), argument that 1+1 /= 2.

DJP

### #40

Posted 21 June 2005 - 03:34 AM

Disagree. The same could be said of physics, but what a physicist would [try to] do is construct a bigger theory that contains both. Why not regard maths the same way?2) These mathematical theories can be valid individually, even whilst contradicting other, equally valid theories in mathematics

DJP

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