Refute me babies!

[Kuciwalker]

Modular mathematics is a self-consistent mathematics which is most accessably described as clock mathematics. A 12-hour clock is basicaly mod 12. 10am + 4 = 2pm

In mod 2, 1+1 would equal 0.

I just realized how this isn't internally consistant - in it, 1 = -1.

[DaShi]

I'll be blunt. This thread has gang rape written all over it.

[Ramo]

I just realized how this isn't internally consistant - in it, 1 = -1.

That's not internally inconsistent at all.

[Peter Triggs]

Whaleboy says: "(i.e., 1+1=2, relies on certain rules, which though variances almost inconceivable to us, are not intrinsically unchangable)."

To which Skywalker replies: "I would argue that this is false, that there is NO internally consistent mathematical system in which 1 + 1 != 2."

Whaleboy might be talking gibberish and Skywalker's reply could have been better phrased, but it seems to me that they're both talking about natural numbers, i.e. Peano Arithmetic. Immortal Wombat's example of a two element algebra where 1+1=0 does contradict what Skywalker said, but not what he meant to say (forgive me for putting words in you're mouth, Skywalker).

Is there a known consistant mathematics where 1+1 != 2?

An abstract algebra? Sure, you just gave one. But the preferred notation is more like "1+1=0 mod 2" which makes it clear that you're not talking about ordinary arithmetic. Likewise with Ramo's examples:

If you want to keep the current structure of math totally intact (with minimal changes), it's pretty easy. For instance, you could start calling the multiplicative identity under complex numbers "0" and the additive identity "1," and then in any given theorem switch around "0" and "1." Which would make 1 + 1 = 1. Or you could assign the properties of division to "+" and addition to "/" and then in any given theorem switch around "+" and "/." Which would also make 1 + 1 = 1.

I think you're going to have some difficulty selling this to the mathematical community.

[Whaleboy]

I'll be blunt. This thread has gang rape written all over it.

Thats the way I like it

I'll come back to your points when I have free time... still at college

[Kuciwalker]

If you want to keep the current structure of math totally intact (with minimal changes), it's pretty easy. For instance, you could start calling the multiplicative identity under complex numbers "0" and the additive identity "1," and then in any given theorem switch around "0" and "1." Which would make 1 + 1 = 1. Or you could assign the properties of division to "+" and addition to "/" and then in any given theorem switch around "+" and "/." Which would also make 1 + 1 = 1.

All you did is switch the symbols "1" and "0". I could use "flourescent" to represent the number 1, and it would have as much significance.

[Kuciwalker]

Originally posted by Ramo

I just realized how this isn't internally consistant - in it, 1 = -1.

That's not internally inconsistent at all.

Uh... yes it is. That's like saying P implies !P is also internally consistent

[Immortal Wombat]

No it isn't. That'd be 1 = 0. Crazy man! Imagine a circular number line. 1 = -1. So what, if the axioms still hold, all is cool.

[Ben Kenobi]

Skywalker:

No. How does that apply?

I originally wanted to refute just you, because I felt the example worked better for your post than for Whaleboy's, but it's taken new life of it's own.

However, there is no objective way to observe this code,

If there is no objective way to observe this code, why is this man crazy?

[Ben Kenobi]

Thanks Ben. It's nice to see you still around. I must say that Alec Guinness looks pretty spiffy in that hat.

You must be pumped at the prospect of the new Canadian Conservative Party.

Yep. Post in the Canadian politics thread... It's a few pages down.

[Whaleboy]

Anyway, it's good to see that you are still philosophizing. I may not agree with everything you say, but I admire your ambition.

Thankyou! that’s a very nice thing to say!

Try to stick with propositions.

Hmmm, regarding philosophy as an art would seem to imply a literal approach, that as a writer I am adopting, but for the sake of this debate and forum, I’ll keep to propositions. Still, metaphorical embellishments and illustrations never hurt anyone

I don't know if they are equally valid, unless you mean by that "equally meaningless".

Since values are regarded as 0, considering that one needs predispositions to assign a value, which will then vary per subjective, I think you have pretty much hit the nail on the head there. This has implications for any epistemological or ethical interpretation of this idea, if not sociological of course, but relativism seems to indicate a solution there. Admittedly, its practically inapplicable at this stage, but more on that in a bit….

And if that is the case, doesn't this mean that if I can really disagree with someone that it is also logically possible for me to determine who is right. If I don't understand what has to be the case in the world for the relation "higher than" to be true of something, doesn't this mean that I don't understand the term?

Well that would imply that you are able to emulate their point of view and work within that, “emulating pseudo-objectivity” is the term I use. I remember a debate we had a while ago about communication (on a similar topic to this), that would seem to confirm this approach. This is an intrinsically rational and sentient thing to do imo, but in terms of simply opposed ideas, you still need to understand that term (presumably as a predisposition), in order to make that judgement.

None of this has anything to do with subjectivity or conceptual relativism. In fact conceptual relativists can't really disagree with each other either, since the objects of their beliefs are untranslatable propositions.

I disagree, since both conceptual relativists and subjectivists have thus far made no reference to perspective-based objectivity, or indeed context. That’s better explained when I address Drogues points.

You have shown that alchemy and quantum mech has a use. So some things that used to be metaphysics are not applicable. Is any metaphysics now applicable? That is what you haven't shown, IMHO.

I intend to show that what is now physics, indeed, applied in every day terms, technological applications and modern philosophy and ethics, was once metaphysics and ethics (the former often leading to the later, as is the case with much moral philosophy, the only exception I can think of off hand is Virtue theory, which as I’m sure we can all agree, unequivocally sucks ).

I wont answer all of your points directly now because time is a concern (at college again, in library, lesson soon, requires faked sick note to be with female friend ). I’ll try to condense my points.

You argument, and correct me if I am wrong is based upon the idea that all is subjective, but some points are more valid than others:

Yes, because his opinion is more valid.

I believe a judge has a more valid opinion on law than a mechanic. His opinion on a legal issue is just as subjective, but it is worth more, because he knows more what he is talking about.

Your position is essentially correct from an objectivist viewpoint (ultimate objective, independent to all, no wildcards, “gods truth”). However, consider a human point of view, a perspective if you will. The judge is undoubtedly more legally aware than a mechanic (well, not some mechanics in my college, who have had more experience with the legal system than the average QC). I consider that, for all intents and purposes, a predisposition wildcard. It is “activated”, or relevant, only in a context where it is required to help judging, for example, the courtroom. When the judges car has broken down, whose view is more valid when the RAC truck comes rolling along two hours late? (ignoring the Swiss dude in the back with a stopwatch).

As human beings, we judge all the time. We are never independent, and as those who have criticised my points have expressed, there can be no independent which is viewed to be contributing to the uselessness of this idea. However, this itself defines the context. We have many on the go at one time, indeed, require them to think, analyse, philosophise and judge rationally. It is an element of choice. Do I use Times or Ariel typeface? Do I skive college and watch films at home? Do I walk over to my old form tutor sitting five computers to my left and scream at her for diverging certain information to my current tutor, or do I continue writing this post? As me, as a subjective in myself, I judge. There are contexts all the time. So in that sense, yes you are correct that some subjective are more valid than others, but only because we are constantly in context. Using the Christian analogy of judgement day, we’re all lined up along the valley of burning fire and brimstone *daydreams of heaven and has idea for short story*, the only context there becomes 6.2 billion equally valid subjectives, and the big guy upstairs with his book of wildcards and pair of tweezers. Even then, we are judging!

Now a practical application. War between nations. Democracy vs Totalitarianism. We live in, and love a democracy. Assume its vice versa for those living in the totalitarian state. Who do we choose? Based on what? Who do they choose, based on what? What does the alien in orbit with no notion of politics, humanity, democracy, totalitarianism etc think? He has yet to be convinced. Who he decides to go with is entirely down to subjectives that we are not aware of. Terrible analogy I know, but I think therein lies sufficient evidence to draw my conclusion.

After insulting someone, she nicknamed him whaleboy as a derogatory term, however he liked it

I’m also a big fan of Moby díck

When you say one ought to do something, you are imposing a moral value on them.

I disagree, because that assumes that what I say has a 100% correlation to the actions and belief of the reader or listener, whereas of course that is not the case, it is a matter of their interpretation. When I say “Should”, that means I believe they should and would presumably make them do so were I in any real power to do so. As a writer, speaker, whatever, I lack any power whatsoever. Which is just as well all considered .

So then you would not restrain me from eating a Jew, if I wanted to?

Ideally, no, but in a society based upon this notion, it would prevent you from imposing upon your meal, so you would not be allowed to do so. It forms something of an equilibrium of maximum liberty. If you were to publish a book advocating Nazism, cannibalism etc, you are perfectly within your rights to do so, but your example is complicated by the fact that the person you are about to consume is a sentient being.

And what could this non-arbitrary solution be? That sound to me like Utalitarianism..judge by happiness.

I’m not even going to bother with all the maths! Unless you’re name is Immanuel, even with a constant quantitative logic, my argument would seem to hold (though obviously, I’m not going to complain if someone thinks they can show there are other internally consistent mathematical systems). Literature on the other hand, is not bound by a constant stream of logic, leaving it down to interpretation. Consider the example of a mathematical, then a literary proposition.

4+4=8, which we hold to be true.

4+4= >=5, which we also hold to be true.

If propositions A+B are sufficient to equal C, then you have made a sound argument, but it is nigh on impossible to get that kind of accuracy, no matter, because a stronger position would be to say A+B =>some point less than C. Nothing in prose could ever be that consistent, I would go so far to say that qualitative logic will never be anything but a matter of individual interpretation, though of course, there can be a very very strong consensus, it does not preclude a compelling alternative.

[East Street Trader]

The proposition that the question "Which is the %^&$*# mountain?" is incapable of an answer does not strike me as too desperately profound.

But maybe I am just a %^&$*#?

[Whaleboy]

The proposition that the question "Which is the %^&$*# mountain?" is incapable of an answer does not strike me as too desperately profound.

Its capable of the answer, this merely affects the viability of that answer outside of the context of the question, unless the answer is attached to the context (Whaleboy prefers mountain A, as opposed to mountain A is better), but then, thats pretty oblique.

But maybe I am just a %^&$*#?

Welcome to the fold..

[Ramo]

I think you're going to have some difficulty selling this to the mathematical community.

I don't have to. Mathematics is an axiomatic system. The axioms underlying the system are only generally agreed upon, not absolutely true.

Uh... yes it is. That's like saying P implies !P is also internally consistent

1. The comparison isn't accurate. 1 = -1 is not a contradictory assertion. If you presuppose basic axioms of mathematics, it is. But theres no reason you need to do that, however useful it may be to do so.
2. P implies not P can be internally consistent. You just have to change what exactly "implies" means.

All you did is switch the symbols "1" and "0". I could use "flourescent" to represent the number 1, and it would have as much significance.

Your point would be...? You seem to attribute some sort of supernatural significance to "0" and "1." Math is an arbitrary system. It's what it is because of how we've defined things. I can say that, "1 + 1 = 2" only because of how I've defined "1," "+" and "2." This assertion is a logical conclusion of a few basic axioms. Change the axioms and you can change "1 + 1." As long as the new axioms are logically consistent, there's no problem.