Master Lawbringer

CMPML, Department of System Failure! Sola fide : The Riemann hypothesis is true. (The failure of Hilbert's Program shows that the numbers cannot be closed in themselves. Yet the ability to define numbers in terms of other numbers depends on this feature. Proving the Riemann would mean going too far into the direction of closing the numbers completely into themselves but if it is false the ability to define numbers in terms of other numbers disappears. So it must be true yet remain unprovable. So justification by faith alone.) End of Document.

No, you have to assume that random functions exist, and then you can study their properties. No modern treatise on probability makes an effort to actually define randomness itself. Saying it like this is better : CMPML, Department of System Failure! Bell's Theorem is just a strange and backwards way of saying : Pure chance cannot be defined. Remember that Lilith does not have a cui bono motivation. Remember the Holy Oath of the CMPML : I swear to eternally Work to banish the Evil Snake so help me God. Amen and Amen and ... End of Document.

Bell's Theorem is just a strange and backwards way of saying : Pure chance cannot be defined.

Actually, one story I always enjoyed is the story about how ancient sheep herders used to know when they didn't have all the sheep at the end of the day, even though their mathematical abilities were similarly basic. They just used rocks. One rock for each sheep. And if there were rocks left at the end of the day they knew, even though they couldn't count that far, that they had missing sheep. The rocks were called calculi and that's where the word calculus comes from. I guess humankind was more pragmatic in those times. Similarly Cantor used this one to one correspondance idea for his proofs on infinities. You can't actually count to infinity, now, can you? But if you know that there's a one to one correspondance ...

I already said that circular reasoning is only fallacious if it is used to imply that new information is added. And you can see that a concept must be assumed to be self-evident when it turns out to be directly circular. Maybe I should have said directly circular? Like 'time'. Just try it. You just get 'time' is ... a 'period' ... and a 'period' is ... a time. When some process like that occurs you know you've hit rock bottom. (Ah, but we _can_ measure it. Which takes me to point 2. of my original document but ... endless debate ...) Are you saying that numbers aren't ubiquitous in our lives or are you still claiming that they can be reduced to simpler things in the philosophical sense? And you don't want to hear what I have to say about Bell's Theorem, so, there.

And the reason I consider numbers fundamental can not be anything else (here) than merely the pragmatic observation on their ubiquitous and irreducible nature.

I mean that if you perform an exhaustive analysis, like reducing any concept to more basic concepts and then see where you end up, the circularity becomes apparent. The ride on the merry go round of rationality might be complicated to the point where its essential circular nature is obfuscated if you're only willing to look at a part of the path and disregard the totality.

I already wrote this and it also concerns Peano's axioms : Logic and set theory, themselves based on self-evident, circular, concepts (try to define 'set') are circularly dependent on each other and even if you reduce everything to just manipulations of symbols you'll just end up with a machine that can count and perform calculations. You can't reduce numbers to something simpler. You might reformulate them and that can be useful pragmatically but there's no real reduction going on, in the philosophical sense. And no, I most certainly do not agree that nothing is circular. The only thing that could make it non-circular is Hilbert's Program and that also failed.

How would you define '2'? First there is the pragmatic observation that we can count. Why can we count? Well ... pragmatically I observe that I'm just able to do such a thing. So that would become circular if I tried to define it in that way. However we also observe that numbers can be defined in terms of other numbers and in this way it appears, at first, to be closed in itself. Is it completely closed in itself? Enter the Foundational Crisis ...

FROM THE WEBSITE : In terms of the geometric product ab we can define two other products, a symmetric inner product (1) a∙b = ½(ab + ba) = b∙a and an antisymmetric outer product (2) a∧b = ½(ab − ba) = − b∧a Adding (1) and (2), we obtain the fundamental formula (3) ab = a∙b + a∧b called the expanded form for the geometric product. END FROM THE WEBSITE. In the development of a mathematical system the circularity becomes obfuscated. Do the first set of rules imply the (circular) definition of the geometric product in terms of the inner and outer product or is it the other way round? And this is irrelevant as long as the system is consistent. Complexity doesn't make this circularity disappear. On analysis, it's always there due to the circular nature of the base concepts.

http://geocalc.clas.asu.edu/GA_Primer/GA_Primer/introduction-to-geometric/defining-and-interpreting.html The first thing that came to my mind is how the geometric product is defined in geometric algebra. The inner and outer product are defined using the geometric product, and the geometric product is defined using the inner and outer product. Just look closely.

Go on in that direction and you'll end up with statements like 'The reason cannot describe itself' which is a Liar Paradox. And then it's just boom ... absurdity. Observing this you can make the decision to either disregard this and stay within the confines of the reason or you could observe that it's just always like this : This explosion into absurdity is just a hint towards the deeper truth behind statements like 'The reason cannot describe itself.' Obviously, I chose the latter option, but this does not mean that I think that reason and mathematics aren't pragmatically useful. Also pragmatically I consider the ability to count as a starting point for mathematics. The concepts that appear then, the numbers, also turn out to be irreducible anyway. Just because the system is consistent, which basically means that it's not logically trivialistic, doesn't explode into absurdity, doesn't mean that the base concepts aren't self-evident and circular notions. And circularity appears the whole time. Rewriting equations is basically circular logic which shows that such logic isn't actually fallicious, unless you mean that a circular definition adds actual new knowledge that the original statement did not contain.

Are you claiming that there are areas of mathematics for which the following does not hold : You can't escape the self-evident and circular nature of the fundamental ideas. ???

Just testing. This used to be uncontroversial : All knowledge is ultimately circular. Break any idea down long enough and you'll end up with ideas, like 'time', for which all definitions end up circular. Specifically concerning numbers : You can't escape the fact that trying to define what a number actually is begins and ends with the pragmatic observation that we, and other machines, are able to count. Logic and set theory, themselves based on self-evident, circular, concepts (try to define 'set') are circularly dependent on each other and even if you reduce everything to just manipulations of symbols you'll just end up with a machine that can count and perform calculations. You can't escape the self-evident and circular nature of the fundamental ideas. Y'all probably disagree with this but tell me why ...

CMPML, Department of System Failure! 1. All knowledge is ultimately circular. Break any idea down long enough and you'll end up with ideas, like 'time', for which all definitions end up circular. Specifically concerning numbers : You can't escape the fact that trying to define what a number actually is begins and ends with the pragmatic observation that we, and other machines, are able to count. Logic and set theory, themselves based on self-evident, circular, concepts (try to define 'set') are circularly dependent on each other and even if you reduce everything to just manipulations of symbols you'll just end up with a machine that can count and perform calculations. You can't escape the self-evident and circular nature of the fundamental ideas. 2. You can't define randomness because actually defining it ceases to make it truly random. Randomness appears when you can't measure any further. This means that measurement, and the knowledge coming from it, stops. The scientific method just stops there. Bell's Theorem is just a strange and backwards way of saying : Pure chance cannot be defined. 3. All mathematical theories of physics end up plagued by logical trivialism and there is no experimental support for new physics beyond the standard model that they hope could solve those problems. Physics is pushed further and further into untestability and pipe dreams like String Theory. And the longer this process lasts, and it has already lasted for over a generation, the more likely it becomes that no further revolution(s) in that area are to be expected. In fact, it's better to notice that the themes of unmeasurability, randomness, logical trivialism and the inability to perform further experiments all imply the absence of further knowledge. 4. And when they venture into metaphysical speculation like many worlds, multiverse or simulation theory they end up on the same playing field as the traditional religions. You get no points for making a metaphysical theory just 'sciency' sounding, it's after all the evidence that counts. But seeing as they end up on the same playing field as religion, those traditional religions all of a sudden have more evidence going for them. After all, a religion _is_ a remarkable event and just that, and other remarkable things about them, is more evidence than just zero for many worlds, multiverse or simulation theory with the last mimicking traditional religion so closely that it's just silly. You should notice that those sciency religions are very close to 'anything goes', to logical trivialism. Here endeth the lesson. End of Document.