Logic and Mathematics

[AntonioLao]

have little respect for history

I only have respect for the chronological sequence of the history of science. Moreover, since respect is earned by the subsequent understanding of the respective scientific discovery, I dont have any respect for Aristotle's theory of falling bodies, Ptolemy's theory of epicycles and geocentric universe, theory of the ether, etc. That is any defunct physical theory that is replaced by more convincing theories. Huygens founded wave theory of light. Newton founded particle theory of light. Independently, none of these two theories can describe the phenomena of the double-slit experiment. But together the experiment can be described by its operational priorities. If one's apparatus is looking for the wave property of photon or electron then one finds properties such as frequency and wavelength. On the other hand, if one's apparatus is looking for the particle property of the photon or electron then one finds such properties as linear momentum and elastic scattering. To find the wave-particle properties of angular momentum such as spin and magnetic moment then one uses quantum field theory or for speed less than light one uses quantum mechanics.

[Lloyd Gillespie]

As I said Antonio, you have little respect for history, by your own admission...

[Lloyd Gillespie]

I moved this earlier post in this thread forward, to clarify my positions...

Hi Guille, this is an excellent thread starter, as it hits the point I have been recently mulling over in my head. Your point, "Probably you know that the basis of mathematics is logic. But, how exactly does mathematics relate to logic? Is it logic's language, or just a type of use of it?", is exactly what I will try to address.

If we truly look at the mind and its possessions, we find the logic processor you mention, and we also find the mathematics processor___why are these two processors so different? IMO, they are drastically different, as are logic and rationality, as you mentioned. Now, what makes these differences? The major difference I see is logic has the intuitive ability to use the infinite probabilities processor, and mathematics is bound to absolute science knowledge and facts, i.e., the largest infinite number mathematics can process is a huge rationalized infinity, or a correspondence logic of infinity to finiteness, which is mainly the same but different[isomorphic] thing, and the mathematics of statistical mechanics probabilities based on incomplete ergodic theorems and axioms, which work for larger than true ground micro states, and the less than true absolute macro states of phase spaces. Thus, we can use mathematics only to a certain level of certainties, limited by the impossible penetration of absolute micro and macro phase space states___while logic, on the other hand, can use its intuitive rationality, mathematics and probabilities of absolute probabilities. Now, the question becomes, how can we process our mind's ability to do logical absolute probabilities, mathematically___or can we at all?

The way I see it, the mind possesses the infinite intuitive process of absolute probability math, yet there is no scientific math, yet, possible to represent this fact. Now, a few examples may make this clear, such as, our mathematical ability to represent quantum packets, yet no true math to represent the actual position and momentum of the electron. Or, our mind's ability to know infinity as a real entity, either through the non-ending rational facts of math, or the facts we witness by experiments and just looking up at the sky at night. We see finite matter and infinite space. We also realize we possess an infinite imagination, yet, we can not mathematize it. So, there are several walls of impenetration between logic's and math's abilities. Kurt Godel was the most advanced in this investigation, when he died. He mentioned the trans-finite rationality, which is very interesting, as it seems a long way past the reasoning powers of Witgenstein and Russell. At least Godel pointed us in the direction math must take to solve the world's and universe's many incomplete problems. He also, along with Brouwer, was the greatest mind in working on the expansion of intuitionistic logic, the field I am always most interested in, as a possible way to achieve the absolute probability math, really a new whole math, which I believe must be based on new and true interpretations of one, zero and infinity. I think if we could develop such a new whole math, we may be able to develop the complete link between logic and math, as Russell, Whitehead, and many others tried, yet failed. Godel did not think his incompleteness theorem spelled the death of ever figuring out the advancement of mathematics, and neither do I, but I do think it will take a new whole mathematics to truly join logic and math completely, and only then will we be able to truly answer and prove the toe, logically and mathematically sound.

IMO, the way we process infinity___logically, scientifically and mathematically___is the key...

Regards,
Lloyd

[Graybeard]

As I said Antonio, you have little respect for history, by your own admission...

I don't get your point. Why should Antonio have respect for History where it does not add to, or is at odds with, scientific knowledge ? History is a conjunct. It is not a matter for sentimental respect ?

cool bananas ... greg

[Lloyd Gillespie]

I don't get your point. Why should Antonio have respect for History where it does not add to, or is at odds with, scientific knowledge ? History is a conjunct. It is not a matter for sentimental respect ?

cool bananas ... greg

We were addressing the history of mathematics and logics which actually goes back to very early times indeed__that's all...

I mentioned Huygens, as he's actually the most important player as to how the proper probalility maths play into our modern assessments of the entire quantum world's maths, and the most recent of gravity's speculative maths and ideas... Without the proper probability maths used, the outcomes of the logics of the sciences are inaccurate, and in many cases outright wrong... These are foundational issues the modern world of maths must re-discuss__in great detail...

Here's an example of what I discussed with Professor Paul Davidson, on the problems with ergodicity in probability theory and statistics:

Hi Paul, imo, everyone dealing with ergodicity should chase the history of probability back through all its founders to arrive at its full truth, and that would be from Keynes, back to C.S.Peirce, to Jevons, to Gauss, to Boole, to Wallace, and finally to Huygens, who developed the modern theory of mathematical, ontological and epistemological, ideas from Pascal and Fermat's letters. C. Huygens'(being the true father of organized probability theory) original work is the best of ontological probability facts of statistics available__Forget Beyes, Laplace, Taleb etc., far too epistemological...

I think you should write a modern history of true probability theory and facts, to make ergodicity(actually from Boltzmann) clear to all. What do ya say...? And make it as clear as your new Keynes' book...

Lloyd

I here include you too Antonio. This issue must be addressed by a mathematician who thoroughly understands the problems involved. I think you should address this major mathematical problem of mis-interpretations of probability methods, and maybe you could get this published, as it's the more important problem in mathematics, due to it relating to measurements' fundamentals...

[AntonioLao]

little respect for history, by your own admission...

If you meant the history of philosophy then I agree. However, if you meant the history of science then I strongly disagree. FYI, I was the only person who ever got an "F" in philosophy during my undergraduate studies.

major mathematical problem of mis-interpretations of probability methods

My interpretation of probability theory is to replace it with a direction theory, which could possibly solve the arrow of time problem in physics.