[Guille]

Greg,

Sorry I misinterpret what you said about science and philsophy, I read it oppositelly.

Actually I believe that both what I said about knowledge and intelligence (ability-capacity) and in Antonio's statement on beauty are true.

About logic and philosophy-science-mathematics, well, you see, there is a dificulty of terminology here, I believe. Because logic exists always inthe mind, it is one of the tools that the brain/mind uses to process/analize information/facts. But then there are science and philsophy. And these two are not simply logic. Thier basis is logic, but they can not be reduced to it. There is something more. In the case of philsophy, it is rationality which is enhaced. In the case of science, both rationality and empiricism are enhaced. Although they appear to be the same, logic and rationality are different. Better said, they are parts of the same thing, but not the same things themselves. Logic is the basis of thought. Ratioanlity is the development of thought. Appliability (empiricism, inventions...) are all the product of the process. These are the three parts of the human mind system. All languages form part of the product of it. And mathematics is alanguage, thus, mathematics is a pruductof rationality. The difference between science-philsophy with mathematics is that the first two are based on logic, but maths is not only based but can be reduced to logic. From this you amyt hink I'm a logicist. But I'm not completely, because I believe logic cannot explain mathematics. Because mathematics deals with a kind of logic called mathematicall logic. Just like the human mind's logic is called mind logic, and cannot be explained by either mathematical logic or logic as a whole.

[Graybeard]

I think i follow you ... would you agree that LOGIC we use in an internal way ...but mathamatics, science and philosophy we use internally as well as to communicate. Therefore these three are a language??

Here is a quote i found at the end of a science book last week ... you may already have read it, if not i think you will like it

"Such, in outline, but even more purposeless, more void of meaning, is the world which Science presents for our belief. Amid such a world, if anywhere, our ideals henceforward must find a home. That man is the product of causes which had no prevision of the end they were achieving; that his origin, his growth, his hopes and fears, his loves and his beliefs, are but the outcome of accidental collocations of atoms; that no fire, no heroism, no intensity of thought and feeling, can preserve an individual life beyond the grave; that all the labours of the ages, all the devotion, all the inspirations, all the noonday brightness of human genius, are destined to extinction in the vast death of the solar system, and that the whole temple of man's achievments must inevitably be buried beneath the debris of a universe in ruins --- all these things, if not quite beyond dispute, are yet so nearly certain, that no philosophy which rejects them can hope to stand.

Only within the scaffolding of these truths, only on the firm foundation of unyielding despair, can the soul's habitation henceforth be safely built. Brief and powerless is Man's life, on him and all his race the slow, sure doom falls pitiless and dark............. " Bertrand Russell

Although it sounds dark on first reading .... This Philosophy shows that this person encompassed 'Science Mathamatics and Logic' in Philosophy ... so maybe whatever we prove with the sciences, the outward expression will only be comprehended in philosophy ?

Greg

[Guille]

The fact that science and philsophy are based on logic and rationality doesn't mean that they are just and only logic. Neither languages of logic. They are logico-rational studies of nature. Mathematics itself is a language, but studying mathematics, and doing mathematics, are not languages, they are action.

[Guille]

I admire Bertrand Russell, but I'm not an "illuminated" by his philsophy or anything, nor by anything else in the world.

Philosophy is the true basis and nature of all studies: history, geography, sociology, biology, psicology, physics, chemistry, mathematics....And any other science or knowledge, including, for example, thinking about sports, is philosophy.

But philsophy is not the set of all studies. This is the sameidea that I was trying to comunicate with my start post, that logic is the basis of all studies but not the set of them.

It's dificult to comunicate, I believe, this is the problem. So, I will conclude thsi post quoting a contemporary of Russell, student of him, and friend, yes, indeed, it's the german philospher of language and logic Ludwig Wittgenstein:

"Whereof one cannot speak, thereof one must be silent."

[michellemfry]

Isn't it more important that you are applying and doing that which is logical? Silence equals death, and the lines of communication that remain open are the living means to understanding. Philosophy is like the seed planted that grows no matter where you plant it. It requires no experiments and no apparatus, just communication of philosophy.

[Guille]

Originally Posted by michellemfry Isn't it more important that you are applying and doing that which is logical? Silence equals death, and the lines of communication that remain open are the living means to understanding. Philosophy is like the seed planted that grows no matter where you plant it. It requires no experiments and no apparatus, just communication of philosophy.

For Hegel, opposition equals death. But as we know, opposition always impplies noise, always impplies discussion: political opposition, economical opposition, physical opposition... Therefore either the great german philosopher who is believed by all and influenced all contemporary thought was wrong, or you, a simple member in an unsignificant internet forum somewhere in the infinitum of this dimension. I decide to believe in you, whiles althouh being rational would have taken to believing in Hegel, still common sense takes to believe in you as based on empirical evidence: if we don't talk about (for example) communism, it will dissapear (death).

I agree with your definition of philosophy. I also agree that we must apply and do what is logical, just as what we know and want are logical (here, want is my crap translation of querer in Spanish, it should actually be what we dessire).

[BRIAN]

Great Guille,


Things work well with the logical events and I do agree that the definition of

Philosophy and the relation inolved with it.Creativity does matter when it comes to

Mathematics.Games coupled with maths gives a good meaning to it.




Online math game at http://www.educationtrak.com

[Lloyd Gillespie]

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

Originally Posted by Guille As a first thread to this forum, I want all of us to keep the high level of abstraction that Robert asks in his introductory thread. I believe that the theme I have chosen is perfect to begin an overal view on the nature of mathematics. 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? Well, In my opinion, mathematics is the language that humans use in doing science to study nature. And all of science has a core which is pure logic. But science is the study of nature. Not the study of logic or the study of the relationship between mathematics and logic. This arises a question in my mind: If the logicists of the 20th century were correct when they said that humanity was (and still is) going through a des-philosophicalization and intro-scientification, then, will there be a science one day that studies mathematics itself, and the relation of mathematics to logic, or of mathematics to science? In theory, the answer should be yes, but this doesn't make sense to our minds. It dosn't make sense because the actual fact of questioning and considering the relationship between the study of nature (science) and the language of the study of nature (mathematics) is itself philosophical. Now, coming back to the top of tis paragraph, well, mathematics is thus a kind of logic, or beter said, a way of using logic. So mathematics is not the language of logic. Mathematics is the study of mathematical logic, and the language of mathematical logic, but not of logic itself. A way of understanding the idfference between mathematical logic and logic itself is by studying human beings: each has a logic, that has been created in the mind by their experiences in their lifes. But these logics differ: differ first inside the same human, who can change of logic by a stron expirience, differs between humans, and, of course, differes to mathematical logic. But it's still logic. Now that we have clear that there are different kinds of logics, a question arises: Are there independent languages for each kind or type of logic, or can a language be created to represent the LOGIC itself, of any kind? The answer depends absolutelly in one property: if the types of logics all have a connection of the type that they can be different but still proccessed in the same way, then they can share a language, but if they don't have a connection of the type that they can be different but still proccessed in the same way, then there can be no language for all, because they are porcessed in different ways. I cannot determine the correct answer myself. But I believe it's more possible that no lanugage exists for all the logics, because we, humans, have invented a laungage for mathematical logic, but we don't manage to invent a language for the logic of our minds. We still odn't understand how it works, and this is because we study mind logic by mathematical logic, but, if mind logic can't be related with mathematical logic, then it must happen that they are processed in different ways, and, thus, that there can be no shared language. I will continue to expose my porfound thoughts in this thread now, I give you all the opportunity to consider my thoughts and discuss them, and expose yours.

[baudrunner]

At least Godel pointed us in the direction math must take to solve the world's and universe's many incomplete problems.

The problem with math is that math can prove the probable and the improbable, the real and the wholly unrealistic, the practical and the impractical, the true and the untrue, the logical and the illogical, the illusion and the truth.

[Lloyd Gillespie]

Thermodynamic math can prove truth___it has a direction___the arrow of time___toward the absolute truth...

Originally Posted by baudrunner The problem with math is that math can prove the probable and the improbable, the real and the wholly unrealistic, the practical and the impractical, the true and the untrue, the logical and the illogical, the illusion and the truth.