Hello. In the last 2 years I kept working a lot to develop and improve my web site on the foundations of mathematics and physics. It is still far from finished but I have much clarified in recent months the first chapters that explain the flow of time in the abstract universe of mathematics. There you can see that the concept of time is not just something for physicists and philosophers, but it can also be found in mathematics (not just as a dimension in geometry but really something that carries the metaphysical aspect of time, that is not symmetric). Enjoy !
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OK, it's on.
Time in the foundations of mathematics
- Thread starter spoirier
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GodOfOrder
Well-Known Member
Is time not just merely a process succession. Therefore 1,2,3,4,5,etc. is also merely a process of succession. And so math, insofar as it is arithmetic, is representative in our minds if time. And other things, such as geometrical laws are representative of space. Together the form a model of the universe.
Or at least this is my understanding. I am sorry though, I have not gone to your web page and thus do not know if this response was appropriate.
Or at least this is my understanding. I am sorry though, I have not gone to your web page and thus do not know if this response was appropriate.
Artsu Tharaz
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Yeah, Kant's Critique of Pure Reason. Brilliant stuff.
Have you redesigned Typology yet? Given it the proper order?
Have you redesigned Typology yet? Given it the proper order?
GodOfOrder
Well-Known Member
Well, In most senses I wouldn't call myself a Kantian. I think he confused in some ways symbols of mathematics, and mathematics themselves. In math, the division between analytic and synthetic a priori reasoning gets destroyed if one were to think of numbers as tallies instead of numerals. In that case, five and seven automatically make twelve. Such a thing is self evident, and also not synthetic. In many ways I think I'm sitting on the beach right next to Hume.
But nevertheless, I think insofar as he shows math to be representative of perception, he isn't far off. Math is a model of relations of objects, both in time and space.
And as for reordering typology, I never dreamed of it.
But nevertheless, I think insofar as he shows math to be representative of perception, he isn't far off. Math is a model of relations of objects, both in time and space.
And as for reordering typology, I never dreamed of it.
BigApplePi
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Nice going spoirier. Your web site looks like fun.
Dig your graphic! I worked on a concept map of various math and philosophy terms...never made the final one in Illustrator but have a giant draft rolled up and stashed somewhere in my closet.
Have you heard of William Rowan Hamilton's book (all the way back in 1837!) "The Metaphysics of Mathematics -- Algebra as Pure Time"? He argued that mathematics is about thought, not about physical reality... Thought is in a constant state of becoming (and not the object-centric being) that can be described with the elements of algebra:
"In algebra relations are between successive states of some changing thing or thought. In other words, algebra is not about some material process but something more general that could be applied to both matter and mind."
I did a paper on time, set theory, Spencer-Brown's Laws of Form, & the Diamondsutra (logic of not; similar to XOR function/ a v -a). Would be interested in hearing your thoughts on it. I talk about the metaphysical aspect of time through speculating on time being the negotiation between possibility and impossibility (1 and 0) (symmetrical expansion) vs. the perception of time as asymmetrical.
Do you know of the uni-logi.org guys? They're a huge inspiration to me...they are working on symmetrical systems of logic (logical hexagon) that can be expressed through geometry. I think they are going to connect modal logic with math and it is going to be awwwhhhhsuuuuummmm. They already have started (paper: "Geometry for Modalities: Yes, through n-Opposition Theory"), but I am sure there is even more progress to be made!
Have you heard of William Rowan Hamilton's book (all the way back in 1837!) "The Metaphysics of Mathematics -- Algebra as Pure Time"? He argued that mathematics is about thought, not about physical reality... Thought is in a constant state of becoming (and not the object-centric being) that can be described with the elements of algebra:
"In algebra relations are between successive states of some changing thing or thought. In other words, algebra is not about some material process but something more general that could be applied to both matter and mind."
I did a paper on time, set theory, Spencer-Brown's Laws of Form, & the Diamondsutra (logic of not; similar to XOR function/ a v -a). Would be interested in hearing your thoughts on it. I talk about the metaphysical aspect of time through speculating on time being the negotiation between possibility and impossibility (1 and 0) (symmetrical expansion) vs. the perception of time as asymmetrical.
Do you know of the uni-logi.org guys? They're a huge inspiration to me...they are working on symmetrical systems of logic (logical hexagon) that can be expressed through geometry. I think they are going to connect modal logic with math and it is going to be awwwhhhhsuuuuummmm. They already have started (paper: "Geometry for Modalities: Yes, through n-Opposition Theory"), but I am sure there is even more progress to be made!
What do you mean by "Dig your graphic!" ?
Well in another way, I do think that physical reality is mostly (but not only) made of mathematical stuff, as I explained in my metaphysics text, but both claims should not be confused. I mean that I see mathematics as a primary self-sufficient reality, while the physical reality is a secondary reality that depends on it.
Sorry but for the few words you mentioned, I don't feel very interested to read what you mentioned, that seems to just be some fuzzy philosophers'speculations (see my comments and quotations about philosophers).
As you can see in my writings on the foundations of maths, I'm not coming to make speculations, but a very intensively cleaned up and precise exposition of things, so I'd like to suggest you to first read this as it may help to clarify your thoughts before coming back here for further discussions.
I just had a look across the paper you said, but I don't feel interested with it. It seems quite long, staying more or less on the same idea (while I give a much higher density of ideas in my texts), and I cannot see what advantage it may have. Generally I am well satisfied with the ordinary first-order predicate logic, as I think it suffices to well express all mathematics, together with many other ideas (for example I express set theory in its own special formalism, translatable into first-order logic but distinct from it) but nothing that I would see as deserving the status of "another logic". I know that some other logicians are interested in other logics, such as modal logics, which may be considered for example as a way to express Godel's incompleteness theorem and its proof. However I presented this theorem too without feeling the need to mention a different logic.
You mean the site uni-log.org
Unfortunately its main entry does not provide a way to browse its contents.
I suspect this to be just vanity reseach, whose main purpose, like so many other philosophical works (and like many religious teachings), is to pretend to be wonderful for "its own reasons" while it actually does not lead to clarify the understanding of anything beyond itself and why it is wonderful (even if its authors themselves may remain unaware of this, but are just led to do it by their own inspiration and as the way they found to earn their living, as approved by administrators, and/or as a profitable business to multiply conferences and sell books).
As for me, I don't just care about foundations for its own sake, but as a first part of a bigger work, actually useful to clean up mathematical concepts and provide a short way to theoretical physics.
I never heard anyone claim that mathematics was about physical reality, did you ? And why this implicit assumption that there would be no third possibility ?
Well in another way, I do think that physical reality is mostly (but not only) made of mathematical stuff, as I explained in my metaphysics text, but both claims should not be confused. I mean that I see mathematics as a primary self-sufficient reality, while the physical reality is a secondary reality that depends on it.
Sorry but for the few words you mentioned, I don't feel very interested to read what you mentioned, that seems to just be some fuzzy philosophers'speculations (see my comments and quotations about philosophers).
As you can see in my writings on the foundations of maths, I'm not coming to make speculations, but a very intensively cleaned up and precise exposition of things, so I'd like to suggest you to first read this as it may help to clarify your thoughts before coming back here for further discussions.
I just had a look across the paper you said, but I don't feel interested with it. It seems quite long, staying more or less on the same idea (while I give a much higher density of ideas in my texts), and I cannot see what advantage it may have. Generally I am well satisfied with the ordinary first-order predicate logic, as I think it suffices to well express all mathematics, together with many other ideas (for example I express set theory in its own special formalism, translatable into first-order logic but distinct from it) but nothing that I would see as deserving the status of "another logic". I know that some other logicians are interested in other logics, such as modal logics, which may be considered for example as a way to express Godel's incompleteness theorem and its proof. However I presented this theorem too without feeling the need to mention a different logic.
You mean the site uni-log.org
Unfortunately its main entry does not provide a way to browse its contents.
I suspect this to be just vanity reseach, whose main purpose, like so many other philosophical works (and like many religious teachings), is to pretend to be wonderful for "its own reasons" while it actually does not lead to clarify the understanding of anything beyond itself and why it is wonderful (even if its authors themselves may remain unaware of this, but are just led to do it by their own inspiration and as the way they found to earn their living, as approved by administrators, and/or as a profitable business to multiply conferences and sell books).
As for me, I don't just care about foundations for its own sake, but as a first part of a bigger work, actually useful to clean up mathematical concepts and provide a short way to theoretical physics.