One can make a mathematical proposition in plain english or one can use the reduced symbolic system that can be called math… the reduction to simpler symbolism seems to aid more complex mental evaluation… but then even in math there can be issues/ideas that simply can not be reduced to simpler symbolism…one can then consider a system of such complex non reducible symbolic complexions… considering that such cannot be reduced we have that there is a limit of symbolic reduction… I imagine that such a limit can be quantified and plausibly some symbolic system can be used to label various degrees of complexity and/or non-reducibility…

So then is it really though that there is a limit or is it that we have yet found a means of thinking, or a symbolic system, that can better handle dealing with those more complex issues currently non-reducible in our given mathematical language?

Further is it plausible to construct a common language that would be best an aid for philosophical thinking and perhaps one full even to the degree as being considered as different a language as German is to english? And would perhaps teaching that language at a young age and spreading it broadly aid more universal philosophical mentalities?

what makes you think it’s ever non-reducible? the only time something is non-reducible is when it’s already been reduced down to one symbol as far as i’m aware. if you give me a system you think is non-reducible, i’ll make up a new symbol for it to be reduced in to. it’s as easy as that.

Well of course you can invent a symbol for which to represent any thing… what I mean rather is reducibility given necessary correspondence to other symbols within the system of symbols being worked with… for example if you reduce the entire thermodynamic equations into a single symbol you lose the capacity to extract other aspects in algebraic manipulation. without recognition of the multi-symbolic format.

To be further reducible I think the meanings need to be more interchangeable and elastic, such that absolutes are removed and one thing can fade into another. Less blocky y’know what I mean.

Perhaps the limitation is that we cannot easily maintain all he functionalities and aspects and associations in our mind when reduced to a simple symbol by standard with the more complex algorithms…

I think of one paradox I once heard. Take any point in the universe and try to connect it to the next. That would create positions one and then two (1, 2). But you can divide that space in half, so you would now have 3 points instead of two. But before you get to that middle there is yet another middle point in between so now you have 4 points, two right between what was once your 1 and 2. And you can do this infinetly, meaning that between any two symbols, be it points in space or numbers, there is an infinite and yet often unaccounted set of symbols that could possibly correspond to infinite sets of symbols. Counting 1 to 2 could never happen, logically, and yet it does happen.
Why is that?
Because I think that we forget that math has an arbitrary sense to it. It is a mental construct that is based on absolutes, on self-inflicted limits without which math would be impossible. Apple 1 is different, in any set of characteristics, from apple 2, and yet we count 2 apples because somehow we stop the strict apprehension of reality to embrace the symbol. And this is not even a conscious decision. Reality is itself filtered during apprehension by the senses. And it is not even a “picture” that is taken, but a pattern of impulses that is interpreted, connected to existing files and assumed as real. Therefore I think that already, and without concern to expediency, we set before ourselves certain limits which are naturally transferred to mathematical and other symbolic systems, say, language.
What I do have a problem with is that the symbols are taken as an accurate image of reality, true and through. Mathematically I can wind down the universe into one “infinitely” small and “infinitely” dense “point”, but what corresponds in my mind to such a thing? What experience do I have other than the symbol of a symbol? Smallness loses it’s meaning as well as any idea of density by the very characterization we give it: it is patently impossible for the finite to conceive of the infinite. But we use it, we package it and declare it almost a certified account of history. So this is what happened billions and billions years ago…

If you divide the space in half don’t you then have points 1 and 2 again? …the half point is no different to the two former points you had as relative to the collection of points. We could think of the first 2nd point as half of a third point you havent reached yet, in the same way as we can think of the half point comparatively.

Equally all points are relative so surely the distances change when you add more points. Its like adding more clocks travelling on trains, no?

There are no infinite points because the point itself doesn’t exist such to make that calculation in real terms, it is purely imaginary/metaphoric. the cardinality cannot work out when we use absolute values.

ps, all I am saying is that math can be too inflexible and we need to be more dextrous and elastic after a point.

Pilots of commercial airplanes, have english as the common language, unfortunaly there are some serious mishaps in understanding the language.

Some latin american pilots was critically low on fuel and said “we need priority” when they should have said “it’s an emergency situation”, therefore they never got an emergency situation out of their distress call to the flight tower.

Such mishaps may be a frequent occurance if the great masses should learn a 2nd language.

It doesn’t necessarily have to be a second language, rather evolution of the language towards one better for particular modes of thinking, not necessarily specifically philosophy, might be able to be influenced by slight alterations of our diction over time… language evolves over time anyways… why not direct that evolution?

It doesn’t have to be english… all languages could be controlled in their evolution such as to, after a long period of time, evolve to one universal language…
of course it is unlikely that such would ever be done…or accepted… that may actually self occur over time anyways…