Post by Eugene 2.0 on Oct 10, 2020 19:14:52 GMT
Let's rewrite "2+2=4" (1) into "two plus two equals four" (2). Now it (2) is the lang representation of the formula. Then we shall continue. "Два плюс два дорівнює чотири" (3) - this is the same to (2), but it's written in Ukrainian. We're gonna go further: "scissors put to scissors together are scissors-scissors" (4). Maybe, the last one example isn't the best, but trying another one: "tim tim pim tim tim eqim fim" (5) we may get some much more weird-looking formula. The fifth one can barely be accepted as senseful, however, if we look closer to it, taking into account that we have changed digits "2", "4", and signs "+" and "=" we, however, have made it pretty legally, just as same as we've done in (2) and (3).
So, okay here's the next one: "zz z zz zzz zzzz (6). In this particularly formula we put some z's as digit's analogue. We could make some other manipulations with it converting letters or symbols to some forms while the (1) form would left as it was. Okay, maybe some objections may occur, but not so much as it may be towards this one:
"|(&7he;')y;_(_!$;'gjj$!db" (7)
Some would skip this (7) too, pointing at that it might be one's intentions to code the formula (or by another rational reason).
The most dangerous objection we can get, at least, in these two cases: a) if there would be logical violation; b) there would appear meaningless statement or the statement with no real reasons behind it.
To show that there's no logic in the formulas (1-7) is harder, than to show that there's a meaning behind the formulation like (7). F or the last one there would be enough to say that there could be some alien folks somewhere in the Universe whose language allowed such formulas or they could understand the statement 7 as we understood (1-3). Anyway, such a presupposition of ours must necessary mean that there's a neutral formula 8 like, for instance "{a,b}U{c,d}←→{a,b,c,d}" that is behind as alien's as ours thoughts, or such a neutral formula can be derived as one of the axiom.
The word axiom here is important, because going into trials with (a) – trying to object that it's logically incorrect to think "2+2=4" we may notice two things: c) math is built with axioms; d) we use logic as the universal tool (to solve something, including the questions about math).
If (c) can be objected as anything that built upon axioms isn't trusted completely – axioms are usually taken freely, the story with logic (d) hides some underwater rocks.
So, allowing a thought according to that logic is an explicit or implicit tool of our reasoning, then there also can be that either this tool isn't the only one, or it has flaws. Who knows, there are no absolutely and steady standards and prescriptions how it must be. So, that's why to claim the logic is absolute may be rightly considered as an exaggeration.
Now, from all the above, viz. possibility of changing (1) to (2-7) and a thought that no axioms and no logic can be seriously taken as something undeniable and absolutely clear we may see how shaky the math is, and how many reasons to doubt it. But doubting what? – Doubting it as a united and internally (coherent) closed thing. Considering it now we're allowed to guess now that if math exist it can be the same as lang or some shuffle-reshuffle of certain elements.
And also we might attempt to make an important note on a thought – that it might be not correct to object math thinking as something different to the others tools of ours. So to claim a man thinking math-like is not true, while the other one guy who doesn't think math-like is more correct – is definitely not a good way of thinking, and not clear representation of what's going on in real.
So, okay here's the next one: "zz z zz zzz zzzz (6). In this particularly formula we put some z's as digit's analogue. We could make some other manipulations with it converting letters or symbols to some forms while the (1) form would left as it was. Okay, maybe some objections may occur, but not so much as it may be towards this one:
"|(&7he;')y;_(_!$;'gjj$!db" (7)
Some would skip this (7) too, pointing at that it might be one's intentions to code the formula (or by another rational reason).
The most dangerous objection we can get, at least, in these two cases: a) if there would be logical violation; b) there would appear meaningless statement or the statement with no real reasons behind it.
To show that there's no logic in the formulas (1-7) is harder, than to show that there's a meaning behind the formulation like (7). F or the last one there would be enough to say that there could be some alien folks somewhere in the Universe whose language allowed such formulas or they could understand the statement 7 as we understood (1-3). Anyway, such a presupposition of ours must necessary mean that there's a neutral formula 8 like, for instance "{a,b}U{c,d}←→{a,b,c,d}" that is behind as alien's as ours thoughts, or such a neutral formula can be derived as one of the axiom.
The word axiom here is important, because going into trials with (a) – trying to object that it's logically incorrect to think "2+2=4" we may notice two things: c) math is built with axioms; d) we use logic as the universal tool (to solve something, including the questions about math).
If (c) can be objected as anything that built upon axioms isn't trusted completely – axioms are usually taken freely, the story with logic (d) hides some underwater rocks.
So, allowing a thought according to that logic is an explicit or implicit tool of our reasoning, then there also can be that either this tool isn't the only one, or it has flaws. Who knows, there are no absolutely and steady standards and prescriptions how it must be. So, that's why to claim the logic is absolute may be rightly considered as an exaggeration.
Now, from all the above, viz. possibility of changing (1) to (2-7) and a thought that no axioms and no logic can be seriously taken as something undeniable and absolutely clear we may see how shaky the math is, and how many reasons to doubt it. But doubting what? – Doubting it as a united and internally (coherent) closed thing. Considering it now we're allowed to guess now that if math exist it can be the same as lang or some shuffle-reshuffle of certain elements.
And also we might attempt to make an important note on a thought – that it might be not correct to object math thinking as something different to the others tools of ours. So to claim a man thinking math-like is not true, while the other one guy who doesn't think math-like is more correct – is definitely not a good way of thinking, and not clear representation of what's going on in real.