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If I were to say, 'this water is not water' would I be breaking the form 'p & ~p'? Of course not. I would be actually making a statement of the form 'p & ~q'.
If you would discover this truth, you wouldn't call this water 'water' but you can make a difference between them and automatically give a new name for it, which is
q then. If you say the sentence 'This water(what was called 'water' after the old laws) is no water(in the sense of the new laws under which we understand 'water' now). So you make a difference between the laws in the past and the laws in the present. And this means that this sentence is useless if you see it in the sense of the new laws, because you automatically from this moment state that this thing is another thing and that means that you have to give this thing another name, which means that you can't refer this sense of new water with the sense of old water.
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2: This water is not water
On the surface, the statement would be of the form 'p & ~p' because both of us believe that the water is the same on twin earth and earth. Once we know that the water is different, the structure of the statement changes to 'p & ~q'.
That means, you say it's the same case as water isn't water, but you say that 'matter(in the old sense=
'p') isn't matter(in a sense that wasn't yet discovered=
'~q'). Hm, that sounds like how a typic physician would argue. -> If there's something you can't describe, then you found a new kind of matter(like dark matter, anti-gravitation matter, etc. which weren't discovered yet).
After you discovered something which widens your range of knowledge and truth-system(logic), the range of the logical system is also widened, but always! limited by this frontier of this logical thinking. It's all about
set theory. You'd be God because you would post the logical laws from an 'outside set'. It's like the lucky numbers. Computer can create them, but these aren't really lucky numbers, because it needs a data on which it has to refer to. And this data it gets from an 'outside set'(the user=the human). The computer would first think(if it were intelligent enough) why it shall be this date, this date which he was given by the user, but he thinks it is logically. And that it how i think of life and God. That God is in an 'outside set'.
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The negation of this is not 'nothing is a goat', but rather
2: It is not the case that for every x, if x is a thing, then x is a goat
But if you say that, you automatically say that between the choices everything and nothing there IS something between. At the end, it is a question of how many events(theory of propabilities) you define and which you allow.
But when you say that the negation '
it's not the case that everything is a goat' is true, the statement 'it IS the case that 'nothing is a goat''(which is one event of many of the statement that '
it's not the case that everything is a goat') is also true at the same time, but this can't be combined with the statement that 'it's the case that almost everything is a goat'(which is also another event of the case that '
it's not the case that everything is a goat), and that is paradox!
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But it's the foundation of philosophy and must be at least basically understood to really get into the meat of philosophy.
Hope that these laws which were stated will be correct for the future(when they're not fully correct nowadays, or even were in the past)........