Rethinking the Principle of Identity

Okay. If I follow you faithfully, I think, your contention is that if not-P is identical to itself, then the number of distinct and different things to which it's identical is, at least, countably infinite, and, as a countable infinity of things is more than one thing, it is not the case, for all things, that that thing is identical only to itself (assuming that a "self" is only one thing). If my interpretation of your thesis is correct, then I would say "fair enough". The problem seems to refer to the status of falsities. Personally, I see no reason to award existential status to falsities, but, apparently, realists about abstract objects do, so I think your argument might be effective against platonists.
In any case, it's a nice enough argument, so I hope you get some worthwhile response.

I don't assume anything about falsehoods, not even their existence: I simply make a falsehood identical to itself, since, according to the principle of identity, anything must be identical to itself, which includes falsehoods -- whatever they are.

ughaibu wrote:

Okay. If I follow you faithfully, I think, your contention is that if not-P is identical to itself, then the number of distinct and different things to which it's identical is, at least, countably infinite, and, as a countable infinity of things is more than one thing, it is not the case, for all things, that that thing is identical only to itself (assuming that a "self" is only one thing). If my interpretation of your thesis is correct, then I would say "fair enough". The problem seems to refer to the status of falsities. Personally, I see no reason to award existential status to falsities, but, apparently, realists about abstract objects do, so I think your argument might be effective against platonists.
In any case, it's a nice enough argument, so I hope you get some worthwhile response.

Although I find you argument interesting, it is not mine. First of all, I don't assume anything about falsehoods, not even their existence: I simply make a falsehood identical to itself, since, according to the principle of identity, anything must be identical to itself -- which includes falsehoods, whatever they are. The problem with such identity does not concern an infinite multiplicity -- which I didn't mention by the way -- but rather it comes from what falsehoods possibly mean: either the same as whatever is false or something else. If they are the same as whatever they falsify, then we have either one of the two following insoluble contradictions (only now a start bothering about a falsehood existing or not):

1. If we take what is false as a being -- and as long as a falsehood is identical to whatever it falsifies -- then being false becomes the same as just being, so everything that exists is false.

2. If we take what is false as a nonbeing -- and as long as a falsehood is identical to whatever it falsifies -- then being false becomes just a nonbeing, so nothing can be truly regarded as false, including all falsehoods.

As a consequence, to avoid insoluble contradictions, being false must be different from whatever is false, by which it becomes the truth of a falsehood, which is the circumstance of something being false. Then, the principle of identity starts dealing only with truths, even if they are true falsehoods.

guigus wrote:

I don't assume anything about falsehoods, not even their existence: I simply make a falsehood identical to itself, since, according to the principle of identity, anything must be identical to itself, which includes falsehoods -- whatever they are.

That's fine and dandy but, if they dont exist, what do you mean by 'they are'? Or, more specifically, if a falsehood is identical to itself, then there is a falsehood, and if there is a falsehood, then a falsehood exists.

guigus wrote:

ughaibu wrote:

Okay. If I follow you faithfully, I think, your contention is that if not-P is identical to itself, then the number of distinct and different things to which it's identical is, at least, countably infinite, and, as a countable infinity of things is more than one thing, it is not the case, for all things, that that thing is identical only to itself (assuming that a "self" is only one thing). If my interpretation of your thesis is correct, then I would say "fair enough". The problem seems to refer to the status of falsities. Personally, I see no reason to award existential status to falsities, but, apparently, realists about abstract objects do, so I think your argument might be effective against platonists.
In any case, it's a nice enough argument, so I hope you get some worthwhile response.

Although I find you argument interesting, it is not mine. First of all, I don't assume anything about falsehoods, not even their existence: I simply make a falsehood identical to itself, since, according to the principle of identity, anything must be identical to itself -- which includes falsehoods, whatever they are. The problem with such identity does not concern an infinite multiplicity -- which I didn't mention by the way -- but rather it comes from what falsehoods possibly mean: either the same as whatever is false or something else. If they are the same as whatever they falsify, then we have either one of the two following insoluble contradictions (only now a start bothering about a falsehood existing or not):

1. If we take what is false as a being -- and as long as a falsehood is identical to whatever it falsifies -- then being false becomes the same as just being, so everything that exists is false.

2. If we take what is false as a nonbeing -- and as long as a falsehood is identical to whatever it falsifies -- then being false becomes just a nonbeing, so nothing can be truly regarded as false, including all falsehoods.

As a consequence, to avoid insoluble contradictions, being false must be different from whatever is false, by which it becomes the truth of a falsehood, which is the circumstance of something being false. Then, the principle of identity starts dealing only with truths, even if they are true falsehoods.

It is true that it is false that the Earth is square. For every false proposition, it is true that proposition is false. What of it? For every true proposition, it is false that proposition is false. So what? Truth and falsity are binary notions. It is false that what is true is not true; and it is true that what is false is not false. That is how the cookie crumbles; I mean, that is how we use the term, "truth" and "falsity". Byt the way, you talk about "something" being false. But what does that mean? My left toe is (I suppose) a something. But my left toe is not false. The somethings that are false (or true) are propositions or statements. Those entities are the bearers of truth (or of falsity). I have no idea what you might mean by "the circumstances" being false. What does that mean?

Are you on drugs ? seriously ? what is it with you ???
One can´t help but be astonished with the easiness of your posts...

while he on turn just don´t make any sense at all

The principle of identity as originally formulated by Aristotle states that everything exists in its own way, which is its identity. However, if we take the word "existence" to mean precisely the way by which anything exists, which is the same as its "being," then we have that anything must be the same as the way of its being, hence that anything must be identical to itself. And since the principle of identity refers to anything, which includes falsehoods, what is the necessary identity between a falsehood and itself? What means the statement "a falsehood must be precisely that falsehood"? First of all, we have an ambiguity here, since a falsehood can be taken as meaning:

1. Something false.

2. The circumstance of something being false.

If a falsehood is taken as meaning something false, then that something becomes the same as its own falsity, so:

1. If we take what is false as a being, then being false becomes the same as just being, so everything becomes false, including the falsity of everything.

2. If we take what is false as a nonbeing, then being false becomes nothing, being destroyed altogether.

To escape such unsolvable contradictions, we must rather choose the meaning according to which a falsehood is the circumstance of something being false. A circumstance that must be true since, if it were false, then it would be the circumstance of whatever is false being true rather than false: the circumstance of something being false is true as the falsity of that something, independently of the truth or falsehood to which it applies -- it is a truth rather than a falsehood. Hence, the only way for us to affirm the principle of identity regarding falsehoods -- without running into unsolvable contradictions -- is by taking any falsehood as meaning rather a truth -- the true falsity of the truth it falsifies -- by which that principle becomes "every truth must be identical to itself." However, to be faithful to the original meaning of such an identity, which is that anything exists in its own way, we should rather say that "every truth must be true," since the way of a truth to exist is to be true.

"Identity" only applies to concrete objects. A cat can be identical to itself. A proposition is an abstract object, and so, does not apply.

Are you on drugs ? seriously ? what is it with you ???
One can´t help but be astonished with the easiness of your posts...

Fil Albuquerque wrote:

Are you on drugs ? seriously ? what is it with you ???
One can´t help but be astonished with the easiness of your posts...

Well he's obsessed with crap, but so to are you. What the **** is wrong with you? Nobody seriously espouses metaphysical determinism, except you.

the circumstance of a unicorn being false

What on earth does that mean? How can a unicorn be false (or true)? Any more that my left big toe can be true or false? What would a false unicorn or a true unicorn be? English please.