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Roberto Vescarelli wrote:
> Dear logicians,
>
> with this post I propose to discuss some topics of the logic of being and
> existence.
>
> From a logical point of view the clear distinction of being and existence
> was done by Russell in the &427 of its Principles of Mathematics: a
> countable thing is a thing that have the being; to talk about something is
> to admitt that such a thing is or have the being. On the other hand, the
> existence is a property that someone of the thing that has the being have.
> Existing objects are a subset of the univers of the being.
>
> The rest of this post is dedicate to the development of these ideas at the
> light of free logics.
>
> Let us consider the univers of speech, named U, of all the things that have
> the being, and M, the world of existing things. The complementary set of M,
> named -M, is the set of all things, if any, that have the being but don't
> exist.
>
> An atomic phormula of the form ?Pa? is true in M, accordingly to the canonic
> rules, if and only if the existent thing denotates by ?a? belongs to the
> set of things denotates by ?P?. But when Pa is true in -M?
>
> Suppose that Father Christmas don't exist. Than what is of the proposition
>
> (1) ?Father Christmas has a white beard??
>
> In M (1) is false, because Father Christmas is supposed do be inexistent,
> but we can wish that (1) is true in -M.
>
> In our logic we can say that the perfect triangle of Euclidean geometry
> doesn't exist in nature and, contemporary, that it is true that its
> internal angles are equal to two right ones.
>
> Propositions that are true in M and in -M are Axioms.
>
> If we abbreviate ?x belongs to U? with ?E!x?, we have the following axiom:
>
> (2) for all x, E!x
>
> But we can easily notate that some of the theorems of first order logic are
> not theorems of our logic.
>
> As an istance we consider the propositions
>
> (3) Exist an x such that (x=y)
>
> It is true in M, according with the ordinary semantic rules, but it is false
> in -M. In fact doesn't exist a thing that is identical with Father
> Christmas, because Father Christmas doesn't exist.
>
> As another istance consider a therorem of firs order logic that is invalid
> in our logic:
>
> (4) Pa -> exist an x such that (Px)
>
> It is easy to see that (4) is true in M but is false in -M. In fact if I
> exist, you can deduce from ?I have a white beard? that ?there exist white
> beared things?, but if Father Christmas doesn't exist, you can not deduce
> that ?there exist white beared things? from ?Father Christmas has a white
> beard?.
>
> Another point of interest is that our logic seems to be more general of the
> logic of Principia. As Russell admitted, the logic of Principia involves
> that the univers of speech is not empty. You can demonstrate in the logic
> of Principia that at leat an individual have to exist:
>
> (5) (a=a) -> (a=a)
>
> (6) (a=a) -> exist an x such that (x=x)
>
> (7) (a=a)
>
> (8) exist an x such that (x=x)
>
> and therefore U would be different from the empty set.
>
> But in our perspective, (6) is false, and can not be derived from (5), that
> is true.
>
> In our logic we must have different rules from the treatment of quantifiers.
>
> I hope someone would like to work with me about these rules or give some
> suggestions to me,
>
> greetings
>
> --
> Roberto Vescarelli
> http://www.faberbox.com/roby/
Roberto Vescarelli wrote:
> Dear logicians,
>
> with this post I propose to discuss some topics of the logic of being and
> existence.
>
> From a logical point of view the clear distinction of being and existence
> was done by Russell in the &427 of its Principles of Mathematics: a
> countable thing is a thing that have the being; to talk about something is
> to admitt that such a thing is or have the being. On the other hand, the
> existence is a property that someone of the thing that has the being have.
> Existing objects are a subset of the univers of the being.
IMO, there cannot be a distinction between being and existence.
Could you further claify what you mean?
Existence, is argueably not a property of things, but rather, it is the
logical sum of properties of things
E!x =df EF(Fx).
> Existing objects are a subset of the univers of the being.
Reality, the universe of being, is: all that exists!
all that exists = all that has being.
>
> The rest of this post is dedicate to the development of these ideas at the
> light of free logics.
>
> Let us consider the univers of speech, named U, of all the things that have
> the being, and M, the world of existing things. The complementary set of M,
> named -M, is the set of all things, if any, that have the being but don't
> exist.
U=M
-U, the class of those things which do not exist ..is empty!
There is no set of things that have being and do not have existence.
To concoct a different meaning for 'being' and 'existence' is wanton
obscurantism...Quine.
>
> An atomic phormula of the form ?Pa? is true in M, accordingly to the canonic
> rules, if and only if the existent thing denotates by ?a? belongs to the
> set of things denotates by ?P?. But when Pa is true in -M?
>
> Suppose that Father Christmas don't exist. Than what is of the proposition
>
> (1) ?Father Christmas has a white beard??
>
> In M (1) is false, because Father Christmas is supposed do be inexistent,
> but we can wish that (1) is true in -M.
Not so. 'Father Christmas has a white beard' is false.
There is no physical property that the described thing 'Father
Christmas' has.
It is not a member of any class.
>
> In our logic we can say that the perfect triangle of Euclidean geometry
> doesn't exist in nature and, contemporary, that it is true that its
> internal angles are equal to two right ones.
>
> Propositions that are true in M and in -M are Axioms.
>
> If we abbreviate ?x belongs to U? with ?E!x?, we have the following axiom:
>
> (2) for all x, E!x
Yes, AxE!x follows from the axiom Ax(x=x).
>
> But we can easily notate that some of the theorems of first order logic are
> not theorems of our logic.
>
> As an istance we consider the propositions
>
> (3) Exist an x such that (x=y)
>
> It is true in M, according with the ordinary semantic rules, but it is false
> in -M. In fact doesn't exist a thing that is identical with Father
> Christmas, because Father Christmas doesn't exist.
(3) is a provable theorem in FOPL.
There is no set -M.
>
> As another istance consider a therorem of firs order logic that is invalid
> in our logic:
>
> (4) Pa -> exist an x such that (Px)
>
> It is easy to see that (4) is true in M but is false in -M. In fact if I
> exist, you can deduce from ?I have a white beard? that ?there exist white
> beared things?, but if Father Christmas doesn't exist, you can not deduce
> that ?there exist white beared things? from ?Father Christmas has a white
> beard?.
??
>
> Another point of interest is that our logic seems to be more general of the
> logic of Principia. As Russell admitted, the logic of Principia involves
> that the univers of speech is not empty. You can demonstrate in the logic
> of Principia that at leat an individual have to exist:
Indeed, in FOPL all values of the individual variable exist.
To be is to be a value of the indidvidual variable...Quine.
>
> (5) (a=a) -> (a=a)
>
> (6) (a=a) -> exist an x such that (x=x)
>
> (7) (a=a)
>
> (8) exist an x such that (x=x)
>
> and therefore U would be different from the empty set.
Yes. Ay(Ex(x=y)) is a theorem.
The set U, the set of all existent individuals is not empty...by
definition.
>
> But in our perspective, (6) is false, and can not be derived from (5), that
> is true.
Not so.
>
> In our logic we must have different rules from the treatment of quantifiers.
>
> I hope someone would like to work with me about these rules or give some
> suggestions to me,
You have assumed that there is meaning (members) of the the set of
non-existent things,
..this assumption is false.
There is an empty set, the null set, i.e. {x:~(x=x)}, but, it does not
have members!
Greetings,
Owen
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