User:Gleki/Existential import: Difference between revisions

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b. Instead quantifiers, negation and their scope change the truth value of the <u>bridi</u> they are in.
b. Instead quantifiers, negation and their scope change the truth value of the <u>bridi</u> they are in.
=== Related pages ===
* [[Existential import]]
* [https://groups.google.com/g/bpfk-list/c/7NUB_ZT6vtI/m/h-WBVrAYxeYJ <nowiki>[bpfk-list]</nowiki> {ro}, existential import and De Morgan]
* [[quantification and the meaning of ⟨ro⟩]]
* [[Talk:BPFK Section: Logical Variables]]
* [[On the meaning of ⟨ro broda cu brode⟩]]
* [[De Morgan's Laws]]

Latest revision as of 07:52, 29 October 2022

Unrestricted variables

De Morgan Laws require that we first declare some existential variable(s), e.g. da, de.

1. We require that each such variable can refer to absolutely anything.

2. We also declare that referents of each such variable must exist in the universe of discourse (even if never talked about or needed), and the result of such declaration is to be called "presupposition".

3. We don't question the existence of references of such variables da, de because we declared such variables and with them the existence of their referents as we wished from the beginning.

In other words, the variable da (and similarly de) refers to the set of unanalyzable atoms in the universe of discourse. Such atoms are not to be questioned for their truth values since they are not propositions.

Now we can apply de Morgan laws:

naku roda su'ode zo'u da prami de ⇒ su'oda naku su'ode zo'u da prami de
(At least) someone doesn’t love anything. ⇒ There is somebody who doesn’t love anything.
It is false that: for every X, there is a Y, such that: X loves Y. ⇒ For some X, it is false that: there is a Y such that: X loves Y. [literally]

a. quantifiers, negation and their scope within a single bridi do not change the truth value of da: referents of da are presupposed to exist no matter what.

b. Instead quantifiers, negation and their scope change the truth value of the bridi they are in.

Restricted variables

Now we wish to use a restricted variable, e.g. di poi pavyseljirna ku'o.

It differs from the unrestricted one in that it filters from the universe of discouse only those referents of di that are unicorns. Other than that the universe of referents of such variable is still big enough, only that each referent is a unicorn.

In other words, the variable di poi pavyseljirna ku'o refers to the set of unanalyzable atoms in the universe of discourse. Such atoms are not to be questioned for their truth values; they are not propositions.

1. We require that each such variable can refer to absolutely any unicorn.

2. We also declare that referents of each such variable must exist in the universe of discourse (even if never talked about or needed), and the result of such declaration is to be called "presupposition".

3. We don't question the existence of references of such variable di poi pavyseljirna ku'o.

Now and only now we can apply de Morgan laws:

naku rodi poi pavyseljirna ku'o naku blabi ⇒ su'odi poi pavyseljirna ku'o blabi
It is false that: for every X-that-is-a-unicorn, it is false that: it is white. ⇒ For some X-that-is-a-unicorn, it is white. [literally]

Notice that de Morgan laws, quantifiers and negation didn't touch the philosophical problem of the existence of unicorns. The existence of unicorns in the universe of discourse is declared earlier than quantifiers and negation were used.

a. quantifiers, negation and their scope within a single bridi do not change the truth value of di poi pavyseljirna ku'o: referents of di poi pavyseljirna ku'o are presupposed to exist no matter what.

b. Instead quantifiers, negation and their scope change the truth value of the bridi they are in.

Related pages