EMTe wrote: ↑September 1st, 2022, 1:51 amWhy does original poster assume "number values" are existent things in opposition to nonexistent ones, whatever they are?
I don't think a numerical truth such as
"The number of US states is 50" implies that
there (really) is such an entity as the number 50.
Note that there is a distinction between
numbers as nonlinguistic mathematical entities and
numerals as linguistic entities (purporting to represent numbers); so the existence of numerals doesn't entail the existence of numbers (as abstract mathematical objects).
However, there is a further distinction between
tokens and
types of numerals:
Numeral-tokens are
concrete (mental or physical) objects, whereas
numeral-types are
abstract (nonmental and nonphysical) objects. Numeral-types are as (ontologically) abstract as numbers, but there is still a difference between them insofar as the former are (arguably)
language-dependent and the latter are not. (By saying so, I'm not implying that there really are abstract numeral-types and numbers.)
EMTe wrote: ↑September 1st, 2022, 1:51 amHow something can not exist, if the sole notion of non-existence is a simple linguistic trick.
Many things do not exist, but…
QUOTE:
"The problem, put crudely, is to make sure that things that don´t exist don´t end up existing after all."
"The complement class of 'exists' is purely intentional—its esse is concipi."
"There are no mind-independent non-existent entities."
"There are no non-existent things that transcend our cognitive acts; all non-existent things are objects of thought, as a matter of necessity."
"When we say that an object does not exist we are ascribing non-existence to a purely intentional object."
"Intentional objects have just those properties our mental acts confer on them."
"To exist is to have the simple property of existence, but non-existence seems to be matter of failed intentionality."
(p. 42)
"The basic truth condition of the negative existential is that there was only an entertaining of existence."
(p. 43)
"Non-existence is essentially and constitutively failed intentionality[.]"
(p. 43)
"[N]on-existence results from the occurrence of a certain kind of mental act—a pretence or an erroneous postulation of existence. Assertions of non-existence really are statements about mental acts."
(p. 43)
"[T]he non-existence of Holmes depends upon the occurrence of certain creative mental acts that have no target in the real world; if you like, such non-existence is supervenient on mental acts that have no real world reference."
(p. 43n45)
"[T]o say that an object does not exist is to allude to mistaken suppositions or acts of make-believe."
(p. 44)
"[N]on-existence really does have a lot more to do with misfirings of the mind than do other kinds of property lack."
(p. 44)
"The negation of existence works differently from the negation of other properties, because of the underlying representation-dependence of non-existence."
(p. 44)
(McGinn, Colin.
Logical Properties: Identity, Existence, Predication, Necessity, Truth. Oxford: Oxford University Press. 2000.)
:QUOTE