Thus, "exists" is not a predicate, in syllogistic terms, because it is not a noun in plural form. — god must be atheist
Existence is not a predicate — TheMadFool
Perhaps Kant was saying that the existence of a metaphysical God is not something that can be predicated (asserted) in the usual empirical manner of physical Science. Religions predicate the existence of their intangible gods as an item of Faith.I don't think I've understood it yet. Any help will be deeply appreciated. — TheMadFool
In my opinion, Kant was right about this, because such ExistsExists predicate is going to be inconsistent. — alcontali
for it is possible to cognize a thing without experiencing the existence of it. — Mww
Perhaps Kant was saying that the existence of a metaphysical God is not something that can be predicated (asserted) in the usual empirical manner of physical Science. — Gnomon
Why? The statement "ghosts exist" isn't inconsistent in and of itself. It becomes inconsistent in relation to other facts but of itself it doesn't violate any logical rules. — TheMadFool
The theorem applies more generally to any sufficiently strong formal system, showing that truth in the standard model of the system cannot be defined within the system. — Wikipedia on Tarski's undefinability of truth
You seem to be saying god is the source of all being and so god must be/exist. — TheMadFool
I'm speculating about the origin of the idea that 'existence is a perfection'. I'm not speaking from the perspective of Christian doctrine or philosophy as such, but from a more anthropological perspective; I think many of the attributes of pagan gods were absorbed into later Christianity. — Wayfarer
How about the category E = things that exist? It's a valid category, isn't it? — TheMadFool
E is the predicate. "Things that exist." Each predicate is a clause, which may contain a subordinate clause. "Things that exist" is a predicate in language; but in syllogisms it is not a predicate.
Sometimes a person has to be extremely careful to be able to make fine and subtle distinctions between natural language and philosophical jargon (or any jargon.) — god must be atheist
all things identical to god are things that exist. — TheMadFool
Your comments... — TheMadFool
You are trying to use the meaning of the term predicate to determine if a particular property can be a predicate.
I just use a purely syntactic procedure, i.e. a bureaucratic formalism devoid of any possible meaning. — alcontali
However, there is no need to create a predicate Bx = x exists because the existential quantifier does the job of expressing existence and to say "rabbits exist" I simply say E(x)(Rx) where Rx = x is a rabbit. — TheMadFool
You seem to be saying predicates are syntactical elements which I don't think is correct. Consider the WFF E(x)(Px & Sx). If predicates are syntactic then they can't be altered at all because that would result in a syntactical error and that isn't the case here: we may say E(y)(Ay & Wy) and there is no syntactical error. — TheMadFool
A syntactic error is not only a violation against the formation rules in the formal language associated with the system. It is not just a language/grammar problem. A WFF -- without any (semantic) interpretation -- can still be syntactically invalid, if it is in violation with other axiomatic rules in the system.
For example, A = { A } is well-formed in the language of set theory but is not well-founded. There are specific axioms in ZFC that forbid a set from containing itself (axiom of foundation and of pairing). This is a purely syntactic requirement, because it does not matter what the meaning of A may be. — alcontali
but also inconsistent — alcontali
It leads to a pardox - Russel's paradox and, if I know anything at all, the axiom of ZFC were crafted in some way to prevent A= {A}. — TheMadFool
A formula A is a syntactic consequence within some formal system F of a set Γ of formulas if there is a formal proof in F of A from the set Γ.
A formula A is a semantic consequence within some formal system F of a set of statements Γ if and only if there is no model I in which all members of Γ are true and A is false.
The study of the syntactic consequence (of a logic) is called (its) proof theory whereas the study of (its) semantic consequence is called (its) model theory.[4] — Wikipedia on syntactic versus semantic entailment
It's not syntax that forbids it but the requirement for consistency. — TheMadFool
I don't think A = { A } is a syntactic error. — TheMadFool
unusual — alcontali
If 'a is P' becomes P(a) in its syntactical/first-order predicate logic, what are the real word implications? — 3017amen
This table is brown becomes, 'here now a brown table' or 'brown of this table' (Wittgenstein/Logical Positivism) — 3017amen
And if we convert them from its present tense (remove the word 'is'), '7 is a prime number' becomes:
1. 7 was a prime number
2. 7 will be a prime number
How do you think that would that square with Kant's view from the OP? — 3017amen
Why are you using unusual meanings/definitions on a "simple" matter of whether existence is a predicate or not? I mean, wouldn't that make your interpretation equally unusual and, ergo, less meaningful? — TheMadFool
It took me quite a bit of irritation to understand the gist of model theory. Initially, it appeared to me as nonsensical and absurd.
So, in the meanwhile, I have adopted their strange-looking definitions of "syntactic" versus "semantic". In fact, I did not have any choice in the matter. I wasn't able to continue reading anything at all on the subject, until I caved in and accepted their vocabulary, no matter how weird it feels.
Still, now I actually like it. In fact, upon reflection, it even makes sense (if you want to ...) — alcontali
I strongly suspect that time does not exist in the abstract, Platonic world(s) that is/are model(s) that satisfy number theory. The axioms of number theory do not depend on the use of the verb "to be" nor on any of its tenses. As far as I am concerned, the world of natural numbers is entirely static. — alcontali
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