Kant was using what contemporary philosophers would consider slightly ambiguous language. "Predicate" is a linguistic term, and existence is certainly a predicate in that technical sense: you can say "X exists", and "X" is the subject and "exists" is the predicate.

What Kant meant was that existence isn't a property of a thing. It's not like you can give a list of all of the properties of a thing and "existence" will be one of them. It's even more the case that you can't bake "existence" into the analytic definition of a thing: in my philosophy class that covered this, we talked about the example of a "perfect pig", and listed a bunch of things that are good properties of a pig, and of course such a pig actually existing is better than it not, so "existence" would have to be one of those properties right? So the perfect pig by definition must exist! It's as valid as the ontological argument for God. Kant's critique is that "existence" isn't the type of thing that belongs on a list of properties for anything; it's not a property.

He just phrased that oddly (to the contemporary ear) as "not a predicate" instead.

1. gives a quality to god, assuming god exists at the same time, since it can't have a quality without existence.
2. presupposes that if god does not exist, then its quality does not exist either.
2.1. There is a hidden assumption or premise: that the quality necessarily exists (i.e. that something is the greatest thing imaginable) as that is a concept without a doubt that anyone can entertain the thought of. You can rank all things for greatness; and if greatness is not equal between things, then there must be one that has the greatest amount of greatness.
3. It is impossible for god not to exist.

---------------

The "predicate" is a part of lines in a syllogism. Syllogisms consists of three lines, and they have strict rules of structures.

All Swedes are protestants.
Some Protestants are blonde people.
Therefore some Swedes are blonde people.

This is an invalid inference, but one of the forms of syllogisms. And syllogisms can be valid or invalid in their conclusions.

in the first line, "Swedes" is the subject, and "protestants" is the predicate.
In the second line, "protestants" is the subject, and "blonde people" is the predicate.
In the third line "Swedes" is the subject, and "blonde people" is the predicate.

In each line, the subject can be set to "all", "no", or "some". "Some" means "at least one", and it is a bit confusing, because in English "Some people are smart" presupposes more than one persons to be smart; but in syllogisms "some" strictly means "at least one".

The predicate, however, must be without a qualifier such as "some", "all" or "no".

Furthermore, in classic syllogisms, both the subjects and the predicates MUST be plural nouns. Countable plural nouns.

Thus, "exists" is not a predicate, in syllogistic terms, because it is not a noun in plural form.

-----------------

Since Aristotle, who invented syllogisms, for thousands of years, this was the shape of logic. Aside from the law of non-contradiction and of the excluded middle, the only form of acceptable arguments had been syllogisms.

This is not the case any more.

But I don't know if in Kant's time this was true or not, or if it was Kant that he himself destroyed the "hegemony" of syllogisms as a valid argument in logic.

--------------

To show what I mean:

"Socrates is a man.
All men are mortal.
Therefore Socrates is mortal."

is an invalid syllogism, although logically it is true. In a proper syllogistic form, it should read:

"All men (or beings) like Socrates are men.
All men are mortal beings.
Therefore beings like Socrates are mortal beings."

Likewise, we can transform Kant's Ontological argument into a syllogism:

All things that are the greatest things imaginable, are god-things.
(The second sentence can't be transformed)
Therefore god exists.

Here, we encounter two problems: 1. the argument is NOT in a syllogistic form, yet 2. it is a reasonable and acceptable argument. This could have presented a problem for Kant or his contemporaries; and since this argument exists, I assume that the invention of this ontological argument was the in-road into the new age of logical arguments where syllogistic forms were no longer necessary in an argument.

Thus, "exists" is not a predicate, in syllogistic terms, because it is not a noun in plural form. — god must be atheist

How about the category E = things that exist? It's a valid category, isn't it?

Thanks for the detailed exposition on Aristotle's syllogisms.
As I understand it, there are two kinds of statements: synthetic statements and analytic statements. Synthetic statements are those whose predicates are outside their subjects and whose truths lie outside the meanings of the words that constitute them.

Analytic statements, on the other hand, are self-contained units of meaning. The predicate in analytic statements is contained in the subject. If that's how it is then it becomes pointless to predicate existence as it merely amounts to repeating yourself; the subject predefined as extant. I'm unsure but it appears to be circular if utilized in a proof; kinda like "proving" a real object exists when you know that for an object to be real, it must exist - tautological.

That out of the way, consider Anselm's conception of god as the greatest possible being with existence being part of the definition of the greatest possible being.If that's Anselm's definition of god then his ontological proof amounts to, in my humble opinion, saying "god exists because god exists". Anselm's premise is an analytic statement and is distinct, per Kant, from a synthetic statement which "god exists" is, and in which the subject lacks a claim of existence, forcing us to look beyond Anselm's main premise to prove it.

I'm just wondering why Kant said what he said: "existence is not a predicate". It seems Kant thinks that existence doesn't add to the essence of god and to say "god exists" is simply to claim that god occurs in reality. In contrast, Anselm makes existence a predicate -as part of god's essence - and this is, according to Kant, wrong. If existence isn't a predicate then Anselm can't claim it as part of god's essence, and that, unfortunately, is the cornerstone of Anselm's ontological proof.

Existence is not a predicate — TheMadFool

In my opinion, Kant was right about this, because such $Exists$ predicate is going to be inconsistent.

Imagine that you have a simple formal language in which you can write "x exists" for any $x$ of your choice. Then, imagine a predicate $Exists$ that parses $x$ out of the number representing that sentence and then figures out if this $x$ exists:

$Exists(\ulcorner x \ exists\urcorner)$

Carnap's diagonal lemma says that there are "x exists" sentences for which the following is true:

"x exists" $\leftrightarrow \neg Exists(\ulcorner x \ exists\urcorner)$

So, there are true sentences "x exists" for which the predicate $Exists$ will be false or false sentences "x exists" for which the predicate $Exists$ will be true.

That is inconsistent. Hence, as suggested by Carnap's diagonal lemma, $Exists$ cannot be defined as a predicate.

What Kant means.....

Existence is a category, which are the pure conceptions of the understanding and serve as the necessary conditions for experience. Just as the definition of a word cannot contain the word, so too cannot a conception of a thing be determined by the merely logical conditions for it.

Adding existence as a real predicate to spheroid, inflatable, leather, in order to cognize basketball adds nothing whatsoever to the cognition, for it is possible to cognize a thing without experiencing the existence of it.

The first was posited to refute Locke’s common sense realism, the second posited to refute Hume’s constant conjunction empiricism.

Bring your own salt.

I don't think I've understood it yet. Any help will be deeply appreciated. — 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.

In my opinion, Kant was right about this, because such ExistsExists predicate is going to be inconsistent. — alcontali

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.

for it is possible to cognize a thing without experiencing the existence of it. — Mww

I think you hit the bullseye. Anselm's ontological proof rests on the claim that it is impossible to imagine a god, defined as the greatest being conceivable, without such a god existing in reality.

Kant, in saying that existence is not a predicate based on the premise that existence adds nothing to the essence of a concept, precludes the use of existence as a predicate. I mean a concept A is identical in essence to A as it appears in a claim "A exists", the mere fact of existence having zero effect on its meaning. Ergo, existence isn't a predicate for it fails to add anything to the essence of a concept, any concept: existence being only a claim about whether something corresponding to a concept occurs in reality or not.

If that's the case then Anselm, by including existence in the definition of god has treated existence as a predicate for he expects the quality of existing to add to the meaning of god in that for Anselm god is not just god but is actually the concept of god + existence. Kant's basic disagreement with Anselm seems to be that existence is not part of the essence of concepts which ties into his concept of analytic-synthetic statement: "God exists" is a synthetic statement and needs proof that is independent of the definition of god.

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

Kindly read my reply above.

I think one unstated premise in much of this is the archaic notion of 'the Pleroma'. The Pleroma was the divine fullness, the sense of the immense abundance of God-or-nature, as signified by the figure of the 'horn of plenty' borne by the Goddess Fortuna. She is depicted with an overflowing vessel out of which brims in some cases money symbolising wealth, or the abundant variety of Good Things (the original meaning of 'cornucopia'.)

So the idea behind this is the sense of the overwhelming fecundity of God, the gods, nature or what have you. This is the Pleroma - the sense that everything that could exist, does exist, as an expression of the unimaginable creative power of God/ the gods/ nature. There's a sense that one is born because of that, and that one must be both in awe of it, and grateful for it, as it is the source of all life/being/goodness. (Consider how that resonated in the last Ice Age, if you have trouble imagining it.)

Conversely, non-existence or non-being is a lack, an absence - the empty field, the failed harvest, and finally death itself. I think this is the origin of the aphorism 'nature abhors a vacuum'. So when it is said that 'being is a good', I think it harks back to this intuition; not to the dry discussion of whether "existence can be predicated". God's being is super-abundant in the sense of being the source of all that is good, in fact the source of everything; how could such a being not be?

I think that's the original sense behind 'the ontological argument' although by the time it becomes scholastic philosophy it's already pretty desiccated.

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 statement "What Peter says is true" isn't inconsistent in and of itself either. However, truth is not a legitimate predicate.

You cannot define a function such as truth("What Peter says") that will return true or false within the context of a "sufficiently strong" formal system. That result is known as Tarski's undefinability theorem (of the truth predicate):

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

So, truth is not a legitimate predicate.

I suggested in my previous comment to use the same proof strategy as in Tarski's undefinability of the truth predicate in order to prove Kant's undefinability of the existence predicate. The proof strategy is based on the following considerations:

If something is a predicate, then:

1) its negation must also a predicate
2) feeding its negation through Carnap's diagonal lemma may not yield contradictions

Unless there is a flaw in the strategy, i.e. a reason why this should not be done for the existence predicate, then in my opinion, we can reuse the standard proof strategy for Tarski's undefinability of truth to prove Kant's undefinability of existence.

(There are also diagonal-free proof strategies for Tarski's undefinability.)

Thanks for the fresh and interesting perspective.

You seem to be saying god is the source of all being and so god must be/exist. I think this runs into problems:

Either you're claiming that
1. god is the source of all being

or

2. All being is god.

The two differ in that the former attributes creation or being to god and the latter claims that being itself is god.

If you're claiming 1 then that's circular reasoning for in saying god is the source of (causes) being you're already assuming god exists

If you're going with 2 then you're changing the meaning of god from god being a creator to god being creation/the universe itself (pandeism).

Am I following you so far?

Thank you very much for your valuable input.

:up:

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.

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

:ok: got it! :up:

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.)

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

Can the statement "god exists" be expressed in categorical logic or not?

I think it can be as follows: all things identical to god are things that exist.

If you think it can't be then kindly explain.

all things identical to god are things that exist. — TheMadFool

I think "things that exist" is not a predicate in a syllogistic sense.

But you can invoke other types of logical arguments.

However, when Kant said "existence is not a predicate", then he, in my opinion, meant syllogism.

If you want to use logic other than syllogism, be my guest. Or your own. Or anybody's.

I actually don't know what "categorical logic" means. I know syllogisms; I know reductio ad absurdum; I know formal logic exists, but I don't know its rules; Alcontali and PFHorrest seem to be experts at it.

There is the Venn diagram, that I understand; there is set theory, some of the rules of which I am familiar with. There are logical connectors, and corresponding truth tables that I fully understand.

But I can't help you to express in categorical logic an argument that reflects what you want to say.

I thank you for your comments. I'm satisfied with my understanding so far. Existence isn't a predicate as it doesn't add to the essence of concepts, according to Kant.

Are you applying mathematical logic to the question of whether existence can be predicated or not?

I thought in math existential statements used E(x) as a notation. I tried once to express statements like "god exist" using existence as a predicate but it turned out to be unnecessary e.g. "god exists" = E(x)(Gx) where Gx = x is god. We don't need a predicate for existence like Bx = x exists which would require us to say, for "god exists", that E(x)(Gx & Bx) = there exists and x such that x is god and x exists where the predicate Bx becomes redundant.

I wonder why that is though. It seems to fit quite beautifully with Kant's view that existence isn't a predicate.

Logics that don't have existence as a predicate work fine because, in my opinion, if existence is a predicate then the following will occur:

If Bx = x exists, Ax = x is an apple, Rx = x is red
Some apples are red = Bx & Ax & Rx where the existential quantifier can't be distributed over other predicates with failure to express particular categorical statements of the form "some apples are red" which in the usual way, not treating existence as a predicate, is translated as E(x)(Ax & Rx)

Your comments...

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.

In this syntactic procedure, the reason why some property $\varphi$ cannot be a legitimate predicate, is not because of what $\varphi$ means. Its meaning does not matter at all.

It goes like this:

• There will be true logic sentences for which the predicate $\varphi$ will be false.
• There will be false logic sentences for which the predicate $\varphi$ will be true.

If the above leads to a contradiction, then $\varphi$ is not a legitimate predicate, regardless of what $\varphi$ may mean.

Furthermore, this bureaucratic formalism is even seemingly absurd. Seriously, Carnap's diagonal lemma truly appears as nonsensical to me. The only reason why I still agree to work with it, is because I cannot reject its proof, of which the canonical version is widely considered to be horrible (but surprisingly short). Seriously, I hate that proof.

So, the reason why any claim is justified, is because there is paperwork for it as well as a mechanical procedure to verify that paperwork. Seriously, that is the only reason. In my opinion, you need to handle the problem like a real pen pusher. Just shove the paperwork around. That is all that it is about.

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

I'm concerned about using the term "existence" as a predicate. That is the issue isn't it? In predicate logic we have statements like Mx is predicate and can be read as x is a Mouse. Same with Px, Ty, Dxy, etc. 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.

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.

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

There is no need for it, but it is also not even possible. Even a redundant existence predicate would be a problem. It would not be merely redundant but also inconsistent. Well, if my analogy with Tarski's truth predicate is correct ...

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.

Theorems derived from syntactic rules can also introduce syntactic requirements. In your example, E(y) may be a WFF but is still syntactically invalid because Carnap's diagonal lemma is a syntactic requirement.

You have the same situation in programming languages. A program may very well satisfy the rules of the BNF grammar for the language but the compiler will still arrest and reject the compilation on grounds of rules that are not (or cannot be) expressed in the grammar of the programming language. Only at run time, an error can become semantic, when the program is populated/interpreted with actual data.

Note: the dreaded "syntax error" is merely one type of syntactic error in a program. In fact, "syntax error" means "not well-formed error" (in mathematical lingo). All other compilation errors are actually also syntactic.

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

I don't think A = { A } is a syntactic error. 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}. It's not syntax that forbids it but the requirement for consistency.

but also inconsistent — alcontali

Show me how existence as a predicate leads to an inconsistency. All I see is redundancy, given predicate logic rules.

Hey Alcontali, quick question if I could. Can you tell me which is correct:

If 'a is P' becomes P(a) in syntactical/first-order predicate logic, what are the real word implications?

For example, you would have two options I think:

1. This table is brown becomes, 'here now a brown table' or 'brown of this table' (Wittgenstein/Logical Positivism)

Or, another sort of paradox is the usage in ordinary language over the tense of the verb 'to be'. 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?

I embrace much of Kant's Critique' relating to the fact that existence (the nature of) can never be conceived by reason alone, but if you remove 'is' from ordinary language, you either get some variation of an a priori logical abstract (which is fine) or something nonsensical.

Thoughts?

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

Agreed, but the terms syntactic and semantic have unusual definitions in mathematical logic:

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

If you can derive a new rule, i.e. theorem, from other rules, then what you are doing, is syntactic.
All axioms and all theorems in a theory are syntactic.

It's not syntax that forbids it but the requirement for consistency. — TheMadFool

Agreed, but according to the model-theoretical definition of the term, axioms are syntactic.

The term "syntactic" is not the same as merely "wellformedness". It means: irrespective of interpretation. A theory is syntactic. A proof is that too. Everything is actually syntactic in mathematics, except for truth, which is always semantic, as it occurs in a model, which is an interpretation of a theory.

The reason for this strange schism is the Löwenheim–Skolem theorem. Every theory that describes an abstract, Platonic world of infinite size, actually describes an infinite number of such worlds, depending on the interpretation of infinity. Given Cantor's work, there is an infinite sequence of infinities, basically the beth numbers. So, the theory is syntactic but truth is about what facts will exist in each of the abstract, Platonic worlds (=semantic models) that satisfy that theory.

I don't think A = { A } is a syntactic error. — TheMadFool

In model-theoretical lingo it is syntactic, because it applies to all possible abstract, Platonic worlds described by set theory. It is not applicable to just one model (such as a world associated to one particular choice of infinity). Regardless of your choice of infinity, this rule applies. So, that is why it is deemed syntactic.

unusual — alcontali

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?

If 'a is P' becomes P(a) in its syntactical/first-order predicate logic, what are the real word implications? — 3017amen

It could have an impact somehow, but that would have to be investigated/discovered by an empirical discipline. The requirement to maintain correspondence between statements and the physical universe is a whole can of worms in itself. Dealing with real-world implications is something that mathematics specifically does not do, simply because it has no empirical regulatory framework for that purpose.

This table is brown becomes, 'here now a brown table' or 'brown of this table' (Wittgenstein/Logical Positivism) — 3017amen

Yes, it is indeed a reification problem caused by the formation syntax of predicates.

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

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.

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 ...)

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

:lol: Sorry. You've been very helpful. I'm like the bad student who's got an exam at 9 AM and partied (hypothetically of course) all night, slept, got up only at 8:45AM and now is hungover, groggy and studying or trying to study at the proverbial 11th hour. I feel like Rip.Van Winkle.

You know a lot (in math :joke: ).

To return to the discussion, thank you for your time & effort but I feel you're explanation is too technical. Kant's objection is based on the meaning/semantics of concepts and existence but you seem to be taking the discussion into syntactics and so my reluctance to buy into your arguments. Thanks a lot.

Just my interpretation. To briefly speak to the OP, and much like Pfhorrest, my opinion is that Kant used the term 'predicate' loosely as a mantra to poke-holes in the ontological argument (a priori/analytical judgements-of course). And that his ongoing mantra (critique) is simply to expose the inescapable truth that we can never really know existing things-in-themselves (and the true nature of their/our existence) through pure reason alone-a priori. Accordingly, he taught math, and believed that there were limitations to such a priori truths... .

Thus, from Pfhorrest's quote: "What Kant meant was that existence isn't a property of a thing. It's not like you can give a list of all of the properties of a thing and "existence" will be one of them. It's even more the case that you can't bake "existence" into the analytic definition of a thing"

Kant was right when he basically said existence can never be conceived by reason alone. (As you've stated, I think you already know that- 'the synthetic a priori'- but just wanted to offer another opinion to maybe arrive at some consensus here.)

His attack was on analytical philosophers... .

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

Thank you for that confirmation.