# Is there anything more fundamental than quantification?

In the prevailing view of the concept of "Existence," it is well-known that it isn't a property of individual objects, but rather a property of properties. As Frege would put it: It is a second-level concept. And you could also phrase it as existence not being a predicate at all, but a quantifier instead.

All of that is fine and dandy, but it does make me question: If existence/quantification stands at the foundation of predication, does it make sense to predicate things of existence itself? And to extend the question: Can you quantify over the existential quantifier itself?

Intuitively, it would seem that you can't, but I believe Type Theory does allow the extension of properties to arbitrarily high 'orders', where first-order properties are instantiations of second-order properties, which then are instantiations of third-order properties, and so on. Following that method, could it be said that you can go "beyond being"? Or does Type Theory simply not deal with the notion of existence as a property of any order at all?

• Those are actually four different positions: existence is a second-level property, existence is just what you can quantify over, existence is a first-level property, and existence is something that objects have but is not, strictly speaking a property. All of these positions have current advocates. Commented Feb 12 at 7:08
• On the contrary, worse than classical logic most type theories are rooted in constructive logic which must bear a witness for any existential type (proposition), thus it cannot express existence as a property up to any order since any witness must be of some other specific type apart from your demanded 'property of existence'. You cannot go beyond the (problematic) type of all types aka universe to reach the type of existence though you can have infinite number of types of other types as the common higher order types, dependent function/sum types, inductive type, equality type, refl type... Commented Feb 12 at 8:34
• Interesting. So would "Existence" simply not be something that is accounted for in the context of type theory, then? Something like a notion that really only exists in the meta-language, rather than in the object-language. Commented Feb 12 at 8:36
• But Quantifier expressions "are marks of generality. They come in many syntactic categories, but determiners like “all”, “each”, “some”, “many”, “most”, and “few” provide some of the most common examples of quantification." These expressions all refer to objects in a domain of real or fictional entities assumed for the sake of discourse as... existing. Thus, it seems hard to believe that they can be defined in some way prior to "existence". Commented Feb 12 at 13:10
• You might be interested in the work of Graham Priest. He argues that existence should be viewed as a regular predicate Ex. He replaces the existential quantifier with a quantifier that means "for some x", but does not imply that x exists. If you think about it, this is the more parallel treatment with the universal quantifier, where we don't assume that the domain of qualification must must be non-empty. So it can be true that all unicorns are blue, because there are no unicorns. Similarly, it could be true that some unicorn is blue, even if no unicorn exists. Commented Feb 12 at 17:41

What is most fundamental to a logic is the set of mechanical procedures by which we may derive theorems in the logic; the inference rules. These procedures are not specified within the logic. The meaning and semantics of ∀ and ∃ depend on these procedures, if the logic has them at all, and it may not.

Some logics, such as ZFC, allow unrestricted quantification: ∀x

Some logics, such as type theory, require all quantification to be restricted: ∀x∈y

Some logics lack quantification, such as lambda calculus.

So, clearly, the nature of quantification is contingent on the logic, not universal among logics. So it can't be fundamental.

But am I missing the point? Perhaps you were asking about existence in reality, not existence as a symbol within a logic. If so, it is important not to muddle the two notions. Logic is at most a description of reality. Reality itself consists of wordless dynamics, and does not throw around quantification symbols. Everything we do in logic is a result of these wordless dynamics, in our brains or in calculating machines. Thus, it is these wordless dynamics that are truly fundamental.

• That's a good point! I've a few Platonist leanings, myself, so perhaps when I made this question I was unconsciously reifying these logics into something identical to reality. Under those lenses, it seems I was thinking specifically of predicate logic and extensions thereof (Third, fourth, fifth...-order logics) when I wrote the post, rather than simply logical systems in general. Commented Feb 12 at 10:44

Existence as a subject of which other things are predicated, vs. as a predicate of other subjects, is where the role of the (mostly classical, even so) subsistence relation comes in to play. That is, we can read "to exist" as "to be predicated of existence," and then existence appears as a sort of general substance, since a substance is (again classically) that which is a subject of predication (as attribution) first and foremost.

One manifestation of this could be monism: rather than say e.g., "There is a table here," we say, "The world exists tablewise here." Or we can think of Aquinas' claim that there is a being that is subsistent being itself (God, of whom all other things are predicated as creations), or Meinong's difference between two grades or kinds of existence/being.P

Now, as to the question of fundamentality, there might not be anything more, but there might be things equally, fundamental. For example, if we equate quantification with extension, then qualification-as-intension can seem just as elementary to the logical scene.

PIt has been said that what we call "the existential quantifier" might be better known as "the particular quantifier," but see e.g. Kant's theory about faculties of intuition for significant overlap between the concept of existing and the concept of being a particular.

• That seems strange to me. If you reify "Being" itself into something that's actually floating around out there (As Aquinas did, though he of course didn't say God is an Universal or something of that like, since he didn't think of existing as a property but an act), then it seems you enter into a situation where something is both a property and something which properties are predicated of. Does that not introduce anything problematic to the table? Commented Feb 12 at 10:56
• @JohnathanGreen perhaps that is the consequence: first-order properties, having second-order properties themselves (like "the property of being a property"), are then second-order substances/objects, and the list goes on... But it seems as if every theory of predication ends up with a Third Man or Bradley's-regress, etc., kind of problem, so maybe the problem is the solution (that something about predication manifests in a similar way in different models/theories). Commented Feb 12 at 11:48
• It brings to mind Kant's distinction between "logical predicates" and "real predicates," where the former was any description whatsoever and the latter was something that actually adds a determination to a thing. Maybe it is that the reified property of "Existence" would have only itself as a "real predicate," whereas other descriptions of it would be only logical predicates. Though if you adopted that, I suspect the usual slogan would have to go from "Existence is not a real predicate" to "Existence is not a real predicate -of objects-" (While remaining one for properties) Commented Feb 12 at 12:55
• @JohnathanGreen Problematic. Some people argue yes. If existence is an abstraction and not something concrete, then to do so is a fallacy. en.wikipedia.org/wiki/Reification_(fallacy) However, in plato.stanford.edu/entries/abstract-objects the argument is made that perhaps to consider a thing as both concrete and abstract at the same time we avoid black and white thinking which is another fallacy en.wikipedia.org/wiki/False_dilemma. The truth is you can manufacture either fallacy as a function of your metaphysical presuppositions, a hallmark of underdetermination.
– J D
Commented Feb 12 at 19:09
• To complicate the matter, as Kristian notes, the problem of universals rears its head. Is a dog a concrete thing, or is it an abstraction over the breeds of dogs. Is a breed a concrete thing or an abstraction over instances of a breed? Is Fido a concrete thing, or Fido over some duration of time a separate set of concrete things? One of the ideas that Kristian has turned me onto, @JohnathanGreen, is the notion of tropes:
– J D
Commented Feb 12 at 19:13

I wasn't going to respond, however:

It is difficult metaphysically to draw the line between what is a property and what is an object. Some people argue yes. If existence is an abstraction and not something concrete, then to do so is a reification fallacy. However, in the SEP's article on abstract objects the argument is made that perhaps to consider a thing as both concrete and abstract at the same time we avoid the false dilemma which is another fallacy. The truth is you can manufacture either fallacy as a function of your metaphysical presuppositions, a hallmark of underdetermination Quine suggests we are constrained by when using evidence and language to describe our experience.

To complicate the matter, as Kristian notes, the problem of universals rears its head. Is a dog a concrete thing, or is it an abstraction over the breeds of dogs. Is a breed a concrete thing or an abstraction over instances of a breed? Is Fido a concrete thing, or Fido over some duration of time a separate set of concrete things? One of the ideas that Kristian has turned me onto is the notion of tropes (SEP): –

"Recently, however, both friends and foes of tropes have started to question whether tropes can be a bit of both. At any rate, this will depend on what being a property and being an object amounts to, an issue on which there is no clear consensus."

This is where metaphysical presupposition arises. What DOES it mean on being a property? What DOES it mean to be an object? Different people have different thoughts on that. Mereological nihilists admit no objects other than particles and configurations, for instance, and insist there are only configurations of atoms as chairs, and not chairs!

Is there anything more fundamental than quantification?

As someone who cleaves to a constructionist epistemology, one possible solution would be to answer in the affirmitive. Yes, more fundamental than quantification is thought, because thought is that by which quantification occurs. This would be consistent with a reading of a nominalist (SEP) of abstract objects. Existential quantification is an abstract object which doesn't exist in the sense of apples and oranges. Rather it is an experience wherein we sense and use language to describe, and that the act proper is not fundamental. It's just one of a range of tools or experiences that allow us to organize our thoughts using language. This is why you'll see fiction used as a metaphor in describing certain positions. Just because we use words doesn't mean we are dealing with physical reality at all. Existential quantification is just vocabulary to describe being devoid of whatever it means to exist in a real sense.

• I reread your question, and within the context of type theory, a type theoretical declaration requires at least two tokens (more in the case of dependent types, subtypes, universal types, etc.) One for the entity and one for the type. Implicit in that there are two existential declarations, one in the metatheory of type theory for the existence of the entity, and one for existence of the type, but note the problem we find here. Implicit in the existential declaration of the entity, is the existence of the category of entity independent of the entity, and the same for the type of type...
– J D
Commented Feb 12 at 20:11
• Each of those then requires that the metatheory have a judgment mechanism in place, but that judgment process is itself generally implicit and derived from the metaphysics of natural language since type theory has the role of moving from natural language ontology to the formal semantics of a formal system. This process is called in type-theory grammar by Ranta, informal formalization. So, as a type theoretician moves from natural language semantics to formal semantics, there are a set of existential declarations as acts that are not reflected in the syntax of the formal semantics itself...
– J D
Commented Feb 12 at 20:14
• and that puts us at my answer. Existential declaration, implicit or explicit, in the act of predication is both an element of the natural language aspect reflected in the metatheory of formal semantics, but also in the artificial language aspect reflected in creating the syntax to represent the psychological act. So, in another sense, existential declaration may not even be codified in the formal semantics, but is part of the semantic action of the compiler itself if the type system is automated. Consider in Haskell 'apple :: Food'...
– J D
Commented Feb 12 at 20:17
• at compile time, the entity apple is created and assigned type 'Food', the 'existential declaration' isn't part of the formal syntax in the same way it would be in first-order logic: '∃Entity(apple), ∃Type(Food); Food(apple)'. Note how there are two statements where Haskell only requires one. But of course, we can go higher order: '∃Type(ExistentialQuantifier)'.
– J D
Commented Feb 12 at 20:23
• Very enlightening answer! That said, something I ought to note with respect to one part of it is that, as said in another comment, when I asked this question, I was (admittedly unconsciously) drawing from my own Platonist leanings and reifying the system of predicate logic and its extensions into something co-extensive with actual reality. While your answer was very informative, saying that "thought" is more fundamental than existence/quantification is already stepping outside of the logical domain and into the realm of the mental processes by which we do logic to begin with. Commented Feb 12 at 21:16

Yes, there is. Observations or, more generically, perception. These are a prerequisite for quantification.

They can be fooled, yes. Hence, we usually correlate these with more than one sense (touch with eyesight, or eyesight with hearing, etc.). Or we create requirements to deal with such error, such as "replication", as in science.