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On “Is”

<<τὸ ὂν λέγεται πολλαχῶς…>> (Bill Clinton and Aristotle)

“Is” (to be) is a tricky word, and I think the ambiguous nature of this word has led to some misunderstandings of some of the arguments I present, which are typically written in Free Logic. “Is” has multiple meanings, and some of the meanings are more “ontologically committing” or “existentially loaded” than others. Some common logical notation that gets translated as “is” in ordinary language include: 1) “(∃x)”, 2) “=”, 3) “Px”, and 4) “≝”, and I would like to emphasize that they are not syntactically equivalent, and do not function in logical arguments in the same way.

1) The “is” of existential quantification: There is an x, e.g. there is something green, or (∃x)Gx,. This can be interpreted as a “particular quantifier” indicating that there is at least one individual x. Depending on the domain of discourse, the existential quantifier can be more or less ontological committing. One could say, there is a fictional detective that Arthur Conan Doyle wrote about, and use the existential quantifer, and one would not be committed to the reality of fictional beings, i.e. (∃x)(Fx & Wax) [read: there is an x such that x is fictional and Arthur Conan Doyle wrote about x], s = x satisfies the formula in this case, where “s” means “Sherlock Holmes”.

2) The “is” of identity: (x = y), e.g. Tully is Cicero, or (t = c). Sometimes the “is” of identity is combined with the existential quantifier to make strong existential claims, e.g. there is a planet named Venus: (∃x) [Px & (x = v)]. There are rules around identity that are, themselves, metaphysically complicated, and it is controversial how those rules should apply to logic. For instance, it is sometimes granted that (∀x)(x = x) can be introduced at any stage of an argument simply because everything is self identical. Also, if a = b, then b can be substituted for a in an argument in some, but not all, contexts. The contexts were such substitutions cannot occur are called “referentially opaque contexts”. For example, Clark = Superman. Lois believes Superman = Superman. But it doesn’t follow that Lois believes Superman = Clark.

3) The “is” of predication:  x is purple, or simply Px. This “is” is not very existentially committing, but merely ascribes properties to individuals, on could say Sherlock, where “s” is Sherlock, and “B” is the predicate “Brave”: Bs. In “Free Logic” to make strong “existentially loaded” or “existentially committing” claims, you might specify “Real Existence” as a kind of predicate said of an individual. This might run contrary to “Kant’s Dictum” that existence is not a real predicate, but alternative ways of forming existential claims about what exists in the world are problematic for other reasons. When I construct ontological arguments, I tend to use Free Logic. This is because free logic allows you to quantify over things that may or may not exist in reality, which is needed, if one is not to beg the question in ontological arguments.

4) The “is” of definition: for example, the name “God” is “the x such that x is perfect”, or g ≝ (ɿx)Px.  I might stipulate such a definition in an argument by writing “D1: God is perfect.” This is not an existentially committing sentence, but a stipulation of the meaning of a term. Definitions are not really propositions in the fullest sense, as they are not true or false, but merely what one means when one uses a term in a proposition. As such, a definition is usually assessed in terms of clarity and coherence rather then whether it is true.  The scholastics would make this point by saying that definitions pertain to the first act of the mind, not the second.  Explicitly adding predicates into a definition in order to prove that the thing defined has those predicates can be question-begging, this would include adding “real existence” as a predicate in the definition, e.g. A shmunicorn is a unicorn that exists, therefore shmunicorns exist would constitute a question-begging proof. Adding “existence” directly into a definition also entails that the thing defined would exist necessarily, since one can add necessity to any conclusion derived from zero premises. It would be unclear and possibly incoherent to say that shmunicorns exist of necessity, so such a proof should not command assent. My ontological arguments for God are never zero-premise, and always require one or more premises to reach the conclusion.

So this can help us to disambiguate.  Consider the following sentence: “There is an individual who is the author of this blog and who is Daniel, who is the only son of James and Kathy Vecchio, and who is.”

Axy ≝ x is the author of y
Sxyz ≝ x is the only son of y and z
d ≝ (ɿx)Sxjk
j ≝ James Vecchio
k ≝ Kathy Vecchio
b ≝ Vexing Questions blog

(∃x){[Axb ∧ (x = d)] ∧ E!x}

There are a lot of “ises” in that expression, but we can now see how each has its own function.

A Modal Argument Against Naturalism from Transcendentals

For any argument against naturalism, we are going to have to specify the sort of naturalism we are discussing.  Here, my target is a rather broad notion of metaphysical naturalism.  Let’s define the notion in the following way: naturalism is the thesis that reality is exhausted by the natural.[1]  This is, admittedly not an informative definition (and somewhat circular), but it will do the job of being relatively broad for this argument, but not so vacuous as to be uninteresting.  Many contemporary naturalists would assent to the definition, and I, being Catholic, believe that naturalism, so defined, is false.

P1. Naturalism is true just in case “natural” is greater than and includes the combined extensions of terms that name each and every one of the categories into which being may be divided.[2]

P2. “Natural” is greater than and includes the combined extensions of terms that name each and every one of the categories into which being may be divided just in case “natural” is a transcendental that is convertible with “being”.

P3. All terms that are transcendental that are convertible with “being” are necessarily transcendentals that are convertible with “being”.

P4. If naturalism is true, naturalism is contingently true.

P5. If naturalism is contingently true, it is false that “natural” is necessarily a transcendental that is convertible with being.

C1. Therefore, naturalism is false.

The argument is a reductio, as the premises lead to an obvious contradiction if one assumes naturalism is true (i.e. “natural” is necessarily a transcendental that is convertible with “being” and it is false that “natural” is necessarily a transcendental that is convertible with “being”). Given the definition of “transcendental” and the plausibility of P3-P5, naturalism cannot be the case.

There are a few ways the naturalist may object (and why I think they are inadequate objections):

Objection 1: “Natural” is not a transcendental.

Reply to 1: If “natural” is not a transcendental, as defined extensionally, then it is not exhaustive of reality.  Let’s say that reality is composed of everything, all beings.  If “natural” doesn’t exhaust all beings, then there are beings that are not natural.  That, to me, is sufficient to falsify metaphysical naturalism.  So this is not a very good move to make, though it may be a knee-jerk move to make in response to the argument.

Objection 2: There are no transcendentals.  The idea that res, unum, aliquid, bonum, et verum or any other supposed transcendental like “beauty” is convertible with being is a quaint notion from an outmoded era of philosophy and theology when people drank in far too many Hellenistic notions.

Reply to 2: Fine, you dislike older ideas.  But the extensional definition of transcendentals are still on the table and there is no reason to think that we cannot categorize being, or devise a notion of a term that is universal.  After all, as I suggested in response to the first objection, to say that “natural” exhaust reality is to say something about the universality of “natural” and that its extension would be as broad as “being” or “reality”.  So, it sounds odd to object to there being transcendental terms when naturalism, so defined, depends on it.  Ah, but “naturalism” could be defined in other ways.  That’s true, but those sorts of “naturalisms” are not the target of this argument.  Moreover, I am not too sure that I am opposed to a form of metaphysical naturalism that is too timid to claim that “natural” exhausts “being”.

Objection 3: P3 is false.  There is no reason to think that if some term is convertible with “being”, then it is necessarily so.  It might be contingently convertible with being, especially if “transcendental” is only being defined extensionally.  That is, the transcendentals could merely happen to be convertible with “being”.

Reply to 3: It would seem, then, that we have two sorts of transcendentals: contingent transcendentals that happen to be convertible with “being” and necessary transcendentals that are necessarily convertible with “being”.  So, for instance, if God were actually to exist, there would be a sense in which res, unum, aliquid, bonum, et verum could be applied to God.  But, presumably, if God were to exist, “natural” could not apply to Him.  In other words, were there super-natural beings, “natural” would have a smaller extension than “being” and “natural” would cease to be a transcendental.  Yet, the other named transcendentals are not like this.  No matter what possibilia comes to be, the transcendentals would remain what they are.  It’s just that the actualization of the possibilia means that the actuality is res, unum, aliquid, bonum, et verum.  It seems, then, that the naturalist would be committed to the thesis that “natural” is convertible with “actual”, i.e. everything is actual if and only if it is natural.  But “actuality” is not a transcendental.  Rather, one can divide the various categories of being into act and potency.  In other words, actuality has a smaller extension than any given category and, a fortiori the combined extensions of all the categories of being.  Now the naturalist might quibble and say that any potential or possibility of the non-natural, or supernatural, is itself natural.  But this is not to address the question of whether “natural” is extensive with all potentials and possibilities, but just the actualities in which those potentials and possibilities obtain.

Another issue is that it is rather question-begging to demand that “natural” is one instance of a “contingent transcendental” convertible with being given what actually happens to exist.  Is there another such transcendental? Why are all the other transcendentals necessary and remain transcendentals no matter what happens to be in the world.

Objection 4: P4 is false.  Metaphysical worldviews, if true, are necessarily true.  Thus, if metaphysical naturalism is true, then it is somehow necessarily true.

Reply to 4: This is a rather strong position to take.  For it not only posits that supernatural entities, like souls, and gods, do not exist.  It posits that they cannot exist for metaphysical or broadly logical reasons.  It is not clear to me why this must be the case, and there seems to be good reason to think this is false.  1) Even if it is not supposed that the Anselmian God is metaphysically possible (from which, some would argue, His existence could be demonstrated), a less than maximally great or perfect divinity is plausibly metaphysically possible.  That is, a being that would sufficiently falsify naturalism, even if it is not morally perfect, omniscient, or omnipotent, could exist.  What’s more, if metaphysical naturalism is metaphysically necessary, then it would satisfy the Leibnizian question “why is there something rather than nothing” in much the way classical theists think God satisfies this question.  The classical theist says that God is metaphysically necessary, so not anything existing is impossible.  But the metaphysical naturalist doesn’t seem to make the same move.  Faced with the radical contingency of reality, the metaphysical naturalist usually doesn’t say that since metaphysical naturalism is metaphysical necessary, there must be at least one natural thing in existence.  If nothing were in existence, then nothing natural would exist.  Now a particularly impish naturalist might suggest that, were there nothing in existence, metaphysical naturalism would be true.  That is, one natural configuration of the world is “there not being anything”.  But if there were nothing, it wouldn’t be the case that “natural” exhausts reality.  “Natural” would not be predicated at all.  It would no more “exhaust” reality than “supernatural”.  So there not being anything is not compatible with metaphysical naturalism being true.  So if metaphysical naturalism is necessary, nothing is intrinsically impossible.  Yet, we have no reason to think that if naturalism is true, some natural thing or other must exist.

Objection 5: Okay, metaphysical naturalism is only contingently true, but “natural” is necessarily a transcendental convertible with being anyways.  In other words, P5 is false.

Reply to 5: Well, if there is no possible world where “natural” fails to exhaust “being”, then metaphysical naturalism would be true in every possible world.  Metaphysical naturalism cannot be contingent while it be necessary the everything is natural.  That just is to claim that metaphysical naturalism is true in every possible world (a strong claim to make).

In Sum: If I were a naturalist, I think I would try to argue that some transcendentals are contingent. I don’t think the argument would be very convincing, for the reasons I mentioned.  After that, I think I would want to argue that metaphysical naturalism is necessary.  Remember, it is not enough to simply say that metaphysical naturalism could be necessary. If all of the other premises of my argument are correct, and one wants to maintain metaphysical naturalism as true, one would have to admit that the only way it could be true is if it is metaphysically necessary.  However, I don’t see any good reason to think metaphysical naturalism is metaphysically necessary for the reasons I’ve outlined above.  So, it seems to me that, since “natural” is not a transcendental of “being”, metaphysical naturalism is false.

[1] Papineau, David, “Naturalism”, The Stanford Encyclopedia of Philosophy (Spring 2009 Edition), Edward N. Zalta (ed.), URL = <>.

[2] This is based on an extensional definition of transcendentals offered by Jorge J.E. Gracia. See Jorge J.E. Gracia, 1992, “The Transcendentals in the Middle Ages: An Introduction,” Topoi 11(2): 113–120. Also Wouter Goris and Jan Aertsen, “Medieval Theories of Transcendentals”, The Stanford Encyclopedia of Philosophy (Summer 2013 Edition), Edward N. Zalta (ed.), URL = <>