I now have in my hands Saul Kripke's Reference and Existence: The John Locke Lectures, Oxford UP, 2013. The lectures were given over forty years ago in the fall of 1973. Why did you starve us for 40 years, Saul? It is not as if you did much in those years to improve the lectures beyond adding some footnotes . . . .
I for one find this 'new' book more interesting than Naming and Necessity because of its fuller treatment of existence, the juiciest, hairiest, and deepest of philosophical topics.
But I hit a snag on p. 6.
On this page Kripke accurately explains the Frege-Russell view of existence, a view which in the terminology of Frege can be put by saying that existence is not a first-level but a second-level concept. What 'exist(s)' expresses is a property of properties or concepts, the property of being instantiated. 'Tigers exists' says that the concept tiger has instances; 'Round squares do not exist' says that the concept round square does not have instances. But what does 'Tony exists' say? Nothing meaningful! Kripke:
To deny that it [existence] is a first-level concept is to deny that there is a meaningful existence predicate that can apply to objects or particulars. One cannot, according to Frege and Russell, say of an object that it exists or not because, so they argued, everything exists: how can one then divide up the objects in the world into those which exist and those which don't? (6)
This exposition of the 'Fressellian' view conflates two different reasons for thinking that existence is second-level only. One reason is that first-level predications of existence involve a category mistake. Russell famously claimed that a first-level predication of existence is senseless in the way that a first-level predication of numerousness is senseless. To give my own example, 'Terrorists are numerous' is meaningful and true; 'Ahmed the suicide bomber is numerous' is meaningless and (presumably) without truth-value. (After he detonates himself he still won't be numerous, only his body parts will!)
The first reason that first-level predications of existence are meaningless is because existence is the property of being instantiated and no "object or particular" can be meaningfully said to be instantiated. But note that if this is right, then it makes no sense to say that everything exists. For among everything are "objects or particulars" and they cannot be meaningfully said to exist. So the reason cited in the Kripke passage above cannot be a valid reason for the view that existence is not a first-level but is instead the second-level concept of instantiation. The reason Kripke gives presupposes that existence is first-level!
I was disappointed to see that Kripke glides right past this difficulty. The difficulty is that Kripke and Russell conflate two different reasons for the view that existence is second-level only. The one reason is that since existence is instantiation, it is meaningless to say of an individual (an "object or particular") that it is instantiated. The other reason is that everything exists. But again, if everything exists, then individuals exist whence it follows that it cannot be meaningless to predicate existence of individuals.
Another way of looking at the matter is that there are two senses of 'meaningless' in play and they are being confused. In the first sense, a meaningless predication is one that involves a category mistake. Thus 'Socrates is numerous' is meaningless in this sense as is 'Some triangles are anorexic.' In the second sense a meaningless predication is one that is true but would be pointless to make. If everything exists, then one might think that there is no point in saying of any particular thing that it exists. There is a failure of contrast. But since not everyone is a philosopher, there would be some point in saying of Anna-Sofia that she is a philosopher. (If, however, one were at a convention all of whose attendees were known to be philosophers, there would be no point in my introducing you to Anna-Sofia by saying 'Anna-Sofia is a philosopher.' Nonetheless what I would be saying would be true and free of category-error.)
We must distinguish between the following two claims:
A. 'Socrates exists' is meaningless because Socrates is not of the right category either to exist or not exist: Socrates is an individual, not a concept or property or propositional function.
B. 'Socrates exists' is meaningless because everything exists and thus to say of any particular thing that it exists is pointless.
Much of what it is pointless to say is meaningful, and true to boot. If I were to walk up to a woman on the street and exclaim, 'I exist,' and she didn't shrink back in horror, she might say 'True, but so what? Everything exists.' In the shallows of everyday life we don't go around saying 'I exist' and 'Things exist.' But 'I exist' and 'Things exist' are deep truths and the beginnings of the philosopher's wisdom. (For the religionist, however, the initium sapientiae is timor Domini.)
My thesis contra Kripke is this. One cannot give as a reason for the Frege-Russell doctrine, according to which first-level predications of existence are meaningless in the sense of involving category error, the proposition that everything exists and that predicating existence of any particular thing is meaningless in the sense of pointless. But that is what Kripke does in the passage quoted, which is why I call it confused. That everything exists is, pace Meinong, an exceedingly plausible proposition to maintain. But if so, then individuals exist and it must be possible to say -- meaningfully in the first sense -- of any given individual that it exists.
In short, 'Everything exists' is not a good reason to maintain that existence cannot be meaningfully -- in the first sense -- predicated of individuals.
Later in the Locke Lectures, at p. 37 f., Kripke points out that the Frege-Russell logical apparatus seems to allow for a definition of 'x exists' in terms of
1. (Ǝy)(x = y).
Kripke then remarks that "it is hard for me to see that they [Frege and Russell] can consistently maintain that existence is only a second-level concept (in the Fregean terminology) and does not apply to indivduals." (37) Kripke's point is that on the above definition 'exists' is an admissible first-level predicate contra the official 'Fressellian' doctrine according to which 'exists' is never an admissible first-level predicate.
Here too I think Kripke is missing something. What he misses is that existence defined in terms of (1) is not genuine existence, the existence that admits of a contrast with nonexistence, and that genuine existence is what Frege and Russell were trying to explicate, even though they failed quite miserably in my humble opinion.
I say that our logical luminaries, Frege and Russell, can consistently maintain that existence is exclusively second-level because defining 'x exists' in terms of (1), though extensionally correct, does not capture what it is for any existing item to exist. For all it says is that a thing that 'already' (in the logical not temporal sense) exists is identical to something. That's not exactly news. Given that Socrates exists, of course he is identical to something, namely, Socrates! That's utterly trivial. Frege and Russell were trying to get at something non-trivial when they kicked existence upstairs to the second level of concepts and propositional functions.
What were they trying to get at? They were trying to get at what one typically means when one either affirms or denies the existence of an individual that is not given in sense perception but for which one has a concept. God, for example. When the theist affirms the existence of God he does not say of something whose existence he presupposes that it is identical to something. Rather, he affirms that the attributes constitutive of deity are jointly exemplified when it is at least epistemically possible that they not be jointly exemplified. To put it in Fregean jargon, the theist affirms that the marks (Merkmalen) of the concept (Begriff) God are instantiated by one and the same individual when it is at least epistemically possible that the marks not be jointly instantiated. Quite simply, the theist affirms that the concept God has an instance. He does not affirm that God has a property (Eigenschaft). He speaks not of God, but of the concept God. The atheist's denial is then the denial that the divine attributes are jointly exemplified. He denies that the concept God has an instance. He does not deny that God lacks the property (Eigenschaft) of existence. There is no such property. And not because everything has it, but because (he thinks) the existence/nonexistence contrast would be inexplicable if everything had it. Existence that contrasts with nonexistence is instantiation. There is no existence/nonexistence contrast at the level of individuals, but there is such a contrast at the level of concepts with existence construed as instantiation and nonexistence construed as non-instantiation.
Or suppose I wonder at my sheer existence, my being 'here,' when as seems obvious I might never have been 'here,' might never have existed at all. So wondering, I am not wondering at my identity with something but at that which makes it possible for me to be identical to something, namely, the fact that I exist. If I exist, then necessarily I am identical to something, namely, myself. But what is it for me to exist when it is at least epistemically possible that I not exist? (I would say that it is really and not merely epistemically possible that I not exist, that I am really and not merely epistemically a contingent being; though how I know this is an interesting question in modal epistemology or rather the epistemology of modal knowledge/belief.) On the Frege-Russell approach, one is driven to posit some sort of individual concept or haecceity property the instantiation of which is the existence of me. But that leads to terrible difficulties (covered in mind-numbing detail in my existence book) that I can't rehearse now.
Frege and Russell were trying to explain how there can be a meaningful contrast between existence and nonexistence on the assumption that everything exists. (Given that everything exists, one cannot say that some items have the property of existence and some items do not. As Kripke puts it, p. 37, "Things are not of two kinds, existers and nonexisters.") Our logical grandpappies thought that to capture the contrast they had to kick existence upstairs to the second level, the level of concepts, properties, propositional functions and the like, and then reinterpret existence as instantiation or, in Russell's jargon, as a propositional functions' being "sometimes true."
My thesis has long been that this leads to disaster. See my "Existence: Two Dogmas of Analysis" in Novotny and Novak eds., Neo-Aristotelian Perspectives in Metaphysics, Routledge, 2014, pp. 45-75.
By making this ascensive move they removed existence from individuals and at the same time removed from individuals the distinction of essence and existence, Sosein and Sein, essentia and esse, pick your terminology. Having situated the existence/nonexistence contrast at the second level, no contrast remains at the first level, the level of individuals or particulars. Yet these individual must exist if they are to instantiate properties. But then either (i) each individual necessarily exists -- which is absurd -- or (ii) genuine existence cannot be noncircularly defined in terms of (1), in terms of identity-with-something-or-other.
Let's explore this a bit.
Kripke points out that 'Everything exists,' i.e. 'Everything is identical to something,' i.e.
2. (x)(Ǝy)(x = y)
is a theorem of quantification theory and thus necessarily true. (p. 37) But from
3. □(x)(Ǝy)(x = y)
one cannot validly infer
4. (x)□(Ǝy)(x = y).
That is, from 'Necessarily, everything is identical to something' one cannot validly infer 'Everything is necessarily identical to something,' i.e., 'Everything necessarily exists.'
Surely most individuals exist contingently: each of these individuals is possibly such that it does not exist. Socrates exists but is possibly nonexistent. The predicate 'possibly nonexistent' is first-level. It is true of Socrates because he is not identical to his existence (in the manner of a necessary being) but really distinct from his existence. Clearly, the possible nonexistence of Socrates -- a feature he actually possesses -- cannot be identified with his possible non-identity with something, namely, Socrates. Socrates is not possibly non-identical to Socrates. If existence is self-identity, then nonexistence is serlf-diversity, and possible nonexistence is possible self-diversity. But surely Socrates' possible nonexistence is not his possible self-diversity.
What this shows is that the definition of 'x exists' in terms of '(Ǝy)(x = y)' does not capture genuine existence, the existence that admits of a contrast with nonexistence. Because of this, Frege and Russell can contrary to what Kripke maintains consistently hold both that (a) existence is a second-level property and that (b) 'x exists' is definable in terms of '(Ǝy)(x = y).' They can consistently hold this because 'exists' so defined has nothing to do with genuine existence, the existence that admits of a contrast with nonexistence.