PHIL HANSON’S NOTES  FOR PHIL 203, GARRETT, CH 3, “EXISTENCE”

Distinguishable questions about existence:

(1)     What exists?

(2)    What sorts of things exist?

(3)    What is the concept of existence?

(4)    What is the nature (if anything) of existence?

Garrett indicates that his main interest in this chapter is (4), and that his method for answering it will be to proceed ‘logico-linguistically’.

Taxonomy of Existence Attributions

                                Positive                                                                                                                                Negative

Singular                                                Plural                                                                     Singular                               Plural

Mt. Baker exists                               Horses exist.                      Santa Claus does not exist           Unicorns don’t exist.

 

Truth-maker Principle:   When an attribution is true, there is something that makes it true.

Question:  So, what makes existence attributions true?

[SIDEBAR: PREVIOUS METHODS FOR ANSWERING THE QUESTION OF THE NATURE OF EXISTENCE

1.       Early Modern Rationalism -- Descartes: reflecting directly on our concept of existence.

 

The transparency principle: everything in our minds (including the concepts in terms of which we formulate our thoughts) is accessible to reflective consciousness. 

 

Existence is a basic concept whose content is not derived from anything external to our (conscious) minds.  (Consider, e.g., the cogito)  The new science shows (contra Aristotle) that all of our ideas are innate1, in the sense that, though their content is occasioned by and correlated with external stimuli, the specific form that they take in the mind is determined by the dispositions of the mind itself.  But some of our ideas are also innate2 in the sense that their content is not occasioned by external stimuli at all, e.g., our ideas of God, the infinite, and existence.

Question: How objective is this method of reflection?

 

2.       Early Modern Empiricism – Hume:  reflecting on our memories of sensory impressions, then querying how our idea of existence could have arisen from them.

 

The transparency principle: (same as above).

 

The empiricism principle: All of our (legitimate) ideas are derived from our sensory impressions.

 

So there are no innate concepts.  Hume, Treatise, Bk I, Pt. II, sec. VI: We have no idea of existence at all separate from our ideas of things that we take to exist.  To exist is to be perceived or conceived (comp. Berkeley).

Question:  Is this method any more objective than that of the rationalist?   END OF SIDEBAR]

 

(Back to Garrett.) 

‘Surface grammar’ vs. ‘Logical grammar’ (or ‘Real grammar’)

Two views about existence claims:

1.        The Property View: existence is a property, and the surface grammar of a positive existence attribution captures the logical (‘real’) grammar of the attribution.

Compare:  ‘John is bald’, and ‘John exists’.   In both cases, the truth-maker for the claim will be the fact that the object denoted (i.e., John) has the property attributed by the predicate (in the 1st case the property of being bald; in the 2nd case, the property of existence).

2.        The Quantifier  View: the logical grammar of existence claims is not their surface grammar.  “Exists” is not a predicate, and so existence is not a property.  “Exists” is a quantifier, meaning roughly “at least one”.  The truth maker of “John exists” is simply John.   The logical grammar of “John exists” is rendered roughly as “There exists an x such that x is numerically identical to John”, or in Standard Logical notation: Ǝx(x = John).

[SIDEBAR:  Note that in one way the Quantifier View  resembles Hume: there is just the object, not the object plus its property of existence.  But this does not let Hume off the hook, given his rejection of innate ideas.  If our idea of existence is the idea of a quantifier, where does it come from?  According to Hume it would have to come from our sensory impressions.  Seems unlikely.]

But both of the Quantifier and Property views have trouble dealing with true negative existential claims, like “Santa Claus does not exist”.     If the negative existential claim is true, then it is asserting that there is nothing to which to attribute the property of existence (or, on one version of the Property View, the property of non-existence), but then what is the truth-maker for the claim supposed to be on the Property View?  Turning to the Quantifier View, is the truth-maker supposed to simply be that there is no object?  If so, this proves hard to represent quantificationally.  Either ‘Santa Claus’ is not admitted into the language of 1st order logic at all because it does not refer to anything in the Domain of discourse,  or it is admitted but then we can easily generate a contradiction.

[SIDEBAR: STANDARD LOGIC, I.E., 1ST ORDER PREDICATE LOGIC WITH IDENTITY.  It was developed by Frege, Russell, and Whitehead for the purpose of formally representing or ‘modeling’ number theory.  Later, Quine proposed that it be used to model natural language semantics and reasoning .  Garrett seems to be following Quine.  So, here are some key ideas about Standard Logic (“SL”)

A rule is deductively valid just in case any interpretation of the formal language of SL that makes its premises all true makes its conclusion true as well.

Consider the Rule of Existential Generalization (EG):

….a…..

Ǝx (….x….)

EG is a valid rule of SL.  But why?  It must be because of the way the intended interpretations of SL are structured.

An interpretation consists of a non-empty, possibly infinite set of objects, called the ‘Domain’ , the set of truth values, {T,F}, and an assignment of values from the Domain to referring expressions of the language and from the set of truth values to sentences of the language.  So for instance,

Individual Constants: a,b,c… are assigned a particular (not necessarily distinct) objects in the Domain of the interpretation as fixed values for that interpretation.  Note:  every constant is assigned a value.

Individual variables: x,y,z….take individuals in the Domain as variable values.

(Monadic) Predicate letters : F,G,H,…are assigned particular subsets (possibly the empty set) of the Domain as fixed values for that interpretation.

The sentence ‘Fa’ is assigned the value T just in case the object assigned to ‘a’ by the interpretation is a member of the subset of objects assigned to ‘F’ by the interpretation.  Otherwise ‘Fa’ is assigned the value F; i.e., The Law of the Excluded Middle holds, that for all sentences P, P or not P.

The sentence ‘ƎxFx’ is assigned the value T just in case the subset of the Domain assigned to ‘F’ is not empty; otherwise it is assigned the value F.

Now, back to the rule EG.  Its premise is   ….a….., Where’…a…. ‘is just some sentence admissible in the language of SL  containing the individual constant ‘a’;   e.g.,  Fa.  If we are given that Fa is true, then of course that means that the object assigned to ‘a’ is in the subset assigned to ‘F’.  And that means that that subset is non-empty.  But then ƎxFx must be true, given the interpretive rule above.  So now we can see why the rule EG is valid.  It is because the intended interpretations of SL do not allow there to be any constants that do not pick out something in the Domain.  No non-referring names like ‘Santa Claus’ are allowed!  So SL doesn’t try to solve or even model the problem in English and other natural languages of what to do about non-denoting names, it just side-steps it.  END OF SIDEBAR]

We are now in a position to be more explicit about the problem that true negative existential claims raises for both the Property View and the Quantifier View.  We will focus here just on true negative singular existential claims.  Here are some examples of such claims:

1.        Santa Claus does not exist.

2.       The tooth fairy does not exist.

3.       A perfect performance does not exist.

4.       It does not exist (referring back to a perfect performance).

5.       This does not exist. (pointing, say, at an hallucination, that one is aware of having at the time, of a pink elephant).

The Property View holds that existence is a property.  But it may hold either that non-existence is also a property just like existence, or not.  Let us take these in turn.

If non-existence is a property, then the truth of the negative existence claim requires that there be an object which is the bearer of the property, ‘not-E’, of non-existence.  But of course that is precisely what the claim is denying. If the object is identified with a proper name, as in sentence 1 above, then the logical grammar of the sentence will be ‘not-Ea’, i.e., a has the property of non-existence.  EG applies to such sentences, yielding (Ǝx)not-Ex., which says that there exists an x that does not exist., an evident contradiction.   

On the other hand, if non-existence is not a property, than according to the Property View, the true negative existence claim is merely a denial of the existence claim , of the form ‘not(Ea’).  No matter, though, EG still gives us the same contradiction.

Solution:  Reject EG and embrace non-existent objects.  So, e.g., there is a Santa Claus (and that is to whom we are referring) but he doesn’t exist.  If Fa, then something is F, but that does not imply that it exists.

[Note:  There is actually an independent reason, that Garrett does not mention, for invoking non-existent objects, if you hold the property view; cf. Penelope Mackie’s nice entry on “Existence”  in  the Routledge Encyclopedia of Philosophy:  doing so makes positive existence claims less trivial seeming: we talk about lots of things, but only some of them exist. ]

The Quantifier View holds that existence is not a property  (or at least not a property of objects, though on a version of the Quantifier View mentioned but not endorsed by Garrett, it is a property of properties).  But consider the claim “Adam does not exist”.  Its logical grammar, according to the Quantifier View, is ~(Ǝx)x =a, where ‘~’ stands for negation.  A problem is that EG still yields the contradiction:  (Ǝy)~(Ǝx) x = y, which says roughly that there exists something y which is numerically identical to something x which does not exist!

Solution: Deny that any singular terms occur in the logical grammar of a natural language: no names, no definite description, no indefinite descriptions, no pronouns, no demonstratives; at least not as singular terms.  So then the problem the problem of true negative existentials (at least for singular ones) cannot arise.  Everything legitimately expressed (i.e., in real grammar not surface grammar) by a singular existential claim will be expressed in terms just of predicates, quantifiers, and identity. 

Indefinite descriptions are the easiest to dispose of.  Sentence (3) above  becomes ~(Ǝx)(x is a performance and x is perfect).  Definite description require a second kind of quantifier, ‘(x)’ which reads “For all x”, to capture the uniqueness expressed by “the” in definite descriptions.  Sentence (2) above becomes, via Russell’s famous theory of Definite Descriptions, ~[(Ǝx)(x is a tooth fairy and (y)( y is a tooth fairy then y=x)], which reads:  there does not exist an x such that x is both a tooth fairy and the only tooth fairy, in that anything y that is a tooth fairy must be identical with x.  Quine was the one who proposed that proper names be replaced by predicate letters.  So sentence (1) above would  become ~(Ǝx)(x Santa-Clausizes), where the predicate ‘Santa-Clausizes’ has as its descriptive content various properties which are taken to uniquely identify  Santa Claus, i.e., in the story of Santa Claus.

Garrett favors this Quantifier View approach to the problem of true negative existentials over the Property View approach.  His main reason seems to be that the Property View violates ‘Ockham’s Razor’; it multiplies entities beyond what is needed to solve the problem, given that the Quanitifier View works.  The Property View posits the property of existence, plus possibly also the property of non-existence, plus tons of ‘non-existing’ objects: all the merely possible ones like the Golden Mountain as well as all the  impossible ones like square circles.

But against the Quantifier View, one might note the following.

  1. The restriction to 1st order quantifiers – i.e. quantifiers whose variables take only objects are values – has not been motivated, just assumed.  So only objects exist, not properties, and therefore not the property of existence.  Surely that is just too easy, pending a justification for the restriction.
  2. It posits a logical grammar starkly at odds with the surface grammars of natural languages, in some cases misrepresenting the semantics of ordinary language singular terms, which seem to function often with little or no descriptive content semantically attached to them at all.
  3. Surface grammar names in particular are to be replaced with complex predicates that would uniquely identify the intended would-be object being picked out by the name.  that is a lot of predicates!  How are they to be determined?
  4. The Rule of Existential Generalization is spared as a valid rule only by having been rendered superfluous.
  5. The Quantifier View still seems to be a kind of property view.  Even Garrett, who sets aside the idea that quantifiers might express ‘higher order properties’  -- properties of properties or the like, such as the property of being instantiated that a property may have – still at one point refers to existence as a ‘formal property’ (cf. p. 29, 13 lines from the  bottom) .  The contrast he seems to have in mind is with natural properties had by objects, and that ground their causal powers.  But what is a formal property?  What has them, and where are they?  We just have not been told.  Just invoking the special syntax of quantifiers does not help.  Recall Quine’s famous slogan:  “To be is to be the value of a bound variable” (and he meant only  1st order variable).  How is that supposed to count as an answer to the question Garrett wants to answer?  How does it help us understand  “the nature(if any) of existence”?  So for all we have been told existence is a special kind of property that needs a special kind of syntax to represent it and distinguish it from other kinds of properties.  But what is its nature??

Of course, someone might still think that we are better off with this Quantifier View, given the extreme ontological excesses of the Meinongian solution to the problem of true negative existential claims on behalf of the Property View.  But Garrett has given no argument that that is the only solution available to the Property View.  And there is another kind of solution not considered by Garrett, but worth considering, that carries with it no new ontological commitments.  It is a solution that is as available to the Quantifier View as it is to the Property View.  It involves simply rejecting the classical Law of the Excluded Middle as a universal law, by holding that sentences with non-denoting names lack truth values:  are neither true nor false.  Therefore, since no negative existential statement containing a non-denoting name will be true, it will never be appropriate to apply the law of Existential Generalization to it, and so it will never yield a contradiction. 

It is beyond these notes to go into the formal details of such a solution, but logicians have been working on so-called ‘Three Valued logics’, and even more generally ‘Multi-Valued Logics’, since the ‘30s, and there is precedent for using them to avoid longstanding semantic paradoxes and contradiction.  And the fact that, if such a solution is viable, it is as available to a property conception of existence as to a quantifier conception suggests that the antagonism that Garrett portrays as holding between these views as a false antagonism.

HANSON’S NOTES ON GARRETT, CH.1, ON ANSELM’S ONTOLOGICAL ARGUMENT

At the end of Ch.3, brief mention was made by Garrett  of Descartes’ version of the Ontological Argument, suggesting  that it suffers the demise of the Property View of existence:

Descartes’ Argument (5th Meditation):

1.        My idea of God is the idea of a being with all the perfections.

2.       Necessary existence is a perfection.

3.       Therefore, God necessarily exists.

In the passage in the 5th Meditation, Descartes also argues that there is no less contradiction in conceiving a supremely perfect being who lacks existence, than there is in conceiving a triangle whose interior angles do not sum to 180 degrees.  Since we do conceive of a supremely perfect being, we must therefore conclude that he exists.  Garrett says that Descartes’s argument seems to presuppose that existence (or necessary existence) is one of God’s properties.   And of course Garrett has argued against the Property View of existence.

Be that as it may, it seems to me that there are other problems with (this reconstruction of) Descartes’ line of argument.  Surely no one would accept the inference from ‘By definition, God is an existent being’ to ‘God exists’.  It is patently invalid.  Perhaps the inference from the same premise to the conclusion ‘By definition God exists’ is valid, but it is uninteresting.   Garrett seems to think that Descartes’ argument is valid but that it is unsound because premise 2 is false because it violates the Quantifier View of existence.  But surely even assuming the Property View of existence it is just invalid to infer that because existence is part of my idea of God that God exists. 

What is needed here is a distinction between an idea that we are entertaining, on the one hand encoding the property of existence, and one the other hand our actually attributing existence to what the idea is supposed to represent.  I can have the idea of ‘smallest really existing Martian’, and that idea encodes real existence.  It is surely perfectly possible to have this idea without supposing that there really are any Martians.  What justifies Descartes’ leap from his having an idea of God, which encodes God’s necessary existence, to his belief that God actually exists? Is it the appeal here to the idea of necessary existence, rather than just existence per se?  The idea of necessary existence is the idea of existence in all possible worlds.  If something exists necessarily then it follows that it exists in this world in particular.  But surely the distinction between encoding and attributing applies as much to the property of necessary existence as it does to existence.

Let’s turn now to Garrett’s discussion of Anselm’s famous argument.    Here is his reconstruction:

  1. God is that than which nothing greater can be conceived
  2. God either exists in the understanding alone or exists both in the understanding and in reality.
  3. If God existed in the understanding alone, a greater being could be conceived, namely, a being with all God’s qualities who exists both in the understanding and in reality.
  4. So, God cannot exist in the understanding alone.
  5. So God exists in both the understanding and reality.
  6. So God exists.

As far as I can tell, Garrett does not challenge the validity of this argument either, but rather takes issue with the truth of premises 2 and 3.  He says that Anselm  “…has identified the mind’s grasping a concept with the mind’s containing the object conceived.” (p.3),  He refers to this as a ‘fallacy of reification”.  Once we (fallaciously) have God actually existing in the mind, then it is a short step, given his definition in premise 1, to having him exist in reality as well.   Maybe.  But maybe Anselm was just using the language of “existing in the mind” as another – poetic?  Medieval? --  way of talking about our having the concept of God in our minds as per the definition in premise 1.   Still, if not, there does still seem to be this leap, as in Descartes,  from our idea of God encoding one of his properties as existence, to his existing.  That is surely also a fallacy of reification, and one that effects the validity of the argument.

Of course Hume, the idealist, could never have raised this objection to the Ontological Argument, since, as we saw, Hume thought that our idea of something existing is no different from our conceiving of it. To raise this objection one needs to believe that there is a mind-independent reality, and then the question is whether or not God is part of that.  I might have come up with the idea of a really existing kind of horse-like animal with black and white stripes.  But does it exist?  I have to look in the external world to see whether or not it does.   Hume has to go through unnatural contortions to try to make sense of that.

Perhaps a word about Meinong is also appropriate here.  He thought that there were non-existent objects, like spherical cubes.  There are spherical cubes, because that is what we are talking about when we say “spherical cubes”.  But they do not exist.  This can be seen as transposing the reasoning of Descartes and Anselm from the sphere of our ideas to the sphere of our utterances.  At least Meinong recognized that just because we talk about something does not mean that it really exists!  Too bad Descartes and Anselm thought that the mere ideas we entertain about something as existing can imply that something really does exist.

Maybe Anselm’s argument goes like this.

  1.  (Even) the Fool has the concept of that than which no greater can be conceived.
  2. (Hence) (Even) the Fool believes that that than which not greater can be conceived exists in the understanding.
  3. No one believes that that than which no greater can be conceived exists in the understanding can reasonably believe that that than which no greater can be conceived exists only in the understanding.
  4. (Hence) (Even) the Fool cannot reasonably deny that that than which no greater can be conceived exists in reality.
  5. (Hence)  That than which no greater can be conceived exists in reality.

Putting it this way brings out its invalidity: e.g., the move from 1 to 2.  3 is also a false premise, but it doesn’t get its purchase in the argument without the invalid move from 1 to 2.  [This reconstruction of the argument may be found in the Stanford Encyclopedia of Philosophy entry on” Ontological Arguments”, by Graham Oppy.  The distinction made above between encoding vs believing  or attributing existence is also developed there;  the ‘smallest really existing Martian’ example too.]

Finally, as far as I can tell, thinking about the role of the notion of existence in these versions of the Ontological Argument does not help us to in any way adjudicate between the Property and Quantifier Views.  Contra Kant, for instance, the central reasons why the argument does not work hold whether or not one thinks that existence is a property.