Here is a remarkable passage from Ayn Rand's Introduction to Objectivist Epistemology, expanded 2nd ed., p. 41:
Ostensive definitions are usually regarded as applicable only to conceptualized sensations. But they are applicable to axioms as well. Since axiomatic concepts are identifications of irreducible primaries, the only way to define one is by means of an ostensive definition -- e.g., to define 'existence,' one would have to sweep one's arm around and say: 'I mean this.'
Now that's an interesting suggestion! Let's put it to the test.
Suppose Peter demands that I define the term 'existence.' Taking my cue from Rand, I make a grand sweeping gesture with my arm while saying 'What I mean by existence is all of this.' Have I thereby ostensively defined the concept of existence? Perhaps I have, but only if it is clear what I am pointing to, or rather gesturing at. And that is the exact opposite of clear. Suppose I am having lunch with Peter and Phil when the former makes his definitional demand of me. What does 'all of this' cover? It covers Peter and Phil and Pasquale the waiter and the wine bottle and the table and the walls and trees outside, etc. But does it also cover Phil's being seated and Peter's looking skeptical? These are states of affairs, proposition-like entities. Presumably Phil and Peter are not proposition-like entities. Phil and Phil's being seated belong to different ontological categories. But don't both exist? And don't I see both Phil and Phil's being seated?
How about the ruby redness of the wine which is exemplified in each of the three glasses of wine on the table. That redness is (arguably) a universal. And it is (arguably) perceivable in each glass of wine. Am I gesturing at universals in addition to spatiotemporal particulars and states of affairs when I make my grand ostensive gesture? And what about the mathematical set consisting of Peter, Phil, and Pasquale, and its eight subsets, and the power set the members of which are these eight sets, and the singleton which has the power set as its sole element, and so on? Don't these abstract objects also exist?
At this point I would expect to be interrupted by a follower of Rand. "There are no abstract objects!" He turns to p. 52 of ITOE and reads, "It is Aristotle who identified the fact that only concretes exist." Now if there are no sets or other abstract items, then I cannot be gesturing at them or including them in 'all of this.' And if there are, then I must be gesturing at them if my grand ostensive gesture is to count as an ostensive definition of the concept of existence. But obviously the gesturing does not decide the question as whether or not the totality of what exists includes abstract items. Or whether it includes states of affairs, or Aristotlean accidents, or invisible physical items, etc. So it is difficult to see how 'existence' could be ostensively defined. I will now explain this in a bit more detail.
Part of the point I am making is the commonplace one that pointing leaves indeterminate what exactly is being pointed to. If a child exclaims 'Look Mommy!' while pointing to a crippled man, presumably the child is pointing out the man's being crippled: he is drawing the mother's attention to a a certain state of affairs. But the child could also be pointing to his infrequently seen but much loved Uncle Joe. Joe is not a state of affairs, but presumably an Aristotelian primary substance. Or the kid is ostending Joe's funny hat or the garish color of his clothes, or his bad sunburn or whatnot. The sunburn is an Aristotlean accident. The same goes for gesturing at the totality of what exists. Exactly which totality is this? The totality of spatiotemporal particulars? The totality of sense-perceivable spatiotemporal particulars? The totality of S/T particulars PLUS all the the sets of same? And so on.
If we think this through we come to realize that the concept of existence cannot be ostensively defined, that the very notion of such a procedure makes no sense. For Rand, existence = what exists. So the concept of existence is the concept of what exists. To know what this concept is one needs to know what exists. But this is exactly the problem. It is not at all clear what categories of entity belong in the ontological inventory. Only a philosophical primitive, a sort of philosophical savage, could imagine that one could ostensively define 'existence' by sweeping her arm around.
In any case, it it clear that Rand did not get her concept of existence by any process of pointing or gesturing. She is cocksure that "only concretes exist." (ITOE, 52, emphasis added) Even if this is true, it is not something that can be learned by gesturing at or observing concretes. Long before Rand swept her arm around she assumed that 'existence' can only apply to concretes. She thinks she is validating her definition of 'existence' ostensively when what she is doing is presupposing a definition of 'existence,' one that she brings to the data.
If I am told that Rand is merely stipulating her use of 'existence,' a use according to which only concretes (or only sense-perceivable concretes, or whatever) exist, then the response is that her stipulation is arbitrary and ungrounded. Of course, she thinks she is grounding her definition in some incontestable fact open to the senses and not merely engaging in an act of arbitrary stipulation. But here is where she fools herself and shows herself to be a philosophical primitive and an amateur. Her craving for an incontestable axiomatic foundation blinds her to the fact that she is merely rigging her terminology in such a way as to get the result she was aiming at all along.
"One does not define a criterion of identity by emphatic stressing of the word 'this'. Rather, what the emphasis does is to suggest the case in which we are conversant with such a criterion of identity, but have to be reminded of it"
Posted by: ocham | Sunday, March 01, 2009 at 12:58 AM
Is the quotation from Wittgenstein? Sounds like something the old boy would say.
Reformulated for the case at hand: One cannot define 'existence' by pointing or gesturing. Rather, what the pointing or gesturing does, and does ineptly, is illustrate the definition of 'existence' one had all along.
Posted by: Bill Vallicella | Sunday, March 01, 2009 at 12:22 PM
What you are doing here is dropping the context of Rand's remark -- specifically the context of the meaning of "definition".
The definition of a concept does not provide an exhaustive list of all the characteristics of the concept being defined.
Rather, "a definition designates the essential distinguishing characteristic(s) (the differentia) and genus of the existents subsumed under a given concept".
And:
"The purpose of a definition is to distinguish a concept from all other concepts and thus to keep its units differentiated from all other existents."
Thus, for instance, the concept man is defined as a "rational animal", with "rational" (i.e.” possessing the capacity to reason") serving as the differentia and"animal" as the genus.
But the concept of "existence" -- as Rand makes clear in ITOE -- is a special case; it cannot be defined by means of genus and differentia because it includes everything that exists. So what you can do in place of a conventional definition is to point to existence. The "sweep" in "sweep one's arm around and say: 'I mean this.'" makes clear that you are referring to everything that exists.
It is false to assert that to know the concept “existence” one must know everything that exists. That’s the equivalent of claiming that I cannot know the concept “man” unless I know everything about every man on the planet.
For more on definitions, go here: http://aynrandlexicon.com/lexicon/definitions.html
Posted by: Michael Smith | Monday, March 02, 2009 at 10:33 AM
The preceding comment is another excellent illustration of the primitive level of the members of the Rand cult. Note that no attempt was made to engage anything that I actually said in my carefully crafted post. Instead, in the manner of the true believer and full-dress dogmatist, the Rand apologist repeats the Party Line, citing the Canonical Writings.
Why, after all, respond to arguments when one has The Truth? He who possesses The Truth knows in advance of all inquiry that no argument can prevail against such a Solid Rock.
>>It is false to assert that to know the concept “existence” one must know everything that exists. That’s the equivalent of claiming that I cannot know the concept “man” unless I know everything about every man on the planet.<<
This sort of intellectual obtuseness, this failure to take in the plain sense of what the critic is saying, is characteristic of the Rand cultists who have shown up here. (There have been a few exceptions.) Once again we see that 'Objectivism' is amateur stuff for amateurs.
Posted by: Bill Vallicella | Monday, March 02, 2009 at 02:00 PM