Monday, June 08, 2015
Few Thoughts about Pegasus
by Carl Pierer
Let us suppose Pegasus does not exist. This simple idea has proven to lead to plenty of philosophical trouble. Because what exactly is the thing that does not exist? Quine puts the "Riddle of Non-being" as: "Nonbeing must in some sense be, otherwise what is it that there is not?" The problematic coin has two sides. First, it seems that in supposing to talk about Pegasus at all, we are simultaneously asserting that something that answers to the name of Pegasus is - in some sense. This is the semantic side: If Pegasus is not, in any sense of the word, what would we be talking about?
In the same essay, Quine states the problem of ontology as: "What is there?" and answers immediately: "Everything". This approach leads to the same problem, albeit from a different angle: if everything exists, how can we deny the existence of any particular thing, e.g. Pegasus? We may call this the logical side of the problem. For example, if A says Pegasus flies, then A is committed to the claim that something that flies exists. However, if A says Pegasus does not exist, how can the obvious contradiction of asserting that something exists that does not exist be avoided?
Quine proposes the following. The apparent contradiction in stating that something does not exist can be resolved thusly: a statement denying the existence of something, say Pegasus, can be analysed in terms of its logical structure. So, to say that Pegasus does not exist means simply ~∃x (x is Pegasus).
This by itself does not solve the problem, as a further instance of existential generalisation creates the same problem this was set to solve: ~∃x (x is Pegasus) becomes ∃y~∃x (x is y) – meaning again there exists a thing such that it does not exist. To avoid this trouble, Quine suggests – following Russell – that the proper name "Pegasus" can be substituted by a description, e.g. "the winged horse that was captured by Bellerophon". Hence if F = the winged horse that was captured by Bellerophon, the sentence becomes: ~∃x Fx and no existential generalisation can be made. The logical part of the problem is thus solved.
In order to apply this method, it might seem that it need be possible to substitute a proper name for some sort of description. Now, Russell's Theory of Description has come under sever attack and it is doubtful that proper names just are like descriptions. It appears that Quine successfully anticipated this objection in suggesting that "we could have appealed to the ex hypothesi unanalysable, irreducible attribute of being Pegasus, adopting, for its expression, the verb ‘is-Pegasus', or ‘pegasises'. Then, F = pegasises, and again ~∃x Fx does not generate Plato's Beard. This avoids the problem of analysing proper names in terms of descriptions.
For what concerns the semantic part of the problem, Quine goes back to draw the Fregean distinction between naming and meaning. It is one thing for a word to name something and a different thing to mean something. The old example is the morning and the evening star – they both name the same thing, namely Venus, but they mean different things. They cannot possibly mean the same thing, otherwise it would be a mere matter of reflection to establish that they are the same thing, rather than an astronomical achievement. Hence, if meaning and naming come apart, there is no reason to suppose that ‘Pegasus' names anything, it suffices to say that it has meaning. It may rightly be asked: what is the ontological status of meaning, then? But for the purpose of the present exposition, this path will not be followed.
With Quine's method it is possible to deny the existence of something, without having to acknowledge that this something is – in some sense or other. At the same time, the term whose referent is denied, can be thought meaningful without postulating something that it refers to.
These considerations lead Quine to suggest that "To be assumed an entity is, purely and simply, to be reckoned as the value of a variable." This means that, as Devitt puts it, "a person is committed to the existence of those things that must exist for the sentence he accepts to be true". So, for example, if A holds "The dog is white", A is committed to the existence of a dog, to whom the predicate white applies. Contrast this with the sentence "The average Brit has 1.8 children". One way of formalising this would be: ∃x (Fx → Gx), where F: is the average Brit and G: has 1.8 children. For simplicity, uniqueness required by the definite article will be ignored. This, however, cannot be true as ‘the average Brit' does not exist. Quine holds that because it is possible to paraphrase this sentence into a different, non-suspicious sentence, we are not required to believe in the existence of anything like the average Brit. What is required for this sentence to be true is that the ratio between adult Brits and British children is 1.8. Of course, this is a gross oversimplification as, in general, adult Brits will be children of other adult Brits, but this is beside the point – it seems that in any case the sentence can be paraphrased in such a way that only the mathematical calculus and the empiric data involved are required to exist. Thus, holding the sentence "The average Brit has 1.8 children" commits us ontologically to the existence of a certain number of adult Brits and British children.
The problem we started with was the seeming difficulty in denying the existence of anything, which came in both a semantic and logical form. Quine provides a solution to this problem and expands the solution to reply to more general concerns about metaphysical concepts. The solution is not able to tell us what there is. Rather, it gives us a method to discern what our views really commit us to believe in.
This is very handy, as it allows for an escape route when being ambushed by unwelcome metaphysicians. No matter how hard they try to nail you down on your commitment to some undesirable concept, provided you have a way of paraphrasing the sentence without the use of a bound variable, they will fail.
At this point, a slight detour is proposed. Consider the sentence "The cat is on the mat". There is hardly any more straightforward sentence. What is required to make this sentence true is that there is a cat that is on the mat – full stop. Or so it seems. In a famous essay, Searle argues against the idea that any sentence, however unsuspicious it may look, has "literal meaning". To be more precise, a sentence has "literal meaning" (read: has truth values) only against a set of background assumptions. To illustrate the idea, he supplies a very neat sketch of a cat on a mat (Fig 1.). The sentence is true, it seems, if and only if the cat and the mat stand in the relation depicted in Fig. 1 to each other. Yet, Searle suggests that there are implicit background assumptions present. Suppose, that there are a number of cat-mat pairs floating in outer-space, yet as there is no gravitational field present the situation could be depicted as in Fig. 1 or - just as well - by rotating Fig. 1. "Is the cat still on the mat?" Searle asks and continues "And was the earth's gravitational field one of the things depicted in our drawing?"
Searle continues with many further examples, taking down the notion that unambiguous sentences such as "the cat is on the mat" have unique truth conditions, independent of any further background assumptions. He also argues that it is impossible to make those background assumptions explicit, by making the sentence "the cat is on the mat" more precise. There are two reasons for this: first, it is not clear that reference to the same background assumptions (here: the gravitational field) is indeed needed in all contexts for the sentence to have a clear application. Suppose that the background assumption about the gravitational field is made explicit in a way akin to the following: "What the sentence really means is expressed by: ‘(At or near the surface of the earth or some similar gravitational field) the cat is on the mat.'" Here is Searle's example:
For example, as we are strapped in the seats of our space ship in outer space we see a series of cat-mat pairs floating past our window. Oddly, they come in only two attitudes. From our point of view they are either as depicted in (…) [Fig. 1], or as would be depicted if (…) [Fig. 1] were upside down. "Which is it now", I ask. "The cat is on the mat", you answer. Have you not said exactly and literally what you meant?
The second reason is that there is an indefinite amount of background assumptions. How could we be sure that in making the background assumptions explicit, we have listed all of them? It seems there is no limit to ingenious counter-examples of the kind given above. Searle's own examples range from outer space cat-mat pairs to cats being suspended on strings, barely touching the mat. To repeat all of these would exceed the scope of this essay.
If it has been established that sentences only have a "literal meaning" or definite truth conditions against a set of indefinitely many, implicit background assumptions, then this might shed some light on Quine's criterion for ontological commitment.
Recall that, according to Quine, "To be assumed an entity is, purely and simply, to be reckoned as the value of a variable." In other words, we are committed only to the existence of things, whose existence is required by the logical structure of our beliefs.
Now, it seems that if Searle's argument is accepted, then there is no single logical structure to any given sentence. For there are no truth conditions independent of an indefinite amount of background assumptions, which cannot be made explicit. Searle used the example of "the cat is on the mat" to cast doubt on the applicability of the relation "on" independent of contexts. Might it not be reasonable to suppose that similar doubts can be elicited about "cat" and "mat"? It seems to me that, just like the relation "on" only finds definite truth conditions against an indefinite number of background assumptions, so do the words "cat", "mat" and others. Examples to this effect tend to be even sillier than the ones given by Searle, but if it is insisted that sentences from natural languages be translated into formal logic, it is not possible to refute these counter-examples as too absurd. It is not possible to both have the cake (the cleansing of ambiguity by a formal language) and eat it (dismiss any objections to a particular way of formalising as still too ambiguous). However, even if this claim should turn out to be false, it is enough for the argument presented here to work that relational words such as "on" be dubious.
On Quine's model, what the sentence "the cat is on the mat" commits us to – ontologically – is the existence of something, such that it is a cat, a different thing, such that it is a mat and the relation "on" to hold between these two things. Formally, again ignoring the uniqueness of the definite article: ∃x∃y [cat(x) ∧ mat(y) ∧ on(x,y)]. In light of Searle's criticism of "literal meaning", there are essentially two possibilities for the Quinean method.
Either we accept the interpretation put forward by Devitt: we are committed to the existence of everything that is required to make the sentence true. This, combined with the need for background assumptions for a sentence to have truth conditions, commits us to the existence of everything postulated by the implicit background assumptions of any sentence/belief we hold. This number, as Searle showed, is indefinite. More troublesome still, what we are committed to depends on the context of the sentence. Whilst a certain background assumption might be present on one occasion of utterance, it need not be present on all occasions. So, it appears, we are committed to some indefinite number of entities sometimes.
Or, alternatively, we may drop Devitt's positive interpretation[i], and keep the bare minimum of Quine's slogan. We might still hold onto the idea that "to be assumed an entity is (…) to be reckoned as the value of a bound variable". For a thing to exist it may still be required to be in the scope of an existential quantifier. Yet, on this view, it is no longer possible to infer from the "literal meaning" of the sentences we hold to be true a commitment to the existence of certain entities, as there is no such "literal meaning" independent of background assumptions. It is anything but obvious to me, what taking this route would mean. At best, the connection between our beliefs and our ontological commitments becomes much more complex than Quine asserted.
Whichever option we choose, it appears that our ontological commitments are not as evident as Quine made them out to be. What exactly does holding "the cat is on the mat" commit us to? If the consequences drawn from Searle's critique are correct, then this question should not have an easy answer. It should be similarly obscure what the sentence "Pegasus does not exist" commits us to.
There may be ways out of this predicament. For one, one might argued that a sentence by itself does not clearly present us with ontologically commitment. Instead, it may be suggested, the sentence is to be seen as part of a general theory or framework, in which it is to be understood and through which it acquires a unique logical structure. It is then the bulk of the theory and the commitments necessary for this theory to be true that ontologically oblige us, rather than any particular sentence. Furthermore, truth-conditional semantics is anything but dead and buried. Perhaps, Searle's argument does not go all that far as has been supposed throughout this essay. Maybe sentences do, after all, have "literal meaning". Neither of these suggestions seem unanswerable from the perspective I've been outlining in this essay, yet to do so is beyond the scope of this essay.
We started this essay with an old philosophical problem, named Plato's beard by Quine. After presenting Quine's attempt at a solution to the problem, we considered Searle's criticism of "literal meaning". In the last section, a possible way of applying this criticism to Quine's solution was sketched. It appeared that our ontological commitment is not quite as evident as we would hope it to be, if Quine's solution is accepted. Let us suppose Pegasus does not exist.
Devitt, M. (1980). Ostrich Nominalism or Mirage Realism? Pacific Philosophical Quarterly, 433-449.
Quine, W. V. (1963). From a logical point of view: 9 logico-philosophical essays. New York: Harper & Row.
Searle, J. R. (1978). Literal Meaning. Erkenntnis, 13(1), 207-224.
[i] I have suggested that this is Devitt's interpretation. However, a passage that supports this view can be found in Quine:
(…) a theory is committed to those and only those entities to which the bound variables of the theory must be capable of referring in order that the affirmations made in the theory be true.
Posted by Carl Pierer at 12:35 AM | Permalink