POST 2 LOGIC PAPER 1

Tuesday
February, 03, 2009
Manila

THE FOLLOWING PAPER CAN ONLY BE APPRECIATED BY SOMEONE WHO HAS TAKEN PREDICATE LOGIC (& NOT JUST ARISTOTELIAN OR PROPOSITIONAL LOGIC) PLKUS A LITTLE BACKGROUND IN MODERN METAPHYSICS. THE U.P. DILIMAN UNDERGRAD COURSES PHILO 11 & PHILO 12 ARE SUFFICIENT (PRE)REQUISITES... BUT THE PAPER WITH ITS BROAD STROKES CAN SERVE AS A USEFUL GUIDE FOR INVESTIGATORS INTO LOGIC & METAPHYSICS.

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ON ONTOLOGICAL COMMITMENT
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by JAMAAL bin JAVIER, A.B. Philosophy, on-going M.A. in Philosophy
University of the Philippines at Diliman

ABSTRACT
This brief but comprehensive paper was submitted in one of the author's graduate courses in logic. Here, he seeks to answer the given guide question posed in the first line of the INTRODUCTION and tries to develop a rough outline, a skeleton for a more expanded and detailed work that serves as a chapter or section in his proposed Master of Arts in Philosophy THESIS on logic.

INTRODUCTION
Where do metaphysical or ontological presuppositions enter into our formal logical systems?
This question may be answered by considering the connection, if there is any, between the areas of logic and metaphysics, both broadly construed as systems in philosophy. There are three notions involved in this consideration, namely,
1) ontology,
defined as
(sense 2) "the assumptions about existence underlying any conceptual scheme or any theory or system of ideas" (FLEW 1984p),
2) logic,
as a symbolic system of formal language, and
3) a third relating term or item.
This third element (which is actually a system of logic according to the Polish logician Alfred Tarski) is semantics. Semantics is, roughly, the study of the relations obtaining between logico-linguistic objects and what they express. By the term "logico-linguistic", I am referring to language in its broadest, most general construal. And this sense includes both natural languages such as English or Bahasa and artificial ones such as computer languages and formal languages such as the various calculuses/calculi of symbolic logic. Now according to...

A formal logical system admits of interpretation of its syntactical elements through or via semantics, and ontologic(al) notions such as existence arise when logical symbols are interpreted or given meaning. In particular, in first-order predicate logic (or equivalenly, quantificational theory or predicate calculus), the philosophical notion of existence is formally expressed using the notion of the quantifier and symbolized by "E". One component of a typical well-formed formula in quantificational logic is the symbol "Ex" which is translated into colloquial English as, "There exists an x." The variable "x" stands for any individual and can take on different values depending on the domain of discourse which, in turn, depends on the intended interpretation, that is, on what is being talked about. A group of statements, a language, or a theory, can be translated into the idioms of predicate logic thereby producing quantified statements that make implicit reference to a totality of individuals. It is relative to such a totality that ontological notions - such as presuppositions about existence and particular entities, come into the picture. Existential presuppositions, i.e., claims about the existence of certain entities or kinds of entities may lie hidden in a theory (i.e. implicitly) and covertly enter its corresponding formal logical system. But these can be laid bare and made explicit using the techniques of higher formal logic.

QUINEAN ONTOLOGY
The American logician WIllard Van Orman Quine (1800-1985) was one of the pioneering theorists who devoted much effort in trying to come up with a workable account of the relation between logic and ontology. In particular, he is noted for his contribution, the idea of (the criterion of) ontological commitment [In his work WORD & OBJECT(19), Quine used the phrase "ontic commitment" instead] which he expounded and developed in his various works in logic. Ontological commitment refers to the metaphysical presuppositions of a theory and Quine sought an answer to the general question, "What are the metaphysical presuppostions of a theory?" He was endeavoring to determine what a given theory (implicitly) says there is. Working within the technical ambit of quantificational logic, Quine tried to solve the problem of how to lay bare the ontological assumptions implicit in a theory. And he came up with his proposed notion of "ontological commitment", articulated in a so-called "criterion". The core idea is expressed in his famous formula or dictum,

"To be is to be the value of a (bound individual) variable." (QUINE, p.)

By "bound", it is meant here that the variable lies within the scope of a quantifier, e.g., (x) or Ey, where the variables x and y range over individuals. Otherwise, it is "free". An expression in the predicate calculus is a statement if and only if all occurrences of its variables are bound. If any occurrence is free, then the expression is not a statement but rather a propositional function and ,therefore, is neither true nor false. It has no truth-value. The predicate calculus takes into account not only statements or propositions but propositional functions as well and its expressions may make implicit reference to (an) individual or to a totality of individuals. This happens whenever there is an expression that contains a quantifier. In a quantified expression, variables take on values or are said to be "instantiated". Instantiation is accomplished by replacing the variables by constant terms that stand for particular individuals. All these individuals that may be substituted as constant terms within a particular theory constitute a
totality, a set of individuals which is called the domain or universe of discourse. This totality, in effect, contains everything one wants to talk about. For example, in mathematics, one normally talks about numbers and in linguistics, words or phrases. It is with reference to such domain of individuals that the notion of ontological commitment applies or arises.

EXISTENCE IS NOT A PREDICATE
An important distinction must be made between the usual or commonsensical existence statements made in ordinary, colloquial language (e.g., "There are stones.") and the logical notion of existence as treated within the formal language of first-order predicate calculus. Formal languages are more regimented and, unlike ordinary language, do not readily admit of changes, variations or nuances.They are subject to strict rules of syntax and are more precise and rigid. Lest we forget, here, under present consideration and subject to scrutiny is the quantificational-logical notion of existence or the notion of existence as expressed in the language of first-order predicate calculus. This is the sense of "existence" used or appealed to by philosophers, paricularly by the logicians, in their formal language of logic whenever they are deliberating about existence. Existence is a fundamental concept in philosophy that lies at the core of most philosophical issues. In higher-order logic, existence is not a first-level [I use "level" instead of "order".] predicate, attribute, or property unlike those expressed in the simple
propositons of propositional logic. Existence is rather a second-level predicate, a "property of properties." In predicate logic, a statement is further broken up (or "analyzed") into an attribute which applies to an individual. [Thus the adjective "predicate"] Formally, this action is captured by using the generic symbol PHI(x) where "PHI" is a first-level predicate and the variable x ranges over individuals of the domain of discourse. The phrase "existence is not a
(first-level) predicate" [cf. Kant & other philosphical writings] means that the notion of existence is NOT captured by simply rendering it (in the formal apparatus of logic) as "E" applied to x as above-mentioned or as it is usually done in the ordinary (lower order) logic of propositions. Here, one may assert that an entity m exists and this is expressed as a simple statement symbolized by a single letter M. Predicate logic allows a more detailed treatment of proofs and arguments and a finer-grained analysis of statements especially those involving the idea of multiple generality. And in first-order predicate logic, the notion of existence is captured and formally expressed by the symbol "E". A well-formed formula of quantificational logic is ExPHI(x) roughly translatable as "There exists an x with the attribute PHI. This clearly shows that existence is not a mere first-level predicate.

The existential quantifier symbolized by "E" carries existential import or is said to assert existence. It is a "logically regimented way" of saying that "There is" or "There exists". Existence is what existential quantification expresses. There are things of kind F if and only if ExFx. For Quine, it is "unreasonable to ask for an explication of existence in simpler terms." QUINE 1969

For Quine, "the question of the ontological commitment of a theory does not properly arise except as that theory is expressed in classical quantificational form." (QUINE p.) This means that any assertion about existence can be made only within a conceptual scheme or a theoretical framework which can be expressed in the language of predicate logic prior to the further application of the criterion of ontological commitment. "Quine's critieerion is framed within that context of the logic of quantification." (SEVERENS [.) [NOTE VERY WELL that the primary concern here is NOT with existence per se but with "Imputations of existence, on what a theory says exists." [QUINE]

ONTOLOGY VS ONTOLOGICAL COMMITMENT OF A THEORY
In his work, Quine was compelled to make a finer distinction between the ontology of a theory and its ontological commitment.[Roughly, between what there is in a theory and what the theory says there is] and this is briefly tackled here in passing.
According to James Oliver,

"The ontology of a theory is the range of values of the variables of the theory whereas
its ontological commitment is often only a part of its ontology. The ontology or range
of values is a matter of the conceptual scheme or language system in which the theory
is stated." (OLIVER, 1974)

Different ontologies, that is, different ranges of values may satisfy a given theory. For example, again in mathematics, a theorem expressed as a statement to the effect that, "For all whole numbers x, x possesses the numerical property P [Formally: (x)(Nx IMPLIES Px)] may be satisfied by the set of even numbers and at the same time also by the set of odd numbers with the two mutually exclusive and jointly exhaustive sets forming the the set of natural numbers N. One may treat as a mathematical theory a subset of the mathematical statements concerned with the properties of whole numbers and thus one may have two ontologies - one containing only the set of even numbers and the other containing only the set of odd numbers wuth both fulfilling the theory that yields the quantified statement Ex(x is a natural number) [or identically, Ex(xeN). Hence, it is shown that the ontology of a theory need not be identical with the ontological commitment of the theory. The objects that the theory assumes may not be those to which it is ontologically committed.
Robert Audi avers,
"A theory is ontologically committed to a given ogbject only if that object is common to all of
the ontologies fulfilling the theory. And the theory is ontologically committed to objects
of a given class provided that class is not empty according to each of the ontologies fulfillling
the theory." (AUDI 1995)

CRITICISMS
At the basic level, a common attack against Quine's work is the apparent circularity in his
conception of existence and this a criticism that applies not only to the notion of logical existence but to logic itself. Various non-academic discussions in the Internet (2004) revolve around this point or issue, what seems to be the assumption of an entity's existence by the very act of one's making a statement about it. This is expressed formally in the formula

a exists = def Ex(x=a)

As it stands, this is an "explication of singular existence". But for Quine, "explication of the existential quantifier itself and of general existence" is "a forlorn cause." (QUINE 1969)
Apparently, it leads nowhere. [The underlying idea is somewhat vaguely similar or analogous to the notion of "bootstrapping" in computers and electronics, or in common experience, "carrying oneself through one's boots or shoelaces."] On a more scholarly vein, Quine's overall postion regarding his doctrine of ontological commitment essentially adopts the so-called objectual interpretation of the quantifier ahd those who subscribe to the substitutional interpretation have a basis or a good reason to reject his criterion. This despite Quine's own objections discussed in his Existence and Quantification (QUINE 1969)

On a still higher level of scholarship, the Japanese-American philosopher Charles Chihara has
vigorously criticized Quinean criterion of ontological commitment. Some of these criticisms shall be mentioned minus any further reaction or detailed discussion. According to Chihara, Quine's use of the term "theory" is ambiguous and equivocates between the notion of a theory as a deductively closed (i.e., covers all its logical consequences) set of fully interpreted sentences and that as otherwise. Moreover, Quine has applied his criterion to single sentences and it would appear that, since his criterion is intended to determine the ontological comittment of theories, he is imputing that "a single sentence is a kind of degenerate theory." (CHIHARA 1974)
Also, Chihara, quoting the works of the American philosopher Donald Davidson and the Finnish logician Jaakko Hintikka, points to a possible risk of misreading Quine, leading to the misconstrual that there is no need to specify a particular universe of discourse for the theory (CHIHARA 1974) Furthermore, Chihara has shared a criticism by John Searle to the effect that Quine's criterion is vulnerable to a reductio for apparently it provides a mere condition of sufficiency and not of necessity and sufficiency as it claims to have. (CHIHARA 1974) Lastly, it is usually assumed that the notion of ontological commitment is a semantic one as Quine himself has admitted that his criterion is a semantical formula. (QUINE 1953) But in his paper, James Oliver considers the question (his seventh) of the pragmatic basis of ontological commitment (OLIVER 1974)

ALTERNATIVES
In his paper, Chihara has provided other alternative criteria of ontological commitment and their formulations. He presented four criteria in all: Quine's, Chateaubriands's, Church's and Chomsky & Scheffler's. Chateaubriand's criterion which was originally presented in that writer's Ph.D. dissertation is extensively if not tortuously discussed by Chihara and involves the "notions of theorems of a theory" to "avoid talk about necessary and/or contingent truths." CHIHARA, 1974 p) On the other hand, Church's critierion is formulated as follows:

"The assertion of (Ex)(M) carries ontological commitment to entities x such that M," where the letter 'x' may be replaced by any variable, the italicized letter 'x' may be replaced by any name of a the same variable, the letter 'M' may be replaced by any open sentence containing only the above variable, and the italicized letter 'M' may be replaced by any name of this open sentence."

Noam Chomsky and Israel Scheffler state a criterion similar to Church's but in the form,

"A theory T makes a _____-assumption if and only if it yields a statement of the form "(Ex)(x is (a) _____)" (CHIHARA 1974)

According to Chihara's analsis, Quine's later writings aparently reflected a move towards a Chateaubriand-type of criterion. Of the four criteria, Chateaubriands's is deemed by Chihara as "the most adequate."

SIGNIFICANCE & APPLICATIONS
The notion of ontological commitment has important applications in philosophy particularly in the philosophy of language, philosophy of mathematics, philosophy of science, and in metaphysics. A specific application is the drawing of the distinction between nominalistic and realistic languages as expressions/manifestations of the metaphysical positions of nominalism and realism, where, in realistic languages, words of abstract or general nature" are "substituents for variables" unlike in the case of nominalistic languages. (CHIHARA 1974) Other important philosophical topics closely related with ontological commitment are:
-the nature and relation of intensionality & extensionality;
-the interpretation of the quantifier;
-the nature of theories and their interpretations;
-the nature of kinds;
-the question of existence of nearly possible entities; and
-the significance of Ockham's Principle (CONCISE ROUTLEDGE ENCYBLOPEDIA OF PHILO)

CONCLUSiON
THe foregoing brief considerations show that the logical system of first-order predicate calculus is closely intertwined with ontology via the semantical interpretation of the syntactical elements of the quantifier and its bound variables. Such is the case whether the intended universe of discourse involves individuals as numbers, words, or the entities of natural science, that is, whether the theory under study is mathematical, linguistic or scientific. Quine's criterion of ontological commitment may be applied by translating the given theory into the quantificational language of the predicate calculus. The notion of ontological commitment lays bare a fertile area of research of sufficient depth and breadth for aspiring researchers in philosophy especially in logic and metaphysics. Its usefulness and applicability in wide ranges
of philosophical topics provides enough warrant for a closer investigation of the deeper implications of the concept and the issues involved. Despite its origins from the highly- technical, forbidding realm of quantificational theory, the concept of ontological commitment, treated qualitatively, can serve as a unifying principle in tackling other less abstruse areas in philosophy. As with Tarski's Conception of Truth which evolved from scientific semantics and the calculus of classes, the concept of ontological commitment as propounded by Quine will continue to be a legitimate topic for scholarly philosophical papers, polemical or otherwise.

REFERENCES:
AUDI
CHIHARA
FLEW
MARTIN
OLIVER
PRESLEY
QUINE
QUINE
QUINE

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PAPER AS IT STANDS MAY BE CHARGED WITH PLAGIARISM...
STILL UNFINISHED ACTUALLY...

UPDATED Friday Feb 13, 2009
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