**Editor for this issue:** Anthony Rodrigues Aristar <aristarlinguistlist.org>

- Mohanan K. P., falsifiability in OT

I haven't seen any responses to Chris Hogan's questions "Is OT a linguistic theory?" and "What kinds of data would falsify OT?" I think these questions are important, so let me make an attempt. Before I do so, however, I need to spell out what I understand by the term "theory", and distinguish it from "formalism" and "conceptual framework". THEORY, FORMALISM, AND CONCEPTUAL FRAMEWORK THEORY 1: In the physical sciences, when we say "Newton's theory of gravitation", "quantum theory", and so on, we refer to a constellation of logically connected empirical laws, definitions and other hypotheses that apply to the domain in question. Such a constellation is empirical in the sense that it yields testable assertions about the world. Binding theory in GB and Kiparsky's (1979) universal syllable template are both theories in this sense of the term. THEORY 2: In the logico-mathematical domain, the term Ttheory" is used to refer to formal systems (= formalisms). Formalisms such as set theory, graph theory, number theory, group theory, etc. are not empirical, because by themselves they do not yield any predictions about the states of affairs in the world. The same remark applies to the formalisms in logic such as propositional calculus, predicate calculus, and fuzzy logic. A formalism is a combination of a formal language and system of calculations such that given certain propositions, we can infer (=calculate) certain other propositions. Theory 1 is evaluated by checking its external consistency (i.e., consistency of the predictions with observations), as well as its internal consistency. Theory 2 is evaluated by checking its internal consistency alone. (De Morgan's laws in propositional calculus, unlike Newton's laws in physics, are not laws about states of affairs in the world.) Thus, theory 1 is substantive, while theory 2 is formal. In the physical sciences, theory 1 is typically accompanied by (or implemented in terms of) theory 2. For instance, the formalisms accompanying Newton's theory of gravitation include Euclidean geometry and calculus. The formalisms accompanying Einstein's theory of gravitation include Riemannian geometry and calculus. Theories in biology and medicine do not seem to have formalisms attached to them. Thus, competing theories of migraine (vascular, neural, neurovascular...) are made up of substantive propositions without an accompanying system of calculations. If a formalism is designed for use in a particular domain, we may call it a formal framework for that domain. Proposals for context free and context dependent PS rules, structure building and structure changing rules, transformational and non-transformational grammars, constraints and repair, extrinsic ordering, rules and constraints, percolation, and so on, are formal frameworks in this sense: they give us a domain specific formal language and a calculating system to deduce the consequences of the laws and representations of the organization of human language, but they do not tell us anything about the content or substance of these laws and representations. Underspecification is a formal framework for phonological laws and phonological representations. A great deal of research during the early days of generative linguistics was aimed at developing formalisms appropriate for the grammars of natural languages. As far as I can tell, the first articulation of theory 1 of human language was A-over-A condition, followed by islands, followed by the RG laws. The counterparts of physical laws in linguistics are "rules", "constraints", "principles" "conditions", and so on. (I will use the term "law" as a neutral cover term, including all these different formalisms for the statement of regularities in representations.) With the exception of the discussion in chapter 9, SPE is not a phonological theory 1 of human language, because it does not contain a set of universal phonological laws. What SPE gives us is a formalism for the statement of laws and representations (theory 2). It also give us a phonological theory 1 of English, because it contains a set of rules for English phonology. THEORY 3: The term theory is also used in the sense of a conceptual framework, which is a vocabulary associated with a set of related concepts. A conceptual framework allows us to formulate theories, laws and descriptions of the world. The vocabulary of gravity, force, acceleration, momentum, distance, time, mass, and so on forms the conceptual framework within which Newton's theory of gravitation is formulated. Einstein's framework replaces "force" with "field". The so called distinctive feature theory is a conceptual framework in this sense: it gives us a set of concepts ([voice], [nasal], ...) that go into the formation of empirical laws and representations. Like theory 1, unlike theory 2, theory 3 is substantive. In sum, theory 1 in the physical sciences, but not necessarily in biology and medicine, includes theory 2 (formalism) and theory 3 (conceptual framework). We can have theory 2 and theory 3 without theory 1. In logic and mathematics, theory 2 does not entail theory 1. Distinctive feature theory (theory 3) does not entail theory 1. OT AS A LINGUISTIC THEORY The way I see it, OT is primarily a formal framework (= domain specific theory 2) that provides a system of calculating the interaction between the laws of the organization of language. In classical propositional calculus, premises (a)-(c) in (1) yield the unresolvable logical contradiction in (d): (1) Derivation 1: a) P -- > Q b) M -- > not Q c) P & M d) therefore Q & not Q Classical propositional calculus is monotonic. Suppose we construct a non-monotonic propositional calculus in which axioms are prioritized. When a combination of axioms results in a potential contradiction, the more highly ranked axiom determines the conclusion. In such a system, we can derive (2e) by ranking (2a) higher than (2b): (2) Derivation 2 a) P -- > Q b) M -- > not Q c) (2a) >> (2b) d) P & M e) therefore Q If we rank (2b) higher than (2a), the inference would be "not Q". If we replace (2d) with (3d), there will be no conflicts. Hence the conclusion will be "not QS: (3) Derivation 3 a) P -- > Q b) M -- > not Q c) (3a) >> (3b) d) M e) therefore not Q We may refer to such a non-monotonic logic as "Optimality Logic" (OL). Even though OT uses the formalism of constraints and OL uses the formalism of if-then conditionals, they use equivalent devices for conflict resolution, and hence may be viewed as variants of the same formalism. Like other logico-mathematical systems, OL/OT do not make any claims about the world: it is simply a formal system for making inferences. However, we can make empirical claims about the relation between formal systems and a given domain, such as those in (4) - (8): (4) The best formalism for the characterization of human reasoning is propositional calculus. (5) The best formalism for the characterization of human reasoning is predicate calculus. (6) The best formalism for the characterization of human reasoning is the combination of fuzzy logic and OL. (7) The best formalism for the characterization of regularities in human languages is that of context sensitive PS rules. (8) The best formalism for the characterization of the interaction of laws in human languages is that of OT. While the formal systems of propositional calculus, OL and fuzzy logic by themselves do not make any empirical claims, the claims in (4)-(8) are empirical. For instance, it is easy to show that (4) and (5) are not tenable. Chomsky tried to show that (7) was untenable, while GPSP tried to show that (7) is tenable if we enrich the formalism with devices like percolation and non-local subcategorization. As far as I know, linguists (and probably economists) are the only people preoccupied with claims of appropriateness of formalisms. If Newton and Einstein were to make claims of the type that we linguists make, physics will have controversies on (9) and (10): (9) The best formalism for gravitational phenomena is Euclidean geometry. (10) The best formalism for gravitational phenomena is Reimannian geometry. The bulk of research in theoretical phonology since SPE has been aimed at developing appropriate formal frameworks for human languages, a preoccupation initiated by Chomsky's Ph.D. thesis. If we distinguish between formalisms per se on the one hand, and claims about the appropriateness of formalisms such as in (4)-(8), it becomes clear that the empirical content of OT, SPE, Syntactic Structures etc. at the level of linguistic theory are the claims of appropriateness rather than the formalisms themselves. In terms of the typology of theories that Hogan lists (IA, IB, IIA, IIB), I guess what I am saying is that OT is a type IIA theory, not a IA. Hogan does not distinguish between formal frameworks and conceptual frameworks, so I should add that the type II category relevant for OT is that of the formal framework, not conceptual framework. EMPIRICAL TESTING OF OT As for Hogan's question, "What kind of data would falsify OT?", the answer is the same for all frameworks, whether conceptual or formal. No data by itself would falsify a framework. We show that a framework is untenable by demonstrating that there exists a body of data which call for an analysis which is inconsistent with the framework in question. The argument can take two forms. If we are lucky, we can demonstrate that there exists a body of data for which we can construct a successful analysis in terms of framework A but not framework B, and hence framework B should be rejected (e.g. the argument against non-transformational grammars based on the "respectively" construction.) Alternatively, we can demonstrate that there exists a body of data for which framework A yields a simpler analysis than framework B, and hence A is superior to B. (e.g. The arguments for the distinctive feature classificatory system as opposed to the IPA classificatory system.) To take an example, consider how conflict resolution is achieved in the framework proposed in my "Fields of Attraction" paper in Goldsmith (ed) TThe Last Phonological RuleU. This framework uses intrinsic strength assignment rather than relational ranking assignment, as illustrated in derivation 4: (11) Derivation 4 a) P - > Q (strength: 0.7) b) M -- > not Q (strength: 0.5) c) P & M d) therefore Q The idea here is that the stronger requirement is the winner in a conflict situation. Since (11a) is stronger than (11b), the former wins when their inferences are contradictory. The strength assignment formalism provides for three things that the ranking formalism does not provide for: (12) If two laws are inherently strong (their strengths are close to 1), neither of them can be violated even when their requirements are contradictory. (13) If a law is inherently weak (its strength is close to 0), it can be violated even if there is no other law that contradicts it. (14) If the combined strength of law X and law Y is greater than law Z, the combination will win even if law Z is stronger than both law X and law Y individually. (ganging up effect). The ganging up effect is illustrated in derivation 5: (15) Derivation 5 a) P - > Q (strength: 0.7) b) M -- > not Q (strength: 0.5) c) S --> not Q (strength: 0.4) d) P & M & S e) therefore not Q In the OT/OL formalism, the inherent strength assignments of (15a-c) translate as "((15a) >> (15b) >> (14c))". Hence the inference will be "Q", where the winner is (15a). If the ganging up effect is required for the analysis of a body of data, it will involve an additional formal device that sanctions the equivalent of ((15b)+(15c)) >> (15a). Mohanan ellkpmohnus.sg Department of English Language and Literature National University of SingaporeMail to author|Respond to list|Read more issues|LINGUIST home page|Top of issue