predication becomes conventional, and this change to conventionality produces an equivocation. The equivocation consists of two literal meanings: the original one and a derivative meaning that is now a dead metaphor. As a dead man is no longer a man, so a dead metaphor is no longer a metaphor. A dead metaphor is a meaning from which the suspended parts in the metaphor have become conventionally excluded to produce a new “literal” meaning. Trite metaphors, when not just forgotten, metamorphose into new literals, as they become conventional.
3.28 Clear and Vague Meaning
Meanings are more or less clear and vague, such that the greater the clarity, the less the vagueness. Vagueness is empirical underdetermination, and can never be eliminated completely, since our concepts can never grasp reality exhaustively. But vagueness in the semantics of a descriptive term is reduced by the addition of universal affirmations and/or negations accepted as true, to the list of the term’s semantic rules with each rule having the term as a common subject. The clarification is supplied by the semantics of the predicates in the added universal affirmations and/or negations.
Adding semantical rules increases clarity by elaboration. Thus if the list of universal statements believed to be true are in the form “Every X is A” and “Every X is B”, then clarification of X with respect to a descriptive predicate “C” consists in adding to the list either the statement in the form “Every X is C” or the statement in the form “No X is C”. Clarity is thereby added by elaborating the meaning of “X”.
Adding semantical rules that relate any of the univocal predicates in the semantical rules for the same subject increases clarity by increasing coherence. Thus if the predicate terms “A” and “B” in the semantical rules with the form “Every X is A” and “Every X is B” are related by the statements in the form “Every A is B” or “Every B is A”, then one of the statements in the list can be logically derived from the others. Awareness of the deductive relationship and the consequent display of structure in the meaning complex associated with the term “X” makes the complex meaning of “X” more coherent, because the deductive relation makes it more semantically integrated. And the coherence also supplies a psychological satisfaction. Clarity is thereby added by exhibiting semantic structure in a deductive system.
These additional semantical rules relating the predicates may be negative as well as affirmative. Additional universal negations offer clarification by exhibiting equivocation. Thus if two semantical rules are in the form “Every X is A” and “Every X is B”, and if it is also believed that “No A is B” or its equivalent “No B is A”, then the terms “A” and “B” symbolize parts of different meanings for the term “X”, and “X” is equivocal. Clarity is thereby added by the negation.
3.29 Semantics of Mathematical Language
The semantics for a descriptive mathematical variable is determined by its context consisting of universally quantified statements believed to be true including mathematical expressions in both theory language proposed for testing and test-design language presumed for testing.
Both test designs and theories often involve mathematical expressions. Thus the semantics for the descriptive variables common to a test design and a theory may be supplied in part by mathematical expressions, such that the structure of their meaning complexes is partly mathematical. The semantics-determining statements in test designs for mathematically expressed theories may include mathematical equations, measurement language describing the subject measured, the measurement procedures, the metric units and any employed apparatus.
Some of these statements may resemble 1946 Nobel-laureate physicist Percy Bridgman’s “operational definitions”, because the statements describing the measurement procedures and apparatus contribute meaning to the descriptive term. But contrary to Bridgman, and as Carnap says in his Philosophical Foundations of Physics, each of several operational definitions for the same term does not constitute a separate definition for the term’s concept for the measured subject, thereby making the term equivocal. Likewise pragmatists say that descriptions of different measurement procedures contribute different parts to the univocal meaning of the descriptive term, unless the different procedures produce different measurement values, where the differences are greater than the estimated measurement error in the same range of measurement.
3.30 Semantical State Descriptions
A semantical state description for a scientific profession is a synchronic display of the semantical composition of the various meanings of the partially equivocal descriptive terms in the alternative theories functioning as semantical rules and addressing a single problem defined by a common test design.
The above discussions in philosophy of language have focused on descriptive terms such as words and mathematical variables, and then on statements and equations that are constructed with the terms. For computational philosophy of science there is an even larger unit of language, which is the semantical state description.
In his Meaning and Necessity Carnap had introduced a concept of linguistic state description in his philosophy of semantical systems. Similarly in computational philosophy of science a state description is a semantical description but with different content and functions than Carnap’s. The statements and/or equations supplying a discovery system’s input state description and those constituting the output state description are semantical rules. Each alternative theory or law has its distinctive semantics for its constituent descriptive terms. A term shared by several alternative theories or laws is thus partly equivocal. But the term is also partly univocal due to the common test-design statements that are also semantical rules.
In computational philosophy of science the state description is a synchronic and thus a static semantical display. The state description contains language actually used in a science both in an initial state description containing object-language input to a discovery system, and in a terminal state description containing object-language output generated by a computerized discovery-system’s execution. The initial state description represents the frontier of research for the specific problem. Both input and output state descriptions for a discovery-system run address only one problem identified by the test design, and thus for computational philosophers of science they represent only one scientific “profession”.
A discovery-system is a mechanized finite-state generative grammar that produces sentences or equations from descriptive terms or variables. As a grammar it is creative in Noam Chomsky’s sense, because when encoded in a computer language and executed, the system produces new statements, i.e., theories that have never previously been stated in the particular scientific profession. A discovery system is Feyerabend’s principle of theory proliferation applied with mindless vengeance. To control the size and quality of the output, the system tests the empirical adequacy of those novel theories and likely rejects most of them. Associating measurement data with the inputted variables enables empirical testing, so that the system designs are typically one or another type of applied numerical methods.
For semantical analysis the state description consists of universally quantified statements and/or equations. The statements and/or equations from which the terms and/or variables were extracted including theories and test design are part of the state description although not for discovery system input, because they would prejudice the output. Statements and/or equations function as semantical rules in the generated output only. Thus for discovery-system input, the input state description is a listing of descriptive terms and/or variables extracted from the statements and/or equations of the several currently untested theories addressing the same unsolved problem as defined by a test design at a given point in time.
Descriptive terms and/or variables extracted from the statements and/or equations of falsified theories can also be included to produce a cumulative
