Appendix B: Axioms and Theorems Note: For simplicity, the propositions borrowed from other parts of the contemporary scientific mosaic are omitted. For detailed discussion of the axioms, theorem, and their deductions, refer to the text. Respective sections of the text are indicated in square brackets. The definitions are provided on a separate page. Legend - axiom - theorem - implication [The Role of Methodology] 1st Law for Theories An accepted theory remains accepted unless replaced by other theories. 1st Law for Methods An employed method remains employed unless replaced by other methods. Insufficiency of Theory-Criticism An accepted theory cannot be overthrown merely by pointing out its drawbacks. Insufficiency of Method-Criticism An employed method cannot be overthrown merely by pointing out its drawbacks. 1st Law: Scientific Inertia An element of the mosaic maintains its state in the mosaic unless replaced by some other elements. 2nd Law: Theory Acceptance In order to become accepted into the mosaic, a theory is assessed by the method actually employed at the time. 3rd Law: Method Employment A method becomes employed only when it is deducible from other employed methods and accepted theories of the time. 0th Law: Compatibility At any moment of time, the elements of the scientific mosaic are compatible with each other. Theory Rejection A theory becomes rejected only when other theories that are incompatible with the theory become accepted. Contextual Appraisal Theory assessment is an appraisal of a proposed modification of the mosaic by the method employed at the time. Method Rejection A method ceases to be employed only when other methods that are incompatible with the method become employed. Synchronism of Method Rejection A method becomes rejected only when some of the theories from which it follows also become rejected. Asynchronism of Method Employment The employment of new methods can be but not necessarily is a result of the acceptance of new theories. Dynamic Substantive Methods All substantive methods are necessarily dynamic. Static Procedural Methods All procedural methods are necessarily static. Necessary Mosaic Split When the current method prescribes that two mutually incompatible theories must be accepted, the mosaic necessarily splits in two. Underdetermined Theory Change The process of theory change is not necessarily deterministic. Possible Mosaic Split When a theory assessment outcome is inconclusive, a mosaic split is possible. Underdetermined Method Change The process of method change is not necessarily deterministic. Scientific Underdeterminism Transitions from one state of the mosaic to another are not necessarily deterministic. Scientific change is not a strictly deterministic process. Methodology Can Shape Method A methodology can shape employed methods, but only if its requirements implement abstract requirements of some other employed method. Dogmatism → No Theory Change If an accepted theory is taken as the final truth, it will always remain accepted; no new theory on the subject can ever become accepted. Split due to Inconclusiveness When a mosaic split is a result of the acceptance of only one theory, it can only be a result of inconclusive theory assessment. Theory Rejection: Disciplines A theory can become rejected not only when replaced by theories of its own discipline, but by theories of other disciplines as well. Sociocultural Factors in Theory Acceptance Sociocultural factors can affect the process of theory acceptance insofar as it is permitted by the method employed at the time. Necessary Method In order for the process of scientific change to be possible, the mosaic must necessarily contain at least one employed method. Nonempty Mosaic In order for the process of scientific change to be possible, the mosaic must necessarily contain at least one element. Scientific change is impossible in an empty mosaic. [Necessary Elements] [Necessary Elements] [The Third Law: Method Employment] [Rejection of Elements] [Static and Dynamic Methods] [Scientific Underdeterminism] [The First Law: Scientific Inertia] [Static and Dynamic Methods] [The First Law: Scientific Inertia] [The Third Law: Method Employment] [Rejection of Elements] [The First Law: Scientific Inertia] [Rejection of Elements] [The Zeroth Law: Compatibility] [Scientific Underdeterminism] [The First Law: Scientific Inertia] [Rejection of Elements] [Rejection of Elements] [The Second Law: Theory Acceptance] [The First Law: Scientific Inertia] [Mosaic Split and Mosaic Merge] [In-mosaic Appraisal] [Sociocultural Factors] [Mosaic Split and Mosaic Merge] [Mosaic Split and Mosaic Merge] [Scientific Underdeterminism] Theory of Scientific Change: Axioms and Theorems Version 1.0, September 1, 2014 © Copyright by Hakob Barseghyan

Appendix B: Definitions of Terms Note: For simplicity, the definitions of the terms borrowed from other parts of the contemporary scientific mosaic are omitted. For detailed discussion of the definitions, refer to the text. Respective sections of the text are indicated in square brackets. Legend - definition ≡ - aggregation (e.g. A consists of B) - use (e.g. A is used to define B) - mutual exclusion of terms See also the Legend at the end of the text. - inheritance (e.g. A is a subtype of B) [Mosaic Split and Mosaic Merge] [Mosaic Split and Mosaic Merge] A scientific change where two mosaics turn into one united mosaic. Mosaic Merge ≡ A scientific change where one mosaic transforms into two or more mosaics. Mosaic Split ≡ Scientific Change ≡ Any change in the scientific mosaic, i.e. a transition from one accepted theory to another or from one employed method to another. The level of the beliefs of the individual scientist about the world and the rules she employs in theory assessment. Individual Level ≡ The level of the scientific community and its mosaic of accepted theories and employed methods. Social Level ≡ [Individual and Social] [Individual and Social] [Theories and Methods] [Theories and Methods] Scientific Mosaic ≡ A set of all accepted theories and employed methods. A method is employed at time t if, at time t, theories become accepted only when their acceptance is permitted by the method. Employed Method ≡ Accepted Theory ≡ A theory which is taken as the best available description of its object. [Explicit and Implicit] Demarcation Criteria ≡ Criteria for determining whether a theory is scientific or unscientific. [Acceptance, Use, and Pursuit] [Theories and Methods] [Theories and Methods] Method ≡ A set of requirements for employment in theory assessment. Used Theory ≡ A theory which is taken as an empirically adequate tool for practical applications. Theory ≡ A set of propositions that attempt to describe something. Acceptance Criteria ≡ Criteria for determining whether a theory is acceptable or unacceptable. [Acceptance, Use, and Pursuit] [Theories and Methods] [Theories and Methods] [Explicit and Implicit] Pursued Theory ≡ A theory that is considered worthy of further development, further elaboration. Compatibility Criteria ≡ Criteria for determining whether two theories are compatible or incompatible. [Acceptance, Use, and Pursuit] [Theories and Methods] A method which presupposes at least one contingent proposition. Substantive Method ≡ A method which doesn’t presuppose any contingent propositions. Procedural Method ≡ [Static and Dynamic Methods] [Static and Dynamic Methods] [Scientific Underdeterminism] An outcome of theory assessment which prescribes that the theory must be accepted. Outcome: Accept ≡ An outcome of theory assessment which prescribes that the theory must not be accepted. Outcome: Not Accept ≡ The result of a theory’s assessment by the requirements of a method. Assessment Outcome ≡ An outcome of theory assessment which allows for the theory to be accepted but doesn’t dictate so. Outcome: Inconclusive ≡ A set of explicitly formulated rules of theory assessment. Methodology ≡ [Explicit and Implicit] [Scientific Underdeterminism] [Scientific Underdeterminism] [Scientific Underdeterminism] Theory of Scientific Change: Definitions of Terms Version 1.0, September 1, 2014 © Copyright by Hakob Barseghyan