A Caltech Library Service

Formal Methods in the Foundations of Science


Randall, David Lawrence (1970) Formal Methods in the Foundations of Science. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/KB5H-4F11.


The intent of this study is to provide formal apparatus which facilitates the investigation of problems in the methodology of science. The introduction contains several examples of such problems and motivates the subsequent formalism.

A general definition of a formal language is presented, and this definition is used to characterize an individual’s view of the world around him. A notion of empirical observation is developed which is independent of language. The interplay of formal language and observation is taken as the central theme. The process of science is conceived as the finding of that formal language that best expresses the available experimental evidence.

To characterize the manner in which a formal language imposes structure on its universe of discourse, the fundamental concepts of elements and states of a formal language are introduced. Using these, the notion of a basis for a formal language is developed as a collection of minimal states distinguishable within the language. The relation of these concepts to those of model theory is discussed.

An a priori probability defined on sets of observations is postulated as a reflection of an individual’s ontology. This probability, in conjunction with a formal language and a basis for that language, induces a subjective probability describing an individual’s conceptual view of admissible configurations of the universe. As a function of this subjective probability, and consequently of language, a measure of the informativeness of empirical observations is introduced and is shown to be intuitively plausible – particularly in the case of scientific experimentation.

The developed formalism is then systematically applied to the general problems presented in the introduction. The relationship of scientific theories to empirical observations is discussed and the need for certain tacit, unstatable knowledge is shown to be necessary to fully comprehend the meaning of realistic theories. The idea that many common concepts can be specified only by drawing on knowledge obtained from an infinite number of observations is presented, and the problems of reductionism are examined in this context.

A definition of when one formal language can be considered to be more expressive than another is presented, and the change in the informativeness of an observation as language changes is investigated. In this regard it is shown that the information inherent in an observation may decrease for a more expressive language.

The general problem of induction and its relation to the scientific method are discussed. Two hypotheses concerning an individual’s selection of an optimal language for a particular domain of discourse are presented and specific examples from the introduction are examined.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Engineering Science and Electrical Engineering)
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Engineering
Minor Option:Electrical Engineering
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • McCann, Gilbert Donald (advisor)
  • Thompson, Frederick B. (advisor)
Thesis Committee:
  • Unknown, Unknown
Defense Date:8 October 1969
Record Number:CaltechTHESIS:08252015-104226727
Persistent URL:
Related URLs:
URLURL TypeDescription ItemComputer Science Technical Report 1970-2275 in CaltechAUTHORS
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9116
Deposited On:25 Aug 2015 19:50
Last Modified:21 May 2024 17:38

Thesis Files

PDF - Final Version
See Usage Policy.


Repository Staff Only: item control page