Thesis:  

Scientific objectivity is best characterized by the concept of 
invariance as explicated in category theory than the concept of 
truth as explicated in mathematical logic.

Argument:

(1) Proponents of Model-Theoretic Logics agree that languages and
logics formalized within specific languages are relativized to the 
mathematical structures that provide the models for these languages.
(Feferman, Barwise)

(2) Mathematical Truth is defined using a satisfaction function 		
between the syntax of a language and the mathematical structures
that provide the semantics for the language. (Tarski) 

(3) Category theorists characterize this language specific truth 
definition as the construction of a functor between the category of the
syntax and the category of the mathematical structure used for the
semantics and the truth definition for this specific language.
(Lawvere, Barwise, Fourman)

(4) The primary activity of science is the use of mathematics to construct 
objective theories about phenomena. (Van Fraasen, Giere, Suppe)

(5) An essential property of objective theories of phenomena is that they 	
contain principles which are invariant across, time, instances of 
application, transformations of coordinate systems and representational 
systems of the phenomena. (Nagel, Lucas)

(6) Scientific theories are best characterized as a class of models,
(including the mathematical structures), which represent the
phenomena (Harre, Structuralists,Van Fraasen, Giere, Pearce)

(7) Both Structuralist philosophers of science (Sneed, Mormann, Balzer,
Moulines) and Abstract-Logic philosophers of science (Pearce, 
Rantala) assert that inter-theoretic symmetry relations and invariance
relations across models of phenomena are best characterized using
functors as expressed within category theory.

(8) Since functors preserve the inter-theoretic invariance relations and
symmetries, they also preserve those parts of the mathematical
structures for the original theory which is needed to provide the 
semantics for the truth-definition of the language for the new theory.

(9) Since mathematical truth is language specific (Carnap's truth-in-L),
and scientific theories are formalized in mathematical languages,
if one theory T1 is replaced by another theory T2, and a reduction 
relation is established between T1 and T2 , then the preservation of
the truths of T1 in the new theory T2  is dependent on the construction
of a functor from the category of T1 to the category of T2. 
(Sneed, Pearce, Mormann and Category Theorist)

(10) If such inter-theoretic functors are constructible, they preserve
the essential mathematical structures needed to represent the
original phenomena. Therefore the phenomena remains constant 
across theory change.

(11) Truths across theory-change are dependent on the construction of a
functor across the models of the two theories. Therefore the concept 
of truth needed for scientific theory construction and theory
development is dependent on the notion of a functor as explicated in
category theory.

(12) Therefore, the objectivity of scientific theories, especially the 
objectivity of theory change, is best explicated using functors and 
category theory. The concept of scientific truth based on Tarski's 
definition of mathematical truth is a derivative concept.

Chapters: (References)

Theories of Truth 

	Tarski, Carnap, Davidson, Field, Dummett, Prosentential, Putnam articles.

	Quine, W.V.O. Philosophy of Logic

	Haack, Susan. Philosophy of Logics

	Devitt, Michael. Realism and Truth

	Putnam, Hilary. Realism and Reason, Words and Life

	Kirkman, Richard. Theories of Truth

	Stefanik, Richard.  "Theories of Truth"

Mathematical Truth and Philosophy of Mathematics

	Stefanik, Richard. "Structuralism, Category Theory and Philosophy of Mathematics"

Structure of Scientific Theories: Received View

	Suppe, Frederick. "Received View of Scientific Theories", 
	The Structure of Scientific Theories

	Stefanik, Richard. "The Received View of Scientific Theories"

Semantic Approach to Scientific Theories

	Van Fraasen, Bas. The Scientific Image, Laws and Symmetry

	Giere, Ronald. Understanding Science

	Suppe, Frederick.The Semantic Approach to Scientifc Theories

	Stefanik, Richard. "Van Fraasen's Philosophy of Science"

Role of Models in Science 

	Harre, Rom.  Reality Rescued, Varieties of Realism

Models of Data and Experiments

	Suppes, Patrick. "The Structure of Theories and the Analysis of Data"
	Studies in the Methodology and Foundations of Science	
	Models and Methods in the Philosophy of Science

	Hacking, Ian. Representing and Intervening

	Savage, F. Philosophical Theories of Measurement

	Heelan, Patrick A. "After Experiment: Realism and Research"
	"Experiments as Fulfilment of Theory"
	"Husserl's Later Philosophy of Natural Science"

	Stefanik, Richard. "Heelan : Theories, Experiments, and Phenomena"

Symmetry, Invariance and Covariance in Physical Theories

	Nagel, Ernest. "Objectivity and Invariance", The Structure of Science

	Lucas, J.R. "Constancy, Invariance, and Symmetry", Space, Time and Causality

	Wigner, Eugene. Symmetries and Reflections

	Weyl, Herman. Symmetry

	Roche, John."A Critical Study of Symmetry in Physics from Galileo to Newton"
	"The Semantics of Graphics in Mathematical Natural Philosophy"

	Redhead, Michael. "Symmetry in Inter-Theory Relations"

	Harre, Rom."Covariance and Conservation" (Mathematical Epistemology), 
	Varieties of Realism

	Van Fraassen,Bas. Laws and Symmetry

	Post, Heinz. "Correspondence, Invariance and Heuristics"

	Brown, Harvey. "Correspondence, Invaraince & Heurisrtics 
	in the Emergence of Special Relativity"

The Abstract Logic Characterization of Scientific Theories

	Feferman, Solomon. "Two Notes on Abstract Model Theory"

	Barwise, Jon. Handbook on Mathematical Logic

	Barwise and Feferman. Model-Theoretic Logics

	Barwise, Jon. "Axioms for Abstract Model Theory"
	Annuals of Mathematical Logic, 7, p.221-265

	Hodges, Wilfrid. Model Theory

	Stefanik, Richard." Pearce-Rantala and the Abstract Logic Characterization of Theories"

Structuralist Characterization of Scientific Theories

	Balzer, Moulines, Sneed. An Architectonic for Science	

	Sneed, Joseph. "Structuralism and Scientific Theories"

	Grandy, Richard. "Theories of Theories: A View from Cognitive Science"

	Stefanik, Richard. "Structuralist Representations of Scientific Theories"

Reduction, Incommensurability and Functors

	Sneed, Joseph. "Reduction, Interpretation and Invariance"

	Mormann, Thomas. "Structuralist Reduction Concepts as Structure Preserving Maps"

	Stefanik, Richard. "Functors and Inter-Theoretic Relations"

Scientific Truth, Objectivity and Invariance

Conclusion and Summation of Argument:
	The objectivity of scientific theories, especially the objectivity of 
	theory change, is best explicated using functors and category theory. 
	The concept of scientific truth based on Tarski's definition of 
	mathematical truth is a derivative concept.

Appendix I: Basic Constructions of Category Theory

Categories

	Pitt, David. "Categories"

	Goguen, Joseph. "A Categorical Manifesto",  "Types as Theories"

	Fourman, Michael. "Theories as Categories"

	MacLane, Saunders. "Logic is neither foundations or philosophy"

	Poigne, Axel.  "Algebra Categorically"

Functors 

	Rydeheard, David. "Functors and Natural Transformations"

	Pierce. Category Theory for Computer Science

Adjunction

	Mac Lane and Birkhoff. "Categories and Adjoint Functors", Algebra  

	Mac Lane. "Adjunction", Categories for the Working Mathematician

Topos

	Barr and Wells. Category Theory for Computer Science

	Fourman, Michael. "The Logic of Topoi"

	Hyland, Martin. "The Effective Topos"

Pure Category Theory

	Blyth, T.S. Categories

	MacLane, Saunders. Categories for the Working Mathematician

	Arbib and Manes. Arrows, Structures and Functors

	McLarty, Colin. Elementary Categories, Elementary Topoi

Appendix II: Applications of Category Theory in Scientific Disciplines

Categorical Logic

	Poigne, Axel. "Category Theory and Logic"

	Kock and Reyes. "Doctrines in Categorical Logic"

	Goldblatt, Robert. Topoi - The Categorical Analysis of Logic

	Pitts, Andrew. Notes on Categorical Logic, Categories and Types

	Lambert and Scott. Introduction to Higher Order Categorical Logic

	Crole,R. Types in Categories

Computer Science

	Pierce, Benjamin: Category Theory in Computer Science

	Barr & Wells: Category Theory for Computer Science

	Adamek: Category Theory for Automata Theory

	Pitt, Abramsky, Poigne, Rydeheard.(ed) Category Theory and Computer Programming

Mathematical Physics

	Geroch, Robert. Mathematical Physics

	MacLane, Saunders. Form and Function in Mathematics

	Frohlich, Jurg and Kerler, Thomas.
	Quantum Groups, Quantum Categories and Quantum Field Theory