"Mathematical Logic and the Philosophy of God and Man" Book

	Preface	v
Part I.	The Philosophy of God
1.	Eternal and Necessary Existence of Some One Unchangeable and Independent Being	1
	Introduction	1
	Proof of "Some One Unchangeable and Independent Being is Eternal"	1
	Proof of "The Unchangeable and Independent Being is Necessarily Self--Existing"	3
	Conclusion	3
	References	4
	Addendum: Alternative Proof of "Some One Unchangeable ... Being is Eternal"	6
Addendum II	Proof of the Lemma "Some Being is Eternal"	7
Appendix	Functional Calculus of First--Order	9
Appendix II	Functional Calculus of First--Order	14
Appendix III	The Greek Alphabet	16
2.	"Some Being is a Necessary Being"--The Thomistic Third Proof of the Existence of God ("possibilia et necessaria"): Mathematically Verified by (I) First--Order Functional Calculus (II) Boolean Algebra, (III) Propositional Calculus	17
	Proof of "Some Being is a Necessary Being"	17
I.	First--Order Functional Calculus	17
II.	Boolean--Algebra	18
III.	Propositional Calculus	19
	Conclusion	20
	References	20
Appendix	Boolean Algebras--Definition, Postulates, Theorems	22
3.	God: Some Attributes Mathematically Proven through the First--Order Functional Calculus of Classes and Relations	25
I.	The Necessary Being is Infinite in Perfection (and Omnipresent)	25
II.	Matter is not Necessarily Self--Existent (not a Necessary Being)	26
III.	The Big--Bang Cosmology and Unified Field Theory: An Overview	27
IV.	Matter is Contingent	28
V.	The Necessary Being is not Matter	29
VI.	The Necessary Being is Spirit	29
VII.	Some One Unchangeable Independent Being is Necessarily Self--Existent (Necessary Being): Calculus of Identity and Russell's Definite Description	30
VIII.	Some One Unchangeable Independent Being is Spirit	31
IX.	"God": An Insight from W.V.O. Quine	31
X.	God is Immutable	32
XI.	The Necessary Being is an Intelligent Being	33
XII.	There is only (exactly) One Independent and Necessary Being	33
	References	34
	Addendum	36
I.	Proof of "Some Necessary Being is Eternal" and "Some Eternal Being Is Necessary	36
II.	The Contingency of Matter and of the Human Soul	37
III.	God: Further Elaboration Upon [paragraph] IX	38
	Addendum II	40
	Proof of the "Teleological" Argument for the Existence of God	40
	Addendum III	42
I.	Proof of "God is a Free Agent"	42
II.	Proof of "God is Omnipotent (i.e. of Infinite Power)"	43
III.	Proof of "God is Omniscient (i.e. of Infinite Knowledge)"	44
4.	God: Existence and Essence--Mathematically Proven by a Boolean Algebra of Sets	47
	Preface	49
	Table of Contents	51
1.	Proof of "There has always existed One Unchangeable Independent Being"	53
2.	Proof of "The Unchangeable and Independent Being is Necessarily Self--Existing"	55
3.	Proof of "The Material World is not the Self--Existent Being"	56
4.	Proof of "Whatever is Self--Existent is Infinite in Perfection"	58
5.	Proof of "There do not exist two Necessary and Independent Beings"	59
	Conclusion	60
	References	60
	Immutability and Intelligence of the Divine Essence Determined by the Boolean Algebra of Sets	61
1.	Proof of "God is Immutable" (God does not suffer change)	61
2.	Proof of "First--Cause, or Self--Existent Being, is an Intelligent Being"	63
	Conclusion	64
	References	64
	"Something Has Always Existed" Theorem Proven by the Boolean Algebra of Sets	66
	Conclusion	67
	References	67
	Select Bibliography	69
Appendix	Boolean Algebras--Definition, Postulates, Theorems	71
5.	W.V.O. Quine's "Existential Conditionals Method" as Validity Test in the Mathematical Logic of the Eternal and Necessary Existence of Some One Unchangeable and Independent Being	73
I.	Some One Unchangeable and Independent Being is Eternal	73
A.	The Premisses
B.	Conclusion
C.	"Existential Conditionals Method"
	Truth Table for the Argument of "Some One Unchangeable...is Eternal"	74
D.	Conclusion	76
II.	The Unchangeable and Independent Being is a Necessary Being	76
A.	The Premisses
B.	Conclusion
C.	"Existential Conditionals Method"	76
	Truth Table for the Argument of "The Unchangeable... is a Necessary Being"	77
D.	Conclusion	78
	Conclusion	79
	References	79
6.	Venn Diagrammatic Analysis of the Mathematical Proofs for the Existence and Essence of God	81
I.	Mathematical Representation	81
II.	Venn Graphical Analyses (Legend)	81
III.	Venn Diagrams (Theorems II.1--II.8)	82
	Conclusion	93
	References	93
	Conclusion to Part I	95
Part II.	The Philosophy of Man	97
7.	The Human Soul--Existence, Spiritual Nature, and Creation by God: Mathematics of a Boolean Algebra and First--Order Functional Calculus	99
I.	The Existence of the Human Soul	99
A.	The Actual Self--Knowledge of the Human Soul through Itself	99
B.	Boolean Algebra: Proof of "I exist"	99
C.	Propositional Calculus: Proof of "I exist"	100
D.	First--Order Functional Calculus: Proof of "I exist"	100
II.	Spiritual Nature of the Human Soul	101
A.	Boolean Algebra: Proof of "I am a Spiritual Substance"	101
B.	First--Order Functional Calculus: Proof of "I exist as a Spiritual Substance"	103
C.	Proof of "The Human Soul is Spiritual"	104
III.	The Human Soul is a Substance (Substantiality of the Human Soul)	105
A.	Proof of "The Human Soul is a Substance": Ontological Subject Method	105
B.	Proof of "The Human Soul is a Substance": Operational Principle Method	106
IV.	The Human Soul is One and Simple	107
A.	Proof of "The Human Soul is One"	107
B.	Proof of "The Human Soul is Simple"	107
V.	The Existence and Freedom of the (Human) Will	109
A.	The Human Will Exists: Proof of "All Human Beings Possess an Immaterial Appetitive (Striving) Faculty (Will)"	109
B.	Freedom of the Human Will: Proof of "All Human Beings are Free"	110
VI.	The Human Soul is Directly Created by God	111
A.	Boolean Algebra: Proof of "The Human Soul is Directly Created by God"	111
B.	First--Order Functional Calculus: Proof of "The Human Soul...by God"	113
	References	114
	Addendum	116
I.	Note on the Time of Creation and Infusion of the Human (Spiritual) Soul	116
II.	Note on the Relation Between Body and Soul in "Hylomorphism"	117
III.	A Philosophical Evaluation of the Theory of Human Evolution	118
1.	Necessity of Intelligent Design by God	119
2.	The Human Soul and "Man" not Products of Evolution	119
3.	Monogenism and the Creation by God	120
4.	Special Creation of Man and Original Sin in the Holy Bible	120
8.	Immortality of the Human Soul: A Leibnizian Proof Mathematically Verified by a Logistic of I. Boolean Algebra, and II. Predicate (Functional) Calculus of First--Order	121
	Proof of "The Human Soul is Immortal"	121
I.	Boolean Algebra	121
II.	Predicate (Functional) Calculus of First--Order	124
	Conclusion	126
	References	126
9.	Immortality of Human Soul: Part II--Leibnizian Proof Validity Established by a Logistic of I. Functional Calculus of First--Order Isomorphic with II. Traditional Scholastic Syllogistic Analysis	129
	Proof of "The Human Soul is Immortal"	129
	Conclusion	132
	References	133
	Addendum	134
I.	Notes on "Functional Abstraction" of an Extended Calculus; Law of the Contrapositive	134
II.	Quine's "Existential Conditionals Method" as Validity Test of the Leibnizian Sorites of the Theorem of the Immortality of the Human Soul	135
III.	Venn Graphical Analysis of the Leibnizian Sorites of the Theorem of the Immortality of the Human Soul	144
10.	Immortality of the Human Soul: Part III--Leibnizian Sorites' Validity Proven by the Scholastic Standard--Form Categorical Syllogistic Analysis	147
	Proof of "The Human Soul is Immortal"	147
	Conclusion	149
	References	149
	Addendum to Parts I, II, III (Chapters 8, 9, 10)	151
	Proof of "The Human Soul is Immortal" (Essential and Existential Immortality)	151
	Conclusion to Part II	153
	Epilogue to Parts I and III	155
	Bibliography	159