"Mathematical Logic and the Philosophy of God and Man"

by Joseph N. Manago

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Product Details

ISBN-13: 9781587213236
Publisher: AuthorHouse
Publication date: 03/28/2000
Pages: 188
Product dimensions: 8.25(w) x 11.00(h) x 0.40(d)

Table of Contents

Prefacev
Part I.The Philosophy of God
1.Eternal and Necessary Existence of Some One Unchangeable and Independent Being1
Introduction1
Proof of "Some One Unchangeable and Independent Being is Eternal"1
Proof of "The Unchangeable and Independent Being is Necessarily Self--Existing"3
Conclusion3
References4
Addendum: Alternative Proof of "Some One Unchangeable ... Being is Eternal"6
Addendum IIProof of the Lemma "Some Being is Eternal"7
AppendixFunctional Calculus of First--Order9
Appendix IIFunctional Calculus of First--Order14
Appendix IIIThe Greek Alphabet16
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 Calculus17
Proof of "Some Being is a Necessary Being"17
I.First--Order Functional Calculus17
II.Boolean--Algebra18
III.Propositional Calculus19
Conclusion20
References20
AppendixBoolean Algebras--Definition, Postulates, Theorems22
3.God: Some Attributes Mathematically Proven through the First--Order Functional Calculus of Classes and Relations25
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 Overview27
IV.Matter is Contingent28
V.The Necessary Being is not Matter29
VI.The Necessary Being is Spirit29
VII.Some One Unchangeable Independent Being is Necessarily Self--Existent (Necessary Being): Calculus of Identity and Russell's Definite Description30
VIII.Some One Unchangeable Independent Being is Spirit31
IX."God": An Insight from W.V.O. Quine31
X.God is Immutable32
XI.The Necessary Being is an Intelligent Being33
XII.There is only (exactly) One Independent and Necessary Being33
References34
Addendum36
I.Proof of "Some Necessary Being is Eternal" and "Some Eternal Being Is Necessary36
II.The Contingency of Matter and of the Human Soul37
III.God: Further Elaboration Upon [paragraph] IX38
Addendum II40
Proof of the "Teleological" Argument for the Existence of God40
Addendum III42
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 Sets47
Preface49
Table of Contents51
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
Conclusion60
References60
Immutability and Intelligence of the Divine Essence Determined by the Boolean Algebra of Sets61
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
Conclusion64
References64
"Something Has Always Existed" Theorem Proven by the Boolean Algebra of Sets66
Conclusion67
References67
Select Bibliography69
AppendixBoolean Algebras--Definition, Postulates, Theorems71
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 Being73
I.Some One Unchangeable and Independent Being is Eternal73
A.The Premisses
B.Conclusion
C."Existential Conditionals Method"
Truth Table for the Argument of "Some One Unchangeable...is Eternal"74
D.Conclusion76
II.The Unchangeable and Independent Being is a Necessary Being76
A.The Premisses
B.Conclusion
C."Existential Conditionals Method"76
Truth Table for the Argument of "The Unchangeable... is a Necessary Being"77
D.Conclusion78
Conclusion79
References79
6.Venn Diagrammatic Analysis of the Mathematical Proofs for the Existence and Essence of God81
I.Mathematical Representation81
II.Venn Graphical Analyses (Legend)81
III.Venn Diagrams (Theorems II.1--II.8)82
Conclusion93
References93
Conclusion to Part I95
Part II.The Philosophy of Man97
7.The Human Soul--Existence, Spiritual Nature, and Creation by God: Mathematics of a Boolean Algebra and First--Order Functional Calculus99
I.The Existence of the Human Soul99
A.The Actual Self--Knowledge of the Human Soul through Itself99
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 Soul101
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 Method105
B.Proof of "The Human Soul is a Substance": Operational Principle Method106
IV.The Human Soul is One and Simple107
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) Will109
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 God111
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
References114
Addendum116
I.Note on the Time of Creation and Infusion of the Human (Spiritual) Soul116
II.Note on the Relation Between Body and Soul in "Hylomorphism"117
III.A Philosophical Evaluation of the Theory of Human Evolution118
1.Necessity of Intelligent Design by God119
2.The Human Soul and "Man" not Products of Evolution119
3.Monogenism and the Creation by God120
4.Special Creation of Man and Original Sin in the Holy Bible120
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--Order121
Proof of "The Human Soul is Immortal"121
I.Boolean Algebra121
II.Predicate (Functional) Calculus of First--Order124
Conclusion126
References126
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 Analysis129
Proof of "The Human Soul is Immortal"129
Conclusion132
References133
Addendum134
I.Notes on "Functional Abstraction" of an Extended Calculus; Law of the Contrapositive134
II.Quine's "Existential Conditionals Method" as Validity Test of the Leibnizian Sorites of the Theorem of the Immortality of the Human Soul135
III.Venn Graphical Analysis of the Leibnizian Sorites of the Theorem of the Immortality of the Human Soul144
10.Immortality of the Human Soul: Part III--Leibnizian Sorites' Validity Proven by the Scholastic Standard--Form Categorical Syllogistic Analysis147
Proof of "The Human Soul is Immortal"147
Conclusion149
References149
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 II153
Epilogue to Parts I and III155
Bibliography159

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