Mathematical Logic and the Philosophy of God and Man
by
Book Cover & Preview Text
PROOF OF THE LEMMA 'SOME BEING IS ETERNAL' (Functional – Calculus of First – Order )
- The Premisses
- Some being presently exists.
- If some being presently exists, then either some being is eternal (has always existed), or all beings which (presently) exist have risen out of nothing.
- If some being presently exists, then either that (presently) existent being is a necessary being, or that (presently) existent being is a contingent being.
- If some (presently) existent being is a necessary being, then some being is eternal.
- If some (presently) existent being is a contingent being, then some beings which (presently) exist have not risen out of nothing.
- Mathematical Representation
- Logical Analysis
Let Ix = x presently exists (is existent).
Ex = x is eternal (has always existed).
Nx = x has risen out of nothing.
Px = x is a necessary being ('exists in the necessity of its own nature': essence.º . existence).
Qx = x is a contingent being ('sometimes in being and sometimes not').
1. ($ x) (Ix) - Given.
2. ($ x) (Ix) .è . ($ x) (Ex) Ñ (x) (Ix è Nx) - Given.
3. ($ x) (Ix) .è . ($ x) (Ix · Px) Ñ ($ x) (Ix · Qx) - Given.
4. ($ x) (lx · Px) è ($ x) (Ex) - Given.
5. ($ x) (Ix · Qx) è ($ x) (Ix · ~ Nx) - Given.
6. ($ x) (Ix · Px) Ñ ($ x) (Ix · Qx) - 1, 3 M.P. (Modus Ponens).
7. ($ x) (Ex) Ñ ($ x) (Ix · ~ Nx) - 4, 5, 6 C.D. (Constructive Dilemma,
Complex).
8. ($ x) (Ex) Ñ (x) (Ix è Nx) - 1, 2 M.P.
9. ~ ($ x) (Ex) .è . ($ x) (Ix · ~ Nx) - 7, Impl. (Implication).
10. (x) (Ix è Nx) Ñ ($ x) (Ex) - 8, Com. (Commutation).
11. ~ (x) (Ix è Nx ) .è . ($ x) (Ex) - 10, Impl.
12. ($ x) (lx · ~ Nx) .è . ($ x) (Ex) - 11, Q.N. (Quantification Negation:
($ x) (Ix · ~ Nx) .º . ~ (x) (Ix è Nx) )
13. ~ ($ x) (Ex) .è . ($ x) (Ex) - 9, 12 H.S. (Hypothetical Syllogism).
14. ($ x) (Ex) Ñ ($ x) (Ex) -13, Impl.
15. ($ x) (Ex) - 14, Taut. (Tautology).
SOME BEING IS ETERNAL. [Q.E.D.]
This theorem (lemma) is the major premiss in the mathematical proof of 'Some One Unchangeable and Independent Being is Eternal'.
SPIRITUAL NATURE OF THE HUMAN SOUL
- Boolean Algebra: Proof of 'I am a spiritual substance'.
- I am (exist). - Given ( ¶ I. B. 3, I. C. 3.3, I. D. 3.6).
- If I am, then I am either a material substance or I am spiritual substance.
- If I am a material substance, then all my 'thoughts' are sensory in nature (non – intellectual; non – abstract).
- Some of my 'thoughts' are not sensory in nature. ‡
‡ But rather intellectual or abstract in nature, 'conceptio intellectus'.
The human intellect apprehends its object in universal and abstractive fashion independently of material conditions. Hence, intellectual activity is immaterial or purely spiritual. (3)
And the Angelic Doctor observes that 'The proper operation of man as man is the activity of the intellect' ('Propria autem operatio hominis inquantum homo, est intelligere') (4)
The object of the intellect is the universal ('intellectus est universalium'), whereas sense can grasp only the particular ('sensus est particularium').
And as both the Angelic Doctor and Aristotle (the 'Philosopher') have affirmed: 'homo est animal rationale' ('Man is a rational animal').
- Mathematical Representation
- Logical Analysis
Let E = I am.
P = I am a material substance.
Q = I am a spiritual substance.
R = All my 'thoughts' are sensory in nature.
|
E = 1 |
['Order' Relation a C b defined: For every a and b in |
|
E C PQ' + QP' |
a Boolean Algebra B, a C b if and only if ab' = 0 : |
|
P C R |
a C b .º . ab' = 0 ] |
|
R |
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Book Details
About the Book
About the Book
In Mathematical Logic and the Philosophy of God and Man is to be found the mathematical exposition of select logical arguments which demonstrate major theorems of the essence of God and of man with the focus being that "God is Spirit" (John 4:24) and that "...Man became a living soul" (Genesis 2:7) utilizing the first-order theories (of mathematical logic) of the Boolean Algebra, Functional Calculus of classes and relations in a "natural deductive" method, and the Propositional Calculus to prove the validity of arguments drawn from the works of Plato, St. Thomas Aquinas, René Descartes, Gottfried Leibniz, the Rev. Dr. Samuel Clarke, and the author himself. Part I mathematically demonstrates the theorems of the eternal (and necessary) existence, spirituality, creativity, unity, infinitude, omnipotence, omniscience, immutability, intelligence, and freedom of God. Part II mathematically proves the existence, creation, spirituality, and immortality of the human soul; also the body - soul relationship. The "Information Age" resource on God and man for every home, church, school, and library! Concise! Cogent! Breathtaking!
About the Author
The author is a mathematician, philosopher, composer - musician, writer, molecular biologist, and former professor in biomedical sciences at a dozen New York universities inclusive of the Health Science Center at Brooklyn (Downstate Medical Center of S.U.N.Y.), City University of New York, Long Island University, New York Institute of Technology, and Pratt Institute. His publications include research in cell biology and popular religious ballads ('The Joy of Christmas', 'Light of the World', 'Bread of Life', 'Happy Father's Day', 'But This Is Eternal Life') on albums released by HillTop Records (Hollywood, CA). Joseph Manago did his doctoral studies at New York University, and earned his M.S. at the Vincentian Fathers' St. John's University (New York).