Mersenne Trademark Argument

 ...mersennes trademark argument modalized...based on maydoles modal model...john konnor...


1. for all x and all y if x is the cause of y's understanding of x then there exists some x which is ontologically supreme


2. for all x and all y either x is the cause of y's understanding of x or there exists a  y that is ontologically perfect


c. God exists ie something ontologically supreme


let:


CxUyx= x is the cause of y's understanding of x

Sx= ~◇(∃y)(Gyx)∧ ~◇(∃y)(~x=y ∧ ~Gxy)

Py= Iy ∧ ◇(∃y))(Ix ∧ Gyx) ∧ ◇(∃y)(Ix ∧ ~x=y ∧~Gxy)

Ix= x is an intellect


g= (℩x)~◇(∃y)Gyx


proof:


1.  (∀x)(∀y)CxUyx ⊃ (∃x)Sx           premise

2.  (∀x)(∀y)CxUyx ∨ (∃y)Py           premise

3.  Iy ∧ ◇(∃y))(Ix ∧ Gyx) ∧ ◇(∃y)(Ix ∧ ~x=y ∧~Gxy)             Def. of P , AIP

4.   Iy ∧ ◇(∃y))(Ix ∧ Gyx)                3 simp.

5.   ◇(∃y))(Ix ∧ Gyx)                         4 simp.

6.   ◇(∃y)Gyx                                      5 simp.

7.   (∃x){~◇(∃y)Gyx ∧ (∀z)(~◇(∃y)Gyz⊃(x=z)) ∧ ◇(∃y)Gyx} 6 Theory of           

                                                             Descriptions

8.{ ~◇(∃y)Gya ∧ (∀z)(~◇(∃y)Gyz⊃(a=z))}∧ ◇(∃y)Gya                                             7 EI

9. {(∀z)(~◇(∃y)Gyz⊃(a=z))∧~◇(∃y)Gya}∧

◇(∃y)Gya                                              8 Comm.

10. (∀z)(~◇(∃y)Gyz⊃(a=z)) ∧ (~◇(∃y)Gya∧◇(∃y)Gya)                  9 Assoc.                      

11. (~◇(∃y)Gya∧◇(∃y)Gya)           10 simp.

12. ~(∃y)Py                                           3-11 IP    

13.  (∀x)(∀y)CxUyx                             2,12  DS 

14.  (∃x)Sx                                            1,13 MP

15.  □(∃x)Sx                                         14 NI

16.  (∃x)Sx⊃ □(∃x)Sx                     14,15 CP

17. □((∃x)Sx ⊃□ (∃x)Sx)                  16 NI

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