Saturday, February 03, 2007

a proof that god exists


Modal Rationalism. C(Φ) --> <>(Φ)[1]

Reflexivity Axiom. [](Φ) --> (Φ)

Euclidian Axiom. <>[](Φ) --> [](Φ)

Theorem 1. [(<>(Φ) & [](Φ <--> Y)) --> <>(Y)]

Assumption 1. [][God exists <--> [](God exists)][2]


1. C(God exists) {given}

2. <>(God exists) {1, Modal Rationalism}

3. [][God exists <--> [](God exists)] {Assumption 1}

4. <>[](God exists) {2, 3, Theorem 1}

5. [](God exists) {4, Euclidian Axiom}

6. God exists {5, Reflexivity Axiom}

see you at church!

(of course by "God" I mean FSM and by "church" I mean a pirate ship.)

pdf version

* Cf. Plantinga (1974), The Nature of Necessity.
[1] Let ‘C’ be an abbreviation for ‘It is conceivable that’, i.e. if it is conceivable that Φ, then it is possible that Φ. For a thorough defense of modal rationalism see David Chalmers’, “Does Conceivability Entail Possibility?”, published in (T. Gendler & J. Hawthorne, eds) Conceivability and Possibility (Oxford University Press, 2002), pp. 145-200.
This is the common assumption that if God exists at all, then he is not a contingent being.


douglys said...

and we can use the same reasoning to prove that God doesn't exist.

1. C(~God exists){datum}
2. <>(~God exists) {1,MR}
3. ~[](God exists) {2, Modal negation}
4. [][God exists <--> [](God exists)] {Ass 1}
5. God exists <--> [](God exists) {4, Reflexivity}
6. ~(God exists) {3, 5, modus tollens}

Richard said...

The problem, I think, is that the modal rationalist is arguably committed to the principle:

C[]p --> ~C~p

and hence would reject the premise "1. C(God exists)". Given that any being could conceivably not exist, it follows (by tollens on my above principle) that it is not conceivably necessary.

douglys said...

i agree, that is the premise i would deny as well. i accept your S5*. the discussion of strong necessities is very helpful. i also like the notation you use for conceptual possibility and necessity.

putting modal rationalism and S5* together we get these principles, right?

(1) C[]p --> <>[]p & ~C~p

(2) C~[]p --> <>~[]p & ~Cp

well i'm not sure if you accept (2).

Richard said...

Yeah, (2) looks a bit fishy -- any contingent claim will be conceivably non-necessary, after all, but that doesn't make it inconceivable.

Perhaps you instead meant:

(3) C[]~p --> <>[]~p & ~Cp

Sachman Bhatti said...


douglys said...

very insightful, sachman. You have proven something at least.