Need help with symbolic logic



I need some help translating some symbolic logic into plain English. It comes from “Proving the Non-Existence of God” by John Pollock, Inquiry 9 (1966):v 193-196

The symbol for God is ‘g’.
The symbol for ‘x exists’ is ‘Ex’.
‘Px’ is the predicate of absolute perfection from Anselm’s version of the ontological argument.
The little box thingy is the modal operator of logical necessity.

[Note: The Df in the original is in subscript format.]

(1) g = Df(the x such that Px);
(2) therefore Pg;
(3) □(x)(Px ⊃ Ex);
(4) therefore □(Pg ⊃ Eg);
(5) therefore □Eg.

1-5 above is Pollock’s version of Anselm’s first argument from Proslogion 2 in symbolic form. Can anyone translate 1-5 in plain language? Any philosophy majors out there?

  1. God is, by definition, the singular absolutely perfect being.
  2. From 1, God is absolutely perfect.
  3. It is necessarily true that anything that is absolutely perfect exists.
  4. Thus necessarily, if God is absolutely perfect, then God exists.
  5. (From 2 and 4,) God necessarily exists.

Mathematics & theoretical computer science major :slight_smile: Hope that’s okay.


Thanks and God bless you!



Item 3 is asserted as true without any supporting reasoning behind that assertion.


Hi Guy,

You are right.

Behind no. 3 is a reductio ad absurdam argument. Also unstated in Pollock’s presentation of the argument are these additional premises: 3(a) There are only two ways for something to exist, in the understanding and reality or in the understanding (mind) alone. 3(b) It is greater to exist in the understanding and reality than in the mind alone. Suppose, then, that God, defined as absolutely perfect, exists in the understanding alone. But this is absurd, for I then could conceive of a being more perfect, namely that which exists in the mind and also in reality. So reject the supposition. There being no other alternative, we must conclude that anything that is absolutely perfect exists.

This is Pollock’s interpretation of Anselm’s first argument from Proslogion Chapter 2. In the paragraph preceding his formalization of the argument he briefly presents the argument in plain language but his formalization of the argument omits the additional premises and the reductio argument. This is the version that supposedly has been vanquished by Hume, Kant, Russell, et al.

Which makes me wonder why Pollock, or anyone else, bothers to formalize the argument. If someone encounters the argument in Pollock’s symbolic form, with no other context, you are indeed left wondering where no. 3 comes from.


I took symbolic logic in college. It was a great alternative to taking algebra! Unfortunately I have largely forgotten the rules :confused:


The ontological argument never sit with me, its defining God into exsistence, without proving why those definitions are like that (without infering to the bible). I think Thomas Aquinas even discarded this, but his arguments prove God by saying “this is what we call God” which is way more reasonable.


Hi Niko,

Aquinas rejected the argument largely on epistemological grounds, namely that fallen man’s ability to reason is so impaired that a purely a priori proof for God’s existence isn’t possible.

It would have been interesting to be a “fly on the wall” in heaven when the two finally met. I am sure Anselm would have had a cogent rebuttal.

I don’t think it is true that Anselm argument defines God into existence. Other versions of the argument, maybe, but not Anselm’s.


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