Philosophy: Basic Questions
Prof. Boedeker
Handout on St. Anselm (1033-1109) and Guanilo
I. Anselm’s proof of the existence of God:
Definition 1: God = the best conceivable entity
Definition 2: good = knowing, powerful, benevolent
Anselm’s proof employs the strategy of reductio ad absurdum, i.e., reduction to absurdity. We
begin by making an assumption for the sake of argument. We then show that this assumption
entails something absurd, and conclude that the assumption must therefore be false. Since
Anselm wishes to prove that God exists (in reality), he begins with the premise that God does not
exist. This is the position known as atheism:
P1 (assumed for sake of argument): The best conceivable entity does not exist in reality.
Now in order for an atheist to have the thought expressed in P1, he must know what he’s talking
about when he denies that the best conceivable entity exists in reality. Thus even the atheist has
an idea of the best conceivable entity. For Anselm, this is equivalent to:
C1: The best conceivable entity exists in the mind.
Next, Anselm now asks the atheist to compare GR (whether or not it exists) and GM, asking
whether the atheist can conceive that GR (if it existed) would be a better entity than GM (i.e., his
idea of God). Now by definition, God is 100% knowing, powerful, and benevolent. But no idea
by itself knows anything, has any power, or has any good will. And the atheist has to admit that
he can conceive this. Thus we have:
C2: The atheist can conceive that a really existent God (i.e., the best conceivable entity existing
in reality), if it existed, would be a better entity than the mere idea of God.
Recall from C1 that the atheist holds that the idea of God exists, i.e., that the best conceivable
entity exists in the mind. This entitles us to re-phrase C2, substituting “the best conceivable
entity ” for “the mere idea of God”, thus yielding:
C3: The atheist can conceive that something (namely a really-existing God) would be a better
entity than the best conceivable entity (i.e., the mere idea of God).
Obviously, C4 is a contradiction. Thus if our argument so far is valid, at least one of our
premises (P1 or P2) must be false. But surely P2 is true. Thus P1 must be false. In other words:
C4: It is false that the best conceivable entity does not exist in reality.
From C5, we can conclude:
C5: The best conceivable entity exists in reality.
Anselm’s argument in symbols:
P1: ~GR.
C1: GM.
C2: The atheist can conceive that GR >e GM.
[Anselm also agrees that this is true.]
C1 and C2 entail:
C3: The atheist can conceive that something (namely GR) would be a better entity than the best
conceivable entity (GM).
[This is a contradiction.]
Since C3 is a contradiction, P1 must be false. Thus:
C4: “~GR” is false.
C5: GR.
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Guanilo attempts to refute Anselm’s argument by the strategy known as “parity of reasoning”.
That is, he attempts to construct an argument that has exactly the same structure as Anselm’s, but
which he claims entails a conclusion that is clearly false (namely, that the best conceivable island
exists in reality). Thus, Guanilo concludes, Anselm’s original argument must be flawed.
Definition: I = the best conceivable island
Guanilo’s argument (1st version) in symbols:
P1´: ~IR.
C1´: IM.
[This is not true, but rather nonsense.]
[This is not a contradiction, but nonsense.]
The problem with this version of Guanilo’s argument is that C2´ isn’t true (or false), but rather
simply nonsense. The problem is that C2´ tries to compare IR and IM as islands. But this is
possible only if both IR and IM are islands. The problem is that IM isn’t an island at all, since
it’s an idea. Thus it’s nonsense to compare IM with any island as an island. For this reason,
C2´, and the rest of the proof that supposedly follows from it is just nonsense. Unlike Anselm’s
argument, this one is just gibberish, and can’t be used to prove anything.
So let’s try to come up with an argument for Guanilo that doesn’t make the “category error” of
comparing an idea as an island:
Guanilo’s argument (2st version) in symbols:
P1´´: ~IR.
C1´´: IM.
C2´´: We can conceive that IR >e IM
[This is true, since physical things have more power
than ideas.]
C1´´ and C2´´ entail:
C3´´: We can conceive that something (namely IR) would be a better entity than the best
conceivable island (IM).
[This is not contradictory, but true]
This 2nd version of Guanilo’s argument, however, faces a different problem than the 1st. The
problem here is that C3´´ is actually true – not contradictory, as with Anselm’s original C3.
After all, it’s quite easy for us to conceive something that would be a better entity – thus more
knowing, powerful, or benevolent – that an idea of a perfect island. Any physical thing, animal,
human being, and certainly God are things (whether or not they exist) that would be better than
my idea of a perfect island. For this reason, the 2nd version of Guanilo’s argument actually can’t
be used to make a reductio ad absurdum argument. For this reason, it’s actually not parallel to
Anselm’s argument, and thus can’t be used against it.
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