Anselm’s Ontological Argument in a Nutshell

• P1: We can conceive of a being than which none greater can be conceived.
  (We’ll call this G)
• P2: If G existed only in the understanding, we could conceive of a greater being—namely, G-plus-real-existence.
• P3: Conceiving something greater than G contradicts G’s definition.
• Conclusion: Therefore G must exist both in the understanding and in reality.

Where the Reasoning Breaks Down

1. Existence Is Not a Great-Making Property
   Kant’s point: treating existence as an additional perfection smuggles an extra predicate into the concept. Describing $100 real dollars$ and $100 imagined dollars$ yields identical descriptive content; adding “and it exists” does not enlarge the concept, it changes its truth-status. Thus P2 equivocates on the nature of “greater.” Making a list longer by writing “really!” at the end adds nothing to the list itself.
2. From Concept to Reality—The Reification Fallacy
   Moving from “I can conceive X” to “X exists” confuses intentional objects (things a mind can reference) with ontological objects (things that obtain). We can coherently conceive of a maximally evil demon, a perfect island, or an unbreakable stick, yet their conceivability carries no entailment of reality. Without a reliable bridge principle (“every perfect concept must be instantiated”), the inference in P2→P3 is question-begging.
3. Parody Arguments Expose the Form’s Instability
   Gaunilo’s “perfect island” shows the same logical skeleton yields absurdities. To block the parody one must add ad-hoc constraints (“greatness applies only to necessary beings”), which again begs the question by baking “must exist” into the definition.
4. Hidden Modal Assumption
   Modern reformulations rely on the S5 axiom: ◇□G ⇒ □G (“If it’s possible that a necessary being exists, then a necessary being exists”). Anselm’s version implicitly assumes that possibility. But that premise itself is as controversial as the conclusion; it is not supported by independent evidence, so the argument fails the bootstrapping test for non-circularity.
5. Conceptual Coherence Is Unestablished
   “A being than which none greater can be conceived” presumes the maxima of all perfections are jointly consistent. Omnipotence + omniscience + pure benevolence + absolute freedom, etc., may be jointly incoherent (e.g., the well-known paradoxes of omnipotence). If the concept is inconsistent, the existential inference collapses because no such possible object exists to begin with.
6. No Evidential Update
   Even granting the logical structure, rational credence demands proportioning belief to evidence. The argument supplies no new empirical data; it merely rearranges definitions. Bayesianly, the prior probability of a maximal being remains untouched—so the conclusion carries no epistemic force.

Bottom Line

The proof trades on a semantic sleight of hand: it embeds real existence in the very definition of greatest and then congratulates itself for “discovering” that existence. Once we disentangle conceptual content from ontological commitment, the move from thought to reality loses its footing, and the argument collapses.

Symbolic Logic Formulations:

◉ Counter-Argument 1: Existence is not a predicate

Anselm assumes:

But this assumes that existence contributes to the greatness of a being. That is:

This is false: existence is not a property that adds greatness. The equivalence fails semantically.

◉ Counter-Argument 2: Reification Fallacy (Concept vs. Reality)

From conceivability:

Anselm infers:

But the inference is invalid. Conceivability does not entail existence.

◉ Counter-Argument 3: Parody Reductio (Gaunilo’s Island)

Let I(x) be “x is the greatest conceivable island.” Then:

Thus:

But that’s absurd. The same form proves a perfect island, dragon, or pizza. So the argument form is invalid.

◉ Counter-Argument 4: Hidden Modal Assumption (S5 Exploitation)

Anselm requires:

This is valid only in modal logic S5. But without independent support for , this is question-begging.

◉ Counter-Argument 5: Conceptual Incoherence (Paradox of Omnipotence)

Assume:

where Omni(x) = “x is omnipotent” and Stone(x) = “x can create a stone it cannot lift.”

But:

So:

The concept is self-contradictory and thus cannot describe a possible being.

◉ Counter-Argument 6: No Bayesian Update (Epistemic Inertness)

Let A = “Anselm’s argument is valid.” Then if no new evidence is introduced:

No rational credence update occurs. The argument is epistemically vacuous.