On semantic ambiguity in St. Anselm of Canterbury’s argument for God’s existence

Benediction Of God The Father, Painting, Canvas, Oil

1 An 11th century benedictine monk’s argument for the existence of God

In the second half of the 11th century, St. Anselm of Canterbury, then a benedictine monk at Bec abbey in northern France, formulated what would become perhaps the most famous argument in all of medieval philosophy. It goes like this.

  1. God is that than which nothing greater can be thought.
  2. That than which nothing greater can be thought really exists.
  3. Therefore, God really exists.

The first premise listed is called the minor premise: it provides the term that will be the subject term in the conclusion, namely ‘God’. The second premise is called the major premise: it provides the term that will be the predicate in the conclusion, namely ‘exists’. Both terms are linked to each other by a common middle term, namely ‘that than which nothing greater can be thought’. The major premise itself is supported by an argument moving from an elucidation of what is implied in this middle term to the conclusion that anything that truly answers to that description must, in fact, exist. That argument, stated informally, is as follows:

Suppose, for the sake of argument, that that than which nothing greater can be thought does not exist. Call this non-existent entity than which nothing greater can be thought a. Now an entity, call it b, can be thought, which is in every way like except that it really exists. But really existing is better than not really existing. Therefore if two entities are alike with respect to all qualities except existing, that which exists is greater. Therefore, is greater than a. Therefore, there is something greater than that can be thought. Therefore, there is something greater than that than which nothing greater can be thought that can be thought. Therefore, since is greater than it, that than which nothing greater can be thought is not that than which nothing greater can be thought. Thus, the assumption that that than which nothing greater can be thought doesn’t really exist leads to a contradiction, and thus must be denied. Therefore, that than which nothing greater can be thought really exists. Therefore, God really exists.

In what follows, I only intend to point out the various ambiguities in the key term of the argument. There are thus multiple different readings of the main premise.

2 Ambiguities in the argument

2.1. Predicative and attributive readings of the argument’s middle term

The first ambiguity is that between what modern linguistics calls predicative and attributive readings of the minor premise.

In a statement of the form ‘A is BC’, where A is the subject term and B and C are adjectives, ‘A is BC’ is predicative if it implies both ‘A is B’ and ‘A is C’. Thus, since ‘Clifford is a red dog’ implies both that Clifford is red and that Clifford is a dog, ‘red’ and ‘dog’ are both predicated predicatively of Clifford. If such an inference cannot be made, then the reading of the predication is attributive. Thus, ‘Rashad is a good quarterback’, is read attributively, since it doesn’t imply anything about him being good as an individual.

In the ontological argument, the predicative reading takes the attributions of God’s thinkability and nothing being greater than him as separate: God is thinkable, and nothing is greater than him. In the attributive reading, these are not separated: this reading states that nothing can be thought to be greater than God – leaving aside whether anything, in fact, is.

2.2 Ambiguities in the domain of the term ‘nothing’

The second ambiguity is in what the term ‘thing’ in the compound word ‘nothing’ ranges over. On the weaker reading, the term ranges over existing things: nothing that exists can be thought to be greater than god – this reading leaves aside whether something that merely could exist can be thought to be so. On the stronger reading, the term encompasses not merely things that do exist, but also things that can exist, used to exist, will exist, or even can be thought to exist: no possible or conceivable thing greater than god can be thought.

2.3 Ambiguities in how the term ‘God’ is taken

The third ambiguity arises for the attributive reading, in whether the term ‘God’ is taken for the thing it refers to, or for the thing it refers to in the manner it refers to it. In the DC comic, Lois Lane believes that Superman is Superman. Since Superman is Clark Kent, she thus believes that the thing that answers to the name ‘Clark Kent’ is Superman. But since glasses are such a great disguise, she doesn’t believe the term ‘Clark Kent’ actually refers to Superman, and thus, doesn’t directly believe that Clark Kent is Superman. In like manner, someone may hold that nothing can be thought to be greater than x, where x is the thing that we call ‘God’, described in some fashion. For instance, one can believe that nothing can be thought to be greater than the creator of the universe. But one can also hold that nothing can be greater than God, taking the term ‘God’ to carry the full weight of its proper meaning – e.g. that if the proper meaning of the term is ‘an all-knowing, all-good, all-powerful being’, than nothing can be greater than that. For short, I will say that when a sentence is assessed by taking a term for what it refers to, but not under the description that the term gives, that term is read objectively; when a sentence is read by taking the object referred to by a term as the term describes it, that term is read descriptively.

2.4 Ambiguities in how the term related to god by the ‘greater than’ relation is taken

The same ambiguity arises for the second related term in the attributive reading. On one reading, nothing x can be thought to be greater than God under its proper description. On another, nothing can be thought to be greater than God, regardless of its description.

3 Summary and conclusion

There are thus, minimally, 10 readings of the claim ‘God is that than which nothing greater can be thought’.

  1. The predicative reading with narrow domain for the term ‘thing’: No existing thing is both thinkable and greater than God.
  2. The predicative reading with a wide domain for the term ‘thing’. No possible or conceivable thing is both thinkable and greater than God.
  3. The attributive reading with narrow domain for the term ‘thing’, with both terms taken objectively: there is no existing thing such that it can be thought to be greater than the being y, where x happens to answer to some description and y to the description ‘God’. In particular, no existing thing can be thought to be greater than that than which nothing greater can be thought – which is a description of God.
  4. The attributive reading with narrow domain for the term ‘thing’, with the term ‘God’ taken descriptively and ‘thing’ taken objectively. There is no existing thing which can be thought to be greater than god, understood as god, irrespective of any description a.
  5. The attributive reading with narrow domain for the term ‘thing’, with the term ‘God’ taken objectively and the term ‘thing’ referring descriptively: No existing thing a can be thought, as a, to be greater than y, where y is God under some description b.
  6. The attributive reading with narrow domain for the term ‘thing’, with both terms taken descriptively. There is no existing thing which can be thought, as a, to be greater than God, as God.
  7. The attributive reading with wide domain for the term ‘thing’, with both terms taken objectively: there is no possible or conceivable thing such that it can be thought to be greater than the being y, where x happens to answer to some description and y to the description ‘God’. In particular, no conceivable thing can be thought to be greater than that than which nothing greater can be thought – which is a description of God.
  8. The attributive reading with wide domain for the term ‘thing’, with the term ‘God’ taken descriptively and ‘thing’ taken objectively. There is no possible or conceivable thing which can be thought to be greater than god, understood as god, irrespective of any description a of x.
  9. The attributive reading with wide domain for the term ‘thing’, with the term ‘God’ taken objectively and the term ‘thing’ referring descriptively: No conceivable or possible thing a can be thought, as a, to be greater than y, where y is God under some description b. For instance, nothing can be thought, as what it is, to be greater than the God worshipped by Abraham.
  10. The attributive reading with wide domain for the term ‘thing’, with both terms taken descriptively. There is no conceivable or possible thing which can be thought, as a, to be greater than God, as God.

In his argument, Anselm uses several of these different readings. He clearly makes use of reading 2, which implies reading 1, when he says an existing that-than-which-nothing-greater-can-be-thought is better than a non-existing one. He also makes use of an objective reading of ‘God’ in the attributive reading of the predicate ‘can be thought greater than’ when he substitutes the description ‘that than which nothing greater than be thought’ itself for the term in the greater than relation. Anselm doesn’t, however, clearly distinguish these different interpretations from each other. Anselm’s argument thus relies on several closely linked, but different, interpretations for its force. The strength of the argument as a whole is dependent on the independent plausibility of the various interpretations of its key phrase which it invokes.

2 thoughts on “On semantic ambiguity in St. Anselm of Canterbury’s argument for God’s existence

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