Eucharistic real predication by syntactical equivalence?

[tonychanyt]

The domain of discourse, D, is the set of objects, e.g., people, numbers, etc. R = {T, F}. Given D, a unary predicate is a function that maps D to R. E.g., Socrates is mortal can be expressed by the predicate Mortal(Socrates)=T. Similarly, Mortal(Tony). The domain is the set of people.

Dr. James M. Arcadi wrote in An Incarnational Model of the Eucharist:

At this point in the analysis, we have come to the point where the consecrated object in Christ’s hands may be referred to both as ‘this bread’ and as ‘the body of Christ’.

Let string S1 = 'this bread’.
S2 = ‘the body of Christ’.

I proffer, we can use first-order logic to express the relations between the terms in the Eucharistic real predication. This section is a brief excursus into the logical relations between the terms ‘this bread’ and ‘the body of Christ’ in real predication. Often first-order logic is used to show how the same predicate can be applied variably to many subjects, or for any subject, or for all subjects, and so on. For, suppose we analyse the predicate ‘is a professor’ and two subjects, ‘Matt’ and ‘Sue’, in the sentences, ‘Matt is a professor,’ and ‘Sue is a professor.’ By first-order logic, the sentence, ‘Matt is a professor,’ can be presented as: Professor(Matt). Likewise, then, the sentence, ‘Sue is a professor,’ can be presented similarly as: Professor(Sue).

Right.

But we can also use this tool to present situations in which different predicates are applied to the same subject. So suppose in addition to being a professor, Matt is a chef. We can present the sentence, ‘Matt is a chef,’ as: Chef(Matt). A range of predicates can be applied to the same subject.

Right.

This, then, seems to be the situation in the Eucharistic real predication by syntactical equivalence, once the conception of renaming is in place. Since this whole project is just about how to think about what it is in Christ’s hands – and in the hands of Eucharistic ministers standing in persona Christi – I will simply stipulate a neutral and generic singular term to refer to that object in Christ’s hands (the object Christ denotes as ‘this’) as ‘the object in Christ’s hands’.

Instead of a string, I'd denote it as a single symbol: the-object-in-Christ’s-hands.

Thus, because of the two names,

S1 and S2

the object in Christ’s hands can be referred to by two predicates, ‘this bread’ and ‘the body of Christ’.

Predicate P1 = this-bread(x) corresponds to S1.
Predicate P2 = the-body-of-Christ(x).

He needed to specify the domain of discourse.

These two predicate situations can both be expressed in the sentences, ‘The object in Christ’s hands is this bread,’

This-bread(the-object-in-Christ’s-hands)

and ‘The object in Christ’s hands is the body of Christ.’

The-body-of-Christ(the-object-in-Christ’s-hands)

Using first-order logic, these sentences can be presented as: This bread(the object in Christ’s hands) and The body of Christ(the object in Christ’s hands).

Sure, but he didn't use the proper math notations.

Now, the question still remains. What is the domain of discourse for these two predicates?

Professor(Tony) and Chef(James) are natural predicates with everyday meanings. P1 and P2 are not.

Is D = {the-object-in-Christ’s-hands}?

If the domain of discourse is a singleton set, then designing these two predicates formally to fit only the-object-in-Christ’s-hands is an exercise to force the point of Eucharistic real predication by syntactical equivalence. I wouldn't place much importance to this artificial train of thought. It is too restrictive to fit the straitjacket of this particular instance of syntactical equivalence. Dr Arcadi used an arbitrary formalization as an artificial construct to fit his theological claim.

See also

• This IS my body or represents my body?