Analytic Theology

Analytic Theology header image

Paul’s Excursus into Predicate Calculus

January 24th, 2007 by David Kronemyer · No Comments

DAVID KRONEMYER: At 1 Corinthians 12:14, Paul writes:

“Now the body is not made up of one part but of many. If the foot should say, ‘Because I am not a hand, I do not belong to the body,’ it would not for that reason cease to be part of the body. And if the ear should say, ‘Because I am not an eye, I do not belong to the body,’ it would not for that reason cease to be part of the body. If the whole body were an eye, where would the sense of hearing be? If the whole body were an ear, where would the sense of smell be? * * * If they were all one part, where would the body be? As it is, there are many parts, but one body. The eye cannot say to the hand, ‘I don’t need you!’ And the head cannot say to the feet, ‘I don’t need you!’”

Paul’s point is about the unity of the Christian Church, and is more-or-less comprehensible. His analogy to parts of the body, though, is confusing. Let’s try to unpack exactly what it is he’s saying. For ease of reference, “p” = “part of the body,” “B” = “the body,” “f” = “foot,” “ha” = “hand,” “ea” = “ear,” “ey” = “eye,” “sh” = “sense of hearing,” “he” = “head,” and “ss” = “sense of smell.”

Proposition 1: “Now the body is not made up of one part but of many.”

{ p1, p2, p3, … pn } ∈ B .
Proposition 2: “If the foot should say, ‘Because I am not a hand, I do not belong to the body,’ it would not for that reason cease to be part of the body.”

haB

fha

├ ⇁{ fB } ,
from which we also might deduce:

{ f ◊ ∈ B } ∧ { f ⇁ □ ∉ B } .
Note, it’s necessary to assume { haB } in order for what Paul’s saying to make sense; he doesn’t really articulate this premise, although it’s implicit.

Proposition 3: “And if the ear should say, ‘Because I am not an eye, I do not belong to the body,’ it would not for that reason cease to be part of the body.”

eyB

eaey

├ ⇁{ eaB } ,
from which we also might deduce:

{ ea ◊ ∈ B } ∧ { ea ⇁ □ ∉ B } .
Proposition 2 and Proposition 3 both are true.

Proposition 4: “If the whole body were an eye, where would the sense of hearing be?”

B ( ∃! p ∧ ( p = ey ))

├ { shB } .
Proposition 5: “If the whole body were an ear, where would the sense of smell be?”

B ( ∃! p ∧ ( p = ea ))

├ { ssB } .
Proposition 4 and Proposition 5 both are false, because the conclusions don’t follow from the premises. This is Paul’s (somewhat rhetorical) point.

Proposition 6: “If they were all one part, where would the body be?”

∃! p ∧ ( p = { p1, p2, p3, … pn } ))

B ∉ { p1, p2, p3, … pn } .
Proposition 6 is confusing and self-contradictory. Paul invites us to imagine all parts of the body, as comprising one single part. Then, he says the single part, comprised of all parts, itself is not the body. His premise doesn’t get us anywhere, because there’s no point to thinking of all of the parts, as a single part. Rather, we might as well think of them the way they are: a collection of separate parts. Furthermore, by definition, the body is the set comprised of all its parts, see Proposition 1. If something still is missing, as Paul implies, then why not just define the absent ingredient, as another part?

Proposition 7: “As it is, there are many parts, but one body.”

{ p1, p2, p3, … pn } ∈ B .
This is a straight-forward reparsing of Proposition 1.

Proposition 8: “The eye cannot say to the hand, ‘I don’t need you!’”

B ( { p1, p2, p3, … pn } ∈ B )

eyB

├ { haB } .
For line 2, we also could say “∧ ey = p1”. Ignoring for a moment the fact eyes can’t speak, I agree with Paul, Proposition 8 is false. A better rendition of Paul’s words, might be: “The eye cannot say to the hand, ‘The body doesn’t need you,’” as the body comprises the set of its constituent parts, and the hand is only one of the set’s members. Therefore, it shouldn’t be speaking on the body’s behalf.

Proposition 9: “And the head cannot say to the feet, ‘I don’t need you!’”

B ( { p1, p2, p3, … pn } ∈ B )

hB

├ { fB } .
Same comments as with Proposition 8, with an added nuance: here, Paul uses the plural “feet,” rather than the singular “foot,” as at Proposition 2. It therefore might be more accurate to render the third line, ├ { ( f + f ) ∉ B } .

I hope this exercise has been helpful in discerning just what it is Paul meant.