A Brief Response to Tuggy’s Challenge

Dale Tuggy has offered a challenge to those who claim that Jesus is God. The challenge takes the form of an argument, with premises that Tuggy thinks orthodox Christians should accept, to the conclusion that Jesus is not God (more precisely, that Jesus is not “a god”).

Here’s Tuggy’s argument:

  1. God and Jesus differ.
  2. Things which differ are two (i.e. are not numerically identical)
  3. Therefore, God and Jesus are two (not numerically identical). (1, 2)
  4. For any x and y, x and y are the same god only if x and y are not two (i.e. are numerically identical).
  5. Therefore, God and Jesus are not the same god. (3, 4)
  6. There is only one god.
  7. Therefore, either God is not a god, or Jesus is not a god. (5, 6)
  8. God is a god.
  9. Therefore, Jesus is not a god. (7, 8)

So where does the argument go wrong?

Well, consider the following parallel argument. Suppose there is a statue of the goddess Athena made out of clay. Let ‘Athena’ refer to the statue and ‘Lump’ to the lump of clay out of which the statue is fashioned. Further, let the neologism ‘clayity’ refer to anything which is clay by nature. Here’s the argument:

  1. Lump and Athena differ.
  2. Things which differ are two (i.e. are not numerically identical)
  3. Therefore, Lump and Athena are two (not numerically identical). (1, 2)
  4. For any x and y, x and y are the same clayity only if x and y are not two (i.e. are numerically identical).
  5. Therefore, Lump and Athena are not the same clayity. (3, 4)
  6. There is only one clayity.
  7. Therefore, either Lump is not a clayity, or Athena is not a clayity. (5, 6)
  8. Lump is a clayity.
  9. Therefore, Athena is not a clayity. (7, 8)

Note that this argument exactly parallels Tuggy’s, except that ‘God’ is replaced with ‘Lump’, ‘Jesus’ with ‘Athena’, and ‘god’ with ‘clayity’ (think ‘deity’).

It should be clear that the conclusion of the argument is false. So which premise is false? (We’ll concede here that the argument is logically valid.)

Premise 1 is true because Lump and Athena don’t have all the same properties. For example, Lump would continue to exist if the statue were remolded, but Athena would not. So Lump has some property like remold-survivability whereas Athena lacks that property. Premise 6 is true because there’s only one clay object. (Imagine looking at the statue. How many clay objects do you see?)

Premises 2 and 8 are true. Let’s also grant that 3 follows from 1 and 2, 5 follows from 3 and 4, 7 follows from 5 and 6, and 9 follows from 7 and 8. That leaves premise 4, which I suggest is the false premise. (5, 7, and 9 are also false as a consequence of 4’s falsity.)

The reason premise 4 is false is because it assumes that numerical sameness entails numerical identity, such that if x and y are not numerically identical then necessarily they are not numerically the same. The Lump/Athena example shows that this assumption is at least disputable, if not clearly false. On account of cases like Lump/Athena, some philosophers have argued for a metaphysical relation known as “numerical sameness without identity”.

I therefore suggest that premise 4 of Tuggy’s argument is disputable in the same way that premise 4 of my parallel argument is disputable.

To be clear: I’m not suggesting that the metaphysical relationship between Jesus and God is the same as the metaphysical relationship between Athena and Lump! I offer the parallel only as a way of disclosing the vulnerable premise in Tuggy’s argument.

Challenge met?

Addendum: Dr. Tuggy replies. I have a few more things to say, so stay tuned.

7 Responses to A Brief Response to Tuggy’s Challenge

  1. Hi James,
    You said: “The reason premise 4 is false is because it assumes that numerical identity entails numerical sameness, such that if x and y are not numerically identical then necessarily they are not numerically the same.”

    Do you mean: “…it assumes that numerical sameness entails numerical identity,…”?

  2. “4. For any x and y, x and y are the same clayity only if x and y are not two (i.e. are numerically identical).”

    It seems natural to take “x and y are the same F” to boil down to: “x is an F & y is an F & x and y are numerically identical”. But if so, 4 is true: part of what it is for x and y to be the same clayity is for them to be numerically identical.

    What about denying 6? If Lump is a clayity and Athena a clayity, and Lump and Athena are numerically distinct, then it seems right to say that there is more than one clayity. You said: “Premise 6 is true because there’s only one clay object. (Imagine looking at the statue. How many clay objects do you see?)” There’s admittedly an intuitive sense in which we only see a single “instance” of clay-ness (it isn’t as if a 1-pound mass of clay, “Lump”, is co-located with a distinct 1-pound mass, “Athena”, resulting in 2 pounds worth of clay), but this may be consistent with multiple objects “participating” in that single clayness – and so multiple objects that are clay (multiple clayities). For example, perhaps Athena “inherits” its clayness from the constituting lump.

    Denying 4 instead of 6 may admittedly seem better in the case of resisting Tuggy’s argument. We don’t want to say that there are two gods! – unless we can couch that as meaning that there are two numerically distinct entities (e.g., divine persons) each of which is divine (or has the property of deity). It seems the Christian will accept 6, that there “is only one god”, in the sense that there is only one divine substance. But if we read the language the same way in 9, Tuggy’s conclusion, it seems that the Christian can accept it: Jesus is not a divine substance (but rather the second divine person, etc.).

    • Daniel,

      I think the point here (or at least one salient point) is that there are different ways of numbering. We can number according to numerical identity or according to numerical sameness (assuming the two are not logically equivalent). The question is: If we have to adopt one or other numbering scheme (another disputable assumption we can leave aside for now!) which scheme is more in line with the biblical language, according to which the number of ‘gods’ is emphatically one?

      BTW, I get into these issues to some extent in chapter 6 of my paradox book.

  3. James Gibson

    Hi James A.,

    It’s late, so hopefully this makes sense. If I remember Rea’s paper, his view is that whether there is one or two objects turns on how we count objects (or something like that…. it’s been a while). I think I favor the two coincident object view. So let me propose another response to Dale.

    Take premise 2: “Things which differ are two (i.e. not numerically identical)”. What is this premise saying exactly? Presumably, this: [Two] things which differ are two things. And that’s true. So from 1 and 2 (rephrased), we get

    3′: God and Jesus are two things. (1,2)

    But then we get to 4 and 5:

    4. For any x and y, x and y are the same god only if x and y are not two (i.e. are numerically identical).
    5. Therefore, God and Jesus are not the same god. (3, 4)

    3′ & 4 do not support 5. 4 needs to be updated as well to get a valid inference:

    4′. For any x and y, x and y are the same god only if x and y are not two things (i.e. are numerically distinct).

    And now I think we can see what is wrong with the argument. The Trinitarian claims that God (the Father) and Jesus are two things. And so does the Arian. But “thing” is a generic, replaced by instances of types. When we replace “things” with “persons”, we get a true statement: they are two different persons; and that’s what premise / sub-conclusion 3 says. But now 4 is obviously contentious:

    4”: For any x and y, x and y are the same god only if x and y are not two distinct persons.

    Why would any orthodox christian grant that?

    This brings me back to why I started with a point about Rea and coincident objects. One might think that it is weird but nevertheless possible for two different things to share exactly the same region of space. One might also think it is weird but possible for two persons to share the same substance.

  4. Ringstraked Calf

    Can Feser comment on this? This is perhaps committing a conflation between formal cause and material cause.

  5. Pingback: Further Thoughts on Tuggy’s Challenge | Analogical Thoughts