Basic Goods are Incommensurable
Source
Shea, Matthew. “Value Incommensurability in Natural Law Ethics: A Clarification and Critique.” American Catholic Philosophical Quarterly 97, no. 3 (2023): 361–386
Original Reconstruction
Basic goods constitute diverse categories.
Basic goods are primary principles.
If basic goods are commensurable, then they are either homogeneous with one another or reducible to something prior by which they can be measured.
If basic goods are homogeneous, then they do not constitute diverse categories.
So, basic goods are not homogeneous. (from 1, 4)
If basic goods are reducible, then they are not primary principles.
So, basic goods are not reducible. (from 2, 6)
Therefore,
C. Basic goods are incommensurable. (from 3, 5, 7)
Commentary
The first thing I noticed is that the first conclusion (5) is not preceded by the minimum number of necessary premises that belong to the argument, which violates rule P1. So, let us isolate proposition 5 and list the premises that it follows.
Basic goods constitute diverse categories.
If basic goods are homogeneous, then they do not constitute diverse categories.
So, basic goods are not homogeneous.
Note that the second premise is a conditional, so it should be listed first, per rule L3.
Now we have this.
If basic goods are homogeneous, then they do not constitute diverse categories.
Basic goods constitute diverse categories.
So, basic goods are not homogeneous.
Next, let us apply the same process to the second conclusion (7), which also does not immediately follow its corresponding premises.
Basic goods are primary principles.
If basic goods are reducible, then they are not primary principles.
So, basic goods are not reducible
Now, I will move the conditional premise up.
If basic goods are reducible, then they are not primary principles.
Basic goods are primary principles.
So, basic goods are not reducible
I will now put these two arguments together and renumber the propositions. Also, I will place the original premise 3 right before the main conclusion.
If basic goods are homogeneous, then they do not constitute diverse categories.
Basic goods constitute diverse categories.
So, basic goods are not homogeneous. (This follows 1 and 2.)
If basic goods are reducible, then they are not primary principles.
Basic goods are primary principles.
So, basic goods are not reducible. (This follows 4 and 5.)
If basic goods are commensurable, then they are either homogeneous with one another or reducible to something prior by which they can be measured.
Therefore,
C. Basic goods are incommensurable. (This follows 3, 6, and 7)
Now that we have the entire argument in front of us, notice that there is no proposition that denies the consequent of 7. It is implicit. Specifically, it is derived by putting 3 and 6 together, resulting in the following proposition: “So, basic goods are not homogenous or reducible.”
According to rule C3, propositions should be implicit if they are unimportant and uncontroversial. I am going to state this proposition explicitly because it is important in the role it plays in the structure of the argument.
Once we add this proposition right before 7, it becomes the new proposition 7.
If basic goods are homogeneous, then they do not constitute diverse categories.
Basic goods constitute diverse categories.
So, basic goods are not homogeneous. (This follows 1 and 2.)
If basic goods are reducible, then they are not primary principles.
Basic goods are primary principles.
So, basic goods are not reducible. (This follows 4 and 5.)
So, basic goods are not homogenous or reducible. (This follows 3 and 6.)
If basic goods are commensurable, then they are either homogeneous with one another or reducible to something prior by which they can be measured.
Therefore,
C. Basic goods are incommensurable. (This follows 7 and 8.)
The main conclusion now follows 7 and 8.
I believe this argument could benefit from a nested list, per rule N1. This will also allow us to move 8 (a conditional) to the top, per rule L3.
Lastly, I will move the conclusion indicator word to the conclusion, and I will number the conclusion. This is simply a stylistic choice.
We now arrive at the final version of the reconstruction.
Final Version
If basic goods are commensurable, then they are either homogeneous with one another or reducible to something prior by which they can be measured.
Basic goods are not homogeneous or reducible.
If basic goods are homogeneous, then they do not constitute diverse categories.
Basic goods constitute diverse categories.
So, basic goods are not homogeneous. (This follows 2.a and 2.b)
If basic goods are reducible, then they are not primary principles.
Basic goods are primary principles.
So, basic goods are not reducible. (This follows 2.d and 2.e)
So, basic goods are not homogenous or reducible. (This follows 2.c and 2.f)
Therefore, basic goods are incommensurable. (This follows 1 and 2.)
Much better!