Abbreviate 'Standard Form Categorical Propositions' to SFCP and 'Ordinary Statements' to OS.

Source: p 256-257, A Concise Introduction to Logic (12 Ed, 2014) by Patrick Hurley.
The textbook did not generalise the translations (from OS into SFCP); please correct my attempts below if necessary.

  1. Exclusive Propositions

Many propositions that involve the words “only,” “none but,” “none except,” and “no . . . except” are exclusive propositions. [...] For a statement involving “only,” “none but,” “none except,” and “no . . . except” to be a genuinely exclusive proposition, the word that follows these words must be a plural noun or pronoun.

[8.1.] Only S are P       => All P are S.
[8.2.] None but X are P     => All P are X.
[8.3.] No S except X are Y    => All S that are Y, are X.
[8.4.] S owned only X and Y.   => All Y that S owns are X and Y.

  1. Exceptive Propositions

Propositions of the form “All except S are P” and “All but S are P” are exceptive propositions. They must be translated not as single categorical propositions but as pairs of conjoined categorical propositions. Statements that include the phrase “none except,” on the other hand, are exclusive (not exceptive) propositions. “None except” is synonymous with “none but.” Here are some examples of exceptive propositions:

[10.1] All but/except X are Y.    => No X are Y, and all non-X are Y.

I see that, and so ask not about how, the SFCP for 8 differ from the SFCP for 10. Instead, what are the subtler differences between 'exclusive' from 'exceptive' (synonyms in ordinary English)?

I am confused how the OS for 8 and 10 produce different SFCP. To me, the Function Morphemes in 8 and 10 both appear to exclude and except. For example, in 8, 'only' and 'none but/except' select a subset (from a set) about which the proposition then asserts something; but 'all but/except' in 10 does this too! So what subtleties did I overlook?

1 Answer 1


From the logical perspective you take at the end, all these forms fall under the rubric like

[All/Some/No] X but Y, are Z.

which becomes

[All/Some/No] X that is not Y, is Z.

Then X can be omitted and filled in from the context.

If I say

None but Y, are Z

I mean

No X but Y, are Z

where X is everything, resulting in the interpretation you already reached

All Z are Y

But if I say

All but Y, are Z

And I take that as

All X but Y, are Z

And I take X to be 'everything', so we get

All of everything that is not Y is Z

The 'everything' does not cancel out in the math, as it does in the other cases. But I cannot reduce that to the right form. We cannot quantify over everything in a positive way by reference to a property. Instead, we have to capture the main point in one statement,

No Y is Z

And the reference to everything indirectly in another, in the form of 'everything else'

All non-Y are Z.

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