As I was reading through The Collected Papers of Charles Sanders Peirce, I came across the following sentence:

I doubt not that readers have been fretting over the ridiculous-seeming phrase “indecomposable element,” which is as Hibernian as “necessary and sufficient condition” (as if “condition” meant no more than concomitant and as [if] needful were not the proper accompaniment of “sufficient”).

(Punctuation modified; emphases and inserted conjunction in original edition.)

What did he mean by the statement in parentheses? How would amending the phrase “necessary and sufficient condition” to “needful and sufficient concomitant” change its connotation?

Regarding the first distinction, I have in mind Hume's criticism of the proposition that induction can serve to show a conditional (causal) relationship between concomitant events, but I don't know if it's justifiable to read that into Peirce's words.

Regarding the second distinction, I suspect but haven't been able to confirm that his preference for “needful” over “necessary” here may simply reflect a difference in common usage that existed at the time, rather than a technical distinction. Is this suspicion accurate?

(Ancillary question: What does he mean by "Hibernian"? Is there some antiquated stereotype that the Irish use ridiculous-seeming verbose phrases?)


As far as I can make out, Peirce is saying that necessary and sufficient condition is doubly tautological. Firstly because condition implies that it's required and doesn't just follow on i.e. isn't just concomitant. Secondly because, if something is sufficient then that implies necessity.

In both cases I think he's mistaken. Just because something is required doesn't mean that it's sufficient; there could be other pre-requisites. Similarly, it doesn't follow that something being sufficient means that it's necessary as other conditions could have met the requirement.

In other words, his argument here is just poorly thought through. In mitigation, it is possible that the meaning of these three words has changed sufficiently in the intervening years for him to be correct then but not now. However, I do not believe this to be the case solely based on the prevalence of this phrase at the time (it was just as meaningful then as it is now).

As to Hibernian, I fear that it's a euphemism for stupid or ignorant, a traditional slur against the Irish. As Peirce was a well known racist and bigot this would be hardly out of keeping.


Peirce seems to be saying is that the phrase "indecomposable element" seems redundant because an element by definition is something that is "indecomposible" (at least in some respect).*

Similarly with "Necessary and sufficient condition": It seems redundant because it seems sufficient implies necessary. (Peirce himself uses the phrase "necessary and sufficient condition" in other contexts, seemingly not considering it Hibernian there…)

*(Peirce also calls his "indecomposible concepts" of Firstness, Secondness, Thirdness by the names of Priman Element, Secundan Element, Tertian Element, respectively.)

  • Does 'sufficient' imply 'necessary' ? In the USA it is sufficient for X to be a member of the Senate for X to be a member of Congress - but not necessary since X may be a member of the House of Representatives, which is also sufficient for membership of Congress. But I can see that if one event is sufficient for another, then given the sufficiency the event cannot but occur - and this implies necessity. You are definitely on to something; question is, just how to phrase or formulate it. Best - GT – Geoffrey Thomas Sep 2 '18 at 9:27

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