# What rule of logic is this referencing?--UPDATE: found it.



## NaphtaliPress (Jun 17, 2010)

Something else as I work my way through Gillespie's book on worship. I believe he is referencing a rule of logic here but I could not pull up a standard phrasing in Latin that matches his? Any ideas? It concerns I take it, all the terms being distributed.

[FONT=&quot]There is (I know) such a distinction of _pars integralis_ [_formal part_], that it is either _principalis_ [_principle_] and _necessaria_ [_necessary_], or _minus principalis_ [_less principal_] and _non necessaria_; but we cannot understand their _pars cultus accidentaria_ [_accidentary part of worship_] to be _pars integralis non necessaria_ [_a formal but non-necessary part_], because, then, their distribution of worship into essential and accidentary parts could not answer to the rules of a just distribution, of which one is, that [/FONT]_[FONT=&quot]distributio debet exhaurire totum distributum [[/FONT]_[FONT=&quot]_distribution ought to exhaust what is being distributed]._[/FONT]​


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## greenbaggins (Jun 17, 2010)

I think he's saying that something formal but not necessary cuts across the categories that he has set up. If something is formal, or principal, then it must be necessary. Non-formal and non-integral would answer to not necessary. I'm not sure this answer to any particular kind of rule of logic, but rather how categories are treated. The upshot of what he's saying seems to be that the categories have to match.


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## CharlieJ (Jun 17, 2010)

Distribution refers to the exhaustion of a term in a categorical syllogism. Gillespie's point seems to be (though I had trouble following it) that if a syllogism is construed in the way his opponents are phrasing it, then in the syllogism the term that is supposed to be distributed doesn't actually get distributed in the line that would distribute it. Without more of the argument, it's hard to be sure. As Lane said, he seems to be saying, in an excruciatingly pedantic way, that there is category confusion going on (though it may simply be in the way he has constructed the categories).

Distribution of terms - Wikipedia, the free encyclopedia
Medieval Theories of the Syllogism (Stanford Encyclopedia of Philosophy)


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## NaphtaliPress (Jun 17, 2010)

I appreciate the analysis; the main thing I'm trying to find is "the rule" that Gillespie seems to be citing at the end. Are you saying it is the rule of distribution? I guess I need to find some standard Latin expression of it.


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## CharlieJ (Jun 17, 2010)

Yes, I think so. The _distributum_, I believe, would correspond to the term that's supposed to be distributed. Which term that is depends on the form of the syllogism. The _distributio_, I believe, is the line in the syllogism in which the _distributum_ is supposed to be distributed. 

So, 

MP: All cats are mammals.
mP: All jaguars are cats.
Conclusion: All jaguars are mammals.

This syllogism works b/c both the minor and middle terms are distributed. 

MP: All cats are mammals.
mP: All cats are jaguars.
Conclusion: All jaguars are mammals.

This conclusion is invalid, b/c the minor term is not distributed. Which terms in the syllogism need distribution is determined by the form.


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## P.F. (Jun 17, 2010)

I think he's referring to some equivalent of Rule 1 here:

An elementary treatise on logic ... - Google Books (Rule 1 toward the bottom of the page, in Section 6)

(see also here - around the middle of the page: http://books.google.com/books?id=4RAEAAAAQAAJ&pg=PA87#v=onepage&q="Law of division" fallacy&f=false

I'm not sure whether a violation of that rule is a named fallacy.


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## NaphtaliPress (Jan 13, 2011)

Just wanted to share that I did find a contemporary reference to this rule, just had to let it sit for six months I guess and come back to it. I found this in a theologian Gillespie used in latter works and was probably familiar with from his schooling. I suspect Keckerman was a standard on things such as logic; if anyone knows that for sure I'd like to confirm that. I give a later English comment as well below.distributio debet exhaurire totum distributum. [Cf. Bartholomäus Keckermann, _Systema Systematum_, vol. 1, “Systema Logicae,” section posterior, De Terminis simplicibus ortis, cap. 3, de Divisione (Hanover: Apud Hæredes Guilielmi Antonii, 1613) 169. “4. “Membra dividentia toti sint adaequata…. Item: Omnis divisio debet totum divisum exhaurire, totumque eius ambitum continere.” “Another end commonly proposed by such divisions, but very rarely attained, is, to exhaust the subject divided.... It is one of the general rules of division in all systems of logic, that the division should be adequate to the subject divided....” Lord Henry Kames, “A Brief Account of Aristotle's Logic. With Remarks,” In Sketches of the History of Man: in four volumes (1775) vol. 3, p. 163.]​


NaphtaliPress said:


> Something else as I work my way through Gillespie's book on worship. I believe he is referencing a rule of logic here but I could not pull up a standard phrasing in Latin that matches his? Any ideas? It concerns I take it, all the terms being distributed.
> [FONT=&quot]There is (I know) such a distinction of _pars integralis_ [_formal part_], that it is either _principalis_ [_principle_] and _necessaria_ [_necessary_], or _minus principalis_ [_less principal_] and _non necessaria_; but we cannot understand their _pars cultus accidentaria_ [_accidentary part of worship_] to be _pars integralis non necessaria_ [_a formal but non-necessary part_], because, then, their distribution of worship into essential and accidentary parts could not answer to the rules of a just distribution, of which one is, that [/FONT]_[FONT=&quot]distributio debet exhaurire totum distributum [[/FONT]_[FONT=&quot]_distribution ought to exhaust what is being distributed]._[/FONT]​


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## jwright82 (Jan 22, 2011)

I hate to say it but both quotes are expressing multiple rules of logic. 

Gillepsie is refering to the old essence vs. accident problem of Aristotle's thinking, essence vs. accident.

He then introduces the laws of distribution into his argument, Guide to Logic, Statements I.
You see his point is that because the essence of worship is unknown from the accidents, uneccessary part of worship, the laws of distribution cannot be satisfied. 

The second quote you stated is refering to the rules of division, there are four of them. Elements of Logic.

I hate to burst your bubble really, I think that you are looking for multiple laws not one single law. Although this combination of laws might have had some name back then I am just unaware that it did.

---------- Post added at 06:35 PM ---------- Previous post was at 06:24 PM ----------

In fact if I understand his argument correctly it is this. Because we, whoever that is, don't know what is essential to their, whoever they are, worship and what is merely formal or accidental, we cannot determine whether or not a single element of worship is essential or not. The bottom part of strikes me as the law of excluded middle, a thing is either neccessary or not, there is no inbetween (exuastion if you will).

---------- Post added at 06:39 PM ---------- Previous post was at 06:35 PM ----------

Again th esecond quote on division is again smacking of the law of excluded middle, either you are in this division or that division there is no in between. That is why they sound similer.


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## jwright82 (Jan 22, 2011)

When did he live anyway? That might help to narrow down where he got it from, but keep in mind he might have been expressing a general rule of logic with no immediate source.


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## NaphtaliPress (Jan 22, 2011)

I'm was searching for the rule of a good division under that Latin; and Keckermann illustrates that. Whether that was Gillespie's logic text I have no idea. Gillespie did cite Keckermann in later books and his works were in favor with the Puritans until the end of the century.


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## jwright82 (Jan 22, 2011)

NaphtaliPress said:


> I'm was searching for the rule of a good division under that Latin; and Keckermann illustrates that. Whether that was Gillespie's logic text I have no idea. Gillespie did cite Keckermann in later books and his works were in favor with the Puritans until the end of the century.


 
Fair enough. I am not sure how to answer your question. I am sure that he used multiple logical principles in your quote. I cannot imagine how hard it is to do what you do. But good luck with everything. You said you looking for a single law of logic, I believe you are dealing with multiple laws of logic.


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