What does "dictum de omni et nullo" mean?
Jim Spriggs
Alan Smaill
> What does "dictum de omni et nullo" mean?
"said of each and of none"
--
Alan Smaill
Jim Spriggs
>
> Jim Spriggs <jim.s...@ANTISPAMbtinternet.com.invalid> writes:
>
> > What does "dictum de omni et nullo" mean?
>
> "said of each and of none"
Thank you for the swift reply!
William Elliot
> Jim Spriggs <jim.s...@ANTISPAMbtinternet.com.invalid> writes:
>
> > What does "dictum de omni et nullo" mean?
> "said of each and of none"
>
"said of none" is rather unusual semantical structure.
How does it mean anything? Have you context to provide, as
a sentence (and translation if appropriate) in which it's used.
Charlie-Boo
> What does "dictum de omni et nullo" mean?
"Everyone here is a dick and doesn't know nothing." (literally
translated.)
How true, how true . . .
C-B
Ken Pledger
Jim Spriggs <jim.s...@ANTISPAMbtinternet.com.invalid> wrote:
> What does "dictum de omni et nullo" mean?
If you want its meaning in mediaeval logic rather than just a
translation of the Latin, you may like to look at Jan Lukasiewicz,
"Aristotle's Syllogistic," pp. 46-7. His paragraph of comment on it
also gives two other references.
Ken Pledger.
Jim Spriggs
>
> In article <4273909B...@ANTISPAMbtinternet.com.invalid>,
> Jim Spriggs <jim.s...@ANTISPAMbtinternet.com.invalid> wrote:
>
> > What does "dictum de omni et nullo" mean?
>
> If you want its meaning in mediaeval logic rather than just a
> translation of the Latin, you may like to look at Jan Lukasiewicz,
> "Aristotle's Syllogistic," pp. 46-7.
That's just where I've come from! I didn't understand it, hence my
question.
philippe
"Jim Spriggs" <jim.s...@ANTISPAMbtinternet.com.invalid>
wrote 4273909B...@ANTISPAMbtinternet.com.invalid...
> What does "dictum de omni et nullo" mean?
This post by Dean Buckner might help :
There was a famous medieval principle called "Dictum de Omni et Nullo".
This derives from Aristotle, An. Prior I.i.8. "We say that an attribute
is predicated of All a subject, when there is no one of the parts of the
subject, of which the attribute is not predicated; and similarly in the
case, in which it is predicated of None". Roughly, whatever is affirmed
(or denied) of any subject is affirmed (or denied) of everything that is
"a part of" that subject. It is mentioned by as late a writer as John
of St Thomas (1589-1644) " Quidquid universaliter dicitur de aliquo
subjecto, dicitur de omni quod sub tali subjecto continetur: quidquid
negatur de aliquo subjecto, negatur et de omni contento sub tali
subjecto. (Logica. Pars I., Lib.3, c.x). (See also St Thomas An.
Post. I., lect 9. Scotus, Sup. Lib. I Priorum, Q.7.)
Ockham and Buridan have "Dici de omni". Lukaziewicz quotes it as
"quidquid de omnibus valet, valet etiam de quibusdam et de singulis" and
adds testily that "this obscure principle" is not found in Aristotle,
since Aristotle had no theory of singular propositions (the "Socrates is
mortal syllogism is not his). The An. Prior I passage (he says) "is
only an explanation of the words 'to be predicated of all/none'"
What on earth does it mean? The difficulty is understanding what "a
part of" the subject means. It is important that the "subject", for
example "all men" is NOT regarded as a collection or aggregate of
individuals. Then the syllogism reduces to a tautology: "all men are
mortal" simply says of Socrates, Aristotle, Plato, that they are men,
and so directly implies "Socrates is mortal" without the intervening
premiss "Socrates is a man". (In fact, there's a dispute that was
famous in the nineteenth century, now probably forgotten, as to whether
the universal syllogism does involves a petitio principii  see Mill,
System of Logic, II, II §2).
So you could say the medieval logicians did have the concept of a class,
and that the Dictum de omni expresses this. The subject of a universal
proposition is the species or genus or "class" as such, the logical
whole, it is not just a collection or aggregate of things, and the
proposition is not a mere enumerative judgement. Hence you could argue
that the idea of a set, as a class or a species was very familiar to
them, indeed was something essential to the whole of medieval logic and
metaphysics. "Omnes linaea" may refer to a "logical subject" that is
not to be confused with a mere aggregation of lines, but a "class" of
them.
A further complication is the word "class". This is the word used by
late traditional logicians like Mill and Whately, for which it is
interchangeable with "genus" or "species". But none of the medieval
texts seem to use it, even though it is Latin (meaning a "calling" or
"summoning" of the military). Peirce says it acquired its logical
signification in the 17C. Pierre Gassendi in (*Institutio logica*,
1658) apparently introducing the idea of a "class", however I don't know
what Latin word he used.
Russell uses "class" in a way that's clearly connected with "set" in
*Principles of Mathematics*.
Philippe