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Scott Crom
June 19th, 2005, 04:59 PM
Tim Lodge asked about the mnemonic from which BAROKO comes.
Here's more than you ever wanted to know:

Aristotle was not only the Father of Logic, but his work in that
area reigned unchallenged and unmodified well into the 19th
century. The core of that logic was the so-called categorical
syllogism.

A categorical syllogism consists of three propositions (two
premisses and a conclusion), each of which states the total or
partial inclusion or exclusion of one category (i.e., a class or
set of objects) in another.

The form of a syllogism is uniquely determined by its figure and
its mood. There are four figures, depending on the location of
the middle term, the one to which both the subject and predicate
of the conclusion (respectively, the minor term and the manor
term) are related. The mood is determined by the kind of each
proposition: universal affirmative (A), universal negative (E),
particular affirmative (I), and particular negative (O).

Thus a syllogism in Barbara is Mood AAA, figure 1, aka AAA-1. The
perennial example is: All men are mortal, Socrates is a man;
therefore, Socrates is mortal. (Actually this example, although
perennial, isn't fully accurate, because 'Socrates' refers not to
a class or category, but to a singular individual. Modern logic
enters here, distinguishing between membership in a class and one
class being included in another.)

There are exactly 19 valid forms of the traditional syllogism.
Medieval logicians developed a mnemonic to remember them easily.
It's a verse supposedly in Latin, stating which moods are valid
in the four figures:

Barbara, Celarent, Darii, Ferioque prioris;
Cesare, Camestres, Festino, Baroko secundae;
Tertia, Darapti, Disamis, Datisi, Felapton,
Bokardo, Ferison, habet; quarta insuper addit
Bramantip, Camenes, Dimaris, Fesapo, Fresison.

BAROKO is thus a syllogism in AOO-2, namely,

All P is M
Some S are not M
Therefore, Some S are not P.

To flesh out that form:

All Dixonary players are intellectuals.
Some street fighters are not intellectuals.
Some street fighters are not Dixonary players.

There are few further refinements. Aristotalian logic was far
more qualitatively oriented than quantitatively; some forms were
just "nicer" than others, although no more valid. Figure 1 was
thought to be the nicest, so in the other three figures,
consonants following some of the vowels show how that form could
be transformed into one in Figure 1. (Details omitted here...)

Now, aren't you sorry you asked?

Scott (who used to teach logic, albeit somewhat past Aristotle's
time)

John Barrs
June 20th, 2005, 04:52 AM
Scott

>
Tim Lodge asked about the mnemonic from which BAROKO comes.
Here's more than you ever wanted to know:
>

Thank you so much

JohnnyB [using email; via corypaheus/yahoogroups]

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Marijke van Gans
June 20th, 2005, 05:52 AM
Scott Crom said on 05-06-19 21:59 GMT:

> A categorical syllogism consists of three propositions (two
> premisses and a conclusion), each of which states the total or
> partial inclusion or exclusion of one category (i.e., a class or
> set of objects) in another.
>
> The form of a syllogism is uniquely determined by its figure and
> its mood. There are four figures, depending on the location of
> the middle term, the one to which both the subject and predicate
> of the conclusion (respectively, the minor term and the manor
> term) are related. The mood is determined by the kind of each
> proposition: universal affirmative (A), universal negative (E),
> particular affirmative (I), and particular negative (O).

I think i understand the A/E/I/O now. Could you please say how the four
"figures" relate to that middle term?

And does the choice of consonants have any mnemonic significance?

> (Actually this example, although
> perennial, isn't fully accurate, because 'Socrates' refers not to
> a class or category, but to a singular individual. Modern logic
> enters here, distinguishing between membership in a class and one
> class being included in another.)

I still wonder how useful that modern distinction really is. Boole
doesn't use it i think, in his own notation if W denotes white (set of
all white entities) and S sheep (set of all sheep) then W*S combines
both properties (or in terms of sets, takes the intersection: all white
sheep). And that remains the case if pile up a combination of properties
so restrictive that there happens to be only a single individual
described by them.

In set theory notation too, if s stands for Socrates and M for the set
of mortals then, true enough, we need to say s ∈ M. But it's easy
to define a set S = {s} with a single member and now we can say that S
⊂ M just like we could for any other set in place of S.

In math, the distinction between items "in" a set and subsets "of" a set
is not there to treat sets of one differently. It's just there to enable
sets of sets, sets of sets of sets and so on, building teetering towers
of thought, which is implicit in the definition of lots of stuff even if
we don't always write it out in full.

Moving away from formalism and notation now, if we say "Socrates is
mortal" do we really mean that one unique irreducible entity is mortal,
very different from "this whole class of people", or is the distinction
possibly not so sharp after all?

If Socrates' mortality is coded for in his genes, then surely the
mortality of his identical twin brother (written out of the history
books after a regrettable indiscretion with a white sheep -- and who
some say impersonated him at the infamous hemlock trial, allowing
Socrates to live out a ripe old age in Glastonbury :) is included in the
same statement? And that of any clones of Socrates that may be produced
in future?

Maybe any mention of "Scocrates" is just shorthand for "any person
sufficiently Socrates-like", where "sufficient" depends on context.

After all, is Socrates the boy really the "same" as Socrates the old
man? Real world means time, which does upset some of our notions of
identity. Real world is quantum physics too, which has some surprising
things to say about identity...

> Scott (who used to teach logic, albeit somewhat past Aristotle's
> time)

<g>

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Regards, marijke [52½°N 2°W]
http://web.mat.bham.ac.uk/marijke/