To understand the nature of Aristotle's logic, see the excellent article here:
https://plato.stanford.edu/entries/aristotle-logic/
These are my notes and examples below. For the spiritual scientist it is important to see the logical connections in intuitive experience on the ideal or concept plane itself. Then, it can be spiritualized or shifted to the virtual with the good graces of the mother of Wisdom. I could not easily draw the 4 Venn diagrams here, but if you are interested or confused contact me. Some of this was worked through with my close colleague and friend, Jeremy Qvick. Enjoy!
A = all or
everything (affirmo – I assert X positively)
I = some IS
E = None IS (nego =
I deny X)
O = Some is NOT
I and E convert =
Iab = Iba etc
The predicate in the
conclusion is the Major term. The subject in the conclusion is the
Minor term.
Only 4 Venn diagram
relationships fundamentally with shifts in variables.
_______First
Figure________AB, BC, AC
1. Barbara – Aab,
Abc, Aac = All Bs are As, All Cs are B, therefore All Cs are As.
Example – All
rivers flow according to the influence of gravity, but all
gravitational forces pull most strongly toward the center of the
Earth, Therefore all rivers flow most strongly toward the center of
the Earth. B river, A gravity, C center
Difference between
basic rules of sentential logic, like modus ponens (If A then B, A
therefore B) and these syllogistic rules of universality and partial
coverage. This shows us why the Universal and Existential quantifier
is helpful. Because Barbara only shows us universal connectivity of
coverage and extension existing between concepts in the deductive
chain, whereas modus ponens shows us that a judgment has been made
that A actually exists, and therefore the connection to the other
cause, effect, object, or genus of B must occur. For example, modus
ponens requires the existence of rivers and the judgment that this X
is a river.
2. Celarent – Eab,
Abc, Eac = No B is A, All Cs are Bs; Therefore No C is A.
[related to Cesare]
Example – 1. No
bee is a mammal. (Eab = Eba) C milk B mammal A
bee
2. All true milk is
produced by mammals to feed their young.
3. No bee produces
milk to feed its young. (Eac = Eca)
3. Darii
– Aab, Ibc, Iac = All Bs are A, Some Cs are B, Therefore
some Cs are A.
True example:
All iron rusts
Some tools are made of iron
Therefore, some tools rust.
A more controversial but also more realistic argument:
A Grammar B S Language C French
All second language learning should include some study of grammar
Some French is taught as a second language
Therefore some French language study should include the study of grammar
False Example – A
cannibal, B carnivore, C pets
1. All carnivores are potential cannibals.
2. Some pets are carnivores.
3. Therefore, some
pets are potential cannibals (or V.V.)
Can you tell why it does not work?
4. Ferio –
Generally analytic or based on definition and essence of concepts
Eab, Ibc, Oac = No B
is A; Some Bs are C; Some C is not A.
Example X – A
fruit, B spruce, C Tree
1. No Spruce
produces fruit (because they produce cones)
2. Some trees are
spruces (Ibc = Icb)
3. Therefore, some
trees do not produce fruit
Example Y – B
plant, A stone, C red flower
1. No stone is a
plant (Eab = Eba)
2. Some plants
develop red flowers
3. Some red flowers
exist but not growing from stones
_____ 2nd
figure_____ AB,
AC, BC
5.
Cesare – Eab, Aac, Ebc = No b is a, All c is a, no c is b
Venn = Identical to
Celarent above, but variables shift.
Example X (B tree, A
underwater, C coral)
1. No trees grow
completely underwater
2. All coral grows
completely underwater
Therefore 3. No tree
is coral. (Ebc = Ecb)
6. Camestres
– Aab, Eac, Ebc = All B is A, No c is a, therefore no c is
b.
Venn diagram – the
same form as Celarent and Cesare, but variables shift.
Example X – B
turtles, A shells, C nests in standing trees
1. All turtles have
shells
2. No animal that
builds a nest in a standing tree has a shell
therefore 3. No
turtles build nests in standing trees
This is a good
example of what Rudolf Steiner says about forming conclusions: we
make the judgment of 3 first, and then we can work outward and
backward to make connections to other genera (thus we can form the
premises afterwards)
7. Festino
– Eab, Iac, Obc = No b is a, some c is a, some c [minor] is not b
[major]
Venn – same form as
Ferio, but variables shift.
Example X – B
carbon, A fluorine, C gas form
1. No Carbon is
Fluorine (F is not C from Eab – Eba)
2. Some Fluorine is
in gas form (Iac = Ica)
3. Some things in
gas form are not Carbon.
8.
Baroco – Aab, Oac, Obc
1. All b is a, some
c is not a, some c is not b
Venn – same as
Darii but now we are focused on the part of the circle that is
outside A and B
Example X = A
feathers, B bird-like, C Dinosaurs
1. All birdlike
animals have feathers
2. Some Dinosaurs
did not have feathers (yet this makes sense, because we know that
some did)
3. Some Dinosaurs
were not bird-like
Example Y = A
flying, B bats, C mammals
1. All bats are
flying animals (some flying animals are bats since Aab = Iba)
2. Some mammals do
not fly
3. Some mammals are
not bats
Example Z = A tree,
B spruce, C needle bearing things, exception = cactus
-----Third
Figure------------------AC, BC, AB
9.
Darapti – Aac, Abc, Iab = All C is A, All C is B, some B is A
Venn – same as
Darii and Baroco, but now focused on part of B that is A
Example X – C
bird-like, A feathers, B Dinosaurs = compare to Baroco example X
1. All birdlike
creatures have feathers
2. Some Dinosaurs
were birdlike (Abc = Icb)
3. Some Dinosaurs
had feathers
Also, flying, bats,
mammals
10.
Felapton – Eac, Abc, Oab
No c is a, All c is
b, some b is not a
Venn – Celarent
mutatis mutandis
C sound, A Silver, B
amplitude
Example X – 1.
Sound is not imprinted on Silver Nitrate film (like light reflections
are in analogue photography)
2. All sound has
amplitude or volume
3. Some things with
amplitude are not imprinted on Silver Nitrate film
11. Disamis
– Iac, Abc, Iab
Some C is A, All c
is A, some B is A
Venn – same as
Darii but mutatis mutandis
Example X – C tax,
A infrastructure, B govt
1. Some taxation is
healthy for the development and upkeep of infrastructure (roads,
etc.)
2. All taxation
arises from individuals and organizations who hand over a portion of
their profit to governmental organizations.
3. Therefore, some
governmental organization is healthy for the development of
infrastructure.
12. Datisti
– Aac, Ibc, Iab = Every C is A; Some Cs are B; Some Bs are
A.
C = subject SINGERS
A = Microphones B. Pianists
Example
A– 1. All singers incline toward using microphones today.
2.
Some singers are pianists, (note that Ibc = Icb, so that one could
also say – some pianists are singers)
3.
Therefore, some pianists incline toward using microphones today.
Example B – 1.
Every person who wears a hat is a guitarist; some drummers wear hats;
therefore some drummers are guitarists. But really the major premise
is not true.
Once you think this
through intuitively or in the pure warmth of the living plane of seen
concepts, you can learn how the world mind sees the reality in a
spiritual scientific sense. So, beyond the form of Datisti, we note
the ahriminic inverted soul machine which exists in the piano; the
ahrimanic temptation to use electrical amplification to destroy the
spiritual nature of the human voice.
13. Bocardo
– Oac, Abc, Oab = some C is not A, All c is B, Some B is not A.
Venn – I bet you
can figure it out :-)
Example X – C,
Ukrainian ppl, A, Russian interests, B NATO
1. Some of the
Ukrainian people do not identify with (or support) Russian interests
2. All Ukrainian
people are supported by the NATO countries
3. Therefore, some
of the NATO countries do not identify with Russian interests
14.
Ferison – Eac, Ibc, Oab
Example – C
exercise, A easy, B fun
Venn – can you
figure it out?
Play with
Super-Ferison = To say something positively about the extent of B,
one needs a 4th variable D
No C is A, All B is
D, Some A is D, some C is D.
Eac, Adb, Ida, Idc =
Super-Ferison
Ramifications: No
Exercise is easy. Some exercise is Fun. Everything fun makes people
happy. Some easy things make people happy. Some exercise makes people
happy. Some fun things are easy. Therefore, fun things can be
something else beside exercise. Some things that make people happy
are not exercise. Etc.
_____________________
Notes on Fallacies
from Prior Analytics 4 – If you universalize the minor premise, it
can lead nowhere, and thus no deduction is possible.
Other fallacy –
All guitarists wear hats, some drummers wear hats, therefore some
drummers are guitarists – no!
Correct = Every
person wearing a hat is a guitarist; Some drummers wear hats;
therefore some drummers are guitarists – YES!
Other issues –
Note that Eab, Ibc, Iac (not part of the 14) does not tell you the
extent of C that is outside A and B, but only that the part of C that
is B or A is not in the other.
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