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.
