
Are A and I as well as E and O. They have the same quality but differ either in being partial instead of total or in being contingent instead of necessary. 


Have the same matter (subject and predicate) but differ in form (quality, quantity, modality, or in two of these). 


A (all S is/must be P) and O (some S is not/may not be P) as well as E (no S is/may be P) and I (some S is/may be P). They differ in quality and either quantity or modality. There is no middle ground between them. 


One must be true and the other false. 


Are A (all S is/must be P) and E (no S is/can be P). They differ in quality and are either total in quantity or necessary in modality. There is a middle ground between them. 


Both cannot be true, but both may be false. 


Are I (some S is/may be P) and O (some S is not/may not be P). They differ in quality and are either partial in quantity or contingent in modality. 


Both cannot be false, but both may be true. 


Are A (all S is/must be P) and I (some S is/may be P) as well as E (no S is/can be P) and O (some S is not/may not be P). They have the same quality but differ in being partial instead of total or in being contingent instead of necessary. 


If the total or necessary proposition is true, the partial or contingent must be true; but if the former is known to be false, the value of the latter is unknown.
And if the partial or contingent proposition is false, the total or necessary must be false; but if the former is known to be true, the value of the latter is unknown. 


Total or necessary affirmation. S a P All S is P S must be P 


Total or necessary negation. S e P No S is P S cannot be P 


Partial or contingent affirmation. S i P Some S is P S may be P 


Partial or contingent negation. S o P Some S is not P S may not be P 


S is distributed while P is not. 






S is not distributed, but P is. 

Distribution of Predicates 

Occurs in negative propositions. 


From the 10 categories of being:
Substantives (nouns and pronouns)
Primary Attributives ( verbs, verbals, adjectives)
Secondary Attributives (attributes of attributes: adverbs) 


Words significant only with other words:
Definitives (articles and pronomials)
Connectives (prepositions and conjunctions)
Pure Copula 


Substance Quantity Quality Relation Action Passion When Where Posture Habiliment 









Opposition of singular empirical propositions for categorical forms 

Is achieved through a difference of quality alone and is restricted to contradiction:
A Mary is tall E Mary is not tall 

Opposition of singular empirical propositions in modal forms 

Includes all four relations:
A Mary must be nice E Mary cannot be nice I Mary may be nice O Mary may not be nice 


Then I is false, A is false, O is true 


Then I is true, A and O are unknown 


Then E is false, A and O are unknown 


Then E is true, A is false, O is true 


Then A is false, E and I are unknown 


Then A is true, E is false 


Changes a proposition’s quality (from affirmation to negation or negation to affirmation) and predicate (from P to P’ = nonP) but not the meaning. 


S a P > S e P’
All voters are citizens>No voters are noncitizens 


S e P>S a P’ No Jews are Muslims>All Jews are nonMuslims 


S i P>S o P’
Some chairs are comfy>Some chairs are not comfy 


S o P>S i P’ Some pupils listen>Some pupils don’t listen 


Reverse the subject and predicate, change the quantity if need be, but don’t change the quality.
No term may be distributed in the converse that was undistributed in the original proposition. 


To P i S
To P a S, but only when P is the definition or property of S, i.e., when it is distributed through the matter.
E.g. Man is a rational animal. A rational animal is man.
Otherwise beware of distributing P in affirmative propositions. 






It may be true to convert to P o S, but the original S is not distributed and yet becomes a P in a negative proposition (and so is then distributed incorrectly).
The truth of P o S is an accident of matter and the proposition is formally invalid. 


The quality of a proposition is changed and the predicate is converted to its contradictory 


A proposition that uses the contradictory of the subject and the predicate of the original proposition. 

Eductions of S a P: All voters are citizens. 

Obverse – S e P’: No voters are noncitizens.
Partial contrapositive – P’ e S: No noncitizens are voters.
Full contrapositive – P’ a S’: All noncitizens are nonvoters.
Full inverse – S’ i P’: Some nonvoters sre noncitizens.
Partial inverse – S’ o P: Some nonvoters are not citizens.
Converse – P i S: Some citizens are voters.
Obverted converse – P o S’: Some citizens are not nonvoters. 

Eductions of S e P: No Jews are Muslims. 

Obverse – S a P: All Muslims are nonJews.
Partial contrapositive – P’ i S: Some nonJews are Muslims.
Full contrapositive – P’ o S’: Some nonJews are not nonMuslims.
Converse – P e S: No Jews are Muslims.
Obverted converse – P a S’: All Jews are nonMuslims.
Partial inverse – S’ i P: Some nonMuslims are Jews.
Full inverse – S’ o P’: Some nonMuslims are not nonJews. 


Alternately and successively use obversion (change quality and substitute P with P’) and conversion (reverse S and P and don’t change quality). Once you arrive at S o P, return to the original proposition and begin with the opposite process of eduction. E.g., if you began with obversion, then use conversion. 

Eduction of S i P: Some chairs are uncomfy. 

Obverse – S o P’: Some chairs are not uncomfy.
Coverse – P i S: Some comfy things are chairs.
Obverted coverse – P o S’: Some comfy things are not nonchairs. 

Eduction of S o P: Some kids are not attentive. 

Obverse – S i P’: Some kids are inattentive.
Partial contrapositive – P’ i S: Some inattentive beings are kids.
Full contrapositive – P’ o S’: Some inattentive beings are not nonkids. 

Eduction of S a P with P fully distributed, i. e., when P is either the definition or a property of S:
All men are rational animals. 

Converse – P a S: All rational animals are men.
Obverted converse P e S’: No rational animals are nonmen.
Partial inverse – S’ e P: No nonmen are rational animals.
Full inverse – S’ a P’: All nonmen are nonrational animals.
Full contrapositive – P’ a S’: All nonrational animals are nonmen.
Partial contrapositive – P’ e S: No nonrational animals are men.
Obverse – S e P’: No men are nonrational animals.
Original – S a P: All men are rational animals. 

Eduction by added determinants 

S is P; therefore Sa is Pa. “a” must affect S and P to the same degree and respect.
Of degree: Original: An ant (S) is an animal (P). Invalid: a large (a) ant (S) is a large (a) animal (P). Valid: a small (a) ant (S) is a small (a) animal (P).
Of respect: Original: A contralto is a woman. Invalid: a low contralto is a low woman. Valid: a blonde contralto is a blonde woman. 

Eduction by omitted determinants 

S is Pa; therefore S is P. A subject included in a more determined predicate is necessarily included in that predicate when it is less determined.
E.g., Socrates is a rational animal; therefore Socrates is an animal. 

Eduction by converse relation 

S r1 P; therefore P r2 S. (r1 and r2=copulas with correlative modifiers rather than simple copulas.)
Relative terms necessarily imply their correlatives (e.g., genus and species), so the subject and predicate with a relative copula may be transposed if the relative copula is supplanted by its correlative.
Original: Aristotle (S) taught (r1) Alexander the Great (P). Valid inference: Alexander the Great (P) was taught (r2) by Aristotle (S).
Original: A (S) is greater (r1) than B (P). Valid inference: B (P) is less (r2) than A (S).
Original: Lily (S) is a species (r1) of flower (P). Valid inference: Flower (P) is a genus (r2) of lily (S). 


Classification of relations a predicate may be affirmed to have to a subject 


Species Genus Differentia Definition Property Accident 

The four relations of propositions 

Conjunction Opposition Eduction Syllogism 

Rules of conjunctional propositions 

True only when every proposition conjoined is true
False if any one of the propositions conjoined is false
Probable if at least one of the propositions conjoined is propable and none are false 


Two propositions (called premises) having one term in common leading to a third proposition (called the conclusion) in which the common term (called the middle term, M) does not appear.
A bat (S) is a mammal (M) No bird (P) is a mammal (M) A bat (S) is not a bird (P) 


Start with the conclusion:
Minor term is the subject (S) of the conclusion
Major term is the predicate (P) of the conclusion
Conclusion: A bat (S) is not a bird (P)
So the Minor Premise is: A bat (S) is a mammal (M)
The Major Premise: No bird (P) is a mammal (M) 


It must contain 3 and only 3 terms. 


It must contain 3 and only 3 propositions 


The middle term must be distributed in at least one of the premises 


No term may be distributed in the conclusion which wasn’t distributed in its own premise 


From 2 negative premises no conclusion can be drawn 


If one premise is negative, the conclusion must be negative. Or, in order to prove a negative conclusion, one premise must be negative 


From two partial or singular or contingent premises, no conclusion can be drawn. See rules 3, 5, and 6. 


If one premise is partial, the conclusion must be partial. See rules 3 and 4. 


If one premise is contingent, thr conclusion must be contingent. 


If one or both premises are empirical, the conclusion must be empirical. 


It is designated by the A, E, I or O forms of propositions and their order.
With 4 propositional forms we get 16 possible combos: AA, AE, AI, AO, EA, EE, EI, EO, IA, IE, II, IO, OA, OE, OI, OO.
Rule 5 eliminates EE, EO, OE, and OO.
Rule 7 eliminates II, IO, OI, and (again) OO.
Special rules (tba) eliminate EI. 

8 standard combos of premises 

AAA (AAI) AEE (AEO) AII AOO EAE (EAO) IAI IEO OAO 


Determined by position of middle term in the premises: is it the subject or predicate of the minor or major term? 


The middle term is the predicate of the minor premise and the subject of the major premise:
S__M M__P S__P
M__P S__M S__P 


The middle term is the predicate of both premises:
S__M P__M S__P
P__M S__M S__P 


The middle term is the subject of both:
M__S M__P S__P
M__P M__S S__P 


The middle term is the subject of the minor premise and the predicate of the major:
M__S P__M S__P
P__M M__S S__P 

The mood and figure of: 1.A bat (S) is a mammal (M). 2.No bird (P) is a mammal (M). >3.A bat (S) is not a bird (P). 



See if the middle term is distributed in at least one premise (rule 3).
See if P or S is distributed in the conclusion but undistributed in its premises (rule 4).
1. A bat (S) is (A) a mammal (M): S is distributed, M is not.
2. No bird (P) is (E) a mammal (M): both P and M are distributed.
3. A bat (S) is not (E) a bird (P): both are distributed. Valid. 


A syllogism omitting one proposition, either the major premise, the minor premise, or conclusion. 

To find the conclusion of an enthymeme 

Look for “because,” “for,” or “since.” These introduce a premise and therefore the other proposition is the conclusion.
Look for therefore, consequently, or accordingly, which introduce a conclusion.
Look for and or but, which connect two premises and indicate that the proposition omitted is rhe conclusion. 


If it is valid in one expansion, it’s valid.
If it is invalid in the first expansion, expand it in the alternate figure to see if it can become valid. For example:
An oak (SD) is a plant (PU) because it (SD) is a tree (MU).
Expansion B: An oak (SD) is a tree (MU). All plants (PD) are trees (MU). An oak (SD) is a plant (PU).
This is invalid Figure 2 syllogism because of an undistributed (U) middle term (M).
So Expansion A: An oak (SD) is a tree (MU). A tree (MD) is a plant (PU). An oak (SD) is a plant (PU).
This is a valid Figure 1 syllogism. 


Has the conclusion (with S and P terms) and one premise stated (with either the S and M or P and M terms).
Either the premise with the minor term S is missing or the premise with the major term P is missing. 


A chain of enthymemes or abridged syllogisms, in which the conclusion of one syllogism becomes a premise of the next 


That in which the conclusion of one syllogism becomes the major premise of the next:
Goclenian sorites (figure 1) 


That in which the conclusion of one syllogism becomes the minor premise of the next:
Aristotelian sorites (figure 1) 

Aristotelian sorites;
The first proposition is the minor premise of its syllogism and all the rest are major premises except for the last, which is a conclusion.
The omitted conclusion in each syllogism becomes the minor premise of the following syllogism. 

Socrates is a man – S a M1 A man is an animal – M1 a M2 (Omitted conclusion and minor premise: Socrates is an animal.) An animal is an organism – M2 a M3 (Omitted conclusion and minor premise: Socrates is an organism.) An organism is a body – M3 a M4 (Omitted conclusion and minor premise: Socrates is a body.) A body is a substance – M4 a P Socrates is a substance – S a P 

Goclenian sorites:
The first proposition is the major premise of its syllogism and all the rest are minor premises, except the last which is a conclusion.
The omitted conclusion in each syllogism becomes the major premise for the following syllogism. 

A body is a substance – M1 a P An organism is a body – M2 a M1 (Omitted conclusion and major premise: An organism is a substance.) An animal is an organism – M3 a M2 (Omitted conclusion and major premise: An animal is a substance.) A man is an animal – M4 a M3 (Omitted conclusion and major premise: A man is a substance.) Socrates is a man – S a M4 Socrates is a substance – S a P 

Aristotelian sorites expanded 

Socrates is a man – S a M1 Man is an animal – M1 a M2 Socrates is an animal – S a M2
Socrates is an animal – S a M2 An animal is an organism – M2 a M3 Socrates is an organism – S a M3
Socrates is an organism – S a M3 An organism is a body – M3 a M4 Socrates is a body – S a M4
Socrates is a body – S a M4 A body is a substance – M4 a P Socrates is a substance – S a P 

Goclenian sorites expanded 

A body is a substance – M1 a P An organism is a body – M2 a M1 An organism is a substance – M2 a P
An organism is a substance – M2 a P An animal is an organism – M3 a M2 An animal is a substance – M3 a P
An animal is a substance – M3 a P A man is an animal – M4 a M3 A man is a substance – M4 a P
A man is a substance – M4 a P Socrates is a man – S a M4 Socrates is a substance – S a P 

Aristotelian sorites rules 

1. Only the last premise may be negative.
2. Only the first (minor) premise may be partial, contingent or singular. 


1. Only the first premise can be negative.
2. Only the last (minor) premise may be partial, contingent or singular. 


An abridged polysyllogism combining any figures, one whose premises is an enthymeme. 


Both premises are enthymemes 

Example of single epicheirma 

Beefsteak is not stored in the body because it is protein. Food that is not stored in the body is not fattening. Beefsteak is not fattening. 

Expanded single epicheirma 

Beefsteak (S) is protein (M). Protein ( M) is food that is not stored in the body (P). Beefsteak (S) is food that is not stored in the body (P).
Fig. 4, mood AAA, valid.
Beefsteak (S) is food thay is not stored in the body (M). Food not stored in the body (M) is not fattening (P). Beefsteak (S) is not fattening (P).
Fig. 4, mood AEE, valid 

Multiple enthymeme v epicheirema 

The multiple enthymeme has only one conclusion and many reasons supporting it.
The epicheirma has two conclusions and the double has three because they become premises which lead to a third conclusion. 


The O and E are false, I is true 


O is true, E and I are unknown 

Exame of Analogical inference 

Sparks (S1) from an electrical machine are electrical charges (P), for they (S1) have rapid motion and conductivity (M): S1 is P because S1 is M.
Lightening (S2) resembles these sparks (S1) in rapid motion and conductivity (M): S2 resembles S1 in M.
Lightening (S2) is probably an electrical charge (P): S2 is probably P. 

Validity of Analogical inference 

Requires that the point of resemblance (M) be a property of P. 

Example of Mediate opposition using mediated contraries 

Mediate Contraries (AE): X: The witness is lying. Z’: The witness is telling the truth.
An immediate opposition uses Contradictories (AO, EI): X: The witness is lying. X’: The witness is not lying. 

Rules of Mediated Opposition 

1. The syllogism must be formally valid.
2. The third proposition, Y, must be materially true. 

Illustrated Mediated Opposition 

Mediated Opposition: The witness is lying. The witness is telling the truth.
Let X = minor premise Y = major premise Z = conclusion
Disputant 1: X = The witness is lying. Y = Whoever lies doesn’t tell the truth. Z = The witness is not telling the truth.
Let X’ = contradictory of X Let Z’ = contradictory of Z
Disputant 2: X’ = The witness is not lying. Y = Whoever lies doesn’t tell the truth. Z’ = The witness is telling the truth.
Y is the omitted but shared proposition held by disputants 1 and 2 in the mediated opposition. 

Relations of Mediated Opposition 

If Y is materially true:
X (the witness is lying) and Z’ (the witness is telling the truth) are mediated contraries (A and E) and both cannot be true, but both can be false.
Z (the witness is not telling the truth) and X’ (the witness is not lying) are subcontraries (I and O) and both cannot be false but both may be true. 

Syllogistic rules of inference 

1. If both premises are true, the conclusion is.
2. If the conclusion is false, at least one of the premises must be false.
3. If one or both premises are false, the conclusion is unknown.
4. If the conclusion is true, the value of the premises are unknown.
5. If one or both of the premises are probable, the conclusion can only be probable.
6. If the conclusion is probable, the value of the premises is unknown 


Figure 2’s middle term, M, is predicate in both premises: S__M P__M S__P
Hence, 1. One premise must be negative to distribute M.
Because a negative premise requires a negative conclusion (rule 6), the major term P will be distributed in the conclusion.
Yet it cannot be distributed in the conclusion without having already been distributed in its own premise. There, however, the major term P is the subject, and only a total or necessary proposition distributes its subject. So
2. The major premise must be total or necessary and so take the mood of either A or E.
So the valid moods of figure 2 are: AEE, EAE, IEO, OAO. 


Figure 1’s middle term (M) is the predicate of the minor term (S) and the subject of the major term (P): S__M M__P S__P
Hence, 1. The minor premise (S) must be affirmative.
This is because if the minor premise were negative, the conclusion would be negative (rule 6). But then the major term P would be distributed in the conclusion, and it could not be distributed in the conclusion without also being distributed in its own premise (rule 4). For that to happen, however, would require the major premise to also be negative, and yet two negative premises lead to no conclusion (rule 5).
2. The major premise must be total or necessary to avoid an undistributed middle term, because that term was not distributed in the (affirmative) minor premise.
So the valid moods of figure 1 are: AAA, AEE, IAI, IEO 


Figure 3’s middle term (M) is the subject of the minor (S) and major (P) premises: M__S M__P S__P
Hence, 1. The minor premise (S) must be affirmative.
2. Because S is formally undistributed it will be undisturbed in the conclusion, and only partial or contingent propositions have undisturbed subjects. Thus the conclusion is partial and contingent.
So the valid moods of figure 3 are: AAI, AII, IAI, AEO, AOO, IEO 


The middle term is the subject of the minor term (S) and predicate of the major term (P): M__S P__M S__P
1. If the major premise is affirmative, M is undistributed and so must be distributed in the minor (rule 3) where it is subject. So M__S must be total or necessary.
2. If the minor is affirmative, the conclusion must be partial or contingent (rule 2 of fig. 3).
3. If the conclusion is negative, the major premise must be total or necessary (rule 2 of fig. 2).
Moods: AAI, EAE, AII, AEO, IEO 


A total or necessary general affirmative proposition as conclusion 


Negative conclusions, unless one premise is a definition.
It’s adapted to disproof. 


Partial, singular or contingent conclusions, unless one premise is the definition.
It’s adapted to proving exceptions. 


A process where a syllogism in an imperfect figure (2, 3 or 4) is expressed as a syllogism of the first figure.
Assumes; 1. Imperfect figures’ premises are true. 2. That the first figure is formally valid. 

Figure reductionValid Moods 

First Figure: Barbara (AAA), Celarent (EAE), Darii (AII), Ferio (EIO), que prioris.
Second Figure: Cesare (EAE), Camestres (AEE), Festino (EIO), Baroco (AOO), secundae.
Third Figure: Tertia Darapti (AAI), Disamis (IAI), Datisi (AII), Felapton (EAO) Bocardo (OAO), Ferison (EIO) habet.
Fourth Figure: Quarta in super addit Bramantip (AAI), Camenes (AEE), Dimaris (IAI), Fesapo (EAO), Fresison (EIO).
Vowels = mood in traditional order: Major premise, minor premise, conclusion.
B, C, D, and F names in second to fourth syllogisms can have their moods reduced to the first figure moods whose names begin with the same letter. E.g., Camestres (AEE) of the second figure can be reduced to Celarent (EAE) of the first figure. 

Mode of reduction to first figure form 

Barbara (AAA), Celarent (EAE), Darii (AII), Ferio (EIO), que prioris.
Cesare (EAE), Camestres (AEE), Festino (EIO), Baroco (AOO), secundae.
Tertia Darapti (AAI), Disamis (IAI), Datisi (AII), Felapton (EAO) Bocardo (OAO), Ferison (EIO) habet.
Quarta in super addit Bramantip (AAI), Camenes (AEE), Dimaris (IAI), Fesapo (EAO), Fresison (EIO).
A name with the letter “s” in it signifies that the vowel preceding it (DisamisIAIof the 3rd syllogism) is reduced to the first figure mood (DariiAII) by simple conversion (reverse subject and predicate).
“P” signifies that the proposition indicated by the proceeding vowel must be converted by limitation (A to I in one case or I to A) to the first figure mood.
“M” signifies premises are to be transposed; “c” by showing that the conclusion in the first figure contradicts a premise given as true in another figure; r, b, l, n, t, d mean nothing. 

Reducing Camestres to Celarent (A to B) 

CaMeStreS (AEE) or A:
All circles (P) are (a) curvilinear (M). MTranspose
No square (S) is (e) curvilinear (M). SConvert
No square (S) is (e) a circle (P). SConvert
Celarent or B:
No curvilinear figure (M) is (E) a square (P). All circles (S) are (A) curvilinear (M). No circle (S) is (E) a square (P). 

Reduction by “c”, per contradictorian propositionem: BoCardo (OAO) to Barbara (AAA) 

From Barbara, using as premises the A of Bocardo and the contradictory of its conclusion draw the conclusion implicit in these premises:
Bocardo or A:
Some lions (M) are not (o) tame (P). All lions (M) are (a) animals (S). Some animals (S) are not (o) tame (P).
Barbara or B:
All animals (M) are (a) tame (P). All lions (S) are (a) animals (M). All lions (S) are (a) tame (P).
Because premise O of Bocardo is true and the conclusion of Barbara is its contradictory, that conclusion, though of a valid syllogism, is false. So the matter rather than the form is to blame, meaning one of the premises must be false. And because the minor premise of Barbara was given by Bocardo as true, then its major premise, All animals are tame, must be false. That premise is the contradictory of Bocardo’s conclusion, Some animals are not tame, which means that Bocardo’s conclusion is true. 


Expresses a conditional relation of propositions 


Expresses a relation of terms 

3 term hypothetical proposition’s formula 


4 term hypothetical proposition’s formula 


Reduction of three term hypothetical proposition 

If S is M, it is P>SM is P 

Reduction of four term hypothetical proposition 

If B is C, D is E> BC is DE 

Hypothetical proposition and its contradictory 

If a man drinks water, he will die.
If a man drinks water, he will not die.
Taken in relation to the first proposition, which is false, the second, its contradictory, is true, though not by itself. 

First of disjunctive propositions 

1. S is P or Q or R.
The alternatives are:
A) collectively exhaustive B) mutually exclusive C) species resulting from division acording to single basis 

Second of disjunctive propositions 


Third type of disjunctive proposition 


Eduction of hypothetical propositions 

Original: if a tree is a pine, it is necessarily an evergreen.
Obverse: if a tree is a pine, it is necessarily not a nonevergreen.
Partial contrapositive: if a tree is a nonevergreen, it is necessarily not a pine.
Full contrapositive: if a tree is a nonevergreen, it is necessarily a nonpine.
Full inverse: if a tree is a nonpine, it may be a nonevergreen.
Partial inverse: if a tree is a nonpine, it may not be an evergreen.
Converse: if a tree is an evergreen, it may be a pine.
Obverted converse: if a tree is an evergreen, it may not be a nonpine. 

Eduction of disjunctive proposition 

Original: a material substance must be either a gas, liquid or solid.
Converse: a substance that is either a gas, liquid or solid must be a material substance.
Obverted converse: a substance that is either a gas, liquid, or solid cannot be a nonmaterial substance.
Partial inversion: a nonmaterial substance cannot be either a gas, liquid or solid
Full inverse: a nonmaterial substance must be neither a gas, liquid nor solid.
Full contrapositive: a substance that is either neither a gas, liquid nor a solid must be a nonmaterial substance.
Partial contrapositive: a substance that is neither a gas, liquid nor a solid cannot be a material substance.
Obverse: a material substance cannot be neither a gas, liquid nor solid.
Original. 

Mixed hypothetical syllogism 

The major premise is a hypothetical proposition, and the minor premise is a simple proposition 

Rules for the mixed hypothetical syllogism 

The minor premise must either:
1. (Modus ponens – the way of affirmation:) posit the antecedent or
2. (Modus tollens – the way of negation:) sublate the consequent of the major premise (by restating as fact its contradictory). 

Example of positing the antecedent: modus ponens 

Major premise: (Antecedent) If a man is not honest, (consequent) he is not a fit public officer.
Minor Premise: (Positing of antecedent) This man is not honest.
Conclusion; (Positing of consequent) This man is not a fit public officer. 

Example of sublating the consequent: modus tollens 

Major premise: (Antecedent) If all students were equally competent, (consequent) each would have the same grade in a given course.
Minor premise: (Sublating of consequent) But each doesn’t acquire the same amount of knowledge from a given course.
Conclusion: (Sublating the antecedent) All students are not equally competent.
The conclusion is the contradictory of the antecedent. 

Fallacy of sublating the antecedent 

If a man drinks poison, he will die. This man has not drunk poison. He will not die.
Syllogistically:
Whoever drinks poison (M) will (a) die (P). This man (S) has not (e) drunk poison (M). He (S) will not (e) die (P).
P is distributed in the conclusion but not in the major premise, hence the syllogism is invalid. 

Fallacy of positing the consequent 

If a man drinks poison he will die. This man died. He must have drunk poison.
Syllogistically:
Whoever drinks poison (P) will (a) die (M). This man (S) died (a and M). He (S) must have (a) drunk poison (P).
The middle term is undistributed. 


Whenever the minor premise posits the antecedent, the conclusion posits the consequent:
(Major premise;) If A (antecedent) then B (consequent). (Minor:) A . (Conclusion;) B. 


Whenever the minor premise sublates the consequent, the conclusion sublates the antecedent.
(Major premise:) If A (antecedent) then B (consequent). (Minor premise:) B. (Conclusion:) A. 

Ponendo tollens of a disjunctive syllogism 

The minor premise posits one alternative, and the conclusion sublates the other.
This woman’s missing husband (S) is either living (P) or dead (Q). He is living (P). He is not dead (Q). 

Tollendo ponens of disjunctive syllogism 

The minor premise sublates one alternative, and the conclusion posits the other.
Th soul (S) is either spiritual (P) or material (Q) The soul is not material (S=Q) The soul is spiritual (S=P). 


Formal: Where the minor premise and conclusion both posit and sublate each alternative.
Material: Where the alternatives are not mutually exclusive or not collectively exhaustive. 


A syllogism with:
1. A disjunctive minor premise
2. A compound hypothetical proposition for its major premise
3. A simple or disjunctive proposition for its conclusion. 


1. Simple constructive
2. Complex constructive
3. Simple destructive
4. Complex destructive 


1. False major premise
2. Imperfect disjunction in the minor premise
3. The dilemmatic fallacy, from a shifting point of view 

Exposing the dilemma with a false major premise 

Taking the dilemma by the horns 

Exposing the dilemma of the imperfect disjunction in the minor premise 

Escaping between the horns 

Exposing the dilemmatic fallacy 

Rebutting the dilemma:
Used when the dilemma open to rebutal and the rebutting dilemma contain a formal and material fallacy.
Accept the alternatives in the minor premise of the original dilemma but transpose the consequents of the major premise and change them into contraries. 


The minor premise posits the two antecedents of the major 


The minor premise sublates the two consequents of the major premise 


1. Equivocation 2. Amphiboly 3. Composition 4. Division 5. Accent 6. Verbal form 


Feathers are light. Light is the opposite of darkness. Feathers are the opposite of darkness. 


Produced by ambiguity of syntax or grammatical structure.
He told his brother that he had won the prize. (Who?) 


Properties of parts are illicitly predicated of the whole. 


When properties of the whole are illicitly predicated of the parts 


Inspiration and inexplicable: if “in” means “not” in one, it means “not” in the other. 


A shifting of usage in one term. For example, to shift from first imposition to second:
1st Imposition – Feathers are light. 2nd Imposition – Light is an adjective. Feathers are adjectives.
Feathers is first used as an adjective and then as a noun (when, ironically, it is called an adjective). 





First imposition and first intention 



Of phonetics and spelling 

Fallacy with grammar used in two impositions 

Carry is a verb. Verb is a noun. Carry is a noun.
Verb shifts from first to second imposition 

Valid syllogism with grammar 

Sing is verb. A verb has tense. Sing has tense. 


Assumes that a proposition true in certain respects is true absolutely 


There are two types of material fallacy of consequent:
1. Positing the consequent – Falsely assumes that because a consequent follows upon the antecedent, the antecedent must follow upon the consequent.
If it rains, the ground is wet. The ground is wet. It rained.
2. Sublating the antecedent – Falsely assumes that from the contrary of the antecedent the contrary of the consequent must follow.
If it rains, the ground is wet. It did not rain. The ground is not wet. 


1. Tautological argument:
Shakespeare is famous because his plays are known all over.
2. The shuttle argument:
The boy is insane. Why? Because he murdered his mom. Why? Because he’s insane.
3. Arguing in a circle:
Shuttle argument plus additional propositions.
4. Questionbegging epithet:
Using a phrase that assumes the point to be proved. 


The derivation of general propositions from individual instances.
The apprehension of the cause common to a number of observed facts. 


1. Efficient cause – the agent and instruments.
2. Final cause – the end or purpose that moved the agent. It is first in intention, last in execution.
3. Material cause – that out of which a thing is made.
4. Formal cause – the kind of thing which is made; its essence. 


Links induction to deduction.
Seeks the cause of natural phenomena, a middle term, which is the formal cause of the relation of the terms in the conclusion of the syllogism.
So we see S is P, and we posit that S is P because of M. We want M to be the only antecedent of P so that M is P and P is M. So we want to say Pif S is M it is P and if S is P it is M.
If so we get this regressive syllogism:
S is P. P is M. Therefore S is M.
So
If S is M, it is P. But S is M. Therefore S is P. 
