LESSON 3 d
INFERENCES
Inference is a process by which a conclusion is drawn from a valid sequence and relationship of premises.
Kinds of inference
1. Inductive inference. A form of reasoning that proceeds from particular premises to a general conclusion.
2. Deductive Inference. A form of reasoning that proceeds from universal /general premises to a particular conclusion.
Types of Induction
1. Essential Induction when the mind grasps in experience the necessary link between a subject and its property. This makes use of formal principles, which are so clear that they do not need any proof for they are self-explanatory and self-evident truths. These principles are:
1. The principle of Identity. Everything is itself.
Ex.: A school is a School.
2. The principle of excluded middle. A thing either is or is not.
Ex.: A school is either a school or not a school
3. The principle of non-contradiction. Nothing can be and not
be at the same time or respect.
Ex.: A school cannot be a school and not a school at
the same time.
4. The principle of sufficient reason. Everything that exist has sufficient reason for its existence.
Ex.: A school is a place of learning.
2. Empirical Induction is the generalization of the connection between the subject and the predicate based not on the essential link between them but on the repeated occurrence of the observed phenomenon.
2 kinds of Empirical Induction
1. Complete or perfect induction. The generalization rest on the knowledge of each instance covered. This is otherwise known as the induction by simple enumeration because it is simply the summation of all individual cases observed.
Example: Since Dr. Marin, Dr. Garcia, Prof. Manad, Prof. Gonzales and the rest of the faculty members of PNU are Master’s degree holders, We can conclude that all PNU teachers are master’s degree holders.
2. Incomplete induction. The conclusion takes the instances as a sample of the class and generalizes from the properties of the sample to the properties of the class.
Example: Since 80 % of survey respondents said that they preferred LRT to Jeepny as mode of transportation, we conclude that LRT is preferred as a mode of transportation by the public.
1. Deductive Inference. A form of reasoning that proceeds from universal /general premises to a particular conclusion.
1. Immediate Inference is a kind of inference by which the mind directly draws the implication of one proposition to arrive at a new proposition without the use of a medium.
It is the process of drawing conclusions from the implication of a statement and its Opposing categorical statements. It does not need a third statement to mediate or to connect the statements and infer from them. It is also the process of restating the same judgment in different forms.
Kinds of Immediate Inferences
1. Eduction or logical Equivalence- the process of creating a new proposition that conveys the same meaning.
2. Oppositional Inference- the process of establishing the relationship of propositions having the same subject and predicate but different qualities and or quantities. The truth or falsity of an opposite proposition is inferred from the truth or falsity of a given proposition.
2. Mediate Inference is the process of drawing new proposition from the relationship of two propositions that are related through a medium or a middle term. Inferences are externally manifested through a syllogism.
Syllogisms are verbal expressions of arguments that are products of reasoning or inferential thinking.
2 kinds of Syllogisms
1. Categorical Syllogism is a syllogism that is made up of categorical propositions
Example: All books are tools for learning;
But the dictionary is a book;
Therefore,the dictionary is a tool for learning.
2. Hypothetical Syllogism is a syllogism wherein at least one proposition is a hypothetical proposition.
Example: If all books are tools for learning then they must be valued.
But all books are tools for learning;
Therefore, they must be valued.
Validity of Inference
Let us analyze how we arrived at these. To illustrate all these, let us consider the table below:
The distinction between truth and validity is the fundamental distinction of formal logic. You cannot understand inference unless this distinction is clear and familiar to you.
The seven sample syllogisms above show the general principles of inferential thinking:
· True premises do not guarantee validity. As proven by examples #1 and #3 in the table above. · A true conclusion does not guarantee validity. As proven by examples #3 and #7. · True premises and a true conclusion together do not guarantee validity. As proven by example #3. · Valid reasoning does not guarantee a true conclusion. As proven by example #4. · False premises do not guarantee invalidity. As proven by examples #4 and #6. · A false conclusion does not guarantee invalidity. As proven by example #4. · False premises and a false conclusion together do not guarantee invalidity. As proven by example #4. · Invalid reasoning does not guarantee a false conclusion. As proven by examples #3 and #5. Therefore, while the truth of propositions and the validity of reasoning are distinct, the relationship between them is not entirely straightforward. We cannot say that truth and validity are utterly independent because the impossibility of "case zero" (a valid argument with true premises and false conclusion) shows that one combination of truth-values is an absolute bar to validity. When an argument has true premises and a false conclusion, it must be invalid. In fact, this is how invalidity is defined..
Thus an argument is sound if (and only if) all its premises are true and its reasoning is valid; all others are unsound. It follows that all sound arguments have true conclusions.
The Validity and soundness of categorical syllogisms and of Hypothetical Syllogisms will be further discussed in the succeeding chapters.
OPPOSITION AND EDUCTION: IMMEDIATE INFERENCES
Immediate Inference is a kind of inference by which the mind directly draws the implication of one proposition to arrive at a new proposition without the use of a medium or a third idea.
Types of Immediate Inference
1. Oppositional inference is a type of immediate inference that proceeds from the relationship between propositions with the same subject and predicate but different quantities and/or qualities. Oppositional inference is the process of determining the truth or falsity of an opposite statement from the truth or falsity of a given statement.
2. Eduction or Logical Equivalence is the process of reformulating one proposition to another kind without changing the meaning. . The resulting proposition may have different quantities, qualities, subjects and predicates but the meaning is essentially the same.
The Square of Oppositions
The square of opposition is a table in which the four opposing propositions are fitted to each other. By using this table one can easily see and determine the truth-value of opposing propositions. It is therefore, a useful tool in oppositional inference.
Types of Oppositions of Categorical Propositions
Categorical Propositions are statements of direct claim of relationship or non-relationship. They are either true or false. They are classified into four types, namely A, E, I, O propositions. In chapter 4, we have learned the following:
· Those propositions that are Universal/Singular in quantity and affirmative in quality are known as A Propositions
ex. All men are rational; Cathy is a student; Every citizen is free to own properties
· Those that are Universal/ Singular in quantity and negative in quality are known as E propositions.
Ex. No man is an island; All students are not teachers; Every dog is not a cat.
· Those that are particular in quantity and affirmative in quality are known as I propositions.
Ex. Some politicians are liars; Many countries are for peace; Filipinos are Christians.
· Those that are particular in quantity and negative in quality are known as O propositions.
Ex. Some civilians are not responsible people; Many are not in favor of war; Not all Filipinos are not rich.
These four types of categorical propositions are actually opposed to each other either as contradictories, contraries, sub-contraries, or sub-alternates.
- Contradictory Opposition exists between two statements of different qualities and quantities. Contradictory propositions cannot be both true and cannot be both false. If one is true then the other is false and if one is false the other is true. A & O Propositions and E & I Propositions are contradictories.
- Contrary Opposition exists between two statements of both universal quantities but of different qualities, that is, one is affirmative and the other is negative. Contrary propositions may be both false but only one can be false. So if one is true the other is false but if one is false the other is doubtful. . A and E propositions are contraries
- Sub-Contrary Opposition exists between two statements that are both Particular in quantities but of different qualities. Sub-Contrary propositions may be both true but only one can be false. So if one is true the other is doubtful but if one is false the other is true. I and O Propositions are sub-contraries.
- Sub- Alternate Opposition exists between two propositions that are of the same quality but different in quantities, that is, one is universal and the other is particular. Sub- alternates may be both true and maybe both false. If the Universal proposition is true the particular proposition is true and if the particular proposition is false the universal proposition is false but if the particular proposition is true the universal proposition is doubtful and if the universal proposition is false the particular proposition is doubtful. A & I propositions and E and O Propositions are sub-alternates.
If one is to apply these rules in analyzing the relationships that exist between and among the four types of categorical propositions, then one can immediately infer that:
· if A is true, then E is false, I is true, and O is false
· if A is false, then E is doubtful, I is doubtful and O is true
· If E is true then A is false, I is false and O is true.
· If E is false then A is doubtful, I is true and O is doubtful
· If I is true then A is doubtful, E is false and O is doubtful.
· If I is false then A is false, E is true and O is true.
· If O is true then A is false, E is doubtful and I is doubtful.
· If O is false then A is true, E is false, and I is true.
To have a visual illustration of these inferences, please remember the square of opposition. Recall that on the upper left hand corner is found the A proposition while on the upper right hand corner is found the E proposition. Recall further that on the lower left hand corner is found the I proposition while on the lower right hand corner is found the O proposition. If we now apply the rules of opposition, we will have the table below
Truth-Value Table of Opposing Propositions
Oppositions of Modal Propositions
Modal propositions are propositions that tell how or in what manner does the predicate affirms or denies the subject.
There are four kinds of modal propositions: Necessary, contingent, possible, and impossible.
1. Necessary. Necessary relationship is not possible to deny because it
cannot be otherwise.
Examples: A square has four sides
The square root of four is two
A surgeon is a doctor
2. Contingent. When the relationship expressed by the proposition is
one that is but not necessarily so.
Example: The square is blue
The students are wearing uniforms.
The principal is a Doctor of Philosophy
3. Possible. The relationship in this proposition signify something that is not, but may eventually be.
Example: The student may be the head nurse by 2010.
You may be successful someday.
It’s possible to have women priest in the Philippines.
4. Impossible. The relationship in this proposition is something that
cannot be and will never be.
Example: A square cannot have six sides
A man can never be a woman.
It is impossible for a one year old baby to be a mother
The rules applied in these oppositions are the same as the rules that govern the oppositions of the four types of propositions, A- proposition is to necessary, I- proposition is to possible, E- proposition is to impossible and O- proposition is to contingent. It follows therefore that:
· If Necessary is true, then Possible is true, Impossible is false and Contingent is false
· If Necessary is false, then Possible is doubtful, Impossible is doubtful and contingent is true
· If Impossible is true then necessary is false, possible is false and contingent is true,
· If Impossible is false then Necessary is doubtful, possible is true and contingent is doubtful.
· If Possible is true then Necessary is doubtful, Impossible is false and contingent is doubtful.
· If possible is false then Necessary is false, Impossible is true and contingent is true
· If contingent is true then Necessary is false, Impossible is doubtful and possible is doubtful.
· If contingent is false then Necessary is true, Impossible is false and possible is true.
Oppositions of Circumstantially Quantified Propositions
Circumstantially quantified propositions are those propositions affected by some contingency of time, place, or circumstances. They are actually A, E, I, O propositions quantified by the use of always, under
all circumstances, in all instance, everywhere, by all means in the A propositions. The E propositions are quantified by never, nowhere, by no means, under no circumstance. The I propositions are quantified by occasionally, sometimes, somewhere, under some circumstances and the O propositions are quantified by sometimes not, not always, occasionally not. The rules applied in these oppositions are the same as the rules applied in the oppositions of the four types of propositions and that of modal propositions
Example: If it is necessary for the patient to be operated on in order to survive. Then the operation is possible but not contingent and impossible.
2. Eduction or Logical Equivalence is the process of restating the same meaning of proposition using different forms. The result of the inference is a new proposition but it has the same meaning and truth- value as the given.
Types of Eduction or Logical Equivalence
1. Conversion is the process of interchanging the position of the subject and predicate terms without extending any term and without changing the quality of the proposition. The original proposition is reformulated by interchanging the subject and the predicate while maintaining the quantities of the terms. The original proposition is called the convertend while the resulting proposition is called the converse.
Ex. All computers are expensive =Some expensive things are computers.
A to I. Partial Conversion
Man is a rational Animal =A rational animal is a man. A to A full conversion
No terrorist is a peace lover= No peace lover is a terrorist. E to E conversion
Note : An O proposition cannot be validly converted because it will extend a term from a particular to a universal extension or quantity
Practice your conversion skill:
1. No man is an Island =_____________________________________
2. Some patients are restless=_________________________________
3. All operating rooms are hygienic=___________________________
2. Obversion is the process of expressing an affirmative proposition in a negative manner or a negative proposition in the affirmative manner. It involves the changing of the copula and contradicting the original predicate. It is the process in which a new proposition is formulated by changing the quality of the original proposition and contradicting the original predicate.
Ex.: All trees are useful = All trees are not non –useful. A to E obversion
Some actions are not good = Some actions are bad. O to I obversion
Practice your obversion skill
1. All babies are special =________________________________
2. Some children are malnourish =_________________________
3. All rooms are not occupied =___________________________
3. Contraposition is the process of interchanging and contradicting the original subject and predicate terms. It obverts, then converts then obverts the original proposition. It is the process of formulating a new proposition by getting the obverse of the converse of the obverse. The original subject and predicate are contradicted and interchanged but the quality is retained.
Contraposition Process
Contraponend = All nurses are health providers
Step 1 : Obvert = All nurses are not non-health providers
Step 2 : Convert = All non-health providers are not nurses = Partial Contraposit
Step 3 : Obvert = All non-health providers are non-nurses= Full Contraposit
Ex. All Nurses are role models = All non- role models are non-nurses
Every virus is not a bacterium = Some non-bacteria are not non-virus.
Practice your contraposition skill
1. Many information were not validated=____________________________
2. Any bleeding is a symptom=_____________________________________
3. No late comers were admitted=__________________________________
4. Inversion is the process of changing the quantity of a proposition and contradicting the original subject and predicate terms. It proceeds by obverting and converting the contraposit of a universal proposition. It is the process of changing the quantity of the original proposition and contradicting both subject and predicate and retaining the quality of the original proposition.
Invertend = No X are Y = All X are Y
Step 1: Obvert =E Propositions start with step 2 = All X are not non-Y
Step 2: Convert= No Y is X or All Y are not X = All non-Y are not X
Step 3: Obvert = All Y are non-X = All non-Y are non-X
Step 4: Convert= Some non-X are Y =Partial = Some non-X are non-Y =Full
Step 5: Obvert = Some non-X are not non-Y =Full = Some non-X are not Y
=Partial
Ex. No vice is virtue = Some non-vices are non-virtues. E to O Inversion
All knights are brave = Some non- knights are non-brave. A to I inversion
Practice your inversion skill
1. No nurse is a liar=__________________________________________________
2. Any hospital administrator is a management expert________________________________________________________
3. All dengue victims are to be admitted immediately_________________________________________________________
Through logical equivalence or eduction one may express a proposition in different forms without significantly altering its meaning. An A-proposition may be expressed as an E or an I or an O proposition. Great care, however, should be exercised when logical equivalence is combined with opposition for the meaning may not be that so evident. The table above may be of help to distinguish the truth value of any statement which is the logical equivalent of the opposite of a given statement
Example: If the given statement “ All nurses are registered professionals” is true then;
1. “Some registered professionals are nurses” is likewise true because it is the Converse of the original statement- a kind of logical equivalence
2. “All registered professionals are nurses” is doubtful because it is the subaltern of the converse of the original statement- a combination of opposition and logical equivalence
3. “All nurses are not unregistered professionals” is true because it is the Obverse of the original statement- a kind of logical equivalence.
4. “All nurses are unregistered” is false because it is the contrary of the obverse, of the original statement- a combination of opposition and logical equivalence
Another way of using the combination of opposition and logical equivalence is when one is asked to give a statement, which is logically equivalent of the opposite of any given statement.
Example:
1. Give the obverse of the sub-contrary of the contradictory of “All technicians are trainees.”
To answer this, one begins with the given statement and proceeds backward, thus;
1. The given statement is an A Proposition
2. The contradictory of A is an O-Proposition- Some technicians are not trainees
3. The sub-contrary of O is an I-Proposition- Some technicians are trainees
4. The obverse of I is an O- Some technicians are not non-trainees
Legend:
Prop= Type of Categorical Proposition Con = Converse Obv = Obverse
PC = Partial Contraposit FC = Full Contraposit P I = Partial Inverse
FI = Full Inverse
Thus if it is true that all technicians are trainees then some technicians are trainees will likewise be true, because it is the sub-altern of the original statement. And the obverse of the sub altern, some technicians are not non-trainees, will likewise be true because it is simply the logical equivalent of the sub-altern of the original statement.
CATEGORICAL AND HYPOTHETICAL SYLLOGISMS: MEDIATE INFERENCES
a. Categorical Syllogism
A Categorical Syllogism is a mediate inference that is made up of categorical propositions. The two propositions, called premises, are related through a middle term. These result into a third proposition, called conclusion, which flows necessarily from such relationship.
Basic Components of a Categorical Proposition
1. The Three Categorical Propositions
1. Major Premise-the proposition of greater extension that is made up of the major term and the middle term. It is usually written as the first premise.
2. Minor Premise- The proposition of lesser extension that is made up of the minor term and the middle term. It is usually written as the second premise.
3. Conclusion- The proposition that flowed from the relationship of the two premises. This contains the inferred truth, which is a necessary implication of the two premises. It is made up of the minor and the major term and is usually written last.
Example:
Major Premise: All rational animals are mortal;
Minor Premise: But all men are rational animals;
Conclusion: Therefore, all men are mortal.
2. The Three Terms
1. The Major Term- is one of the terms found in the major premise and the predicate of the conclusion.
2. The Minor Term- is one of the terms found in the minor premise and the subject of the conclusion.
3. The Middle Term- is found in both major and minor premises but not in the conclusion. It is the term that mediates and connects the two premises. The common idea that allows the truth to flow from the premises to the conclusion.
Example:
All health workers are professionals;
But, some public servants are health workers;
Therefore, some public servants are professionals.
Major Term: professionals
Minor Term: public servant
Middle Term: health workers
Rules on the Validity of Categorical Syllogism
1. There must be three terms only; the major term, the minor term, and the middle term.
2. Each of the terms must be used twice univocally.
3. The middle term must be used in both premises and not in the conclusion.
4. The middle term must be universal at least once.
5. The Major and the minor terms may only be universal in the conclusion if they are universal in the premises
6. Two affirmative proposition results into an affirmative conclusion.
7. Two negative premises cannot have a valid conclusion
8. One affirmative and one negative premise results into a negative conclusion.
9. The premises must be universal at least once
10. One universal and one particular premise results into a particular conclusion.
11. Two particular premises cannot have a valid conclusion.
12. Never claim something in the conclusion something that was not claimed and proven in the premises
Valid Moods of Categorical Syllogisms
Figure 1 : Barbara, Celarent, Darii, Ferio or AAA,EAE,AII,EIO.
Figure 2: Cesare, Camestres, Festino, Baroco or EAE, AEE, EIO, AOO
Figure 3: Darapti, Disamis, Datisi, Felapton, Bocardo, Ferison or AAI, IAI, AII, EAO, OAO, EIO
Figure 4: Bramantip, Camenes, Dimaris, Fesapo, Fresison or AAI, AEE, IAI, EAO, EIO
(Note: The 1st vowel refers to the major premise, the 2nd to the minor premise and the 3rd to the conclusion)
Examples of the valid moods
Figure 1: Subject: Predicate Middle Terms
1. BARBARA:
A- All X are Y; A- All spiritual are immortal;
A- But all W are X; A- but all human souls are spiritual;
A- therefore, all W are Y A- thus, all human souls are immortal
2. CELARENT
E- All X are not Y E- All spiritual are not immortal
A- but all W are X A- but all human souls are spiritual;
E- All W are not Y E- Thus, all human souls are not immortal
3. DARII
A- All X are Y A- All spiritual are immortal;
I- but some W are X I- but some human souls are spiritual;
I- thus, some W are Y I- thus, some human souls are immortal
4. FERIO
E- No X is Y; E- No spiritual being is immortal;
I- but some W is X; I- but some human souls are spiritual;
O- thus, some W are Y O- thus, some human souls are immortal
Figure II: Predicate: Predicate Middle Terms
1. CESARE
E- All Y are not X E- Every Manual is not a newspaper
A- but all W are X A- but all Bulletin Today are newspapers
E- thus, All W are not Y E-Thus, all Bulletin today are not manuals.
2. CAMESTRES
A- All Y are X A- All manuals are newspapers
E- but no W is an X E- but no Bulletin Today is a newspaper
E- thus, no W is an Y E- therefore, no Bulletin Today is a manual
3. FESTINO
E- All Y are not X E- All manuals are not newspapers
I- but some W are X I- but some Bulletin Today are newspapers
O-thus, some W are Y O- thus, some Bulletin Today are not manuals
4. BAROCO
A- All Y are X A- All manuals are newspapers
O-but some W are not X O- but some Bulletin Today are not newspapers
O- thus some W are not Y O- thus, some Bulletin Today are not manuals
Figure III: Subject: Subject Middle Terms
1. DARAPTI
A- All X are Y A- All transparencies are plastic
A-but all X are W A-but all transparencies are instructional materials
I- thus, some W are Y I- thus, some instructional materials are plastic
2. DISAMIS
I- Some X are Y I- Some transparencies are plastic
A- but all X are W A- but all transparencies are instructional materials
I- thus, some W are Y I- thus, some instructional materials are plastic
3. DATISI
A- All X are Y A- All transparencies are plastic
I- but some X are W I-but some transparencies are instructional materials
I- thus, some W are X I- thus, some instructional materials are plastic
4. FELAPTON
E- No X is Y E- No transparencies are plastic
A- but all X are W A- but all transparencies are instructional materials
O- thus, some W are not Y O- thus, some instructional materials are not plastic
5. BOCARDO
O- Some X are not Y O- Some transparencies are not plastic
A- but all X are W A- but all transparencies are instructional materials
O- thus, some W are not Y O- thus, some instructional materials are not plastic.
6. FERISON
E- All X are not Y E- All transparencies are not plastic
I- but some X are W I- but some transparencies are instructional materials
O- thus, some W are not Y O- thus, some instructional materials are not plastic
Figure IV: Predicate: Subject Middle Term
1. BRAMANTIP
A- All Y are X A- Education is an investment of human capital
A- but all X are W A- but all investments of human capital are precious
I- thus, some W are Y I- thus some precious things are education
2. CAMENES
A- All Y are X A- Education is an investment of human capital
E- but no X is W E- but no investment of human capital is precious
E- thus, no W is Y E- thus, no precious thing is education
3. DIMARIS
I- Some Y are X I- Some Education are investment of human capital
A- but all X are W A- but all investments of human capital are precious
I- thus some W are Y I- thus, some precious things are education
4. FESAPO
E- No Y is X E- No education is an investment of human capital
A- but all X are W A- but all investments of human capital are precious
O-thus, some W are not Y O- thus, some precious things are not education
5. FRESISON
E- No Y is X E- No education is an investment of human capital
I- but some X are W I- but some investments of human capital are precious
O- thus, some W are not Y O- thus some precious things are not education.
a. Hypothetical Syllogism
Rules for the Validity of Mixed Conditional Syllogism
1. There must be sequence. The consequent must necessarily flow from the antecedent
2. Posit or assert the truth of the antecedent in the minor, posit or assert the truth of the consequent in the conclusion.
3. Sublate or deny the truth of the consequent in the minor premise, sublate or deny the truth of the antecedent in the conclusion.
4. Posit or sublate completely, never partially.
5. It is invalid to sublate the antecedent in the minor premise.
6. It is invalid to posit the consequent in the minor premise
(Note: Mutually exclusive alternatives or sequential correlatives are exempted from rule 5 and 6)
Rules for the Validity of Disjunctive Syllogism
1. If the disjunction is a strict disjunction or contradictory disjunction:
a. If the Disjunction is Posit one alternative in the minor premise then sublate the other in the conclusion
b. Sublate one alternative in the minor premise then posit the other in the conclusion.
2. contrary or a third alternative is implied:
a. Posit one alternative in the minor premise then sublate the other or the rest in the conclusion.
b. It is invalid to sublate one alternative in the minor premise then posit another in the conclusion.
3. If the disjunction is sub-contrary or both alternatives could be true:
a. Sublate one alternative in the minor premise then posit the other in the conclusion.
b. It is invalid to posit one alternative in the minor premise then sublate the other in the conclusion.
Rules for the Validity of Conjunctive Syllogism
1. Posit one alternative in the minor premise then sublate the other in the conclusion.
2. It is invalid to sublate one alternative in the minor premise then posit the other in the conclusion.
Refuting a Syllogism and Making a Counter-Argument using Figures and Moods of Syllogisms
Suppose somebody argued that nurses lack the love of country because they tend to prefer working abroad upon completion of their studies, how then will you offer a counter argument that will show that nurses have the love of country. The following steps may be employed
1. Rewrite the argument into a syllogism of any of the valid moods in any figure
Example:
All who prefer working abroad are people who lack love of country
But nurses are people who prefer working abroad
Therefore, nurses are people who lack love of country
The syllogism above is in the 1st figure with an AAA mood or a Barbara, thus it is valid.
2. Refute the argument by claiming that the syllogism is invalid (not applicable on this case because the sample syllogism is valid) or if it is valid, by showing that the major premise and/ or the minor premise/s is/are false and thus the conclusion is false or at least doubtful.
To do this, one must present evidence or show that there are people who prefer working abroad who still have love of country or that there are nurses who do not prefer working abroad.
Example 1:
All possible contributors to national development are not people who lack love of country
But All who prefer working abroad are possible contributors to national development
Therefore, All who prefer working abroad are not people who lack love of country
The conclusion of this syllogism is contrary to the original major premise and if this argument is sound then the major premise of the first argument must be false making the first argument unsound.
Example 2:
Fe, Martha and Andrew are not people who prefer working abroad
But Fe, Martha and Andrew are nurses
Therefore, Some nurses are not people who prefer working abroad
This syllogism is a valid 3rd figure EAO mood or a Felapton and its conclusion refutes the minor premise of the original argument.
3. Offer a counter-argument with a contrary or contradictory conclusion. Since the conclusion in the first argument above is an A-proposition, the counter argument that one may offer should have an O or E proposition for its conclusion.
Thus, one may advance the following syllogisms:
All who prefer working abroad are not people who lack love of country
But all nurses are people who prefer working abroad
Therefore, all nurses are not people who lack love of country
The syllogism above is a valid 1st figure EAE mood, or a Celarent and its conclusion is the contrary of the conclusion of the first argument
All who lack love of country are people who prefer working abroad
But some nurses are not people who prefer working abroad
Therefore, some nurses are not people who lack love of country
The syllogism above is a valid 3rd figure OAO mood, or a Bocardo and its conclusion is the contradictory of the first argument
All who lack love of country are not people who prefer working abroad
But some nurses are people who prefer working abroad
Therefore, Some nurses are not people who lack love of country
The syllogism above is a valid 4th figure EIO mood or a Fresison and its conclusion is the contradictory of the first argument
4. Show that the particular sub-alternate conclusion of the original universal conclusion is false. Thus if the argument is an AAA or Barbara, show that Darii is false. If one is able to do this, then he has proven that the conclusion of Barbara is likewise false using oppositional inference.
The conclusion of the first argument is “ All nurses are people who lack love of country” and its sub- alternate is “some nurses are people who lack love of country”. This can be shown false by offering a valid argument that has an E- conclusion that is “ All nurses are not people who lack love of country”
All people who lack love of country are not contributors to national development
But all nurses are contributors to national development
Therefore, all nurses are not people who lack love of country
The syllogism above is a valid 2nd figure EAE mood or a Cesare and if the major and the minor premises are true then the conclusion will be true and if this conclusion is true its contradictory “some nurses are people who lack love of country” will be false. Now, through oppositional inference, the conclusion “All nurses are people who lack love of country” can be inferred to be also false.
