Immediate Inference - Eduction

is a type of immediate inference in which we deduce the truth of other propositions with a different structure from a given proposition.

Rule:  Particular terms cannot be turned into universal. What is true to some may not be true to all.

For example:

                All men are mortals.

From this proposition, I can deduce an apparently equivalent proposition: Some mortals are men, but NOT all mortal are men.

Remember that we do not give additional knowledge when we deduce propositions from a given proposition when we use eduction. In fact, all other new propositions deduced from a given proposition are not something new. In meaning, they are the same with the original proposition.

Kinds of Eduction:

1.       Conversion – it is done by simply interchanging the subject and the predicate. We call the original proposition convertend, and the new proposition converse.

Examples:

Convertend                                                                        Converse

All men are mortals.                                                       Some mortals are men.

Some politicians are liars.                                             Some liars are not politicians.

No stones are flowers                                                   No flowers are stones.

Some animals are not mammals.                              no converse

2.       Obversion – it is done by changing the quality of the proposition (from affirmative to negative, from negative to affirmative) and replacing the predicate with its contradictory. We call the original proposition obvertend, and the new proposition obverse.

Examples:

Obvertend                                                                          Obverse

All men are mortals.                                                       No men are non-mortals.

Some politicians are liars.                                             Some politicians are not non-liars.

No stones are flowers.                                                  All stones are non-flowers.

Some animals are not mammals.                              Some animals are non-mammals.

3.       Contraposition 1 – It is done by doing obversion, and then conversion. We call the original proposition contraposend  and the new proposition contraposit 1.

Examples:

Contraposend                                                                   Contraposit 1

All men are mortals.                                                       No non-men are mortals.

Some politicians are liars.                                             no contraposend 1

No stones are flowers.                                                  Some non-flowers are stones.

Some animals are not mammals.                              Some non-mammals are animals.

4.       Contraposition 2 – it is done by doing obversion, then conversion, then obversion again. We call the original proposition contraposend and the new proposition contraposit 2.

Examples:

Contraposend                                                                   Contraposit 2

All men are mortals.                                                       All non-men are non-mortals.

Some politicians are liars.                                             no contraposend 2

No stones are flowers.                                                  Some non-flowers are not non-stones.

Some animals are not mammals.                              Some non-mammals are not non-animals.

Immediate Inference - Oppositional Inference

A.      Oppositional Inference – it is a type of immediate inference in which we deduce the truth value of another proposition (can be A, E, I, O) from a given truth value of a proposition of the same structure.

Example:

                                “All men are mortals” is true.

                                Therefore, “No men are mortals” is _______.

                                The answer is false.

Types of Oppositional Inference:

1.       Contrary – it is the opposition between A and E propositions.

                        Rule: If one is true, the other is false. If one is false, the other is unknown.

Example:

        If one is true:

                        (A) All men are mortals. – True                  (E) No men are angels. – True

                        (E) No men are mortals. – False                 (A) All men are angels. – False

        If one is false:

                        (A) All men are angels. – False                   (E) No men are mortals. – False

                        (E) No men are angels. – Unknown         (A) All men are angels. – Unknown

Explanation: If one is false, we cannot immediately infer that the other is true because it might be the case that if one is false the other might also be false. Hence, the better answer is unknown.

2.       Sub-contrary – it is the opposition between I and O propositions.

                        Rule: If one is true, the other is Unknown. If one is false, the other is true.

Example:

        If one is true:

                        (I) Some animals are mammals. – True                  

                        (O) Some animals are not mammals. – Unknown

                        (O) Some animals are not mammals. – True

                        (I) Some animals are mammals. – Unknown

Explanation: If one is true, we cannot immediately infer that the other is false since it is possible that the other could also be true; hence, Unknown.

        If one is true:

                        (I) Some animals are flowers. – False                     

                        (O) Some animals are not flowers. – True

                        (O) Some mammals are not animals. – False

                        (I) Some mammals are animals. – True

3.       Sub-altern – it is the opposition between A & I propositions and E & O propositions.

Rule:      If the universal proposition is true, the particular proposition is true. If the universal proposition is false, the particular proposition is Unknown.

                If the particular proposition is false, the universal proposition is false. If the particular proposition is true, the universal proposition is Unknown.

Example:

        If the universal is true:

                        (A) All men are mortals. – True                  (E) No men are angels. – True

                        (I) Some men are mortals. – True             (O) Some men are not angels. – True

If the universal is false:

                (A) All men are angels. – False                   (E) No men are mortals. – False

                (I) Some men are angels – Unknown      (O) Some men are not mortals. Unknown

Explanation: If the universal is false, we cannot immediately infer that the particular is also false since it is possible that the particular can be true.

If the particular is true:

                (I) Some animals are mammals. – True

                (A) All animals are mammals. – Unknown

                (O) Some animals are not mammals. – True

                (E) No animals are not mammals. – Unknown

Explanation: If the particular is false, it is possible that the universal can be true or can be false; hence, Unknown.

If the particular is false:

                (I) Some animals are mammals. – False

                (A) All animals are mammals. – False

                (O) Some animals are not mammals. – False

                (E) No animals are not mammals. – False

4.       Contradictory – the opposition between A & O propositions and E & I propositions.

Rule: If one is true, the other is false. If one is false, the other is true.

Examples:

 (A) All men are mortals. – True | False

(O) Some men are not mortals. – False | True

(O) Some men are not mortals. – False | True

(A) All men are mortals. – True | False

(E) No men are angels. – True | False

(I) Some men are angels. – False | True

(I) Some men are angels. – False | True

(E) No men are angels. – True | False

INFERENCE

Inference – it is a process by which the mind proceeds from one proposition to another proposition seen to be implied in the former. It is the fundamental element in an argument. Without inference, there can never be an argument.

Example:

                Givens                                                                                                  Therefore:

The cloud is dark.                                                             It will rain.

All people have dignity.                                                 That poor man has dignity.

“All people are mortals” is true.                                 “Some people are not mortals” is false.

Some politicians are corrupt.                                      Some corrupt people are politicians.

Two Kinds of Inference

1.       Mediate Inference – an inference which requires a mediating proposition.

Example:

(a)    All people are mortals.

(b)   Socrates is a person.

(c)    Therefore, Socrates is mortal.

It is a mediate inference because we cannot arrive from (a) to (c) without going through (b).

Other example:

(a)    Some students are rich.

(b)   She is a student.

(c)    Therefore, she might be rich.

2.       Immediate Inference – a kind of inference which does not require a mediating proposition.

Example:

(a)    No people are immortals.

(b)   Therefore, all people are mortals.

(a)    All objects occupy space and have mass.

(b)   Therefore, there are no objects that do not occupy space and have no mass.

There is no need for a mediating proposition here. You proceed from (a) to (b) without going through any proposition.

Caution: There are inferences which seem to be an immediate inference but will be found to be mediate inferences upon careful analysis.

Example:

(a)    The cloud is dark.

(b)   Therefore, it will rain.

It seems that there is no need for us to go through a mediating proposition to arrive at proposition (b). However, if we analyze it carefully we will discover that proposition (a) is not enough in order for us to arrive at proposition (b). This entails that there is a hidden proposition which mediates (a) and (b). That mediating proposition is: “Whenever the cloud is dark, it will rain.”

Other examples:

(a)    Today is February 14.

(b)   Therefore, it is Valentine’s Day.

(a)    Students must be diligent in their students.

(b)   Therefore, you must be diligent.

Fallacies of Ambiguity

-          These are fallacies that occur because of the ambiguous or unclear use of language.

Types of Fallacies of Ambiguity

1.       Equivocation

2.       Accent

3.       Amphiboly

4.       Division

5.       Composition

6.       Hooded Man

1.       Equivocation

Equivocation is the illegitimate switching of the meaning of a term during the reasoning.

Examples:

Brad is a nobody, but since nobody is perfect, Brad must be perfect, too. (The word “nobody” has equivocal meanings.)

Don’t fall in love because everything that falls breaks. (“Fall” is equivocal; one is falling in love, while the other one is a literal falling of objects).

2.       Accent

The accent fallacy is a fallacy of ambiguity due to the different ways a word is emphasized or accented.

Example:          

A member of Congress is asked by a reporter if she is in favor of the President’s new missile defense system, and she responds, “I’m in favor of a missile defense system that effectively defends America.”

With an emphasis on the word “favor,” her response is likely to favor the President’s missile defense system. With an emphasis, instead, on the words “effectively defends,” her remark is likely to be against the President’s missile defense system.

“You shall not bear false witnesses against your neighbor.”

The intended meaning of this passage is that I should not speak ill against my fellow human being. Fallacy of accent is committed when I interpret this passage differently by emphasizing or accenting one of its words. For example, if the words “false witnesses” is accented, then I mean that it is alright to bear witnesses against my neighbor as long as it is true. If I emphasized, “neighbor”, then I might understand the passage as saying that it is alright to speak ill against someone as long as he is not my neighbor.

3.       Amphiboly

                This is an error due to taking a grammatically ambiguous phrase in two different ways during the reasoning.

Examples:

“Lost and found: an umbrella by an old lady with two broken ribs.” How poor this old lady was; she has two broken ribs!

If Croesus wages a war against the Persians, he will destroy a mighty kingdom. (Whose mighty kingdom will Croesus destroy: the Persians’ or his own?)

4.       Division

We commit the fallacy of division when we take separately what must be taken as a group.

Examples:

                “Askalz is a good soccer team. Therefore, each of its members is a good soccer player.”

                “The choir signs excellently. It must follow that each member of the choir sings well.”

5.       Composition

                The opposite of division, this fallacy occurs when we take as a unit or group what must be taken separately.

Examples:

“Each member of the team is a good player. Therefore, the team is a good team.”

“Each human cell is very lightweight, so a human being composed of cells is also very lightweight.”

6.       Hooded Man

This is an error in reasoning due to confusing the knowing of a thing with the knowing of it under all its various names or descriptions.

Examples:

“You claim to know Socrates, but you must be lying. You admitted you didn’t know the hooded man over there in the corner, but the hooded man is Socrates.”

“I thought you knew your father, yet you could not even recognize that man who was wearing a coat over there, and that was your father.”

Fallacies of Defective Induction

These are arguments whose premise seems to provide ground for the conclusion but proven to be insufficient upon analysis.

1.       Ad Ignorantiam or Appeal to Ignorance

2.       Ad Verecundiam or Appeal to Inappropriate Authority

3.       False Cause

4.       Converse Accident or Hasty Generalization

5.       Anecdotal Evidence

6.       Faulty Comparison

7.       Far-fetched Hypothesis

8.       Confusing an explanation with an excuse

9.       Guilt by Association

1.       Argumentum ad Ignorantiam or Appeal to Ignorance

It is arguing that a belief is false because it is not proven to be true, or true because it is not proven to be false.

Examples:

                                                “Nobody has ever proved to me that there is God. So God does not exist.”

                                                “The suspect is guilty because there is no proof that he is not guilty.”

2.       Argumentum ad Verecundiam or Appeal to Inappropriate Authority

This fallacy comes when one argues for a claim on the basis of someone who has no knowledge about the matter at issue.

Examples:

“John Lloyd, a notable actor, said the Biogesic is safe and effective. So, Biogesic is indeed safe and effective.”

“My genius professor in Math said that Alexander the Great was gay. No wonder why most historians do not include this fact in their books.”

3.       False Cause

This is an error when one attributes a false cause to a phenomenon.

Examples:

                                                “I passed the interview because I wore a red t-shirt.”

“The Philippines has a rapid increase in GDP because many buildings are being erected.”

4.       Converse Accident or Hasty Generalization

This fallacy consists in making a generalization on basis of few instances of a case in question. Stereotyping is also a form of hasty generalization.

Examples:

“We have passed through two villages already, and people there were not nice. Therefore, all people in the villages of this province are not nice to strangers.”

“Indigenous people from hill top tribes are illiterate. There were indigenous people studying here and I had to send them back to grade school because they do not know how to read and right.”

5.       Anecdotal Evidence

This is a fallacious generalizing on the basis of some story that provides an inadequate sample. If you discount evidence arrived at by systematic search or by testing in favor of a few firsthand stories, then your reasoning contains the fallacy of overemphasizing anecdotal evidence.

Examples:

“They say smoking is dangerous to our health. My father is a chain smoker and he has never been sick in all his life. So, I don’t believe that smoking is dangerous to our health.”

“I don’t think education can bring us success. There are billionaires who are not even college graduates like Bill Gates and Henry Sy.”

6.       Faulty Comparison

Occurs when you try to make a point about something by comparison, and you do so by comparing it with the wrong thing.

Examples:

“We gave half of the patients pain reliever and paracetamol to the other half. After one hour we observed that those whom we have given pain reliever are more energized than anyone else. Hence, we concluded that pain reliever is more effective than paracetamol.”

Wearing Addidas shoes is more comfortable than wearing Levi’s jeans.

7.       Far-fetched Hypothesis

This is the fallacy of offering a bizarre (far-fetched) hypothesis as the correct explanation without first ruling out more mundane explanations.

Example:

“Look at that mutilated cow in the field, and see that flattened grass. Aliens must have landed in a flying saucer and savaged the cow to learn more about the beings on our planet.”

8.       Confusing an explanation with an excuse

It is treating someone’s explanation of a fact as if it were a justification of the fact. Explaining a crime should not be confused with excusing the crime, but it too often is.

Examples:

“She happened to kill her husband out of her hatred of him. She has been a battered wife for almost ten years. So, she is not guilty.”

“I cheated in the exam because I had no other choice. I was sick the night before the exam so I could not study, and I realized that if I would not pass, then my scholarship could be withdrawn.” [Explains a student who was caught cheating]

9.        Guilt by Association

Guilt by association is a version of the ad hominem fallacy in which a person is said to be guilty of error because of the group he or she associates with. The fallacy occurs when we unfairly try to change the issue to be about the speaker’s circumstances rather than about the speaker’s actual argument.

Examples:

“Senator Cruz is pro-RH Law because he is a friend of those senators who authored the RH Law.”

“He is a thief because he comes from the family of thieves.”

Fallacies of Presumption

These are arguments whose conclusion is supported by false or unproved assumptions.

1.       Accident

2.       Complex Question

3.       Petition Principii or Begging the Question

4.       Ad Consequentiam or Appeal to Consequence

5.       Ad Hoc Rescue

6.       Avoiding the Issue

7.       Red Herring

8.       Excluded Middle or Black/White

9.       Selective Attention

10.   Gambler’s

11.   Inconsistency

12.   Slippery Slope

13.   Straw Man

1.       Accident

                It is when we reason with a generalization as if it has no exemption.

Examples:

“People should keep their promises, right? I loaned Dwayne my knife, and he said he’d return it. Now he is refusing to give it back, but I need it right now to slash up my neighbour who disrespected me.”

“The pull of gravity from this object is 23 kg. So it follows that at the top of Mt. Everest, it is still 23 kg.”

2.       Complex Question

You use this fallacy when you frame a question so that some controversial assumption is made by the wording of the question.

Examples:

“Did you use a knife in killing that man?” [Man: “No”] “Aha! So you did kill him!”

“[Reporter's question] Mr. President: Are you going to continue your policy of wasting taxpayer’s money on missile defense?”

3.       Petitio Principii or Begging the Question

Also known as circular reasoning, this type of fallacy argues by drawing out conclusion that is the same with the premise although expressed differently.

Examples:

“We have the freedom of speech because we have the freedom to express our own opinions.”

“Murder is an immoral act because it is wrong.”

4.       Argumentum ad Consequentiam or Appeal to Consequence

It is arguing that a belief is false because it implies something you’d rather not believe.

Examples:

I don’t believe in your DNA test result. He is my son so we must have the same genes. (The father would not believe since it would imply that the child is not his son.)

Jose Rizal cannot have concubines. He is our national hero.

5.       Ad Hoc Rescue

This fallacy is committed when one tries to rescue a belief by denying a contrary evidence or examples that would falsify it.

Examples:

“If you take Vitamin C every day, you will never get a cold.” [Friend: “But I tried it last year for several months and I still got a cold.”] “Well, I’ll bet you bought some bad tablets.”

“Filipinos are hospitable. If you met a Filipino who is not hospitable, then he is not a true Filipino.”

6.       Avoiding the Issue

It is when one who is supposed to address an issue changed the topic that is not relevant to the issue under consideration assuming that by doing so one can easily dismiss the issue that has to be addressed.

Examples:

When a person is being asked about the status of his marriage but then answered by talking about the schooling of his children, the status of his job, and his relationship to his parents.

“My wife is not a criminal. You see, she’s a good gardener and she loves nature.”

7.       Excluded Middle or Black/White

                You commit this fallacy when you unfairly limit someone to only two choices.

Examples:

“Well, it’s time for a decision. Will you contribute $10 to our environmental fund, or are you on the side of environmental destruction?”

“Either you join our group or you are against us.”

8.       Selective Attention

It is the tendency to look only for evidence in favor of one’s controversial hypothesis and not to look for disconfirming evidence, or to pay insufficient attention to it.

Example:

She loves me, and there are so many ways that she has shown it. When we signed the divorce papers in her lawyer’s office, she wore my favorite color. When she slapped me at the bar and called me a “handsome pig,” she used the word “handsome” when she didn’t have to. When I called her and she said never to call her again, she first asked me how I was doing and whether my life had changed. When I suggested that we should have children in order to keep our marriage together, she laughed. If she can laugh with me, if she wants to know how I am doing and whether my life has changed, and if she calls me “handsome” and wears my favorite color on special occasions, then I know she really loves me.

9.       Gambler’s

Gambler’s fallacy occurs when the gambler falsely assumes that the history of outcomes will affect future outcomes.

Examples:

“I know this is a fair coin, but it has come up heads five times in a row now, so tails is due on the next toss.”

“There was no raid for three months now. So, it’s probably unsafe to continue our drug production next month since there would probably be raid.”

10.   Inconsistency

This fallacy occurs when we accept an inconsistent set of claims, that is, when we accept a claim that logically conflicts with other claims we hold.

Examples:

“I’m not racist. Some of my best friends are white. But I just don’t think that white women love their babies as much as our women do.”

“I agree that everything has a price. But I believe that life is priceless.”

11.   Slippery Slope

This fallacy occurs when one claims that a certain action will lead to an event or chain of events which we do not want.

Examples:

“Do you drink coffee? I am pretty sure that caffeine will not be strong enough, then you will take something stronger, maybe a diet pill. Then, something even stronger. Eventually, you will be doing cocaine. Then you will be a crack addict! So don’t drink that coffee.”

“If we let homosexuals marry each other, then sooner or later, we would also allow people to marry their pets.”

12.   Straw Man

Your reasoning contains the straw man fallacy whenever you attribute an easily refuted position to your opponent, one that the opponent wouldn’t endorse, and then proceed to attack the easily refuted position (the straw man) believing you have undermined the opponent’s actual position.

Examples:

You claim that we must allow same-sex marriage. Therefore, you also claim that marriage is never sacred. If that is your claim, then why should partners (even same-sex partners) be married at all? [The straw man here is you claim that the opponents said that marriage is not sacred even though they did not].

Ladies and gentlemen of the jury, our worthy opponents here believes that capital punishment or death sentence will not help decrease the number of crime incidents in this country. And for that claim they have led themselves into a dangerous pit hole: the belief that every form of punishment is ineffective. As we all know, that is a mistaken belief. Hence, we won this case. [Straw man: your claim that the opponents believe that every form of punishment in ineffective].