Tools of Apologetics 1.17.3
Logic and Fallacies of Logic
Formal Fallacies (Fallacies Of Form)
Formal fallacies, or errors of form, are another type within the fallacies of deduction and occur when the laws of logical sentence construction are overlooked. Some of them are:
1-The Fallacy of Four Terms: In deductive logic one starts with the given premises and arrives at conclusions or logical deductions. In the simplest type of deduction, one starts with two related premises and arrives at a single conclusion. This combination is usually called a syllogism. For example.
All men are sinners
I am a man
———————————–
Therefore I am a sinner
The above set of three statements is a syllogism and in such simple cases the premises are called the major premises and the minor premises. These two premises contain three important constituents: major term, minor term, and the middle term. These three terms and their relationship must conform to certain rules of logic. Every violation of these rules will give rise to errors of logic.
The fallacy of four term occurs when four terms occur instead of the permitted three. For example, look at the following premises:
All men are sinners.
All angels are spirits.
The above statements contain four terms (men, sinners, angels, and spirits) but there is no common middle term between the premises. No valid deduction is possible from such syllogisms.
The example given above does not look very threatening because even a child can see that they cannot be used to obtain a valid deduction. However, there is a variation of this fallacy of four terms that is of great interest to apologists. In this fallacy, the syllogism apparently contains only three terms as demanded by logic. However, it really has four terms due to a catch: the middle term is used with two different meanings in the two premises. For example,
The judge looked into the case
Boxes are a type of case
———————————————–
The judge looked into a box
The conclusion is false because the middle term "case" has two different meanings here. In the first premise it means a court-case while in the second premise it refers to a container. Therefore even though there are only three terms here, it is actually a case of four-term fallacy because the middle term has been used with two different meanings. The same type of error can be seen when the major or minor terms have more than one meaning in the given context.
Examples related to the Bible abound, but the classic case is the story of the woman who refused to believe that the Israelites carried the "ark" [of the covenant] with them because nobody could carry "Noah’s ark" on their shoulders. The argument goes something like this:
Noah built a giant ark
The Israelites carried the ark through the wilderness
——————————————————————————
The Israelites carried Noah’s ark through the wilderness
Another common example is,
Evolution is change
We see change everywhere
———————————————
We see evolution everywhere
Even though change is seen everywhere, this is drastically different from the "change" that is demanded by proponents of evolution. Change in the universe always produces degeneration whereas evolution is supposed to be a self-building change. Thus the word "change" has been used in two different meanings here, giving rise to the fallacy of four terms in support of evolution.
2-Error of undistributed Middle: The middle-term is very important for arriving at deductions because it is this term that establishes the connection between the two given premises. For deduction to work properly, the given middle term must be common to both of the given premises in a meaningful way.
If the given middle-term does not satisfy this condition, then the first premise will have the first half of the middle term while the second premise will contain the second half of the middle term, and the deduction will turn out to be ridiculous. For example.
All dogs have four legs
All tables have four legs
——————————————-
Therefore all dogs are tables
The conclusion is not only false but also ridiculous. The correct way of presenting it would be:
All dogs have four legs
Rover is a dog
———————————–
Rover has four legs
and,
All tables have four legs
This is my table
9 of 40
————————————
My table has four legs
Further, a person who understands the rules of deduction and distribution of the middle term might make a move adventurous deduction and safely conclude; All dogs have four legs
All tables have four legs
All dogs have four legs
——————————————————————
Therefore all dogs and tables have four legs
3-Error due to illicit major: Not only should the middle term be distributed, the major term of the major premise should also be distributed properly. If the major term is stated in way that it cannot be connected or related to other terms, then the "distribution" is improper. For example.
Every cat is a mammal
A dog is not a cat
———————————-
A dog is not a mammal
Or,
Every man is a sinner
A woman is not a man
————————————-
A woman is not a sinner
The conclusion is obviously false. The proper way of stating the case can be illustrated in two stages:
Every man is a sinner.
Every woman is a sinner
—————————————————
Every man and woman is a sinner
and,
Every man and woman is a sinner
A woman is not a man
——————————————
A woman is not a man, but she is a sinner
4-Error due to illicit minor: Just as the major term should be distributed properly in the major premises, the minor term should also be properly distributed in the minor premises. The error produced by non distribution is seen in:
Every generous person is liked by the poor
Every generous person is meek
—————————————————————–
Every meek person is liked by the poor
The conclusion is obviously false because every meek person need not be generous. The correct way of stating the case would go something like this:
Every generous person is meek
Not every meek person is generous
——————————————————
Some meek persons are generous
and,
Every generous person is liked by the poor
Some meek persons are generous
—————————————————————–
Some meek persons are liked by the poor
The following are some spiritual examples of the same fallacy:
Every Christian is a child of God
Every Christian is an ambassador
——————————————————
Every ambassador is a child of God
and,
The Bible is the inspired Word of God
The Bible contains the speeches of men, animals, spirits and God
————————————————————————
The speeches of men, animals, spirits and God in the Bible are the
inspired Word of God
5-Fallacy arising out of two negative premises: Negative premises are a very important constituent of human language, and accurate deductions would not have been possible in many cases if they did not exist. However, negative premises in themselves may not always furnish sufficient information to make a meaningful deduction.
Therefore it is a rule of syllogism that it is not possible to arrive at a meaningful deduction from two negative premises. Whenever a deduction is made from such premises, the conclusion is bound to be erroneous. For example,
Anger is not good
Treachery is not anger
——————————————
Therefore treachery is good
Errors of this type are seen when people use negatives to attack statements of the Bible. A large number of objections brought against persons or events fall into this category. (These objections are usually based upon history/archaeology). The typical argument goes something like this,
1. (I do not believe what Luke has recorded).
2. Politarches mentioned in the book of Acts are not mentioned outside the Bible
—————————————————————————————–
"Politarches" is a term that does not exist outside the Bible
The first premise above is shown in brackets because even though it is the first and the major premise upon which the critics base their arguments, they do not mention it openly or explicitly. Acknowledgment of the existence of this premise only very rarely comes from them. But whether they acknowledge its existence or not, it is always there as a negative premise.
The second premise, as it is almost always presented, is also negative. Thus the deduction is bound to be erroneous. The difficulty is compounded by the critic’s assertion that the second premise is the major premise — which it is not. In fact the above objection has been raised against Dr Luke by many critics, The term "politarch" was not found in archaeological records for a very long time, but eventually it was found in some inscription, vindicating Dr Luke and illustrating the fallacy of arguing from two negative premises. Similar arguments have been raised about almost all historical narratives of the Bible. Once people understand the logical fallacy of such arguments, they can cut critics down to size.
6-Fallacy arising out of two particular premises: Premises can embrace a wide area or just a narrow field. However, to obtain a meaningful deduction it is essential that the given premises meet each other at some point. Therefore, according to the rules of syllogism, it is not possible to arrive at a valuable deduction from particular statements (that are so narrow that they do not meet each other). If this is done, the deduction will be false. For example,
Some radio broadcasts are false propaganda
Some radio broadcasts are educational
——————————————————————————
Some educational broadcasts are false propaganda
The deduction is wrong. For it to be right or valid, at least one of the premises must be universal. For example,
All radio broadcasts contain some error
Some radio broadcasts are educational
———————————————————–
All educational broadcasts contain some error
7-Fallacy arising out of denying the antecedent: Many hypothetical statements will have two parts: the antecedent (precedent) and the consequent. The fulfillment of the consequent depends upon the fulfillment of the precedent. In such cases, the precedent should not be denied because this would give rise to erroneous deduction. For example,
If it rains, she will not take a bath
It did not rain
————————————————-
She took a bath.
The conclusion cannot be sustained, and therefore the deduction is invalid. This is because the major premise (the precedent) does not indicate that she will surely take a bath in the absence of rain. For a valid deduction, another premise and another set of syllogism is necessary. This will be :
If it rains, she will not take a bath
It did not rain.
————————————————-
No deduction.
and,
If it does not rain, she will take a bath
It did not rain.
——————————————————–
She took a bath.
In this, and many other cases, the information usually given might not be sufficient for a valid deduction. The best course in such cases would be to seek additional information, not to jump to erroneous conclusions from improper premises.
8-Fallacy arising out of affirming the consequent: In hypothetical statements that have a precedent as well as a consequent, the consequent depends upon the precedent but not necessarily the other way round. Thus any deduction made when the consequence is denied is bound to be false. For example,
If it rains, she will not take a bath
She did not take a bath
————————————————-
It rained
The conclusion is invalid because it doesn’t say that not taking a bath would take place only if it rained. In fact she might decide not to take bath even when it is not raining. Thus not taking a bath does not guarantee that it did not rain. This one is frequently used against the Christian faith, and people easily fall in for it. For example,
If God exists, people should be happy (they should not suffer)
People are not happy (they suffer)
———————————————————————————————-
God does not exist
The consequent depends upon the precedent, but not necessarily the other way round.
9-Fallacies arising out of improper disjunction: Many premises contain more than one possibility. Sometimes only one of them is true while at other times both of them might be true. The way in which the premise is stated should make this clear. Many times people use disjunctive statements so that one possibility seems to exclude the other, even though both should have been given equal weight. If the premises themselves are wrong, the conclusion is bound to be wrong. For example,
Either the driver or the conductor is accountable to the owner
The conductor is accountable to the owner
———————————————————————————————
The driver is not accountable to the owner.
The conclusion is, in most cases, not valid because both the driver as well as the conductor of a bus are accountable to the owners. The error does not arise due to faulty deduction, but due to improperly stated premises. In this case "either" should be replaced by "both" to make the premises right.
10-Material Fallacies: Even if a given syllogism satisfies all the rules of logic, the conclusion will still be wrong if the premises contain error about the relevant subject matter. These are called material fallacies. For example,
Every dog has four legs
The tail shall also be counted as a leg
—————————————————————–
Therefore every dog has a total of five legs.
The above deduction necessarily follows from the given premises, yet it is wrong because the second premise is erroneous. Calling a tail a leg does not make it a leg! This kind of argument is very common among those who like to criticize the Bible. Many of them first establish a false premise, then obtain a false deduction and then use this deduction to attack the Bible. For example.
Paul could not have written the epistles
The computer doesn’t indicate that Paul wrote the Epistles
——————————————————————————————-
The computer indicates that Paul DID NOT write the Epistles.
The above argument has been raised by many, but it contains a material fallacy because neither of the premises has been established. A recent one, from a book attacking the morality of the Bible, has an argument that can be expressed as:
Cain got married
Eve was the only woman on earth at that time
———————————————————————
Cain married his own mother
The book then goes on to attack the Bible by claiming that it teaches incest.
Two other types of material fallacies are also common. They are called FALLACY OF PRESUMPTION and FALLACY OF EQUIVOCATION.
11. Fallacy Of Presumption: What is being deduced should necessarily follow from the components of the syllogism. If a deduction has been made that does not automatically follow from the premises, then the person making the deduction has presumed something additional as true also. This kind of a material fallacy is called Fallacy of Presumption.
Fallacies of presumption are widespread, and many times it is difficult to discover them because people who make these assumptions do not readily reveal them. Almost all who have campaigned against the Bible or the Christian faith has based a good number of their arguments upon presumptions that are not obvious or even visible to others. Also, many of them have successfully played upon widespread presumptions against Christian faith and thought. For example.
The fundamentalists believe in fiat creation
(Fundamentalists are narrow-minded bigots)
——————————————————————-
The fundamentalists believe in fiat creation
because they are narrow-minded bigots.
The premise shown in parenthesis is usually not stated publicly, but its presence is assumed by the attacker. Most of the rationalists use arguments in such a manner that their listeners unconsciously supply this presumption without even being aware of what they are doing. This way everyone listening to them is convinced that a logical discussion of the topic has yielded conclusions against the Bible. In reality it is not logic but the illogical presumption that has influenced people to make a false deduction against the Bible.
12. Fallacy Of Equivocation: Words can be used in many ways. For example, some words are so broad and general in nature that they are capable of being stretched. On using them, the conclusion is bound to be misleading. This kind of usage is a great tool of attack in the hands of those people who would like to discredit the Christian faith. They usually start with the well-known meaning of the "broad" word, and eventually switch over to that meaning which brings them benefit. This is fallacy of equivocation. For example,
Change is the rule of nature
Moral standards are changing everywhere
—————————————————————-
Changing moral standards are the rule
The conclusion is false because even though change is seen everywhere, these natural changes are different from the contrived change that is seen in the moral realm. Natural changes take place because they are a rule of nature, but with contrived change the mere fact that they have to be contrived shows that they are not natural.
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