Logic takes care of itself; all we have to do is to look and see how it does it. – Ludwig Wittgenstein
An argument is a reason or set of reasons given in support of a conclusion. It need not be contentious and is distinct from an argument in the sense of an aggressive exchange. Arguments are presented as a number of statements or propositions, one or more of which is presented as a conclusion. A simple example of a deductive argument is:
P1. All cats are mammals
P2. Max is a cat
C. Therefore Max is a mammal
In this example, P1 and P2 are the premises and C is the conclusion. The three propositions above are connected in a way in which the first two support the third. The support is generated by the form (or structure) of the argument. If we were to change the order of the argument as follows, the two premises would not support the conclusion:
P1. Max is cat
P2. Max is a mammal
C. Therefore all cats are mammals
The form of this argument is such that the premises do not support the conclusion.
As we have seen above, it is not necessarily the case that the premises of an argument always support the conclusion and the premises used may even be false. There are therefore four possible outcomes for any argument:
- The premises are true and they support the conclusion
- The premises are true but they do not support the conclusion
- The premises are not true but they do support the conclusion
- The premises are not true and they do not support the conclusion
Below is an example of the first outcome in which the premises are true and they support the conclusion:
P1. All men are mortal
P2. Socrates is a man
C. Therefore Socrates is a mortal
Below is an example of the second outcome in which the premises are true but they do not support the conclusion:
P1. All men are mortal
P2. Socrates is a man
C. Therefore Socrates is a philosopher
It is important to note that even though the conclusion is true, the conclusion isn’t supported by this argument.
Below is an example of the third outcome in which the premises are not true but they do support the conclusion:
P1. All men can fly
P2. Socrates is a man
C. Therefore Socrates can fly
Below is an example of the fourth outcome in which the premises are not true and they do not support the conclusion:
P1. All men can fly
P2. Socrates can fly
C. Therefore Socrates is a bird
Of the four examples above, only the first one is considered a good argument because it meets two criteria:
- The form of the argument is valid (i.e. the premises do support the conclusion)
- It has true premises
An argument which satisfies the first criteria is known as a valid argument. But valid arguments may have untrue premises. Valid arguments on their own are still not any good. An argument which is valid in form and also contains true premises is known as a sound argument, or a good argument.
In the examples above it is quite easy to see which arguments are good, but in practice it’s not always so easy to see. This is because not all arguments are deductive syllogisms (i.e. two premises and a conclusion) and there are different types of arguments to become familiar with:
Each of these will be explained below.
Deductive arguments are considered the strongest of all argument forms. If a deductive argument is valid in form and the premises are true then the conclusion must be true. There is no way that a valid deductive argument can have true premises and the conclusion be false at the same time.
There are various forms of deductive arguments which are valid such as:
- Disjunctive syllogism (Either A or B. Not A, therefore B)
- Hypothetical syllogism (If A, then B. If B, then C. Therefore if A, then C)
- Modus ponens (If A, then B. A therefore B)
- Modus tollens (If A, then B. Not B, therefore not A)
The form of inductive arguments are such that even if the premises are true, they do not guarantee that the conclusion is true. However they do give us good reason to think that the conclusion is true. The form of inductive arguments are not considered valid or invalid, but instead can range from being inductively weak to inductively strong.
An example of an inductive argument is as follows:
P1. It has rained every day for the past 6 months
C. Therefore it will rain tomorrow
In this example above, we cannot guarantee that the conclusion is true (because it is possible that it will not rain tomorrow even though it has rained for the past 6 months) however if the premises are true then there is a level of confidence that the conclusion is actually true. In the example above, we can reason that if it has rained every day for 6 months then there is a good chance that it will also rain tomorrow.
Abductive arguments (otherwise known as abductive reasoning or hypothetical reasoning) look to provide the best explanation for a series of facts or experiences. Consider the following argument:
P1. Peter is walking out the library
P2. Peter is holding a book
C. Therefore Peter has borrowed a book from the library
There are several possible conclusions we could draw from the first two premises, it may be the case that the book Peter is holding is his own and he brought it to the library. However in abductive reasoning, we look to find the best explanation which can account for all the facts. The criteria for determining which explanation is the best varies however usually includes the following:
- Simplicity – Which explanation does not posit unnecessary entities
- Explanatory scope – Which explanation can account for all the evidence (not just part of it)
It is important when engaging in abductive reasoning to evaluate all the available and relevant evidence before coming to a conclusion.
Burden of proof
As well as evaluating different types of arguments, it is also important to understand the burden of proof. A burden of proof is the obligation of the person presenting the argument to demonstrate that the argument is valid (or inductively strong) and contains true premises. It is not the obligation of the person hearing the argument to demonstrate that the argument is not valid (or inductively strong) and it is not the obligation of the person hearing to demonstrate that the premises are not true.
In many cases, the person being presented an argument can simply be agnostic to the conclusion of the argument if the person presenting the argument fails to demonstrate that it is sound. Most arguments against the restored gospel fail one of the following and do not give us a good enough reason to accept the conclusion:
- Open-ended question – It is not stated as an argument and has no conclusion
- Formal fallacies – The form of the argument is such that the content is irrelevant because the form alone shows the argument is unsound
- Informal fallacies – The premises, even if true, do not adequately support the conclusion
- Untruths – It contains a premise which is untrue or a bad assumption
We will look at each one in turn.
1. Open-ended question with no conclusion
This is probably the most common form of argument against the restored gospel. It is not structured as an argument and does not give a reason or set of reasons in support of a conclusion. An example of an open-ended question with no conclusion is as follows:
If Joseph Smith was a true prophet then why did he marry young girls?
The problem with presenting an argument as a question is that there are no clear premises or even a clear conclusion. The word “then” implies there is a contradiction between Joseph Smith being a true prophet and marrying young girls but the person being presented the argument must form the argument themselves.
If the question was put into argument form it would be much easier to evaluate. For example:
P1. True prophets do not marry young girls
P2. Joseph Smith married young girls
C. Therefore Joseph Smith was not a prophet
When it is put in argument form, we can see the conclusion and can evaluate whether it is valid in form (or inductively strong) and whether the premises are true. In this case the form is good, it is a deductive argument but we can object to premise 1. What reason do we have for thinking that true prophets do not marry young girls? The open ended question certainly does not give us any reason to believe P1 so unless we have other reasons for believing that true prophets do not marry young girls, we can either be agnostic to the conclusion or reject the conclusion as false if we have reason to believe that it is not true that true prophets do not marry young girls.
2. Formal fallacies
For some arguments it is not even necessary to evaluate whether the premises are true or not because the form or the argument is such that the argument is guaranteed to fail. These errors in form are called formal logical fallacies.
An example of a formal fallacy is affirming the consequent. This takes the form: If P then Q, Q therefore P. For example:
P1. If X is a beetle then X is an insect
P2. X is an insect
C. Therefore X is a beetle
The conclusion may well be true but this is not a good argument simply because of its form affirms the consequent. This type of fallacy can be difficult to notice in practice. For example:
P1. Dangerous cults put great emphasis on obedience
P2. The Church of Jesus Christ puts great emphasis on obedience
C. Therefore The Church of Jesus Christ is a dangerous cult
When a formal fallacy is committed the argument is void. The conclusion may well be true but we cannot use the argument to justify our conclusion. Other formal fallacies include:
- Denying the antecedent: If P then Q. Not p, therefore not Q
- Affirming a disjunct: P or Q. P, therefore not Q
3. Informal fallacies
The other type of fallacy is informal. Informal fallacies do not immediately invalidate the argument but instead must be judged based on the premises. An example of an informal fallacy is the ad populum fallacy (appealing to the people). For example:
P1. Most people in the world do not believe the Book of Mormon is true
C. Therefore the Book of Mormon is probably not true
This argument appeals to the people but the number of people who hold a belief does not make it true. However in other cases it would be appropriate to appeal to the people based on experience and context. For example:
P1. Most people at temple square saw the protesters
C. Therefore there were probably protesters
Even though it is not guaranteed that there were protesters, it is reasonable to conclude that there were protesters because they were many eye witnesses so it justifies the conclusion.
Other informal fallacies include:
- Argument from ignorance – e.g. something is true because it has not been shown to be false
- Cherry picking – e.g. ignoring all the evidence when forming conclusions
- Hasty generalization – e.g. using a small data sample to unreasonable infer a conclusion
- Begging the question – e.g. when the conclusion forms one of the premises
See Fair’s huge library of fallacy definitions and examples.
4. Untruths / bad assumptions
Some claims are just unproven assumptions whereas other claims are demonstrably not true because they are clearly falsifiable. For example the claim “all swans are white” would be immediately falsified if you saw a non-white swan. But other claims are much more difficult to falsify or verify. For example:
P1. If the first vision is true, then Joseph Smith would have written it down in detail straight away
P2. Joseph Smith did not write down the first vision in detail straight away
C. Therefore the first vision is not true
Here we can challenge the assumption in P1. Why believe that if the first vision happened then Joseph would have written it down in detail straight away? What are we appealing to except our own anticipated behavior and assuming Joseph’s behavior would be the same? It is important to question our assumptions and the reasons behind them.
In order to identify untruths or bad assumptions it is important to consider context and cherry picking, reliability, and our assumptions about God.
Context and cherry picking
One of the biggest challenges in understanding truth is to put things in context. Imagine the following scenarios:
- If someone pushed you, then you’d probably be upset
- If someone pushed you out the way of an oncoming bike, then you’d probably not be upset
- If someone pushed you out the way of an oncoming bike into the path of an oncoming train, then you’d probably be upset
- If someone pushed you out the way of an oncoming bike into the path of an oncoming train which was only a toy, then you’d probably not be upset
For this reason it is important to understand the context of quotes and actions. Many criticisms of the restored gospel contain quotes or events that are simply taken out of context. This is similar to cherry picking, where only some of the evidence is presented but in reality there are other important facts to consider. Presentism is another example of putting things in context. We can’t simply use what we know about today’s society when trying to understand what has happened in the past
Not all quotes or actions used in arguments are reliable. In some cases, information from a particular historic person may be used as evidence, however many quotes from people are not credible and we should consider:
- Who has it come from?
- How close were they to the events?
- Were they hostile or biased?
- How reliable are they?
- Are there any contradictory accounts or information?
- Does anyone else corroborate their account?
- It is important to consider the reliability of witnesses.
Similarly when it comes to scientific claims we must always question the reliability of scientific claims. Science is based on observation and forming theories so there are no such things as true scientific facts, only the best explanation of the current observations.
Assumptions about God
Many arguments simply assume what God and his church would be like. Assumptions are hugely important to our individual inquiries as Terryl and Fiona Givens have said:
We all inhibit geographical, linguistic, and social worlds that shape our vision and our impressions of what is normal, what is real. Our worldview is a collective set of assumptions we carry with us that condition every question we ask. These “paradigms” make it possible to guide inquiry, but they can also limit and impede our inquiry. They can get us off on the wrong foot, obscure our line of sight, or simply misdirect our focus. This is because, all too often, we don’t realize the limiting assumptions with which we are working.
We can’t easily step outside most such preconceptions. Even recognizing the extent of our unexamined assumptions can be the hardest thing of all. It is like asking a fish what it is like to be wet. 1
It is important to question our assumptions and be careful to not assume too much about what we think God or his church would be like.
The restored gospel does not need to be free from all sound arguments against it, there are many sound arguments against the restored gospel, in the same way there are many sound arguments in favor of untrue conspiracy theories. However by being able to evaluate arguments you are in a better position to understand what is true and what they can teach us.
- Terryl Givens, 2014. The Crucible of Doubt. Deseret Book