How to construct a logical argument?

Logic
Here is an extremely simple example of a logical argument.

1. Too much fat is extremely unhealthy.
2. MacDonald’s food tends to be high in fat.
3. Therefore, eating Macdonald’s food too often is unhealthy.

The sequence is as such: when constructing a logical argument, one first starts with a base premise, or premises. In this example, my premises would be statements 1 and 2. In any argument, it is extremely important that the premise is sound. One will find that many arguments can be demolished simply by pointing out that the premise is false. In order to avoid this, make sure that the premise can be supported and backed up by facts. In the case of this example, it is very easy to find articles from health experts, as well as independent sources, to verify the validity of statements 1 and 2. Therefore, both statements are sound. (For simplicity’s sake, we will not go into the details).

Then, from the two premises, we can form a logical conclusion. Having established that the premises are sound, we can conclude that 3 is also true. Since Macdonald’s food is high in fat, and excess fat is unhealthy, it is fair to say that Macdonald’s food is unhealthy.

Logical Fallacies
The example above is just a simple demonstration of how to apply logic. Some reminders, however. In the construction of a logical argument, always avoid falling into the trap of logical fallacies. Similar to the problem of a false premise, a logical fallacy can destroy the entire argument. A list of logical fallacies can be found here.

Burden of Proof
Something worth further explanation is the burden of proof. Note that logical arguments always start from what I term the zeroth position. That is to say, there are no assumptions or presumptions at this point. When a claim is made, the burden of proof falls upon the person making the claim to prove what he is saying.

E.g. When a theist proposes the idea of a God, it is up to him to prove it. It is not the atheist’s job to disprove his concept. If the theist is unable to prove his claim, there is no reason to accept it as valid.

In this case, at the zeroth point, there was no presumption that God existed. Therefore, anyone proposing the existence of God would have to provide evidence for such a claim. This applies to any possible logical argument. In the Macdonalds example, I made a claim that fat was unhealthy, so I had to prove that it was valid.

Beware of those who would twist and turn the burden of proof. Because their own position is basically untenable, or they lack evidence, they will try to shift the burden of proof onto the opposing party, despite the fact that they are the ones who originally made a claim, and therefore have the burden of proof.

Something extra
At the risk of complication, it is worthwhile to understand that the conclusion of one line of argument, if valid, can be used as supporting evidence, or as the premise, for another line of argument. Since it is difficult to come up with an example that would not overly complicate matters, I’ll explain this simply.

1. Premise A
2. Premise B
-> Conclusion C, via logic.

Given that C is correct, we can formulate a new argument using C.
1. Premise C
2. Premise D (Assuming D is valid).
-> Conclusion E, via logic.

This process can be repeated for as long as is necessary.

Here’s some more refinements of logic:

An argument may be logically valid, but not factually true.
All men are mortal (major premise)
Socrates is a man (minor premise)
Therefore Socrates is mortal. (Conclusion)

This is a valid argument of the form (All As are Bs, C is an A, therefore C is B).

However the truth of the conclusion depends upon it being true that the major premise is true. In this case we know that the premises and the conclusion are also factually true. This is not always the case:

Here is an example of a valid argument, but one that is not actually true, because one or other of it’s premises is false.

All men are adulterers
Socrates is a man
Therefore Socrates is an adulterer.

Also watch out for logically valid arguments the conclusions of which are logically VALID, and factually TRUE but one or other of the premises are factually FALSE.

All men are bald
Yul Brynner is a man
Therefore Yul Brynner is bald.

We know the conclusion is AS A MATTER OF FACT TRUE, and that the argument is LOGICALLY VALID, but we also know that the MAJOR PREMISE IS FALSE.

An example

So logical validity is important in constructing an argument, but watch out for false premises! Here is one of my favourites:

(A)
Everthing that begins to exists has a cause. (a)
The universe began to exist. (b)
Therefore the universe has a cause. (c)

(B)
Nothing that begins to exist is the cause of itself (d)
What does not cause itself is caused by another (e)
The universe is not the cause of itself (f)
Therefore the universe is caused by another. (g)

The argument is logically valid as far as I can see, but it’s truth depends upon the truth of the premises.

The truth of the conclusion of (A) depends upon the truth of (b). If the universe is eternal, then the argument is false. The second argument (B) is introduced because “cause” could refer to “self cause”, but usually means “caused by another”, however, so (B) is the form in which you might find the argument presented in Xtian apologetics. The argument is I think valid, but not necessarily true. (d) could be false, at least we cannot be certain on the basis of our current knowledge that it is actually true. (e) seems fairly uncontroversial, and again, (f) depends upon both (b) and (d) being true, both of which are questionable.

For the whole argument to be false, all we need to say is that we don’t know that the universe did have a beginning, and if it did, in what SENSE did it have a beginning?. (How can you have a “before the universe began, when time is itself a dimension of the universe? Was there a time before time?)

And even if the universe can be said to have had a beginning, that is not IN ITSELF, enough to demonstrate that SOMETHING ELSE CAUSED IT.

It seems to me that although the argument is valid, our present state of knowledge is insufficient for us to say that it is true.

What is a “logical fallacy”?

A fallacy is an error in reasoning committed in an argument. When making an argument one selects premises, and then from those premises one draws a conclusion. A fallacy is committed when the conclusion is not supported by the premises. If you have committed a fallacy in your argument then your argument is wrong. A fallacy is not the same as a factual error, if I make the statement “cancer can be cured by the digestion of pepperoni, therefore if you eat pepperoni and you have cancer then you will be cured” I have not made an error in reasoning. It follows that if cancer can be cured by pepperoni then the consumption of pepperoni will cure cancer. It is an error of fact that invalidates this argument, not an error in reasoning. If I make the statement “cancer can be cures by the digestion of pepperoni, therefore if you eat pizza and you have cancer then you will be cured” I have committed an error of reasoning: Not all pizza has pepperoni in its topping, so my argument is not sound.

What are some well known logical fallacies?

Here are some common logical fallacies:

Ad Homenim

Ad homenim means “against the person”. An argumentum ad homenim is committed when a personal attack is made.

Eg. Mr A’s argument is not sound because Mr A is addicted to drugs.

Mr A’s addiction to drugs does not make his argument unsound, to demonstrate that his argument is unsound it must be demonstrated that he has committed an error.

Ad Baculum

Ad baculum means “appeal to the stick”. An argumentum ad baculum is committed when someone argues that you must agree with their conclusion or something bad will happen to them.

Eg. If Mr A does not agree with my argument I will break his legs, therefore my argument is correct.

Attempting to scare your opponent into accepting your argument does not make your argument sound.

Eg2. If atheists do not accept Jesus as their savior they will burn in hell.

Burden of Proof

The burden of proof fallacy is committed when a claim is unproven but argued correct until proven wrong.

Eg. Mr A cannot prove my claim wrong, therefore I am right.

Mr A is not obliged to disprove the claim if you have no evidence to support it.

Eg2. You can’t prove that God does not exist.

Composition

The fallacy of composition is committed when the attributes of the parts are attributed to the whole.

Eg. All the coins in this bucket have a value of one dollar; therefore this bucket of coins is worth one dollar.

The value of currency is cumulative.

Eg2. Events within the universe require a cause; therefore the universe requires a cause.

Special Pleading

Special pleading is committed when a person argues that one thing is subject to specific rules but another thing is not.

Eg. Stealing is a crime. Mr A stole money and should be punished. I stole money but I gave it all to charity, so it was Ok.

Stealing is a crime then it is a crime regardless of what you do with your loot.

Eg2. Nothing can exist without a cause, therefore God must have caused the universe, but God doesn’t need a cause.

Straw Man

A straw man is an oversimplification or misinterpreted version of a person’s argument is rebutted.
Eg. Mr A argues X. Mr B interpets X as Y and argues against Y.

Mr A’s argument of X is not Y; no matter how thoroughly Y is disproved X remains unanswered.

Eg2. Atheists believe that the universe came from nothing, something can’t come from nothing.

Begging the Question

Begging the question occurs when the conclusion is included in the premises.

Eg. I know that Christianity is the correct religion because the bible tells me so.

The bible is only an accurate source on which is the correct religion if Christianity is, therefore it can’t be used as evidence for Christianity.

What is Occam’s razor?

Occam’s razor is an inductive principle which is used to select between competing explanations.

When hypothesizing an explanation of a set of facts Occam’s razor states that the explanation which petitions the least number of assumptions should be considered the best explanation. This is because the more assumptions we make, the higher our chance of being wrong becomes. This principle has important applications in science but it is also a form of common sense used in day to day life.

What about Pascal’s Wager?

Pascal’s Wager is an argument proposed by seventeenth-centaury mathematician Blaise Pascal. Pascal made the following statement;

“Let us weigh the gain and the loss in wagering that God is. Let us estimate these two chances. If you gain, you gain all; if you lose, you lose nothing. Wager, then, without hesitation that He is.”
Pascal’s argument is that if the atheist looses his wager that God does not exist then he is sent to hell and if he wins his wager he wins nothing, where as if the theist looses his loss is nothing and if he wins he wins heaven. The flaws in Pascal’s argument are numerous.

Pascal assumes that it is not possible to know that God does or does not exist, he states “Reason can decide nothing here”. If you can know the truth then there is no need to gamble over the correct answer; Pascal’s Wager can only be a tool of any worth assuming we can’t know.

When Pascal refers to God he means the Christian God, but the same dilemma could be posed for other God’s as well. The wager then becomes more complicated, as assuming God does exist does not mean that you will not end up in hell.

Pascal also states;

“If there is a God, He is infinitely incomprehensible, since, having, neither parts nor limits, He has no affinity to us.”

However if God is infinitely incomprehensible then there are an infinite number of possible Gods. If there are an infinite possible number of Gods then the chance of selecting the correct one is infinitely small; whether you believe or not then according to Pascal’s premises you chance of making a successful wager is insignificant.

What is Abduction and Induction?

Abduction

Abduction is also known as “argument to the best explanation”. Abduction relies on the inductive principle that the present resembles the past, i.e beleif in the uniformity of nature. In abduction, one considers a phenomena, or set of phenomena, and decides out of a competing set of explanations which is the best one. A good abductive argument will usually have the following qulaities:

1. Simplicity
2. Coherence.
3.Comprehensiveness.
4. They may also be testable.

1. Simplicity. A good abductive argument will usually be simpler than it’s rivals. For example, what explains the “fine tuning” of the universe that led to the formation of life. One explanation is that God created the initial boundary conditions. Another is that there are a vast multiplicity of universes, so sooner or later, one was likely to come into being that has just the physical qualities that ours has.

Which is the simpler?

It is actually the multiple universe explantion, because although multiple universes are many, and God is only one – God belongs to a different category altogether. Universes belong in the same category, call it the category of “natural systems”. God belongs in the category of “supernatural entities” So on the God hypothesis, although we only have two things we have two very different things. On the multiple universe model, although we have more than two things, they are the same kind of thing.

To explain our universe in terms of a multiverse is to explain it in terms of natural laws, and although we do not know what they are yet, we are familiar with natural laws, and the way in which they explain things. To explain the universe by saying a God made it is much less simple because we are now explaining the natural in terms of the supernatural, and we have no idea (a) what a description of a supernatural law would be, or how the personal volition of a supernatural agent could give rise to a physical effect, and (b) we would still be left with something unexplained, i.e God.

The multiple universes hypothesis is simpler. And mathematically it makes sense. Whether it is true of course, is another matter.

2. Coherence. A good abductive argument is more internally consistent than it’s rivals. Let’s take another example. What causes consciousness? One answer is that it is the brain. Another is that it is an immaterial soul. Which is the most consistent? I think that the explanation in terms of the brain being the cause. We know that changes to brain chemistry can cause changes in consciousness. In a serious trauma, when the brain is severely damaged, we lose consciousness. On the soul hypothesis, one has to explain why this is the case if the soul is a nonphysical entity that presumably cannot be affected physically. One would also have to explain why consciousness continues after death, when it does not do so following a trauma. After all, at death, the brain suffers an irreversible trauma. This not only violates our principle of simplicity, it also appears to be incoherent.

On the other hand, the physicalist explanation does not encounter this problem, and is not therefore required to resort to an ad hoc explanation.

3. Comprehensiveness. This would appear to mean that a good abductive explanation will explain more than it’s rivals. Einstein’s theory of relativity will explain more than Newton’s physics, although within a limited range, Newtononian physics still holds good.

4. Testability. This will depend upon what you are attempting to explain of course. But back to the brain/consciousness/soul debate. Hypotheses based on correlating brain activity to consciousness are testable, hypotheses correlating consciousness to the soul is not.

Both atheists and theists of course have appealed to abductive arguments in support of their position, but this is not the place to rehearse any of those arguments in detail.

Induction

An inductive argument is based on the principle that nature is uniform, and that the present resembles the past, and that therefore the future is likely to as well. David Hume seems to be using a variant of this principle in his “Essay on Miracles”. His position sems to be that because our experience is overwhelmingly of nature acting uniformly, it is highly improbable that any reported event that “goes against nature” is likely to be true. So his argument is a noetic one, and not ontic, although some critics think that he was also trying to exclude the mere possibility of miracles. But that’s another issue.

Induction is as a rule, a good argument, but may have to be supplemented. Bertrand Russell gave the example of a Turkey that had been fed every morning for all it’s life and awoke on one particular Christmas day with the perfectly reasonable expectation, based on past experience, of being fed this morning too. But this particular morning it had it’s neck wrung.

Both induction and abduction are very effective forms of argument, but as with any other form of argument, need to be used appropriately.