iLogic

A sound argument is the most compelling reason one can come up with to convince others to agree with her belief or position. A sound argument is a proof. A logical person has to accept the conclusion of a sound argument as either true or acceptable. Refusing to accept the conclusion of a sound argument would be illogical, and thus unreasonable and irrational.

As long as a deductive argument fails to meet one of these two conditions, then it is unsound. So if a deductive argument is invalid, then it is unsound. The argument

If John F. Kennedy was assassinated, then he is dead.

John F. Kennedy is dead.

is invalid despite all of its premises being true. The best way to recognize an invalid deductive argument is to identify its argument form. We will study how to do so in two deductive systems. Another way to see that (1.3g) is invalid is to compare it to the next argument:

If John F. Kennedy was killed in a plane crash, then he is dead.

John F. Kennedy is dead.

We notice there is something wrong with (1.3h) because its two premises are true, but the conclusion is false. If it were valid, then according to the definition of soundness it would be sound. But it cannot be sound because its conclusion is false. This shows that (1.3h) cannot be valid. Since (1.3g) shares the same logical structure (form) with (1.3h), it is also invalid. An argument such as (1.3h) is called a counterexample. Using a counterexample is a clear and effective way of showing that any other argument with the same argument form is also invalid.

A deductive argument is also unsound if one or more of its premises are false/unacceptable. For example, the argument

All Republicans are social conservatives.

All social conservatives are against gay-marriage.

is a valid categorical syllogism (we will learn how to determine the validity of categorical syllogisms in Chapter 2). But it is unsound because its first premise is not true.

If a deductive argument has false premises and a false conclusion, people tend to think that it must be invalid. But this is incorrect. Whether a deductive argument is valid or not is determined by its argument form, and not by whether its sentences are true or acceptable. Compare (1.3i) with (1.3j).

All Democrats are conservatives.

All conservatives are against stem cell researches.

Notice that the premises and the conclusion of (1.3j) are false; yet it is valid because it has the same argument form as (1.3i).

1.3.4 Strength and Reliability

Recall that the inferential claim in inductive arguments is more modest. It claims only that its premises make its conclusion more likely to be true/acceptable. The degree of support its premises lend on its conclusion is call the strength. It can also be defined in three ways:

1. An inductive argument is strong if its conclusion indeed probably follows from its premises.
2. If the premises are true/acceptable, then the conclusion is likely to be true/acceptable.
3. more than 50% supporting

When an argument is claimed to be less than 100% supporting, then it is inductive. If the supporting relation is in fact greater than 50%, then it is strong. Otherwise it is weak.

Here is a simple example of strong induction.

All the ravens observed so far are black.

Since the premise of (1.3k) is true, the argument is said to be reliable. A reliable argument is a strong inductive argument with true/acceptable premises.

If an inductive argument fails to meet one of these two conditions, then it is unreliable. The argument (1.3e) we saw early on is unreliable because it is weak. So is the next example.

Preliminary studies show that patients treated with Xanafin recover without serious side effects.

A strong argument may nevertheless be unreliable if it has one or more false/unacceptable premises. The next argument is strong but unreliable because its premise is false.

Most swans observed so far are black.

Inductive reasoning by its very own nature can never give us one hundred percent certainty. However, one cannot dismiss inductive reasoning simply because of its lack of absolute certainty. It would still be illogical and irrational to reject the conclusion of a reliable argument. Even in our criminal justice system, the best we can demand is the benchmark of “beyond reasonable doubt.” By the same token, it would be unreasonable to refuse to accept a well-confirmed scientific theory by insisting on the lack of absolute certainty.

The chart below shows how arguments are classified based on the concepts introduced so far:

1.3.5 Proof vs. Confirmation

The purported controversy surrounding whether the theory of evolution is “just a theory” was whipped up by exploiting the failure to distinguish deductive proofs from inductive confirmations. The charge that there is no proof for the theory of evolution plays on the word “proof”. If by “proof” one means deductive proof, then the charge is misplaced, for we ought not to insist on deductive proof for scientific theories. The deductive proofs that we are most familiar with are derivations of mathematic theorems from axioms or postulates. In contrast, scientific theories are accepted as true when they are well confirmed by evidence. Since such a confirmation is inductive, and not deductive, it would be unreasonable to demand a deductive proof for a scientific theory. The insistence on a deductive proof for the theory of evolution and the refusal to accept it unless it has been proven amount to a demand for certainty, and thus reflect a lack of understanding of how science works. Carlo Rovelli, a theoretical physicist, has stated very clearly on whether scientific theories can be proven:

Science is not about certainty. Science is about finding the most reliable way of thinking at the present level of knowledge. Science is extremely reliable; it’s not certain. In fact, not only is it not certain, but it’s the lack of certainty that grounds it. Scientific ideas are credible not because they are sure but because they’re the ones that have survived all the possible past critiques, and they’re the most credible because they were put on the table for everybody’s criticism.

The very expression “scientifically proven” is a contradiction in terms. There’s nothing that is scientifically proven. The core of science is the deep awareness that we have wrong ideas, we have prejudices. We have ingrained prejudices. In our conceptual structure for grasping reality, there might be something not appropriate, something we may have to revise to understand better. So at any moment we have a vision of reality that is effective, it’s good, it’s the best we have found so far. It’s the most credible we have found so far; it’s mostly correct.

But, at the same time, it’s not taken as certain, and any element of it is a priori open for revision...¹

If by “proof” one means evidence, then it is obviously false that there is no evidence for the theory of evolution. On the contrary, the theory of evolution has been one of the best-confirmed theories in the history of science. It has been accepted as one of our best scientific theories given the wide scope of evidence that confirms and supports it.²

The issue of the evolution theory touches many people’s nerves because they perceive it as part of the clash between science and religion. What is said here in this section is not meant to be the final words on such a big topic, but only serves to clear up the confusion caused by the word “proof”. On the topic of science vs. religion, Rovelli points out that a deeper clash, which goes beyond any conflict between a scientific theory and a religious belief, lies in the difference between scientific thinking and religious thinking:

The question is, Why can’t we live happily together and why can’t people pray to their gods and study the universe without this continual clash? This continual clash is a little unavoidable, for the opposite reason from the one often presented. It’s unavoidable not because science pretends to know the answers. It’s the other way around, because scientific thinking is a constant reminder to us that we don’t know the answers. In religious thinking, this is often unacceptable. What’s unacceptable is not a scientist who says, “I know...” but a scientist who says, “I don’t know, and how could you know?” Many religions, or some religions, or some ways of being religious, are based on the idea that there should be a truth that one can hold onto and not question. This way of thinking is naturally disturbed by a way of thinking based on continual revision, not just of theories but of the core ground of the way in which we think.³

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Exercise 1.3

2. Determine whether each of the following arguments is deductive or inductive. If it is deductive, assess its validity and soundness. If it is inductive, estimate its strength and reliability.

1. The lights were all out and the car was gone, so we conclude that nobody was home.
2. Since many people believe that there are other life forms in the universe, extraterrestrial beings must have visited the earth.
3. Women office workers work just as hard as men office workers, and are just as productive. Women office workers should receive the same pay as men in comparable positions.
4. Marijuana should not be legalized because it is potentially dangerous and not enough is known about its long-term effects.
5. Thinking is taken as the main function of the human mind. So if computers can think, that would strongly suggest that the human mind is a material thing.
6. Most Toyota cars are very reliable, so the Toyota you just bought will be reliable too.
7. If we had state sponsored religion, then religious freedom would be threatened. To make sure we do not have state sponsored religion, we need to uphold the separation of church and state. This means that religious freedom requires the separation of church and state.
8. Given that there are billions of galaxies in the universe and billions stars in each galaxy, there must be other life forms beyond the earth.
9. Many people believe that near death experiences are evidence for life after death. Since there are so many reports about the near death experience. There must be life after death.
10. To be a sentient being one needs to exist in time. This means that if consciousness and memory are retained in the afterlife, then the afterlife cannot be a timeless existence.

 

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